<p>When working with a metric space, we are dealing the additive group (R, +). Replacing +) an Abelian (G, ?), offers new structure of space. We call it G-metric space and induced topology is called topology. In this paper, studying spaces based on L-groups (i.e., partially ordered groups which lattices). Some results in obtained. The defined further studied for its topological properties...

Let ${(g{n}){n\\geq 1}}$ be a sequence of independent and identically distributed (i.i.d.) ${d\\times d}$ real random matrices. For ${n\\geq 1}$ set ${G_n = g_n \\ldots g_1}$. Given any starting point ${x=\\mathbb R v\\in\\mathbb{P}^{d-1}}$, consider the Markov chain ${X_n^x \\mathbb G_n v }$ on projective space ${\\mathbb P^{d-1}}$ define norm cocycle by ${\\sigma(G_n, x)= \\log (|G_n v|/|v|)}...

A collocation method is presented for numerical solution of a typical integral equation Rh := R D R(x, y)h(y)dy = f(x), x ∈ D of the class R, whose kernels are of positive rational functions of arbitrary selfadjoint elliptic operators defined in the whole space R, and D ⊂ R is a bounded domain. Several numerical examples are given to demonstrate the efficiency and stability of the proposed meth...

For a graph G and a set D ⊆ V (G), define Nr[x] = {xi ∈ V (G) : d(x, xi) ≤ r} (where d(x, y) is graph theoretic distance) and Dr(x) = Nr[x] ∩D. D is known as an r-identifyingcode if for every vertex x, Dr(x) 6= ∅, and for every pair of vertices x and y, x 6= y ⇒ Dr(x) 6= Dr(y). The various applications of these codes include attack sensor placement in networks and fault detection/localization i...

An electron/positron linear collider with a center-of-mass energy between 0.5 and 1 TeV is recognized as an important complement to the physics program of the LHC. The Next Linear Collider (NLC) is being designed by a US collaboration (FNAL, LBNL, LLNL, and SLAC) which is working closely with the Japanese collaboration that is designing the Japanese Linear Collider (JLC). The NLC/JLC main linac...

Let (X, d) be a metric space and m ∈ X. Suppose that φ : X×X → R is a nonnegative symmetric function. We define a metric d on X which is equivalent to d. If d is totally bounded, its completion is a compactification of (X, d). As examples, we construct two compactifications of (R, dE), where dE is the Euclidean metric and s ≥ 2. key words. equivalent metric; completion; compactification Mathema...

Under the assumption λ > 0 and f verifying f (x, y,0)= 0 in D, 2F(x, y,u)−u f (x, y,u)≥ 0, u = 0, and ifΩ= R×D, we show the convexity of function E(t)= ∫∫D |u(t,x, y)|2dxdy, where u :Ω→R is a solution of problem λ(∂2u/∂t2)−(∂/∂x)(p(x, y)(∂u/∂x))−(∂/∂y)(q(x, y)(∂u/∂y)) + f (x, y,u)= 0 in Ω, u+ ε(∂u/∂n)= 0 on ∂Ω, considered in H2(Ω)∩L∞(Ω), p,q :D→R are two nonnull functions on D, ε is a positive ...

A 1.6MeV X-Band traveling wave linear accelerator is being developed in our Lab. in view of X-band Linac R&D and industrial purposes. One section of accelerator structure has been fabricated successfully. In this paper, the RF coupler computer simulation, the constant powerloss collinear load study and the accelerator section development are described in detail. The manufacture technology and s...

Let D be an integral domain with quotient field K, X be an indeterminate over D, K[X] be the polynomial ring over K, and R = {f ∈ K[X] | f(0) ∈ D}; so R is a subring of K[X] containing D[X]. For f = a0 + a1X + · · ·+ anX ∈ R, let C(f) be the ideal of R generated by a0, a1X, . . . , anX n and N(H) = {g ∈ R | C(g)v = R}. In this paper, we study two rings RN(H) and Kr(R, v) = { fg | f, g ∈ R, g 6=...

The niche graph of a digraph D is the (simple undirected) graph which has the same vertex set as D and has an edge between two distinct vertices x and y if and only if N D (x)∩N + D (y) 6= ∅ or N − D (x)∩ N D (y) 6= ∅, where N + D (x) (resp. N − D (x)) is the set of out-neighbors (resp. in-neighbors) of x in D. A digraph D = (V,A) is called a semiorder (or a unit interval order) if there exist ...