Concave compositions are ordered partitions whose parts are decreasing towards a central part. We study the distribution modulo a of the number of concave compositions. Let c(n) be the number of concave compositions of n having even length. It is easy to see that c(n) is even for all n 1. Refining this fact, we prove that #{n < X : c(n) ⌘ 0 (mod 4)} p X and also that for every a > 2 and at leas...

We establish the existence of solutions to Cauchy problem for a large class nonlinear parabolic equations including fractional semilinear equations, higher-order and viscous Hamilton–Jacobi by using majorant kernel introduced in Ishige et al. (2020).

We study the expected volume of random polytopes generated by taking convex hull independent identically distributed points from a given distribution. show that for log-concave distributions supported on bodies, we need at least exponentially many (in dimension) samples to be significant and super-exponentially suffice concave measures when their parameter concavity is positive.

We give exact estimations of certain weighted L-norms of the k-th derivative of polynomials which have a curved majorant. They are all obtained as applications of special quadrature formulae.

We examine the Concave Topology Capacity and Flow Assignment (TCFA) problem. Only two algorithms in the literature are appropriate for solving TCFA problems with concave link cost functions: Kleinrock and Gerla’s Concave Branch Elimination (CBE) procedure, [26][20], and a greedy link elimination procedure developed by Gersht [21]. However, neither works well in practice. The CBE procedure does ...

In this paper, we study the approximation and estimation of s-concave densities via Rényi divergence. We first show that the approximation of a probability measure Q by an s-concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [Ann. Statist.38 (2010) 2998-3027] if and only if Q admits full-dimensional support and a first moment. We also show c...

In this work, we propose a novel and robust method for the accurate separation of elliptical overlapped nuclei in microscopic images. The method is based on both the information provided by the global boundary of the nuclei cluster and the detection of concavity points along this boundary. The number of the nuclei and the area of each nucleus included in the cluster are estimated automatically ...

Raw cow milk has short supply market in summer and over supply in winter, which causes consumers and dairy industry concern about the quality of raw milk whether is adulated with reconstituted milk (powdered milk). This study prepared 307 raw cow milk samples with various adulteration ratios 0%, 2%, 5%, 10%, 20%, 30%, 50%, 75%, and 100% of powdered milk. Least square support vector machine (LS-...

We consider a convex variational problem related to a time-step problem in elasto-plastic models with isotropic hardening. Our goal it to derive a posteriori error estimate of the difference between the exact solution and any function in the admissible (energy) class of the problem considered. The estimates are obtained by a advanced version of the variational approach earlier used for linear b...