It is well-known that the number of non-crossing perfect matchings of 2k points in convex position in the plane is Ck, the kth Catalan number. Garćıa, Noy, and Tejel proved in 2000 that for any set of 2k points in general position, the number of such matchings is at least Ck. We show that the equality holds only for sets of points in convex position, and for one exceptional configuration of 6 p...

Given a set of n points P in the plane, each colored with one of the t given colors, a color-spanning set S ⊂ P is a subset of t points with distinct colors. The minimum diameter color-spanning set (MDCS) is a color-spanning set whose diameter is minimum (among all color-spanning sets of P ). Somehow symmetrically, the largest closest pair color-spanning set (LCPCS) is a color-spanning set whos...

background: the dosimetric performance of eclipse 6.5 three dimensional treatment planning system (3dtps) is evaluated by comparing the calculated and measured dose in two dimensions following the guide lines of american association for physicists in medicine task group 53. materials and methods: the calculations were performed by the 3dtps for symmetric as well as asymmetric fields for standar...

The pre-Schwarzianand Schwarzian derivatives of analytic functions f are defined in U, where U is the open unit disk. pre-Schwarzian as well popular tools for studying geometric properties mappings. These can also be used to obtain either necessary or sufficient conditions univalence a function f. Because computational difficulty, norm has received more attention than norm. It applications theo...

The spectra of self-adjoint operators in Krein spaces are known to possess real sectors as well as sectors of pair-wise complex conjugate eigenvalues. Transitions from one spectral sector to the other are a rather generic feature and they usually occur at exceptional points of square root branching type. For certain parameter configurations two or more such exceptional points may happen to coal...

A condition for a statistical manifold to have an equiaffine structure is studied. The facts that dual flatness and conjugate symmetry of a statistical manifold are sufficient conditions for a statistical manifold to have an equiaffine structure were obtained in [2] and [3]. In this paper, a fact that a statistical manifold, which is conjugate Ricci-symmetric, has an equiaffine structure is giv...

In late 50th E. Wigner studied the moments of N N random symmetric matrices whose entries are independent identically distributed real random variables [Wig55]. He observed that if the law of these variables is symmetric, then after certain normalization, the leading contribution to the 2k-th moment M N 2k as N ∞ is described by the set of simple random walks of 2k steps in the upper half-plane...

A square array whose all rows and columns are different permutations of the same length over symbol set is known as a Latin square. may or not be symmetric. For classification enumeration purposes, symmetric, non-symmetric, conjugate totally symmetric squares play vital roles. This article discusses Eigenproblem non-symmetric in well max-plus algebra. By defining certain vector corresponding to...

We show that higher order intergroup covariances involving even number of qubits are necessarily positive semidefinite for N-qubit separable states, which are completely symmetric under permutations of the qubits. This identification leads to a family of sufficient conditions of inseparability based on the negativity of 2kth order intergroup covariance matrices (2k</=N) of symmetric N-qubit sys...