Bowman, D. Burke, E. Burke, Serta, Davis, Graf, Kittleson, Manny, Meyer, Montemayor, Radke, Sagalli, Steffen, Susha, Van Akron, and Vanderwill, 16 present. Quarum's present. All aboard, Bowman, would you please lead us in the Pledge of Allegiance? I pledge allegiance to the flag of the United States of America and to the Republic for which it stands, one nation under God, indivisible, with liberty and justice for all. Thank you, Alderman Bowman. Alderman Graf. Thank you, Your Honor. This time I would make a motion that all ROs be accepted and filed, and all ROCs be accepted and adopted, and they would be 1538, 1539, 1571, 2345, 678, 980, 81, 82, 83, 84, 85, 86, and 1636 and 1638. Is there a second? Second. Under discussion? Under discussion. These are all the reports of officers and the reports of committees, which we can't make any changes to, so this would be just eliminating all those and getting us to the resolutions that we have to act on. Thank you, Alderman Graf. Any other discussion?  It's not. All those in favor, state aye. Aye. Any opposed? Motion carries. 1561, resolution number 160506 by Alderman Graf, Stafford, Montemayor, Susha, and Davis, ordering the 206 budget appropriations for the city of Sheboygan funds. Alderman Graf. Thank you, Your Honor. At 1561, I would move that that resolution be put upon its passage. Is there a second? Under discussion? Under discussion. Here again, this is for the appropriations and really there are no additional funds that are coming in, I believe, at this particular time. So there's really no additional changes to be made on this particular document. And these are matters that don't impact the levy also. Okay. Any further discussion? Not please call the roll. D. Berg, E. Berg, Serta, Davis, Graf, Kittleson, Manny, Meyer, Montemayor, Ratke, Segali, Stefan, Susha, Van Akron, Vanderweal, and Bauman. 16 ayes. Motion carries. 1562, resolution number 170506 by Alderman Graf, Stefan, Montemayor, Susha, and Davis ordering the 206 budget appropriations and the 205 tax levy for use during the calendar year 2006, Alderman Graf. Thank you, Your Honor. At this time I'd move that that resolution be put upon its passage. Is there a second? There's a motion to put the resolution put upon its passage. In the second, under discussion, Alderman Segali. Thank you, Your Honor. On the RC, the 2980506, I would like to make a motion and amend the report of officers that the 16,400 be put back on for the tasers for the police department. No, that has been already accepted and adopted. I believe what you're trying to do is make a motion to amend to make a proposed amendment to the budget, amend the budget by that amount? To add it in. Yes, to add it in. 16,400 for the tasers. And that was what amount? 16,400 for the tasers. I'm sorry, 16,400 for the tasers. And who seconded that? I did. Thank you. Under discussion, Alderman Graf. Thank you. If the police or somebody could answer a question. I know there's a $5,000 donation and with that $5,000 donation I'd like to know why instead of the $16,400 why we couldn't ask for only $11,400. Deputy Chief Weiss, please step up. Thank you. Thank you, Your Honor. I believe I can answer that question. First of all, it's a pledge. We don't have it yet. And with that pledge, the 16,400 will be added with the 2100 that we already have and that will make just a right amount of money for 20 tasers. So we need all the funds as well. Okay, you need 16 plus the 2 that you have. Right, plus the 2100. And that would give you, excuse me. That is the amount that I had originally proposed in the budget. Okay.  That'll get us what we need for 20 weapons. All in my honor. Thank you, Mr. Mayor. Please stand up. Deputy Chief Weiss, does this include, who's my balance? Does this include cameras for the tasers? Because now they do make cameras for them. And I think it would be in the best interest to have them. That figure did not include the cameras. And I do agree with you, Alderman Mayer, that it was, the cameras would be an additional $8,000 for the 20 tasers. Okay. Call me Ratke. Okay. Thank you very much. We'll take a vote on that. Please call the roll. And the vote is on the amendment to add $16,400 to the budget for tasers. Is that correct? Yes. Okay. Eberg. Hi. Serda. Hi. Davis. Hi. Graf. Kittleson. Hi. Manny. No. Mayer. No. Montemayor. No. Ratke. No. Sagali. Hi. Stefan. Hi. Susha. No. Vanakren. Hi. Vanderwheel. Hi. Bowman. Hi. And Deberg. 11 ayes and five noes. Motion carries. Alderman Ratke. Thank you, Your Honor. This time I want to make a motion to adjust the city tax levied to the amount allowed by the state, which is from 20,000,605,521 to 20,000,675,661. And the difference of 70,140,000, the amount to be allocated as follows. $20,000 for mapping a crime analysis program for the Sheboygan Police Department. $8,000 for cameras for the tasers and then the rest, the $42,140 the balance for the contingency fund. Is there a second to that motion? Second. Second under discussion. Alderman Sagali. Thank you, Your Honor. Do you think Alderman Ratke could please repeat that and just go a little bit slower? I didn't get some of the numbers that he had placed. Did we have a second on that? Yes. Okay. Alderman Graf, thank you. There's a second. Alderman Ratke, would you please read that a little slower? Thank you. Okay, I have this all written down here, something a little bit simpler. The motion is to adjust the total city tax levied to the amount allowed by the state, which is from 20,000,605,521 to 20,000,675,661. And at the difference of 70,140,000, that amount to be allocated as follows. $20 million for a mapping and crime analysis program for the Sheboygan Police Department. $8,000 for cameras for the tasers and then the remaining balance of 42,140 would go to the contingency fund. Thank you. Alderman Ratke, Alderman Stefan. Just a friendly thing. I think he met $20,000 for the 20 million mapping rather than 20 million. Just a question on procedure, Your Honor. First of all, now we don't quite have that much money. Am I correct? Because we just increased it by 16,000. What happened is that the total city tax levy was at 20 million, a little over, as was read. The state levy limit allows an amount that can be adjusted up, which is about $70,000, $140,000, $40,000, $40,000. Right, I get my point was we just raised at 16,400, so that would, I guess, your thought is to reduce the contingency by that amount? If the entire 70 was going to contingency to reduce, that has never been appropriated as such. Right. The budget came in at 20 million, 605,521. The tax levy limit allows 20 million, 675,661. So it's a difference of 70,140. I believe what Alderman Ratke is saying is that he's asking the motion to, asking to adjust that amount to the allowable amount allowed by the state and that that amount be divided accordingly. Okay, and I understand that. Which puts as well within the levy 3.339 percent. Sure, I guess my question is, obviously I see some proposals that are coming up and if those would pass and bring the specific items lower, does that come off that total then or does that just go into the contingency if we approve this ahead of time or should we wait until the end to approve this? We can do it now. If the next motion is to reduce $100,000 from something and we do it, does that take the $100,000 out of the budget or does it just move it from that line item to the contingency? The next motion will propose to remove or add. It's got to pass and then when that's got to, when that's proposed, that's where we give you this form here. Sure, right. Okay, I'm just kind of worried about having the to be determined amount in the contingency, but I guess we'll see how it goes. Yes, Alderman Ratke, there's a question for you. I'll be right with you. Alderman Graf and Alderman Serra. Alderman Ratke, do you have a copy of that motion that I could have, please? Sure. Please come up. Thank you, sir. Alderman Graf and then Alderman Serra. Giving back to Alderman Stephan's question, the $16,400 that we just added, does that not reduce this $70,000 by approximately $16,400? So therefore, what goes into contingency is $16,400 less than what the motion was. Is that correct? Right. Okay, thank you. Alderman Sedler. Thank you, Your Honor. That's exactly what I was going to be reiterating, that we can take that $16,400 out of the contingency of $4,200. Any further discussion? Please call the roll. Do you need to have me reread what Alderman Ratke did, or are you all clear? You need to read. Okay, Alderman Ratke, can I just read the first paragraph? Making a motion to adjust the total city tax levy to the amount allowed by the state, which is from $20,605,521 to $20,675,661, and that the difference of $70,140 amount be allocated as followed, $20,000 for a mapping and crime analysis program for the police department, $8,000 for cameras for tasers, and $42,140 balance for the contingency fund. Is that correct, Alderman Ratke? And the difference is $25,737 for contingency, yes. Please call the roll. Eberg. Hi. Thank you. Serta. Hi. Davis. Hi. Graf. Hi. Kittleson. Hi. Manny. Hi. Meyer. Hi. Montemayor. Hi. Ratke. Hi. Segali. Hi. Stefan. Hi. Sushia. No. Van Akron. Hi. Vanderweel. Hi. Bauman. Hi. And D. Berg. Hi. 15 ayes, one no. Motion carries. Under discussion, still. Anything else? Alderman Sushia. Thank you, Mr. Mayor. Well, coming into this evening, I was told that if we reduced the budget by about $300,000, the increase in the tax rate would be zero, and that is one of my goals. So I do have 11 motions to make to try to decrease the budget. Starting with the first one on the document that I handed out, I'd like to make a motion to decrease $500 in the bike maintenance division, which would be expenditure number 52352 in cost number 201120. Who seconded? Thank you. There's a motion and a second. Further discussion? Alderman Groff. Thank you, Your Honor. Deputy Chief, please. A reduction of $500 in that particular budget will cause what? I haven't seen that list. I'm sorry. I'm not exactly sure which to do. A $500 reduction in the bike maintenance account. Thank you. Which would take all your funds out of there, if I'm reading this correctly. Okay. A $500, I think, is a reduction that we can withstand. Not that I'm looking at this list, there are a number of items on there that I certainly would take issue with, but I think we can absorb that bike maintenance and I myself would vote against it, but I think we can absorb that $500. Okay. And that's the only motion before us right now. That's right. Thank you. Alderman Manny. Thank you, Your Honor. My question is, how would you absorb it? My presumption is you'll take the costs out of some other category of the budget. That's correct. That's correct. Oh, Matsusha. Just to put things in perspective, I believe that we have two bikes that were purchased for $1,800 each for the bike patrol. And when you think about $500 in repairing bicycles, in my family, what we would do is go to Walmart and buy five new bikes, rather than stick $500 into maintenance. I mean, I think it's important that the wheels move and that the pedals go, but I think $500 is too much. And during the public protection safety meeting, Chief Kirk did make the comment that if you're going to take any money from me, take it out of the bike maintenance. And I was unable to make any motions at that meeting because I'm chairperson of the committee. So I did remember that he said that, so that is why this motion is being made. Thank you, Alderman Manny. Anything else? Thank you, Deputy Chief. Okay, we have a motion before us in the second. And that, call the roll. This is on the $500 reduction in the bike maintenance. Serta. Hi. Davis. Hi. Graf. Hi. Kittleson. Hi. Manny. Hi. Mayer. Hi. Montemayor. Hi. Radke. Hi. Segali. No. Stefan. Hi. Sushia. Hi. Van Akron. Hi. Vanderweel. Hi. Bauman. Hi. D-Berg. No. And E-Berg. Hi. Fourteen ayes, two nos. Motion carries. Alderman Sushia. Thank you, Mr. Mayor. The second item would be a motion to remove $20,000 from the training schools in the police service fund cost number 2011-00 expenditure number 520-804. And that is from the current 45 taking 20, leaving a balance of 25. Under discussion. Oh, I'm sorry. There's a second. Under discussion. Alderman Segali. Thank you, Mr. Mayor. Could we please have Deputy Chief Weiss kind of explain what would be going out of the training? Yes, we can. Deputy Chief, would you please step forward? Thank you. I wish I would have had an opportunity to see this prior to this meeting, so I would have some accurate answers. If we had a budget of $45,000, $20,000 taken on it would greatly affect our training. The training that the officers go to is vital. It's necessary. We have ongoing training virtually year long. There is a number of issues that in the legal department that change. We have to continuously upgrade our training. $20,000 I believe will be devastating to our training budget. I would ask for your support not to take that much money out of that fund. Okay, Alderman Susha. Thank you, Mr. Mayor. When you look at the total amount of money that goes for training the police department, when you add it up in all the different budgets, it comes close to about $70,000. And what we were told during public protection and safety is that that $70,000 covers the mandatory training by the state, which is 24 hours worth of training. Plus it includes at least one optional training for everybody in the police department. Now I have trouble covering optional training. When you look at something on page 62 in the general funds under training schools for engineers, it talks about this line item was reduced to zero, the previous two budgets. It is important to provide training opportunities to the engineering staff to learn new innovative methods and keep current on engineering standards. If we're only allowing the engineers of the city to attend training schools once every three years, I don't think it's right that we continually pay for everyone in the police department to have optional training above their mandatory training. I mean, obviously we have to cover the mandatory training, but as far as covering the optional, I think that it's time to tighten the belt. And then I also wanted to mention that to cover, to help cover the costs of this mandatory training, the state does give the police department $200 per officer to cover their training or to put towards their training. So you have $200 that is currently covered. When you look at the training for the building inspectors, each person is allotted $300 to cover their mandatory 24 hours in training. The building inspection department has requested the same amount, $300 per person for the past 18 years. Any money above that has to come out of their pocket. And it's for these reasons that I think it's appropriate that we reduce the amount of money that we're putting into the training schools, because also it has a triple over effect into overtime. Because when you keep sending these people off to get more training, to get more training, you're starting to increase the overtime that you see. So it's kind of a hand in hand situation. So I would ask that you support this motion. Thank you. Just a point of clarification here of Alderman Sousha, you put under the second to the last column, where it says current 206 budget $45,000. I've just been made aware that the amount now is $40,000 passed by public protection and safety. So that number, Council Alderman, older persons should read $40, not $45, which will leave a balance of 20. Okay, next we have Alderman Serda. Thank you, Your Honor. This is for Deputy Chief Weiss. If you could expound a little bit on as far as any mandates for the training where I guess we're being left with the impression that we're sending officers needlessly. And then mind you, just for the public, that if I go through the budget, each department has also allotted for some training expenses. I know just for example, the mayor, I tried to get an answer for the $800 as far as, and this wasn't to the mayor personally, but I did check with Richard Gephard and Susan Hart as far as $800 and what that would be earmarked for training for the mayor's office. Deputy Chief. Thank you, Your Honor. First of all, I disagree with what Alderman Sushia said. This is not luxurious training. It's not unnecessary training. Mandatory training is one thing, like shooting, pursuit driving, hand-to-hand tactics. But you don't grow with that. That's just mandatory training that you continue to maintain skills at a level where you're proficient. Now, the extra training or unnecessary training that you're pointing out is things like evidence technician, officers want to become photographers, officers want to increase skills on how to interview people, officers want to go to drug training school over and above the average to develop an area of expertise that the department then relies on their expertise. This is none of this training is unnecessary. We could easily double that. These are classes that are looked forward to by officers as a way to improve their services to the city and their ability to be a good police officer. Again, I would I hope you vote against that $20,000 reduction. Thank you, Alderman. Thank you, Your Honor. I just wanted to say that if the city was sued because somebody was questioning the training of our officers, $40,000 would be a drop in the bucket if civil litigation would be brought because of training issues. Thank you. Alderman Ebert. Yes, sir. Thank you, Your Honor. Does the training budget include travel and expenses, or is that just tuition costs? It's hard for me to say exactly what it includes. Usually it covers on most schools the meals, the lodging, if that's necessary, and the cost of the school itself. My understanding, most of the training officers are so willing to go that they don't put in for overtime.  And I can't say that it's a contractual obligation, but it does, to my knowledge, it does not increase the overtime budget. And one additional question. This evening earlier, we approved funding $20,000 for new mapping software. It's presumptive that there are some training costs that are loaded into any new program or any new effort that you engage in. And also with the tasers, do you have a general estimate of what the cost of, we have about 125 sworn officers? Not quite that many. We would like to have that many, but no. That's a separate question. We have about 87 sworn, however, the training would probably be undertaken by officers who are on the street. So this would be in-house. Reduced absolutely, yes. Thank you, Alderman Byrne. Alderman Ratke. Thank you, Your Honor. I'm going to vote in favor of cutting this because we look at the different departments, including this department, the legislative. There's not one nickel appropriate to help us grow in our field. Yet we're giving other departments, such as the police department, above and beyond their state mandated training, there's a lot of things that I see that I'd like to go to conferences and things like that. That comes out of my pocket. Those are several hundred dollars in some cases if we want to learn these types of things. And it's kind of funny that they're a bit more prepared that they weren't committee this evening because when we asked these questions in committee, we didn't get many answers. It was very ill-prepared and I'm going to vote in favor of this amendment. Hold on and drop. Thank you, Your Honor. Because of the reduction of $5,000 already to $40,000, what is the amount of mandatory training or mandated training? I just can't give you that number off the top of my head. Alderman Susha, you want to ask for that? Yes. Lieutenant Gerving, who's in charge of the training, told me it's 24 hours of training per year. Thank you. Do we have a dollar? If I may, do we have a dollar amount on there that equates to? Okay. Anything else? Please call the roll. This is on the... It would be reducing the training school budget by $20,000 is what you're voting on. Davis? Graf? Aye. Kittleson? No. Manny? Aye. Mayer? Aye. Montemayor? Aye. Radke? Aye. Segali? No. Stefan? No. Susha? Aye. Van Akron? No. Vanderweel? No. Bauman? No. Deberg? No. Eberg? No. Serda? No. Six Eyes and Ten Nose. Motion fails. Alderman Susha. Thank you, Mr. Mayor. I'd like to make a motion to remove $50,000 from the Patrol Division over time. And that would be from Cost Center 201120, expenditure number 5103. And there's a $225,000 amount budgeted for 06. The proposed motion proposes to take away $50,000. Alderman Stefan under discussion. Thank you, Your Honor. Those of you who follow finance know that I've continually questioned the police department on overtime. Can I make an amendment to this amendment, or would that not be in order? I guess I could support reducing this in $50,000. Assuming we put the other $50,000 into an officer on the street, put it into their general salary account, because I feel, I believe as you're budgeted, you'll be three officers short or four. And if we're never going to get a grip on the overtime, in my opinion, unless we have a full staff or close to it, and I think it's a good idea to get rid of some of the overtime, but I'd rather see it used in putting officers on the street. So I guess I would make that amendment to reduce the overtime by $50,000, but then make that into the general salary portion of it, the Patrol Division. Okay, there's an amendment. But keep in mind, $50,000 may not cover one police officer, maybe more. So you're actually going to spend up more. Okay. Under discussion on the amendment, Alderman Susha, Alderman Susha on the amendment. Okay, thank you. I think that possibly what he is proposing is actually going to backfire and create more overtime, because $92,000 of the overtime budget in the police department actually comes from contractual overtime that is required due to the holiday pay. So actually, if you add more people, I think that it could kind of backfire. My point with sending people to the training schools is that it creates more overtime because they're not here to fill in for their shifts. For example, the trip to North Carolina, three officers drove, it took them six days by the time they went down and got back. So in that six-day time frame, when they were gone to their training, it actually created more overtime. So I'm concerned that if we hire another officer, what we're going to do is send them off for more training and it will in turn create more overtime because of it. So I don't think that's a good idea. Alderman Ebert. Yes, thank you, Your Honor. I'd like the idea of transferring money to hire another officer. The difficulty we have with this budget is the limitations we have in light of our salary situation and that we currently are under arbitration. And were that to happen, we don't have money or shortfall money in the budget. I think we have $340,000 in our contingency fund, which under funds, if you would, a potential salary award by something like $640,000. So to hire an officer would likely mean if the arbitrator awards to the city unions that the first event would be training him or her and then laying them off. And I think that that's a realistic probability, given the budget shortfall. So for that reason and that reason only, I can't support this. Alderman Cigali. Thank you, Mr. Mayor. If I can ask Deputy Chief Weiss, how much overtime was put out there when these gentlemen went to receive that award in North Carolina? Because Todd Prevy, he's not on the streets, so. To my knowledge, there was no overtime. And those officers did not create a vacancy that required an influx or calling in officers to cover their positions. Also, when we go to school, those officers go to school when the shift can afford to leave them off. That's why you'll see a lot of officers go into school early in the spring. And throughout the whole summer, nobody goes to school because the shifts can't afford the loss of manpower. So we don't staff on overtime to fill a vacancy for an officer going to school. We just don't do it the way. It's a waste of money. Okay, we'll call the roll on the amendment. And that's to remove $50,000, but to use that $50,000 for the hiring of a new police officer. This is the amendment to the amendment. So an I-Vote would be putting it into the patrol officer general salary. Okay. Recky, Segali? Aye. Stefan? Aye. Sushia? No. Van Akron? Aye. Vanderweal? Aye. Bauman? No. Dberg? Aye. Eberg? No. Serta? No. Davis? Aye. Graf? No. Kittleson? No. Manny? No. Meyer? No. Montemayor? No. Degenerate size and ten noes? Motion fails. Back to the motion to remove $50,000. Please call the roll. Okay. Graf? Kittleson? Manny? No. Meyer? Aye. Montemayor? Aye. Radke? Aye. Segali? No. Stefan? No. Sushia? Aye. Van Akron? No. Vanderweal? No. Bauman? No. Dberg? No. Eberg? No. Serta? No. And Davis? No. Five ayes, 11 noes. Motion fails. All room and Sushia? Thank you, Mr. Mayor. I'd like to make a motion to remove $4,000 from the training school public safety account cost center two zero one one three zero expenditure number five two zero eight oh four. There's a motion and a second under discussion. Sorry. Okay. Just made a where again second to the last column current 206 budget the $7,000 amount should be $6,448. Taking away $4,000 would leave a balance of $2,000, $1,000 and the balance. I can't do the math. Sushia? I'm not about to get into this. All room and Sushia you're on. Okay. Thank you, Mr. Mayor. I'm sorry. I guess I should excuse me. Did we have a second on your motion? Yes, right. Thank you. I guess it all you know the total for the entire police budget for training like I said is close to $70,000. Just to put this in perspective, if you look on page 51, you will see that the fire department only schedules $6,500 in training. I mean they are also a very important player in public safety in this community. But this is an example of where the police department could learn from the best practices of the fire department. Because what they do is something called train the trainer. The fire department will send one person to a training class and that one person will bring the knowledge and the handouts and all of the information back and train everybody else. So all the training is done locally and then you're not paying for all of the overnight stays. You're not sending two to five people to each training event. This adjustment here is in the telecommunication area. Perhaps this will leave roughly $2,000 in that particular cost center. But remember in addition to that, the state is going to give each of those people and I believe there's 19 of them. Each of them will receive an additional $200 towards the expenditure of their training. And when you think about it, aside from some advanced customer service training, these folks really could benefit from just sitting down and looking at the map of the city and make sure they know the streets because that's something that's very important to what they do and that's free training. It doesn't cost anything. So I would ask that you support this motion. Thank you. Hold on to golly. Thank you, Mr. Mayor. I would have to say that I will definitely not support this one. Our telecommunicators are probably one of the most integral parts of our police department. They're the first ones that answer the phones when we need help. And I would like to ask Deputy Chief Weiss what he could tell us concerning their training place. Deputy Chief Weiss. Thank you. This training is for the telecommunicators. I'm not exactly sure what we used last year. I'd like to remind the council anything we don't use goes right back into the general fund. So these budgets were created to be used as necessary to enhance the skills of our telecommunicators. What isn't used isn't go to waste. So without knowing and for the first time seeing this here tonight at this moment without knowing exactly what we spent last year and this is a gauge that we used to anticipate what we're going to spend next year it's hard to support any kind of any kind of decrease. Thank you. Please call the roll. This is to take 4,000 out of the training schools for the telecommunicators. Kittleson. Manny. Meyer. Montemayor. Radke. Segali. Stefan. Susha. Van Akron. Vanderwheel. Bowman. Deberg. Eberg. Serda. Davis. Gruff. Four eyes and 12 nos. Motion fails. Alderman Susha. Thank you Mr. Mayor. I'd like to attempt to make a motion to remove $10,000 from the public safety over time. That would be from Cost Center 201130 expenditure number 510103. Is there a second motion and a second under discussion? Alderman Segali. He won out Deputy Chief Weiss to talk to us. Deputy Chief Weiss. Thank you. Thank you Your Honor. I don't have. It's coming. Thank you. I don't have that Cost Center. I'm not exactly sure what that overtime is for. If somebody can explain to me what were that. Pardon. The 35,000. Okay. Actually we've got vacancies in there. And some of that is the result of those vacancies. We have to have coverage. We're 24 hours a day and there's times when the dispatch center is extremely busy and there's times when there's a lull. And we try to schedule people in accordance with the historic need.  We have to call somebody in. There's no spares. So what happens is the shift commanders will start calling telecommunicators and ask them to give up their day off and come in and contractually that's time and a half. So we're basically running as lean as we can. And over time is the result of filling in where it's necessary. I have to compliment our shift commanders. They do an excellent job of trying to only use what's necessary. We have one person in a dispatch room that can get real busy in a hurry. And all of a sudden you're inundated. Remember those people are calling, okay. They're not calling to say hi. There's something that's really important going on in their life. And the last thing you want is phone ringing off the hook. It really reflects on the city. I don't think we want to go that way. Okay. There's a motion to take 10 from 35,000. Please call the roll. Manny. No. Meyer. Aye. Montemayor. Aye. Radke. No. No. Sagalli. No. Stefan. No. Sousha. Aye. Van Akron. No. Vanderweel. No. Bauman. No. Dieberg. No. Eberg. No. Serta. No. Davis. No. Graf. No. And Kittleson. No. No. Three eyes, 13 no's. Motion fails. Alderman Sousha. Thank you. I'd like to make a motion to remove $11,000 from the criminal investigation over time, which would be cost center 2-0-1-2-0-0 expenditure number 5-1-0-1-0-3. There's a motion to second to remove $11,000 from the budget at amount of $53,000 under discussion. Alderman Sagalli. Thank you, Mr. Meyer. Can we have Deputy Chief Plays discuss this? Yes, Deputy. Thank you. Thank you. Thank you. I certainly wish we could do that. I just wish I could just say go ahead and take $11,000. Just Thanksgiving Day holiday, we had an attempt at homicide where an individual ran, deliberately ran over another person. I had to get two detectives at a bare minimum, one on each shift to work with the patrol division and come in on a holiday to handle this. We can't control in criminal investigation. We can't control what crimes come in and when they come in. Had that incident occurred the day before, there'd been no problem. It would have been handled with detectives that were on duty, and we wouldn't have had to pay any overtime. When it happens on a holiday, well, holiday, you have to pay extra. It's a contractual obligation. Some years, our overtime as far as calling in detectives for major crimes is low. That's just the way it happened. Some years, it's high. A few years back, we had four homicides in the city in one year. So over time, if it happens when the detectives are off, we have to call them in. We don't have 24-hour-a-day detectives. We have two shifts, skeleton crew on the weekend. That's just because we don't want to pay the overtime. But when something happens, major crime, in we come. And we work until we solve it as best we can. How much we spent last year is directly correlated with the crimes that come in. And so where we're at this year, I can't tell you, but we're probably going to use that up. And if we don't, it goes back in the general fund. So hopefully, we won't need it. Thank you. Paula Massuscio. Thank you, Mr. Mayor. In the first six months of the year, this line item spent about $20,000. And in 2004, the actual amount spent was $40,000. So next year, they won $53,000. Just doing the math, considering they spent $20,000 in the first six months. And that last year, they spent $40,000. I'm not comfortable upping them to $53,000. And that's primarily why the motion was to reduce $11,000 from this account. Thank you. Thank you. Oh, many? Thank you, Your Honor. Question. For your scheduling, is there no detective regularly scheduled on weekends? Are they only Monday through Friday, folks? No, there is a detective working the day shift and the night shift, one detective each Saturday. And of course, that detective is on call for Sunday. And those are not overtime hours for those people? No, the Saturday is not overtime. If you're called in on a Sunday, that's overtime. Thank you, everyone. Okay, please call the roll. This is to reduce $11,000 out of the criminal investigation overtime. Meyer? Montemayor? Aye. Radke? Aye. Segali? No. Stefan? Aye. Sushia? Aye. Van Akron? No. Vanderweel? No. Bauman? No. Dberg? No. Eberg? No. Aye. Serda? No. Davis? Groff? Aye. Kittleson? No. Manny? No. Nine Ayes, Seven Noes. Motion carries. Alderman Sushia? Thank you, Mr. Mayor. I'm going to skip item number seven on here and go to item number eight and make a motion to decrease the fleet division maintenance by $6,000 in cost center 201140 expenditure number 520201. And that motion will be to reduce $29,006 budget by $6,000. Leaving a balance of $23,000 under discussion. There's a motion and a second under discussion. Alderman Segali? Thank you, Mr. Mayor. Could you please explain the fleet division? Are you speaking of squad cars or what are you speaking of? Okay. May I ask FDT for you? Yes, please. Alderman. Thank you. Thank you. Had I known this was going to be brought up I would have had our fleet maintenance manager here. If anything is happening costs are going up, not down. I don't understand why we would have a reduction in the need for maintenance. This did the general increase alone, you know, based on inflation and cost. Again, I would I would be against any reduction in that. Thank you. Alderman Sushia? Thank you, Mr. Mayor. When you look at the first six months of expenditure in this line item only $7,000 was spent. And if you were to double that it would appear that this year they will spend approximately $14,000 on maintenance. When they come out with the budget they also give you an estimated expense for 2005. Their estimated expense is $23,000 for this year. And originally they asked for $27,000 for this year. So they've already decreased it by $4,000 with what they originally asked for last year. And looking at how much they've spent in the first six months this year. They've already decreased that by $4,000. So, you know, to go up to $29,000 next year just doesn't make sense. And that's why the motion was made to remove $6,000 from this budget. Okay. Please call the roll. Okay. This is Theresa with $6,000 out of the maintenance fleet division. Montemay or? Radke. Segali. Stefan. Sushia. Van Akron. No. Vanderweel. No. Bowman. Dieberg. No. Eberg. No. Serda. No. Davis. Aye. Graf. Kittlesen. No. Manny. Yes. And Meyer. Seven Ayes and nine Noes. Motion fails. Hallerman Sushia. Thank you, Mr. Mayor. I'd like to make a motion to remove $50,000 from the fire department's overtime costs under number 202-100, expenditure 5103. Is there a second? Second. Motion to the second. Under discussion. Chief, Zair, would you please come up? I believe you will have some questions, sir. Thank you. Hallerman Sushia, under discussion. Do you not? Oh, sir. You hit the money. Is that accidental? No, I have a statement. Okay. Just to justify what's going on. This year it looks like their overtime was $20,000. They're asking for an increase of $63,000 to bring next year's request up to $84,000. Chief, Zair? Thank you, Mayor Perez. Hallerman Sushia's comments here are somewhat correct about what it says in the budget for last year, but in the budget for last year, knowing that we were in a crunch for staffing to avoid laying off three firefighters and to save three jobs, the overtime account was cut from the $104,000 that was requested down to $20,810. That $20,000 is approximately our liability under federal law for the Fair Labor Standards Act. So basically left us at zero to operate for overtime. But knowing that it was happening last year, as you know, trying to operate within the budget and try to do the best job we can in the fire department, we carried over $23,000 and $34,000 from last year. We went thinner at the end last year, tried to avoid some of the overtime and some of the calling at the end of the year. We also threw out the year from within our own budget, made transfers of $55,800 when people left, new hires came in into the overtime account. Really, we operated under $78,834 last year of overtime money. The proposal before you now, which started at a request of this year, the request was to be at $98,000, was cut to make my budget by $13,866. Our actual liability under the Fair Labor Standards Act is probably close to $90,000. We're lucky that the firefighters take time off when the staffing occurs, not to create overtime. But the law states that for every hour, the firefighter works over 53 hours a week, which they work 56. We're liable for an hour and a half overtime for every hour that they work. Our liability is there for that exposure. It never comes to that exposure, but it is there. The exposure usually is somewhere between $15,000 and $20,000. And that's what was approved for last year, the liability. As you know, this last year, we've had, I think, five or six call-ins of major fires in the country village in other areas, where we've had a call in 12 firefighters. Didn't have the money. We had to make transfers from within our department. We don't have that availability to make those transfers this year. By running so thin, as we did with three firefighters less, we kept the budget. We didn't come back and ask for money, but we operated under the budget that was approved, and I guess that's what I'm asking for you. As the chief of the department, we've been operating efficiently under the budget. I need the money to operate the future. The commitment of this council three years ago and two years ago and last year, when we built a new fire station, our commitment from the fire department was we will run that station with the present people and the present equipment. That's what this budget provides, with the commitment you made to me and to the community three years ago, two years ago and this year. We need this to operate the budget for next year. Thank you. Thank you. Okay. Please call the roll. This would be $50,000 out for the fire services over time. Radki. Sugali. Stefan. Sushia. Van Akron. Vanderweel. Bowman. D. Berg. E. Berg. Serda. Davis. Graf. Kittlesen. Manny. Meyer. And Montemayor. Three ayes, 13 noes. Motion fails. Alderman. Sushia. Thank you, Mr. Meyer. I had, well, the motion is to remove $100,000 from the vehicle depreciation account in the fleet division of the police department, cost center 2-0-1-1-4-0 expenditure number 64-1-1-9-9. Is there a second? Second. Under discussion. Alderman Sugali. Thank you, Mr. Meyer. I'd like to have Deputy Chief Weiss speak because it is concerning the depreciation of the squads. 14 noes up. Which Deputy Chief Weiss? Thank you. Step up. Thank you. Which Alderman Steffen, can you explain at which one it is? Thank you. Okay. This might be a serious mistake if you take that kind of money out of that depreciation account, I believe. We're in a situation where we maintain the squads for three years instead of two. That, by the way, was one of the increases in that vehicle maintenance account. Obviously, everybody knows that the longer you keep the vehicles, the more expensive it is to repair them into things that normally would hold out for two years, give way at three years. This is such a drastic number. I can't help thinking that we're going to cut ourselves short and we're going to have to clump that money again later. Again, without having the fleet maintenance manager here to explain this, certainly would be against that kind of money being pulled out of a budget. I would hardly think that we're that over-budgeted for the squad car. Okay. Alderman Sousha. Thank you, Mr. Meyer. I do agree that we need to have the vehicle depreciation. What I had wanted to do this morning was transfer the money from the Incinerator Fund directly to the General Fund, but I found out you can't do that at this meeting. What I was told is that we can do a budget transfer next week to transfer $100,000 from the Incinerator Fund to reinstate this line item. But it's more of a procedural step because everybody knows we do need new squad cars next year. There's no doubt about it. So we're not taking it out of the budget. It's not coming from the taxpayers. This is a way of utilizing the money that's left over in the Incinerator Account. And actually this morning, I thought that number was $180,000. And as the day went on, I found out that it's actually only $100,000. So it's just more of a procedural way of utilizing that money and bringing the tax rate down. And that'll put the money right back afterwards. Alderman Stephan. Thank you, Your Honor. I guess I won't speak on the merits of the depreciation because I think we all agree we need that. I'm concerned about the budget transfer of $100,000, I think Alden Berg mentioned earlier, that we have a looming liability out there in our arbitration contracts. And I understand that police and fire have kind of been lyrical about hiring people because why would you want to hire somebody, bring them in from out of state, out of town, just to lay them off sometime next year if we lose the arbitration contracts. I've been talking to Rich Kevhard about possible sources of money. One I thought of was the land sale we're working on. And certainly this $100,000 would be something that I think, in my mind, would be better put to take care of that upcoming liability because I and I know most of the Alderman, there's going to be some liability there. I know Rich wants to comment on it, but we're funded for the one and a half percent from last year. We know, you know, that we're not going to end up with that. I guess I'd rather see this money available for that use to keep our departments at full staff than to, you know, use it here. Thank you. Okay, please call the roll. Okay, this is to take $100,000 out of the fleet division vehicle depreciation. Segali. No. Stefan. No. Sushia. Then Akron. No. Vanderweal. No. Bauman. Deberg. No. Eberg. No. Serta. No. Davis. No. Graf. No. Kittleson. No. Manny. Meyer. Aye. Montemayor. Aye. Ratke. Aye. That's it. Four ayes, 12 noes. Motion fails. Alderman Sushia. Thank you. My last motion would be to decrease, I'll actually eliminate 34 of the 39 parking stalls, which would decrease the budget $11,016. There's a second under discussion. Alderman Segali. Thank you, Mr. Meyer. If I'm not mistaken, please correct me if I am. Isn't parking part of their, in their contract a contractual matter that they have parking in, like you talk about the public works, etc., things like this, or am I all mistaken by that? I believe some of it is. I'm not sure if this is part of it, Rich. Is this parking as part of their contractual? It's probably mainly non-represented. Non-represented. Meaning it's not. Alderman Sushia. Actually, I have learned that there is actually a waiting list in the parking department for some of these spots. So the city would not lose any revenue if we were to release these spots. And the first person who would have an option to buy this person is currently parking there. I've also spoken to transit, and I asked about the question of free bus rides to and from work for city employees. Right now it's in the transit union contract that transit employees and their family can ride the bus for free whenever they want. And I was told that that's definitely a possibility, that the city employees could take the bus to work at no charge if we choose to follow that in the future. And the city would possibly qualify for a job access and reverse commute grant down the road. So I think that by eliminating these we'll bring the tax rate down, and also we would actually save the employees money because they could hop on the bus and they wouldn't have to pay for their own gas to come down the city hall. But of course, the large number of city employees that live all the time probably wouldn't be able to utilize the bus and have to pay for their own parking spot after the first of the year. Alderman Vanderweel. Thank you, Your Honor. I need to know what five people will still have parking stalls, and what are the consequences of taking away 34 parking spots if any, whoever can answer it. Who can answer that question? Mr. McAddle? As Alderman Sushia mentioned, there is a waiting list for a number of those stalls. So if the council did decide to act on that, my guess is they would be rented out because parking is at a premium in the downtown area. So again, if the council decides to act on that, I'm sure we can overcome that. Alderman Sushia. Thank you, Mr. Mayor. I would leave it up to the Mayor's discretion as to who would get those five stalls, probably for positions that would require a car to be here because the position needs to come and go throughout the day, such as building inspection. But for the majority of administrative positions where you come here and you stay all day, there wouldn't be necessarily a need for you to have a parking spot on site. Alderman, Ben Akron. Thank you, Your Honor. Is there a seven-street parking over there on Penavela? Is that a premium? On 7th Street? Actually, there are stalls that we lease out on 7th and 9th Street, and there are some stalls available.  Thank you. Alderman Ratke. Thank you, Your Honor. One more question for Mr. McDonald. If I may, last week I was at the transit meeting, and you guys come up with a new park and ride program or such for the hospital, I believe it was he discussed.  Would that make it more, these spots around here more of a premium? I think the, what happened at the last meeting of the transit commission, there was a number of stalls rented out, about a hundred of them, and those were primarily in lots that were underutilized. One was on St. Clair Avenue and a couple other right off of Niagara, and so those were less used, but the lots in question, where the employees are parking, are at a premium. There are a lot of people trying to get into it, whether it's employees or business owners, those stalls in the immediate central downtown area are at a premium. Thank you, Mr. McLean. I thank you, Your Honor. I don't know if anybody can answer this question, but I'm not sure where this is coming from. I know in my budget, I've budgeted for four parking stalls for next year. Typically in the past, it had been two for myself and my assistant, but because the council and the salary and grievance committee had approved making payments for the non-reps for parking, that included my two secretaries who were non-reps, so budgeted for four parking stalls. I'm not sure who's getting eliminated from paid parking, the 34 out of the 39, like I say, I budgeted for four stalls, and I assume a bunch of the other administrative departments did too. I can appreciate Alderman Sushi's comment that the mayor could decide who gets the four, I guess, but it's kind of ironic that the council just approved that in the past maybe two months ago to allow that, and the first time we're putting it in the budget for next year, the proposal is to take it out. Thank you. Alderman Serta. I'll refrain from my comment. Thank you. Okay, thank you, Mr. McDonnell. Mr. Holton, I believe you may have some comments regarding that, sir. Thank you. Please come up. Thank you, Mr. Mayor and Council. As far as the job descriptions in our inspectors and the senior engineer tech and engineer tech, they're required to have vehicles on the job to use for inspection. And I don't know if that's right, they're required to have vehicles and they have to pay them for the parking spots. I know they build inspections the same way with four, five, maybe six inspectors there, they're required to have their vehicles on site. Okay, thank you. Okay, please call the roll. This is to eliminate $11,000 and $16 from, to eliminate 34 of the 39 parking stalls. Stefan. Sushia. Van Akron. Vanderweel. Bauman. Deberg. Eberg. Serta. Davis. Graf. Kittleson. Manny. Meyer. Montemayor. Racky. Segali. Five eyes, 11 nose. Motion fails. Alderman Graf. Thank you, Your Honor. I'd like to make a motion based on overtime again and going back to the police overtime. Alderman Sushia had proposed to eliminate approximately $71,000 worth of overtime. Of that $11,000 was approved, but I believe that we have to be able to work smarter, and one way to do that is to eliminate some of the overtime that is in the police department right now. So my motion at this time would be to reduce account 201, 120, 510, 103 from the patrol division overtime by $25,000 to bring that current budget down to $200,000. There's a motion in the second. If everybody will please look at your little sheet here. The third one down, patrol division overtime. The original motion was to reduce $50,000. This motion now calls for a reduction of $25,000 instead, leaving the amount of $200,000. And there was a second. Any discussion? Call the roll. Sushia. Hi. Van Akron. Van Derweel. Bowman. Deberg. No. Eberg. Serda. Davis. No. Groff. Aye. Kittlesen. No. Manny. Meyer. Aye. Montemayor. Aye. Radke. Aye. Segali. No. And Stefan. 8-8. Hi. Motion carries. Anything else? Alderman Groff. Thank you, Your Honor. Then at this time I'd move that the resolution we put upon its passage as amended. Is there a second? Second. Any discussion? Alderman Racky. What's my vote? Okay. Alderman Sushia. Thank you, Mr. Mayor. I just wanted to thank you for trimming $2 million from the budget before it even came to us. I'm really glad that you cut $2 million out. But I failed in my attempt to reduce it by another $300,000 tonight. So I will not be able to support this because I can't increase the tax rate on the taxpayers. Thank you. Alderman Stefan. Thank you, Your Honor. I guess at this time I'd like to go back to my original question. How much did we cut tonight? And is the balance of that going into the contingency fund or are we lowering our limit again? Lowering. No, it was more than that. I'm sorry. Rich. Which is this one? Thank you. Mr. Gabbard. Excuse me. I'm trying to get this to add all the changes for tonight. We have a net of an increase of $33,637 in the general fund budget. The general fund budget would now stand at $33,752,554 which is an increase from last year 672,296 or a 2% increase. Again, that's in the general fund budget. If you'd like any other on the levy, whatever I can give that to you. Alderman Stefan. So we're not at that top limit. The changes we made brought it down is what I wanted to make sure. Yeah, okay. Yes, instead of adding $70,000, we have a net of $33,000. Which is acceptable. Okay. Please call the roll. Oh, I'm sorry. Alderman Manning. Thank you. Before we vote, I would just like to speak a word on behalf of the library, even though I will be supporting the budget as currently structured. Simply want to note that decreased support for the library in 2006 is a deep concern for me and certainly for others who value the library and who serve on the library board. I want to be very clear also that costs in the library have been under control and have been reduced by approaching 30% over the last 10 plus years. At the same time, the library has done some significant things. This year just let me point out with the latest statistics done by an accountant with whom I am familiar and she shared these detailed analyses with me. Library service in 05 to date and with projections will cut the unit cost per service by about 5%. In addition, circulation will be increasing at the end of 2005 by about 7%. With the cuts that are in place now for 06, there will be cuts in library personnel, which means service, especially of those personnel who have resource capabilities and expertise. My argument would be that the library is as important as fire and police long-term. Long-term libraries are an essential aspect for the good of a free and enlightened society. And I think we need to look at the library in that way. The library staff and the library board and others will be looking at possibilities of further program extension perhaps by putting together a volunteer program of service. Ours will not be cut in 2006. Staffing levels will be, which means that people coming in with information needs might not well be serviced at that point in time when they come in. I would suggest that long-term the strongest way we can go as a society is to encourage our state legislators to change the law to establish municipal libraries in such a way that they will be their own political and economic entities. With elected board members accountable directly to their constituencies, they therein set the tax rate for the library services as established. It encourages accountability. It puts service directly to the individual with the dollar's cost. And I would say that the library today is an incredible value. If I didn't have a library available to me free, I would pay vastly more today than I do for that service. I would vote that way with a library entity as a political entity. And I think we, if we establish a law along those lines, will then be able to provide the service in the community that we and majority in that community so desire. So please speak to your legislators. Encourage them with library legislation that would change current legislation so they can move ahead and have a much more direct and accountable and fully funded library service in the future. Thank you very much. Thank you all very much. Okay. Let's pass the budget. All right. Van Akron. Hi. Vanderwheel. Hi. Bowman. Hi. D. Berg. Hi. E. Berg. Hi. Serta. Hi. Davis. Hi. Groff. Hi. Kittleson. Hi. Manny. Hi. Meyer. Hi. Montemayor. Hi. Radke. Hi. Segali. Hi. Stefan. Hi. And Sushia. No. No. 15 ayes, one no. Motion carries. Is there a second? All those in favor?


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Hello students. In the previous lecture, we set out to develop a differential equation formulation for stochastic phenomena. We started with the Chapman-Colmogorov equation, then developed Taylor expansions, constructed moments and then arrived at a differential equation formulation and that differential equation is actually known as the Fokker-Planck equation. So, the equation we derived is if W is the occupancy probability at space point x and time t, then the equation read dw by dt equal to d by dx of minus u effective which is of course, a function of x could be a function of x, w which is a function of x and t, we are just omitting its arguments plus d which could be a function of x, dw by dx bracket close where u effective of x was defined as u x, where u is the sum drift velocity minus d prime x, where primes denote differentiation with respect to the argument and here the argument is only space point x. So, d prime is basically d by dx. So, this is the effective drift velocity and the dx is the space dependent diffusion coefficient and u x of course, is space dependent actual drift velocity. Just to point out that true or effective drift does include the derivative of diffusion coefficient if the diffusion coefficient is space dependent. So, this is a sometimes very useful when we discuss mass transfer in turbulent fluids etcetera, where near a wall or a boundary the diffusion coefficient in the medium could vary from point to point. However, when both u and d are constant when u equal to constant meaning not a function of x and d also is constant the equation becomes simpler dw by dt will be d by dx of minus uw plus d dw by dx, where now u and these are constant d prime is 0. So, u effective becomes the same as u. So, we can call this family of equation as the Fokker Planck same Planck who discovered the Planck's law of radiation Fokker Planck equation. So, what were the assumptions we made when we arrived at this equation? Basically, we assume that the transition probability in the derivation of FPE FPE means Fokker Planck equation following assumptions are remain. That is the transition probability p at a space point x making a transition by a length xi in a time interval tau had properties such that p d xi equal to 1 xi p d xi which is xi bar this had a property proportional to tau. So, we said this has a property of u which could be a function of x tau and for small tau at least and xi square bar had the property 2 d tau plus of the order of tau square or so or more than tau in any case and higher moments xi to the power n bar they were of the order of tau square or so and higher. With these assumptions we could take the limit we can say specifically for small tau take Taylor expansion limits of tau going to 0 and then we found that all that survives strictly are the only these two terms xi bar and xi square bar that to those containing the coefficients u x and d x. This was illustrated that is such function such transition probability is physical this was illustrated by constructing a Gaussian right. We took the example that this could be realized say p x xi tau for small tau had the property 1 by sigma root 2 pi e to the power minus xi minus let us say some u tau whole square divided by 2 sigma square where sigma square was 2 d tau we assume this form u and d could be functions of x. So, with that we completed the derivation I wish to point out here that the assumption of a Gaussian transition probability was only an illustration, but it is not a necessary situation. One can obtain Fokker Planck equation by considering transition probabilities other than Gaussian functions providing they have moments of at least second order and perhaps higher order also which is better, but at least for us to say a an equation up to second order we need its moment up to second order. Just to illustrate that such a possibility exists let us consider let us consider non Gaussian transition probability when you say Gaussian transition probability what we meant was a function xi having a form like this this is a Gaussian supposing with consider a function let us say p x xi tau through a function such that let us say 1 by sigma phi of xi minus a where phi has some properties we will come to that soon it is a general function where a we stipulate to be u x into tau like earlier it was something like a function which is linearly dependent on tau and sigma is twice square root of 2 d tau supposing we merely have to assume that there exists a scaling function phi where phi has the following properties function phi u has the following property that is phi u is symmetric in u or even function of u it can be a function of mod u for example, not necessarily differentiable at u equal to 0, but it should be integrable such that it should have first of all it should be normalizable let us say 1 then it should be let us keep the domain as minus infinity to infinity then since it is an even function phi u d u will be 0 and it should be possible for us also to insist that u square phi u d u is finite it should be possible to make that finite as unity by tuning the some some constants let us say and higher order moments might exist, but we can even stop at this point then we can proceed exactly through the steps that we have carried out and show that the mean of xi the mean of xi square etcetera have the required tau dependence the phi function in in for example, need not be Gaussian for example, it can be supposing it can be a function like this this is in the u variable it can have a mod u behavior like this maybe an exponential it could be e to the power minus u mod u here. So, same reflected on the left side or it could be even a function on symmetric which is 0 beyond some length it does not matter for moments because we our space which is of course, from minus infinity to infinity. So, we extend the function saying that beyond some length l the probability is 0 this is a function which will have infinite all the moments for example. So, the situation is somewhat analogous to when we started with central limit theorem there is a recurrent there is a recurrent story about central limit theorem in the derivation of the Fokker-Planck equation also. So, long as the function has all these properties we can show that the Chapman-Colmogorov equation necessarily leads to a Fokker-Planck equation of a second order higher order moments will necessarily go to 0 there will be of the order of tau cube and beyond. Just to make sure that we are on the right path let us understand as I mentioned the transition probability expressed in the following form P x xi tau equal to 1 by sigma phi of xi minus a divided by sigma where we note that a is proportional to tau where a equal to u tau and sigma equal to square root of 2 d tau we assume these two properties, but the function is not Gaussian then can very easily see that integral P d xi I am not writing the argument because we know that the argument for our purpose xi is sufficient others are like parameters. So, it is integral is going to be just to carry out 1 by sigma integral xi varying from minus infinity to infinity phi of xi minus a divided by sigma d xi a and sigma are functions of x and tau, but not of xi. So, I can make a transformation to a new variable transform u equal to xi minus a by sigma which implies that I can replace xi through the equation a plus u sigma which means d xi is equal to sigma d u and you can note that integral minus infinity to infinity P d xi is going to be 1 by sigma minus infinity to infinity for the u variable now xi has been replaced with the u variable and that will be phi of the whole thing is u and d xi is sigma d u sigma does not depend on u. So, it is a function of tau and xi, but not on u. So, it cancels out. So, which is integral minus infinity to infinity phi u d u and since the function phi is normalized this will be 1. So, the transition probability is normalized if you take a function generalized function phi similarly you can show that integral minus infinity to infinity xi bar as I mentioned by definition it is xi P which is a function of xi d xi and we work through the same transformation u then we note that it is going to be 1 by sigma which remains there minus infinity to infinity what is xi from the transformation here xi is a plus u sigma. So, we substitute that a plus u sigma here.  So, you write there are two terms here. So, the first one is a is a constant in so far as u variable is concerned.  Hence xi bar is equal to a only and a is nothing but u we get back the relationship that we obtained regardless of the function that we have chosen same way we can confirm ourselves that xi square bar which is by definition xi square p d xi minus infinity to infinity let us work through by substitution. So, we have to go back here. So, wherever xi square comes we are going to replace it with this a plus u sigma whole square and d xi will be sigma d u. So, it is going to be minus infinity to infinity xi square is a plus u sigma whole square p is going to be replaced with phi u now and d xi sigma d u. So, like earlier of course, first sigma cancels and if we expand this there will be three terms one will be a square second will be 2 a sigma and u and the third one will be u square sigma square and this is phi u d u. We can note that the first one will be simply a square here now the first integral is a square and then integral phi u d u we know its unity the second one is going to be 0 because it is multiplied by u and it is an even function multiplied by u integrated over the domain minus infinity to infinity is going to be 0. So, that will be 0 and the third function sigma square will stand out and it will be u square phi d u and we decided to construct phi in such a way that this is constant and we can take it as 1. Since sigma is having a pre factor we can always adjust it in sigma. So, this let us say is equal to 1. So, it will be sigma square plus a square and sigma square we know is 2 d tau 2 d tau and a square is going to be u square tau square. So, it has a term proportional to tau and of the order of tau square and we know that when we take finally, the limit of tau going to 0 the coefficient u square tau square is going to go to 0. So, we can always write it as 2 d tau and a term of the order of tau square which is going to go to 0 when we take the limit. So, the for the operative purposes what matters is the term 2 d tau we can now go like this and show that the higher order terms xi cube and xi to the power n for all n greater than or equal to 3 are going to be at least of the order of tau square and higher in any case may be may be tau to the power 3 by 2 or something, but more than tau. So, that in the limit when tau goes to 0 all those terms are going to vanish higher terms xi to the power n average will be of the order of tau square or so and not of tau. Hence, they will so in the limit tau going to 0 in the limit tau turns to 0 xi to the power n bar by tau will tend to 0 that is the point whereas, other coefficients will survive. The main learning point in this exercise is that as I indicated earlier it is not necessary to only have a Gaussian distribution for deriving the Schaplan Walker Planck equation from the Chapman Kolmogorov equation just like we made a statement in central limit theorem that regardless of the original distribution after certain number of samples the mean tends to a Gaussian. We have not arrived at a Gaussian solution yet, but we arrived at a differential equation formulation. Later we see why this is very important this statement because the differential equation formulation is a restrictive formulation which basically implies transition probabilities with the at least second moment. On the other hand the Chapman Kolmogorov equation is a much more general equation of transition probabilities which could address problems where these transition probabilities may not even have moments they may only be normalized. We will soon come to that clarification. So, having come to this point we now discuss certain solutions to the Fokker Planck equation. So, let us do some solutions simple solutions most of which basically we are revisiting the random walk problem straight away from the differential formulation solutions to Fokker Planck equation. When we discuss the random walk problem on a real line we started with the simplest problem of a walker starting from a point with the equal probabilities to the left or right that is called the unbiased or symmetric random walk and we had exact solutions and we even showed that in the asymptotic limit that goes to a Gaussian. We are basically now going to confirm that Gaussian distribution that we obtained directly by solving the differential equation that is the Fokker Planck equation. The side benefit of this exercise is that it also helps us to understand more about the method of Fourier transforms in handling linear differential equations partial differential equations. We do this exercise in the next lecture. Thank you.


At Audiology Associates of Prestonsburg, you can live your life the way you want and find the freedom of better hearing. You'll experience patient care that is specific to you with exceptional follow-up care that ensures your hearing and balance needs are being met. Audiology Associates at 1428 Northlake Drive in Prestonsburg. 25 years after the elk restoration program began, the Kentucky Department of Fish and Wildlife has opened applications for their annual elk hunt drawing, which began in 2001. Our elk herd is a precious resource that we have been fortunate enough to have back into the Commonwealth of Kentucky. You know, right around the middle 1800s, we've seen these elk leave and in 1997, we've seen the first elk hit the ground back in Kentucky as free-ranging, free-roaming animals. Elk is a native species to Kentucky and has few natural predators, but were wiped out in the 1800s due to overhunting and habitat loss. We were able to, you know, put together a plan in the early 1990s, the Kentucky Department of Fish and Wildlife was, and then with other organizations like the Rocky Mountain Elk Foundation, other state agencies from the West, you know, along with the National Wild Turkey Ferrations, a lot of organizations were able to bring those elk back to Kentucky in a re-introduction program. These elk were here flourishing and doing very well. They were wiped out and then they were brought back. In accordance with the Kentucky Department of Fish and Wildlife's conservation plan, the elk were reintroduced into a 16-county region in southeastern Kentucky known as the Elk Restoration Zone. Within that zone, you know, we have a carrying capacity just like with any wildlife species. So through conservation management, one big part of that with big game species, of course, is a regulated hunting season.  Applications are open until April 30th and there are 594 permits available. For more information or to apply for a hunting permit, visit ky.gov. For Mountain Top News, I'm Brianna Robinson.