Polynomials and spatial Pick-type theorems

Pick's theorem about the area of a simple lattice planar polygon has many extensions and generalizations even in the planar case. The theorem has also higher-dimensional generalizations, which are not as commonly known as the 2-dimensional case. The aim of the paper is, on one hand, to give a few new higher-dimensional generalizations of Pick's theorem and, on the other hand, collect known ones. We also study some relationships between lattice points in a lattice polyhedron which lead to some new Pick-type formulae. Another purpose of this paper is to pose several problems related to the subject of higher-dimensional Pick-type theorems. We hope that the paper may popularize the idea of determining the volume of a lattice polyhedron P by reading information contained in a lattice and the tiling of the space generated by the lattice.     

Sasaki projections

We collect, correct, and extend results on the properties of the Sasaki projection in orthomodular lattices. We bring arguments as to why this operation can extend tools for simplification of formulas and automated computing.     

链与链竞争下闭环供应链中制造商纵向整合策略选择

基于链与链竞争情形下,探讨了闭环供应链中制造商纵向整合策略选择。以制造商单位生产成本为基准,发现制造商不仅有动机整合正向物流或逆向物流,而且整合正向物流总是有利于增加其闭环供应链利润。若存在规模不经济,虽然制造商同样有动机整合正向物流或逆向物流,但是整合正向物流时闭环供应链利润是否高于其整合逆向物流取决于规模不经济系数。规模不经济系数较小时,制造商整合正向物流时闭环供应链利润高于其整合逆向物流;反之,制造商整合正向物流时闭环供应链利润低于其整合逆向物流。     

Jets of line bundles on curves and Wronskians

We collect a few results about jets of line bundles on curves and Wronskians, with a special emphasis to those arising from the canonical involution of a hyperelliptic curve.     

Multistep Methods for Conservative Problems

We discuss the use of linear multistep methods for the solution of conservative (in particular Hamiltonian) problems. Despite the lack of good results concerning their behaviour, linear multistep methods have been satisfactorily used by researchers in applicative fields. We try to elucidate the requirements that a linear multistep method should fulfill in order to be suitable for the integration of such problems, relating our analysis to their use as boundary value methods. We collect a number of results obtained for the linear autonomous case and also consider some numerical tests on the Kepler problem.Work supported by GNCS and MIUR.     

Image data analysis and classification in marketing

Nowadays, the diffusion of smartphones, tablet computers, and other multipurpose equipment with high-speed Internet access makes new data types available for data analysis and classification in marketing. So, e.g., it is now possible to collect images/snaps, music, or videos instead of ratings. With appropriate algorithms and software at hand, a marketing researcher could simply group or classify respondents according to the content of uploaded images/snaps, music, or videos. However, appropriate algorithms and software are sparsely known in marketing research up to now. The paper tries to close this gap. Algorithms and software from computer science are presented, adapted and applied to data analysis and classification in marketing. The new SPSS-like software package IMADAC is introduced.     

Algebraic topology of special Lagrangian manifolds

In this paper, we prove various results on the topology of the Grassmannian of oriented 3-planes in Euclidean 6-space and compute its cohomology ring. We give self-contained proofs. These spaces come up when studying submanifolds of manifolds with calibrated geometries. We collect these results here for the sake of completeness. As applications of our algebraic topological study we present some results on special Lagrangian-free embeddings of surfaces and 3-manifolds into the Euclidean 4 and 6-space.     

Modularity and Total Ellipticity of Some Multiple Series of Hypergeometric Type

We collect some new evidence for the validity of the conjecture that every totally elliptic hypergeometric series is modular invariant and briefly discuss a generalization of such series to Riemann surfaces of arbitrary genus.     

On essential variables of dual operations and the consequences for operations

We investigate essential variables of dual operations (or co-operations) in a rather general category-theoretic setting. During this investigation, we collect some results about the essential arities and arity gaps of dual operations in concrete categories. Afterwards, we use duality theory to show that this approach and the obtained results can also be beneficial for questions regarding essential variables of operations on sets.     

Problems and conjectures concerning connectivity, paths, trees and cycles in tournament-like digraphs

In this paper we collect a substantial number of challenging open problems and conjectures on connectivity, paths, trees and cycles in tournaments and classes of digraphs which contain tournaments as a subclass. The list is by no means exhaustive but is meant to show that the area has a large number of interesting open problems. We also mention problems for general digraphs when they are relevant in the context.     

A collection of results on Hamiltonian cycle systems with a nice automorphism group

We collect some old and new results on Hamiltonian cycle systems of the complete graph (or the complete graph minus a 1-factor) having an automorphism group that satisfies specific properties.     

Local time stepping and discontinuous Galerkin methods for symmetric first order hyperbolic systems

We present a new non-conforming space-time mesh refinement method for the symmetric first order hyperbolic system. This method is based on the one hand on the use of a conservative higher order discontinuous Galerkin approximation for space discretization and a finite difference scheme in time, on the other hand on appropriate discrete transmission conditions between the grids. We use a discrete energy technique to drive the construction of the matching procedure between the grids and guarantee the stability of the method.     

A Survey on Recent Results of the Mathematical Seminar in Perugia, inspired by the Work of Professor P.L. Butzer

Here we give a survey on recent results in approximation theory obtained by a group of mathematicians of the University of Perugia, inspired by the work of Professor Butzer. We collect some results concerning linear integral operators in various settings.     

Necessary and sufficient conditions for the two-weight weak type maximal inequality in Orlicz class

Czechoslovak Mathematical Journal - We collect known and prove new necessary and sufficient conditions for the weighted weak type maximal inequality of the form $${\Phi _1}(\lambda)\varrho (\{x \in...     

Computable upper bounds for the constants in Poincaré‐type inequalities for fields of bounded deformation

We collect various Poincaré‐type inequalities valid for fields of bounded deformation and give explicit upper bounds for the constants being involved. Copyright © 2011 John Wiley & Sons, Ltd.     

A note on the Weber location problem

In this note, we collect some interesting and useful results about the Weber problem. We investigate an accelerated Weiszfeld procedure which increases the step size and find a formula for the step size that empirically produces the fastest convergence rate. We also derive an estimate for the optimal cost of the system.     

Controlling monotonicity of nonlinear operators

Controlling the monotonicity and growth of Leray–Lions’ operators including the $p$-Laplacian plays a fundamental role in the theory of existence and regularity of solutions to second order nonlinear PDEs. We collect, correct, and supply known estimates including the discussion on the constants. Moreover, we provide a comprehensive treatment of related results for operators with Orlicz growth. We pay special attention to exposition of the proofs and the use of elementary arguments.     

Method of limiting equations for the stability analysis of equations with infinite delay in the Carathéodory conditions: I

We consider systems of nonautonomous nonlinear differential equations with infinite delay. We introduce Carathéodory type conditions for the right-hand side in an equation, which permit one, on the one hand, to cover a fairly broad class of systems and, on the other hand, include the right-hand side in a compact function space and construct the so-called limiting equations. In the investigation, we use the construction of admissible spaces with fading memory, which permits one to obtain constructive results for the class of equations under study.     

Improved seed methods for symmetric positive definite linear equations with multiple right‐hand sides

We consider symmetric positive definite systems of linear equations with multiple right‐hand sides. The seed conjugate gradient (CG) method solves one right‐hand side with the CG method and simultaneously projects over the Krylov subspace thus developed for the other right‐hand sides. Then the next system is solved and used to seed the remaining ones. Rounding error in the CG method limits how much the seeding can improve convergence. We propose three changes to the seed CG method: only the first right‐hand side is used for seeding, this system is solved past convergence, and the roundoff error is controlled with some reorthogonalization. We will show that results are actually better with only one seeding, even in the case of related right‐hand sides. Controlling rounding error gives the potential for rapid convergence for the second and subsequent right‐hand sides. Polynomial preconditioning can help reduce storage needed for reorthogonalization. The new seed methods are applied to examples including matrices from quantum chromodynamics. Copyright © 2013 John Wiley & Sons, Ltd.