Bulletin of The Iranian Mathematical Society最新文献

Thomassen’s chord conjecture from 1976 states that every longest cycle in a 3-connected graph has a chord. This is one of the most important unsolved problems in graph theory. We pose a new conjecture which implies Thomassen’s conjecture. It involves bound vertices in a longest path between two vertices in a k-connected graph. We also give supporting evidence and analyze a special case. The purpose of making this new conjecture is to explore the surroundings of Thomassen’s conjecture.

We develop a complete obstruction theory for the (mathbb {Z}_2)-index of a compact connected 4-dimensional manifold with free involution. This (mathbb {Z}_2)-index, equal to the minimum integer n for which there exists an equivariant map with target the n-sphere with antipodal involution, is computed in two steps using cohomology with twisted coefficients. The key ingredient is a spectral sequence computing twisted cohomology of the orbit space of a free involution on odd complex projective spaces. We illustrate the main results with various examples including computation of the secondary obstruction.

We introduce the concept of Hom-associative algebra structures in Loday–Pirashvili category. The cohomology theory of Hom-associative algebras in this category is studied. Some applications on deformation and abelian extension theory are given. We also introduce the notion of Nijenhuis operators to describe trivial deformations. It is proved that equivalent classes of abelian extensions are one-to-one correspondence to the elements of the second cohomology groups.

In this article, we investigate the higher-order nonsmooth optimality conditions for vector optimization problems with inequality, equality and set constraints in terms of the higher-order Gâteaux derivatives. First, we propose various higher-order Mangasarian–Fromovitz nonsmooth constraint qualifications for such problems. Second, we formulate higher-order KKT-type necessary optimality conditions for the local weak efficient solutions of the nonsmooth vector equilibrium problem with constraints (CVEP) and its special cases. An application of the result to the resources assignment problem with set, inequality, equality constraints is derived. Under some suitable assumptions involving a set constraint, the higher-order nonsmooth necessary optimality conditions become the higher-order sufficient optimality conditions via the higher-order directional/Gâteaux derivatives.

The Surányi–Hickerson conjecture is a long-standing unsolved problem of Diophantine equations. This conjecture states that all the solutions to (ell _1!cdots ell _m!=k!) with (k-ell _mge 2) are ((ell _1,ldots ,ell _m;k)=(6,7;10),(3,5,7;10),(2,5,14;16)) and (2, 3, 3, 7; 9). In this paper, we generalize the Surányi–Hickerson conjecture to (ell _1!cdots ell _m!=k_1!cdots k_n!). We say that a solution ((ell _1,ldots ,ell _m;k_1,ldots ,k_n)) is trivial if there exists a pair (i, j) such that (|ell _i-k_j|=1). As in the Surányi–Hickerson conjecture, we give theoretical and computational results. In particular, we suggest that all non-trivial solutions to the equation (ell _1!ell _2=k_1!k_2!) are ((ell _1,ell _2;k_1,k_2)=(7,13;4,15)), (14, 62; 7, 66) and (22, 54; 18, 57).

We show that the uniform radius of spatial analyticity (sigma (t)) of solutions at time t to the fifth order, KdV-BBM type equation cannot decay faster than (1/ sqrt{t}) for large t, given initial data that is analytic with fixed radius (sigma _0). This improves a recent result by Belayneh, Tegegn and the third author [2], where they obtained a 1/t decay of (sigma (t)) for large time t.

Over Prüfer domains, we characterize idempotent by nilpotent 2-products of (2times 2) matrices. Nilpotents are always such products. We also provide large classes of rings over which every (2times 2) idempotent matrix is such a product. Finally, for (2times 2) matrices over GCD domains, idempotent–nilpotent products which are also nilpotent–idempotent products are characterized.

In this paper we have found a number of commutator formulas between the weighted divergence, the weighted Laplacian, the weighted Lichnerowicz Laplacian and the Lie derivtive on closed orientable gradient Ricci shrinkers, then using them we have generalized a Theorem of Cao and Zhu about the necessary condition for linear stability of a gradient Ricci shrinker. Recentlly they have also extended our results.

Let C(X) be the ring of all continuous real-valued functions on a completely regular Hausdorff space X. A subalgebra A(X) of C(X) is said to be closed under local bounded inversion, briefly an LBI-subalgebra, if for every function f in A(X) that is bounded away from zero on a cozero-set E of X, there exists (gin A(X)) such that (fg|_E=1). In this paper, for an LBI-subalgebra A(X) the compactification (beta _AX) of X which is homeomorphic with the structure space of A(X) is investigated. Some properties of (beta _AX) similar to the counterparts in (beta X) and some main differences between these compactifications are given. Using the compactification (beta _AX), we establish an m-closure formula for ideals in a class of LBI-subalgebras which provides a generalization of m-closure of ideals in intermediate algebras of C(X) and (C_c(X)). We also investigate a characterization of (beta )-ideals for LBI-subalgebras from which it turns out that m-closed ideals coincide with (beta )-ideals in that class of LBI-subalgebras.

We study the Banach algebras (textrm{C}(X, R)) of continuous functions from a compact Hausdorff topological space X to a Banach ring R whose topology is discrete. We prove that the Berkovich spectrum of (textrm{C}(X, R)) is homeomorphic to (zeta (X) times mathscr {M}(R)), where (zeta (X)) is the Banaschewski compactification of X and (mathscr {M}(R)) is the Berkovich spectrum of R. We study how the topology of the spectrum of (textrm{C}(X, R)) is related to the notion of homotopy Zariski open embedding used in derived geometry. We find that the topology of (zeta (X)) can be easily reconstructed from the homotopy Zariski topology associated with (textrm{C}(X, R)). We also prove some results about the existence of Schauder bases on (textrm{C}(X, R)) and a generalization of the Stone–Weierstrass Theorem, under suitable hypotheses on X and R.