let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

in this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $x$,  where $x$ is a $c$-distinguished topological space. then, we show that their dual spaces can be identified in a natural way with certain spaces of radon measures.

Relying on properties of the inductive tensor product, we construct cyclic type homology theories for certain nuclear algebras. In this context, we establish continuity theorems. We compute the periodic cyclic homology of the Schwartz algebra of p-adic GL(n) in terms of compactly supported de Rham cohomology of the tempered dual of GL(n). 1. Complete nuclear locally convex algebras Cyclic type ...

Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.

We prove that the Hodge metric completion of the Teichmüller space of polarized and marked Calabi–Yau manifolds is a complex affine manifold. We also show that the extended period map from the completion space is injective into the period domain, and that the completion space is a domain of holomorphy and admits a complete Kähler-Einstein metric.

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.

Abstract: We introduce a dual lifting of unified gauge theories, the We introduce a dual lifting of unified gauge theories, the first characterized by the isotopies, which are axiompreserving maps into broader structures with positive-definite generalized units used for the representation of matter under the isotopies of the Poincare’ symmetry, and the second characterized by the isodualities, ...

Existence and uniqueness theorems for unstable manifolds are well-known. Here we prove certain refinements. Let f : (C, 0) → C be a germ of an analytic diffeomorphism, whose derivative Df(0) has eigenvalues λ1, . . . , λn such that |λ1| ≥ · · · ≥ |λk| > |λk+1| ≥ · · · ≥ |λn|, with |λk| > 1. Then there is a unique k-dimensional invariant submanifold whose tangent space is spanned by the generali...