ON NUMBER OF LIMIT CYCLES FOR THE QUADRATIC SYSTEMS WITH A WEAK FOCUS AND A STRONG FOCUS

It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system has at most two(one) limit cycles which have (1,1) distribution ((0,1) distribution).

The Circular Current Loop as a Model of Fundamental Particles

The presented circular current loop model reveals that charged fundamental particles such as the electron consist essentially of electric and magnetic energy. The magnetic properties have the same order of magnitude as the electric ones. The electromagnetic field energy is the origin of the inertial mass. The Higgs boson, existing or not, is not needed to “explain” particle mass. The magnetic moment of fundamental particles is not anomalous! The “anomaly” indicates the existence of a small additional amount of kinetic energy. Thus, fundamental particles are not purely field-like such as photons and not (essentially) mass-like such as atoms, they represent a special kind of matter in between. Their kinetic energy is obviously not due to any relativistic effect but is related to an independent physical law that provides, together with the magnetic energy, the angular momentum exactly to be ħ/2. Fundamental particles are (at least) two-dimensional. In the simplest case their core consists of two concentric, nearly identical current loops. Their relative design details, the “anomaly” factor, and the rotational velocity of the uniformly distributed elementary charge follow from the stability condition, i.e. electric and magnetic force balance, and do not depend on the particle’s rest mass! Fundamental particles are objects of classical physics. Their magnetic forces are the true origin of the weak and strong nuclear interactions. For their explanation bosons and gluons are not needed.

The Substructure of Elementary Particles Demonstrated by the I-Theory

Present studies in physics assume that elementary particles are the building blocks of all matter, and that they are zero-dimensional objects which do not occupy space. The new I-Theory predicts that elementary particles do indeed have a substructure, three dimensions, and occupy space, being composed of fundamental particles called I-particles. In this article we identify the substructural pattern of elementary particles and define the quanta of energy that form each elementary particle. We demonstrate that the substructure comprises two classes of quanta which we call “attraction quanta” and “repulsion quanta”. We create a model that defines the rest-mass energy of each elementary particle and can predict new particles. Lastly, in order to incorporate this knowledge into the contemporary models of science, a revised periodic table is proposed.

Space Topologies and Their Dual Space Topologies for Conventional Functional Space Topologies

In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(Rn) of functions of class C∞ on Rn which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C∞ with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.

Checking weak and strong optimality of the solution to interval convex quadratic program

In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various forms of feasible region,are established respectively.By using the concept of feasible direction,these conditions are formulated in the form of linear systems with both equations and inequalities.In addition,we provide two specific examples to illustrate the efficiency of the conditions.

THE FIRST BOUNDARY VALUE PROBLEM FOR STRONGLY DEGENERATE QUASILINEAR PARABOLIC EQUATIONS IN ANISOTROPIC SOBOLEV SPACES

This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotropic Sobolev spaces an existence result is proved.

Global existence of weak solutions to a prey-predator model with strong cross-diffusion

Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also shown.

Developing Strong and Hybrid Formulation for the Single Stage Single Period Multi Commodity Warehouse Location Problem: Theoretical Framework and Empirical Investigation

We note that the Single Stage Single Period Multi Commodity Warehouse Location Problem (SSSPMCWLP) has been first attempted by Geoffrion and Graves [1], and that they use the weak formulation (in context of contribution of this paper). We give for the first time “strong” formulation of SSSPMCWLP. We notice advantages of strong formulation over weak formulation in terms of better bounds for yielding efficient Branch and Bound solutions. However, the computation time of “strong” formulation was discovered to be higher than that of the “weak” formulation, which was a major drawback in solving large size problems. To overcome this, we develop the hybrid strong formulation by adding only a few most promising demand and supply side strong constraints to the weak formulation of SSSPMCWLP. So, the formulations developed were put to test on various large size problems. Hybrid formulation is able to give better bound than the weak and takes much less CPU time than the strong formulation. So, a kind of trade off is achieved allowing efficiently solving large sized SSSPMCWLP in real times using hybrid formulation.

A Quantum Dynamics of Heisenberg Model of the Neutron Associated with Beta Decay

In this work we re-examine a model of the nucleons that involve the weak interaction which was once considered by Heisenberg;that is a neutron may have the structure of a dwarf hydrogen-like atom. We formulate a quantum dynamics for the Heisenberg model of the neutron associated with interaction that involves the beta decay in terms of a mixed Coulomb-Yukawa potential and the More General Exponential Screened Coulomb Potential (MGESCP), which has been studied and applied to various fields of physics. We show that all the components that form the MGESCP potential can be derived from a general system of linear first order partial differential equations similar to Dirac relativistic equation in quantum mechanics. There are many interesting features that emerge from the MGESCP potential, such as the MGESCP potential can be reduced to the potential that has been proposed to describe the interaction between the quarks for strong force in particle physics, and the energy spectrum of the bound states of the dwarf hydrogen-like atom is continuous with respect to distance. This result leads to an unexpected implication that a proton and an electron may also interact strongly at short distances. We also show that the Yukawa potential when restrained can generate and determine the mathematical structures of fundamental particles associated with the strong and weak fields.

DIRECT TITRATION OF VERY WEAK ACIDS(BASES)IN AQUEOUS SOLUTION WITH STRONG BASES(ACIDS)USING VISUAL END-POINT INDICATION WITHOUT INDICATOR

This paper reports a new method of titration for very weak acids and bases using the appearance of incisions on oscillopolarogram to indicate the end-point.This method has the advantages of rapidity,simplicity,no indicator needed as well as good precision.

Study on Design and Safety Evaluation Methods of Mechanical-Thermal Weak-Link

In an abnormal high-temperature fire environment,a structure with mechanical-thermal weak-link can be used to predict the permanent failure before the failure of some strong-links,such as explosive initiator,thus to protect the latter. An effective design can be defined as that the weak-link fails before the failure of the strong-link,and the system is safe; while an unsuccessful design means that the weak-link fails after the failure of the strong-link,and the system loses in safety. The probability of safety failure exists due to the uncertain failure temperatures of the weak-link and strong-link. In order to obtain the probability of safety failure,a statistical method was used to deal with the uncertainty of the failure temperatures. The integral method and stochastic simulation method were used in calculations. Finally,a sample was given to verify the consistence of the results given by two methods.

Is the“Weak Form”of CLT Being Adoptedin China ?

This paper, based on the hi sto rical background of CLT(communicative language teaching), mainly addresses the k ey issues concerning the weak form of CLT. This is an area few people have paid attention to in the past few years in China. Therefore, its main concepts and f e atures are discussed with relevance to literature and an empirical study on four novice teachers of English. Finally, the research shows that the weak form of CLT is being conducted in Chinese secondary schools.

Kthe-Bochner空间的凸性(英文)

本文利用Kothe函数空间的性质以及Kothe函数空间与Kothe-Bochner空间的关系,讨论了Kothe-Bochner空间E(X)的凸性,主要结果如下: (a)给出E(X)的端点的充分条件,得到了E(X)严格凸的判据,相应地推广了Lp(μ,X) 以及Lφ(X)的结果; (b)讨论了E(X)的弱局部一致凸和局部完全k-凸; (c)刻画了E(X)的强凸,给出了F(X)强凸的充要条件．

Modification of rock mass rating system:Interbedding of strong and weak rock layers

Rock mass classification systems are the very important part for underground projects and rock mass rating(RMR) is one of the most commonly applied classification systems in numerous civil and mining projects. The type of rock mass consisting of an interbedding of strong and weak layers poses difficulties and uncertainties for determining the RMR. For this, the present paper uses the concept of rock bolt supporting factor(RSF) for modification of RMR system to be used in such rock mass types. The proposed method also demonstrates the importance of rock bolting practice in such rock masses. The geological parameters of the Shemshak Formation of the Alborz Tunnel in Iran are used as case examples for development of the theoretical approach.

The Study on the Interannual Variation and the Mechanism of the South China Sea Monsoon

By using the USA NCAR / NCEP reanalysis data, the characteristics of climatic elements and the temporal and spatial structures of precipitation in the strong and weak years of the SCS monsoon are analyzed, the mechanism of the interannual variation of the SCS monsoon is discussed. It is found that the climatic elements in SCS have great differences, and there are great differences in the spatial and temporal structures of the precipitation anomalies between the strong and weak monsoon years. The variation of climatic elements in the south of Indochina Peninsula in April is a good index of the strength of the SCS monsoon. There is a good connection between the SCS monsoon and the sea surface temperature. The SCS monsoon is weak in the EL Nino years, and strong in the La Nina years. The strength of the SCS monsoon depends on the local heating differences between the eastern continent of China and the western Pacific. It depends on the intensity and the position of the western Pacific Subtropical High. The western Pacific Subtropical High is weak and eastward in the strong monsoon years, and the case is reversed in the weak monsoon years.

A Wave Equation including Leptons and Quarks for the Standard Model of Quantum Physics in Clifford Algebra

A wave equation with mass term is studied for all fermionic particles and antiparticles of the first generation: electron and its neutrino, positron and antineutrino, quarks u and d with three states of color and antiquarks and . This wave equation is form invariant under the group generalizing the relativistic invariance. It is gauge invariant under the U(1)×SU(2)×SU(3) group of the standard model of quantum physics. The wave is a function of space and time with value in the Clifford algebra Cl1,5. Then many features of the standard model, charge conjugation, color, left waves, and Lagrangian formalism, are obtained in the frame of the first quantization.

Evaluation of the fishbone model in simulating the seismic response of multistory reinforced concrete moment-resisting frames

The fishbone model is a simplified numerical model for moment-resisting frames that is capable of modelling the effects of column-beam strength and stiffness ratios. The applicability of the fishbone model in simulating the seismic responses of reinforced concrete moment-resisting frames of different sets of column-beam strength and stiffness ratios are evaluated through nonlinear static, dynamic and incremental dynamic analysis on six prototype buildings of 4-, 8-and 12-stories. The results show that the fishbone model is practically accurate enough for reinforced concrete frames, although the assumption of equal joint rotation does not hold in all cases. In addition to the ground motion characteristics and the number of stories in the structures, the accuracy of the model also varies with the column-beam stiffness and strength ratios. The model performs better for strong column-weak beam frames, in which the lateral drift patterns are better controlled by the continuous stiffness provided by the strong columns. When the inelastic deformation is large, the accuracy of the model may be subjected to large record-to-record variability. This is especially the case for frames of weak columns.

Entropy and Negentropy Principles in the I-Theory

Applying the I-Theory, this paper gives a new outlook about the concept of Entropy and Negentropy. Using S∞ particle as 100% repelling energy and A1 particle as the starting point of attraction, we are able to define Entropy and Negentropy on the quantum level. As the I-Theory explains that repulsion force is driven by Weak Force and attraction is driven by Strong Force, we also analyze Entropy and Negentropy in terms of the Fundamental Forces.

Study on the effect of the infill walls on the seismic performance of a reinforced concrete frame

Motivated by the seismic damage observed to reinforced concrete （RC） frame structures during the Wenchuan earthquake, the effect of infill walls on the seismic performance of a RC frame is studied in this paper. Infill walls, especially those made of masonry, offer some amount of stiffness and strength. Therefore, the effect of infill walls should be considered during the design of RC frames. In this study, an analysis of the recorded ground motion in the Wenehuan earthquake is performed. Then, a numerical model is developed to simulate the infill walls. Finally, nonlinear dynamic analysis is carried out on a RC frame with and without infill walls, respectively, by using CANNY software. Through a comparative analysis, the following conclusions can be drawn. The failure mode of the frame with infill walls is in accordance with the seismic damage failure pattern, which is strong beam and weak column mode. This indicates that the infill walls change the failure pattern of the frame, and it is necessary to consider them in the seismic design of the RC frame. The numerical model presented in this paper can effectively simulate the effect of infill walls on the RC frame.