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Pd has been regarded as one of the alternatives to Pt as a promising hydrogen evolution reaction (HER) catalyst. Strategies including Pd-metal alloys (Pd-M) and Pd hydrides (PdH

Mechanical engineering is a discipline of engineering that applies the principles of engine ering, physics and materials science for analysis, design, manufacturing, and maintenance of mecha nical systems. In this work, the construction of 4-band tight wavelet frames with symmetric proper-ties using symmetric extension and parameterization of the paraunitary matrix. The notion of an 4-band generalized multiresolution structure of subspace is proposed. The characteristics of affine pseudoframes for subspaces is investigated. The construction of a generalized multiresolution structure of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obta-ined based on such a generalized multiresolution structure and a sufficient condition for its exist-ence is presented. A constructive method for affine frames of based on a generalized multi-resolution structure is presented.

Active materials are a group of solid-state materials whose geometric shape can be related to an energy input in the form of heat, light, electric field, or magnetic field. In the application of active materials to electromechanical energy conversion, electrical energy may be input to the material and the resulting deformation of the material can be used to move a load. The most common active materials used in actuators are piezoelectrics, magnetostrictives, and SMAs. In this paper, a piezoelectric actuation concept is presented that uses a new feed-screw motion accumulation technique. The feed-screw concept involves accumulating high frequency actuation strokes of a piezoelectric stack (driving element) by intermittently rotating nuts on an output feed-screw. The main parts of piezoelectric actuation such as clamp mechanism, rotary mechanism and “L type” driving mechanism are investigated. From the analysis, the deformation and stress of it are all under allowed value of 65Mn. The mathematics model of upside of rotary mechanism rotation motion is established. The results indicate that, the mechanisms of actuator all are satisfy the need of design

In this work, the notion of biorthogonal two-directional shortly supported wavelets with poly-scale is developed. A new method for designing two-directional biorthogonal wavelet packets is proposed and their properties is investigated by means of time-frequency analysis methodand, operator theory. The existence of shortly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A new method for designing a class of biorthogonal shortly supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory.

In this article, the notion of orthogonal nonseparable four-dimensional wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is introduced. A new approach for constructing them is presented by iteration method and wavelets as well wavelet frames. The biorthogonality properties of four-dimensi- -onal wavelet packets are discussed. Three biorthogonality formulas concerning these wavelet packs are estabished. A necessary and sufficient condition for the existence of the pyramid decomposition scheme of space is presented.

Wavelet analysis is nowadays a widely used tool in applied mathematics. The advantages of wavelet wraps and their promising features in various application have attracted a lot of interest and effort in recent years. In this paper, we develop the notion of a sort of multivariate vector wavelet wraps. A new approcah for designing the multidimensional vector wavelet wraps is formul- ated. Their characters are investigated by virtue of iterative method, time-frequency analysis metho- d and matrix theory. There biorthogonality formulas regarding the wavelet wraps are provided. Biorthogonality decomposition relation formulas of the space L2(Rn)r are obtained by constructing a series of subspaces of the vector-valued wavelet wraps. Moreover, several Riesz bases of space L2(Rn)r are constructed from the wavelet wraps.

Wavelet analysis is a popular subject in science research. The notion of univariate orthog- -onal wavelet packs is generalized. First, the notion of biorthogonal nonseparable trivariate wavelet packs is proposed and a procedure for constructing them is presented. Next, the biorthogonality pro- -perty of trivariate wavelet packs is investigated, and three biorthogonality formulas of wavelet packs are established. Moreover, it is shown how to gain new Riesz bases of space from these wavelet packs.

Frame theory has been the focus of active research for twenty years, both in theory and applications. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established.

In this paper, we introduce a sort of vector four-dimensional wavelet packets according to a dilation matrix, which are generalizations of univariate wavelet packets. The definition of biortho- gonal vector four-dimensional wavelet packets is provided and their biorthogonality quality is researched by means of time-frequency analysis method, vector subdivision scheme and functional analysis method. Three biorthogonality formulas regarding the wavelet packets are established. Finally, it is shown how to draw new Riesz bases of space from these wavelet packets. The sufficient condition for the existence of four-dimensional wavelet packets is established based on the multiresolution analysis method.

In this paper, the notion of biorthogonal nonsepar-able trivariate wavelet packs£¬which is the generalization of biorthogonal univariate wavelet packs, is introduced. A new procedure for constructing them is presented. Their biorthogonality property is characterized by the filter bank theory and time-frequency analysis method. Three biorthogonality formulas concerning these wavelet packs are established.