In this paper, applying the concept of generalized A-valued norm on a right $H^*$-module and also the notion of ϕ-homomorphism of Finsler modules over $C^*$-algebras we first improve the definition of the Finsler module over $H^*$-algebra and then define ϕ-morphism of Finsler modules over $H^*$-algebras. Finally we present some results concerning these new ones.

Disk traffic modeling is useful in designing effective storage systems. One of the most difficult aspects of modeling disk trace data is understanding the underlying process which generates the trace. This work shows a novel method to model and learn the spatio-temporal locality in the trace generating process by using a conditional distribution based on recent disk accesses observed in the tra...

We show that the recently proposed matrix model for M theory obeys the cyclic trace assumptions underlying generalized quantum or trace dynamics. This permits a verification of supersymmetry as an operator calculation, and a calculation of the supercharge density algebra by using the generalized Poisson bracket, in a basis-independent manner that makes no reference to individual matrix elements...

In this paper, we present a general framework for image retrieval that is invariant to translation, rotation, scaling, local texture distortion and local geometrical deformation of an image. We first solve the problems in image database retrieval by transforming the image space into the Trace transform space. The Trace transform captures the key characteristics of an object by suppressing varia...

We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kürsten and the second author. The quantum spaces are chosen such that their coordinate algebras do not admit bounded Hilbert space representations and their self-adjoint generators have continuous spectrum. Operator algebras of trace class operators are assoc...

This paper establishes an efficient method for the synthesis of modular, delay-insensitive circuits, specified by a class of directed trace structures. The notion of trace graphs is introduced for the purpose of facilitating the d~scription of relevant trace structures. A suitable mathematically precise theory is developed and the synthesis algorithm is for­ mally proven to be correct. Further ...

The requirement that an entropy function be composable is key: it means that the entropy of a compound system can be calculated in terms of the entropy of its independent components. We prove that, under mild regularity assumptions, the only composable generalized entropy in trace form is the Tsallis one-parameter family (which contains Boltzmann–Gibbs as a particular case). This result leads t...

This article provides sufficient conditions for positive maps on the Schatten classes Jp; 1 p < 1 of bounded operators on a separable Hilbert space such that a corresponding Perron-Frobenius theorem holds. With applications in quantum information theory in mind sufficient conditions are given for a trace preserving, positive map on J1, the space of trace class operators, to have a unique, stric...

The spectral shift function for pairs of selfadjoint operators was introduced in the paper by I.M. Lifshits [17]. In the same paper a trace formula for the difference of functions of the perturbed operator and the unperturbed operator was established. Ideas by Lifshits were developed in the paper by M.G. Krein [14], in which the spectral shift function ξ in L1(R) was defined for arbitrary pairs...

In trace processors, a sequential program is partitioned at run time into “traces.” A trace is an encapsulation of a dynamic sequence of instructions. A processor that uses traces as the unit of sequencing and execution achieves high instruction fetch rates and can support very wide-issue execution engines. We propose a new class of hardware optimizations that transform the instructions within ...