Plane Elasticity and Dislocation of One-Dimensional Hexagonal Quasicrystals with Point Group 6

Plane elasticity theory of one-dimensional hexagonal quasicrystals with point group 6 is proposed and established. As an application of this theory, one typical example of dislocation problem in the quasicrystals is investigated and its exact analytic solution is presented. The result obtained indicates that the stress components of (elastic) fields of a straight dislocation in the quasicrystals still first order singularity, which is the same as the (general crystals,) but are related with the Burgers vector of phason fields, which is different from the general (crystals.)

Point Groups and Single Forms of Quasicrystals with Eightfold and Twelvefold Symmetry

This paper mainly deals with the point groups and single forms of octagonal quasicrystals and the description of one-dimensional quasilattice. The authors present a new sequence for describing the arrangement of quasiperiods in one-dimensional quasilattice. The first ten numbers of quasiperiods of this sequence are 1, 1, 2, 5, 12, 29, 70, 169, 408 and 985. The arrangement of quasiperiods in the first five steps are a, b, ab. babab and babababbabab. Seven p(?)nt groups and nine single forms for the octagonal system have been deduced, They are as follows: Point groups: 8.8m, 82, 8/m, 8/mmm, 8 and 82m; single forms: octagonal prism, dioctagonal prism. octagonal pyramid. dioctagonal pyramid. octagonal dipyramid, dioctagonal dipyramid, octagonal scalenohedron, dioctagonal scalenohedron and octagonal trapezohedron. Besides seven point groups and nine single forms for the dodecahegonal system have also been deduced.

Complex method of the plane elasticity in 2D quasicrystal with point group 10 mm tenfold rotational symmetry and holey problems

The complex method of the plane elasticity in 2D quasicrystal with point group 10 mm tenfold rotational symmetry is established. First displacement potential function in the quasicrystal is represented by four analytic functions. Then by utilizing the properties of analytic function and through a great deal of derivation, the complex representations of stresses and displacementscomponents of phonon fields and phason fields in the quasicrystal are given, which are the theo-retical foundation for this method. From this theory, and by the help of conformal transformations in the theory of complex function, the problems of elliptic hole in the quasicrystal are solved. Its spe-cial cases are the solutions of well-known crack problem. Meanwhile, the results show that even if under the self-counterbalance force in the quasicrystal plane with elliptic hole, the stress compo-nents of phonon fields are also related to material constants of the quasicrystal when the phonon fields and phason fields are coupled, which is another distinctive difference from the properties of classical elastic theory. Besides, the present work is generalization and application of the complex method in the classical elastic theory established by Muskhelishvili to 2D quasicrystal. As in the classical elastic theory, if only conformal transformation from the quasicrystal plane to unit circle isfound, any holey and crack problem in the quasicrystal plane could be solved.

Flag-transitive point-primitive 2-(v,k,4) symmetric designs and two dimensional classical groups

Let D be a 2-（v, k, 4） symmetric design and G be a flag-transitive point-primitive automorphism group of D with X ≥G ≤Aut（X） where X ≌ PSL2（q）.Then D is a 2-（15,8,4） symmetric design with X = PSL2（9） and Xx = PGL2（3） where x is a point of D.

Ih POINT GROUP AND ELECTRONIC STRUCTURES OF AI-Mn CLUSTERS WITH Ih SYMMETRY

The existence of diffraction spots possessing icosahedral (Ih) point-group symmetry, discovered by D. Shechtman et al. on electron diffraction patterns of rapidly solidified Al-Mn alloys, has changed the conventional way of dividing solid states into crystalline and noncrystalline. Quasicrystalline, a new state

Lie point symmetry algebras and finite transformation groups of the general Broer-Kaup system

Using a new symmetry group theory, the transformation groups and symmetries of the general Broer-Kaup system are obtained. The results are much simpler than those obtained via the standard approaches.

A new group contribution-based method for estimation of flash point temperature of alkanes

Flash point is a primary property used to determine the fire and explosion hazards of a liquid. New group contribution-based models were presented for estimation of the flash point of alkanes by the use of multiple linear regression(MLR)and artificial neural network(ANN). This simple linear model shows a low average relative deviation(AARD) of 2.8% for a data set including 50(40 for training set and 10 for validation set) flash points. Furthermore, the predictive ability of the model was evaluated using LOO cross validation. The results demonstrate ANN model is clearly superior both in fitness and in prediction performance.ANN model has only the average absolute deviation of 2.9 K and the average relative deviation of 0.72%.

The Homotopy Perturbation Renormalization Group Method to Solve the WKB Problem with Turn Points

In this paper,we give the homotopy perturbation renormalization group method,this is a new method for turning point problem.Using this method,the independent variables are introduced by transformation without introducing new related variables and no matching is needed.The WKB approximation method problem can be solved.

Endpoints of Multi-Valued Weak Contractions on the Metric Space of Partially Ordered Groups

The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).

Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces

The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.

斑岩系统中低熔点亲铜元素与稀贵金属赋存状态和富集机制研究:以藏东南普朗超大型斑岩Cu-Au矿床为例

斑岩铜矿床常伴生大量低熔点亲铜元素(LMCE,包括Te、Se、Bi、Sb、As等)和稀贵金属(NM,包括Au、Ag、PGE),但这些元素的相互作用关系、富集分异机制及其控制因素尚不清楚。普朗斑岩Cu-Au矿床是位于特提斯-喜马拉雅成矿带中的超大型矿床,矿床中富集伴生元素,具有重要的经济价值,成为探讨这些问题的理想研究对象。本文利用扫描电镜、电子探针及硫化物LA-ICP-MS等原位分析技术对普朗矿床中伴生元素的分布规律、赋存状态及形成过程开展研究。结果表明,LMCE和NM主要以微粒包体形式赋存于硫化物中,并形成富硒方铅矿、辉碲铋矿、辉铋矿、辉硒铋矿、硫银铋矿、银金矿/金银矿、硒银矿、碲银矿、碲钯矿、碲铂矿、砷碲钯矿和富钯辉钴矿等矿物。普朗矿床中的铂族元素矿物(PGM)至少存在早期高温、晚期低温两个阶段的结晶,其中自形粒状的碲钯矿和碲铂矿结晶温度高、结晶空间开阔,可能是高温下直接由LMCE-Pt-Pd熔体固结形成,PGM形成后继续在流体中迁移并被后期结晶的硫化物捕获;而碲银矿±砷锑钯矿±辉碲铋矿±辉铋矿矿物组合具有固溶体分解和二面角等典型的熔体固结结构,推测为低温下NM-LMCE熔体充填在已结晶的硫化物裂隙和孔洞中形成。斑岩铜矿床从岩浆形成到热液出溶再到矿质沉淀的全过程均伴随着LMCE和NM的分异和富集,其中LMCE熔体对NM的高效富集具有重要意义。

MULTIPLICITY RESULTS FOR THE TWO-POINT BOUNDARY VALUE PROBLEMS AT RESONANCE

In this article several existence theorems on multiple solutions for the twopoint boundary value problem with resonance at, both infinity and zero are proved.

Effects of slip condition on MHD stagnation-point flow over a power-law stretching sheet

The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group transformation is used to get the invariants. Using the invariants, a third-order ordinary differential equation corresponding to the momentum is obtained. An analytical solution is obtained in a series form using a homotopy analysis method. Reliability and efficiency of series solutions are shown by the good agreement with numerical results presented in the literature. The effects of the slip parameter, the magnetic field parameter, the velocity ratio parameter, the suction velocity parameter, and the power law exponent on the flow are investigated. The results show that the velocity and shear stress profiles are greatly influenced by these parameters.

Morita Equivalent Blocks in Subgroups of Finite Groups

Let （K, O, k） be a p-modular system and G be a finite group. We prove that block A of RG and block B of RH are nalurally Morita equivalent of degree n if and only if A≌B＋…＋B}→n^2 as right R[H×H]-modules and A and B have the same defect（where R∈{k,O}）, which is a generalization of the result of Külshammer Burkhard in a p-modular system for an arbitrary subgroup H of G. It is proved that naturally Morita equivalent blocks are equivalent blocks and Morita equivalent via a bimodule with trivial source.

Late Palaeogene palynoflora from Point Hennequin of the Admiralty Bay,King George Island,Antarctica with reference to its stratigraphical significance

The present paper is to discuss the geological age and sedimentary environment based mainly on the characteristics of the palynological assemblage in the intercalated tuffaceous sand mudstones of the Upper Point Hennequin Group in the Admirelty Bay, King George Island, Antarctica. More than 40 species, mainly the Late Paleogene plant community in Gondwana and belonging to Weddellian biogeographic Province, were encountered within the volcano sedimentary rocks of the Upper Point Hennequin Group. The index member is the genus Nothofagidites . The occurrence of N. cf. saraensis and N. cf. flemingii and the absence of Proteacidites spp. indicates that the sporopollen bearing rocks is of Oligocene age, which were deposited in a limnetic zone near medium lower mountains environment with warm and humid climate.

The breaking point between fast-and slow-light in a degenerate two-level atomic system

This paper investigates the breaking point between fast- and slow-light in a degenerate two-level atomic system, where fast-light can be converted to slow-light arbitrarily on a single transition line by adjusting the strength of the pumping field. An equivalent incoherent pumping rate is introduced in this simplified theoretical model which exploits the dependence of this feature. The experimental observation is presented as evidence of the breaking point where the injected power is about 0.08 mW.

A CLASS OF ALTERNATING GROUP METHOD OF BURGERS' EQUATION

Some new Saul'yev type asymmetric difference schemes for Burgers' equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers' equation is constructed here. The basic idea of the method is that the grid points on the same time level is divided into a number of groups, the difference equations of each group can be solved independently, hence the method with intrinsic parallelism can be used directly on parallel computer. The method is unconditionally stable by analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy.

3D Braided Material Based on Space Group <i>R</i>3 Symmetry

A unit cell geometrical structure was found with the use of symmetry operations corresponding to the point group C3. Based on the symmetry of space group R3, a 3D braided geometrical structure was obtained by transforming the unit-cell. The features corresponding to this braided structure were studied. The fiber volume percentage and variational tendencies of the material were predicted by establishing a geometric model.

Group solution for an unsteady non-Newtonian Hiemenz flow with variable fluid properties and suction/injection

The theoretic transformation group approach is applied to address the problem of unsteady boundary layer flow of a non-Newtonian fluid near a stagnation point with variable viscosity and thermal conductivity. The application of a two- parameter group method reduces the number of independent variables by two, and consequently the governing partial differential equations with the boundary conditions transformed into a system of ordinary differential equations with the appropriate corresponding conditions. Two systems of ordinary differential equations have been solved numerically using a fourth-order Runge-Kutta algorithm with a shooting technique. The effects of various parameters governing the problem are investigated.

Spectrum behavior for the nonlinear fractional point reactor kinetics model

The nonlinear fractional point reactor kinetics equation in the presence of Newtonian temperature reactivity feedback with a multi-group of delayed neutrons,which describes the spectrum behavior of neutron density into the homogenous nuclear reactors, is developed. This system is one of the most important stiff coupled nonlinear fractional differentials for nuclear reactor dynamics. The generalization of Taylor's formula that involves Caputo fractional derivatives is developed in an attempt to overcome the difficulty of the stiffness of the nonlinear fractional differential model. Moreover, the general fractional derivatives are calculated analytically throughout this work. Furthermore, the local and global estimated errors were analyzed, which suggest that the error quantification should take into account the possible grow in time of the error. This observation provides a motivation for going beyond more classical local-in-time concepts of error(local truncation error). The neutron density response with time is analyzed for the anomalous diffusion, sub-diffusion, and super-diffusion processes.