Data loci in algebraic optimization

We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.     

Tachibana-type theorems and special Holonomy

Annals of Global Analysis and Geometry - In the present paper, we consider star-shaped mean convex hypersurfaces of the real, complex and quaternionic hyperbolic space evolving by a class of...     

Yet another way of calculating moments of the Kesten's distribution and its consequences for Catalan numbers and Catalan triangles

We calculate moments of the so-called Kesten distribution by means of the expansion of the denominator of the density of this distribution and then integrate all summands with respect to the semicircle distribution. By comparing this expression with the formulae for the moments of Kesten's distribution obtained by other means, we find identities involving polynomials whose power coefficients are closely related to Catalan numbers, Catalan triangles, binomial coefficients. Finally, as applications of these identities we obtain various interesting relations between the aforementioned numbers, also concerning Lucas, Fibonacci and Fine numbers.     

Hamilton cycles in line graphs of 3-hypergraphs

We prove that every 52-connected line graph of a rank 3 hypergraph is Hamiltonian. This is the first result of this type for hypergraphs of bounded rank other than ordinary graphs.     

两台自私型机器上自私工件排序的PoA紧界

本文研究了两台自私型机器上有自私型工件的关于二元均衡的排序问题。对任意工件序列$L$, 证明了二元均衡排序的PoA的紧界为$\frac{8}{7}$。如果工件尺寸在区间$[1, r](r\ge1)$内, 得到了二元均衡排序的PoA的紧界为关于$r$的分段线性函数。     

Generalized Sidon sets of perfect powers

The Ramanujan Journal - For $$h \ge 2$$ and an infinite set of positive integers A, let $$R_{A,h}(n)$$ denote the number of representations of the positive integer n as the sum of h distinct terms...     

On the convergence of the exponential multiplier method for convex programming

In this paper, we analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalty function in place of the usual quadratic. We also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it uses a logarithmic/entropy proximal term in place of a quadratic. We strengthen substantially the available convergence results for these methods, and we derive the convergence rate of these methods when applied to linear programs.Research supported by the National Science Foundation under Grant DDM-8903385, and the Army Research Office under Grant DAAL03-86-K-0171.     

A numerical method using the Prfer transformation for the calculation of eigenpairs of two-parameter Sturm-Liouville problems

A shooting method for coupled Prfer equations is discussedfor numerical solution of two-parameter Sturm-Liouville problems. Research supported in part by grants from the NSERC of Canada.     

L X-ray emission from fast highly charged Cu ions in collisions with gaseous targets: Saturation effect in excitation and transfer

We have measured L X-ray production cross sections for highly charged 156 MeV Be-like Cu ions in collisions with gaseous targets of H₂, Ne, Ar, Kr and Xe. In the present collision systems, measured projectile L X-ray intensity is contributed by the excitation as well as electron transfer processes. The projectile L X-ray production cross sections are found to increase initially and then saturate with increasing target atomic number. The charge state dependence of projectile L X-ray production cross sections have been measured with Kr target.     

Electrooxidative C–H thiocyanation of hetarenes: voltammetric assessment of thiocyanogen reactivity

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