Discrete state space method and modal extension method based impact sound synthesis model

The efficient and accurate synthesis of physical parameter-controllable impact sounds is essential for sound source identification. In this study, an impact sound synthesis model of a cylinder is proposed based on discrete state space（DSS） method and modal extension method（MEM）. This model is comprised of the whole three processes of the physical interaction, i.e., the Hertz contact process, the transient structural response process, and the sound radiation process. Firstly,the modal expanded DSS equations of the contact system are constructed and the transient structural response of the cylinder is obtained. Then the impact sound of the cylinder is acquired using improved discrete Raleigh integral. Finally, the proposed model is verified by comparing with existing models. The results show that the proposed impact sound synthesis model is more accurate and efficient than the existing methods and easy to be extended to the impact sound synthesis of other structures.

On AP-property of Function Spaces

In this paper, it is discussed the AP-property of function spaces. We prove that for any compact network α for a space X which is closed under finite unions, (1) if C α (X) is an AP-space and X is paracompact, then X is a Hurewicz space; (2) if C α (X) is an AP-space which has countable tightness, then C α (X) is discretely generated.

Minimax designs for linear regression models with bias in a reproducing kernel Hilbert space in a discrete set

Consider the design problem for estimation and extrapolation in approximately linear regression models with possible misspecification. The design space is a discrete set consisting of finitely many points, and the model bias comes from a reproducing kernel Hilbert space. Two different design criteria are proposed by applying the minimax approach for estimating the parameters of the regression response and extrapolating the regression response to points outside of the design space. A simulated annealing algorithm is applied to construct the minimax designs. These minimax designs are compared with the classical D-optimal designs and all-bias extrapolation designs. Numerical results indicate that the simulated annealing algorithm is feasible and the minimax designs are robust against bias caused by model misspecification.

A DISCRETE CHARACTERIZATION OF BESOV SPACES

The characterization of isotropic Besov spaces for in terms of progressive differences of a function on dyadic points is obtained. Moreover, for withan analogous characterization of anisotropic Besov spaces is presented.

F_(p) as a Discrete Metric Space

We define a metric that makes the algebraic closure of a finite field F_(p) into a UDBG(uniformly discrete with bounded geometry)metric space.This metric stems from algebraic properties of F_(p).From this perspective,for F_(p)we explore common research themes in metric spaces,reveal how peculiar properties naturally arise,and present it as a new type of example for certain well-studied questions.

Particle-Wave Duality Resulting from the Granulation of Fields in a Hypercubic Lattice

The possibility of granulated discrete fields is considered in which there are at least three distinct base granules. Because of the limited size of the granules, the motion of an endlessly extended particle field must to be split into an inner and an outer part. The inner part moves gradually in a point particle-like fashion, the outer is moving step-wise in a wave-like manner. This dual behaviour is reminiscent of the particle-wave duality. Field granulation can be caused by deviations of the structure of the lattice at the boundaries of the granule, causing some axes of the granule to be tilted. The granules exhibit relativistic effects, inter alia, caused by the universality of the coordination number of the lattice.

The Basic Idea behind the Relativistic and the Quantum Concepts

A new aspect of unification is presented in this paper. This aspect depends on two postulates of our recent theory concerning light propagation in a specific medium. The special theory of relativity is demonstrated as a reflection of our first postulate, regarding the existence of multiple, equivalent rest frames in our medium. The second postulate is concerned with energy forms in nature, and it deals with the quantum behavior of light and wave behavior of matter. By using this postulate, we are able to justify the existence of these two phenomena. As a consequence of this, gravity as described by general relativity is unified as a background-independent interaction under the same postulate.

Kolmogorov's ε-Entropy of Bounded Sets in Discrete Spaces and Attractors of Dissipative Lattice Systems

We obtain an estimate of the upper bound for Kolmogorov＇s ε-entropy for the bounded sets with small ＂tail＂ in discrete spaces, then we present a sufficient condition for the existence of a global attractor for dissipative lattice systems in a reflexive Banach discrete space and establish an upper bound of Kolmogorov＇s ε-entropy of the global attractor for lattice systems.

The Boundedness of Composition Operators on Triebel–Lizorkin and Besov Spaces with Different Homogeneities

In this paper, we introduce new Triebel–Lizorkin and Besov Spaces associated with the different homogeneities of two singular integral operators. We then establish the boundedness of composition of two Calder′on–Zygmund singular integral operators with different homogeneities on these Triebel–Lizorkin and Besov spaces.

DISCRETE CHARACTERIZATION OF THE PALEY-WIENER SPACE WITH SEVERAL VARIABLES

In this paper, we obtain a characterization of the Paley-Wiener space with several variables, which is denoted by Bπ,p(Rn), 1≤p<∞, i.e., for 1<p<∞, Bπ,p(Rn) is isomorphic to lp(Zn), and for p=1, Bπ,1(Rn) is isomorphic to the discrete Hardy space with several variables, which is denoted by H(Zn).