Spectral C*-Algebras

Contrary to the classical wisdom, processes with independent values (defined properly) are much more diverse than white noises combined with Poisson point processes, and product systems are much more diverse than Fock spaces. This text is a survey of recent progress in constructing and investigating nonclassical stochastic flows and continuous products of probability spaces and Hilbert spaces.

We generalize Bhat's construction of product systems of Hilbert spaces from E0-semigroups on B(H) for some Hilbert space H to the construction of product systems of Hilbert modules from E0-semigroups on Ba(E) for some Hilbert module E. As a byproduct we find the representation theory for Ba(E) if E has a unit vector. We establish a necessary and sufficient criterion for the conditional expectation generated by the unit vector to define a weak dilation of a CP-semigroup in the sense of [1]. Finally, we also show that white noises on general von Neumann algebras in the sense of [2] can be extended to white noises on a Hilbert module.

We have seen in Theorem 2.4.10 that the cocycle conjugacy class of an E0-semigroup is completely determined by the structure of its product system. Thus the classification of E0-semigroups up to cocycle conjugacy should begin with a systematic development of a general theory of continuous tensor products of Hilbert spaces that is appropriate for E0-semigroups.KeywordsHilbert SpaceProduct SystemGauge GroupCovariance FunctionAutomorphism GroupThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We classify all continuous tensor product systems of Hilbert spaces which are “infinitely divisible” in the sense that they have an associated logarithmic structure. These results are applied to the theory of E 0-semigroups to deduce that every E 0-semigroup possessing sufficiently many “decomposable” operators must be cocycle conjugate to a CCR flow (Theorem 12.3).A path space is an abstraction of the set of paths in a topological space, on which there is given an associative rule of concatenation. A metric path space is a pair (P, g) consisting of a path space P and a function g : P 2 → ℂ which behaves as if it were the logarithm of a multiplicative inner product. The logarithmic structures associated with infinitely divisible product systems are such objects. The preceding results are based on a classification of metric path spaces.Key words and phrasesvon Neumann algebrassemigroupsautomorphism groups

The multipartite quantum systems are of particular interest for the study of such phenomena as entanglement and non-local correlations. The symmetry group of the whole multipartite system is the wreath product of the group acting in the “local” Hilbert space and the group of permutations of the constituents. The dimension of the Hilbert space of a multipartite system depends exponentially on the number of constituents, which leads to computational difficulties. We describe an algorithm for decomposing representations of wreath products into irreducible components. The C implementation of the algorithm copes with representations of dimensions in quadrillions. The program, in particular, builds irreducible invariant projectors in the Hilbert space of a multipartite system. The expressions for these projectors are tensor product polynomials. This structure is convenient for efficient computation of quantum correlations in multipartite systems with a large number of constituents.

In the paper, it is proposed to develop a machine learning based intelligent defect detection system for metal products. The common machine vision system has the surface (stain, shallow pit, shallow tumor, scratches, Edge defects, pattern defects) detection, or for the processing of the size, diameter, diameter, eccentricity, height, thickness and other parts of the non-contact numerical parameters of detection. Considering the quality of the work piece and the defects of the standard, so for the quality of customized testing requirements, the study is the development of machine vision and machine learning metal products defect detection system, mainly composed of three procedures: Image preprocessing, training procedures and testing procedures. The system architecture consists of three parts: (1) Image preprocessing: we first use the machine vision. OPENCV to carry out the image pre-processing part of the product before the detection. (2) Training procedures: The algorithm of the machine learning includes the convolution neural network (CNN), chunk-max pooling is used to train the program, and the generative adversarial network (GAN) based architecture is used to solve the problem of small datasets for surface defects. (3) Testing procedures：The Python language is used to write the program and implement the testing procedures with the GPU-Based embedded hardware In industries, collecting training dataset is usually costly and related methods are highly dataset-dependent. So most companies cannot provide Big-data to be analyzed or applied. By the experimental results, the recognition accuracy can be obviously improved as increasing data augmentation by GAN-Based samples maker. Manual inspection is labor intensive, costly and less in efficiency. Therefore, this study will contribute to technological innovation, industry, national development and other applications. (1) The use of intelligent machine learning technology will make the industry 4.0 technology more sophisticated. (2) It will make the development of equipment industry be better by the machine learning applications. (3) It will increase the economics and productivity of countries for the aging of the population by machine learning.

We explore the solvability of a general system of nonlinear relaxed cocoercive variational inequality (SNVI) problems based on a new projection system for the direct product of two nonempty closed and convex subsets of real Hilbert spaces.

Evaluation of the mechanical properties and durability of self-compacting alkali-activated mortar made from boron waste and granulated blast furnace slag

We consider a two-person zero-sum pursuit-evasion differential game in the Hilbert space l2. The control functions of the players are subject to integral constraints. It is assumed that the control resource of the pursuer is greater than that of the evader. The pursuer tries to force the state of the system towards the origin of the space l2, and the evader tries to avoid this. We give a solution to the optimal pursuit problem for the differential game. More precisely, we obtain an equation for the optimal pursuit time and construct optimal strategies for the players in an explicit form. To prove the main result we solve a time-optimal control problem.

We study necessary conditions on the weight w for the spline wavelet systems to be bases in the weighted space LP (w) . In this article we study some questions arising in the investigation of the prob- lem of describing those classes of weight functions w for which the wavelet systems are bases or unconditional bases in the weighted spaces LP (w) = LP(R, w). A priori these conditions depend on the concrete system. But there are some features which are common to all wavelet systems. Here we examine only the case of spline wavelet systems defined on the real line R. For a given non-negative integer m, the spline wavelets are defined in the following way: Let V0 = {f E L2(R) n Cm-l(R) such that the restriction of f to each interval )n, n + 1 ( is a polynomial of degree < m}, where by C (R) we denote the class of functions on R whose derivatives of order r are continuous and by C-' (R) we denote the class of piecewise continuous functions on R. Defining Vj+j = {f(2x) : f(x) E Vj} , we get a multiscale analysis of L2(R) in the sense of Mallat and Meyer (see (M), (D)).

Evaluation of concrete recycling system efficiency for ready-mix concrete plants

We present an object-oriented method to represent knowledge about a set of digital systems. Based on this representation, concrete systems can easily be specified, their implementations in various models such as VHDL or Petrinets can be derived automatically from a specification by a knowledge based configuration system. In this paper, we focus on the set-theoretic foundations of our model.KeywordsDomain ModelFunction LevelConceptual HierarchyInstruction CacheConcrete SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We associate a family of Hilbert spaces Hq2;λ(D) of analytic functions on the unit disk D=z∈\(\mathbb{C}\):|z|<1 the q-continuous Gegenbauer polynomials Cnλ(x;q) on the interval]−1;1[ and give a q-analogue of the unitary integral transform that Watanabe constructed from the Hilbert space L2(]−1;1[;(1−x2)λ−\(\frac{1}{2}\)dx onto the weighted Hilbert space H2;λ(D).

Evaluation of interface rapid bond strength between normal concrete and ternary system fast setting and rapid hardening self-compacting concrete

In the process of the rapid development of science and technology, people study many problems with the help of the independent variables, but the according descriptions have not been accurate enough. Therefore, many problems must be described by a function of more than one variable to more accurately get the results that people need to use the functions containing more than one variable and their partial derivatives to study the real problems of the method. Partial differential equations are closely and directly related to many problems in physics, mechanics, and engineering. It becomes an important bridge between mathematical theory and practical problems in physics, mechanics, and engineering. And the elements in Hilbert space, vectors, can represent vectors, functions, and phase quantities, while the special solutions of partial differential equations in solving physical problems can satisfy the common properties of Hilbert space. The analogy of functions and phase quantities to vectors can establish the function space and phase quantity space with geometric intuition. Based on Hilbert space theory, the key and difficult problems in engineering management can be explained by clear mathematical models by using the analogy method. The purpose of this study is to enrich the means of the building engineering management model, to broaden the horizon of managers, and to solve the problems in engineering management from a new dimension.