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5303 Spectrum Drive, Suite G
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Main office phone:
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Licensing Specialist

IMPORTANT NOTICE!  The FBI has moved to an all-electronic criminal background check (CBC) application process and no longer accepts hard-copy fingerprint cards.  Because the Maryland Criminal Justice Information System (CJIS) follows FBI guidelines, the use of hard-copy CBC applications at the State level is also being phased out.  Instead, all CBC applicants are being encouraged to submit their applications electronically.  However, hard-copy applications are still being accepted by CJIS if electronic submission is not possible.  Click here for a list of State-approved private electronic fingerprinting services and State-operated electronic fingerprinting locations.  Child care programs that have their own State-certified electronic fingerprinting equipment and operators may continue to submit CBC applications.

Visit the Office of Child Care's online child care licensing inspection results site – www.CheckCCMD.org!  The site offers detailed compliance findings from child care licensing inspections conducted since January 2011.  The site may also be used to find licensed child care programs and providers, and to link to a wide variety of information about early care and education in Maryland.

The Family Child Care Provider Grant Program
The Family Child Care Provider Grant Program (FCCPGP) exists to help registered family child care providers offset some of the costs of opening their child care programs.  For information about the FCCPGP, click here.

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Maryland's Child Passenger Safety Law was changed effective October 1, 2012.  Under this change, every child under 8 years old must ride in an appropriate child restraint unless the child is 4 feet, 9 inches or taller.  Every child from 8 to 16 years old who is not secured in a child restraint must be secured in a vehicle seat belt.  If you would like to learn more about this law, or would like information on selecting or using child restraints, please call Maryland Kids in Safety Seats (Maryland KISS) at 410-767-6016 or log on to www.mdkiss.org.

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If you are a new applicant, we encourage you to view the applicable licensing regulations before you attend your orientation session. The complete text of Family Child Care (COMAR 13A.15.), Child Care Centers (COMAR 13A.16), and Child Care-Letters of Compliance (COMAR 13A.17) regulations can be downloaded in .pdf format by clicking Here.

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     Programmatic Support and Technical Assistance
  Student, Family, and School Support
Divisions > Special Education and Early Intervention > Policy and Accountability Branch
Policy and Accountability Branch

Functions and Responsibilities

The Policy and Accountability Branch assists local lead agencies, local school systems, and public agencies in the development, revision, and implementation of policies, procedures, and practices for the provision of early intervention services and special education and related services, as required under the Individuals with Disabilities Education Act (IDEA) and the Code of Maryland Regulations (COMAR). The Branch fulfills the role of federal liaison to the Office Of Special Education Programs (OSEP) for Part C and Part B of the IDEA.  It is the Branch’s responsibility to lead the Maryland Infants and Toddlers Program (MITP), to manage the Part C and Part B database systems, and to develop Statewide resource documents, guidelines, and technical assistance materials.  The Branch coordinates cross-divisional teams, the State Interagency Coordinating Council (SICC), the Special Education State Advisory Committee (SESAC),and other stakeholders to develop and submit federal Part C and Part B 618 data, and the Part C and the Part B State Performance Plan (SPP) and Annual Performance Report (APR) to the OSEP.  The Branch is charged with aligning Part C and Part B general supervision and oversight responsibilities by developing and implementing a data-informed, differentiated, birth through 21 monitoring system focused on results driven accountability.

Unofficial Working Draft of the Maryland Infants & Toddlers Program (MITP) Regulations

Contact Information
Donna R. Riley, Chief
Policy and Accountability Branch
Division of Special Education/Early Intervention Services
Maryland State Department of Education
200 West Baltimore Street
Baltimore, MD 21201
Phone:  410-767-0249
TTY/TDD:  410-333-6442
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Email:  driley@msde.state.md.us
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Programs > School Wellness Policy
School Wellness Policy

Making Wellness Work: A Guide to Implementing and Monitoring School Wellness Policies in Maryland

Wellness policies in Maryland have come a long way since the initial development prior to the 2006 – 2007 school year. Creating a school-wide culture of wellness for students and staff is crucial for the health of future generations. A Wellness Policy will benefit our children only when we are able to follow through with successful implementation, monitoring and evaluation activities. This guide was developed to support the efforts of school systems’ in Maryland to monitor and evaluate their Wellness Policy. Each of the four required components of Wellness Policies–physical activity or education, nutrition standards, nutrition education, and other school-based activities that promote student wellness–is addressed in the guide. The guide provides information on:

• Wellness Policy goals;
• implementation activities;
• steps to support implementation;
• expected outcomes aligned with activities; and
• monitoring opportunities.

In Focus
Making Wellness Work: A Guide to Implementing and Monitoring School Wellness Policies in Maryland
The Making Wellness Work Guide was developed by a team representing Maryland State Department of Education, school food and nutrition services, health education, and physical education from Maryland school systems. The guide was tested by school systems in Maryland and released at the April 2009 conference on wellness. For more information on Maryland’s School Wellness Policies, please contact the School and Community Nutrition Programs Branch at MSDE at 410-767-0216 or email Stewart Eidel at stewart.eidel@maryland.gov.

Contact Information
Stewart Eidel, Section Chief
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Maryland Department of Education
200 West Baltimore Street
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Phone:  410-767-0216
Email:  stewart.eidel@maryland.gov
 Making Wellness Work Guide
A Guide to Implementing and Monitoring School Wellness Policies in Maryland
 A Guide to School Level Implementation
A Guide for School-Level Implementation of Wellness Policies & Practices
 Maryland State Department of Education School Wellness Team Action Plan
Bullet MSDE Wellness Team Action Plan
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A Field Guide to Heaven

Chapter 0 – Prologue

This book is a field guide to Heaven. It provides directions on how to reach Heaven and gives description of some of the many beautiful things that Heaven is. The main purpose of this guide is to help people recognize Heaven and to be excited about the possibilities of endless life in it.

Most versions of Heaven are comprised of ideas and images from human history, literature and experience. Those versions fail to reveal the scope, the height, the depth of what  Heaven is.  A good place to start to understand Heaven is with the realization that we are already in Heaven, with an acceptance that most of us have a limited ability to recognize it. What we see instead is the world created by each of us, by all of us in our daily activity that we call history.

We are by our nature committed to the world as we know it. This reality reflects both our strength and our weakness as human beings. We have the power given to us by the loving God to create, to make real our world. We however lack the humility to accept that our world is only part of God’s creation. We are compelled by our own creation and vision of the world and stubbornly fail to look beyond it. God loves us for our creative activity and vision, and for our stubborness. Holding on to what we see and know is the essential power that defines us as partners with God. God calls us to share in the action of building the world. God also understands that it is hard for us to see outside our personal worlds. Much of God’s activity in human history has involved helping us to see beyond the world as we know it.

We often ask the question, “How do we get to Heaven?”

We don’t actually get to Heaven because we are already there. We are inside Heaven. It surrounds us, but we each have to mature to see and recognize it. We have to grow to understand how who we are, what we’ve done, and where we live fits into Heaven. Each of our worlds, created by us, our families, and  our communities, by history are destinations in Heaven. New places in Heaven are always being made and discovered. Being part of this creation is our inheritance from the loving God.

Heaven is basically in the direction of our moving to God or in the direction of God moving toward us. This field guide hopes to show us How to move in those directions and navigate the many wonderful paths that we can follow.

Keeping the Context

The basic context of this field guide is that the one God needs space to be in loving relationship with all of creation. This guide is not a treatise on the nature of the one God. People with many different ideas and images of God find their way to Heaven. In fact one of the big rooms of Heaven is like a large sitting room. If you look around the sitting room, you see many different images of the one God meeting and talking to many people. All the images represent a truth about God, but part of the fun of Heaven is that no ever totally knows God. Every moment, in Heaven reveals more about the true nature of God.

The path to Heaven is found by individuals loving God, themselves, and others. Even people, who are unclear about God, but love themselves and love others can find their way there. They will just be surprised like the rest of us to see God as God is.

My knowledge of God leads me to believe in the Trinity. For me, Heaven has to have space for the 3 Persons of God to be in loving relationship with each other. My experience shapes my understanding of Heaven, but this guide doesn’t demand that you see it my way.  To travel through Heaven, however, you have to accept that Heaven is always being created and has endless places and possibilities that allow the one God to be in loving relationship with all that has been created.

Heaven is eternal because the ways of God being in loving relationship are endless. One creation leads to another loving relationship to another creation and on and on throughout eternity. No end to the potential ways for God to be in love can ever be reached.


text:
Rotunda Murals

A Brief History

Marywood College was founded in 1915 and chartered under the laws of the state of Pennsylvania in 1917 as a Catholic College for the higher education of women. It was the first Catholic college for women in the state.

What would become the first college building was constructed between 1900 and 1902. The Congregation of the Sisters, Servants of the Immaculate Heart of Mary occupied it as the motherhouse of the community, though the foundations of their college work were laid in 1845 when the Sisterhood was formed.

In the early 20th century, the Sisters developed the actual foundation of Marywood College that has been the ideal of the institution ever since.

Artistic appreciation is not the least of the abundant fruits of Catholic training. Galleries and exhibits, paintings, etchings, sculpture, music, literature, all the fine arts are are in their true home at Marywood, for it is a well known fact that Catholic culture is a gracious fostering mother of art.

Many treasures were transferred from the motherhouse when the Liberal Arts building, the first of the college group, was opened. In the 1930s, work was finally completed on the most breathtaking addition to the campus during this period—the Rotunda interior—a task which had been deferred since 1924. Artist Gonippo Raggi was commissioned to paint the murals of the Rotunda. The ambitious effort artistically synthesized the religious and educational mission of the IHM Congregation and of Marywood.


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Social Media

Protected iPhone Survives 1,000-Foot Drop [VIDEO]

Accessory maker G-Form really enjoys torture testing iOS devices using its technology. Its most recent video is definitely a blast to watch as a protected iPhone survives a free-fall from more than 1,000 feet.

Base jumper Gary Connery, who was recently seen "posing" as the Queen while parachuting into the Opening Ceremonies of the London Olympic Games, traveled to Switzerland with a group of other jumpers to test G-Form's protective compression athletic gear.

The jumpers had iPhone's protected with the company's cases during the jumps to take video. On a whim, one of the testers decided to drop the iPhone from around 1,000 feet. And as you can see, the iPhone recorded the entire fall and painful impact on the ground.

And the iPhone survived completely undamaged. Connery was able to find the iPhone after the fall and make a quick video (even though someone should tell him about videos in portrait mode.)

This is far from the first stunt that G-Form has recorded to show off its technology. Earlier this summer, the company dropped iPads protected by its series of new cases, from 35 feet onto a Best Buy parking lot. Not surprisingly, the tablets were just fine.

But that doesn't hold a candle to a video made earlier this year that saw an iPad, protected by the company's Reactive Protective Technology, surviving a 100,000-foot fall from near space.

We recently reviewed G-Form's Extreme Grid case and was really impressed with the technology that provides, lightweight rugged protection.

This article originally published at AppAdvice here

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Social Media

Less Than 30 Percent of Companies Have Social Media-Focused Employees, Survey Says

Less than one-third of companies have employees dedicated solely to social-media tasks, according to a recent survey.

Conducted by Ragan Communications and NASDAQ OMX Corporate Solutions, it found that "organizations are cautious about dedicating resources to social media, and adding social media to the list of tasks traditionally assigned to communicators," a release said.

The survey, which polled more than 2,700 social-media professionals, revealed that 27% of companies have someone focusing exclusively on social. On the other hand, 65% of companies add social media on top of other duties.

For more on the results, check out the video above. Then, tell us in the comments: Does your company prioritize social media?

Image courtesy of Flickr, eldh

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Welcome to Financial Aid!

The Basics

“How will I pay for my education? Am I eligible for financial aid? Where do I begin?”  The Office of Financial Aid can answer your questions.

Application Process

"How do I apply?"  Dates and deadlines for financial aid as well as helpful tips on starting the financial aid process.

Scholarships and Grants

"What kind of scholarships do you offer?"  View a variety of federal, state and institutional aid offered at The Master's College.

"What if I need more money?"  You may qualify for government loans! (Parents click here)

Tuition and Fees

"How much will school cost?"  View a breakdown of expected costs for attendance at The Master's College.

"I have more questions, where should I go?"  You may find your answer here among our frequently asked questions.

Office Info

On Campus Location:
Rutherford Hall

Office Hours:
Mon-Fri 8:30-5:00

800.568.6248 x2290
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Our Philosophy:

It’s a well-known fact that education is one of the best investments you can make in life. That’s why The Master’s College is committed to providing a first-rate education in an academic environment unashamedly focused on the Christian faith. While the primary burden of providing an education is the responsibility of the student and parents, we are also determined – and able – to provide a substantial package of financial aid to the vast majority of our applicants. Please choose from the selections above for more information.

Disclosures and Notifications

Complaint Notice

TMC provides the following link in order to comply with federal regulations that require us to provide students and prospective students with contact information for filing complaints with state officials or agencies that would handle any student complaints:


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« Flexible batteries based on graphene paper | Main | The Microbes Come Through! »

March 03, 2011

elliptical reviews

No offense, but if there's a facebook like button, it'll be much easier for me to share.

Lynn Daven

How does changing the material affect the efficiency or energy capacity of the cell? It would be equally important to know if the quality is the same. I hope this technology will be developed further.

metal beads

Renewable energy should be encouraged to use. Big companies should provide more research and study to look for effective and convenience way to produce energy.

Solar Lights

Anything that can be done to reduce the cost of photovoltaic cells would be tremendously welcome by all.

The comments to this entry are closed.


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Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am having a problem with this question:

Coffee A costs $75$ cents per pound and coffee B costs $80$ cents per pound to form a mixture that costs $78$ cents per pound.IF there are $10$ pounds of Mixture how many pounds of Coffee A are used?

According to the text the answer is 4. I don't know how they came up with this answer since they haven't given the clue or percentage of the how much of each coffee is used in the mixture. Maybe I am missing something here. Any suggestions?

Here is what I could think of:

$\$0.75 + \$0.80 = 155$ so $75$ is $\left(\frac{7500}{155}\right)$% of $155$ cents

Now taking $\left(\frac{7500}{155}\right)$% of $78$ cents (Price of the mixture) we get $\frac{1170}{31}$ cents.

Now if $75$ cents is $1$ pound $\frac{1170}{31}$ would be $\frac{78}{155} pound.

So for ten pounds it would be $\frac{780}{155}$ which is still not the answer.

share|improve this question
Others will tell you how to do it, but first let's just check that the answer in the text is right: 10 pounds of mixture, of which 4 pounds is A, means 6 pounds are B. 4 pounds at 75 cents per, plus 6 pounds at 80 cents per, is $4\times75+6\times80=300+480=780$ cents, or \$7.80, for 10 pounds, so 78 cents per pound. –  Gerry Myerson Jun 15 '12 at 1:53

5 Answers 5

up vote 3 down vote accepted

I would model it with a system of equations which are relatively simple to solve.

$$A + B = 10$$ $$75A + 80B = 78 \cdot 10 \implies 75A + 80B= 780$$

Multiply the top equation through by $80$ to get

$$80A + 80B = 800$$

We also have $$ 75A + 80B= 780$$

Simply subtract them to get

$$5A = 20 \implies A = 4 $$

If you need to me to add some details on how I set up the original two equations, let me know and I will gladly add in some details.

share|improve this answer
Thanks that did the trick. I was way off. –  Rajeshwar Jun 15 '12 at 1:57
No problem. If you need any clarification, let me know. –  Joe Jun 15 '12 at 1:57

Instead of trying to solve these in an ad hoc way, try to look at these problems as systems of equations. For example, let $a$ be the pounds of coffee A in the mix and $b$ be the pounds of coffee B. Then, we can write two equations that describe the problem:

$$.75a +.8b = .78*10=7.8$$ $$a + b=10$$

Can you take the problem forward from there?

share|improve this answer

Hint $\rm\ 20\,(7.8 = 0.75 a + 0.8 b)\:\Rightarrow\: 156 = 15\,(a\!+\!b)\!+\!b = 150 + b\:\Rightarrow\: b = 6\:\Rightarrow\: a=4.$

share|improve this answer
Nice one-liner, yet again. Never cease to amaze me with your succinctness Bill. –  Joe Jun 15 '12 at 4:44

Since there are ten lbs of coffee, $A + B = 10$. Notice that both sides are unitted in pounds.

Next $$.75A + .80 B = 7.80.$$ This is unitted in dollars. Now solve these two equations. We get $B = 6, A = 4$.

share|improve this answer
A great short "To the point" answer ! –  Rajeshwar Jun 15 '12 at 1:57

With these problems, there is a shortcut we can use that solves it faster.

Notice that $78$ is $3/5$ the way from $75$ (Coffee A) to $80$ (Coffee B). Therefore, the ratio of Coffee B to total coffee will be $3/5$.

So, since there are $10$ pounds of coffee total, there are $6$ pounds of Coffee B and $4$ pounds of Coffee A.

share|improve this answer
Nice clear solution, with the intuition in control all the way. –  André Nicolas Jun 15 '12 at 23:13

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Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I came across an interesting identity involving binomial coefficients. I'm not sure if I'm looking at the identity the wrong way but I am not aware if this identity is known and if there is an (easy) proof for it.

Take a nonnegative integer $n$ and form two $k$-tuples consisting of integers at most $n$, say, $(a_1,a_2,\ldots,a_k)$ and $(b_1,b_2,\ldots,b_k)$ such that $a_i\geq a_{i+1}$ and $b_i\geq b_{i+1}$. Let $a_0=b_0=n$ and $a_{k+1}=b_{k+1}=0$. Let $j\in\mathbb N$. The sum goes as follows:

$$\sum_{x_1+x_2+\cdots+x_{k+1}=j} ~~\sum_{m=1}^{k+1} \binom{a_{m-1}-a_m+x_m}{a_{m-1}-a_m} = \sum_{x_1+x_2+\cdots+x_{k+1}=j} ~~\sum_{m=1}^{k+1} \binom{b_{m-1}-b_m+x_m}{b_{m-1}-b_m}.$$

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Is it okay to post this on MO? –  Ken Gonzales Jul 17 '12 at 3:22
I think it is ok, but it would be nice to give a link to your MO post also here. –  Martin Sleziak Sep 2 '12 at 19:16

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What is the definition of a Burau matrix of a braid? Where can I find a definition?

share|improve this question

2 Answers 2

I personally like Birman's exposition in her book Braids, Links and Mapping Class Groups which gives a very topological introduction to the subject.

I also know that Daan Krammer gives a rather nice algebraic approach in a set of online lecture notes. He also has a list of exercises associated to the notes.

share|improve this answer

The other answer seems to be correct, but in the interest of providing a non-link-only answer, I'll give the definition here.

The Burau matrix of a braid is the matrix representing the braid in the Burau representation, so it's a matrix over $\mathbb Z [t, t^{-1}]$, i.e. the entries of the matrix are Laurent polynomials in the variable $t$ with integer coefficients. The Burau representation is a representation (i.e. group homomorphism) $\psi_n: B_n \rightarrow \operatorname{GL}_n(\mathbb Z [t, t^{-1}])$. As with any group homomorphism, it's sufficient to define it on a generating set and check that the resulting map is well-defined.

We define in block form as $$\psi_n : \sigma_i \mapsto \left( \begin{array}{ccc} I_{i-1} & 0 & 0 & 0 \\ 0 & 1-t & t & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & I_{n-i-1} \end{array} \right) ,$$ where $I_m$ is the $m \times m$ identity matrix, and $i$ ranges from $1$ to $n-1$. For this to be a valid homomorphism, we need to check that these matrices are invetible and that the braid relations are preserved, i.e. that $\psi_n(\sigma_i) \psi_n(\sigma_j) = \psi_n(\sigma_j) \psi_n(\sigma_i)$ for $|i-j| \ge 2$, and that $\psi_n(\sigma_i) \psi_n(\sigma_{i+1}) \psi_n(\sigma_i) = \psi_n(\sigma_{i+1}) \psi_n(\sigma_i) \psi_n(\sigma_{i+1})$ for $i=1, \ldots, n-2$. I'll exhibit the inverse matrix here, but leave it up to you to check that the computations work out. $$\psi_n(\sigma_i)^{-1} = \left( \begin{array}{ccc} I_{i-1} & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & t^{-1} & 1-t^{-1} & 0 \\ 0 & 0 & 0 & I_{n-i-1} \end{array} \right)$$

With that out of the way, for any braid $\gamma$, to compute its Burau matrix, just write $\gamma = \sigma_{i_1}^{e_1} \cdots \sigma_{i_m}^{e_m}$ as a word in the generators, and then you have $\psi_n(\gamma) = \psi_n (\sigma_{i_1})^{e_1} \cdots \psi_n (\sigma_{i_m})^{e_m}$, which is now easy to compute.

For some intuition, the case $t=1$ is good to look at. Setting $t=1$, we get a permutation matrix. This is the permutation matrix corresponding to the underlying permutation of the braid, i.e. the composite homomorphism $B_n \rightarrow S_n \rightarrow \operatorname{GL}_n(\mathbb Z)$ where $S_n$ is the symmetric group on $n$ letters. The Burau representation is thus 1-parameter deformation of the permutation representation.

The above is, of course, only one of several conventions, but it's the one I usually see chosen in the literature when one needs to do these calculations explicitly.

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This is a great basic overview of the Burau representation. Hopefully the OP sees this answer. –  Dan Rust Jul 22 '13 at 15:37

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I'm reading Robert Gilmore's "Lie Groups, Physics, and Geometry," and trying to understand his brief presentation of Galois theory. I think I get the gist of the method, but would be grateful for help understanding some details. Let me first quote a bit from page 10, highlighting the terminology I don't understand, and after the quotes, I will focus on specifics. Please bear with me while I try to clarify my questions:

The general quadratic equation has the form $$(z-r_1)(z-r_2)=z^2-I_1 z+I_2=0$$ $$\begin{equation}\tag{1.17}I_1=r_1 + r_2\end{equation}$$ $$I_2=r_1 r_2$$ The Galois group is $S_2$ with subgroup chain shown in Fig. 1.3. [elided]

The character table for the commutative group $S_2$ is $$\begin{equation}\tag{1.18}\begin{array}{r|crc} \text{Irreducible Rep's} & I & (12) & \text{Basis Functions} \\ \hline \Gamma^1 & 1 & 1 & u_1 = r_1 + r_2 \\ \Gamma^2 & 1 & -1 & u_2 = r_1 - r_2 \end{array}\end{equation}$$

Linear combinations of the roots that transform under the one-dimensional irreducible representations $\Gamma^1, \Gamma^2$ are $$\begin{equation}\tag{1.19}\begin{bmatrix} u_1 \\ u_2 \end{bmatrix}=\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}\begin{bmatrix} r_1 \\ r_2 \end{bmatrix}=\begin{bmatrix} r_1+r_2 \\ r_1-r_2 \end{bmatrix}\end{equation}$$

The equations (1.17) and (1.19) are trivial to understand. What's bugging me is (1.18) and how the group representations fit into the scheme. Please bear with me while I clarify my questions.

I understand that $\Gamma^1$ and $\Gamma^2$ are one-dimensional (scalar) representations of the group $S_2 = \{I, (12)\}$. That means that the group elements of $S_2$ map to the elements of $\Gamma^1$ in such a way that (group-theoretic) products of elements in $S_2$ map to (matrix) products of the corresponding elements in $\Gamma^1$; ditto $\Gamma^2$.

I see that we want to apply the elements of $S_2$ to the sequence of roots $(r_1, r_2)$, permuting them, and then examine the corresponding actions on the linear combinations $r_1+r_2$ and $r_1-r_2$.

Now arises the first question: how did we find these linear combinations? It looks like magic that the $\Gamma$'s, castrated one-dimensional group representations that they are, just copied into a square matrix and applied to a column vector of the roots, deliver up exactly the linear combinations that we need to investigate, the ones that will generate solutions to the quadratic equation. This gets even more spooky as we graduate up the line to the cubic and quartic, where the character tables feed us, similarly, exactly the linear combinations we need to solve the general equations. Of course, when we get to quintics, the game is over, and that's the whole point of (at least this elementary corner of) Galois theory.

My confusion deepens. Gilmore writes, on page 9, that these linear combinations are "basis functions" for the irreducible representations, the $\Gamma$s. I usually conceptualize archetypes for "basis functions" as sine waves for Fourier transforms, or Dirac deltas, or other orthonormal polynmomials, and such. I'm scratching my head wondering what on Earth Gilmore could mean. The irreducible representations are elements of a vector spaces, to be sure, and there should be various bases for these vector spaces, to be sure. But how are the linear combinations basis functions for the $\Gamma$? Functions of what, to what? What's the domain (the set of roots, $\{r_1, r_2\}$?)? What's the range? The linear combinations of roots don't map to the set of roots, and I can't see the sense in which they might be bases for the vector space in which the one-dimensional irreducible representations $\Gamma^1$ and $\Gamma^2$ live.

I now sink completely when Gilmore says that the "linear combinations of roots transform under the one-dimensional irreducible representations...". Transform? To what? "Transform" is a transitive verb, and it needs a subject and an object, doesn't it? These one-dimensional irreducible representations are just scalar numbers, so using them to transform a linear combination of roots can only be to multiply the linear combinations by the scalars? Or did we magically back out from the representations to the group, $S_2$, where I can understand how to apply the group elements, $I$ and $(12)$, to the sequence of roots, permuting them.

I can see the machinery at work, it's not difficult at all, but I can't connect what Gilmore writes with what I think I know. I am sure he uses abbreviated terminology, to save space, but I am not connecting.

I apologize in advance if I haven't clarified my questions sufficiently or if it's too long, but I hoped that someone out there with mastery of the subject might clear the fog for me.

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A brief Google search suggests to me that the author is using chemists' terminology for representation theory. The so-called basis functions appear to be the character functions for each representation. These form the basis of an auxiliary vector space (called the space of class functions). But it's still a mystery to me what exactly the author means for things to transform under a representation... –  Zhen Lin Aug 7 '11 at 9:57
Also, the relevant part of the book is available online here from the author's website. –  Zhen Lin Aug 7 '11 at 9:58
If you actually want to learn this material, I recommend getting a good thorough book on the representation theory of finite groups (e.g. James-Liebeck) before tackling the Lie theory. –  Qiaochu Yuan Aug 7 '11 at 16:05
thanks. Just ordered James-Liebeck (the only one on amazon with 5 stars under a search for "representation theory of finite groups" -- though Fulton-Harry gets four and a half). –  Reb.Cabin Aug 7 '11 at 20:37

4 Answers 4

up vote 3 down vote accepted

Let's first consider the general case of an $n$th-degree polynomial. The elements $\sigma \in S_n$ act by permutation on the roots $z_1,\dots,z_n$ by $z_i \mapsto z_{\sigma(i)}$. This same action also acts on functions of the roots: $$(\sigma f)(z_1,\dots,z_n)=f(z_{\sigma(1)},\dots,z_{\sigma(n)})$$ Here it's best to think of the roots $z_i$ as indeterminates. For example, the symmetric functions $I_k$ (e.g. $I_1=z_1+\dots+z_n)$ are invariant under the $S_n$ action.

Now we also have one-dimensional representations $\Gamma$ (a.k.a. characters) of the group $S_n$, which are just group homomorphisms from $S_n$ to $\mathbb C^\times$. Let's consider functions $f$ on the roots such that $$\sigma f =\Gamma(\sigma)f$$ for all $\sigma \in S_n$. This is what Gilmore means by functions that "transform under the one-dimensional representation." Here $f$ will actually be a linear combination of roots.

For example, if $n=2$, and we have $\Gamma^2:S_2 \rightarrow \mathbb C$, defined by $I \mapsto 1$, $(12) \mapsto -1$. If $f(r_1,r_2)=r_1-r_2$, then $$If=f=\Gamma(I)f$$ $$(12)f=-f=\Gamma((12))f$$ since: $$(12)f(r_1,r_2)=f(r_2,r_1)=r_2-r_1=-f(r_1,r_2)$$

I hope this clarifies at least what he means by "functions that transform under the representation." Anyway, it seems interesting to approach Galois theory from the point of view of representation theory, so I wonder if anyone is aware of a clearer treatment in the same vein.

Another resource for Lie and representation theory you might want to look at are Brian Hall's notes http://arxiv.org/abs/math-ph/0005032.

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Thanks. Very helpful! I will read Brian Hall's notes. –  Reb.Cabin Aug 7 '11 at 16:50

There is a lot of background here, and again, the best way to learn it is to find a good textbook on the representation theory of finite groups. But here's a brief sketch.

Any finite group $G$ has a finite list of irreducible representations. Maschke's theorem guarantees that any (say, complex, finite-dimensional) representation decomposes into a direct sum of irreducible representations. More concretely, this says that given any representation, we can simultaneously block-diagonalize all of the elements of $G$ so that the blocks correspond to irreducible representations.

$S_2$ has a $2$-dimensional representation $V$ given by its action as permutation matrices. This representation decomposes into a direct sum $V_0 \oplus V_1$ of the trivial representation and the nontrivial (sign) representation. We can say that the elements of $V_0$ transform under the trivial representation, and the elements of $V_1$ transform under the sign representation. (This seems to be physics / chemistry terminology. In mathematics we would just say that $V_0$ is, or perhaps is isomorphic to, the trivial representation, and so forth.)

Okay, so how do we find this decomposition? Write $V = \text{span}(a, b)$ where the nontrivial element $g$ of $S_2$ exchanges $a$ and $b$. Then $g$ fixes the vector $a + b$, so $a + b$ spans the trivial subrepresentation. Next, we want to find a vector that $g$ multiplies by $-1$, and such a vector is given by $a - b$. So $V$ decomposes into a direct sum $\text{span}(a + b) \oplus \text{span}(a - b)$ where $S_2$ acts by the trivial representation on the first summand and by the sign representation on the second summand.

There is a more general projection formula here, but to learn what it is, again, you really should find a good textbook on the representation theory of finite groups.

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Thank you. That explains how we find the linear combinations given the one-dimensional representations. –  Reb.Cabin Aug 7 '11 at 16:50

The key idea of solution by radicals is intimately tied up with representation theory, although it wasn't originally seen in that light. Suppose that we have an extension $K$ of a field $F$ with $[K:F] = n$, and that $K$ is the splitting field of some irreducible polynomial $p(x) \in F[x]$ (with no repeated root). Suppose also (for convenience) that $K$ contains a primitive $n$-th root of unity $\omega$, and that $G$, the Galois group of $K$ over $F$ is known to be cyclic, generated by $\alpha$, say. Let $r_0$ be one root of $p(x)$. Since $|G| = [K:F],$ the roots of $p(x)$ are the elements of $\{\alpha^{j}(r_0):0 \leq j \leq n-1 \}$. We let $r_j = \alpha^j(r_0 )$ for $0 \leq j \leq n-1$. Again for convenience, we suppose that these roots are linearly independent over $F$. What happens in Galois theory is that we can replace $r_0$ with an element $s_0 \in K$ such that $\alpha^j(s_0) = \omega^j s_0$ for each $j$. Then $s_0$ has minimum polynomial $x^n - s_0^n$ over $F$. In other words, $K$ is shown to be the radical extension $F[s_0]$ of $F$. The quadratic case of the question is an easy example of this. What has this to do with representation theory?

The roots of $p(x)$ form an $F$-basis for $K$, so every element of $K$ may be expressed in the form $\sum_{j=0}^{n-1} f_{j}\alpha^{j}(r_0),$ where each $f_j \in F$. The element $r_0$ is almost irrelevant here: it is the linear combination $\sum_{j=0}^{n-1} f_j \alpha^{j}$ which is important, and we can think of the element of $K$ as obtained by applying this linear combination of automorphisms to $r_0$. I suppose this is why the writer of the book talked of "transforming" the roots.

The important object now is the group algebra $F\langle \alpha \rangle$, which consists of all $F$-linear combinations of $\{\alpha^j : 0 \leq j \leq n-1 \}.$ This is isomorphic as an $F$-vector space to $K$, but it has additional structure. The group algebra inherits an obvious multiplication from $\langle \alpha \rangle$, extending it by $F$-linearity. Now comes the representation theory, which is relatively straightforward in the case of cyclic groups. Our assumptions guarantee that the integer $n$ is invertible in $F$ (that is, the characteristic of $F$ is either $0$ or coprime to $n$). There are $n$ different group homomorphisms from $\langle \alpha \rangle$ to $F$, say $\{ \lambda_i: 0 \leq i \leq n-1 \}$, each uniquely specified by $\lambda_i(\alpha) = \alpha^{i}$. These may be extended by $F$-linearity to $F$-algebra homomorphisms (that is, ring homomorphisms which are also $F$-linear) from $F \langle \alpha \rangle$ to $F$.

The key idea is to find a new basis $\{e_{i}: 0 \leq i \leq n-1 \}$ for $F\langle \alpha \rangle$ such that $\lambda_{j}(e_i) = \delta_{ij}$. If we can do this, we must have $\alpha^{j} = \sum_{i=0}^{n-1} \omega^{j} e_i,$ because the right hand combination is the unique $F$-combination of $e_i$'s which has the correct evaluation under each $\lambda_j$. In this particular case, and in most treatments of Galois theory in texts, this can be done by inverting a Van der Monde matrix. But it can also be done by orthogonality relations for group characters (for which, as Qiaochu suggests, you really need to consult a representation theory text).

The upshot is that we may set $e_i = \frac{1}{n} \sum_{j=0}^{n-1} \lambda_{i}(\alpha^{-j}) \alpha^{j}$ for each $i$. It is an instructive exercise with roots of unity to confirm that $\lambda_{k}(e_i) = \delta_{ik}$, but note that the case $i = k$ is clear. By the way, this "orthogonality" property forces the $e_{i}$ to be linearly independent, hence a basis for $F\langle \alpha \rangle$. Notice that $\lambda_j(\alpha.e_i) = \lambda_j(\alpha ) \delta_{ij},$ so that (by comparison of the evaluations of each $\lambda_j$), we have $\alpha.e_i = \lambda_i(\alpha)e_i = \omega^i.e_i$ for each $i$.

Now the pieces are in place to complete the Galois theory: we set $s_0 = e_1(r_0).$ This makes sense, because $e_1$ is an $F$-linear combination of field automorphisms (of $K$), so may be applied to $r_0$ to produce a new element of $K$. Notice that $\alpha(s_0) = (\alpha.e_1)(r_0) = \omega.e_1(r_0) = \omega.s_0 .$ Hence $\alpha^j(s_0) = \omega^{j}.s_0$ for $0 \leq j \leq n-1$, which was what we wanted. (We should note that $e_1(r_0) \neq 0$, since $ne_1(r_0) = \sum_{j=0}^{n-1}\omega^{-j} r_j$ (as each $r_j = \alpha^j(r_0)),$ while $\{r_0,\ldots ,r_{n-1} \}$ is linearly independent over $F$).

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Excellent road map! Thank you. –  Reb.Cabin Aug 8 '11 at 13:46

Because the many different types of applications of repn theory are themselves important, and the comparisons among them shed light on aspects otherwise possibly overlooked... perhaps another "answer" here won't hurt: I think there is yet-another reasonable segue from more primitive notions to "repn theory"...

(Also, it is not clear to me that anyone needs to read a whole book about repns of finite groups in characteristic $0$, especially over $\mathbb C$. Many of these suffer from "completeness", so that critical ideas are swamped by compulsion to include all-possible...)

When we have a finite group $G$ with $n$ elements acting linearly on a vectorspace $V$ over a field $k$ of characteristic $0$ (so we can divide by positive integers such as $n$), it is easy to form $G$-invariant elements, by averaging: given $v\in V$, the element $\frac{1}{n}\sum_{g\in G} g\cdot v$ is easily checked to be invariant, by changing variables in the sum. Further, if $v$ was already $G$-invariant, this map just returns $v$. That is, this averaging is some kind of projector to the "trivial $G$-isotype" in $G$, that is, things un-moved by $G$. This is where expressions like $r_1+r_2$ come from. The application to Galois theory has the vector space $V$ be the larger field.

Slightly more generally, let $\chi:G\rightarrow k^\times$ be a group hom (maybe to ${\pm 1}\subset k^\times$). To say that a vector "transforms by/under/whatever-verb" is that $g\cdot v=\chi(g)v$. In the previous paragraph, $\chi=1$. It is a small step from the pure averaging as in the previous paragraph to try $\hbox{proj}_\chi v=(?) \frac{1}{n}\sum_{g\in G} \chi(g)\,g\cdot v$. In fact, the obvious change-of-variables argument shows that this weighted average transforms by $\chi^{-1}$, so, in fact, and inverse has to be inserted somewhere, for example, $\hbox{proj}_\chi v=\frac{1}{n}\sum_{g\in G} \chi^{-1}(g)\,g\cdot v$.

As far as Galois theory goes, to solve equations in radicals following Lagrange and Vandermonde (when possible), the previous paragraph explains why we'd want to adjoin sufficiently many roots of unity to the ground field, and how to form expressions varying by prescribed characters $\chi$ of the group. The expressions are Lagrange resolvents.

An interesting complication occurse for non-abelian groups $G$, that in an action of $G$ on $V$, there are typically more vectors than those that transform by a one-dimensional repn $\chi$ as above. Namely, $V$ may break up into "irreducible" pieces some of which are larger than one-dimensional. In this case, it requires more set-up to explain what "transforms by" could mean, as well as to write down the corresponding "projector". (There still is a projector, namely, averaging against the function $\Theta_\pi(g)=\hbox{trace}(\pi(g))$ where $\pi:G\rightarrow GL_n(k)$...)

The "traditional" treatment of Galois theory occurs much prior to the traditional treatment of repn theory, and the traditional treatments of both ignore each other... for no mathematical reason... so there aren't so many available references.

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Thank you, Paul. Excellent info and more grist for the mill! –  Reb.Cabin Aug 11 '11 at 3:20

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I want to check an element if it's in a circle in my browser. I know the circle formula from my high school:

enter image description here

But I'm not sure if it's same in browser XY system too. Because browsers zero coordinate is on left top of the page and from there to right is positive x axis and to bottom is positive y axis.

Browser XY

For example in this picture point c have positive x and y. Please optimize the circle formula for this system and also give me the correct formula for a circle centered in c = (200,200) with 150 radius.

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2 Answers 2

up vote 4 down vote accepted

For any affine change of variables $x \to a_1 x + a_2 y + a_3$ and $y \to b_1 x + b_2 y + b_3$ the equation of the circle $(x-x_0)^2 + (y-y_0)^2 = r^2$ translates into $$ ( a_1 x + a_2 y + a_3 - x_0)^2 + (b_1 x + b_2 y +b_3 - y_0)^2 = r^2 $$ Expanding $$ \begin{eqnarray} & & x^2 ( a_1^2 + b_1^2) + y^2 (a_2^2 + b_2^2) + 2 x y ( a_1 a_2 + b_1 b_2) \\ && + 2 x ( a_1 (a_3 - x_0) + b_1 (b_3-y_0) ) + 2 y ( a_2 (a_3 - x_0) + b_2 (b_3-y_0) ) \\ && + (a_3-x_0)^2 + (b_3 - y_0)^2 = r^2 \end{eqnarray} $$ Now, choosing $a_1$, $a_2$ and $b_1$ and $b_2$ so that $$ a_1^2 + b_1^2 = a_2^2 + b_2^2 = 1 \qquad a_1 a_2 + b_1 b_2 = 0 $$ and completing squares will again arrive at $(x-\hat{x}_0)^2 + (y-\hat{y}_0)^2 = \hat{r}^2$.

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Even with the $y$-coordinate flipped, the equation for your circle is still $$ (x-200)^2+(y-200)^2=150^2\tag{1} $$ In the normal coordinates, this would be the circle of radius $150$ and center $(200,-200)$ so the equation with flipped $y$-coordinate would be $$ (x-200)^2+(-y-(-200))^2=150^2\tag{2} $$ Equation $(2)$ is the same as equation $(1)$ since $(-1)^2=1$.

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Why -y in second statement? –  Mohsen Sep 21 '11 at 0:59
@Mohsen: He's demonstrating that changing the signs of $y$-coordinates has no effect here. –  Guess who it is. Sep 21 '11 at 3:24

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If you have $a,b\in\mathbb{N}$ such that $a^2+b^2=M$, are there other natural numbers $c,d$ such that $c^2+d^2=M$? If so, is there an algorithm for generating such pairs or an equation relating them to $a$ and $b$? I tried messing around with a few ideas using $\mathbb{Z[i]}$, but didn't really get anywhere.

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Yes - let $a=c,b=d$! :-) –  user122283 Apr 1 '14 at 23:19
If $M > 2$ is prime then $a$ and $b$ are unique. See this theorem of Fermat's and Thue's lemma. –  Antonio Vargas Apr 1 '14 at 23:27

3 Answers 3

up vote 2 down vote accepted

Let us consider the equation $$a^2+b^2=c^2+d^2\\ \implies a^2-c^2=d^2-b^2$$ See page 13 of here for a geometric interpretation.

Let $A+Bi=u,C+Di=v\in\mathbb{C}$. Then, you can show that $|u\overline{v}|=|uv|$. Square both sides and compute the norms to get $$(AC+BD)^2+(BC-AD)^2=(AC-BD)^2+(AD+BC)^2$$ Showing that for arbitrary $A,B,C,D$ we must have a bijection between the sets $$\{a,b,c,d\}\text{ and }\{AC+BD,BC-AD,AC-BD,AD+BC\}$$ Alternatively, you could factor $M$ as a product of Gaussian primes, allowing us to easily produce all representations of $M$ as a sum of two squares. Yet another way is to use Bramhagupta's identity ($(a^2+b^2)(c^2+d^2)=(ac+bd)^2+(ac-bd)^2$) repeatedly.

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The others have nicely answered your question. But there is something else worth saying. According to a theorem of Jacobi, the number of solutions to $x^2+y^2=M$ in integers is equal to eight times the number of odd divisors of $M$ which are $1$ mod $4$ minus eight times the number of odd divisors of $M$ which are $3$ mod $4$. One recovers as a particular case Fermat's theorem on sums of two squares.

This theorem follows from the fact that the Dedekind zeta function of $\mathbf Q[i]$ equals $\zeta(s)L(\chi,s)$, where $\chi$ is the primitive quadratic character of conductor $4$.

(The reason for the factor $8$ is that solutions generally occur in "octopules": $(x,y),(y,x),(-x,y),(x,-y),...$).

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There are definitely $a,b,c,d\in\mathbb{N}$ so $a^2+b^2=c^2+d^2=M$. Consider $2,9,6,$ and $7$. $2^2+9^2=85=6^2+7^2 $. You can easily find these by looking for integer solutions for the level set $a^2+(a+x)^2-(c^2+(c+y)^2)=0$ where $x,y\in\mathbb{N}, x\neq y$. Then your $a,b$ and $c,d$ are $a,a+x$, and $c, c+y$

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As a kind of aside to this question, where one of the answers assumed that if $S^n=X \times Y$ then we can assume that $X$ and $Y$ are manifolds.

If we have a manifold $M$, such that $M$ is homeomorphic to $X \times Y$, then must $X$ and $Y$ be manifolds? The converse ($X,Y$ manifolds implies $X \times Y$ is a manifold) is certainly true. I'd like to think it is true, but I have seen enough strange topological behaviour to suggest this may not be true.

For this question take 'manifold' to mean a second countable Hausdorff space that is locally homeomorphic to $\mathbb{R}^n$, for some finite $n$.

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+1 for questioning your intuition! –  Grumpy Parsnip Nov 2 '11 at 18:41
Thanks for following up on this! My intuition told me it was false, but maybe I'm just a cynic when it comes to spaces that aren't at least CW complexes. Or does that make me an optimist? I guess it all depends on your perspective :o) –  Aaron Mazel-Gee Nov 4 '11 at 5:59
Juan, @Aaron: In case you missed it: there's a new related thread on MO. –  t.b. Dec 17 '11 at 3:13

1 Answer 1

up vote 25 down vote accepted

Disclaimer: I'm by no means knowledgeable in this field and I haven't read the papers or books I mention below. I found these by digging in the literature and hope these pointers are useful.

The answer to your question is no.

  1. The first example was given by R.H. Bing, The Cartesian Product of a Certain Nonmanifold and a Line is $E^4$, Ann. of Math. (2) 70 (1959) 399–412. MR107228.

    Bing describes a topological space $B$ — in fact a quotient space of $\mathbb{R}^3$, sometimes called the Dogbone space — which is not a manifold and has the property that $B \times \mathbb{R}$ is homeomorphic to $\mathbb{R}^4$.

  2. Modifying this construction and relying heavily on work of Andrews and Curtis, K.W. Kwun, Product of Euclidean Spaces Modulo an Arc, Ann. of Math. (2) 79 (1964) 104–108, MR159312, produced product decompositions of $\mathbb{R}^n \cong X \times Y$ for $n \geq 6$ where neither $X$ nor $Y$ is a manifold.

  3. Here are two freely available papers by A.J. Boals:

  4. Quoting C.D. Bass, Some products of topological spaces wich are manifolds, Proc. Amer. Math. Soc. 81 (1981), 641–646, MR601746, Corollary 3 on page 645 “gives abundant examples of factorizations of certain manifolds into nonmanifold factors.”

  5. A textbook covering these and many more topics:

    Daverman, Robert J., Decompositions of manifolds, Pure and Applied Mathematics, 124, Academic Press, 1986, MR872468. (Reprinted by the AMS, 2007).

Here are two related MO-threads:

Added: A further MO-thread was posted and answered a couple of hours ago:

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Thanks Theo! Nice detective work...I thought about searching through all of Bing's paper's. I had a feeling if it was not true he would have provided a counter example –  Juan S Nov 2 '11 at 21:44
@Juan (Qwirk): you're welcome. I wanted to look up this stuff for quite a while, so now I had the opportunity... Interesting stuff, but the details seem somewhat messy. –  t.b. Nov 2 '11 at 22:10
Great answer t.b.! You write "I'm by no means knowledgeable in this field" What would it be if you were:-) –  Georges Elencwajg Nov 2 '11 at 23:22
Dear @Georges: Thank you, but yes, I meant it. I know little about geometric topology and the question at hand. I knew the Dogbone space and the two MO-questions, but not more. –  t.b. Nov 2 '11 at 23:24

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Re: Position Announcement: Univ. of Alabama
Posted: Aug 18, 2012 12:37 PM
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Haim posted Aug 18, 2012 5:29 PM:
> http://www.nytimes.com/2012/08/18/world/asia/panic-rad
> iates-from-indian-state-of-assam.html?_r=1&hp
> August 17, 2012
> Panic Seizes India as a Region?s Strife Radiates

<The rest of Haim's post, quoting the Yardley article, follows for reference below my comments, for ready reference>

Yes, it has indeed been a harrowing 10-15 days or so for a vast number of people from NE India living in various other regions India.

Thousands have fled from various locations in India back to the north-east from whence they hailed, even from Bangalore (and surrounding regions), earlier more or less immune to such 'ethnic strife'.

Certainly a gross failure in governance. It also certainly will shake the faith of many of us in the 'meaning of India' as we've had it all along.

Certainly we need to learn to handle much better how we live with each other in a hugely diverse country as India. We shall have to.

Because the 'mono-culturalism' that Haim is apparently recommending (or even yearning for) can never be again - in India. Or, in the USA (or, for that matter, practically anywhere else in the world). That part of human history is over - forever.

We had better learn to live peaceably with other cultures - or we just do not have a world any more.

(Meanwhile, we do see here that most leaders of most communities are indeed trying to bring peace and build bridges between the communities.

I for one do sincerely believe that we will succeed.

But yes, it is a terrible time that we are now suffering.

> BRAJAKHAL, India ? Like a fever, fear has spread
> across India this week, from big cities like
> Bangalore to smaller places like Mysore, a contagion
> fueling a message: Run. Head home. Flee. And that is
> what thousands of migrants from the country?s distant
> northeastern states are doing, jamming into train
> stations in an exodus challenging the Indian ideals
> of tolerance and diversity.
> What began as an isolated communal conflict here in
> the remote state of Assam, a vicious if obscure fight
> over land and power between Muslims and the
> indigenous Bodo tribe, has unexpectedly set off
> widespread panic among northeastern migrants who had
> moved to more prosperous cities for a piece of
> India?s rising affluence.
> A swirl of unfounded rumors, spread by text messages
> and social media, had warned of attacks by Muslims
> against northeastern migrants, prompting the panic
> and the exodus. Indian leaders, deeply alarmed, have
> pleaded for calm, and Prime Minister Manmohan Singh
> appeared in Parliament on Friday to denounce the
> rumor mongering and offer reassurance to northeastern
> migrants.
> ?What is at stake is the unity and integrity of our
> country,? Mr. Singh said. ?What is at stake is
> communal harmony.?
> The hysteria in several of the country?s most
> advanced urban centers has underscored the deep roots
> of ethnic tensions in India, where communal conflict
> is usually simplified as Hindu versus Muslim, yet is
> often far more complex. For decades, Indian leaders
> have mostly managed to isolate and triangulate
> regional ethnic conflicts, if not always resolve
> them, but the public panic this week is a testament
> to how the old strategies may be less effective in an
> information age.
> Last week, the central government started moving to
> stabilize Assam, where at least 78 people have been
> killed and more than 300,000 have fled their homes
> for refugee camps. Then Muslims staged a large, angry
> protest in Mumbai, the country?s financial capital,
> on the western coast. A wave of fear began sweeping
> through the migrant communities after several people
> from the northeast were beaten up in Pune, a city not
> far from Mumbai.
> By Wednesday and Thursday, the exodus had begun. So
> many people were pouring into train stations in
> Bangalore and Chennai that the Railways Ministry
> later added special services to certain northeastern
> cities. By Friday, even as some of the fears eased in
> the biggest cities, people were leaving smaller
> cities, including Mysore and Mangalore.
> To many northeastern migrants, the impulse to rush
> home ? despite the trouble in Assam ? is a reminder
> of how alienated many feel from mainstream India. The
> northeast, tethered to the rest of the country by a
> narrow finger of land, has always been neglected.
> Populated by a complex mosaic of ethnic groups, the
> seven states of the northeast have also been plagued
> by insurgencies and rivalries as different groups
> compete for power.
> Here in Assam, the underlying frictions are over the
> control of land, immigration pressures and the fight
> for political power. The savagery and starkness of
> the violence have been startling. Of the 78 people
> killed, some were butchered. More than 14,000 homes
> have been burned. That 300,000 people are in refugee
> camps is remarkable; had so many people fled across
> sub-Saharan Africa to escape ethnic persecution, a
> humanitarian crisis almost certainly would have been
> declared.
> ?If we go back and they attack us again, who will
> save us?? asked Subla Mushary, 35, who is now living
> with her two teenage daughters at a camp for Bodos.
> ?I have visited my home. There is nothing left.?
> Assam, which has about 31 million people, has a long
> history of ethnic strife. The current violence is
> focused on the westernmost region of the state, which
> is claimed by the Bodos as their homeland. For years,
> Bodo insurgent groups fought for political autonomy,
> with some seeking statehood and others seeking an
> independent Bodo nation.
> In 2003, India?s central government, then led by the
> Bharatiya Janata Party, brokered a deal in which Bodo
> insurgents agreed to cease their rebellions in
> exchange for the creation of a special autonomous
> region, now known as the Bodoland Territorial
> Autonomous Districts. It was a formula long used by
> Indian leaders to subdue regional rebellions:
> persuade rebels to trade the power of the gun for the
> power of the ballot box.
> Now the Bodos dominate the government overseeing the
> autonomous districts, even though they are not a
> majority, accounting for about 29 percent of a
> population otherwise splintered among Muslims, other
> indigenous tribal groups, Hindus and other native
> Assamese. Competition over landownership is a source
> of rivalry and resentment: the land rights of Muslims
> are tightly restricted inside the special districts,
> even though they constitute the region?s
> second-largest group, after the Bodos.
> ?This whole fight is about land and capturing power,?
> said Maulana Badruddin Ajmal, a member of Parliament
> and a Muslim leader in a neighboring district. ?It is
> not a religious fight.?
> These resentments exploded in July and early August,
> after an escalating cycle of attacks between Muslims
> and Bodos. Soon entire villages were being looted and
> burned. The authorities have made few arrests, and
> each side has blamed the other. The Bodos say illegal
> Muslim immigrants from Bangladesh are streaming into
> the autonomous districts and taking over vacant land;
> Muslims say such claims are a smokescreen intended to
> disguise a Bodo campaign to drive out rightful Muslim
> residents in a campaign similar to so-called ethnic
> cleansing.
> During the worst violence, the state government in
> Assam seemed paralyzed. One issue is that many former
> Bodo rebels never turned over their automatic
> weapons; some Muslims driven from their homes say
> Bodos scared them off by firing AK-47s into the air.
> To visit some of the affected villages is to witness
> the eerie silence of lives brutally interrupted. In
> Brajakhal, the entire Muslim section was burned and
> looted, while the homes of non-Muslims were left
> untouched. In the nearby village of Chengdala, each
> side apparently attacked the other ? both the Bodo
> and Muslim homes are destroyed, with a handful of
> others left standing.
> Sumitra Nazary, a Bodo woman, said her elderly father
> was bludgeoned to death with an ax.
> ?He was paralyzed,? she said. ?He couldn?t run away.?
> It is uncertain when the people in the refugee camps
> will be able to return to their villages.
> Paramilitary units and Assam police officers have
> erected temporary guard posts outside many of the
> destroyed or looted villages, promising security.
> Assam?s chief minister ordered refugees to begin
> returning to their homes this week, even as new
> violence was reported in some areas.
> At the camps, life is increasingly miserable. This
> week, two members of the National Commission for
> Minorities visited the region and documented problems
> with sanitation, malnutrition and living conditions
> at different camps, particularly those inhabited by
> Muslims. One camp had 10 makeshift toilets for 4,300
> people. At another camp, they reported, more than
> 6,500 people were crammed into a converted high
> school, including 30 pregnant women.
> The scene was little different at a Muslim refugee
> camp created at the Srirampur R.M.E. School. More
> than 5,200 people were living on the grounds, crowded
> under the shade of trees to hide from the broiling
> midday sun.
> Goi Mohammad Sheikh, 39, brought his wife and five
> children to the camp, but was returning to their
> village at night to protect their home. It had been
> looted but not burned, he said, and he and a group of
> other men were standing guard.
> ?We want to protect our houses,? he said. ?In some
> villages, it will not be possible to go back. It is
> too dangerous. But we will not leave our village. If
> they kill us, let them kill us. How do we leave our
> motherland??

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Topic: Converting a .bmp file to an int file
Replies: 4   Last Post: May 24, 2013 1:01 PM

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Steven Lord

Posts: 17,944
Registered: 12/7/04
Re: Converting a .bmp file to an int file
Posted: May 24, 2013 10:24 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"Ali Khan" <alikhan@email.arizona.edu> wrote in message
> Help!
> I would like to read a file as bmp and then convert it to an int file!

Reading in a BMP file is possible with IMREAD.

I'm not familiar with the INT file format. There are several possibilities
listed here:

If you know the specific INT format in which you want to write your data,
you can check appropriate MathWorks toolboxes:

or the File Exchange to try to locate a writer:

or use the low-level file I/O functions to create a file writer for that

Steve Lord
To contact Technical Support use the Contact Us link on

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Kenneth Kunen in his “The Foundations of Mathematics” writes:

  1. ‘Set theory is the study of models of ZFC’ (p. 7)
  2. ‘Set theory is the theory of everything’ (p. 14)

With (1) Kunen is pointing to a change in the intended use of the axioms of ZFC: ‘there are two different uses of the word “axioms”: as “statements of faith” and as “definitional axioms”.’ (p. 6).

With (2) he means ‘set theory is all-important. That is

  • All abstract mathematical concepts are set-theoretic.
  • All concrete mathematical objects are specific sets.’ (p. 14)

According to (1), to be a set is to be any of the individuals of the universe of a particular model of ZFC, just like being a numeral (standard or not) is being any of the individuals of the universe of a particular model of PA (here I am using Shoenfield’s terminology in “Mathematical Logic”, p. 18).

But, according to (2), models are sets too, as any other objects dealt with in the metatheory.

What's more, models of set theory are defined in terms of relative interpretations of set theory into itself, a syntactical concept. (See Kunen’s “Set Theory. An Introduction to Independence Proofs”, p. 141), which makes the whole thing a bit more confusing.

The view of the axioms of set theory as "definitional axioms" is appealing. And more in regard of (2) since then they pretend to define all that there is. The study of models of set theory has an intrinsic interest, but why reduce the study of set theory to it? Or stated another way, why abandoning the old view?

I would like to know if set theorists do stick to one view or another or shift comfortably between both at need, and the reasons they have to do so.

share|improve this question
Community wiki? –  Kiochi Jun 20 '10 at 18:15
I don't think this has a good answer. Compare with: What do you have in mind when you look at the ring of integers? –  François G. Dorais Jun 20 '10 at 20:18
Rainbows and sunshine. –  Harry Gindi Jun 20 '10 at 20:58
I would just like to make a statement: set theory is not the foundation of the mathematics I do, and neither are the mathematical objects I study sets in the sense of classical set theory. There, I feel better now. –  Andrej Bauer Jun 20 '10 at 21:26
Come now, François -- no question is as bad as the "integers" question! –  Pete L. Clark Jun 21 '10 at 0:12

2 Answers 2

up vote 5 down vote accepted

I highly recommend reading Andrej Bauer's excellent answer to an earlier question along the same lines. To summarize the situation in a few words: the fact that set theory is anterior to model theory does not preclude the model theoretic study of set theoretic structures. The reason for that is the same as why we can study the ring Z even though integers are conceptually anterior to abstract algebra.

I will attempt to answer your revised question as I understand it.

First, it is important to note that set theorists only rarely work with general models of ZFC, so it would be unfair to reduce set theory to the model theory of ZFC. Indeed, set theorists almost exclusively work with well-founded models of (fragments of) ZFC. In fact, the models that set theorists consider are usually of the form (M,∈) where M is a set and ∈ is the true membership relation. While model theoretic ideas play a very important role in set theory, this is very different from how a model theorist would approach models of a given theory.

Second, the language commonly used by set theorists is designed to accomodate multiple philosophical views and focus on the mathematical ideas. When dealing with forcing, set theorist often use a lingo popularized by Baumgartner. In this lingo, one talks of the generic extension V[G] as an object of the same level and equally tangible as the set theoretic universe V. This is easily translated in the multiverse view, but it is just as easy to think of this as no more than a linguistic convenience: set theorists who prefer working with countable transitive models à la Kunen can mentally replace V by such a model M and interpret the words as those of an inhabitant of M; set theorists who prefer working with boolean valued models à la Jech can simply interpret the generic filter G as a convenient abstraction; set theorists who prefer the formal approach can translate the lingo into purely syntactic arguments; etc. In my case, none of these translations ever take place, but I do hold the possibilities in a safe place for comfort.

In conclusion, my advice is to focus on the mathematics and use models as tools just like any other mathematical object.

share|improve this answer
I have restated my question to make clear I have no problem with that, but with the idea that set theory is only the study of models of set theory. –  Marc Alcobé García Jun 21 '10 at 13:03
This answer is much closer to my expectations. I did not know about set theorist's lingo and its translations (it looks like this would have been helpful). Is there some reference (or a collection of them) about it? Or should I work it out myself form the standard literature on the subject? I'd be grateful if you could you expand a bit on how the approches of set theorists and model theorists diverge. Thanks a lot. –  Marc Alcobé García Jun 22 '10 at 8:29
I have found another Andrej's answer to another question that suits fine the kind of views I was asking for: mathoverflow.net/questions/25227/… –  Marc Alcobé García Jun 22 '10 at 10:35
In relation to the previous comment. Why should the existence of "just one mathematical universe" entail the rejection of model theory as a fiction? –  Marc Alcobé García Jun 22 '10 at 19:39
It's better to ask Andrej directly. –  François G. Dorais Jun 22 '10 at 20:12

I think the more fundamental question to ask is why set theorists insist that the axioms of set theory be strictly first-order in nature (*). I claim that you can't really explain the motivations of set theorists until you address this phenomenon.

In light of this near-universal assumption, I think it is fair to say that:

  • First-order logic is the foundation of set theory (which is in turn the foundation of other things)

  • The axioms selected for set theory are those which enable as much model theory as possible, without risking inconsistency.

The fact that one can then turn around and use model theory to study set theory itself is a major bonus, but not really a part of the foundations argument. I've heard some quasi-mystical tales about sets existing in some alternate universe out there, but I feel far more comfortable using "it lets me do model theory and hasn't led to contradictions" as a justification for the axioms.

(*) Excluding, for example, second-order quantification, the logic $L_{\omega_1,\omega}$ of countable conjunctions, or the "exists uncountably many" quantifier.

share|improve this answer
Infinitary logics are often useful in model theory (e.g. Scott sentences). The issue with full second-order semantics and the "uncountably many" quantifier is that they only shift the problem. With first-order semantics, the truth definition for a structure only depends on quantifying over that structure. With stronger semantics, it can require quantifying over sets in the metatheory. For example, because we know that "is countable" is not absolute in the usual sense, it is much harder to justify as "logical" a semantics that itself references countability. –  Carl Mummert Jun 20 '10 at 21:13
I agree completely, but this just shifts the problem to what "in the usual sense" means. Generally, "in the usual sense" means "in first order logic", which is a circularity! It doesn't really make sense to say that non-first-order logics aren't "logical" because they let you define things which aren't first-order properties -- that should be expected! There's a hidden assumption here which equates "logical" and "first-order" which should be more explicit. By the way, my gravatar icon is a photograph of the person who discovered that countability of a model is not a first-order property. –  Adam Jun 21 '10 at 1:08
You may be interested in "The Road to Modern Logic-An Interpretation" by Jose Ferreiros ( jstor.org/pss/2687794 ) which directly addresses your point. –  Carl Mummert Jun 21 '10 at 2:40

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‘He played it for all the ancestors all over the world’

November 1, 2012
By LEE IMADA - Managing Editor ( , The Maui News

Anthony Natividad, renowned for his playing and building of nose flutes and an original cast member of 'Ulalena, died Sunday. He was 48.

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A government official from Nassau in Germany complained in 1846 that the emigrants were infected by "delusions of freedom and fantastic ideas about the institutions of government" and that the emigration fever made the "lower classes" rebellious. A group of 160 tenant farmers in an area of intense emigration petitioned the Duke of Braunschweig in 1848, the year of the revolution, to grant them the following:

  1. Complete relief from the head tax (Personensteuer)
  2. Ending of the practice of purchasing substitutes for military service
  3. Representation in the state assembly (Landtag) and the village council
  4. Freedom from the school tax and other ecclesiastical taxes, and improvements in the common schools
  5. Ending of all unpaid road work
  6. Assignment of sufficient acreage in the divided and undivided common lands for free use
  7. Regulation of rental conditions; no more unpaid service; fixed duration and price of rentals
  8. Erection of a public institution for the care of old and invalid Heuerleute (tenant farmers)

Further statements by these dependent tenant farmers who worked tiny plots and relied on jobs such as linen weaving and migratory labor in Holland to supplement their income, clarify their aims:

"...We are obliged to pay taxes and render military service, and formerly road work, too, but are not represented in the Landtag."

Regarding military service: "Those with means can purchase a substitute, but we, the proletariat, must...bleed for the so called Fatherland."

"We are responsible for school, church, and other taxes, but are neither represented nor consulted in the village council about measures that affect our interests."

Kamphoefner in his book, The Westfalians. From Germany to Missouri, expalins what these "interests" were: "Foremost among these was the division of common lands, whereby the Heuerling (tenant farmer) lost grazing and pasture land, wood for fuel, and peat for mulching crops--rights previousy enjoyed for generations by custom but without legal base"

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Formal Concept Analysis: applications in computational genomics

Dustin Potter
MBI, The Ohio State University

(December 8, 2005 10:30 AM - 11:30 AM)

Formal Concept Analysis: applications in computational genomics

The central ideas of Formal Concept Analysis revolve around the notion of a formal context and a formal concept. Of interest is the duality called Galois connection that arises naturally in different contexts. This duality is often observed between sets whose elements are related, such as objects and their attributes. In a Galois connection between two sets, the increase in size of one set corresponds to the decrease in size of the other set and vice versa. For example, an increase in the number of search terms used in a Google query corresponds, in general, to a decrease in the number of hits.

I will introduce the fundamentals of Formal Concept Analysis and demonstrate how we applied the ideas of the field to problems in microarray analysis. In this work we integrate biological attributes related to genes along with their expression values obtained from a microarray experiment. The integrated data is represented as a partially ordered set that respect Galois connections inherent in the data. Metrics are applied to the representations of multiple samples to discover biological similarities.


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What is 'Economics (ECON)'?

Economists study how society distributes resources, such as land, labor, raw materials, and machinery, to produce goods and services. They may conduct research, collect and analyze data, monitor economic trends, develop models, evaluate public policy decisions, or develop forecasts. Economists research a wide variety of issues including energy costs, inflation, interest rates, trade balances, exchange rates, business cycles, production levels, taxes, and employment levels, among others.

(For more information, see http://www.bls.gov/oco/ocos055.htm#nature.)

Is it for you?

Some entry-level positions for economists are available to those with a bachelor's degree, but higher degrees are required for many positions. Prospective economists need good quantitative skills.

Economists have structured work schedules. They often work alone, writing reports, preparing statistical charts, and using computers, but they also may be an integral part of a research team. Most work under pressure of deadlines and tight schedules, which may require overtime. Their routine may be interrupted by special requests for data and by the need to attend meetings or conferences. Frequent travel may be necessary.

(For more information, see http://www.bls.gov/oco/ocos055.htm#nature.)

Jobs and Salary expectations

Individuals with a background in economics should have opportunities in various occupations. Some examples of job titles often held by those with an economics background are financial analyst, market analyst, public policy consultant, researcher or research assistant, and purchasing manager.

The median annual wage of economists was $89,450 in May 2010. The median wage is the wage at which half the workers in an occupation earned more than the amount and half earned less. The lowest 10 percent earned less than $48,250, and the top 10 percent earned more than $155,490.

Employment of economists is projected to grow 6 percent from 2010 to 2020, slower than the average for all occupations.

(For more information, see http://www.bls.gov/oco/ocos055.htm#nature.)

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Saturday, July 17, 2010

TDF 2010 Stage 13: Rodez to Revel

Up today is Ben Wood, gypsy jazz guitarist, cycling enthusiast, wine buyer at 67 Wine, and all around good guy.

Hi all,

Today I'm honored to be guest posting on David McDuff's blog. He has covered the Tour De France in a vinous way for the last several years. We managed to have him up to 67 wine for a tasting last week (while the race was in the Jura region). Today, I am writing about Stage 13 from Rodez to Revel. The course for this day is a fast rolling romp through the southwest part of the French countryside. The riders roll quite near to one of my favorite wine regions, Gaillac, and also pass Fronton, another great wine region in the southwest of France.

Unlike the stereotypical professional cycling racer, these wines are not steroidal monsters with chemical injections (kidding). The wines are, however, racy, controversial and fascinating. All of the great wines of these areas are made from native grapes that grow for the most part only in the southwest. Fascinating grapes like Braucol and Duras for red wines; Ondonc, Mauzac and Len De l'El for white and sparkling wines. These are unique grapes rescued from obscurity by winemakers like Patrice Lescarret at Domaine de Causse Marines.

These are wines of whimsy, interest and intensity. A member of the "vins naturels" movement, Lescarret practices organic farming with some biodynamic ideas as well as extremely minimal intervention in the cellar. The wines are focused on the native grapes in the region and include a cuvee named "Les Greilles," an AOC Gaillac made from all of the local grapes. A beautiful crisp white wine with honeysuckle and mineral notes, dry on the palate and refreshing, one of my favorite wines to drink.

There are some telling images on the label:

(the saluting mouse, and the no badger symbol) involving the personal mythology (M. Lescarret is called the mouse, and badgers hunt mice . . . This was the story I was given. A good mystery for you!).

A second wine from Gaillac that I love is made by Brigitte and Alain Cazottes of Domaine des Terrisses. Racy and good, the red from this estate has proven to be one of our best selling wines. The grapes are farmed biodynamically, and the soil site has quite a lot of clay (up to 60% in some parcels); because of this the wine comes through with strong aromatics and great flavor. Firmly in the Syrah camp, this wine smells of garrigue (a bit) and dark red fruit, with soil-y mineral notes and a hint of game. Beautiful and complex, it is racy and thirst quenching with just enough weight to make you know it is wine!

Tomorrow will be a fast and hopefully interesting stage as the riders pass some very great vineyards. Makes me wish I was there to eat the food, drink the wines and cheer on the riders!!

Up next: your guess is as good as mine....

saignee said...

From what a producer we will be working for tells me the badger is the a play on the French word for "redneck-douchebags"

David McDuff said...

Nice. Maybe there should be a saluting squirrel on the label...?

David McDuff said...

Glad to hear you enjoy the wines from the Cazottes at Domaine des Terrisses. Used to sell the wines -- red, white and rosé. Solid wines and great values across the board. I miss them.

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Tuesday, May 30, 2006

Now that we've gotten that out of the way and have celebrated this historic achievement, we can now move on to the business at hand. The business at hand is a country that stills wrestles with old demons that haunt and destroy the progress that we have made here in the land of the free, as a country and as a people. For every man that truly took issue with Barry Bonds surpassing the Babe because he thought Barry had an unfair advantage I have no issues with you.

My issue is only with the man who couldn't live with a Black hero overtaking his White hero and him using the steroid accusations to cover his true feelings. I hope that this is a small group and I pray that even this group learns to look beyond race and gender and look to the man and the accomplishment. We have such a great country and there is still a lot of work to be done in race relations, and learning to respect and celebrate our diversity. However, lets not use baseball as a negative platform to further divide a country that is in the middle of a mid life crisis. We need to use the game as a bridge of harmony and tolerance. Baseball itself, is already a great successful melting pot on the field. Let the game influence society and teach it how to prosper and win as a diverse team. All other issues not related to the game itself should be worked out in other venues. The game represents domestic tranquility. Fields of dreams.
Summer romances. Graduations and proms. Ice cream and soda. Hot dogs and popcorn.
Pennant drives and World Champions.

Barry we salute you. Well done. Hank Aaron will now receive the respect and honor he earned and America was not ready to give at the time.
The Babe should have never been the issue. He's not the home run champ. We do owe Babe for all he did to make the game what it is today. Home run King? That honor belongs to Hank. What was all the fuss about?

Nascar: New Fan

This was my first time at Nascar and I must say there is no comparison between what you see on television and the exhilaration you feel at the live race.
I was surprised by the energy and excitement. I have great respect
for the drivers who handle the cars at over 200 mph for hours at a time.
These are men of men. The expertise and teamwork of the crews is remarkable.

The precision of what happens in the pit and the technology behind improved times and finishes is astounding. Seeingit all work live gives you at different perspective
and appreciation for the sport.

Hearing and feeling the cars zoom by is awesome! I will forever be a fan
and I plan on catching a few more races this season.

Saturday, May 27, 2006


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First Annual International Table Top Day is March 30: Play more games!

Geek & Sundry, the award-winning original YouTube channel, is proud to announce the first International TableTop Day on March 30, 2013. International TableTop Day encourages people from around the globe to participate in the joys of board gaming by empowering the community to host thousands of gaming events internationally. Participants can sign up at for free events at their favorite local game stores or submit their own event at their home, community center or business.

Inspired by tremendous fan response to the the critically acclaimed show TableTop co-created and hosted by Wil Wheaton (Star Trek, Big Bang Theory, Leverage), Felicia Day and her team hope that the day will grow the gaming community by encouraging fans to come together and play more games.

In conjunction with this announcement, Geek & Sundry has revealed their website, the central hub for the community to bring together tabletop fans, publishers, and retailers from around the world. The website provides fans with resources such as the interactive event map which tracks all #TableTopDay events worldwide, inspirational videos from their favorite YouTube stars, blog posts by popular columnists on how to plan for their event, and fun downloadable content to keep fans excited leading up to March 30th, 2013. Organizations, businesses, community centers, retail stores, and fans worldwide are invited to submit their own events for free and help make International TableTop Day a community-driven celebration of tabletop gaming.

About Geek & Sundry

Original YouTube channel Geek & Sundry features the best of indie geek culture and the internet’s foremost geek voices. Founded by the producers of the hit web series The Guild, Geek & Sundry offers a diverse lineup of shows that create a hub for fans of comedy, gaming, comics, music, and literature around the world. Spearheaded by prominent geek figureheads, Geek & Sundry features original content by Felicia Day (The Guild, Dr. Horrible, Eureka), Wil Wheaton (Star Trek, The Big Bang Theory).

For more information, visit & watch on YouTube at

Want to learn more about McNeill Designs for Brighter Minds award-winning games like You’ve been Sentenced! and more? Visit McNeill Designs for game rulesprintable score sheets, or even order online!

Need more fun and games? Find You’ve been Sentenced! on TWITTER and Like us on FACEBOOK  for special offers, coupons, and insider gaming news!

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Discover nature with MDC outdoor preparedness classes

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Girls Drink From Water Bottle on Hike

Published on: Mar. 8, 2013

COLUMBIA, Mo. – The Missouri Department of Conservation (MDC) invites you to discover nature with a series of Outdoor Preparedness classes. There will be a classroom session 6 to 8 p.m. on April 11 at the MDC Central Regional Office in Columbia. Additional field dates will occur from 5:30 – 8:30 p.m. on May 1 and May 22. This program is open to families, and youth age 11 years and up with a parent or adult mentor.

The series of classes will cover basic outdoor skills such as how to build a campfire, finding wild edible foods in Missouri woods, how to purify water, how to build a shelter and much more. Whether a person wants to be more prepared when venturing outdoors on a nature hike, or to learn new skills to use on a hunting or camping trip, this series of classes will prepare you for your next outdoor adventure.

“Outdoor preparedness begins with the right mental attitude and then builds upon several key skills,” said MDC Outdoor Skills Specialist Brian Flowers. “With a backpack containing several key items, outdoor enthusiasts can feel better prepared to take on most outdoor emergency situations.”

To register, or for more information, contact Flowers at or 573-815-7901, ext. 3388.

The E. Sydney Stephens Central Regional Office and Conservation Research Center is conveniently located off of US Highway 63 just west of the Discovery Parkway exit on the south side of East Gans Road.

For more information about this and other Discover Nature programs, go online to

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We help people discover nature.

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Commissioners Weigh In On Beach Funds, Wind Farm

SNOW HILL – Offshore wind farms should be kept well out to sea and beach replenishment money should be preserved, the Worcester County Commissioners said this week, in agreement with Ocean City’s stance on those issues.

On Tuesday, county elected officials voted to support Ocean City’s position on proposed state laws covering offshore wind farms and the removal of money from the beach replenishment fund to balance the state budget.

The town of Ocean City is concerned that the visual impact of ocean-based wind turbines would have negative tourism consequences, if those turbines are visible from the resort’s beaches. The resort is asking that proposed legislation governing the energy lines as they come ashore require that offshore wind turbines be located a minimum of ten miles out to sea.

Although the state of Maryland’s authority over ocean waters extends only three miles off the shore, the state does have the authority to control the landfall of energy lines, a letter from the town of Ocean City notes, which should allow that 10-mile minimum.

The commissioners voted unanimously to take the same position as Ocean City.

The commissioners also agreed Tuesday that the state’s plan to take money from the Beach Maintenance Fund to balance the state budget provokes some serious concern.

The fund, which is for beach maintenance and not for major replenishment projects, is supplied with money by state, county and the city, with the state contributing 50 percent and the county and city contributing 25 percent each.

The state plans to compensate the fund with future state general obligation bonds.

The entire fund is in jeopardy, county staff explained.

“They’re talking about taking their share, our share, and the city’s share,” said county administrator Gerry Mason.

Commissioner Virgil Shockley asked if there was any way to protect the county’s contribution to the fund from being taken, perhaps through establishing an escrow fund.

“I don’t really think they can take our share,” said Mason.

Commissioner Louse Gulyas made a motion to write a letter “in very strong terms” supporting Ocean City’s position on the beach replenishment fund. The commissioners voted unanimously to send that letter.

“Leave our money alone,” Gulyas said.

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