The general equation of state which was found for dense fluids, both compressed liquids and dense supercritical fluids, namely "Linear Isotherm Regularity," is extended to the lower density range, specifically for densities lower than the Boyle density. This new equation of state which is called "ELIR" is shown to be compatible with the equations of state based on statistical-mechanical the...

‎Let $M$ be a non-zero finitely generated module over a commutative Noetherian local ring $(R,mathfrak{m})$ with $dim_R(M)=t$‎. ‎Let $I$ be an ideal of $R$ with $grade(I,M)=c$‎. ‎In this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎The main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎Tor^{R}_c(k,H^c_I(M))to kotim...

If (R,M) and (S,N) are quasilocal (commutative integral) domains and f : R → S is a (unital) ring homomorphism, then f is said to be a strong local homomorphism (resp., radical local homomorphism) if f (M) = N (resp., f (M) ⊆ N and for each x ∈ N , there exists a positive integer t such that xt ∈ f (M)). It is known that if f : R→ S is a strong local homomorphism where R is a pseudovaluation do...

For digraphs G and H, a homomorphism of G to H is a mapping f : V (G)→V (H) such that uv ∈ A(G) implies f(u)f(v) ∈ A(H). If, moreover, each vertex u ∈ V (G) is associated with costs ci(u), i ∈ V (H), then the cost of a homomorphism f is ∑ u∈V (G) cf(u)(u). For each fixed digraph H, the minimum cost homomorphism problem for H, denoted MinHOM(H), can be formulated as follows: Given an input digra...

The submodules with the property of the title ( a submodule $N$ of an $R$-module $M$ is called strongly dense in $M$, denoted by $Nleq_{sd}M$, if for any index set $I$, $prod _{I}Nleq_{d}prod _{I}M$) are introduced and fully investigated. It is shown that for each submodule $N$ of $M$ there exists the smallest subset $D'subseteq M$ such that $N+D'$ is a strongly dense submodule of $M$ and $D'bi...

In this paper we find a secure routing protocol for computer networks, which finds minimum optimum path using homomorphic encryption schemes. We briefly look into the existing homomorphic encryption algorithms. We make use of ElGamal encryption, Elliptic Curve encryption and a privacy homomorphism, which exhibits the property of homomorphism in our new routing protocol. Elliptic curve exhibits ...

where (x, g) denotes % evaluated at g. Each % thus yields a homomorphism of M(G) onto the complex numbers. Every such homomorphism of L(G) is obtained in this way. Let be a homomorphism of L{G) into M(H). After composing with <[>, every homomorphism of M(H) onto the complex numbers either is identically zero, or can be identified with a member of G. We thus have a map <£* from Ê into {G, 0 ...

|We use a laser range nder with a scanning mirror on a panning platform to acquire range data in a local environment (range < 15m). In this paper, we discuss the hardware components, the software, show several examples of the range data, and discuss problematic issues such as material properties. We conclude with our future plans for improving the data and integrating it into our research progr...