The Pauli-Fierz Hamiltonian describes an interaction between a low energy electron and photons. Existence of ground states has been established. The purpose of this talk is to show that its ground states is exactly two-fold in a weak coupling region. 1 The Pauli-Fierz Hamiltonian This is a joint work with Herbert Spohn . The Hamiltonian in question is the PauliFierz Hamiltonian in nonrelativisi...

Unger studied the balanced leaf languages defined via poly-logarithmically sparse leaf pattern sets. Unger shows that NP-complete sets are not polynomial-time many-one reducible to such balanced leaf language unless the polynomial hierarchy collapses to Θp2 and that Σ p 2-complete sets are not polynomial-time bounded-truth-table reducible (respectively, polynomial-time Turing reducible) to any ...

This study was aimed at extraction optimization of antibacterial agents from Carica papaya seed against S. enteritidis, B. cereus, V. vulnificus and P. mirabilis as affected by sonication-assisted (SAE), contact time (CT) solid-to-solvent ratio (SSR). The principal component analysis (PCA) individual evaluation approaches identified that no SAE, 8 CT 1:10 SSR were the best treatments with highe...

let e be an edge of a g connecting the vertices u and v. define two sets n1 (e | g) andn2(e |g) as n1(e | g)= {xv(g) d(x,u) d(x,v)} and n2(e | g)= {xv(g) d(x,v) d(x,u) }.thenumber of elements of n1(e | g) and n2(e | g) are denoted by n1(e | g) and n2(e | g) ,respectively. the szeged index of the graph g is defined as sz(g) ( ) ( ) 1 2 n e g n e g e e    . inthis paper we compute the sz...

Boolean function f on n variables is represented by set I of disjoint intervals of non-negative n-bit integers, if the following condition holds: vector x of length n is a truepoint of f , if and only if integer x, binary representation of which corresponds to vector x, belongs to some interval from I. In this paper we present a polynomial-time algorithm recognizing, whether a Boolean function ...

Let [Formula: see text] represent a set of proper nonzero ideals (respectively, t-ideals text]) an integral domain and let P be valid property D. We say S(D) meets (denoted if each is contained in ideal satisfying P. If cannot controlled. When does not imply I(R) while implies usually. with twist text]written such that, for some study as its predecessor. A modification the above approach used t...

We consider a non-associative generalization of MV-algebras. The underlying posets of our non-associative MV-algebras are not lattices, but they are related to so-called λ-lattices. c ©2007 Mathematical Institute Slovak Academy of Sciences 1. Non-associative MV-algebras As known, MV-algebras were introduced in the late-fifties by C . C . C h a n g as an algebraic semantics of the Lukasiewicz ma...

A total Roman dominating function on a graph $G$ is a function $f: V(G) rightarrow {0,1,2}$ such that for every vertex $vin V(G)$ with $f(v)=0$ there exists a vertex $uin V(G)$ adjacent to $v$ with $f(u)=2$, and the subgraph induced by the set ${xin V(G): f(x)geq 1}$ has no isolated vertices. The total Roman domination number of $G$, denoted $gamma_{tR}(G)$, is the minimum weight $omega(f)=sum_...

In the last years, computers became a useful tool in some mathematical proofs. We argue that modern computer algebra systems simplify this work. Their usefulness can be demonstrated on recent results in quantum logic theory. We give two examples of highly nontrivial mathematical results which required computer veriication that was performed by CASs. 1 The structure of quantum logic Looking for ...

a watching system in a graph $g=(v, e)$ is a set $w={omega_{1}, omega_{2}, cdots, omega_{k}}$, where $omega_{i}=(v_{i}, z_{i}), v_{i}in v$ and $z_{i}$ is a subset of closed neighborhood of $v_{i}$ such that the sets $l_{w}(v)={omega_{i}: vin omega_{i}}$ are non-empty and distinct, for any $vin v$. in this paper, we study the watching systems of line graph $k_{n}$ which is called triangular grap...