Description:
Mathematical discussions and pursuits.
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Known integer sequence for series?
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Hi all, can someone tell me if there exists an integer sequence for the following series : I + x + 1/10*I*x^2 - 9/200*I*x^4 + 57/2000*I*x^6 - 1653/80000*I*x^8 + 64467/4000000*I*x^10 - 1052961/80000000*I*x^12 + 8874957/800000000*I*x^14 - 612372033/64000000000*I*x^16 + 5375265623/640000000000*I*x^18 - 478398640447/64000000000000*I* x^20 +... more »
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Yang Mills Paper, Draft of Complete Part I
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I have posted below, a current draft of the Yang Mills paper on which I am presently working: [link] This draft is complete, through the development and integration by parts of a full, Yang-Mills action. This is something of a breakpoint in my... more »
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Covariant and Contravariant
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Hello, all, and while I understand the math behind and use of the above in vector analysis, I can't figure out why vector components are labeled as such. The fact that a vector in space can be represented in space in two ways (via the metric tensor) as either with "contravariant" components and one... more »
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MatheRealism
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...If every real number had an infinite binary sequence representing it, then each one would exist independently of the others, like the four sequences representing the four numbers 0. /\ 0 1 /\ /\ 0 1 0 1 0.00, 0.01, 0.10, 0.11. There can be no doubt that these exist. The infinite binary tree is not large enough to contain all infinite... more »
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Credit Limit Optimization
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I am starting a project with regards to credit limit optimization for a certain lending instrument. Can someone give me some ideas for building an optimization model that will determine how much money to lend out to a particular customer?
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free Worksheet solution
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I first derived the solution to this problem when I was a patient in the mental hospital. Math has always partly been a cornerstone of my mental health. I tested my solution but found it unsuitable, so I went after it again with a vengeance. Now I get the right answer every time. The theory for the solution is at my web site,... more »
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time stamp
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If you have 3 poles of random lengths, this calculates where they will meet to form an irregular pyramid. [link] This is also *part* of the math used for GPS. There are many other factors to consider. transmitter stamp 12:00 at 12:01 receiver transmitter stamp 12:02 at 12:04 receiver... more »
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L2 and dirac delta function as a tempered distribution
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Hi i'm unsure about the following problem: if f(x)=u(x)*exp{-x*alpha} alpha>0 where u(x)is the step function then does f prime (1st derivative wrt x) belong to lebesgue space with p=2 on the real line. f prime is a linear combination of a piecewise function and a tempered distribution. The latter is because the derivative of the step function is the dirac delta function. From wikipedia i know all square integrable functions are tempered distributions but i am wondering whether the converse is true. Any suggestions would be terrific. thanks.... more »
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