Mathematics

Let us work in the [math]\mathbb{Z}_{2}[/math] graded category. A Loday algebra is a "crippled" or "wonky" Lie algebra. That is it satisfies the bracket satisfies the Jacobi identity, but is not skew symmetric. An interesting question is if there exists a homotopy version. I suspect that one can consider "crippled" [math]L_{\infty}[/math] -algebras. So, a series of brackets that satisfy higher Jacobi identities, but do not have a symmetry property. Any body seen anything like that? A differential over such an algebra would also be straight forward to define. I myself have defined notions of a differential [math]L_{\infty}[/math]-algebra and a differen…

i accidentally erased my memory and deleted all my orginal programs, those that came with it. is there a way to get them back without having to download them agian?

Hi everybody. I want to find suitable range for four parameters: x(1), x(2), x(3) and x(4); in a way that: 326.705<x(1)*x(2)*(1+x(4))^2*(1-x(4))*x(3)^3<378.29 What should i do? Is there any way to find the answer by MATLAB?

So recently I was watching a movie (I'll not specify which in the interest of avoiding spoilers) where a character claims she'll curse another character's name until the day she dies, and then the character dies that same day. I know it sounds pedantic as all hell, but it got me wondering whether what she said was technically true. For the word "until" to be applicable in a discrete context, would more than one day have to be involved, or would one-day intervals also count? More generally, would "until" have to include the end date in the interval? I'm going to leave this thread open to other words as well, in case others are wondering about how other words' m…

is it a dependence between d ( diagonal of square from equal of area of circle ) to r ( ray of this circle ) d / r pi * r ^ 2, pi * sqrt(2) ^ 2, d = sqrt(2) * d ( for third value ) ....

For those who haven't used a rubix cube there are certain patterns you simply cannot achieve, for example if you flip exactly 1 corner to the right or left, either by taking it out or by simply twisting it you can not solve it without either twisting it back or twisting all other corners relative to it, or you can turn all but one other corner in different directions and then be able to solve it. Or you can turn all of the corners and try to solve it and you will only have one corner turned wrong. I can not figure out the math behind this. Can someone explain if you can.

6 balls are drawn from a total of 49 balls randomly. Order does not matter, as long as 6 balls are matched, first prize is won, what is the probability of winning the first prize? Another question is horse racing. For certain three matches, which may have 10 to 14 horses in total, different horses may have different conditions and abilities so the winning odds of each horse may not be as simple as 1/10 or 1/14. You choose three horses from each of the three matches so you are choosing 9 horses in total, if all 9 horses in three matches finish for the 1st, 2nd and 3rd place, order isn't counted, i.e. ABC, ACB, BAC, BCA, CAB, CBA don't matter.), then you win the jackpo…

When does the generic equation of the 2nd degree not represent a conic section or does it always represent a conic section (unless it has no possible solutions in real numbers)? The other topic I would like like to devote this thread to is families (or sometime called pencils) of conics. [math] C_1 + \lambda C_2 = 0 [/math] represents the zero sets of the family of conics passing through the intersection points of conics [math] c_1 and c_2 [/math] please note that [math]\lambda[/math] is a parameter and assumes all possible real values. [math] C_1 + C_2 = 0 [/math] is the same as the logical operation of this must satisfy both [math] C_1 AND C_2 = 0[/math].howe…

The camera is always oriented in a way that lower border of HFOV (horizontal field of view) is aligned with bottom side of the object. Dimension of the object for reference camera tilt angle are given as well as contour area of this object on image plane. Parameters of camera (fields of view, focal length) are also known. Is it possible to calculate new changed contour area on image plane when camera tilt angle is changed (due to changing object distance or/and camera height)? I would be grateful if someone could point me to methods of calculations applicable here. I have found such method as camera transform using pinhole camera model to represent object…

I have watched a video about the p-adic numbers: Then, there is the Ramanujan's summation which is used in quantum mechanics (Casimir effect): 1+2+3+4+5+6...=-1/12 https://en.wikiversity.org/wiki/Quantum_mechanics/Casimir_effect_in_one_dimension This forum does not support Latex maths? Then, we have one more such summation: 1+x+x*x+x*x*x+x*x*x*x+x*x*x*x*x...=-1/(1-x) This is simple for x<1 and for x>1 we get: 1+2+4+8+16+32+64...=-1 1+10+100+1000+10000...=-1/9 1+20+400+8000+160000...=-1/19 Can we obtain all these sums with the p-adic numbers?

1) what's the difference between: something is supplied by R, given that it fails during the warranty period and something is supplied by R, and it fails during the warranty period ?? 2) What's the definition of conditional probability? the def I found is: This is the probability of an event given (or conditional upon) the occurrence of another event, eg the probability of disease Y given exposure to factor X. can any explain this with a real life example? 3) There are 15 balls, where 8 blue, 7 red. I draw 5 balls, replacing each ball after I draw it. I tell you that four of the five balls were blue. What then is the probability that the first two bal…

I am assuming that since the amount of arrangements possible for a set of elements is equal to the amount of elements within the set to the factorial, that for a matrix it would be the area of the matrix factorial. Is this true?

I have been tearing my hair out over this lol. I am trying to work my holiday (vacation) entitlement out. Can somebody please tell me if I am right? I get 27 days holiday plus the bank holidays (public holidays). My work year is 1st of April to 31st of March. Due to Easter moving about that means this year I get 7 days as bank holidays. In total this year I get 34 days holiday entitlement If I worked full time I would do 7.5 hours per day and work 5 days per week = 37.5 hours per week. 34 holidays days x 7.5 hours a day = 255 hours holiday entitlement. If I was full time every time I take holiday day I would lose …

As the following: Find the maximum value of: (a^2/sinb)*[cos(b-2n)-cosb] express in terms of a and b; where n is varied (find a formula in a and b that is the greatest) In fact, this question is derived from a figure, the topic is compound angles, and I would like to know if there is any way to get the answer more faster and make less error, if yes, how to do so.

Which type of Integral is this?? I want to solve this integral in MATLAB.

Is i - i 0? how do we know that epi*i=0? what would a sigma notation with an upper limit of i look like? Is my "take this with a grain of salt" topic dead?

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Which of these relation on the set of all people are equivalence relation ? Determine the properties of an equivalence relation that the other lack. (1) {(a,b) | a and b are the same age} (2) {(a,b) | a and b have the same parents} (3) {(a,b) | a and b share a common parents} (4) {(a,b) | a and b have met} (5) {(a,b) | a and b speak common language} Appreciate your reply.

1. Disregarding the messier LHS, how can I intuit the simpler RHS? I know [math]\color{green}{\dfrac{1E6}{T} = \Pr(}[/math] winning $1E6 in the Gold Ball Draw). 2. But why multiply this [math]\color{green}{\dfrac{1E6}T}[/math] by [math]\color{red}{\dfrac{69 - B}B}[/math]? 3. What does [math]\color{red}{\dfrac{69 - B}{B}}[/math] mean?

Hi i am doing my dissertattion and have run a GLM repeated measures ANOVA on my data - I know need to perform a Tukey HSD, but cant do it on SPSS so doing it by hand. The problem that I have is that I cant seem to find where the significant difference is. Stats is not my strong suit i am really bad at it. I have a significant difference between condition and between condition*Time Name: Blood Lactate (Cond*Time) Significance = 0.01 K= 12 dfe= 24 (K,dfe) = 6.105 MSE = 0.74 N= 5 HSD = 2.348640394 Works = YES but when i do it for condition it wont work Name: Blood Lactate (Cond) S…

http://img693.imageshack.us/img693/3950/calcw.png http://rapidshare.com/files/325308950/operators.xlsx.html http://www.filehosting.org/file/details/91934/operators.xlsx Above is an image of a spreadsheet and two link to the spreadsheet itself. My thoughts are based on the way that multiply can even if not the most efficient way of performing the calculation can be thought of as repeated add, and power repeated multiplication. Although there are differences beyond that and other calculations just as simple and multiply that don't have names. Columns C and D of the spreadsheet show the descriptions of increment and decrement. Thease add and subtract 1. I do…

Hello everyone In math class, we solved the next problem: How many numbers, composed out of 5 different digits, varying from 0 to 6, can be formed? So we concluded that the number of possibilities = [math]6\cdot 6\cdot 5\cdot 4\cdot 3[/math], excluding 0 as first digit. Conclusion: [math]N=6\cdot V^4_6[/math]. Then, suddenly, something came in my head; as we were working with variation formulas, I wanted to put the number of possibilities in a formula, solely using variation formulas; the first thing that came in my head was: [math]V^5_7-V^4_6[/math] My math teacher did some thinking and accepted my resolution (she said it was also a good solution), my …

Are there any formulas for finding the LCM of at least 2 numbers? All I know is tedious methods which give you a long amount of time of computing (not always? If yes, then what is it? If no then is it still possibe that we can find a formula?

Solve for x in the below: \ ( x⋏2 = 16⋏x \) Systematic procedure required if possible, please.