Homological determination of Γ-modules

It is proved that if M is a profinitely generated -module which is free as a module over the ring of p-adic integers, then M is determined up to free direct factors by its homology. This result generalizes the theorem on homological determinacy of p-adic representations of a cyclic group [Ref. Zh. Mat., 3A, 318 (1971)].Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeieniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 64, pp. 104–126, 1976.     

Limiting angles of Γ-martingales

Suppose that M is a complete, simply connected Riemannian manifold of non-positive sectional curvature with dimension m≥ 3 and that, outside a fixed compact set, the sectional curvatures are bounded above by −c ₁/{r ² ln r} and below by −c ₂ r ², where c ₁ and c ₂ are two positive constants and r is the geodesic distance from a fixed point. We show that, when κ≥ 1 satisfies certain conditions, the angular part of a κ-quasi-conformal Γ-martingale on M tends to a limit as time tends to infinity and the closure of the support of the distribution of this limit is the entire sphere at infinity. This improves both a result of Le for Brownian motion and also results concerning the non-existence of κ-quasi-conformal harmonic maps from certain types of Riemannian manifolds into M. Received: 19 September 1997     

Fuzzy generalized Bi-ideals of Γ-semigroups

In this paper, we introduce the concept of fuzzy generalized bi-ideal of a ??-semigroup, which is an extension of the concept of a fuzzy bi-ideal of a ??-semigroup and characterize regular ??-semigroups in terms of fuzzy generalized biideals.     

Some properties of Γ-limits of integral functionals

Summary We prove some integral representation theorems for the Γ limit in L¹ of sequences of the form dx in coercivity and bounded growth hypothesis which are optimal as it is checked with examples. These results are utilized to describe the L¹ lower semicontinuous envelope of a given functional. We consider also the stability of Γ limits with respect to obstacle type perturbations and prove the homogenization formulas in conditions more generals of those already considered by several authors. Entrata in Redazione il 10 gennaio 1978.     

Study on the Structure of Γ-Semihypergroups

In this article, we study Γ-semihypergroups introduced recently. We introduce the hyper versions of Green's relations in Γ-semihypergroups and give some related characterizations. We introduce the n-prime Γ-hyperideal and n-semiprime Γ-hyperideal of a Γ-semihypergroup and show that for any integer n ≥ 2, n-prime Γ-hyperideals are a generalization of prime Γ-ideals. We also give the relationship between n-prime Γ-hyperideals and Γ-hyperideal extensions in Γ-semihypergroups. Then, we deal with prime ideal and introduce the notion of prime radical in a Γ-semihypergroup M, and also, we obtain some results and relations among the prime radicals of M and S, where S is the left operator semihypergroup of M.     

Special radicals of near-rings and Γ-near-rings

It was previously shown that every special radical classR of rings induces a special radical class R of -rings. Amongst the special radical classes of near-rings, there are some, called the -special radical classes, which induce, special radical classes of -near-rings by the same procedure as used in the ring case. The -special radicals of near-rings possess very strong hereditary properties. In particular, this leads to some new results for the equiprime andI ₃ radicals.     

On the Operator Semirings of a Γ-Semiring

In this paper we introduce the notion of operator semirings of a -semiring to study -semirings. It is shown that the lattices of all left (right) ideals (two-sided ideals) of a -semiring and its right (respectively left) operator semiring are isomorphic. This has many applications to characterize various -semirings.AMS Subject Classification (2000): 16Y60, 16Y99     

Invariants of an augmentation of Γ0(n)

Let G _n ^× be the 2-group of primary factors of a positive integer n and fix a direct product decomposition of this group. We define an augmentation of Γ₀(n) based on G _n ^×, paralleling augmentations used by Fricke, Cohn and Knopp, and others. Using the decomposition of G _n ^×, we then define a family of functions based on η-functions and use these functions to construct invariants of the augmented group. Along with proving results analogous to those of Cohn and Knopp, we make a complete determination of the multiplier systems for these new functions.     

Linearized Elasticity as Γ-Limit of Finite Elasticity

Linearized elastic energies are derived from rescaled nonlinear energies by means of Γ-convergence. For Dirichlet and mixed boundary value problems in a Lipschitz domain Ω, the convergence of minimizers takes place in the weak topology of H ¹(Ω,R ⁿ ) and in the strong topology of W ^1,q (Ω,R ⁿ ) for 1≤q<2.     

Study of Noetherian Γ-Semirings via Operator Semirings

In this paper we study Noetherian -semirings and obtain Cohens theorem for a special class of -semirings. Weak primary decomposition theorem for a particular type of -semirings is also obtained.Presently Lecturer in Mathematics, University of Burdwan, GOLAPBAG, W.B. INDIA.     

EQUIPRIME Γ-NEAR-RINGS

Abstract

Equiprime and strongly equiprime near-rings were recently defined by the present authors, together with S. Veldsman. In the present paper, the concepts are introduced for Γ-near-rings, and give rise to Kurosh- Amitsur radicals. If M is a Γ-near-ring and L is its left operator near-ring, then R(L)⁺ = R(M), where R(—) in both cases denotes either the equiprime or the strongly equiprime radical.     

On Γ−-convergence of functionals with analytic integrand

Sunto Si dimostra, sotto opportune ipotesi l'analiticità dell'integrando del ^–-limite di una successione di funzionali semplici del C.d.V. ad integrando analitico.

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This work has been performed as a part of a National Research Project supported by M.P.I. (40% 1987).     

Homogenization of Random Fractional Obstacle Problems via Γ-Convergence

We show that solutions to the viscous conservation laws in several space dimensions converge to rarefactions as time tends to infinity, when the initial data belongs to some large global class of functions. The convergence takes place in, and in L^p(RxK), where K is compact in Rn–1, and we determine the asymptotic rate.     

Hereditary uniform property Γ

We study the uniform property Γ for separable simple C^*-algebras which have quasitraces and may not be exact. We show that a stably finite separable simple C^*-algebra A with the strict comparison and uniform property Γ has tracial approximate oscillation zero and stable rank one. Moreover in this case,its hereditary C^*-subalgebras also have a version of uniform property Γ. If a separable non-elementary simple amenable C^*-algebra A with strict compariso...     

On Γ-limit classes of perturbations defined by integral conditions

For the coefficients of linear differential systems, we consider classes of piecewise continuous perturbations that are infinitesimal in mean on the positive half-line with some positive piecewise continuous weight belonging to a given set. We obtain sufficient conditions for such a class to be Γ-limit, i.e., to admit the computation of a reachable upper bound of the exponents of linear differential systems with perturbations in that class by a formula similar to the well-known formulas for the central and exponential exponents.     

The Reissner-Mindlin plate is the Γ-limit of Cosserat elasticity

The linear Reissner-Mindlin membrane-bending plate model is the rigorous Γ-limit for zero thickness of a linear isotropic Cosserat bulk model with symmetric curvature. For this result we use the natural nonlinear scaling for the displacements u and the linear scaling for the infinitesimal microrotations Ā ∈ so(3) affecting the in-plane drill rotations. No boundary conditions on the microrotations are prescribed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A class of hyperrings connected to preordered generalized Γ-rings

In this paper, we define the notion of preordered weak $\Gamma$-rings as a generalization of the concept of $\Gamma$-rings, the basic properties of prime ideals in weak $\Gamma$-rings are developed. At the end we construct a class of hyperrings in the sense of Rota from weak $\Gamma$-rings and also a connection between morphisms of the weak $\Gamma$-rings and the morphism of associated weak $\Gamma$-hyperrings has been investigated.