Quantum information processing is the study of methods and efficiency in storage, manipulation and conversion of information represented by quantum states. Many quantum information theoretic concepts are closely related to geometry. For instance, trace distance and fidelity, which come out of the study of distinguishability between quantum states, are closely linked with Bures and Fubini-Study ...

Function spaces on skeletons arise in the numerical treatment of elliptic boundary value problems by certain domain decomposition methods. In this note, we discuss such function spaces, which can be interpreted as trace spaces. We construct a well{deened trace operator and present a characterization of the trace spaces by means of multi-level expansions.

Thompson’s partition of a cyclic subnormal operator into normal and completely non-normal components is combined with non-commutative calculus for hyponormal operators separating outliers from the cloud, in rather general point distributions plane. The main result provides exact transformation formulas power moments prescribed distribution uniform mass carried by cloud. proposed algorithm solel...

We consider the case of scattering by several obstacles in Rd for d?2. In this setting, absolutely continuous part Laplace operator ? with Dirichlet boundary conditions and free ?0 are unitarily equivalent. For suitable functions that decay sufficiently fast, we have difference g(?)?g(?0) is a trace-class its trace described Krein spectral shift function. article, study contribution to (and hen...

In this paper, an anomaly detection method in cluster-based mobile ad hoc networks with ad hoc on demand distance vector (AODV) routing protocol is proposed. In the method, the required features for describing the normal behavior of AODV are defined via step by step analysis of AODV and independent of any attack. In order to learn the normal behavior of AODV, a fuzzy averaging method is used fo...

We consider the Hartree equation for infinitely many electrons with a constant external magnetic field. For system, we show local well-posedness result when initial data is pertubation of Fermi sea, which non-trace class stationary solution to system. In this case, one particle Hamiltonian Pauli operator, possesses distinct properties from Laplace example, it has discrete spectrum and infinite-...

Abstract We address the computational spectral theory of Jacobi operators that are compact perturbations free operator via asymptotic properties a connection coefficient matrix. In particular, for finite-rank we show computation spectrum can be reduced to polynomial root finding problem, from is derived explicitly entries A formula measure also these entries. The analysis extended trace-class p...

ÖZET Bu çalışmada, sonlu bir aralıkta verilmiş sınırsız operatör katsayılı ikinci mertebeden diferansiyel operatörün düzenli izi için bir formül bulunmuştur. Anahtar Sözcükler: Hilbert uzayı, Kendine eş operator, çekirdek operatör ABSTRACT In this work; a formula for the regularized trace of second order differential operator, which is given in a finite interval and with unbounded operator coef...