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Apr
16
answered Polynomial identity for a sum
Apr
15
comment Polynomial identity for a sum
Thanks for the prompt attempt. To me it doesn't seem correct, because $f(x)^j$ will have all possible products of $j-$coefficients of f(x). Whereas, the polynomial $r(x)$ in my question does not have this structure.
Apr
15
asked Polynomial identity for a sum
Mar
24
comment Trace of a product of a recursive series of non-full rank matrices
According to en.wikipedia.org/wiki/Hadamard_product_(matrices) we can say: $\text{Tr}(P_n) = \sum_{i,j}[P_0]_{i,j}[P_{(n-1)}]_{i,j}$, i.e, an element-wise product of $P_0$ and $P_{(n-1)}$, but I am interested if it can be some function of the rank of $H$ or $n$ ?
Mar
24
comment Trace of a product of a recursive series of non-full rank matrices
Addition: $\text{Tr}(P_n) = \text{Tr}(P^T_0 P_{n-1})$ by cyclic property of trace.
Mar
24
asked Trace of a product of a recursive series of non-full rank matrices
Mar
15
comment Solving an overdetermined system of inequalities using null-space arguments
I mean element-vise inequalities. Sorry, I skipped to mention it as I thought it was implicit.
Mar
15
asked Solving an overdetermined system of inequalities using null-space arguments
Mar
7
asked Lower bound on diophantine system of inequalities with all but one non-linear constraint
Jan
28
comment Unknown result in probability theory relating CDF of any density to the CDF of normal distribution
I meant that, in the above case, $\Phi(x)$ is the CDF of a normal distribution with mean 0 and variance 1. I was asking how the mean and variance values depend on the particular CDF function $A(z)$.
Jan
28
asked Unknown result in probability theory relating CDF of any density to the CDF of normal distribution
Jan
26
awarded  Commentator
Jan
26
comment Upper Bounding an exponential integral with complex terms
But that is true for the case where there is no $i$ (the first integral), but it still converges. Is there a contour method to solve this integral. I'm aware that for functions which have simple poles, a contour integral method can be used to compute the integral.
Jan
26
revised Upper Bounding an exponential integral with complex terms
added 7 characters in body
Jan
26
asked Upper Bounding an exponential integral with complex terms
Dec
12
comment Upperbound on the number of Isolated zeros of a bivariate polynomial
However, this pdf arxiv.org/pdf/1102.5391.pdf seems quite helpful.
Dec
12
comment Upperbound on the number of Isolated zeros of a bivariate polynomial
@GerryMyerson Sorry, I didn't get why the function must have a minimum or a maximum at a zero ? I thought it could be increasing/decreasing or the zero can be an inflection point. But maybe I am missing the main point here.
Dec
11
comment Isolation of zeros in the case of univariate analytic functions expressed as a bivariate function.
Suppose L(v,p(v)) is a bivariate polynomial of degree n in variables {v,p(v)} , we know the number of zero curves of it are bounded by a quadratic function of its degree, say M(n). Can we use that information and claim to bound the number of zeros of L(v) also by M(n) ?
Dec
11
comment Isolation of zeros in the case of univariate analytic functions expressed as a bivariate function.
@RobertIsrael What I did was first to consider all the zeros of L(v,p) : these will, in general, be curves on the v-p plane. Then I consider the points at which the curve p=f(v) intersects these zero curves. These intersecting points would be zeros of L(v,p(v)). However, can it happen that p=f(v) itself is one of the zero curves ? (In which case the zeros of L(v,p(v)) would not be isolated.) Sorry if I seem to be confusing.
Dec
11
awarded  Tumbleweed