Frames arising from irreducible solvable actions I

In this work, we provide a unified method for the construction of reproducing systems arising from unitary irreducible representations of some solvable Lie groups. In contrast to other well-known techniques such as the coorbit theory, the generalized coorbit theory and other discretization schemes, we make no assumption on the integrability or square-integrability of the representations of interest. Moreover, our scheme produces explicit constructions of frames with precise frame bounds. As an illustration of the scope of our results, we highlight that a large class of representations which naturally occur in wavelet theory and time–frequency analysis is handled by our scheme. For example, the affine group, the generalized Heisenberg groups, the shearlet groups, solvable extensions of vector groups and various solvable extensions of non-commutative nilpotent Lie groups are a few examples of groups whose irreducible representations are handled by our method. The class of representations studied in this work is described as follows. Let G be a simply connected, connected, completely solvable Lie group with Lie algebra $\mathfrak{g}=\mathfrak{p}+\mathfrak{m}$. Next, let π be an infinite-dimensional unitary irreducible representation of G obtained by inducing a character from a closed normal subgroup $P=\exp ?\mathfrak{p}$ of G. Additionally, we assume that $G=P?M$, $M=\exp ?\mathfrak{m}$ is a closed subgroup of G, $d{\mu }_M$ is a fixed Haar measure on the solvable Lie group M and there exists a linear functional $\lambda \in {\mathfrak{p}}^{?}$ such that the representation $\pi ={\pi }_{\lambda }={\mathrm{ind}}_P^G\left({\chi }_{\lambda }\right)$ is realized as acting in $L^2(M,d{\mu }_M)$. Making no assumption on the integrability of ${\pi }_{\lambda }$, we describe explicitly a discrete subset Γ of G and a vector $\mathbf{f}\in L^2(M,d{\mu }_M)$ such that ${\pi }_{\lambda }\left(\mathrm{\Gamma }\right)\mathbf{f}$ is a tight frame for $L^2(M,d{\mu }_M)$. We also construct compactly supported smooth functions s and discrete subsets $\mathrm{\Gamma }?G$ such that ${\pi }_{\lambda }\left(\mathrm{\Gamma }\right)\mathbf{s}$ is a frame for $L^2(M,d{\mu }_M)$.     

A classification of continuous wavelet transforms in dimension three

This paper presents a full catalogue, up to conjugacy and subgroups of finite index, of all matrix groups $H<\mathrm{GL}(3,\mathbb{R})$ that give rise to a continuous wavelet transform with associated irreducible quasi-regular representation. For each group in this class, coorbit theory allows to consistently define spaces of sparse signals, and to construct atomic decompositions converging simultaneously in a whole range of these spaces. As an application of the classification, we investigate the existence of compactly supported admissible vectors and atoms for the groups.     

Correlation of Moments and Critical Phenomenon in Disassembly of Hot Nuclei

We used Monte Carlo method to generate the configurations of disassembly of hot nucleus Au* based on the Atomic Mass Table and the conservation of mass and charge number.The resulted charge distribution of fragments was then used to calculate the conditional moments.The logarithm correlation between second and third moments of experimental charge distribution is very well reproduced by theory.It seems that no connection to the critical phenomenon of concerned system exists.     

THE EFFECT OF THE FREEZE-OUT VOLUME IN THE MULTIFRAGMENTATION OF VERY HOT NUCLEAR REMNANT

In this paper a simplified method for the calculation of average Coulomb energy in statistical model of the disassembly processes of hot nuclei is proposed.The effect of freeze-out volume is studied based on the assumption of Gaussion-like distribution.It is indecated that the centre and dispersion of Gaussion-like distribution somewhat reflect the location and the renge of liquid-gas coexistence phase.     

THE EVIDENCE OF DECONFINEMENT PHASE TRANSITION OF SU(2) LATTICE GAUGE MODEL BY MONTE CARLO METHOD

In this paper,we have calculated the SU(2) lattice gauge by the Monte Carlo method.For the finite temperature problem 8³×4 lattice is used and for the zero temperature problem 8⁴ lattice.From the calculations of the energy density,heat capacity and entropy density,the results indicate that there is a deconfinement phase transition when T/Λ_L=40—50.     

DIRECT SIMULATION OF DEEP INELASTIC SCATTERING OF HEAVY-IONS (I) ONE PARAMETER DISTRIBUTION

The distributions of dynamic variables in the deep inelastic scattering (DIS) of heavy-ions are studied by a direct simulation technique based on the single-nucleon-transfer-mechanism. The relative motion of the two collision partners is described by a Lagrange equation, and the transition probability of a single nucleon during the interaction time is calculated by the statisti-cal spectroscopy method.The occurrence of the transition event and the corresponding change of the dynamic variables are both treated randomly according to the transition probability. The calculated results for the reaction of ⁴⁰Ar+⁵⁸Ni(E_L=280MeV) are compared with experimental data.     

Exploration for Degradation of Λ Polarization Produced in Relativistic Nucleus Nucleus Collisions

The degradation of Λ transverse polarization produced in S+Pb central collisions at energy 200 GeV per nucleon has been studied in detail. The S+Pb central collision events have been generated using Monte-Carlo generator——LUCIAE at 200 GeV per nucleon. The various factors degrading Λ transverse polarization have been analysed quantitatively. The ratios of Λ′s produced from rescattering, secondary production and decays of Σ, Ξ hyperons to the total measurable Λ′s in experiment have been investigeted and the degradation effect of these Λ on the total polarization has been determined. The simulation and calculation show that above three factors decrease the Λ transverse polarization strongly, however, can not eliminate the polarization completely when the Λ′s are assumed to be produced from hadronic gas in the final state. To explan the experimental data of vanished Λ polarization, it probably needs to consider new mechanisms of Λ production, including a weak effect of QGP formation.     

200A GeV S+Au反应中光子产生的低横动量增强

用建立在LUND弦模型特别是PYTHIA事件产生器基础上的描写极端相对论性核-核碰撞的强子和弦级联模型--JPCIAE研究了入射能量为200A GeV的S+Au中心碰撞中光子产生.模型同时考虑了部分子QCD散射过程、强子末态相互作用以及强子衰变等光子产生反应道并作了协调处理.JPCIAE模型计算结果很好再现了WA93实验数据所呈现的低横动量增强效应.     

AxMn1-xFe2O4铁氧体(A=Zn,Ni)中阳离子的占位有序化行为研究

基于尖晶石晶体结构信息,本文采用热力学三亚晶格模型,将材料热力学计算和第一性原理计算相结合,研究了Zn_xMn_(1-x) Fe_2O_4和Ni_xMn_(1-x)Fe_2O_4立方相中的Zn~(2+)、Ni~(2+)、Mn~(2+)以及Fe~(3+)在8a和16d亚晶格上的占位有序化行为。结果表明:在锰铁氧体中,室温下Mn~(2+)完全占据在8a亚晶格上,Fe~(3+)完全占据在16d亚晶格上,属于正尖晶石结构;随着热处理温度升高,在1 273 K达到热处理平衡时的占位构型为(Fe~(3+)0.09Mn~(2+)0.91)[Fe~(3+)1.91Mn~(2+)0.09]O_4,在热处理温度升至1 473 K时,达到热处理平衡时的占位构型为(Fe~(3+)0.11Mn~(2+)0.89)[Fe~(3+)1.89Mn~(2+)0.11]O_4,均与实验结果符合较好。在锌铁氧体中,室温下Zn~(2+)完全占据在8a亚晶格上,Fe~(3+)完全占据在16d亚晶格上,属于正尖晶石结构;在热处理温度较高时,Zn~(2+)和Fe~(3+)发生部分置换,符合实验结果。在镍铁氧体中,半数的Fe~(3+)在室温下占据在8a亚晶格上,Ni~(2+)与剩下另一半的Fe~(3+)共同占据在16d亚晶格上,仅在热处理温度较高的时候发生微弱变化,亦与已有的实验结果吻合。在此基础上,本文进一步通过热力学模型研究了立方相尖晶石结构的Zn_xMn_(1-x)Fe_2O_4、Ni_xMn_(1-x)Fe_2O_4复合体系中阳离子占位行为与热处理温度对占位的影响规律。     

甘肃岷县不同生长年限当归药材的红外光谱分析

采用傅里叶变换红外光谱(FTIR)及其二阶导数谱对不同生长年限当归药材进行分析研究.结果表明,不同生长年限当归药材的红外图谱较为相似,仅从一维谱图上无法反映出不同生长年限当归药材的红外特征谱明显的异同,但通过二阶导数图谱中1771、1747、1712、1559、1514、1466、766、711cm-1和668cm-1处的峰型差异可发现不同生长年限当归药材之间的一些成分存在较明显的差异.由于生长时间不同,导致它们的化学成分存在差异,所以体现了各自的红外特征谱,其中第三年当归药材与第一年和第二年当归药材间差异较大.