Frame Wavelets with Compact Supports for L^2（R^n）

The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n × n real expansive matrix A, the frame-sets with respect to A are a family of sets in R^n. Based on the frame-sets, a class of high-dimensional frame wavelets with analytic forms are constructed, which can be non-bandlimited, or even compactly supported. As an application, the construction is illustrated by several examples, in which some new frame wavelets with compact supports are constructed. Moreover, since the main result of this paper is about general dilation matrices, in the examples we present a family of frame wavelets associated with some non-integer dilation matrices that is meaningful in computational geometry.     

Experimental investigation on large deflection response of a frame impacted by a moving body

This paper reports on the experimental investigation of the dynamic large deflection response of a portal frame impacted at its midspan by a body moving at a certain speed. Both the deflection and velocity vs. time curves of the midspan and the dynamic history of a number of desired locations were recorded during the process of response. On the basis of the test data, the momentum and kinetic energy conversion between the frame and the moving body in the impact process are realized, and the occurrence and expansion of plastic regions are described. Investigation results show that the initial collision is approximately ideally inelastic, and that the elastic deformation plays a considerable role in the response though the input energy is much larger than the maximum elastic energy capacity of the beam member; therefore, in a general impact, the energy ratio should not be regarded as a sufficient criterion for a rigid—plastic solution. The ratios of the impulse transferred to and the energy absorbed by the frame in the initial collision to that carried by the moving body before impact is only related to the ratiobetween the equivalent mass of the frame paticipating in the initial collision and the mass of the impacting body, having nothing to do with the impacting velocity to a certain extent.     

双核银络合物[Ag_2(dppm)_2(Py)_2(μ-Cl)]ClO_4的合成与结构

二-(二苯基膦)甲烷(dppm)是一种易与金属形成多核络合物的有机膦配体。我们用dppm作为配体合成了一系列银的多核络合物,并对其结构进行了研究。本文报导了其中一个双核化合物[Ag_2(dppm)_2(Py)_2(μ-Cl)]ClO_4的合成及晶体结构、分子结构的测定。     

Über Perrhenate. 3 Zum Aufbau des Mesoperrhenates Na3[ReO5]

About Perrhenates. 3 On the Structure of the Mesoperrhenate Na₃[ReO₅] By tempering powder samples (prepared from mixtures of binary oxides: Na₂O₂/ReO₂ and Na₂O/ReO₃ respectively, Na : Re = 3 : 1, Ar and O₂ atmosphere respectively, 400–450°C, corundum boat) in a closed Ag cylinder (500–550°C, 10 d) yellow single crystals of Na₃ReO₅, sensitive to moisture, were grown. The compound crystallizes trigonal, space group P3₁, P3₂ respectively, with a = 5.544(1), c = 13.580(7) Å, Z = 3, d_rö. = 4.62 g/cm³. The crystal structure [4-circle diffractometer data, 1091 I₀(hkl), AgKα, R = 6.14, R_w = 6.08%] is characterized by “isolated” bipyramids ReO₅. Na⁺ ions are occupying all the tetrahedral (Na2, Na3) and octahedral (Na1) holes of the pseudocubic face centred (c/a = 2.441) Re part of the lattice; resulting in a Na₃Re kation framework corresponding to the Li₃Bi type of structure. Effective Coordination Numbers (ECoN), the Madelung Part of Lattice energy (MAPLE) and the charge distribution (CHARDI) are computed and discussed.     

The effect of a coriolis force on Taylor-Couette flow

Taylor-Couette flow subject to a Coriolis force is studied experimentally and numerically. In the experiment, the Couette apparatus is mounted on a turntable with the axis of the cylinders orthogonal to the rotation vector of the turntable. The Coriolis force stabilizes the fluid against the onset of Taylor vortices and alters the velocity fields, both above and below the transition from the initial flow. At small dimensionless turntable frequencies, the transition yields time-independent Taylor vortices which are tilted with respect to the cylinder axis. At larger there is a direct transition to turbulence. We determine the first-order correction to the classical Couette initial flow, to account for the effects of the Coriolis force, by expanding in powers of. We present numerical results for the axial velocity (the only nonvanishing correction term to order) in the infinite-cylinder approximation.     

Decomposable super‐simple NRBIBDs with block size 4 and index 6

Necessary conditions for the existence of a super‐simple, decomposable, near‐resolvable ‐balanced incomplete block design (BIBD) whose 2‐component subdesigns are both near‐resolvable ‐BIBDs are (mod ) and . In this paper, we show that these necessary conditions are sufficient. Using these designs, we also establish that the necessary conditions for the existence of a super‐simple near‐resolvable ‐RBIBD, namely (mod ) and , are sufficient. A few new pairwise balanced designs are also given.     

Construction of Multivariate Tight Framelet Packets Associated with Dilation Matrix

In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles.We also prove how to construct various tight frames for L2(Rd) by replac-ing some mother framelets.