On coordination and continuous hawk-dove games on small-world networks

It is argued that small-world networks are more suitable than ordinary graphs in modelling the diffusion of a concept (e.g. a technology, a disease, a tradition, ...). The coordination game with two strategies is studied on small-world networks, and it is shown that the time needed for a concept to dominate almost all of the network is of order , where N is the number of vertices. This result is different from regular graphs and from a result obtained by Young. The reason for the difference is explained. Continuous hawk-dove game is defined and a corresponding dynamical system is derived. Its steady state and stability are studied. Replicator dynamics for continuous hawk-dove game is derived without the concept of population. The resulting finite difference equation is studied. Finally continuous hawk-dove is simulated on small-world networks using Nash updating rule. The system is 2-cyclic for all the studied range. Received 8 July 2000 and Received in final form 23 July 2000     

关于谐振子第一积分的研究

提出一维谐振子基本积分的概念, 并利用它们构造其他积分. 将上述概念和方法推广到多维谐振子, 利用直接构造法证明不同类型的二维谐振子都存在三个与时间无关的独立的第一积分, n维谐振子系统存在2n-1个与时间无关的独立的第一积分. 讨论了分振动频率比为有理数和无理数的二维非对称谐振子的特征. 关键词： 谐振子 第一积分 基本积分 不含时积分     

Universal Differential Calculus on Ternary Algebras

General concept of ternary algebras is introduced in this article, along with several examples of its realization. Universal envelope of such algebras is defined, as well as the concept of tri-modules over ternary algebras. The universal differential calculus on these structures is then defined and its basic properties investigated.     

Information-theoretical aspects of quantum measurement

We present criteria for comparing measurements on a given system from the point of view of the information they provide. These criteria lead to a concept ofinformational completeness of a set of observables, which generalizes the conventional concept of completeness. The entropy of a state with respect to an arbitrary sample space of potential measurement outcomes is defined, and then studied in the context of configuration space and fuzzy stochastic phase space.Supported in part by the National Research Council of Canada.     

Proposal for Fourier-Transform Phase-Modulation Fluorometer

I propose a concept of a novel Fourier-transform phase-modulation fluorometer by which a fluorescence decay waveform can be obtained. In the fluorometer, the modulation frequency of the excitation light source is swept continuously from a start frequency f_min to an end frequency f_max with a time duration T. The resultant fluorescence signal waveform is Fourier-transformed to obtain amplitude and phase spectra. The ratio of the amplitude spectrum and the difference of the phase spectrum over those of the reference spectra that are obtained from a non-fluorescent material are calculated, respectively, and the pair of both spectral data is inverse-Fourier-transformed again to obtain the fluorescence decay waveform. To verify and demonstrate the effectiveness of the concept, I carried out (1) numerical simulations, (2) determination of a time constant of a passive resistor-capacitor (RC) differential circuit, and (3) measurement of a fluorescent decay waveform of YAG materials packed in Nichia’s white LED.     

Catastrophes in the multi-fractal dynamics of social-economic systems

In the present paper, the concept of multi-fractal dynamics is developed. The problem concerning catastrophes in this dynamics is studied in detail. In the framework of the concept of fractal curve as a thick curve, it is proved that the cell approach to measuring the fractal dimension D is equivalent to measuring the dependence of the length L of the line on the scope δ. The introduction of a fractal scale of temperatures T ^f is suggested.     

Mixture of new ideal gases and the solution of the Gibbs and Einstein paradoxes

A new concept of ideal gas is presented (i.e., of gas for which no particle interaction is assumed). This concept is based on number theory in which phase transitions of the first kind occur for T ⩽ T _cr on the isotherms, rather than on the law PV = RT. Formulas for a mixture of ideal gases that solve the Gibbs and Einstein paradoxes and also formulas for the transition to imperfect gases, which use the concept of Zeno line, are presented.     

Theory of Tensor Invariants of Integrable Hamiltonian Systems. II. Theorem on Symmetries and Its Applications

The theorem on symmetries is proved that states that a Liouville-integrable Hamiltonian system is non-degene\-rate in Kolmogorov's sense and has compact invariant submanifolds if and only if the corresponding Lie algebra of symmetries is abelian. The theorem on symmetries has applications to the characterization problem, to the integrable hierarchies problem, to the necessary conditions for the strong dynamical compatibility problem, and to the problem on master symmetries. The invariant necessary conditions for the non-degenerate C-integrability in Kolmogorov's sense of a given dynamical system V are derived. It is proved that the C-integrable Hamiltonian system is non-degenerate in the iso-energetic sense if and only if the corresponding Lie algebra of the iso-energetic conformal symmetries is abelian. An extended concept of integrability of Hamiltonian systems on the symplectic manifolds M ⁿ , n= 2k, is introduced. The concept of integrability describes the Hamiltonian systems that have quasi-periodic dynamics on tori or on toroidal cylinders of an arbitrary dimension . This concept includes, as a particular case, all Hamiltonian systems that are integrable in Liouville's classical sense, for which . The A-B-C-cohomologies are introduced for dynamical systems on smooth manifolds. Received: 16 January 1996 / Accepted: 3 July 1996     

Clifford Space as the Arena for Physics

A new theory is considered according to which extended objects in n-dimensional space are described in terms of multivector coordinates which are interpreted as generalizing the concept of center of mass coordinates. While the usual center of mass is a point, by generalizing the latter concept, we associate with every extended object a set of r-loops, r=0,1,...,n–1, enclosing oriented (r+1)-dimensional surfaces represented by Clifford numbers called (r+1)-vectors or multivectors. Superpositions of multivectors are called polyvectors or Clifford aggregates and they are elements of Clifford algebra. The set of all possible polyvectors forms a manifold, called C-space. We assume that the arena in which physics takes place is in fact not Minkowski space, but C-space. This has many far reaching physical implications, some of which are discussed in this paper. The most notable is the finding that although we start from the constrained relativity in C-space we arrive at the unconstrained Stueckelberg relativistic dynamics in Minkowski space which is a subspace of C-space.     

Soliton model of atom

The Einstein-de Broglie soliton concept is applied to simulate stationary states of an electron in a hydrogen atom. According to this concept, the electron is described by the localized regular solutions to some nonlinear equations. It is shown that the electron-solilon center travels along some stationary orbit around the Coulomb center. The electromagnetic radiation is absent as the Poynting vector has non-wave asymptote O(r ^–3)after averaging over angles.     

Relaxation kinetics of photoconductivity in <Emphasis Type="Italic">р</Emphasis>-silicon compensated by phosphorus atoms

The relaxation kinetics of photoconductivity in neutron-doped silicon (NDS) of the p-type is discussed. It is found that the relaxation process in the compensated p-Si<B, P> differs from that in the reference p-Si<B> sample. The difference is explained on the basis of concept of different micrononuniformity of the material conductivity. A method based on studying the dependences of charge-carrier mobility on annealing time is developed for determining thermal annealing of structural defects.     

Parton-hadron duality in event generators

The validity of local parton-hadron duality within the framework of HERWIG and JETSET event generators is investigated. We concentrate one ⁺ e ^– annihilations in LEP 2 energy range as these interactions provide theoretically the cleanest condition for the discussion of this concept. We conclude that the concept of local parton-hadron duality is not valid in either of the two generators considered.     

Temporal asymmetry as precondition of experience. The foundation of the arrow of time

Knowledge as knowledge of facts is based on the appearance of time as fundamental difference between past and future. Taking asymmetry in time as precondition of experience, the time symmetry of the basic laws of physics has to be explained. We give an explanation founded on the abstraction leading from semigroups to groups and the essential role of the concept of groups to define stationary states and observables. We then present a short outline of the construction of an abstract quantum theory as theory of knowledge based on the asymmetry between facts and possibilities. It is well known that the second law of thermodynamics cannot be derived from theH-theorem without a further hypothesis. We show that the application of the concept of probability to the past yields inconsistency of theH-theorem and a derivation of the second law via a Boltzmann-type hypothesis. The question remains whether the distinction of facts and possibilities as precondition of a theory of knowledge is rooted in a theory of cognition itself.     

Reparametrization invariance: a gauge-like symmetry of ultrametrically organised states

The reparametrization transformation between ultrametrically organised states of replicated disordered systems is explicitly defined. The invariance of the longitudinal free energy under this transformation, i.e. reparametrization invariance, is shown to be a direct consequence of the higher level symmetry of replica equivalence. The double limit of infinite step replica symmetry breaking and is needed to derive this continuous gauge-like symmetry from the discrete permutation invariance of the n replicas. Goldstone's theorem and Ward identities can be deduced from the disappearance of the second (and higher order) variation of the longitudinal free energy. We recall also how these and other exact statements follow from permutation symmetry after introducing the concept of “infinitesimal" permutations. Received 21 July 2000     

Phonons in mixed crystals

A concept is presented which gives qualitative information concerning the phonon behaviour of ionic mixed crystalsAB _1–x C _x at certain symmetry points on the zone boundary and consequently through the zone to the center. The model assumes that the end-member phonons and the impurity-modes ofAB:C andAC:B are known and uses the assumption that mixed crystal phonons behave symmetry-wise as the corresponding end-member phonons. The concept is demonstrated for several cases of mixed crystals.     

Propagation of distributions by a Monte Carlo method,with an application to ratio models

The GUM uncertainty framework, namely the law of propagation of uncertainty and the characterization of the measurand Y by a Gaussian distribution (or a scaled and shifted t-distribution), is seen as an approximate implementation of a fundamental concept, the propagation of distributions. This concept and a Monte Carlo method that implements it in a numerically controlled way are outlined. A family of models, relating to comparison measurement, and solvable analytically in algebraic form, is treated by both approaches to assess the degrees of approximation involved.     

Minkowski space-time is locally extendible

An example of a real analytic local extension of Minkowski space-time is given in this note. This local extension is not across points of theb-boundary since Minkowski space-time has an emptyb-boundary. Furthermore, this local extension is not across points of the causal boundary. The example indicates that the concept of local inextendibility may be less useful than originally envisioned.Partially supported by a grant from the Research Council of the Graduate School of the University of Missouri-Columbia     

Phonons in mixed crystals

A concept is presented which gives qualitative information concerning the phonon behaviour of ionic mixed crystalsAB _1–x C _x at certain symmetry points on the zone boundary and consequently through the zone to the center. The model assumes that the end-member phonons and the impurity-modes ofAB:C andAC:B are known and uses the assumption that mixed crystal phonons behave symmetry-wise as the corresponding end-member phonons. The concept is demonstrated for several cases of mixed crystals.     

High order “ZIP” differencing of convective terms

The ZIP flux form for differencing the term (wv)_x, where w is a convected quantity and v is a convective velocity, is observed to be equivalent to differencing the alternative expression wv_x + wx_v using centered second order finite differences. The advantage of this form is that one class of nonlinear computational instabilities is eliminated. Based on this observation, the extension of the ZIP flux concept to arbitrarily high order accuracy is given. Computational examples show the advantage both of the ZIP flux concept itself and of its higher order forms within the context of flux-corrected transport (FCT) algorithms.     

CPT invariance and interpretation of quantum mechanics

This paper is a sequel to various papers by the author devoted to the EPR correlation. The leading idea remains that the EPR correlation (either in its well-known form of nonseparability of future measurements, or in its less well-known time-reversed form of nonseparability of past preparations) displays the intrinsic time symmetry existing in almost all physical theories at the elementary level. But, as explicit Lorentz invariance has been an essential requirement in both the formalization and the conceptualization of my papers, the noninvariant concept ofT symmetry has to yield in favor of the invariant concept ofPT symmetry, or even (asC symmetry is not universally valid) to that ofCPT invariance. A distinction is then drawn between macro special relativity, defined by invariance under the orthochronous Lorentz group and submission to the retarded causality concept, and micro special relativity, defined by invariance under the full Lorentz group and includingCPT symmetry. TheCPT theorem clearly implies that micro special relativityis relativity theory at the quantal level. It is thus of fundamental significance not only in the search of interaction Lagrangians, etc., but also in the basic interpretation of quantum mechanics, including the understanding of the EPR correlation. While the experimental existence of the EPR correlations is manifestly incompatible with macro relativity, it is fully consistent with micro relativity. Going from a retarded concept of causality to one that isCPT invariant has very radical consequences, which are briefly discussed.