The purpose of the paper is studying the relaxation time of product{ type Markov chains on product spaces which approach a product distribution. We determine bounds to approach stationarity for such Markov chains in terms of the mixing times of the component Markov chains. In cases where the component mixing times vary much we propose an optimized visiting scheme which makes such product{type M...

We discuss the inner product spaces of the middle homology groups of manifolds of dimensions 2 and 4. We prove that two compact 2-manifolds are homeomorphic if and only if the inner product spaces of their first homology groups are isomorphic. We outline a proof that every inner product space can be realized as the first homology group of some surface. We conclude by proving that two simply con...

1. Matrices, Vectors and their Basic Operations 1.1. Matrices 1.2. Vectors 1.3. Addition and Scalar Multiplication of Matrices 1.4. Multiplication of Matrices 2. Determinants 2.1. Square Matrices 2.2. Determinants 2.3. Cofactors and the Inverse Matrix 3. Systems of Linear Equations 3.1. Linear Equations 3.2. Cramer’s Rule 3.3. Eigenvalues of a Complex Square Matrix 3.4. Jordan Canonical Form 4....

A Grüss type inequality for sequences of vectors in inner product spaces which complement a recent result from [6] and applications for differentiable convex functions defined on inner product spaces and applications for Fourier and Mellin transforms, are given.

Some inequalities in 2-inner product spaces generalizing Bessel’s result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.

We onsider ”Riesz Theorem” in the 2-inner product spaces and give some results in this field. Also, we give some characterizations about 2-inner product spaces in b-approximation theory. AMS Mathematics Subject Classification (2000): 41A65, 41A15

Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.

Exploration of design spaces is an important step in decision-based design. In consumer product development, precise design specifications are not known at the beginning of the design process. It is usually design team’s responsibility to find out the specifications as a part of the design process. This results in large design spaces in consumer product development. Furthermore, market window i...

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...