We prove the existence, uniqueness, and strict positivity of ground states possibly massless renormalized Nelson operator under an infrared regularity condition for Kato decomposable electrostatic potentials fulfilling a binding condition. If is violated, then we show non-existence with arbitrary potential. Furthermore, in non-Fock representation where unnecessary. Exponential superexponential ...

We demonstrate that for any well-defined cryptographic protocol, the symbolic trace reachability problem in the presence of an Abelian group operator (e.g., multiplication) can be reduced to solvability of a decidable system of quadratic Diophantine equations. This result enables complete, fully automated formal analysis of protocols that employ primitives such as Diffie-Hellman exponentiation,...

We consider algebras over a field K, generated by two variables x and y subject to the single relation yx = qxy + αx+ βy + γ for q ∈ K∗ and α, β, γ ∈ K. We prove, that among such algebras there are precisely five isomorphism classes. The representatives of these classes, which are ubiquitous operator algebras, are called model algebras. We derive explicit multiplication formulas for y · x in te...

In the following work, we consider Boltzmann equation that models a polyatomic gas by representing microscopic internal energy continuous variable I. Under some convenient assumptions on transition function $ \mathcal{B} $, prove linearized operator \mathcal{L} of this model is Fredholm operator. For this, write as perturbation collision frequency multiplication operator, and \mathcal{K} compac...

in this paper, we consider a particular class of integral equations of the fourth kind and show that tractability and differentiability index of the given system are 3. tractability and dierentiability index are introduced based on the-smoothing property of a volterra integral operator and index reduction procedure, respectively. using the notion of index, we give sucient conditions for the...

A graph G is called randomly H − decomposable if every maximal H − packing in G uses all edges in G. G is called H − equipackable if every maximal H − packing in G is also a maximum H − packing in G. M2 − decomposable graphs, randomly M2 − decomposable graphs and M2 − equipackable graphs have been characterized. The definitions could be generalized to multigraphs. And M2 − decomposable multigra...

Abstract In this note we study the spectrum and Waelbroeck of derivative operator composed with isomorphic multiplication operators defined in space smooth functions [0, 1] which are flat at 0.

"Let $\B_X$ be a bounded symmetric domain realized as the open unit ball of JB*-triple $X$ which may infinite dimensional. In this paper, we characterize weighted composition operators from Hardy space $H^{\infty}(\mathbb{B}_X)$ into $\alpha $-Bloch $\mathcal{B}^\alpha (\B_X)$ on $\mathbb{B}_X$. Later, show multiplication operator is bounded. Also, give norm operator."

Let H be a Hilbert space of analytic functions on the unit disk D. For an analytic function ψ on D, we can define the multiplication operator Mψ : f → ψf, f ∈ H. For an analytic selfmapping φ of D, the composition operator Cφ defined on H as Cφf f ◦ φ, f ∈ H. These operators are two classes of important operators in the study of operator theory in function spaces 1–3 . Furthermore, for ψ and φ,...