Bulletin of Iranian Mathematical Society
Volume:42 Issue: 4, 2016

In this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the Cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um upsint. Our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete Riemannian manifold floating in space RN햩 is tangent to the space RN at ∂H0(t); (2)the surface u = u(x,t) is tangent to the hyperplane W(t) at ∂Hu(t).

ýRecentlyý, ýsome techniques such as adding whiskers and attaching graphs to vertices of a given graphý, ýhave been proposed for constructing a new vertex decomposable graphý. ýIn this paperý, ýwe present a new method for constructing vertex decomposable graphsý. ýThen we use this construction to generalize the result due to Cook and Nagelý.

This study concerns with a trust-region-based method for solving unconstrained optimization problems. The approach takes the advantages of the compact limited memory BFGS updating formula together with an appropriate adaptive radius strategy. In our approach, the adaptive technique leads us to decrease the number of subproblems solving, while utilizing the structure of limited memory quasi-Newton formulas helps to handle large-scale problems. Theoretical analysis indicates that the new approach preserves the global convergence to a first-order stationary point under classical assumptions. Moreover, the superlinear and the quadratic convergence rates are also established under suitable conditions. Preliminary numerical experiments show the effectiveness of the proposed approach for solving large-scale unconstrained optimization problems.

In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces (M,g) and (M,g˜) of a K\"ahler-Norden manifold (M¯¯¯¯¯,J¯¯¯,g¯¯¯,g˜¯¯¯) of constant totally real sectional curvatures ν¯¯¯ and ν˜¯¯¯ (g and g˜ are the induced metrics on M by the Norden metrics g¯¯¯ and g˜¯¯¯, respectively). We obtain a condition for ν˜¯¯¯ (resp. ν¯¯¯) which is equivalent to each of the following conditions: (M,g) (resp.(M,g˜)) is locally symmetric, semi-symmetric, Ricci semi-symmetric and almost Einstein. We construct an example of a totally umbilical radical transversal lightlike hypersurface, which is locally symmetric, semi-symmetric, Ricci semi-symmetric and almost Einstein.

ýIn this short noteý, ýwe present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropyý, ý{\em Mathý. ýInequalý. ýAppl.}ý ý{18} (2015)ý, ýnoý. ý2ý, ý401--406]ý. ýMeanwhileý, ýwe also show some new lower and upper bounds for relative operator entropy and Tsallis relative operator entropy.

Let M be an R-module and 0neqfinM∗=rmHom(M,R). We associate an undirected graph gf to M in which non-zero elements x and y of M are adjacent provided that xf(y)=0 or yf(x)=0. We observe that over a commutative ring R, gf is connected and diam(gf)leq3. Moreover, if Gamma(M) contains a cycle, then mboxgr(gf)leq4. Furthermore if |gf|geq1, then gf is finite if and only if M is finite. Also if gf=emptyset, then f is monomorphism (the converse is true if R is a domain). If M is either a free module with rmrank(M)geq2 or a non-finitely generated projective module there exists finM∗ with rmrad(gf)=1 and rmdiam(gf)leq2. We prove that for a domain R the chromatic number and the clique number of gf are equal.

We introduce center-like subsets Z*(R,f), Z**(R,f) and Z1(R,f), where R is a ring and f is a map from R to R. For f a derivation or a non-identity epimorphism and R a suitably-chosen prime or semiprime ring, we prove that these sets coincide with the center of R.

For two given graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G2. Let Tn denote a tree of order n and Wm a wheel of order m. To the best of our knowledge, only R(Tn,Wm) with small wheels are known. In this paper, we show that R(Tn,Wm)=3n-2 for odd m with n>756m^{10}.

In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk. Upper bounds for the second and third coefficients of functions in this subclass are founded. Our results, which are presented in this paper, generalize and improve those in related works of several earlier authors.

We investigate the relative cohomology and relative homology theories of F -Gorenstein modules, consider the relations between classical and F -Gorenstein (co)homology theories.

In this paper, Heir-equations method is applied to investigate nonclassical symmetries and new solutions of the Black-Scholes equation. Nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

Let (R,P) be a Noetherian unique factorization do- main (UFD) and M be a finitely generated R-module. Let I(M) be the first nonzero Fitting ideal of M and the order of M, denoted ord_R(M), be the largest integer n such that I(M) ⊆ P^n. In this paper, we show that if M is a module of order one, then either M is isomorphic with direct sum of a free module and a cyclic module or M is isomorphic with a special module represented in the text. We also assert some properties of M while ord_R(M) = 2.

It is known that the condition mathfrakReleftzf′(z)/f(z)right>0 , |z|

Let R be an associative ring and let M be a left R-module. Let SpecR(M) be the collection of all prime submodules of M (equipped with classical Zariski topology). There is a conjecture which says that every irreducible closed subset of SpecR(M) has a generic point. In this article we give an affirmative answer to this conjecture and show that if M has a Noetherian spectrum, then SpecR(M) is a spectral space.

Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule C, C--perfect complexes have the ability to detect when a ring is strongly regular. It is shown that there exists a class of modules which admit minimal resolutions of C--projective modules.

The study of stability problems of functional equations was motivated by a question of S.M. Ulam asked in 1940. The first result giving answer to this question is due to D.H. Hyers. Subsequently, his result was extended and generalized in several ways. We prove some hyperstability results for the equation
g(ax)(cx)=Ag(x)(y)
on restricted domain. Namely, we show, under some weak natural assumptions, that functions satisfying the above equation approximately (in some sense) must be actually solutions to it.

The concept of mathscrFst -fundamentality is introduced in uniform spaces, generated by some filter mathscrF. Its equivalence to the concept of mathscrF -convergence in uniform spaces is proved. This convergence generalizes many kinds of convergence, including the well-known statistical convergence.

In this paper, we show how certain metabelian groups can be found within polynomial evaluation groupoids. We show that every finite abelian group can be obtained as a polynomial evaluation groupoid.

An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingular R-modules; (3)absolutely coneat modules are strongly noncosingular if and only if R is a right Max-ring and injective modules are strongly noncosingular; (4) a commutative ring R is semisimple if and only if the class of injective modules coincides with the class of strongly noncosingular R-modules.

Let TX be the full transformation semigroups on the set X. For an equivalence E on X, let TE(X) = {α ∈ TX : ∀(x, y) ∈ E ⇔ (xα, yα) ∈ E} It is known that TE(X) is a subsemigroup of TX. In this paper, we discuss the Green's *-relations, certain *-ideal and certain Rees quotient semigroup for TE(X).