A signed graph (G,σ) on n vertices is called a parity if there bijection f:V(G)→{1,2,…,n} such that for each edge e=uv of G, f(u) and f(v) have the same σ(e)=1, opposite parities σ(e)=−1. The signature σ parity-signature G. Let Σ−(G) denote set number negative edges over all possible parity-signatures σ. rna σ−(G) G given by σ−(G)=minΣ−(G). In other words, minimum cardinality an edge-cut in two...

ion by fresh free variables is the main tool to obtain a rigid system from one which is not, therefore explaining our notation RA. Example 8.5. Consider the system R = {f(λx.h(@(H, c(x)))) → g(H)}, in which H : α→ β is the only free variable. R can be abstracted by RA = {f(X)→ g(X), h(Y )→ Y, c(z)→ z} The rule in R is abstracted by the rule f(X) → g(X) added to RA with {X 7→ λz.h(@(H, c(z)))} a...

It was shown in [2] that if T is a contraction in a Hilbert space with finite defect (‖T‖ ≤ 1, rank(I−T ∗T ) <∞), and its spectrum σ(T ) doesn’t coincide with the closed unit disk D, then the following Linear Resolvent Growth condition ‖(λI − T )−1‖ ≤ C dist(λ, σ(T )) , λ ∈ C\σ(T ), implies that T is similar to a normal operator. The condition rank(I − T ∗T ) < ∞ characterizes how close is T to...

A natural deduction system NDIL described here admits normalization and has subformula property. It has standard axioms A ` A, ` 1, standard introduction and elimination rules for &,−◦ (linear implication), ⊕ and quantifiers. The rules for ⊗ are now standard too. Structural rules are (implicit) permutation plus contraction and weakening for m-formulas. The rules for ! use an idea of D. Prawitz....

We construct an empirical Bayes (EB) prediction interval for the finite population mean of a small area when data are available from many similar small areas. We assume that the individuals of the population of the i area are a random sample from a normal distribution with mean μi and variance σ 2 i . Then, given σ 2 i , the μi are independently distributed with each μi having a normal distribu...

let a be a banach algebra and x be a banach a-bimodule. in this paper, we dene a new product on a  x and generalize the module extension banach algebras. we obtain characterizations of arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new banach algebra.

I construct a minimal formalism to describe transport of non separable correlations arising when a superconductor is in contact with several electrodes (being ferromagnetic or normal metal). Transport theory is expressed in terms of effective single site Green’s functions. Part of the circuit is decimated exactly by renormalizing only one physical parameter (the density of states). I show that ...

in the present study, the cooperative and diminutive interplay between halogen, hydride, and cation-σ interactions are studied in hmgh···li+(na+)···nccl, li+(na+)···hmgh···clcn and hmgh···clcn···li+(na+) complexes by means of ab initio calculations. to better understand the cooperative or diminutive effects in the ternary systems, the corresponding binary complexes are also considered. the esti...

Abstract We present the analysis of ∼100 pc scale compact radio continuum sources detected in 63 local (ultra)luminous infrared galaxies (U/LIRGs; L IR ≥ 10 11 ⊙ ), using FWHM ≲ 0.″1–0.″2 resolution 15 and 33 GHz observations with Karl G. Jansky Very Large Array. identify a total 133 effective radii 8–170 pc, which are classified into four main categories—“AGN” (active galactic nuclei), “AGN/SB...