Examples concerning absolute flatness and amalgamation in pomonoids

Flatness properties of acts over monoids have been studied for almost four decades and a substantial literature is now available on the subject. Analogous research dealing with partially ordered monoids acting on posets was begun in the 1980s in two papers by S.M. Fakhruddin, and, after a dormancy period of some 20 years, has recently been rekindled with the appearance of several research articles. In comparing flatness properties of S-acts and S-posets, it has been noted that the imposition of order results in severe restrictions as far as absolute flatness is concerned. For example, whereas every inverse monoid is absolutely flat (meaning all of its left and right acts are flat), even the three-element chain in its natural order, considered as a pomonoid, fails to have this property. It has long been understood that absolutely flat monoids, in particular, inverse monoids, are amalgamation bases in the class of all monoids. The purpose of the present article is to further investigate absolute flatness of pomonoids and to begin to study its connection with amalgamation in that context. T.E. Hall’s results, that amalgamation bases in the class of all monoids have the so-called representation extension property (REP), which in turn implies the right congruence extension property, are first adapted to the ordered context. A detailed study of the compatible orders (of which there are exactly 13) on the three-element chain semilattice U then reveals a wide range of possibilities: exactly four of these orders render U absolutely flat as a pomonoid, two more give it the right order-congruence extension property in every extension (RCEP) (but fail to make it an amalgamation base because of the failure of the ordered analogue of (REP)), and for the remaining seven, even (RCEP) fails.     

Consistent Numerical Schemes for Solving Nonlinear Inverse Source Problems with Gradient-Type Algorithms and Newton–Kantorovich Methods

In this paper, algorithms of solving an inverse source problem for systems of production–destruction equations are considered. Numerical schemes that are consistent to satisfy Lagrange’s identity for solving direct and adjoint problems are constructed. With the help of adjoint equations, a sensitivity operator with a discrete analog is constructed. It links perturbations of the measured values with those of the sought-for model parameters. This operator transforms the inverse problem to a quasilinear system of equations and allows applying Newton–Kantorovich methods to it. A numerical comparison of gradient algorithms based on consistent and inconsistent numerical schemes and a Newton–Kantorovich algorithm applied to solving an inverse source problem for a nonlinear Lorenz model is done.     

A Note On the Existence of Consistent Estimatein the Simple Regression Model

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Criterion for π-supersolvability for finite groups

It is proved that the class of finite -supersolvable groups is precisely the class of all finite -solvable groups with the following property: For each maximal subgroup M of a -solvable group G with index p for some p , there exists a cyclic subgroup S of order p ( ) such that G = MS and S commutes with each element of the Sylow system _M of the subgroup M.Translated from Matematicheskie Zametki, vol. 52, No. 1, pp. 57–61, July, 1992.     

Instruction for Soliciting Contributions for English Edition

1. Applied Mathematics—A Journal of Chinese Universities is a nationwide magazine spon-sored by Zhejiang University. The Journal aims to issuing academic works in Applied Mathematics:original theoretical and (or) methodological research results, and innovative applications in practicalfields. Besides, reviews referring to progressive developments are also welcome. The Journal ispublished quarterly and distributed domestically and overseas.     

Instruction for Soliciting Contributions for English Edition

1. Applied Mathematics—A Journal of Chinese Universities is a nationwide magazine spon-sored by Zhejiang University. The Journal aims to issuing academic works in Applied Mathematics:original theoretical and (or) methodological research results, and innovative applications in practicalfields. Besides, reviews referring to progressive developments arc also welcome. The Journal ispublished quarterly and distributed domestically and overseas.     

Topologies on the n-Element Set Consistent with Topologies Close to Discrete on an (n−1)-Element Set

Ukrainian Mathematical Journal - Topologies on a finite set are described by a nondecreasing sequence of nonnegative integers (vector of topologies). We study T0-topologies on the n-element set...     

Interior Estimates for the First-Order Differences for Finite-Difference Approximations for Elliptic Bellman’s Equations

We establish interior estimates for the first-order finite differences of solutions of finite-difference approximations for uniformly elliptic Bellman’s equations.     

Information for Authors

Science in China Series A: Mathematics, a mathematical journal cosponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China, and published by Science in China Press, is committed to publishing high-quality, original results in both basic and applied research.Science in China Series A: Mathematics is published in both print and electronic forms. It is indexed by Science Citation Index.     

Information for Authors

Science in China Series A:Mathematics,a mathematical journal cosponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China,and published by Science in China Press,is committed to publishing high-quality,original results in both basic and applied research. Science in China Series A:Mathematics is published in both print and electronic forms.It is indexed by Science Citation Index. Categories of articles:     

Information for Authors

Science in China Series A:Mathematics,a mathematical journal cosponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China,and published by Science in China Press,is committed to publishing high-quality,original results in both basic and applied research. Science in China Series A:Mathematics is published in both print and electronic forms.It is indexed by Science Citation Index. Categories of articles:     

Information for Authors

Science in China Series A: Mathematics, a mathematical journal cosponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China, and published by Science in China Press, is committed to publishing high-quality, original results in both basic and applied research. Science in China Series A: Mathematics is published in both print and electronic forms. It is indexed by Science Citation Index.     

Guide for Authors

Scope The aim of ACTA MATHEMATICA SCIENTIA is to present to the specialized readers (from the level of a graduate student and upward) important,novel achievements in the areas of mathematical sciences. The Journal considers for publication of original research (expository) papers in all areas related to the frontier branches of mathematics with other science and technology.     

Information for authors

Science in China Series A:Mathematics,a Peer re- view mathematical journal cosponsored by the Chi- nese Academy of Sciences and the National Natural Science Foundation of China,and published by Sci- ence in China Press and Springer,is committed to publishing high-quality,original results in both basic and applied research. Science in China Series A:Mathematics is published monthly in both print and electronic forms.It is indexed by SC1-CD,Chemical Abstracts Service,Personal Alert.Current Contents.CompuMath Citation Index.     

Information for authors

Science in China Series A:Mathematics,a peer review mathematical journal cosponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China,and published by Science in China Press and Springer,is committed to publishing high-quality,original results in both basic and applied research.     

Guide for Authors

Scope The aim of ACTA MATHEMATICA SCIENTIA is to present to the specialized readers(from the level of a graduate student and up- ward)important,novel achievements in the areas of mathematical sciences.The Journal considers for publication of original research(ex- pository)papers in all areas related to the frontier branches of mathematics with other science and technology.