When decomposing database schemas, it is desirable that a decomposition is lossless and dependency preserving. A well-known and frequently used result for the relational model states that a functional dependency preserving decomposition is lossless if and only if it contains a key. We will show that this result does not always hold when domains are allowed to be finite, but provide conditions u...

The interface problem for the linear Schrödinger equation in one-dimensional piecewise homogeneous domains is examined by providing an explicit solution in each domain. The location of the interfaces is known and the continuity of the wave function and a jump in their derivative at the interface are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-siz...

groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.

A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $ mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (...

0. Introduction Our object is to study domains which are the region of negative definiteness of an operator-valued Hermitian form defined on a space of operators and to investigate the biholomorphic linear fractional transformations between them. This is a unified setting in which to consider operator balls, operator half-planes, strictly J-contractive operators, strictly J-dissipative operator...

Studies of multicomponent membranes suggest lateral inhomogeneity in the form of membrane domains, but the size of small (nanoscale) domains in situ cannot be determined with current techniques. In this article, we present a model that enables extraction of membrane domain size from time-resolved fluorescence resonance energy transfer (FRET) data. We expand upon a classic approach to the infini...

The straightforward representation of many real world problems is in terms of discrete random variables with large or infinite domains. For example, in a domain where we are trying to identify a person, we may have variables that have as domains, a set of all names, a set of all postal codes, and a set of all credit card numbers. The task usually reduces to performing probabilistic inference, i...

We show a Wolff–Denjoy type theorem in complete geodesic spaces the spirit of Beardon's framework that unifies several results this area. In particular, it applies to strictly convex bounded domains R n or C with respect large class metrics including Hilbert's and Kobayashi's metrics. The are generalized 1-Lipschitz compact mappings infinite-dimensional Banach spaces.

let $r$ be an infinite ring. here we prove that if $0_r$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin x}$ for every infinite subset $x$ of $r$, then $r$ satisfies the polynomial identity $x^n=0$. also we prove that if $0_r$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in x}$ for every infinite subset $x$ of $r$, then $x^n=x$ for all $xin r$.

In generalized semi-infinite programming the feasible set is known to be not closed in general. In this paper, under natural and generic assumptions, the closure of the feasible set is described in explicit terms.