title: Chiton

text: The primary sense organs of chitons are the subradular organ and a large number of unique organs called aesthetes. The aesthetes consist of light-sensitive cells just below the surface of the shell, although they are not capable of true vision. In some cases, however, they are modified to form ocelli, with a cluster of individual photoreceptor cells lying beneath a small aragonite-based lens. Each lens can form clear images, and is composed of relatively large, highly crystallographically-aligned grains to minimize light scattering. An individual chiton may have thousands of such ocelli. These aragonite-based eyes make them capable of true vision; though research continues as to the extent of their visual acuity. It is known that they can differentiate between a predator's shadow and changes in light caused by clouds. An evolutionary trade-off has led to a compromise between the eyes and the shell; as the size and complexity of the eyes increase, the mechanical performance of their shells decrease, and vice versa.


title: Chiton

text: A relatively good fossil record of chiton shells exists, but ocelli are only present in those dating to or younger; this would make the ocelli, whose precise function is unclear, likely the most recent eyes to evolve.


title: Chiton

text: Although chitons lack osphradia, statocysts, and other sensory organs common to other molluscs, they do have numerous tactile nerve endings, especially on the girdle and within the mantle cavity.


title: Chiton

text: The order Lepidopleurida also have a pigmented sensory organ called the Schwabe organ. Its function remains largely unknown, and has been suggested to be related to that of a larval eye.


title: Chiton

text: Similar to many species of saltwater limpets, several species of chiton are known to exhibit homing behaviours, journeying to feed and then returning to the exact spot they previously inhabited. The method they use to perform such behaviors has been investigated to some extent, but remains unknown. One theory has the chitons remembering the topographic profile of the region, thus being able to guide themselves back to their home scar by a physical knowledge of the rocks and visual input from their numerous primitive eyespots.


title: Chiton

text: The sea snail "Nerita textilis" (like all gastropods) deposits a mucus trail as it moves, which a chemoreceptive organ is able to detect and guide the snail back to its home site. It is unclear if chiton homing functions in the same way, but they may leave chemical cues along the rock surface and at the home scar which their olfactory senses can detect and home in on. Furthermore, older trails may also be detected, providing further stimulus for the chiton to find its home.


title: Chiton

text: The radular teeth of chitons are made of magnetite, and the iron crystals within these may be involved in magnetoception, the ability to sense the polarity and the inclination of the Earth's magnetic field. Experimental work has suggested that chitons can detect and respond to magnetism.


title: Chiton

text: Chitons are eaten in several parts of the world. This includes islands in the Caribbean, such as Trinidad, Tobago, The Bahamas, St. Maarten, Aruba, Bonaire, Anguilla and Barbados, as well as in Bermuda. They are also traditionally eaten in certain parts of the Philippines, where it is called kibet if raw and chiton if fried. Native Americans of the Pacific coasts of North America eat chitons. They are a common food on the Pacific coast of South America and in the Galápagos. The foot of the chiton is prepared in a manner similar to abalone. Some islanders living in South Korea also eat chiton, slightly boiled and mixed with vegetables and hot sauce. Aboriginal people in Australia also eat chiton; for example they are recorded in the Narungga Nation Traditional Fishing Agreement.


title: Chiton

text: A chiton creeps along slowly on a muscular foot. It has considerable power of adhesion and can cling to rocks very powerfully, like a limpet.


title: Chiton

text: Chitons are generally herbivorous grazers, though some are omnivorous and some carnivorous. They eat algae, bryozoans, diatoms, barnacles, and sometimes bacteria by scraping the rocky substrate with their well-developed radulae.


title: Chiton

text: A few species of chitons are predatory, such as the small western Pacific species "Placiphorella velata". These predatory chitons have enlarged anterior girdles. They catch other small invertebrates, such as shrimp and possibly even small fish, by holding the enlarged, hood-like front end of the girdle up off the surface, and then clamping down on unsuspecting, shelter-seeking prey.


title: Chiton

text: Chitons have separate sexes, and fertilization is usually external. The male releases sperm into the water, while the female releases eggs either individually, or in a long string. In most cases, fertilization takes place either in the surrounding water, or in the mantle cavity of the female. Some species brood the eggs within the mantle cavity, and the species "Callistochiton viviparus" even retains them within the ovary and gives birth to live young, an example of ovoviviparity.


title: Chiton

text: The egg has a tough spiny coat, and usually hatches to release a free-swimming trochophore larva, typical of many other mollusc groups. In a few cases, the trochophore remains within the egg (and is then called lecithotrophic – deriving nutrition from yolk), which hatches to produce a miniature adult. Unlike most other molluscs, there is no intermediate stage, or veliger, between the trochophore and the adult. Instead, a segmented shell gland forms on one side of the larva, and a foot forms on the opposite side. When the larva is ready to become an adult, the body elongates, and the shell gland secretes the plates of the shell. Unlike the fully grown adult, the larva has a pair of simple eyes, although these may remain for some time in the immature adult.


title: Chiton

text: Chitons have a relatively good fossil record, stretching back to the Cambrian, with the genus "Preacanthochiton", known from fossils found in Late Cambrian deposits in Missouri, being classified as the earliest known polyplacophoran. However, the exact phylogenetic position of supposed Cambrian chitons is highly controversial, and some authors have instead argued that the earliest confirmed polyplacophorans date back to the Early Ordovician. "Kimberella" and "Wiwaxia" of the Precambrian and Cambrian may be related to ancestral polyplacophorans. "Matthevia" is a Late Cambrian polyplacophoran preserved as individual pointed valves, and sometimes considered to be a chiton, although at the closest, it can only be a stem-group member of the group.


title: Chiton

text: Based on this and co-occurring fossils, one plausible hypothesis for the origin of polyplacophora has that they formed when an aberrant monoplacophoran was born with multiple centres of calcification, rather than the usual one. Selection quickly acted on the resultant conical shells to form them to overlap into protective armour; their original cones are homologous to the tips of the plates of modern chitons.


title: Chiton

text: The chitons evolved from multiplacophora during the Palaeozoic, with their relatively conserved modern-day body plan being fixed by the Mesozoic.


title: Chiton

text: The earliest fossil evidence of aesthetes in chitons comes from around 400 Ma, during the Early Devonian.


title: Chiton

text: Chitons were first studied by Carl Linnaeus in his 1758 10th edition of "Systema Naturae". Since his description of the first four species, chitons have been variously classified. They were called Cyclobranchians (round arm) in the early 19th century, and then grouped with the aplacophorans in the subphylum Amphineura in 1876. The class Polyplacophora was named by de Blainville 1816.


title: Chiton

text: The name chiton is New Latin derived from the Ancient Greek word "khitōn", meaning tunic (which also is the source of the word chitin). The Ancient Greek word "khitōn" can be traced to the Central Semitic word "*kittan", which is from the Akkadian words "kitû" or "kita'um", meaning flax or linen, and originally the Sumerian word "gada" or "gida".


title: Chiton

text: The Greek-derived name Polyplacophora comes from the words "poly-" (many), "plako-" (tablet), and "-phoros" (bearing), a reference to the chiton's eight shell plates.


title: Chiton

text: Most classification schemes in use today are based, at least in part, on "Pilsbry's Manual of Conchology" (1892–1894), extended and revised by Kaas and Van Belle (1985–1990).


title: Chiton

text: Since chitons were first described by Linnaeus (1758), extensive taxonomic studies at the species level have been made. However, the taxonomic classification at higher levels in the group has remained somewhat unsettled.


title: Chiton

text: The most recent classification, by Sirenko (2006), is based not only on shell morphology, as usual, but also other important features, including aesthetes, girdle, radula, gills, glands, egg hull projections, and spermatozoids. It includes all the living and extinct genera of chitons.


title: Electrochemistry

text: Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an outcome of a particular chemical change, or vice versa. These reactions involve electrons moving via an electronically-conducting phase (typically an external electrical circuit, but not necessarily, as in electroless plating) between electrodes separated by an ionically conducting and electronically insulating electrolyte (or ionic species in a solution).


title: Electrochemistry

text: When a chemical reaction is driven by an electrical potential difference, as in electrolysis, or if a potential difference results from a chemical reaction as in an electric battery or fuel cell, it is called an "electrochemical" reaction. Unlike in other chemical reactions, in electrochemical reactions electrons are not transferred directly between atoms, ions, or molecules, but via the aforementioned electronically-conducting circuit. This phenomenon is what distinguishes an electrochemical reaction from a conventional chemical reaction.


title: Electrochemistry

text: Understanding of electrical matters began in the sixteenth century. During this century, the English scientist William Gilbert spent 17 years experimenting with magnetism and, to a lesser extent, electricity. For his work on magnets, Gilbert became known as the ""Father of Magnetism."" He discovered various methods for producing and strengthening magnets.


title: Electrochemistry

text: In 1663, the German physicist Otto von Guericke created the first electric generator, which produced static electricity by applying friction in the machine. The generator was made of a large sulfur ball cast inside a glass globe, mounted on a shaft. The ball was rotated by means of a crank and an electric spark was produced when a pad was rubbed against the ball as it rotated. The globe could be removed and used as source for experiments with electricity.


title: Electrochemistry

text: By the mid-18th century the French chemist Charles François de Cisternay du Fay had discovered two types of static electricity, and that like charges repel each other whilst unlike charges attract. Du Fay announced that electricity consisted of two fluids: ""vitreous"" (from the Latin for ""glass""), or positive, electricity; and ""resinous,"" or negative, electricity. This was the "two-fluid theory" of electricity, which was to be opposed by Benjamin Franklin's "one-fluid theory" later in the century.


title: Electrochemistry

text: In 1785, Charles-Augustin de Coulomb developed the law of electrostatic attraction as an outgrowth of his attempt to investigate the law of electrical repulsions as stated by Joseph Priestley in England.


title: Electrochemistry

text: In the late 18th century the Italian physician and anatomist Luigi Galvani marked the birth of electrochemistry by establishing a bridge between chemical reactions and electricity on his essay ""De Viribus Electricitatis in Motu Musculari Commentarius"" (Latin for Commentary on the Effect of Electricity on Muscular Motion) in 1791 where he proposed a ""nerveo-electrical substance"" on biological life forms.


title: Electrochemistry

text: In his essay Galvani concluded that animal tissue contained a here-to-fore neglected innate, vital force, which he termed ""animal electricity,"" which activated nerves and muscles spanned by metal probes. He believed that this new force was a form of electricity in addition to the ""natural"" form produced by lightning or by the electric eel and torpedo ray as well as the ""artificial"" form produced by friction (i.e., static electricity).


title: Electrochemistry

text: Galvani's scientific colleagues generally accepted his views, but Alessandro Volta rejected the idea of an ""animal electric fluid,"" replying that the frog's legs responded to differences in metal temper, composition, and bulk. Galvani refuted this by obtaining muscular action with two pieces of the same material. Nevertheless, Volta's experimentation led him to develop the first practical battery, which took advantage of the relatively high energy (weak bonding) of zinc and could deliver an electrical current for much longer than any other device known at the time.


title: Electrochemistry

text: In 1800, William Nicholson and Johann Wilhelm Ritter succeeded in decomposing water into hydrogen and oxygen by electrolysis using Volta's battery. Soon thereafter Ritter discovered the process of electroplating. He also observed that the amount of metal deposited and the amount of oxygen produced during an electrolytic process depended on the distance between the electrodes. By 1801, Ritter observed thermoelectric currents and anticipated the discovery of thermoelectricity by Thomas Johann Seebeck.


title: Electrochemistry

text: Sir Humphry Davy's work with electrolysis led to the conclusion that the production of electricity in simple electrolytic cells resulted from chemical action and that chemical combination occurred between substances of opposite charge. This work led directly to the isolation of metallic sodium and potassium by electrolysis of their molten salts, and of the alkaline earth metals from theirs, in 1808.


title: Electrochemistry

text: Hans Christian Ørsted's discovery of the magnetic effect of electric currents in 1820 was immediately recognized as an epoch-making advance, although he left further work on electromagnetism to others. André-Marie Ampère quickly repeated Ørsted's experiment, and formulated them mathematically.


title: Electrochemistry

text: In 1821, Estonian-German physicist Thomas Johann Seebeck demonstrated the electrical potential between the juncture points of two dissimilar metals when there is a temperature difference between the joints.


title: Electrochemistry

text: In 1827, the German scientist Georg Ohm expressed his law in this famous book ""Die galvanische Kette, mathematisch bearbeitet"" (The Galvanic Circuit Investigated Mathematically) in which he gave his complete theory of electricity.


title: Electrochemistry

text: In 1832, Michael Faraday's experiments led him to state his two laws of electrochemistry. In 1836, John Daniell invented a primary cell which solved the problem of polarization by introducing copper ions into the solution near the positive electrode and thus eliminating hydrogen gas generation. Later results revealed that at the other electrode, amalgamated zinc (i.e., zinc alloyed with mercury) would produce a higher voltage.


title: Electrochemistry

text: William Grove produced the first fuel cell in 1839. In 1846, Wilhelm Weber developed the electrodynamometer. In 1868, Georges Leclanché patented a new cell which eventually became the forerunner to the world's first widely used battery, the zinc–carbon cell.


title: Electrochemistry

text: Svante Arrhenius published his thesis in 1884 on "Recherches sur la conductibilité galvanique des électrolytes" (Investigations on the galvanic conductivity of electrolytes). From his results the author concluded that electrolytes, when dissolved in water, become to varying degrees split or dissociated into electrically opposite positive and negative ions.


title: Electrochemistry

text: In 1886, Paul Héroult and Charles M. Hall developed an efficient method (the Hall–Héroult process) to obtain aluminium using electrolysis of molten alumina.


title: Electrochemistry

text: In 1894, Friedrich Ostwald concluded important studies of the conductivity and electrolytic dissociation of organic acids.


title: Electrochemistry

text: Walther Hermann Nernst developed the theory of the electromotive force of the voltaic cell in 1888. In 1889, he showed how the characteristics of the voltage produced could be used to calculate the free energy change in the chemical reaction producing the voltage. He constructed an equation, known as Nernst equation, which related the voltage of a cell to its properties.


title: Electrochemistry

text: In 1898, Fritz Haber showed that definite reduction products can result from electrolytic processes if the potential at the cathode is kept constant. In 1898, he explained the reduction of nitrobenzene in stages at the cathode and this became the model for other similar reduction processes.


title: Electrochemistry

text: In 1909, Robert Andrews Millikan began a series of experiments (see oil drop experiment) to determine the electric charge carried by a single electron.


title: Electrochemistry

text: In 1911, Harvey Fletcher, working with Millikan, was successful in measuring the charge on the electron, by replacing the water droplets used by Millikan, which quickly evaporated, with oil droplets. Within one day Fletcher measured the charge of an electron within several decimal places


title: Electrochemistry

text: In 1923, Johannes Nicolaus Brønsted and Martin Lowry published essentially the same theory about how acids and bases behave, using an electrochemical basis.


title: Electrochemistry

text: In 1937, Arne Tiselius developed the first sophisticated electrophoretic apparatus. Some years later, he was awarded the 1948 Nobel Prize for his work in protein electrophoresis.


title: Electrochemistry

text: The term "redox" stands for reduction-oxidation. It refers to electrochemical processes involving electron transfer to or from a molecule or ion, changing its oxidation state. This reaction can occur through the application of an external voltage or through the release of chemical energy. Oxidation and reduction describe the change of oxidation state that takes place in the atoms, ions or molecules involved in an electrochemical reaction. Formally, oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic. An atom or ion that gives up an electron to another atom or ion has its oxidation state increase, and the recipient of the negatively charged electron has its oxidation state decrease.


title: Electrochemistry

text: For example, when atomic sodium reacts with atomic chlorine, sodium donates one electron and attains an oxidation state of +1. Chlorine accepts the electron and its oxidation state is reduced to −1. The sign of the oxidation state (positive/negative) actually corresponds to the value of each ion's electronic charge. The attraction of the differently charged sodium and chlorine ions is the reason they then form an ionic bond.


title: Electrochemistry

text: The loss of electrons from an atom or molecule is called oxidation, and the gain of electrons is reduction. This can be easily remembered through the use of mnemonic devices. Two of the most popular are ""OIL RIG"" (Oxidation Is Loss, Reduction Is Gain) and ""LEO"" the lion says ""GER"" (Lose Electrons: Oxidation, Gain Electrons: Reduction). Oxidation and reduction always occur in a paired fashion such that one species is oxidized when another is reduced. For cases where electrons are shared (covalent bonds) between atoms with large differences in electronegativity, the electron is assigned to the atom with the largest electronegativity in determining the oxidation state.


title: Electrochemistry

text: The atom or molecule which loses electrons is known as the "reducing agent", or "reductant", and the substance which accepts the electrons is called the "oxidizing agent", or "oxidant". Thus, the oxidizing agent is always being reduced in a reaction; the reducing agent is always being oxidized. Oxygen is a common oxidizing agent, but not the only one. Despite the name, an oxidation reaction does not necessarily need to involve oxygen. In fact, a fire can be fed by an oxidant other than oxygen; fluorine fires are often unquenchable, as fluorine is an even stronger oxidant (it has a weaker bond and higher electronegativity, and thus accepts electrons even better) than oxygen.


title: Electrochemistry

text: For reactions involving oxygen, the gain of oxygen implies the oxidation of the atom or molecule to which the oxygen is added (and the oxygen is reduced). In organic compounds, such as butane or ethanol, the loss of hydrogen implies oxidation of the molecule from which it is lost (and the hydrogen is reduced). This follows because the hydrogen donates its electron in covalent bonds with non-metals but it takes the electron along when it is lost. Conversely, loss of oxygen or gain of hydrogen implies reduction.


title: Electrochemistry

text: Electrochemical reactions in water are better analyzed by using the ion-electron method, where H, OH ion, HO and electrons (to compensate the oxidation changes) are added to the cell's half-reactions for oxidation and reduction.


title: Electrochemistry

text: Finally, the reaction is balanced by multiplying the stoichiometric coefficients so the numbers of electrons in both half reactions match


title: Electrochemistry

text: In basic medium, OH ions and water are added to balance each half-reaction. For example, in a reaction between potassium and sodium sulfite:


title: Electrochemistry

text: Here, 'spectator ions' (K, Na) were omitted from the half-reactions. By multiplying the stoichiometric coefficients so the numbers of electrons in both half reaction match:


title: Electrochemistry

text: The same procedure as used in acidic medium can be applied, for example, to balance the complete combustion of propane:


title: Electrochemistry

text: By multiplying the stoichiometric coefficients so the numbers of electrons in both half reaction match:


title: Electrochemistry

text: An electrochemical cell is a device that produces an electric current from energy released by a spontaneous redox reaction. This kind of cell includes the Galvanic cell or Voltaic cell, named after Luigi Galvani and Alessandro Volta, both scientists who conducted experiments on chemical reactions and electric current during the late 18th century.


title: Electrochemistry

text: Electrochemical cells have two conductive electrodes (the anode and the cathode). The anode is defined as the electrode where oxidation occurs and the cathode is the electrode where the reduction takes place. Electrodes can be made from any sufficiently conductive materials, such as metals, semiconductors, graphite, and even conductive polymers. In between these electrodes is the electrolyte, which contains ions that can freely move.


title: Electrochemistry

text: The galvanic cell uses two different metal electrodes, each in an electrolyte where the positively charged ions are the oxidized form of the electrode metal. One electrode will undergo oxidation (the anode) and the other will undergo reduction (the cathode). The metal of the anode will oxidize, going from an oxidation state of 0 (in the solid form) to a positive oxidation state and become an ion. At the cathode, the metal ion in solution will accept one or more electrons from the cathode and the ion's oxidation state is reduced to 0. This forms a solid metal that electrodeposits on the cathode. The two electrodes must be electrically connected to each other, allowing for a flow of electrons that leave the metal of the anode and flow through this connection to the ions at the surface of the cathode. This flow of electrons is an electric current that can be used to do work, such as turn a motor or power a light.


title: Electrochemistry

text: A galvanic cell whose electrodes are zinc and copper submerged in zinc sulfate and copper sulfate, respectively, is known as a Daniell cell.


title: Electrochemistry

text: In this example, the anode is the zinc metal which is oxidized (loses electrons) to form zinc ions in solution, and copper ions accept electrons from the copper metal electrode and the ions deposit at the copper cathode as an electrodeposit. This cell forms a simple battery as it will spontaneously generate a flow of electric current from the anode to the cathode through the external connection. This reaction can be driven in reverse by applying a voltage, resulting in the deposition of zinc metal at the anode and formation of copper ions at the cathode.


title: Electrochemistry

text: To provide a complete electric circuit, there must also be an ionic conduction path between the anode and cathode electrolytes in addition to the electron conduction path. The simplest ionic conduction path is to provide a liquid junction. To avoid mixing between the two electrolytes, the liquid junction can be provided through a porous plug that allows ion flow while minimizing electrolyte mixing. To further minimize mixing of the electrolytes, a salt bridge can be used which consists of an electrolyte saturated gel in an inverted U-tube. As the negatively charged electrons flow in one direction around this circuit, the positively charged metal ions flow in the opposite direction in the electrolyte.


title: Electrochemistry

text: A voltmeter is capable of measuring the change of electrical potential between the anode and the cathode.


title: Electrochemistry

text: A cell diagram can be used to trace the path of the electrons in the electrochemical cell. For example, here is a cell diagram of a Daniell cell:


title: Electrochemistry

text: First, the reduced form of the metal to be oxidized at the anode (Zn) is written. This is separated from its oxidized form by a vertical line, which represents the limit between the phases (oxidation changes). The double vertical lines represent the saline bridge on the cell. Finally, the oxidized form of the metal to be reduced at the cathode, is written, separated from its reduced form by the vertical line. The electrolyte concentration is given as it is an important variable in determining the exact cell potential.


title: Electrochemistry

text: To allow prediction of the cell potential, tabulations of standard electrode potential are available. Such tabulations are referenced to the standard hydrogen electrode (SHE). The standard hydrogen electrode undergoes the reaction


title: Electrochemistry

text: which is shown as a reduction but, in fact, the SHE can act as either the anode or the cathode, depending on the relative oxidation/reduction potential of the other electrode/electrolyte combination. The term standard in SHE requires a supply of hydrogen gas bubbled through the electrolyte at a pressure of 1 atm and an acidic electrolyte with H activity equal to 1 (usually assumed to be [H] = 1 mol/liter, i.e. pH = 0).


title: Electrochemistry

text: The SHE electrode can be connected to any other electrode by a salt bridge and an external circuit to form a cell. If the second electrode is also at standard conditions, then the measured cell potential is called the standard electrode potential for the electrode. The standard electrode potential for the SHE is zero, by definition. The polarity of the standard electrode potential provides information about the relative reduction potential of the electrode compared to the SHE. If the electrode has a positive potential with respect to the SHE, then that means it is a strongly reducing electrode which forces the SHE to be the anode (an example is Cu in aqueous CuSO with a standard electrode potential of 0.337 V). Conversely, if the measured potential is negative, the electrode is more oxidizing than the SHE (such as Zn in ZnSO where the standard electrode potential is −0.76 V).


title: Electrochemistry

text: Standard electrode potentials are usually tabulated as reduction potentials. However, the reactions are reversible and the role of a particular electrode in a cell depends on the relative oxidation/reduction potential of both electrodes. The oxidation potential for a particular electrode is just the negative of the reduction potential. A standard cell potential can be determined by looking up the standard electrode potentials for both electrodes (sometimes called half cell potentials). The one that is smaller will be the anode and will undergo oxidation. The cell potential is then calculated as the sum of the reduction potential for the cathode and the oxidation potential for the anode.


title: Electrochemistry

text: At standard temperature, pressure and concentration conditions, the cell's emf (measured by a multimeter) is 0.34 V. By definition, the electrode potential for the SHE is zero. Thus, the Cu is the cathode and the SHE is the anode giving


title: Electrochemistry

text: Changes in the stoichiometric coefficients of a balanced cell equation will not change the "E"° value because the standard electrode potential is an intensive property.


title: Electrochemistry

text: During operation of an electrochemical cell, chemical energy is transformed into electrical energy. This can be expressed mathematically as the product of the cell's emf "E" measured in volts (V) and the electric charge "Q" transferred through the external circuit.


title: Electrochemistry

text: "Q" is the cell current integrated over time and measured in coulombs (C); it can also be determined by multiplying the total number "n" of electrons transferred (measured in moles) times Faraday's constant ("F").


title: Electrochemistry

text: The emf of the cell at zero current is the maximum possible emf. It can be used to calculate the maximum possible electrical energy that could be obtained from a chemical reaction. This energy is referred to as electrical work and is expressed by the following equation:


title: Electrochemistry

text: Since the free energy is the maximum amount of work that can be extracted from a system, one can write:


title: Electrochemistry

text: A positive cell potential gives a negative change in Gibbs free energy. This is consistent with the cell production of an electric current from the cathode to the anode through the external circuit. If the current is driven in the opposite direction by imposing an external potential, then work is done on the cell to drive electrolysis.


title: Electrochemistry

text: A spontaneous electrochemical reaction (change in Gibbs free energy less than zero) can be used to generate an electric current in electrochemical cells. This is the basis of all batteries and fuel cells. For example, gaseous oxygen (O) and


title: Electrochemistry

text: hydrogen (H) can be combined in a fuel cell to form water and energy, typically a combination of heat and electrical energy.


title: Electrochemistry

text: Conversely, non-spontaneous electrochemical reactions can be driven forward by the application of a current at sufficient voltage. The electrolysis of water into gaseous oxygen and hydrogen is a typical example.


title: Electrochemistry

text: The relation between the equilibrium constant, "K", and the Gibbs free energy for an electrochemical cell is expressed as follows:


title: Electrochemistry

text: The standard potential of an electrochemical cell requires standard conditions (Δ"G"°) for all of the reactants. When reactant concentrations differ from standard conditions, the cell potential will deviate from the standard potential. In the 20th century German chemist Walther Nernst proposed a mathematical model to determine the effect of reactant concentration on electrochemical cell potential.


title: Electrochemistry

text: In the late 19th century, Josiah Willard Gibbs had formulated a theory to predict whether a chemical reaction is spontaneous based on the free energy


title: Electrochemistry

text: Here Δ"G" is change in Gibbs free energy, Δ"G"° is the cell potential when "Q" is equal to 1, "T" is absolute temperature (Kelvin), "R" is the gas constant and "Q" is the reaction quotient, which can be calculated by dividing concentrations of products by those of reactants, each raised to the power of its stoichiometric coefficient, using only those products and reactants that are aqueous or gaseous.


title: Electrochemistry

text: Gibbs' key contribution was to formalize the understanding of the effect of reactant concentration on spontaneity.


title: Electrochemistry

text: Based on Gibbs' work, Nernst extended the theory to include the contribution from electric potential on charged species. As shown in the previous section, the change in Gibbs free energy for an electrochemical cell can be related to the cell potential. Thus, Gibbs' theory becomes


title: Electrochemistry

text: Here "n" is the number of electrons (in moles), "F" is the Faraday constant (in coulombs/mole), and Δ"E" is the cell potential (in volts).


title: Electrochemistry

text: Finally, Nernst divided through by the amount of charge transferred to arrive at a new equation which now bears his name:


title: Electrochemistry

text: Assuming standard conditions ("T" = 298 K or 25 °C) and "R" = 8.3145 J/(K·mol), the equation above can be expressed on base—10 logarithm as shown below:


title: Electrochemistry

text: Note that "" is also known as the thermal voltage "V" and is found in the study of plasmas and semiconductors as well. The value 0.05916 V in the above equation is just the thermal voltage at standard temperature multiplied by the natural logarithm of 10.


title: Electrochemistry

text: A concentration cell is an electrochemical cell where the two electrodes are the same material, the electrolytes on the two half-cells involve the same ions, but the electrolyte concentration differs between the two half-cells.


title: Electrochemistry

text: An example is an electrochemical cell, where two copper electrodes are submerged in two copper(II) sulfate solutions, whose concentrations are 0.05 M and 2.0 M, connected through a salt bridge. This type of cell will generate a potential that can be predicted by the Nernst equation. Both can undergo the same chemistry (although the reaction proceeds in reverse at the anode)


title: Electrochemistry

text: Le Chatelier's principle indicates that the reaction is more favorable to reduction as the concentration of Cu ions increases. Reduction will take place in the cell's compartment where the concentration is higher and oxidation will occur on the more dilute side.


title: Electrochemistry

text: The value of "E"° in this kind of cell is zero, as electrodes and ions are the same in both half-cells.


title: Electrochemistry

text: However, this value is only approximate, as reaction quotient is defined in terms of ion activities which can be approximated with the concentrations as calculated here.


title: Electrochemistry

text: The Nernst equation plays an important role in understanding electrical effects in cells and organelles. Such effects include nerve synapses and cardiac beat as well as the resting potential of a somatic cell.


title: Electrochemistry

text: Many types of battery have been commercialized and represent an important practical application of electrochemistry. Early wet cells powered the first telegraph and telephone systems, and were the source of current for electroplating. The zinc-manganese dioxide dry cell was the first portable, non-spillable battery type that made flashlights and other portable devices practical. The mercury battery using zinc and mercuric oxide provided higher levels of power and capacity than the original dry cell for early electronic devices, but has been phased out of common use due to the danger of mercury pollution from discarded cells.


title: Electrochemistry

text: The lead–acid battery was the first practical secondary (rechargeable) battery that could have its capacity replenished from an external source. The electrochemical reaction that produced current was (to a useful degree) reversible, allowing electrical energy and chemical energy to be interchanged as needed. Common lead acid batteries contain a mixture of sulfuric acid and water, as well as lead plates. The most common mixture used today is 30% acid. One problem, however, is if left uncharged acid will crystallize within the lead plates of the battery rendering it useless. These batteries last an average of 3 years with daily use but it is not unheard of for a lead acid battery to still be functional after 7–10 years. Lead-acid cells continue to be widely used in automobiles.


title: Electrochemistry

text: All the preceding types have water-based electrolytes, which limits the maximum voltage per cell. The freezing of water limits low temperature performance. The lithium metal battery, which does not (and cannot) use water in the electrolyte, provides improved performance over other types; a rechargeable lithium-ion battery is an essential part of many mobile devices.


title: Electrochemistry

text: The flow battery, an experimental type, offers the option of vastly larger energy capacity because its reactants can be replenished from external reservoirs. The fuel cell can turn the chemical energy bound in hydrocarbon gases or hydrogen and oxygen directly into electrical energy with a much higher efficiency than any combustion process; such devices have powered many spacecraft and are being applied to grid energy storage for the public power system.


title: Electrochemistry

text: Corrosion is an electrochemical process, which reveals itself as rust or tarnish on metals like iron or copper and their respective alloys, steel and brass.


title: Electrochemistry

text: For iron rust to occur the metal has to be in contact with oxygen and water. The chemical reactions for this process are relatively complex and not all of them are completely understood. It is believed the causes are the following:


title: Electrochemistry

text: Iron corrosion takes place in an acid medium; H ions come from reaction between carbon dioxide in the atmosphere and water, forming carbonic acid. Fe ions oxidize further, following this equation:


title: Electrochemistry

text: Iron(III) oxide hydrate is known as rust. The concentration of water associated with iron oxide varies, thus the chemical formula is represented by FeO·HO.


title: Electrochemistry

text: An electric circuit is formed as passage of electrons and ions occurs; thus if an electrolyte is present it will facilitate oxidation, explaining why rusting is quicker in salt water.


title: Electrochemistry

text: A patina of green-blue copper carbonate forms on the surface of copper with exposure to the water and carbon dioxide in the air. Silver coins or cutlery that are exposed to high sulfur foods such as eggs or the low levels of sulfur species in the air develop a layer of black silver sulfide.


title: Electrochemistry

text: Gold and platinum are extremely difficult to oxidize under normal circumstances, and require exposure to a powerful chemical oxidizing agent such as aqua regia.


title: Electrochemistry

text: Some common metals oxidize extremely rapidly in air. Titanium and aluminium oxidize instantaneously in contact with the oxygen in the air. These metals form an extremely thin layer of oxidized metal on the surface, which bonds with the underlying metal. This thin oxide layer protects the underlying bulk of the metal from the air preventing the entire metal from oxidizing. These metals are used in applications where corrosion resistance is important. Iron, in contrast, has an oxide that forms in air and water, called rust, that does not bond with the iron and therefore does not stop the further oxidation of the iron. Thus iron left exposed to air and water will continue to rust until all of the iron is oxidized.


title: Electrochemistry

text: Attempts to save a metal from becoming anodic are of two general types. Anodic regions dissolve and destroy the structural integrity of the metal.


title: Electrochemistry

text: While it is almost impossible to prevent anode/cathode formation, if a non-conducting material covers the metal, contact with the electrolyte is not possible and corrosion will not occur.


title: Electrochemistry

text: Metals can be coated with paint or other less conductive metals ("passivation"). This prevents the metal surface from being exposed to electrolytes. Scratches exposing the metal substrate will result in corrosion. The region under the coating adjacent to the scratch acts as the anode of the reaction.


title: Electrochemistry

text: A method commonly used to protect a structural metal is to attach a metal which is more anodic than the metal to be protected. This forces the structural metal to be cathodic, thus spared corrosion. It is called ""sacrificial"" because the anode dissolves and has to be replaced periodically.


title: Electrochemistry

text: Zinc bars are attached to various locations on steel ship hulls to render the ship hull cathodic. The zinc bars are replaced periodically. Other metals, such as magnesium, would work very well but zinc is the least expensive useful metal.


title: Electrochemistry

text: To protect pipelines, an ingot of buried or exposed magnesium (or zinc) is buried beside the pipeline and is connected electrically to the pipe above ground. The pipeline is forced to be a cathode and is protected from being oxidized and rusting. The magnesium anode is sacrificed. At intervals new ingots are buried to replace those dissolved.


title: Electrochemistry

text: The spontaneous redox reactions of a conventional battery produce electricity through the different reduction potentials of the cathode and anode in the electrolyte. However, electrolysis requires an external source of electrical energy to induce a chemical reaction, and this process takes place in a compartment called an electrolytic cell.


title: Electrochemistry

text: When molten, the salt sodium chloride can be electrolyzed to yield metallic sodium and gaseous chlorine. Industrially this process takes place in a special cell named Down's cell. The cell is connected to an electrical power supply, allowing electrons to migrate from the power supply to the electrolytic cell.


title: Electrochemistry

text: This process can yield large amounts of metallic sodium and gaseous chlorine, and is widely used in mineral dressing and metallurgy industries.


title: Electrochemistry

text: The emf for this process is approximately −4 V indicating a (very) non-spontaneous process. In order for this reaction to occur the power supply should provide at least a potential difference of 4 V. However, larger voltages must be used for this reaction to occur at a high rate.


title: Electrochemistry

text: Water can be converted to its component elemental gases, H and O, through the application of an external voltage. Water does not decompose into hydrogen and oxygen spontaneously as the Gibbs free energy change for the process at standard conditions is very positive, about 474.4 kJ. The decomposition of water into hydrogen and oxygen can be performed in an electrolytic cell. In it, a pair of inert electrodes usually made of platinum immersed in water act as anode and cathode in the electrolytic process. The electrolysis starts with the application of an external voltage between the electrodes. This process will not occur except at extremely high voltages without an electrolyte such as sodium chloride or sulfuric acid (most used 0.1 M).


title: Electrochemistry

text: Bubbles from the gases will be seen near both electrodes. The following half reactions describe the process mentioned above:


title: Electrochemistry

text: Although strong acids may be used in the apparatus, the reaction will not net consume the acid. While this reaction will work at any conductive electrode at a sufficiently large potential, platinum catalyzes both hydrogen and oxygen formation, allowing for relatively low voltages (~2 V depending on the pH).


title: Electrochemistry

text: Electrolysis in an aqueous solution is a similar process as mentioned in electrolysis of water. However, it is considered to be a complex process because the contents in solution have to be analyzed in half reactions, whether reduced or oxidized.


title: Electrochemistry

text: The presence of water in a solution of sodium chloride must be examined in respect to its reduction and oxidation in both electrodes. Usually, water is electrolysed as mentioned above in electrolysis of water yielding "gaseous oxygen in the anode" and gaseous hydrogen in the cathode. On the other hand, sodium chloride in water dissociates in Na and Cl ions. The cation, which is the positive ion, will be attracted to the cathode (−), thus reducing the sodium ion. The chloride anion will then be attracted to the anode (+), where it is oxidized to chlorine gas.


title: Electrochemistry

text: Reaction 1 is discarded as it has the most negative value on standard reduction potential thus making it less thermodynamically favorable in the process.


title: Electrochemistry

text: When comparing the reduction potentials in reactions 2 and 4, the reduction of chloride ion is favored. Thus, if the Cl ion is favored for reduction, then the water reaction is favored for oxidation producing gaseous oxygen, however experiments show gaseous chlorine is produced and not oxygen.


title: Electrochemistry

text: Although the initial analysis is correct, there is another effect, known as the overvoltage effect. Additional voltage is sometimes required, beyond the voltage predicted by the "E"°. This may be due to kinetic rather than thermodynamic considerations. In fact, it has been proven that the activation energy for the chloride ion is very low, hence favorable in kinetic terms. In other words, although the voltage applied is thermodynamically sufficient to drive electrolysis, the rate is so slow that to make the process proceed in a reasonable time frame, the voltage of the external source has to be increased (hence, overvoltage).


title: Electrochemistry

text: Finally, reaction 3 is favorable because it describes the proliferation of OH ions thus letting a probable reduction of H ions less favorable an option.


title: Electrochemistry

text: As the overall reaction indicates, the concentration of chloride ions is reduced in comparison to OH ions (whose concentration increases). The reaction also shows the production of gaseous hydrogen, chlorine and aqueous sodium hydroxide.


title: Electrochemistry

text: Quantitative aspects of electrolysis were originally developed by Michael Faraday in 1834. Faraday is also credited to have coined the terms "electrolyte", electrolysis, among many others while he studied quantitative analysis of electrochemical reactions. Also he was an advocate of the law of conservation of energy.


title: Electrochemistry

text: Faraday concluded after several experiments on electric current in a non-spontaneous process that the mass of the products yielded on the electrodes was proportional to the value of current supplied to the cell, the length of time the current existed, and the molar mass of the substance analyzed. In other words, the amount of a substance deposited on each electrode of an electrolytic cell is directly proportional to the quantity of electricity passed through the cell.


title: Electrochemistry

text: Faraday devised the laws of chemical electrodeposition of metals from solutions in 1857. He formulated the second law of electrolysis stating ""the amounts of bodies which are equivalent to each other in their ordinary chemical action have equal quantities of electricity naturally associated with them."" In other words, the quantities of different elements deposited by a given amount of electricity are in the ratio of their chemical equivalent weights.


title: Electrochemistry

text: An important aspect of the second law of electrolysis is electroplating, which together with the first law of electrolysis has a significant number of applications in industry, as when used to protectively coat metals to avoid corrosion.


title: Electrochemistry

text: There are various important electrochemical processes in both nature and industry, like the coating of objects with metals or metal oxides through electrodeposition, the addition (electroplating) or removal (electropolishing) of thin layers of metal from an object's surface, and the detection of alcohol in drunk drivers through the redox reaction of ethanol. The generation of chemical energy through photosynthesis is inherently an electrochemical process, as is production of metals like aluminum and titanium from their ores. Certain diabetes blood sugar meters measure the amount of glucose in the blood through its redox potential. In addition to established electrochemical technologies (like deep cycle lead acid batteries) there is also a wide range of new emerging technologies such as fuel cells, large format lithium-ion batteries, electrochemical reactors and super-capacitors that are becoming increasingly commercial. Electrochemical or coulometric titrations were introduced for quantitative analysis of minute quantities in 1938 by the Hungarian chemists László Szebellédy and Zoltan Somogyi. Electrochemistry also has important applications in the food industry, like the assessment of food/package interactions, the analysis of milk composition, the characterization and the determination of the freezing end-point of ice-cream mixes, or the determination of free acidity in olive oil.


title: Hinder

text: Hinder is an American rock band from Oklahoma City, Oklahoma, formed in 2001 by lead singer Austin John Winkler, guitarist Joe "Blower" Garvey, and drummer Cody Hanson with bassist Mike Roden and guitarist Mark King joining in 2003, solidifying the line-up. The band released four studio albums with Winkler; "Extreme Behavior" (2005), "Take It to the Limit" (2008), "All American Nightmare" (2010) and "Welcome to the Freakshow" (2012). Cody Hanson, along with former lead singer Austin Winkler, wrote the majority of the band's music on their first four albums. After Winkler left the band in 2013, they looked for a new lead vocalist, and added Marshal Dutton. They have since released "When the Smoke Clears" (2015) and "The Reign" (2017) with their new vocalist. Their seventh studio album is currently in the works. The band was inducted into the Oklahoma Music Hall of Fame in 2007.


title: Hinder

text: Before the band formed, Austin John Winkler sang in an Oklahoma City cover band until July 2001, when he met drummer Cody Hanson and lead guitarist Joe Garvey at a college party. Soon after meeting, the three formed Hinder. Hanson commented on Austin Winkler shortly after the band formed saying he was "blown away" and "he has the kind of charisma very few people have and that unique voice. You can't really compare him to anybody." After recruiting bassist Cole Parker, they recorded a 4 track demo disc, with the track listing "Someday", "Like Me", "Broken", and "Worthless Home". The tracks "Someday" and "Broken" would later be re-recorded and put on their debut EP "Far From Close" and the other two tracks "Like Me" and "Worthless Home" still remain unreleased, only being able to find them on their demo CDs, although they are now posted on YouTube. The band began performing at an Oklahoma City club called The Blue Note, building a local fan base. Profits from the shows went to advertising, as well as paying the expenses for the group's first release. In April 2003, Hinder entered the March Bandness contest for Oklahoma City radio station KHBZ-FM (94.7). They made it to the Final Four out of a field of thirty-two, ultimately losing to the OKC group Falcon Five-O. After saving enough money from local concerts the band's debut EP "Far From Close" was released in 2003 on the independent label Brickden Records and sold around 5,000 copies. Bassist Mike Rodden was recruited from Oklahoma City band Shade Seven and rhythm guitarist Mark King joined the band later that year.


title: Hinder

text: After the release of "Far from Close", Hinder was offered record deals by Atlantic Records, Roadrunner Records, and Universal Records, eventually signing with Universal Records in 2005; later that year, their major-label debut album, "Extreme Behavior", was released. The album was produced by Brian Howes, who, along with Cody Hanson and Austin Winkler, wrote most of the material on the album. The album was engineered by Mike Fraser and Jay Van Poederooyen. The album reached triple-platinum certification for sales.


title: Hinder

text: Hinder toured and released singles in support of their first album. Hinder's debut single, "Get Stoned", was released in October 2005. The band's second single, "Lips of an Angel", entered charts in the US, Canada, Australia, New Zealand, and Singapore; the song lasted for 41 weeks in the New Zealand charts, two weeks of which were spent at the number one spot. The band's third single, "How Long", was released in September 2006 and appeared at number six on the US "Billboard" Hot Mainstream Rock Tracks chart. Their second song to be released in New Zealand was "Better Than Me", which spent three weeks on the New Zealand charts, peaking at number 16. In 2007, Hinder was inducted into the Oklahoma Music Hall of Fame, and in October of the same year, the band released their limited edition CD/DVD of "Extreme Behavior" entitled "You Can't Make This S**t Up".


title: Hinder

text: The first single from the band's second album, "Use Me", was released on July 15, 2008, and peaked at No. 3 on the US Mainstream Rock Tracks chart. The second album, "Take It to the Limit", was released on November 4, 2008; the album marked a change in style in Hinder's music in that it moved the band in a slightly more glam metal-influenced direction. The title track features Mötley Crüe's Mick Mars on guitar. They announced the release of the album's second single, "Without You," through their official MySpace page on September 13, 2008. "Take It To the Limit" debuted at number four on the Billboard 200 with 81,000 sales its first week and ended up going Gold in the US


title: Hinder

text: Through late 2008, Hinder headlined the Jägermeister Music Tour with Trapt and Rev Theory also on the bill. In early 2009, Hinder embarked on Mötley Crüe's Saints Of Los Angeles Tour, which also included Theory of a Deadman and The Last Vegas. In July, Hinder embarked on Nickelback's Dark Horse Tour, which ran through Live Nation outdoor amphitheaters; other bands involved on the tour were Papa Roach, Breaking Benjamin and Saving Abel. On March 27, 2013 "Take It To The Limit" was certified gold in the US.


title: Hinder

text: During early 2010, the band was engaged in writing and recording material for their third album, titled "All American Nightmare". The album was released on December 7, 2010, with the first single, the title track, released on September 14, 2010. Although the album was originally planned to be produced by Howard Benson, Kevin Churko was later announced to be the producer.


title: Hinder

text: Winkler said that the group started recording during the touring cycle for "Take It To The Limit". "We wrote 70 or so songs, recorded about 50 and cut it down to 12," the singer explained. "It's something that we've never done before, so it's like our ultimate baby. A lot of the [other] songs could be shit, too, we don't know. You don't really know until you put it out there and have more than two people's opinion on it." Both he and drummer Cody Hanson mentioned the song "Memory" as one that was a strong contender for the final cut. "It's about being with your chick – the chick you've been with for a while, not some chick you've met on the road – and about being able to still have a good time with your wife or long-time girlfriend," said Hanson. "I've been in a relationship myself for nine years, so it was cool to write a song like that."


title: Hinder

text: On August 9, 2012, Hinder announced via Facebook and Twitter that their then-upcoming album would be titled "Welcome to the Freakshow". It was released on December 4, 2012. Hinder released their first single, "Save Me", on August 30. On July 10, 2013, it was announced that lead singer Austin Winkler had entered rehab, and would not be touring with the band for the remainder of the year. Marshal Dutton, one of the band's producers, was brought in to fill in on lead vocals for a couple shows until Jared Weeks, of Saving Abel, joined the band to fill in for Winkler for the rest of the tour. On November 20, 2013, it was announced via Loudwire that Austin Winkler had left the band.


title: Hinder

text: On July 7, 2014, the band posted a video on their social media sites apologizing to fans for their inactivity and to announce that they had been writing new songs for the new album while searching for a new lead singer. They also announced a string of shows throughout the rest of the summer. Although never announced officially, the band played their shows with Nashville-based singer Nolan Neal on lead vocals.


title: Hinder

text: On December 9, 2014, Hinder officially announced their new album, and that it would be titled "When the Smoke Clears". On January 20, 2015, Hinder officially announced that Marshal Dutton would be their new lead singer, via social media sites. Dutton has been affiliated with the band since his former band Faktion toured with Hinder and Rev Theory on the Girls Gone Wild tour back in 2006. He had also been writing and recording for the band since 2009 when they were going through the writing and recording sessions for "All American Nightmare". Dutton had been working on every Hinder album since, even co-producing "Welcome to the Freakshow" alongside drummer Cody Hanson. On March 17, 2015, the band released a preview of the first song on their record, "Rather Hate Than Hurt" via loudwire, making it the second song to be released since founding vocalist Austin John Winkler departed the band in November 2013. The band also revealed their new album "When the Smoke Clears" will be released on May 12, 2015. The band went on tour in support of the new album starting in March 2015, they did a Summer tour throughout the U.S. with Full Devil Jacket Integrity Music Management and AGES APART supporting them. In November 2015, Hinder announced their Winter tour with Shaman's Harvest, Within Reason, Sons Of Texas, David Adkins and AGES APART. "When the Smoke Clears" spawned 4 singles, the most successful single "Intoxicated" debuted at #38 on the US Active Rock Chart, the song was co-written with upcoming country music singer-songwriter Ryan Hurd.


title: Hinder

text: After playing a show at the venue "Ziggy's By The Sea" in Wilmington, North Carolina the group did an interview with The Baltimore Sun and talked about the band's place over the course of the past year. The group stated that they had no choice but to find a new lead singer in order to keep the band alive. The band went on to say that the change in singers was a fresh start for both Hinder and Austin Winkler, and that they are searching for another hit song as big as "Lips of an Angel".


title: Hinder

text: On March 7, 2016, the band announced that their upcoming acoustic EP would be titled "Stripped" and will be released May 13, 2016. The EP will feature six tracks with one newly recorded track titled "Not an Addict", which was originally recorded by K's Choice.


title: Hinder

text: The band went out on tour in support of the new EP on the "Stripped Tour" with new rock band Like a Storm as the opening act. the tour consisted of 22 shows over the course of June through July 2016. On March 2, 2017, the band announced a summer tour with Nonpoint. On June 12, 2017, the band finally announced the title of their sixth studio album "The Reign", which was released on August 11, 2017. On August 29, 2017, it was revealed the remaining original members of Hinder were suing former lead singer Austin Winkler for trademark infringement. The lawsuit alleges Winkler is currently promoting his own performances for his fall 2017 solo tour and music by the "unlawful use and exploitation of the Hinder trademark," and the group are asking Winkler to cease infringement and to pay over "all gains, profits and advantages realized from his infringing." In support of their new album "The Reign", on September 22, 2017, Hinder announced a fall co-headlining tour with Josh Todd & the Conflict. The tour will run from October through December with Wayland and Adelitas Way supporting.


title: Hinder

text: Throughout the winter and spring of 2018 drummer Cody Hanson and vocalist Marshal Dutton have been working on new music for a yet-untitled project. They've released numerous song clips throughout social media including a new Hinder song titled "Halo".


title: Hinder

text: In December 2018, the band announced a winter 2019 tour with Soil. In early January 2019, the band announced their new single titled "Halo" would be released January 25; this single serves as their lead single for their untitled upcoming seventh studio album which was to be released later that year. In July 2019 the band released a cover of the hit song Life in the Fast Lane. The song was released as a single to purchase and stream wherever music is sold.


title: Hinder

text: In February 2020 Hinder announced an Extreme Behavior 15th-anniversary tour for the summer and fall of 2020. The tour was delayed due to the COVID-19 pandemic.


title: Hinder

text: The band's influences include: Bush, Collective Soul, Creed, Foo Fighters, Guns N' Roses, Kiss, Nickelback, Nirvana, Soundgarden, The Rolling Stones, Led Zeppelin, Aerosmith, Rainbow, Bob Seger, Ozzy Osbourne, Def Leppard, Bon Jovi, AC/DC, and Mötley Crüe.


title: Saxe-Coburg and Gotha

text: Saxe-Coburg and Gotha (), or Saxe-Coburg-Gotha ( ), was an Ernestine, Thuringian duchy ruled by a branch of the House of Wettin, consisting of territories in the present-day states of Thuringia and Bavaria in Germany. It lasted from 1826 to 1918. In November 1918, Charles Edward, Duke of Saxe-Coburg and Gotha, was forced to abdicate. In 1920, the northern part of the duchy (since 1918 the Free State of Gotha; culturally and linguistically Thuringian) was merged with six other Thuringian free states to form the Free State of Thuringia: Saxe-Weimar-Eisenach (until 1918 a grand duchy), Saxe-Altenburg and Saxe-Meiningen (until 1918 duchies), Schwarzburg-Rudolstadt and Schwarzburg-Sondershausen (until 1918 principalities), as well as the People's State of Reuss (until 1918 the principalities of Reuss-Gera and Reuss-Greiz). The southern part of the duchy (since 1918 the Free State of Coburg; culturally and linguistically Franconian), as southernmost of the Thuringian states, was the only one which, after a referendum, became part of the Free State of Bavaria.


title: Saxe-Coburg and Gotha

text: The name "Saxe-Coburg-Gotha" also refers to the family of the ruling House of Saxe-Coburg and Gotha, which played many varied roles in the dynastic and political history of Europe in the 19th and 20th centuries. In the early part of the 20th century, before the First World War, it was the family of the sovereigns of the United Kingdom, Belgium, Portugal, Bulgaria, and Saxe-Coburg-Gotha. In 1910, the Portuguese king was deposed, and the same thing occurred in Saxe-Coburg-Gotha in 1918 and in Bulgaria in 1946. , branches of the family still reign in Belgium, the United Kingdom, and the other Commonwealth realms. The former Tsar of Bulgaria, Simeon II (reigned 1943–46), kept his surname while serving as the Prime Minister of Bulgaria from 2001 to 2005.


title: Saxe-Coburg and Gotha

text: The Duchy was born when the arbitration of the King of Saxony, Frederick Augustus, produced the Treaty of Hildburghausen on 12 November 1826 for the "Gothaische Teilung" (Gothan Division), the extensive rearrangement of the Ernestine duchies. After the extinction of the Saxe-Gotha-Altenburg line, the Duke of Saxe-Hildburghausen exchanged his Duchy for that of Saxe-Altenburg. The Saxe-Meiningen line became Saxe-Hildburghausen and got from Saxe-Coburg-Saalfeld the Saalfelder territories as well as the District of Themar and the places of Mupperg, Mogger, Liebau and Oerlsdorf. The Duchy of Saxe-Coburg-Saalfeld received for that the Duchy of Saxe-Coburg, Districts of Königsberg and Sonnefeld from Saxe-Hildburghausen, and the properties of Callenberg and Gauerstadt from Saxe-Meiningen.


title: Saxe-Coburg and Gotha

text: By then, the Principality of Lichtenberg, on the Nahe River, had already been a part of the Duchy of Coburg for ten years. Ernest III, the sovereign of Saxe-Coburg-Saalfeld, had received it in 1816 from the Congress of Vienna for providing assistance to the Allies in their war against France. But, because of the great distance from Coburg and of the unrest caused by the Hambach Festival, the Duke sold the Principality in 1834 to Prussia.


title: Saxe-Coburg and Gotha

text: The newly created Duchy of Saxe-Coburg and Gotha was initially a double duchy, ruled by Ernest III as Duke Ernest I in a personal union, but with only one vote in the "Bundesrat". The opportunity to unify the two duchies in 1826 was missed. After the "Staatsgrundgesetz" (House laws) of 1852, the duchies were bound in a political and real union. They were then a quasi-federal unitary state. Later attempts to merge the duchies failed in 1867 because the "Landtag" of Gotha did not want to assume the higher state debts of Coburg and in 1872 because of the questions about the administration of the whole union.


title: Saxe-Coburg and Gotha

text: The Duchy of Saxe-Coburg and Gotha received on 3 May 1852 a national constitution, which had taken substantial parts of the fundamental rights from the Constitution of the National Assembly in Frankfurt. It also joined the German Zollverein in 1834, the North German Confederation in 1866 and the German Empire in 1871. At the "Bundesrat" in Berlin, where it had a seat, it kept its agents but, since 1913, like most of the other Thuringian states, it had to defer to the Grand Duchy of Saxe-Meiningen for the representation.


title: Saxe-Coburg and Gotha

text: Ernest I died in 1844. His elder son and successor, Ernest II, ruled until his own death in 1893. Because he had died childless, the throne of the two duchies would have passed to his late brother Prince Albert's male descendants. But Prince Albert was the husband of Queen Victoria of the United Kingdom and his eldest son, Edward, the Prince of Wales, was already her heir apparent. Besides, he was prohibited by the Constitutions of both duchies from inheriting the throne if there were other eligible male heirs. But he had already renounced his claim in favour of his next brother, Prince Alfred, Duke of Edinburgh. So Alfred became the next Duke of Saxe-Coburg and Gotha.


title: Saxe-Coburg and Gotha

text: Alfred's only son, also named Alfred, died in 1899, so when Duke Alfred died in 1900 he was succeeded by his nephew the Duke of Albany, the 16-year-old son of Queen Victoria's youngest son, Leopold, as Duke Alfred's next brother Prince Arthur, Duke of Connaught and his son Prince Arthur of Connaught had renounced their own claims to the succession. Reigning as Duke Carl Eduard, Charles Edward, because of his age, began under the Regency of Prince Ernst von Hohenlohe-Langenburg until he came of age in 1905. The new Duke also continued to use his British title, the Duke of Albany. But, because he chose to side with the Germans against the British in the First World War, he was stripped of his British titles in 1919.


title: Saxe-Coburg and Gotha

text: After the November Revolution ended the monarchy in 1918, the two duchies became two different and independent states, the Free State of Coburg, and the Republic of Gotha, later renamed the Free State of Gotha. Their leaders believed, however, that their new countries were not economically viable, so they began to search for possible mergers. Eventually, a referendum was held on 30 November 1919 and the decision was made. On 1 May 1920, the Free State of Gotha merged with the new State of Thuringia, and the Free State of Coburg followed two months later, on 1 July 1920, by uniting with the Free State of Bavaria.


title: Saxe-Coburg and Gotha

text: In the German Empire, the Duchy had only one vote in the "Bundesrat" and two votes (for the two Duchies of Coburg and Gotha) in the "Reichstag".


title: Saxe-Coburg and Gotha

text: Each Duchy had its own "Landtag", elected every four years by male taxpayers over 25 years of age. Only males 30 years or older were eligible to stand for the elections. The Coburger assembly had 11 members and its twin in Gotha had 19. The assemblies met every year but, every two years, they would combine, alternatively in Gotha and Coburg, for the matters and questions that involve both Duchies.


title: Saxe-Coburg and Gotha

text: For both duchies, however, there was a Ministry of State in Gotha but Coburg and Gotha had their own subordinate and almost independent ministries. The Minister of State directed Gotha's Ducal ministry but, for both Duchies, he was responsible for the state affairs, the economical and commercials policies, the judiciary and the conduct of Imperial laws. In Coburg, for state matters as such as community services, police duties, support of the state church, and education, as well as management of assets and finances, and also, until 1891, court matters, the local authorities could not interfere with the decisions from Gotha.


title: Saxe-Coburg and Gotha

text: The finances of both Duchies remained basically disconnected. But, in their management, a distinction was always made between the Crown revenue from the domains and the State revenue from taxes and duties. Every four years, a common budget, especially in the financial dealings with the German Empire, was made, even if it interfered with the local and national operations of the two Duchies. Grants from the state budgets of both Duchies were made in the ratio of 7 to 3 between Gotha and Coburg.


title: Saxe-Coburg and Gotha

text: Because of its size and finances, the Duchy did not have ambassadors but it did have trade consuls. They were for trade with Austria-Hungary, Belgium, Brazil, Chile, Cuba, Ecuador, France, Great Britain, Italy, Mexico, Peru, Portugal, Prussia, Russia, Spain, Switzerland, and Turkey. The United States had its own consul in Coburg from 1897 to 1918.


title: Saxe-Coburg and Gotha

text: During the American Civil War, Ernst Raven was assigned to the position of consul in the state of Texas. He applied to the Confederate Government for a diplomatic exequatur on 30 July 1861 and was accepted.


title: Saxe-Coburg and Gotha

text: Before 1867, the Duchy of Saxe-Coburg and Gotha had its own Army. But, on 26 June 1867, because of a treaty signed in 1866 with Prussia, its Army was added, for defending and recruiting purposes, to the 6th Thuringian Infantry Regiment No. 95 of the 22nd Division of the XIth Army Corps. Three battalions of the 6th Thuringian were assigned to Gotha (No. 1), Hildburghausen (No. 2) and Coburg (No. 3) but the Corps headquarters was in Kassel. Unlike Prussia, where military service was mandatory, Saxe-Coburg and Gotha filled its quota in the Imperial Army with the draft.


title: Saxe-Coburg and Gotha

text: The capitals of Saxe-Coburg and Gotha were Coburg and Gotha. By 1914 the area and populations of the two duchies were:


title: Saxe-Coburg and Gotha

text: There are two residences in Gotha and Coburg. Therefore, the whole ducal court, including the Court Theater, had to move twice a year: from Gotha to Coburg for the summer, from Coburg to Gotha for the winter. For the Court Theater, two almost identical buildings had to be built in 1840 in Gotha (destroyed in the Second World War) and Coburg (now the Coburg State Theater) and thereafter maintained at the same time. In addition to the residential castles, "Friedenstein" in Gotha and "Ehrenburg" in Coburg, the Ducal family also used the "Schloss" Reinhardsbrunn in Gotha as well as the Rosenau and Callenberg castles in Coburg and the hunting lodge Greinburg Castle, Grein, Austria (the latter two still today owned by the ducal branch of the House of Saxe-Coburg and Gotha).


title: Saxe-Coburg and Gotha

text: Only the Duchy of Gotha, along with nearby Duchies of Saxe-Meiningen and Saxe-Altenburg and especially the Grand Duchy of Saxe-Weimar-Eisenach – was able to be one of the sponsoring states of the University of Jena. Coburg did not have its own university. It did not have its court of law, either. Gotha had its own court of law while Coburg had to go to Meiningen for the legal administration.


title: Saxe-Coburg and Gotha

text: According to the "Staatsgrundgesetz" (House laws) of the Duchy of Saxe-Coburg and Gotha, the full title of the Duke was:


title: Saxe-Coburg and Gotha

text: "Wir, Ernst, Herzog zu Sachsen-Coburg und Gotha, Jülich, Cleve und Berg, auch Engern und Westphalen, Landgraf in Thüringen, Markgraf zu Meißen, gefürsteter Graf zu Henneberg, Graf zu der Mark und Ravensberg, Herr zu Ravenstein und Tonna usw."


title: Saxe-Coburg and Gotha

text: Translation: We, Ernest, Duke of Saxe-Coburg and Gotha, Jülich, Cleves and Berg, also Angria and Westphalia, Landgrave in Thuringia, Margrave of Meissen, Princely Count of Henneberg, Count of the Mark and Ravensberg, Lord of Ravenstein and Tonna, et cetera.


title: Saxe-Coburg and Gotha

text: The use of Ducal and Princely titles may be restricted if the marriage conflicts with the requirements of the "Staatsgrundgesetz" or if a member of the House renounces his claims for himself and his descendants.


title: Dr Pepper Snapple Group

text: Dr Pepper Snapple Group (also called Dr. Pepper/7up Inc.) was an American multinational soft drink company based in Plano, Texas, and as of July 2018 it is a business unit of the publicly traded conglomerate Keurig Dr Pepper.


title: Dr Pepper Snapple Group

text: Formerly Cadbury Schweppes Americas Beverages, part of Cadbury Schweppes, on May 5, 2008 it was spun off from Cadbury Schweppes as Dr Pepper Snapple Group, with trading in its shares starting on May 7, 2008 on the NYSE as "DPS". The remainder of Cadbury Schweppes become Cadbury, a confectionery group, on May 5, 2008.


title: Dr Pepper Snapple Group

text: On July 9, 2018, Keurig Green Mountain acquired Dr Pepper Snapple Group, and became Keurig Dr Pepper; the following day the merged company began trading anew on the NYSE as "KDP".


title: Dr Pepper Snapple Group

text: Beverage America and Select Beverages bottlers were purchased from the Carlyle Group in February 1998. Snapple, Mistic and Stewart's (formerly Cable Car Beverage) were sold by Triarc Companies, Inc. to Cadbury Schweppes in 2000 for $1.45 billion. That October, Cadbury Schweppes purchased Royal Crown Cola from Triarc.


title: Dr Pepper Snapple Group

text: In 2006 and 2007, Cadbury Schweppes purchased the Dr Pepper/Seven Up Bottling Group, along with several other regional bottlers. This allowed DPS to bottle many of its own beverages and combat the recent decision by many Pepsi and Coke bottlers who had dropped their Dr Pepper and Snapple products to promote new product additions from Pepsi and Coke. Some of the Dr Pepper/Seven Up brands are still licensed to Pepsi, Coke and independent bottlers in various regions of the United States and Canada.


title: Dr Pepper Snapple Group

text: In November 2007, Cadbury Schweppes announced it would take the beverages unit public. In May 2008, Cadbury Schweppes demerged its beverage holdings forming the Dr Pepper Snapple Group.


title: Dr Pepper Snapple Group

text: Dr Pepper Snapple Group holds naming rights to the Dallas Stars' practice facility, the Dr Pepper Arena, which is located in Frisco, Texas. It also retains non-alcoholic beverage rights to each facility's concessions as a result of the deals as well as sponsorships with the NHL franchise.


title: Dr Pepper Snapple Group

text: In 2008, Dr Pepper Snapple Group purchased minority interest in Big Red, Inc, makers of Big Red, NuGrape, Nesbitt's and other flavored drinks.


title: Dr Pepper Snapple Group

text: In 2014, the company announced that it accomplished its goal of reducing use of polyethylene terephthalate (PET) in its plastic bottles. Dr Pepper Snapple lowered the amount of PET in its bottles by over 60 million pounds between 2007 and 2014.


title: Dr Pepper Snapple Group

text: On November 22, 2016, Dr Pepper Snapple announced plans to make a cash purchase of Bai Brands for $1.7 billion. It had previously purchased a minority stake in the company for $15 million in 2015.


title: Dr Pepper Snapple Group

text: On January 29, 2018, Keurig Green Mountain announced it was acquiring the Dr Pepper Snapple Group in an $18.7 billion deal. The combined company would be named Keurig Dr Pepper and would trade publicly on the New York Stock Exchange. Shareholders of Dr Pepper Snapple Group would own 13% of the combined company, while Keurig shareholder and Cadbury current owner Mondelez International owning 13 to 14%, and JAB Holdings owning the remaining majority stake. The buyout and merger was closed on July 9, 2018. Larry Young, President and CEO of the Dr Pepper Snapple Group, retired those positions and joined the board of directors of Keurig Dr Pepper.


title: Point (basketball)

text: Points in basketball are used to keep track of the score in a game. Points can be accumulated by making field goals (two or three points) or free throws (one point). If a player makes a field goal from within the three-point line, the player scores two points. If the player makes a field goal from beyond the three-point line, the player scores three points. The team that has recorded the most points at the end of a game is declared that game's winner.


title: Deterministic finite automaton

text: In the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state automaton (DFSA)—is a finite-state machine that accepts or rejects a given string of symbols, by running through a state sequence uniquely determined by the string. "Deterministic" refers to the uniqueness of the computation run. In search of the simplest models to capture finite-state machines, Warren McCulloch and Walter Pitts were among the first researchers to introduce a concept similar to finite automata in 1943.


title: Deterministic finite automaton

text: The figure illustrates a deterministic finite automaton using a state diagram. In this example automaton, there are three states: S, S, and S (denoted graphically by circles). The automaton takes a finite sequence of 0s and 1s as input. For each state, there is a transition arrow leading out to a next state for both 0 and 1. Upon reading a symbol, a DFA jumps "deterministically" from one state to another by following the transition arrow. For example, if the automaton is currently in state S and the current input symbol is 1, then it deterministically jumps to state S. A DFA has a "start state" (denoted graphically by an arrow coming in from nowhere) where computations begin, and a set of "accept states" (denoted graphically by a double circle) which help define when a computation is successful.


title: Deterministic finite automaton

text: A DFA is defined as an abstract mathematical concept, but is often implemented in hardware and software for solving various specific problems such as lexical analysis and pattern matching. For example, a DFA can model software that decides whether or not online user input such as email addresses are syntactically valid.


title: Deterministic finite automaton

text: DFAs have been generalized to "nondeterministic finite automata (NFA)" which may have several arrows of the same label starting from a state. Using the powerset construction method, every NFA can be translated to a DFA that recognizes the same language. DFAs, and NFAs as well, recognize exactly the set of regular languages.


title: Deterministic finite automaton

text: Let be a string over the alphabet . The automaton accepts the string if a sequence of states, , exists in with the following conditions:


title: Deterministic finite automaton

text: In words, the first condition says that the machine starts in the start state . The second condition says that given each character of string , the machine will transition from state to state according to the transition function . The last condition says that the machine accepts if the last input of causes the machine to halt in one of the accepting states. Otherwise, it is said that the automaton "rejects" the string. The set of strings that accepts is the language "recognized" by and this language is denoted by .


title: Deterministic finite automaton

text: A deterministic finite automaton without accept states and without a starting state is known as a transition system or semiautomaton.


title: Deterministic finite automaton

text: The following example is of a DFA , with a binary alphabet, which requires that the input contains an even number of 0s.


title: Deterministic finite automaton

text: The state represents that there has been an even number of 0s in the input so far, while signifies an odd number. A 1 in the input does not change the state of the automaton. When the input ends, the state will show whether the input contained an even number of 0s or not. If the input did contain an even number of 0s, will finish in state , an accepting state, so the input string will be accepted.


title: Deterministic finite automaton

text: The language recognized by is the regular language given by the regular expression codice_1, where codice_2 is the Kleene star, e.g., codice_3 denotes any number (possibly zero) of consecutive ones.


title: Deterministic finite automaton

text: According to the above definition, deterministic finite automata are always "complete": they define from each state a transition for each input symbol.


title: Deterministic finite automaton

text: While this is the most common definition, some authors use the term deterministic finite automaton for a slightly different notion: an automaton that defines "at most" one transition for each state and each input symbol; the transition function is allowed to be partial. When no transition is defined, such an automaton halts.


title: Deterministic finite automaton

text: A local automaton is a DFA, not necessarily complete, for which all edges with the same label lead to a single vertex. Local automata accept the class of local languages, those for which membership of a word in the language is determined by a "sliding window" of length two on the word.


title: Deterministic finite automaton

text: A Myhill graph over an alphabet "A" is a directed graph with vertex set "A" and subsets of vertices labelled "start" and "finish". The language accepted by a Myhill graph is the set of directed paths from a start vertex to a finish vertex: the graph thus acts as an automaton. The class of languages accepted by Myhill graphs is the class of local languages.


title: Deterministic finite automaton

text: When the start state and accept states are ignored, a DFA of states and an alphabet of size can be seen as a digraph of vertices in which all vertices have out-arcs labeled (a -out digraph). It is known that when is a fixed integer, with high probability, the largest strongly connected component (SCC) in such a -out digraph chosen uniformly at random is of linear size and it can be reached by all vertices. It has also been proven that if is allowed to increase as increases, then the whole digraph has a phase transition for strong connectivity similar to Erdős–Rényi model for connectivity.


title: Deterministic finite automaton

text: In a random DFA, the maximum number of vertices reachable from one vertex is very close to the number of vertices in the largest SCC with high probability. This is also true for the largest induced sub-digraph of minimum in-degree one, which can be seen as a directed version of -core.


title: Deterministic finite automaton

text: If DFAs recognize the languages that are obtained by applying an operation on the DFA recognizable languages then DFAs are said to be closed under the operation. The DFAs are closed under the following operations.


title: Deterministic finite automaton

text: For each operation, an optimal construction with respect to the number of states has been determined in state complexity research.


title: Deterministic finite automaton

text: Since DFAs are equivalent to nondeterministic finite automata (NFA), these closures may also be proved using closure properties of NFA.


title: Deterministic finite automaton

text: A run of a given DFA can be seen as a sequence of compositions of a very general formulation of the transition function with itself. Here we construct that function.


title: Deterministic finite automaton

text: For a given input symbol formula_4, one may construct a transition function formula_5 by defining formula_6 for all formula_7. (This trick is called currying.) From this perspective, formula_8 "acts" on a state in Q to yield another state. One may then consider the result of function composition repeatedly applied to the various functions formula_8, formula_10, and so on. Given a pair of letters formula_11, one may define a new function formula_12, where formula_13 denotes function composition.


title: Deterministic finite automaton

text: Clearly, this process may be recursively continued, giving the following recursive definition of formula_14:


title: Deterministic finite automaton

text: formula_20 is defined for all words formula_21. A run of the DFA is a sequence of compositions of formula_20 with itself.


title: Deterministic finite automaton

text: Repeated function composition forms a monoid. For the transition functions, this monoid is known as the transition monoid, or sometimes the "transformation semigroup". The construction can also be reversed: given a formula_20, one can reconstruct a formula_24, and so the two descriptions are equivalent.


title: Deterministic finite automaton

text: DFAs are one of the most practical models of computation, since there is a trivial linear time, constant-space, online algorithm to simulate a DFA on a stream of input. Also, there are efficient algorithms to find a DFA recognizing:


title: Deterministic finite automaton

text: Because DFAs can be reduced to a "canonical form" (minimal DFAs), there are also efficient algorithms to determine:


title: Deterministic finite automaton

text: DFAs are equivalent in computing power to nondeterministic finite automata (NFAs). This is because, firstly any DFA is also an NFA, so an NFA can do what a DFA can do. Also, given an NFA, using the powerset construction one can build a DFA that recognizes the same language as the NFA, although the DFA could have exponentially larger number of states than the NFA. However, even though NFAs are computationally equivalent to DFAs, the above mentioned problems are not necessarily solved efficiently also for NFAs. The non-universality problem for NFAs is PSPACE complete since there are small NFAs with shortest rejecting word in exponential size. A DFA is universal if and only if all states are final states, but this does not hold for NFAs. The Equality, Inclusion and Minimization Problems are also PSPACE complete since they require forming the complement of an NFA which results in an exponential blow up of size.


title: Deterministic finite automaton

text: On the other hand, finite-state automata are of strictly limited power in the languages they can recognize; many simple languages, including any problem that requires more than constant space to solve, cannot be recognized by a DFA. The classic example of a simply described language that no DFA can recognize is bracket or Dyck language, i.e., the language that consists of properly paired brackets such as word "(()())". Intuitively, no DFA can recognize the Dyck language because DFAs are not capable of counting: a DFA-like automaton needs to have a state to represent any possible number of "currently open" parentheses, meaning it would need an unbounded number of states. Another simpler example is the language consisting of strings of the form "ab" for some finite but arbitrary number of "a"'s, followed by an equal number of "b"'s.


title: Deterministic finite automaton

text: Given a set of "positive" words formula_25 and a set of "negative" words formula_26 one can construct a DFA that accepts all words from formula_27 and rejects all words from formula_28: this problem is called "DFA identification" (synthesis, learning).


title: Deterministic finite automaton

text: While "some" DFA can be constructed in linear time, the problem of identifying a DFA with the minimal number of states is NP-complete.


title: Deterministic finite automaton

text: The first algorithm for minimal DFA identification has been proposed by Trakhtenbrot and Barzdin in and is called the "TB-algorithm".


title: Deterministic finite automaton

text: However, the TB-algorithm assumes that all words from formula_29 up to a given length are contained in either formula_30.


title: Deterministic finite automaton

text: Later, K. Lang proposed an extension of the TB-algorithm that does not use any assumptions about formula_27 and formula_28 the "Traxbar" algorithm.


title: Deterministic finite automaton

text: Gold's algorithm assumes that formula_27 and formula_28 contain a "characteristic set" of the regular language; otherwise, the constructed DFA will be inconsistent either with formula_27 or formula_28.


title: Deterministic finite automaton

text: Other notable DFA identification algorithms include the RPNI algorithm, the Blue-Fringe evidence-driven state-merging algorithm,


title: Deterministic finite automaton

text: Another research direction is the application of evolutionary algorithms: the smart state labeling evolutionary algorithm allowed to solve a modified DFA identification problem in which the training data (sets formula_27 and formula_28) is "noisy" in the sense that some words are attributed to wrong classes.


title: Deterministic finite automaton

text: Yet another step forward is due to application of SAT solvers by Marjin J. H. Heule and S. Verwer: the minimal DFA identification problem is reduced to deciding the satisfiability of a Boolean formula. The main idea is to build a augmented prefix-tree acceptor (a trie containing all input words with corresponding labels) based on the input sets and reduce the problem of finding a DFA with formula_39 states to "coloring" the tree vertices with formula_39 states in such a way that when vertices with one color are merged to one state, the generated automaton is deterministic and complies with formula_27 and formula_28.


title: Deterministic finite automaton

text: Though this approach allows finding the minimal DFA, it suffers from exponential blow-up of execution time when the size of input data increases.


title: Deterministic finite automaton

text: Therefore, Heule and Verwer's initial algorithm has later been augmented with making several steps of the EDSM algorithm prior to SAT solver execution: the DFASAT algorithm.


title: Deterministic finite automaton

text: Another way of reducing the search space has been proposed in by means of new symmetry breaking predicates based on the breadth-first search algorithm:


title: Deterministic finite automaton

text: the sought DFA's states are constrained to be numbered according to the BFS algorithm launched from the initial state. This approach reduces the search space by formula_43 by eliminating isomorphic automata.


title: Deterministic finite automaton

text: Read-only right-moving Turing machines are a particular type of Turing machine that only moves right; these


title: Deterministic finite automaton

text: The machine always accepts a regular language. There must exist at least one element of the set (a HALT state) for the language to be nonempty.


title: Russell Hitchcock

text: Russell Charles Hitchcock (born 15 June 1949) is an Australian musician and lead vocalist of the soft rock duo Air Supply.


title: Russell Hitchcock

text: Born in Melbourne, Hitchcock attended South Brunswick State School, and later studied at Princes Hill High School in Carlton North. In 1965, he left school to work as a salesman. At that time, he played the drums and was the lead vocalist in a band called "19th Generation". At the age of 20, Hitchcock obtained a job at a computer company where he continued work for three years, before being promoted and transferred to Sydney.


title: Russell Hitchcock

text: After meeting British musician Graham Russell in 1975 on the set of a production of "Jesus Christ Superstar", Air Supply was formed. The group went on to have many hit records from 1976 into the 1990s; among their biggest hits are "All Out of Love", "The One That You Love", "Lost in Love" and "Making Love Out of Nothing at All".


title: Russell Hitchcock

text: After the band took a break in 1987, Hitchcock released several solo singles followed by his self-titled solo debut album in 1988. In 1990, the single "Swear to Your Heart" was released, which is from the soundtrack of the film "Arachnophobia".


title: Russell Hitchcock

text: In 1991, Air Supply made a comeback with the album "The Earth Is ..." featuring the singles "Without You" and "Stronger Than the Night". In 1995, Hitchcock recorded a duet, "Is It You", with Rita Coolidge from her album "Behind the Memories".


title: Russell Hitchcock

text: Hitchcock lives in Atlanta. On September 3, 2021, Hitchcock tested positive with COVID-19, thus postponing two shows in Beverly Hills and Oak Grove, Kentucky.


title: The Caine Mutiny (film)

text: The Caine Mutiny is a 1954 American military trial film directed by Edward Dmytryk, produced by Stanley Kramer, and starring Humphrey Bogart, José Ferrer, Van Johnson, Robert Francis, and Fred MacMurray. It is based on Herman Wouk’s Pulitzer Prize-winning 1951 novel of the same name.


title: The Caine Mutiny (film)

text: Set in the Pacific theatre of World War II, the film depicts the events on board a fictitious U.S. Navy destroyer-minesweeper and the subsequent court-martial of its executive officer for mutiny.


title: The Caine Mutiny (film)

text: The film was well-received by critics and was the second highest-grossing film in the United States in 1954.


title: The Caine Mutiny (film)

text: During World War II, newly commissioned Ensign Willis Seward "Willie" Keith reports to the minesweeper USS "Caine," commanded by Lieutenant Commander William De Vriess, also meeting the executive officer (XO), Lieutenant Stephen Maryk, and the communications officer, Lieutenant Thomas Keefer. De Vriess, popular with the men but disliked by Keith, is relieved by Lieutenant Commander Queeg. Keith is freshly out of college and officer candidate school and is courting May Wynn, who is not approved by his mother. Maryk is a career officer and Keefer is an aspiring novelist.


title: The Caine Mutiny (film)

text: Queeg attempts to instill strict discipline on the "Caine's" lax crew, which makes him unpopular with the officers and men.


title: The Caine Mutiny (film)

text: After a day of gunnery target towing, Queeg orders a turn to head back to Pearl Harbor, but distracts himself by berating Keith and Keefer over a crewman's appearance. Ignoring the helmsman's repeated warnings, he allows the "Caine" to turn in a full circle and cut the towline, setting the target adrift. Queeg tries to cover up the incident.


title: The Caine Mutiny (film)

text: During a shore leave, May breaks off her relationship with Keith after she asks him to essentially choose between her and his mother, and he makes the wrong choice. Keith returns to the ship for its next assignment.


title: The Caine Mutiny (film)

text: Assigned to escort a group of landing craft during an invasion of a small Pacific island, Queeg abandons his mission before he reaches the designated departure point, and instead orders the dropping of a yellow dye marker, leaving the landing craft to fend for themselves. Queeg asks his officers for their support, but they remain silent and nickname him "Old Yellowstain", which implies cowardice.


title: The Caine Mutiny (film)

text: Keefer, believing Queeg to be paranoid, encourages Maryk to consider relieving Queeg on the basis of mental incapacity under Article 184 of Navy Regulations. Though Maryk angrily rejects that possibility, he does begin keeping a medical log documenting the captain's behavior.


title: The Caine Mutiny (film)

text: When strawberries go missing from the officers' mess, Queeg convenes an elaborate investigation to determine the culprit. The investigation involves searching the ship and stripping all crew members. Convinced of Queeg's instability, Maryk asks Keefer and Keith to go with him to see Admiral Halsey about the matter. Arriving aboard Halsey's flagship, Keefer backs down and they return to the ship.


title: The Caine Mutiny (film)

text: At the height of a typhoon, Maryk urges the captain to reverse course into the wind and take on ballast, but Queeg refuses. Maryk, supported by Keith, relieves Queeg of command under Article 184. The "Caine" returns to San Francisco, where Maryk and Keith face a court-martial for mutiny. Wounded Naval Aviator, Lieutenant Barney Greenwald, an attorney before entering the Navy, becomes Maryk's defense counsel.


title: The Caine Mutiny (film)

text: At the court-martial, Keefer claims he never observed any mental illness in Queeg and was "flabbergasted" when he was relieved. Under Greenwald's relentless cross-examination, Queeg exhibits odd behavior on the stand, and Maryk is acquitted.