Euclidean 4-Simplices and Invariants of Four-Dimensional Manifolds: II. An Algebraic Complex and Moves 2↔4

We present sequences of linear maps of vector spaces with fixed bases. Each term of a sequence is a linear space of differentials of metric values ascribed to the elements of a simplicial complex determining a triangulation of a manifold. If a sequence is an acyclic complex, then we can construct a manifold invariant using its torsion. We demonstrate this first for three-dimensional manifolds and then construct the part of this program for four-dimensional manifolds pertaining to moves 24.     

H1–L1 Boundedness of Riesz Transforms on Riemannian Manifolds and on Graphs

We prove that the Riesz transforms are bounded from H ¹ to L ¹ on complete Riemannian manifolds and on graphs with the doubling property and the Poincaré inequality.     

Quantitative stability of variational systems: III.ε-approximate solutions

We prove that the-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that the-subgradient mapping is Lipschitz continuous.Research supported in part by the National Science Foundation and the Air Force Office of Scientific Research.     

Markov models of occupational mobility: Theoretical development and empirical support. Part 1: Careers†

This paper, consisting of two parts, presents an analysis of the current state of Markov model , building for intragenerational occupational mobility. Part One examines theories of careers and Part Two theories of continuously operative job systems. Stress is given to the empirical support of the models and to the cumulative development of theory. Among the paper's findings are that several models proposed to span both occupational and geographical mobility have used only migration data; that analytic development is more cumulative for career models; and that there exists a basic divergence of findings from tests of models of careers and continuously operative job systems. In Part One we focus on individual behavior or subaggregates (cohorts).     

Journal of Mathematical Research with Applications Vol.38, No.1–5 Contents

正~~     

Forcing axioms and the continuum hypothesis. Part II: transcending ω 1-sequences of real numbers

The purpose of this article is to prove that the forcing axiom for completely proper forcings is inconsistent with the continuum hypothesis. This answers a longstanding problem of Shelah.     

Striking patterns in natural magic squares’ associated electrostatic potentials: Matrices of the 4th and 5th order

A magic square is a square matrix whereby the sum of any row, column, or any one of the two principal diagonals is equal. A surrogate of this abstract mathematical construct, introduced in 2012 by Fahimi and Jaleh, is the “electrostatic potential (ESP)” that results from treating the matrix elements of the magic square as electric charges. The overarching idea is to characterize patterns associated with these matrices that can possibly be used, in the future, in reverse to generate these squares. This study focuses on squares of order 4 and 5 with 880 and 275,305,224 distinct (irreducible/unique) realizations, respectively. It is shown that characteristic patterns emerge from plots of the ESPs of the matrices representing the studied squares. The electrostatic potentials for natural magic squares exhibit a striking pattern of maxima and minima in all distinct 880 of the 4th order and all distinct 275,305,224 of the 5th order matrices. The minimum values of ESP of Dudeney groups are discussed. Equipotential points and certain constants are found among the ESP sums along horizontal and vertical lines on the square lattice. These findings may help to open a new perspective regarding magic squares unsolved problems. While mathematics often leads discovery in physics, the latter (physics) is used here to detect otherwise invisible patterns in a mathematical object such as magic squares.     

Readjustment of the Paper [J.Kaur and S.S.Bhatia,Integrability and L~1-Convergence of Double Cosine Trigonometric Series,Anal.Theory Appl.,27(1)(2011),pp.32–39.]

In this paper, we show that new modified double cosine trigonometric sums introduced in [1] are inappropriate, the class of double sequences Jd introduced there is unusable for such sums and consequently the results obtained in it are completely incorrect. We here introduce appropriate modified double cosine trigonometric sums making the class Jd usable considering a particular double cosine trigonometric series.     

Maximal subalgebras of rank n −1 of the algebra AP(1, n) and reduction of nonlinear wave equations. I

The concept of canonical decomposition of an arbitrary subalgebra of the algebraAO(1,n) is introduced. With the help of this decomposition all maximal subalgebras L of rankn–1 of the algebraAP(1,n), satisfying the conditionL V=1,...;P _n>, whereV=<P ₀,P ₁,...,P ₁> is the space of translation are described.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1552–1559, November, 1990.