region πa2 (26,50) πa1 (13,98) Figure 7 – Phase Transition curves in (L,m) and (N,L) plane with the useful area for abstraction Ideally, if a ground problem lies in the mushy region and has solution, then a useful abstraction operator shall map it into an abstract problem lying in the YES region. On the contrary, if a ground problem lies in the mushy region and has no solutions, then a useful a...

In this paper, we present two quite general approximation theorems for the propagators of higher order (in time) abstract Cauchy problems, which extend largely the classical Trotter-Kato type approximation theorems for strongly continuous operator semigroups and cosine operator functions. Then, we apply the approximation theorems to deal with the second order dynamical boundary value problems.

Abstract. Here we utilize operator–valued Lq → Lp Fourier multiplier theorems to establish lower bound estimates for large class of elliptic integrodifferential equations in R. Moreover, we investigate separability properties of parabolic convolution operator equations that arise in heat conduction problems in materials with fading memory. Finally, we give some remarks on optimal regularity of ...

*Correspondence: [email protected] 1Luleå University of Technology, Luleå, 971 87, Sweden 2Narvik University College, P.O. Box 385, Narvik, 8505, Norway Full list of author information is available at the end of the article Abstract We consider the q-analog of the Riemann-Liouville fractional q-integral operator of order n ∈ N. Some new Hardy-type inequalities for this operator are proved and dis...

The recently introduced concept of a spectral shift operator is applied in several instances. Explicit applications include Krein's trace formula for pairs of self-adjoint operators, the Birman-Solomyak spectral averaging formula and its operator-valued extension, and an abstract approach to trace formulas based on perturbation theory and the theory of self-adjoint extensions of symmetric opera...

It is shown that an operator can be defined in the abstract space of a random matrix ensemble whose matrix elements statistical distribution simulates the behavior of the distribution found in real physical systems. It is found that the key quantity that determine these distributions is commutator of the operator with the Hamiltonian. Application to symmetry breaking in quantum many-body system...

In this abstract, we develop a solid theoretical foundation for a bottom-up program specialisation technique, capable of specialising a logic program w.r.t. a set of unit clauses. Extending a well-known operator, originally introduced for composing logic programs, we deene a bottom-up partial deduction operator and prove correctness of the transformation with respect to the S-semantics.

Abstract. The Balescu-Lenard equation from plasma physics is widely considered to include a highly accurate correction to Landau’s fundamental collision operator. Yet so far it has seen very little mathematical study. We perform an extensive linearized analysis of this equation, which includes determining the asymptotic behavior of the new components of the linearized operator and establishing ...

A generalized anti-hermitian staggered Dirac operator is formulated. Its relation with noncommutative geometry is briefly reviewed. Once this antihermitian operator is modified to be “γ5-hermitian”, it will provide a new solution to Ginsparg-Wilson relation, basing on an abstract algebraic analysis of Neuberger’s overlap construction and a redefinition of chirality.