Arbitrary Terms Research Articles

Study of critical properties of the Potts model by the modified variational cumulant expansion method

The modified variational cumulant expansion (VCE) method valid for the whole temperature range and for arbitrary fields is developed to study the critical properties of the general q-state Potts model used to stimulate various magnetic systems. The series expansion is generated directly in terms of the Potts Hamiltonian. The free energy and the internal energy are calculated up to the third-order cumulant terms for the d-dimensional hypercubic q-state Potts model. The expression for the critical temperature Tc is derived in a closed form which allows to determine Tc up to arbitrary order cumulant terms. The modified VCE method eliminates the unphysical first-order phase transition at the mean-field critical point in the internal energy of the Potts model which plagues the conventional VCE method.

Implications of [formula omitted] for supersymmetry searches and model-building

Assuming that the actual values of M t at FNAL and of Γ(Z → b b ̄ )/Γ(Z → hadrons) at LEP are within their current 1σ reported ranges, we present a No-Lose Theorem for superpartner searches at LEP II and an upgraded Tevatron. We impose only two theoretical assumptions: the Lagrangian is that of the Minimal Supersymmetric Standard Model (MSSM) with arbitrary soft-breaking terms, and all couplings remain perturbative up to scales ∼ 10 16 GeV; there are no assumptions about the soft supersymmetry breaking parameters, proton decay, cosmology, etc. In particular, if the LEP and FNAL values hold up and supersymmetry is responsible for the discrepancy with the Standard Model prediction of Γ(Z → b b ̄ ) , then we must have charginos and/or top squarks observable at the upgraded machines (for LEP the superpartner threshold is below √ s = 140 GeV). Furthermore, little deviation from the Standard Model is predicted within “super-unified” supersymmetry, so these models predict that the discrepancy between experiment and the Standard Model prediction for Γ(Z → b b ̄ ) will fade with time. Finally, it appears to be extremely difficult to find any unified MSSM model, regardless of the form of soft supersymmetry breaking, that can explain Γ(Z → b b ̄ ) for large tan β; in particular, no model with t b τ Yukawa coupling unification appears to be consistent with the experiments.

Equivalence of Hamiltonian and Lagrangian path integral quantization: Effective gauge theories.

The equivalence of correct Hamiltonian and naive Lagrangian (Faddeev-Popov) path integral quantization (Matthews's theorem) is proven for gauge theories with arbitrary effective interaction terms. Effective gauge-boson self-interactions and effective interactions with scalar and fermion fields are considered. This result becomes extended to effective gauge theories with higher derivatives of the fields.

Exact Solutions for Free Vibration in an Asymmetrical Duffing Equation

An algorithm is proposed for determining the exact solutions for free vibration in an asymmetrical Duffing oscillator. The system is composed of a spring function of the Duffing type (with linear and cubic terms with respect to displacement) accompanied by a constant force. It is reduced from the most comprehensive 3rd-order polynomial having arbitrary terms from a constant to the 3rd power. By employing a bilinear transformation, the system is successfully converted into a regular Duffing equation whose exact solutions already exist and are abstracted here. The whole procedure of obtaining the present solution is summarized in a flow chart. Numerical values of conversion constants, skeleton curves and waveforms are computed and illustrated for the typical cases of asymmetrical (hard, soft and snap-through) spring systems. It is demonstrated that the skeleton curves and waveforms are asymmetrical and that some of them exhibit multivalued responses for a given frequency.

Prospects for development of automotive fuels with improved ecological properties

The continuous growth of the automotive fleet, which numbered about 0.5 billion vehicles in 1993, has consumed major fuel and energy resources and created a serious problem in pollution of the air basin with exhaust gases. In Russia today, more than 30% of all pollutants released to the ambient medium can be attributed to automotive transport. In major cities, automotive vehicles contribute as much as 80% of all pollution. In Moscow, for example, the annual exhaust gas emissions include more than 750,000 tonnes of carbon monoxide, more than 50,000 tonnes of hydrocarbons, more than 70,000 tonnes of nitrogen oxides, and more than 2,000 tonnes of solid particles. Any improvement of the ecological indexes of automotive vehicles must involve the combined efforts of engine manufacturers, petroleum industry personnel, chemmotologists, and vehicle operators. Some purely arbitrary terms have appeared in recent years, such as {open_quotes}ecologically clean{close_quotes} automotive vehicles, fuels, lubricants, and fluids. The drop in total volume of oil produced and refined in our country has stimulated efforts to solve problems of economy and rational utilization of crude oil, and to improve the ecological products of fuels and lubricants. In the world petroleum market, today, as never before, ecologically clean products aremore » highly valued. In the development of new types of fuels, ecological requirements are placed on a par with requirements imposed by engine design, engine operating conditions, and economics. The increased costs in producing specially developed fuels are compensated by their improved ecological properties. In the United States, for example, a required component of the so-called reformulated (or modified) gasolines EC-1 and EC-X is oxygen, which is introduced in amounts of 1.0-2.7% (in the form of oxygen-containing organic compounds) in order to reduce the harmful effects of emissions to the atmosphere.« less

The Cramer-Rao bound for pole and amplitude coefficient estimates of damped exponential signals in noise

A complete Cramer-Rao bound (CRB) derivation is provided for the case in which signals consist of arbitrary exponential terms in noise. Expressions for the CRBs of the parameters of a damped exponential model with one set of poles and multiple sets of amplitude coefficients are derived. CRBs for the poles and amplitude coefficients are derived in terms of rectangular and polar coordinate parameters. For rectangular parameters it is shown that CRBs for the real and imaginary parts of poles and amplitude coefficients are equal and uncorrelated. In polar coordinates, the angle and magnitude CRBs are also uncorrelated. Furthermore, the CRBs of the pole angles and relative magnitudes are equal and are logarithmically symmetric about the unit circle. >

Symmetries and integrability of generalized diffusion reaction equations

Using Lie group methods and the Painleve test, the authors analyse nonlinear diffusion reaction equations ut=(D(u)u)+f(u) with power law diffusion coefficients (D approximately uv) and arbitrary nonlinear reaction terms f(u) which have a wide spectrum of applications in many areas of science. The Lie-group-based similarity method leads to a classification of the reaction terms according to its symmetry properties. With the help of the adjoint representation, the optimal system of similarity reductions is calculated. To check the integrability of the partial differential equation, the existence of generalized (Lie-Backlund) symmetries is investigated. Apart from three known cases, no further cases with third-order symmetries exist. Examining the integrability of the second-order ordinary differential equations resulting from the reductions, only a few parameter combinations can be found for which the Painleve property is given. However, they are able to construct unknown integrals of motion for a much larger range of parameter values. From the integrals, exact similarity solutions may be derived. This is demonstrated by examples corresponding to the important moving-wave reduction.

HiLog: A foundation for higher-order logic programming

We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higher-order syntax and allows arbitrary terms to appear in places where predicates, functions, and atomic formulas occur in predicate calculus. But its semantics is first-order and admits a sound and complete proof procedure. Applications of HiLog are discussed, including DCG grammars, higher-order and modular logic programming, and deductive databases.

TRANSFORMATION TO AUTONOMOUS SYSTEMS VIA HAMILTON’S EQUATIONS

A semiclassical Hamiltonian with arbitrary time-dependent external term is transformed via Hamiltonian’s equations into a time-independent autonomous system. Iteration gives Hamilton’s equations which are functions of the initial values and time-independent external terms. For the harmonic oscillator it is found that no external term gives constants of the motion or semiclassical chaos. A quartic anharmonic oscillator is discussed.

Computational aspects for Cohen-Macaulay and Buchsbaum ideals

In 1913, F.S. Macaulay introduced the concept of perfectness for homogeneous polynomial ideals. An aim of this paper is to obtain a direct method based on Macaulay's definition to decide computationally the perfectness of an ideal. We extend our methods to a certain class of Buchsbaum ideals. Another goal is to examine the hereditary property of being perfect between a homogeneous ideal α andin (α), the latter being the ideal generated by the initial terms with respect to an arbitrary admissible term order.

One-loop Vilkovisky-DeWitt counterterms for two-dimensional gravity plus scalar field theory.

The divergent part of the one-loop off-shell effective action is computed for a single scalar field coupled to the Ricci curvature of 2D gravity ($c \phi R$), and self interacting by an arbitrary potential term $V(\phi)$. The Vilkovisky-DeWitt effective action is used to compute gauge-fixing independent results. In our background field/covariant gauge we find that the Liouville theory is finite on shell. Off-shell, we find a large class of renormalizable potentials which include the Liouville potential. We also find that for backgrounds satisfying $R=0$, the Liouville theory is finite off shell, as well.

Contraction algebras and unification of (infinite) terms

We introduce the class of contraction algebras in which the algebra of infinite and finite terms is free over the set of variables. We develop a general theory of systems of equations at the level of categories in close connection with the Banach Principle of Contraction. Two applications of this theory are given. The first is the case of regular systems of equations with arbitrary terms. The second is the case of systems of equations attached to a context-free grammar (sometimes called ALGOL-like systems). Systems of equations with terms are used to extend the original unification algorithm of Robinson to the case of infinite terms.

Exact Solutions for the Free Vibration in an Asymmetrical Duffing Equation.

An algorithm is proposed to find exact solutions for the free vibration in an asymmetrical Duffing oscillator. The system is composed of a spring function of the Duffing type (with linear and cubic terms with respect to displacement) accompanied by a constant force. It is reduced from the most comprehensive 3rd order polynomial having arbitrary terms from constant to the 3rd power. By employing a bilinear transformation, the system is successfully converted into a regular Duffing equation whose exact solutions already exist and are abstracted here. The whole procedure to obtain the present solution is summarized in a flow chart. Numerical values of conversion constants, skeleton curves and waveforms are computed and illustrated for the typical cases of asymmetrical (hard, soft and snap-through) spring systems. It is demonstrated that the skeleton curves and waveforms are asymmetrical and that, some of them exhibit multivalued responses for a given frequency.

Electromagnetic field analysis by boundary element method using spatial eigenmodes

This paper proposes a boundary-element method using spatial eigenmodes for electromgnetic field analysis. Mapping the computation model with rotational symmetries, reflective symmetries or rotational symmetries including reflective symmetries to a group of spatial eigenmodes, the equivalent reduced models are obtained. In the method, the applicability becomes wide because arbitrary external source terms can be chosen. Furthermore, in a model including asymmetry regions, a new method which can save the merit of the symmetries is proposed. Finally, the validity of the proposed method is proved by numerical simulations.

Four-variable AND-EXOR minimum expressions and their properties

An AND-EXOR expression (exclusive-or sum-of-products expression: ESOP) is obtained by EXORing arbitrary product terms. First, some properties are shown of minimum ESOPs which are useful for the minimization of ESOPs. Second, a catalog of minimum ESOPs for the representative functions of 4-variable NP-equivalence classes is presented. Minimality is defined as first minimizing the number of the product terms and then the number of the literals in the ESOP. Minimum ESOPs are obtained by an exhaustive method. The average number of products to realize the 4-variable functions by AND-OR sum-of-products expressions is 4.13 and 3.66 by ESOPs. Minimum ESOPs with four variables or less are obtained easily by the table look-up of the catalog. The catalog is useful for the minimization and the complexity analysis of ESOPs with five or more variables.

Inversions on northern and southern slopes of the Low Tatras

This work deals with the occurrence of inversions on the northern and southern slopes of the Low Tatras in the Chopok region. The data for the northern exposure have been taken from the meteorological stations at 648 m a.s.l., 1200 m a.s.l., and 1660 m a.s.l. For the southern exposure from the meteorological stations 506 m a.s.l., 1208 m a.s.l., 1490 m a.s.l., and from the top of Chopok (2008 m a.s.l.). The evaluated 10-year period covers the years 1973–1982. The inversion have been determined by means of the comparison of regular observations (at 7 a.m., 2 and 9 p.m.), of the average daily temperature, maximum and minimum temperatures and an arbitrary term of the determinate day. It follows from this evaluation, that the inversion has a characteristic course, with maximum frequency during winter, particularly during anticyclonic situations. With increasing altitude, the number of inversion days decreases.

Universal aspects of the Hasselmann nonlinear interaction

The asymptotic spectrum of the wave-height autocorrelation is of power-law form for surface gravity waves in deep water. Physical oceanographers have utilized Kolmogorov-type scaling arguments within transport theory in order to predict the exponent of the power law once the wave statistics become stationary. I advance the hypothesis that the asymptotics can be achieved using Hamilton's equations correct to third order with an arbitrary nonsingular interaction term which has the symmetry, degree of homogeneity, and quasilocality in k space of the full Hasselmann interaction term. Examples which support the hypothesis are presented, and its further implications are discussed.

On Forward-in-Time Differencing for Fluids

Abstract This note discusses the extension of the dissipative advection schemes, often referred to in meteorological literature as Crowley-type schemes, on advection equations with arbitrary forcing and/or source terms included. Since such equations constitute a prototype of prognostic equations for fluids, the considerations herein are relevant to a variety of atmospheric problems. The thesis of this note is that, no matter how accurate the advection scheme employed, the entire equation is approximated to, at most, O(Δt), which is a consequence of disregarding forcing terms in the derivation of Crowley-type schemes. The consequences of this truncation error may be quite severe depending on the particular problem at hand. The remedy proposed is simple and easy to implement in any numerical model using forward-in-time differencing. Theoretical considerations are illustrated with an example of a flow of the density-stratified fluid past a two-dimensional mountain.

Perturbation-induced perestroika of a nonlinear-Schrödinger breather

The evolution of an N-soliton state (breather) is considered in the nonlinear Schrödinger equation with a sufficinetly arbitrary conservative perturbing term. Arguments are given in favor of a perestroika (rearrangement) of the breather into the exact one-soliton state via emission of radiation. For the two-soliton breather, it is demonstrated that an approximate kinematic analysis, based on the balance equation for the wave action and energy, makes it possible to find the amplitude of the one-soliton state as a function of the two initial amplitudes of the breather, provided one of them is sufficiently small compared to the other. The expression for the final amplitude proves to be very simple, and it is universal in the sense that it does not depend on a particular form of the conservative perturbation. As an example, nonlinear surface elastic modes in a crystal are considered. It is shown that N-soliton surface modes may undergo the emission-assisted prestroika into the exact one-soliton mode under the action of a nonlinear correction to the boundary condition at the surface.

Semantics-Based Translation Methods for Modal Logics

A general framework for translating logical formulae from one logic into another logic is presented. The framework is instantiated with two different approaches to translating modal logic formulae into predicate logic. The first one, the well known ‘relational’ translation makes the modal logic‘s possible worlds structure explicit by introducing a distinguished predicate symbol to represent the accessibility relation. In the second approach, the ‘functional’ translation method, paths in the possible worlds structure are represented by compositions of functions which map worlds to accessible worlds. On the syntactic level this means that every flexible symbol is parametrized with particular terms denoting whole paths from the initial world to the actual world. The ‘target logic’ for the translation is a first-order many-sorted logic with built in equality. Therefore the ‘source logic’ may also be first-order function symbols are allowed. Furthermore flexible function symbols are allowed. The modal operators may be parametrized with arbitrary terms and particular properties of the accessibility relation may be specified within the logic itself.