多重胞元和规则多重分形

以超级分形纤维和双重分形纤维的研究结果为基础,达成了如下目标:首先,归纳、抽象出了多重胞元概念;其次,基于多重胞元概念,证实:具有严格自相似性的规则多重分形,不仅是可构造的,而且其构造模式具有普遍性;再者,通过分析构造模式,发现:任何规则多重分形,都可以在多重胞元意义下,被精确地等价成具有多重精细结构的广义单重分形．而基于这种等价性,单重分形维数公式就能够推广至规则多重分形维数公式,单重分形几何就能够推广至规则多重分形几何;最后,借助规则多重分形,构造了几种黄金分形．     

Simplified Scheme for Test of Quantum Nonlocality Without Using Bell Inequality

A simplified scheme is proposed for the test of quantum nonlocality of the type described by Hardy [Phys.Rev.Left.71 (1993) 1665] .In the scheme two appropriately prepared atoms are simultaneously sent through a cavity and dispersively interact with the cavity field.Then state-selective measurements are performed on these atoms,which may reveal quantum nonlocality without using Bell inequality.We also propose a simple scheme for the generation of multi-atom entangled states.     

锰/磷、钛/磷二元团簇的激光溅射产生与光解

利用激光溅射法直接产生了锰／磷、钛／磷二元团簇正、负离子MxPy^±(M=Mn、Ti） ,并用串级飞行时间质谱仪研究了团簇离子的组成与激光光解规律。实验表明钛与磷间成簇的能力强于锰与磷间成簇的能力,且MPy^+(M=Ti、Mn)团簇离子系列表现出峰强度了胡所含磷原子数目的奇偶性变化,这可能与P4结构的特殊稳定性有关。激光光解实验表明,失去中性P2、P4的通道为主要光解通道。随着团簇离子的生长,锰／磷团簇正离子逐渐由富磷簇向富金属簇过渡,钛／磷则趋向于形成钛原子数目与磷原子数目接近相等的团簇正离子,而二者与磷形成的团簇负离子MxPy^-(M=Mn、Ti) 逐渐趋向于x ≈ y,随样品中磷含量增加,锰／磷易形成富磷簇,钛／磷的组成趋向不改变。     

First return probabilities of birth and death chains and associated orthogonal polynomials

For a birth and death chain on the nonnegative integers, integral representations for first return probabilities are derived. While the integral representations for ordinary transition probabilities given by Karlin and McGregor (1959) involve a system of random walk polynomials and the corresponding measure of orthogonality, the formulas for the first return probabilities are based on the corresponding systems of associated orthogonal polynomials. Moreover, while the moments of the measure corresponding to the random walk polynomials give the ordinary return probabilities to the origin, the moments of the measure corresponding to the associated polynomials give the first return probabilities to the origin.

As a by-product we obtain a new characterization in terms of canonical moments for the measure of orthogonality corresponding to the first associated orthogonal polynomials. The results are illustrated by several examples.

     

Chromatographic study of adsorption from binary and ternary solutions

Adsorption of benzene, anisole, and nitrobenzene on hydroxylated silica gel from binary and ternary solutions (adsorbate--n-hexane and adsorbate--n-hexane--terahydrofuran) was studied by HPLC. The equation that describes the adsorbate retention as a function of its concentration in binary and ternary solutions was proposed. The equation makes it possible to calculate the adsorption isotherms and adsorption equilibrium constants directly from chromatograms using the retention parameters and equilibrium concentrations of the adsorbate in the mobile phase.     

拓扑指数Y_M与二元氧化物的光学碱标

提出了一个新的拓扑指数YM,并用YM 研究了二元氧化物光学碱度的新标度。研究表明 ,YM 与二元氧化物的光学碱度呈良好的线性关系。计算了一百多个二元氧化物的光学碱度值 ,结果与二元氧化物的实际酸碱性顺序符合得很好。新方法可标度周期表中二元氧化物的光学碱度。     

Thermal Analysis of Solid-Solid Interactions in Binary Mixtures of Alkylcyclohexanes Using DSC

Differential scanning calorimetry (DSC) was used to construct phase diagrams of binary mixtures of alkylcyclohexanes and to characterize metastable phases formed in the binary mixtures. The experimentally measured liquidus curves were compared to the liquidus curves calculated using ideal solution theory. The measured phase diagrams of pentadecylcyclohexane/nonadecylcyclohexane and octadecylcyclohexane/nonadecylcyclohexane binary mixtures are consistent with theoretical phase diagrams constructed based on the assumption that these mixtures form eutectic systems. It was also observed that a metastable phase formed in some binary mixtures of pentadecylcyclohexane/nonadecylcyclohexane under fast cooling conditions. It is hypothesized that this metastable phase recrystallizes into the eutectic phase upon heating. This revised version was published online in July 2006 with corrections to the Cover Date.     

Evolution Induced Catastrophe in a Nonlinear Dynamical Model of Material Failure

In order to study the failure of disordered materials, theensemble evolution of a nonlinear chain model was examined by using astochastic slice sampling method. The following results were obtained.(1) Sample-specific behavior, i.e. evolutions are different from sampleto sample in some cases under the same macroscopic conditions, isobserved for various load-sharing rules except in the globally meanfield theory. The evolution according to the cluster load-sharing rule,which reflects the interaction between broken clusters, cannot bepredicted by a simple criterion from the initial damage pattern and eventhen is most complicated. (2) A binary failure probability, itstransitional region, where globally stable (GS) modes andevolution-induced catastrophic (EIC) modes coexist, and thecorresponding scaling laws are fundamental to the failure. There is asensitive zone in the vicinity of the boundary between the GS and EICregions in phase space, where a slight stochastic increment in damagecan trigger a radical transition from GS to EIC. (3) The distribution ofstrength is obtained from the binary failure probability. This, likesample-specificity, originates from a trans-scale sensitivity linkingmeso-scopic and macroscopic phenomena. (4) Strong fluctuations in stressdistribution different from that of GS modes may be assumed as aprecursor of evolution-induced catastrophe (EIC).     

Bifurcation in a Nonlinear Autoparametric System Using Experimental and Numerical Investigations

Experimental and numerical investigations are carried out on anautoparametric system consisting of a composite pendulum attached to aharmonically base excited mass-spring subsystem. The dynamic behavior ofsuch a mechanical system is governed by a set of coupled nonlinearequations with periodic parameters. Particular attention is paid to thedynamic behavior of the pendulum. The periodic doubling bifurcation ofthe pendulum is determined from the semi-trivial solution of thelinearized equations using two methods: a trigonometric approximation ofthe solution and a symbolic computation of the Floquet transition matrixbased on Chebyshev polynominal expansions. The set of nonlineardifferential equations is also integrated with respect to time using afinite difference scheme and the motion of the pendulum is analyzed viaphase-plane portraits and Poincaré maps. The predicted resultsare experimentally validated through an experimental set-up equippedwith an opto-electronic set sensor that is used to measure the angulardisplacement of the pendulum. Period doubling and chaotic motions areobserved.     

Estimates of the maximal value of angular code distance for 24 and 25 points on the unit sphere in ℝ4

The present paper is devoted to the well-known problem of determining the maximum number of elementsτ _m (s) of a sphericals-code (−1<-s<1) in Euclidean space ℝ ^m of dimensionm>-2; to be exact, here we consider the Delsarte functionw _m (s) related toτ _m (s) via the inequalityτ _m (s) ≤w _m (s). In this paper, the solution of the equationw _m (s)=N is obtained form=4 andN=24,25. As a consequence, we obtain the assertion that among any 25 (24) points on the unit sphere in the space ℝ⁴ there always exist two points with angular distance between them strictly less than 60.5° (61.41°). Translated fromMatematicheskie Zametki, Vol. 68, No. 4, pp. 483–503, October, 2000.