In this paper, we consider the T-space structure of the relatively free Grassmann algebra F.sup.(3) without unity over an infinite field of prime and zero characteristic. Our work is focused on ...T-spaces W.sub.n generated by all n-words. A question about connections between W.sub.r and W.sub.n for different natural numbers r and n is investigated. The proved theorem on these connections allows us to construct the diagrams of inclusions that, to some extent, clarify the structure of the algebra: the basic T-spaces produce infinite strictly descending chains of inclusions in the algebra F.sup.(3).
This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient ...algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part.
In connection with the problem of describing holomorphically homogeneous real hypersurfaces in the space ??, we study five-dimensional real Lie algebras realized as algebras of holomorphic vector ...fields on such manifolds. We prove the following assertion: If on a holomorphically homogeneous real hypersurface M of the space ??, there is a decomposable, solvable, five-dimensional Lie algebra of holomorphic vector fields having a full rank near some point P member of M, then this surface is either degenerate near P in the sense of Levy or is a holomorphic image of an affine-homogeneous surface.
In the present paper, we introduce the notion of Csup.*-algebra-valued partial modular metric space satisfying the symmetry property that generalizes partial modular metric space, ...Csup.*-algebra-valued partial metric space, and Csup.*-algebra-valued modular metric space and discuss it with examples. Some fixed point results using (ϕ,MF)-contraction mapping are discussed in such space. In addition, we study the stability of obtained results in the spirit of Ulam and Hyers. As an application, we also provide the existence and uniqueness of the solution for a system of Fredholm integral equations.
Let n≥2 be a fixed integer and A be a Csup.∗-algebra. A permuting n-linear map G:Asup.n→A is known to be symmetric generalized n-derivation if there exists a symmetric n-derivation D:Asup.n→A such ...that G(ςsub.1,ςsub.2,…,ςsub.iςsub.i sup.′,…,ςsub.n)=G(ςsub.1,ςsub.2,…,ςsub.i,…,ςsub.n)ςsub.i sup.′+ςsub.iD(ςsub.1,ςsub.2,…,ςsub.i sup.′,…,ςsub.n) holds ∀ςsub.i,ςsub.i sup.′∈A. In this paper, we investigate the structure of Csup.∗-algebras involving generalized linear n-derivations. Moreover, we describe the forms of traces of linear n-derivations satisfying certain functional identity.
In this paper we study twisted conjugacy classes and isogredience classes for automorphisms of reductive linear algebraic groups. We show that reductive linear algebraic groups over some fields of ...zero characteristic possess the
and
properties.
In this paper we study the class of laterally complete commutative unital regular algebras A over arbitrary fields. We introduce a notion of passport GAMMA(X) for a faithful regular laterally ...complete A-modules X, which consist of uniquely defined partition of unity in the Boolean algebra of all idempotents in A and of the set of pairwise different cardinal numbers. We prove that A-modules X and Y are isomorphic if and only if GAMMA(X) = GAMMA(Y). Further we study Banach A-modules in the case A = C.sub.infinity(Q) or A = C.sub.infinity(Q)+i*C.sub.infinity(Q). We establish the equivalence of all norms in a finite-dimensional (respectively, sigma-finite-dimensional) A-module and prove an Aversion of Riesz Theorem, which gives the criterion of a finite-dimensionality (respectively, sigma-finite-dimensionality) of a Banach A-module.
Character measure is a probability measure on irreducible representations of a semisimple Lie algebra. It appears from the decomposition into irreducibles of tensor power of a fundamental ...representation. In this paper we calculate the asymptotics of character measure on representations of so.sub.2n+1 in the regime near the boundary of weight diagram. We find out that it converges to a Poisson-type distribution. Bibliography: 8 titles.
In this manuscript, we proposed a novel framework of the q-rung orthopair fuzzy subfield (q-ROFSF) and illustrate that every Pythagorean fuzzy subfield is a q-rung orthopair fuzzy subfield of a ...certain field. We extend this theory and discuss its diverse basic algebraic characteristics in detail. Furthermore, we prove some fundamental results and establish helpful examples related to them. Moreover, we present the homomorphic images and pre-images of the q-rung orthopair fuzzy subfield (q-ROFSF) under field homomorphism. We provide a novel ideology of a non-standard fuzzy subfield in the extension of the q-rung orthopair fuzzy subfield (q-ROFSF).
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