A SUFFICIENT CONDITION FOR AFFINE FRAMES WITH MATRIX DILATION

A sufficient condition for affine frame with an arbitrary matrix dilation is presented. It is based on the univariate case by Shi, and generalizes the univariate results of Shi, Casazza and Christensen from one dimension with an arbitrary real number a （a 〉 1） dilation to higher dimension with an arbitrary expansive matrix dilation.

Chemical, mechanical, and thermal expansion properties of a carbon nanotube-reinforced aluminum nanocomposite

In the present study,the chemical and mechanical properties and the thermal expansion of a carbon nanotube（CNT）-based crystalline nano-aluminum（nano Al） composite were reported.The properties of nanocomposites were tailored by incorporating CNTs into the nano Al matrix using a physical mixing method.The elastic moduli and the coefficient of thermal expansion（CTE） of the nanocomposites were also estimated to understand the effects of CNT reinforcement in the Al matrix.Microstructural characterization of the nanocomposite reveals that the CNTs are dispersed and embedded in the Al matrix.The experimental results indicate that the incorporation of CNTs into the nano Al matrix results in the increase in hardness and elastic modulus along with a concomitant decrease in the coefficient of thermal expansion The hardness and elastic modulus of the nanocomposite increase by 21%and 20%,respectively,upon CNT addition.The CTE of CNT/A1 nanocomposite decreases to 70%compared with that of nano Al.

Mechanical, electrical, and thermal expansion properties of carbon nanotube-based silver and silver–palladium alloy composites

The mechanical, electrical, and thermal expansion properties of carbon nanotube（CNT）-based silver and silver–palladium（10：1, w/w） alloy nanocomposites are reported. To tailor the properties of silver, CNTs were incorporated into a silver matrix by a modified molecular level-mixing process. CNTs interact weakly with silver because of their non-reactive nature and lack of mutual solubility. Therefore, palladium was utilized as an alloying element to improve interfacial adhesion. Comparative microstructural characterizations and property evaluations of the nanocomposites were performed. The structural characterizations revealed that decorated type-CNTs were dispersed, embedded, and anchored into the silver matrix. The experimental results indicated that the modification of the silver and silver–palladium nanocomposite with CNT resulted in increases in the hardness and Young＇s modulus along with concomitant decreases in the electrical conductivity and the coefficient of thermal expansion（CTE）. The hardness and Young＇s modulus of the nanocomposites were increased by 30%？40% whereas the CTE was decreased to 50%-60% of the CTE of silver. The significantly improved CTE and the mechanical properties of the CNT-reinforced silver and silver–palladium nanocomposites are correlated with the intriguing properties of CNTs and with good interfacial adhesion between the CNTs and silver as a result of the fabrication process and the contact action of palladium as an alloying element.

Modifed Multifdelity Surrogate Model Based on Radial Basis Function with Adaptive Scale Factor

Multifdelity surrogates(MFSs)replace computationally intensive models by synergistically combining information from diferent fdelity data with a signifcant improvement in modeling efciency.In this paper,a modifed MFS(MMFS)model based on a radial basis function(RBF)is proposed,in which two fdelities of information can be analyzed by adaptively obtaining the scale factor.In the MMFS,an RBF was employed to establish the low-fdelity model.The correlation matrix of the high-fdelity samples and corresponding low-fdelity responses were integrated into an expansion matrix to determine the scaling function parameters.The shape parameters of the basis function were optimized by minimizing the leave-one-out cross-validation error of the high-fdelity sample points.The performance of the MMFS was compared with those of other MFS models(MFS-RBF and cooperative RBF)and single-fdelity RBF using four benchmark test functions,by which the impacts of diferent high-fdelity sample sizes on the prediction accuracy were also analyzed.The sensitivity of the MMFS model to the randomness of the design of experiments(DoE)was investigated by repeating sampling plans with 20 diferent DoEs.Stress analysis of the steel plate is presented to highlight the prediction ability of the proposed MMFS model.This research proposes a new multifdelity modeling method that can fully use two fdelity sample sets,rapidly calculate model parameters,and exhibit good prediction accuracy and robustness.

LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES

Let p∈（0, 1], q∈（0, ∞] and A be a general expansive matrix on Rn. Let HAp,q （Rn） be the anisotropic Hardy-Lorentz spaces associated with A defined via the non-tangential grand maximal function. In this article, the authors characterize HAp,q（Rn） in terms of the Lusin-area function, the Littlewood-Paley g-function or the Littlewood-Paley gλ＊-function via first establishing an anisotropic Fefferman-Stein vector-valued inequality in the Lorentz space Lp,q（Rn）. All these characterizations are new even for the classical isotropic Hardy-Lorentz spaces on Rn. Moreover, the range of λ in the gλ＊-function characterization of HAp,q （Rn） coincides with the best known one in the classical Hardy space Hp（Rn） or in the anisotropic Hardy space HAp （Rn）.

Systematic Synthesis of Compressive VDTA-Based T-T Filter with Orthogonal Control of f_o and Q

Based on sixteen nullor-mirror models of the voltage differencing transconductance amplifier (VDTA) and port admittance matrices of the tow-Thomas (T-T) filter with orthogonal control between the characteristic frequency(f_0) and figure of merit (Q),two different categories of the voltage-mode and transconductance-mode T-T filters are synthesized by the means of the nodal admittance matrix (NAM) expansion method.The category A filter that employs two compressive VDTAs and two grounded capacitors includes four structures,and the category B filter that uses two compressive VDTAs,two grounded capacitors,and one grounded resistor,also includes four structures.These circuits are suitable for integrated circuit manufacture,and their parameters f_0 and Q can be orthogonally adjusted with varying the bias currents of VDTAs.After the paper and pencil test is completed,the computer analyses,including alternating current (AC),parameter sweep,Monte Carlo (MC),and noise analyses,are performed to support the synthesis approach.

Thermal properties of diamond/Al composites by pressure infiltration:comparison between methods of coating Ti onto diamond surfaces and adding Si into Al matrix

This study was pertained to the effects of Ti coating on diamond surfaces and Si addition into Al matrix on the thermal conductivity（TC） and the coefficient of thermal expansion（CTE） of diamond/Al composites by pressure infiltration.The fracture surfaces,interface microstructures by metal electro-etching and interfacial thermal conductance of the composites prepared by two methods were compared.The results reveal that Ti coating on diamond surfaces and only12.2 wt% Si addition into Al matrix could both improve the interfacial bonding and increase the TCs of the composites.But the Ti coating layer introduces more interfacial thermal barrier at the diamond/Al interface compared to adding 12.2 wt% Si into Al matrix.The diamond/Al composite with 12.2 wt% Si addition exhibits maximum TC of 534 W·m^-1·K^-1and a very low CTE of 8.9×10^-6K^-1,while the coating Ti-diamond/Al composite has a TC of 514 W·m^-1·K^-1 and a CTE of 11.0×10^-6K^-1.

Synthesis for Current-Mode Sallen-Key Filter Using VDTAs

In this work, an original Sallen-Key second-order low-pass filter is first turned into a current-mode one by means of the adjoint network theorem. Two nodal admittance matrices(NAM) of the filter are then educed. Furthermore, these two matrices are expanded through NAM expansion approach, generating one current-mode Sallen-Key filter, which uses two compact voltage differential trans-conductance amplifiers(VDTAs) and two grounded capacitors, implements not only one low-pass transfer function but two band-pass transfer functions, and provides the non-interrelated control between the natural frequency and quality factor. As an example of the synthesized filter, a second-order VDTA filter with fo=1 MHz, Q=1, HLP=-HBP1=HBP2=1 is designed. The used synthesis approach has been confirmed with the help of circuit and computer analysis.

Pathological Models of EXCCCII and Its Applications in Oscillator Synthesis

After giving six different forms of the extra X second-generation current-controlled conveyor(EXCCCII),pathological models of six EXCCCIIs are found by the nodal admittance matrix(NAM)expansion approach.Furthermore,these ideal pathological circuit models are employed and 36 Wien oscillators and 8 third-order quadrature oscillators are synthesized by the NAM expansion.The hand analysis and computer analysis are introduced to prove the synthesized circuits are correct and effective.

Anisotropic Hardy-Lorentz spaces and their applications

Let p ∈(0, 1], q ∈(0, ∞] and A be a general expansive matrix on Rn. We introduce the anisotropic Hardy-Lorentz space H^(p,q)_A(R^n) associated with A via the non-tangential grand maximal function and then establish its various real-variable characterizations in terms of the atomic and the molecular decompositions, the radial and the non-tangential maximal functions, and the finite atomic decompositions. All these characterizations except the ∞-atomic characterization are new even for the classical isotropic Hardy-Lorentz spaces on Rn.As applications, we first prove that Hp,q A(Rn) is an intermediate space between H^(p1,q1)_A(Rn) and H^(p2,q2)_A(R^n) with 0 < p1 < p < p2 < ∞ and q1, q, q2 ∈(0, ∞], and also between H^(p,q1)_A(Rn) and H^(p,q2)_A(R^n) with p ∈(0, ∞)and 0 < q1 < q < q2 ∞ in the real method of interpolation. We then establish a criterion on the boundedness of sublinear operators from H^(p,q)_A(R^n) into a quasi-Banach space; moreover, we obtain the boundedness of δ-type Calder′on-Zygmund operators from H^(p,∞)_A(R^n) to the weak Lebesgue space L^(p,∞)(R^n)(or to H^p_A(R^n)) in the ln λcritical case, from H^(p,q)_A(R^n) to L^(p,q)(R^n)(or to H^(p,q)_A(R^n)) with δ∈(0,(lnλ)/(ln b)], p ∈(1/(1+,δ),1] and q ∈(0, ∞], as well as the boundedness of some Calderon-Zygmund operators from H^(p,q)_A(R^n) to L^(p,∞)(R^n), where b := | det A|,λ_:= min{|λ| : λ∈σ(A)} and σ(A) denotes the set of all eigenvalues of A.

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.

Thermal Properties of Mg–Al/AlN Composites Fabricated by Powder Metallurgy

Magnesium matrix composites reinforced with AlN particles were fabricated by the powder metallurgy technique.Different mixing methods were used in this study to control the distribution of Al N particles.The microstructure,thermal diffusivity and thermal expansion of the Mg–Al/Al N composites using different mixing methods were investigated.The results showed that the intergranular and intragranular distributions of Al N particles were obtained,respectively,by controlling the mixing methods.The composite with intragranular particles exhibited lower thermal diffusivity because of the existences of more interfaces,defects and grain boundaries,which acted as scattering centers and reduced the mean free path of electrons and phonons.The existence of Al N particles lowered the coefficient of thermal expansion（CTE）and enhanced the dimensional stability of the composites.And the use of the improved mixing method further reduced the CTE of Mg–Al/Al N composites.

A Survey on Some Anisotropic Hardy-Type Function Spaces

Let A be a general expansive matrix on Rn.The aims of this article are twofold.The first one is to give a survey on the recent developments of anisotropic Hardy-type function spaces on Rn,including anisotropic Hardy–Lorentz spaces,anisotropic variable Hardy spaces and anisotropic variable Hardy–Lorentz spaces as well as anisotropic Musielak–Orlicz Hardy spaces.The second one is to correct some errors and seal some gaps existing in the known articles.Some unsolved problems are also presented.