Functional Inequalities and Hamilton–Jacobi Equations in Geodesic Spaces

We study the connection between the p-Talagrand inequality and the q-logarithmic Sololev inequality for conjugate exponents p ≥ 2, q ≤ 2 in proper geodesic metric spaces. By means of a general Hamilton–Jacobi semigroup we prove that these are equivalent, and moreover equivalent to the hypercontractivity of the Hamilton–Jacobi semigroup. Our results generalize those of Lott and Villani. They can be applied to deduce the p-Talagrand inequality in the sub-Riemannian setting of the Heisenberg group.     

Cameron–Liebler line classes in PG(n,4)

We derive a new existence condition for Cameron–Liebler line classes in \(PG(3,q)\) . As an application, we obtain the characterization of Cameron–Liebler line classes in \(PG(n,4),\,n\ge 3\) .     

Convergence to Stationary Measures in Nonlinear Fokker–Planck–Kolmogorov Equations

The convergence of solutions of nonlinear Fokker–Planck–Kolmogorov equations to stationary solutions is studied. Broad sufficient conditions for convergence in variation with an exponential bound are obtained.     

On Approximate Additive–Quartic and Quadratic–Cubic Functional Equations in Two Variables on Abelian Groups

We establish the generalized Hyers–Ulam stability of the additive–quartic and quadratic–cubic mappings with two variables on abelian groups.     

Solutions to Polynomial Generalized Bers–Vekua Equations in Clifford Analysis

In this paper, we mainly study polynomial generalized Vekua-type equation _boxclose)w=0{p(\mathcal{D})w=0} and polynomial generalized Bers–Vekua equation p(D)w=0{p(\mathcal{\underline{D}})w=0} defined in W ì \mathbbRⁿ⁺¹{\Omega\subset\mathbb{R}^{n+1}} where D{\mathcal{D}} and D{\mathcal{\underline{D}}} mean generalized Vekua-type operator and generalized Bers–Vekua operator, respectively. Using Clifford algebra, we obtain the Fischer-type decomposition theorems for the solutions to these equations including (D-l)^kw=0,(D-l)^kw=0(k ? \mathbbN){\left(\mathcal{D}-\lambda\right)^{k}w=0,\left(\mathcal {\underline{D}}-\lambda\right)^{k}w=0\left(k\in\mathbb{N}\right)} with complex parameter λ as special cases, which derive the Almansi-type decomposition theorems for iterated generalized Bers–Vekua equation and polynomial generalized Cauchy–Riemann equation defined in W ì \mathbbRⁿ⁺¹{\Omega\subset\mathbb{R}^{n+1}}. Making use of the decomposition theorems we give the solutions to polynomial generalized Bers–Vekua equation defined in W ì \mathbbRⁿ⁺¹{\Omega\subset\mathbb{R}^{n+1}} under some conditions. Furthermore we discuss inhomogeneous polynomial generalized Bers–Vekua equation p(D)w=v{p(\mathcal{\underline{D}})w=v} defined in W ì \mathbbRⁿ⁺¹{\Omega\subset\mathbb{R}^{n+1}}, and develop the structure of the solutions to inhomogeneous polynomial generalized Bers–Vekua equation p(D)w=v{p(\mathcal{\underline{D}})w=v} defined in W ì \mathbbRⁿ⁺¹{\Omega\subset\mathbb{R}^{n+1}}.     

A polynomial algorithm for finding (g,f)-colorings orthogonal to stars in bipartite graphs

Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two nonnegative integer-valued functions defined on V(G) such that g(x)≤ f(x) for every vertex x of V(G). A (g. f)-coloring of G is a generalized edge-coloring in which each color appears at each vertex x at least g(x) and at most f(x) times. In this paper a polynomial algorithm to find a (g. f)-coloring of a bipartite graph with some constraints using the minimum number of colors is given. Furthermore, we show that the results in this paper are best possible.     

A survey of generalized goal programming (1970–1982)

This paper provides a survey of the literature on Goal Programming (GP) from 1970 through 1982. Almost 300 references of methodological and applied papers on GP are categorized according to 18 areas of application and according to 12 different variants of GP.     

Construction of Families of Equations to Describe Irregular Solutions in the Fermi–Pasta–Ulam Problem

Doklady Mathematics - The asymptotics of solutions of the spatial distributed chain in the Fermi–Pasta–Ulam problem is considered. Continual families of irregular solutions depending on...     

Using Zionts–Wallenius method to improve estimate of value efficiency in DEA

Halme et al. [M. Halme, T. Joro, P. Korhonen, S. Salo, J. Wallenius, A value efficiency approach to incorporating preference information in data envelopment analysis, Management Science 45 (1) (1999) 103-115] proposed value efficiency analysis as an approach to incorporate preference information in Data Envelopment Analysis (DEA). In this paper, we develop some related concepts, and present a refinement to Halme et al.’s approach to measure value efficiency scores more precisely. For do this, we will introduce an MOLP model which its objective functions are input/output variables subject to the defining constraints of Production Possibility Set (PPS) of DEA models. Then by using the so-called Zionts–Wallenius method, we aid the Decision Maker (DM) in searching for the Most Preferred Solution (MPS) and generating input/output weights as the DM’s underlying value structure about objective functions. Finally, value efficiency scores are calculated by comparing the inefficient units to units having the same value as the MPS.     

Distribution of values of σ2 (n) in residue classes

IntegersN for which ₂ (n has weak uniform distribution (modN) are determined.     

On the Nonexistence of Global Weak Solutions to the Navier–Stokes–Poisson Equations in ℝ N

In this paper we prove nonexistence of stationary weak solutions to the Euler–Poisson equations and the Navier–Stokes–Poisson equations in ? ^N , N ≥ 2, under suitable assumptions of integrability for the density, velocity and the potential of the force field. For the time dependent Euler–Poisson equations we prove nonexistence result assuming additionally temporal asymptotic behavior near infinity of the second moment of density. For a class of time dependent Navier–Stokes–Poisson equations in ? ^N this asymptotic behavior of the density can be proved if we assume the standard energy inequality, and therefore the nonexistence of global weak solution follows from more plausible assumption in this case.     

The generalized Roper-Suffridge extension operator in Banach spaces (Ⅲ)

Suppose that X is a complex Banach space with the norm ||·|| and n is a positive integer with dim X ≥n≥ 2. In this paper,we consider the generalized Roper-Suffridge extension operator Φn,β2,γ2,...,βn+1,γn+1(f) on the domain Ωp1,p2,...,pn+1 defined by     

General approximation schemes for min–max (regret) versions of some (pseudo-)polynomial problems

While the complexity of min–max and min–max regret versions of most classical combinatorial optimization problems has been thoroughly investigated, there are very few studies about their approximation. For a bounded number of scenarios, we establish general approximation schemes which can be used for min–max and min–max regret versions of some polynomial or pseudo-polynomial problems. Applying these schemes to shortest path, minimum spanning tree, minimum weighted perfect matching on planar graphs, and knapsack problems, we obtain fully polynomial-time approximation schemes with better running times than the ones previously presented in the literature.     

Corrigendum to “Global existence of solutions to 2-D Navier–Stokes flow with non-decaying initial data in half-plane” [J. Differential Equations 265 (10) (2018) 5352–5383]

A misuse of notations generates confusion in the statements. It does not influence the proofs that are coherently developed with the right notations.