An orbital motion study of globular cluster NGC6205

The positions and absolute proper motions of 264 stars in the field of about 70′×70′ around the globular cluster NGC6205 were determined. In the astrometric reduction, three early and three late epoch plates taken with the 40-cm refractor at Shensan, Shanghai, China, were used, with the epoch span of 73 a. The reduction was done using the central overlapping method, with 5 Hipparcos stars and 38 Tycho-2 stars as reference stars. Based on the reduced data of proper motion, the membership probabilities of the sample stars were determined. An absolute proper motion of the cluster of（1.49±0.36）mas a-1 in R.A. and （3.06±0.35）mas a-1 in Decl. was obtained. From this proper motion, together with distance and radial velocity data, we derived the space motion of NGC6205 and the orbit of the cluster in the Galaxy via numerical integration.     

Spaces in which every dense subset is a Gδ

A topological space X is called a DG_δ-space if every subset of X is a G_δ-set in its closure. In this paper we study DG_δ-spaces that contains subspaces in which every dense subset is open and spaces in which every subset is a G_δ . We give some new results in these classes of topological spaces.     

Abundances of heavy elements in ultra-metal-poor star CS 22892-052

Based on the heavy element nucleosynthesis theory, with the solar heavy-nuclide abundances and the observed abundances of three elements which are the representatives of the individul neutron-capture processes, a method to determine the relative contributions from the individul neutron-capture processes to the abundances of heavy elements in metal-poor stars is applied. With this method, the abundances of heavy elements in ultra-metal-poor star CS 22892-052 are calculated. It is found that the observed abundances of heavy elements in this star are well matched by our calculations in error limits, except for thorium Project supported by the National Natural Science Foundation of China (Grant No. 19673008). The visiting scholar of Shijiazhuang Teacher’s College.     

Gradient Estimates of Solutions to the Conductivity Problem with Flatter Insulators

We study the insulated conductivity problem with inclusions embedded in a bounded domain in R~n. When the distance of inclusions, denoted by ε, goes to 0, the gradient of solutions may blow up. When two inclusions are strictly convex, it was known that an upper bound of the blow-up rate is of order ε~(-1/2) for n = 2, and is of order ε~(-1/2+β)for some β 0 when dimension n ≥ 3. In this paper, we generalize the above results for insulators with flatter boundaries near touching points.     

Harmonic mappings onto stars

A general version of the Radó-Kneser-Choquet theorem implies that a piecewise constant sense-preserving mapping of the unit circle onto the vertices of a convex polygon extends to a univalent harmonic mapping of the unit disk onto the polygonal domain. This paper discusses similarly generated harmonic mappings of the disk onto nonconvex polygonal regions in the shape of regular stars. Calculation of the Blaschke product dilatation allows a determination of the exact range of parameters that produce univalent mappings.     

On Maclaurin and Jacobi Objects Embedded in Halos: The Shift in the Point of Bifurcation

This paper concerns the equilibrium structure of Maclaurin spheroids and Jacobi ellipsoids embedded in nonrotating halos of uniform density. The halo is assumed unresponsive to the embedded object, whereas the embedded object is allowed to respond to the gravitational field of the halo. We also ignore the effects of the halo pressure field on the embedded object. It is shown how the halo modifies the classical Maclaurin and Jacobi sequences. In particular, we locate the intersection of these two sequences, i.e., the point of bifurcation, and present a formula for the eccentricity at bifurcation (e_b) as a function of the ratio of halo density to density of rotating matter (ρ_H/ρ_B). We find that the halo increases the eccentricity at bifurcation; thus, it has a stabilizing influence. However, secular instability is never entirely suppressed, since e_b→1 only for ρ_H/ρ_B→∞. It is seen that the Ostrike-Peebles conjecture does not apply to the case of ρ_H/ρ_B?1.     

Complexity in close binary evolution

The complex nature of close binary evolution is briefly reviewed. Population synthesis calculations of zero‐age cataclysmic variable stars (ZACVs) are presented using a common envelope (CE) efficiency parameter, α_CE, that is a function of the core mass of the primary. Specifically, we investigate the possibility that α_CE is different for CE evolution involving red giant branch (RGB) primaries than for asymptotic giant branch (AGB) primaries. We calculate a sequence of model orbital period distributions in present‐day ZACVs for 11 different combinations of efficiency parameters (α_RGB, α_AGB). We find that if CE evolution is much less efficient for RGB primaries than for AGB primaries (α_RGB ～ 0.1 or less), the number of CVs that form below 2 h is significantly decreased compared with standard constant α_CE models. © 2008 Wiley Periodicals, Inc. Complexity, 2008.     

Contingent derivative of the perturbation map in multiobjective optimization

Consider a parametrized multiobjective optimization problem with parameteru. LetG(u) be the objective space image of the feasible region, and letW(u)=MinG(u) (the perturbation map) be the efficient set in the objective space. The purpose of this paper is to investigate the relationship between the contingent derivativeDW ofW with respect tou and the contingent derivativeDG ofG with respect tou. Tanino (Ref. 1) proves that MinDGDW under certain conditions. In this paper, we prove that MinDG=MinDW under weaker conditions than Tanino's and that MinDG=DW under certain conditions. The paper does this by introducing a weaker notion of set-valued derivative. Along the way, the paper improves another of Tanino's results by using weaker conditions.The author would like to thank two anonymous referees for helpful comments. The author would also like to thank Professor P. L. Yu for encouragement and useful suggestions.     

Solution of the equations of the relativistic theory of gravitation for equilibrium massive bodies with allowance for their equations of state

The solutions of the equations of the relativistic theory of gravitation that describe the equilibrium state of a spherically symmetric isolated massive body are analyzed. It is shown that if the mass of the body is greater than the critical value equilibrium states do not exist; the minimum sizes of such bodies are always greater than the Schwarzschild sizes. We investigate the equilibrium sizes, the structure of the exterior gravitational field, and the distributions of the interior pressures and densities in the case of characteristic astrophysical objects such as the earth, Jupiter, the sun, neutron stars, and white dwarfs. The results agree satisfactorily with observations.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 1, pp. 122–139, January, 1993.     

Interface interaction and inter-osmosis effect of Fe x (SiO2)1-x nanocomposite materials on magnetic properties

Fe _x (SiO₂)_1-x nanocomposites prepared by using mechanical alloying method were reported. The microstructure character and magnetic properties of Fe _x (SiO₂)_1-x nanocomposite samples with different Fe content and different ball milling time were studied by using X-ray diffraction (XRD), transmission electron microscopy (TEM), Mössbauer spectroscopy, and Faraday magnetic balance in a wide temperature range. The results indicate that the rnicrostructure and magnetic properties are closely related to ball milling time and Fe content. When Fe content is less than 20 wt%, the sample after 80-h ball milling has very complex microstructure. Small α-Fe grains and Fe cluster are implanted in SiO₂ matrix. And there are not only isolated α-Fe granular and Fe cluster, but also nanometer scaled sandwich network-like structure. Fe _x (SiO₂)_1-x nanocomposite samples display a rich variety of physical and chemical properties as a result of their unique nanostructure, strong interface interaction and inter-osmosis effect in Fe-SiO₂ boundaries, and the grain size effect.     

On the number of certain subgraphs contained in graphs with a given number of edges

All graphs considered are finite, undirected, with no loops, no multiple edges and no isolated vertices. For two graphsG, H, letN(G, H) denote the number of subgraphs ofG isomorphic toH. Define also, forl≧0,N(l, H)=maxN(G, H), where the maximum is taken over all graphsG withl edges. We determineN(l, H) precisely for alll≧0 whenH is a disjoint union of two stars, and also whenH is a disjoint union ofr≧3 stars, each of sizes ors+1, wheres≧r. We also determineN(l, H) for sufficiently largel whenH is a disjoint union ofr stars, of sizess ₁≧s ₂≧…≧s _r>r, provided (s ₁−s _r)²<s ₁+s _r−2r. We further show that ifH is a graph withk edges, then the ratioN(l, H)/l ^k tends to a finite limit asl→∞. This limit is non-zero iffH is a disjoint union of stars.     

On rotating axisymmetric solutions of the Euler–Poisson equations

We consider stationary axisymmetric solutions of the Euler–Poisson equations, which govern the internal structure of barotropic gaseous stars. We take the general form of the equation of states which cover polytropic gaseous stars indexed by $6/5<\gamma <2$ and also white dwarfs. A generic condition of the existence of stationary solutions with differential rotation is given, and the existence of slowly rotating configurations near spherically symmetric equilibria is shown. The problem is formulated as a nonlinear integral equation, and is solved by an application of the infinite dimensional implicit function theorem. Oblateness of star surface is shown and also relationship between the central density and the total mass is given.     

基于BP神经网络的山坡平均坡度解

用BP神经网络方法对山坡平均山坡的解法进行分析,以29个小流域样本的水文数据为基础,通过应用人工神经网络反向传播BP(Back Propagation)算法,引入与山坡平均坡度密切相关的流域影响因子,并且通过调整网络结构中的权因子和阈值,建立了山坡平均坡度与流域影响因子之间的BP网络模型.计算结果表明,用拓扑结构为5-12-1的BP网络,经过学习150000次后,随机测试小流域样本的山坡平均坡度其计算结果和测试结果的相对误差不超过5%;证明该ANN模型的拟合能力强,从而为小流域山坡平均坡度的计算提供了一条新途径.     

Bending analysis of a functionally graded rotating disk based on the first order shear deformation theory

The theoretical formulation for bending analysis of functionally graded (FG) rotating disks based on first order shear deformation theory (FSDT) is presented. The material properties of the disk are assumed to be graded in the radial direction by a power law distribution of volume fractions of the constituents. New set of equilibrium equations with small deflections are developed. A semi-analytical solution for displacement field is given under three types of boundary conditions applied for solid and annular disks. Results are verified with known results reported in the literature. Also, mechanical responses are compared between homogeneous and FG disks. It is found that the stress couple resultants in a FG solid disk are less than the stress resultants in full-ceramic and full-metal disk. It is observed that the vertical displacements for FG mounted disk with free condition at the outer surface do not occur between the vertical displacements of the full-metal and full-ceramic disk. More specifically, the vertical displacement in a FG mounted disk with free condition at the outer surface can even be greater than vertical displacement in a full-metal disk. It can be concluded from this work that the gradation of the constitutive components is a significant parameter that can influence the mechanical responses of FG disks.     

Radon concentration of air over the Eastern Arabian Sea

The radon concentrations of air samples collected during the South West monsoon period at altitudes up to 4 km over the Arabian Sea at two locations,i.e., 0–50 km and 300–400 km west of Bombay, are reported. Radon was extracted from air, using a simple single stage apparatus. The concentration of radon in the monsoon air mass was found to range around 80–100 dpm/m³ STP, indicative of its recent continental origin. The results suggest that the coastal monsoon air mass, up to 400 km west of Bombay coast, is generally homogeneous and vertically well mixed. During the post-monsoon condition, a strong gradient in the radon concentration in the vertical is observed. The concentration of radon decreases from 157 dpm/m³ at sea level to 35 dpm/m³ at about 3·7 km altitude, suggesting a vertical turbulent diffusion coefficient of ～6×10⁴ cm²/sec. In contrast, the near absence of vertical gradient of radon in the monsoon air mass indicates that the vertical turbulence is much stronger during the monsoon period.     

Finite element analysis of thermoelastic field in a rotating FGM circular disk

This study focuses on the finite element analysis of thermoelastic field in a thin circular functionally graded material (FGM) disk subjected to a thermal load and an inertia force due to rotation of the disk. Due to symmetry, the FGM disk is assumed to have exponential variation of material properties in radial direction only. As a result of nonuniform coefficient of thermal expansion (CTE) and nonuniform temperature distribution, the disk experiences an incompatible eigenstrain which is taken into account. Based on the two dimensional thermoelastic theories, the axisymmetric problem is formulated in terms of a second order ordinary differential equation which is solved by finite element method. Some numerical results of thermoelastic field are presented and discussed for an Al₂O₃/Al FGM disk. The analysis of the numerical results reveals that the thermoelastic field in an FGM disk is significantly influenced by temperature distribution profile, radial thickness of the disk, angular speed of the disk, and the inner and outer surface temperature difference, and can be controlled by controlling these parameters.     

On a Problem of Schoenberg and Wills in Diophantine Approximation

Let n be a fixed natural number. Wills has shown that there exist irrational numbers α₁,..., α_n and real numbers β₁,..., β₁ with max_1≤i≤n ‖qα_i-β_i‖ > 1/2 – 1/2n for all integers q (‖·‖ denotes the distance to the nearest integer). His example is α_i = α and β_i = i/n + δ, δ suitably chosen. Beyond that, he asked if α_i can be found with pairwise different ‖α_i‖. We prove that this does not hold for n ≤ 5, thereby revealing the close relation to Schoenberg's billiard ball problem for cubes and classifying its critical lines in these dimensions.     

A new algorithm for the small-field astrometric point-pattern matching problem

The small-field astrometric point-pattern matching problem is a fundamental problem in astronomy, that although considered a long time ago still lacks a formal definition. It can be textually stated as: given two lists of positions of stars, find the common stars between these lists, taking into account rotation, translation, reflection and scaling operations. It is expected that there might be missing stars between the lists. In this work, we give the astronomical context, review some heuristic methods adopted in the literature, present distance matrix formulations for the problem and propose a new algorithm to solve it.     

Minimizing mean squared deviation of completion times with maximum tardiness constraint

We consider a nonpreemptive single-machine scheduling problem to minimize mean squared deviation of job completion times about a common due date with maximum tardiness constraint (MSD/T_max problem), where the common due date is large enough so that it does not constrain the minimization of MSD.The MSD/T_max problem is classified into three cases according to the value of maximum allowable tardiness Δ: Δ-unconstrained, Δ-constrained and tightly Δ-constrained cases. It is shown that the Δ-unconstrained MSD/T_max problem is equivalent to the unconstrained MSD problem and that the tightly Δ-constrained MSD/T_max problem with common due date d is equivalent to the tightly constrained MSD problem with common due date Δ. We also provide bounds to decide when the MSD/T_max problem is Δ-unconstrained or Δ-constrained. Then a solution procedure to the MSD/T_max problem is presented with several examples.