We study parabolic stochastic partial differential equations (SPDEs), driven by two types of operators: one linear closed operator generating a C0−semigroup and one linear bounded operator with Wick-type multiplication, all of them set in the infinite dimensional space framework of white noise analysis. We prove existence and uniqueness of solutions for this class of SPDEs. In particular, we al...

0. Introduction. In this paper we consider factorizations of finite rank operators through finite-dimensional C∗-algebras. We are interested in factorization norms involving either the completely bounded norm ‖ ‖cb or Haagerup’s decomposable norm ‖ ‖dec (see [11]). Let us denote byMn the C∗-algebra of all n×n matrices with complex entries. Let A and B be two C∗-algebras, and let us consider a f...

Monotone operators are of basic importance in optimization as they generalize simultaneously subdifferential operators of convex functions and positive semidefinite (not necessarily symmetric) matrices. In 1970, Asplund studied the additive decomposition of a maximal monotone operator as the sum of a subdifferential operator and an “irreducible” monotone operator. In 2007, Borwein and Wiersma [...

The problem of quantum time and evolution systems, where is not a parameter, considered. In our model, following some earlier works, represented by operator. this paper, similarly to the position operators in Schrödinger representation mechanics, operator multiplication-type It can be also an appropriate positive operator-valued measure (POVM) which together with 3D operators/measures provide o...

We present a numerical approximation scheme for the Tomita-Takesaki modular operator of local subalgebras in linear quantum fields, working at one-particle level. This is applied to subspaces double cones vacuum sector massive scalar free field (1 + 1)- and (3 1)-dimensional Minkowski spacetime, using discretization time-0 data position space. In case wedge region, one component generator well-...

A completely decomposable group is an abelian group of the form ⊕ i Hi, where Hi ≤ (Q,+). We show that every computable completely decomposable group is ∆5-categorical. We construct a computable completely decomposable group which is not ∆4-categorical, and give an example of a computable completely decomposable group G which is ∆4-categorical but not ∆3-categorical. We also prove that the inde...

We show that there is a set of transformations that relates all of the 24 dimensional even self-dual (Niemeier) lattices, and also leads to non-lattice objects that cannot be used as a compactification torus. We extend our observations to higher dimensional conformal field theories where we generate c = 24k theories with spectra decomposable into the irreducible representations of the Fischer-G...

Some bipartite Hamilton decomposable graphs that are regular of degree δ ≡ 2 (mod 4) are shown to have Hamilton decomposable line graphs. One consequence is that every bipartite Hamilton decomposable graph G with connectivity κ(G) = 2 has a Hamilton decomposable line graph L(G).

Recently, we witness a significant amount of effort being put into a research of robustness of complex computer systems. Computer scientists noticed that, despite decades of investigations into dependability, computer systems still lack the degree of resilience which can be seen in biological systems. In the biological context, one of the main aspects that stand behind a system’s robustness is ...