# Robert Israel

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## Registered User

 Name Robert Israel Member for 2 years Seen 3 hours ago Website Location Vancouver BC Age 62
Associate Professor Emeritus, University of British Columbia, and Optimization Algorithms Researcher, D-Wave Systems, Burnaby BC
 May3 revised Extension of power bounded operators over a finite subspaceadded 1 characters in body May2 accepted Extension of power bounded operators over a finite subspace May2 revised Extension of power bounded operators over a finite subspaceadded 590 characters in body May2 answered Extension of power bounded operators over a finite subspace May1 accepted An Interesting variant of Rayleigh Quotient Apr30 awarded ● Scholar Apr29 accepted On solution of a recursion with rectangular matrices Apr26 awarded ● Student Apr25 asked A regular polytope Apr25 answered What is the effect of adding 1/2 to a continued fraction? Apr25 comment What is the effect of adding 1/2 to a continued fraction?See also Knuth, "The Art of Computer Programming", vol. 2, sec. 4.5.3 ex. 14. Apr23 answered An Interesting variant of Rayleigh Quotient Apr21 answered On solution of a recursion with rectangular matrices Apr19 awarded ● Nice Answer Apr8 comment Distance between poisson points in two disjoint unit discsIntegrate over $x \in D_1$ the area of the intersection of $D_2$ with the disk of radius $r$ about $x$. I doubt that you'll end up with a closed-form expression. Apr6 accepted Is there an analog of determinant for linear operators in infinite dimensions as that of finite dimensions? Apr6 answered Fitting algebraic expression to a number [algorithm] Apr5 accepted Methods for solving two variable recurrence Apr4 answered Distance between poisson points in two disjoint unit discs Apr4 answered Is there an analog of determinant for linear operators in infinite dimensions as that of finite dimensions? Apr3 answered Methods for solving two variable recurrence Apr3 comment Does this matrix shape have a name?@SSra: I don't think you heard about them from me. I don't recall ever writing (or reading) "Bose-Mesner" before. Mar31 comment Does this matrix shape have a name?Looking at en.wikipedia.org/wiki/Bose%E2%80%93Mesner_algebra it appears that Bose-Mesner matrices are somewhat more general: I think you have the case $n=2$. Mar31 comment Does this matrix shape have a name?By the way, for this $n \times n$ matrix to be non-singular you also need $a + (n-1)b \ne 0$. Mar31 comment Iterates converging to a continuous mapBut that counterexample is not the iterates of some $\varphi$. Mar30 answered easter problem - egg shapes Mar25 comment Bounding the second derivative of the log-determinantBy "positive" you mean "positive definite"? Mar24 accepted is there any algebraic function that has a specific relation to transcendental one? Mar24 answered is there any algebraic function that has a specific relation to transcendental one? Mar22 answered eigenvalues of two nonnegative matrices Mar22 revised Possible to find a set of log-concave functions with log-concave sums?added 156 characters in body Mar22 answered Possible to find a set of log-concave functions with log-concave sums? Mar22 revised Software to numerically solve partial differential equationadded 1 characters in body Mar22 answered Software to numerically solve partial differential equation Mar21 answered “Wild” solutions of the heat equation: how to graph them? Mar21 comment “Wild” solutions of the heat equation: how to graph them?That should be $x^{2n}$, not $x^2$. Mar20 awarded ● Good Answer Mar19 accepted TSP, but for all routes not all points Mar19 comment Solid angles of a tetrahedronIn a triangle with two equal angles, the sides opposite these are equal. This is because of symmetry. But a tetrahedron with two equal solid angles need not have any symmetry. Mar18 accepted When are two operators simultaneously diagonalisable? Mar17 answered When are two operators simultaneously diagonalisable? Mar17 answered TSP, but for all routes not all points Mar15 comment Mean minimum distance for N random points on a unit square (plane)I asked Maple to evaluate your quadruple integral numerically. This uses the NAG procedure DCUHRE (TOMS algorithm 698). With the default settings it was unable to obtain the desired accuracy, but with relative error tolerance epsilon $= 10^{-4}$ the result was $.5214059909$. Mar14 awarded ● Yearling Mar13 comment Why to count integers that are relatively prime to their euler function?In general, mathematicians count things because that's what they do. No deeper reason is really required. The fact that in this case there is a connection to group theory, as well as to Carmichael numbers, is a bonus. Mar12 comment Why to count integers that are relatively prime to their euler function?See also oeis.org/A003277 and references there. Mar11 comment Expectation of $(c+e^{N(0,\sigma^2)})^{-n},\, n>0$Another possibility is to use Laplace's method, expanding around the maximum of the integrand $\dfrac{(c+e^x)^{-n}}{\sqrt{2\pi} \sigma} e^{-x^2/(2 \sigma^2)}$, which is at the real root of $(n \sigma^2 + x) e^x + c x$. Mar7 revised modulo of sums of consective powersadded 17 characters in body Mar6 revised modulo of sums of consective powersedited body; added 58 characters in body Mar6 comment modulo of sums of consective powersYes, thanks. I'll edit.