Showing papers on "Constant (mathematics) published in 1976"
TL;DR: The best constant for the simplest Sobolev inequality was proved in this paper by symmetrizations (rearrangements in the sense of Hardy-Littlewood) and one-dimensional calculus of variations.
Abstract: The best constant for the simplest Sobolev inequality is exhibited. The proof is accomplished by symmetrizations (rearrangements in the sense of Hardy-Littlewood) and one-dimensional calculus of variations.
2,011 citations
TL;DR: In this article, the authors considered both first and second-order contributions to Δy with respect to Δc for atmospheric chemical kinetics using constant as well as time varying (diurnal) rate parameters.
253 citations
Journal Article•
145 citations
TL;DR: In this paper, the asymptotic behavior of solutions of the functional differential equation where a is a complex constant, and 0 b is a constant such that Re b = 0, but b ≠ 0.
Abstract: The paper discusses the asymptotic behaviour of solutions of the functional differential equation where a is a complex constant, 0 b is a constant such that Re b = 0, but b ≠ 0.
143 citations
01 Jan 1976
TL;DR: Sewall Wright has provided the best general classification of the processes changing gene frequency under the simplified conditions outlined in Chapter 1, and it is used in the following account.
Abstract: Micro-evolution consists of change in the population either to fit it to a new place or time in a changing environment, or to improve its success in a constant environment. The modifications which take place are genetic. Sewall Wright pointed out in an article written in 1949 that ‘the elementary evolutionary process in a reasonably large homogeneous population maybe considered to be change in gene frequency’. He has provided the best general classification of the processes changing gene frequency under the simplified conditions outlined in Chapter 1, and it is used in the following account.
131 citations
TL;DR: In this article, the authors present a dynamic model of the behavior of OPEC viewed as a monopolist sharing the oil market with a competitive sector, and the main conclusion is that the recent increase in the price of oil was a once and for all phenomenon due to the formation of the cartel and that prices should remain approximately constant during the next twenty years.
108 citations
TL;DR: A model is developed which indicates that the pure strategy of "majoring" is always better than random foraging if the reward structure remains approximately constant through time.
Abstract: We have developed a model which indicates that the pure strategy of "majoring"is always better than random foraging if the reward structure remains approximately constant through time. "Minoring" is a necessary compromise required to track resources changing through time.
88 citations
87 citations
TL;DR: In this paper, the nonsimilar moving wall stagnation point solution derived by Rott has been redefined so as to show that a second related solution exists, which corresponds to a constant wall velocity with an external velocity proportional to the distance from the stagnation point.
Abstract: : The nonsimilar moving wall stagnation point solution derived by Rott has been redefined so as to show that a second related solution exists. Rott's solution corresponds to a constant wall velocity with an external velocity proportional to the distance from the stagnation point. A counterpart solution corresponds to the case of a constant edge velocity proportional to the wall coordinate. Numerical and analytical solutions of the equations have defined the characteristics of the boundary layer including their integral properties.
87 citations
TL;DR: In this paper, an extended form of the method of Q-mode factor analysis is used if the rows of the data matrix sum to a constant, which provides a means for scaling the factor model to conform to the units of the original data in such forms as proportions, percentages, or parts per million.
69 citations
TL;DR: In this paper, it was shown how particles can separate into subsystems between which the distances are asymptotic to constant multiples of time, and within which the mutual distances are at most of the order t 2 3.
TL;DR: In this paper, a procedure for designing a constant gain feedback matrix which assigns the closed-loop poles of a linear time-invariant multivariable system to desired locations and at the same time minimizes the sensitivity of these poles to variations in the parameters of the plant is described.
Abstract: A procedure for designing a constant gain feedback matrix which assigns the closed-loop poles of a linear time-invariant multivariable system to desired locations and at the same time minimizes the sensitivity of these poles to variations in the parameters of the plant is described in this paper. It is shown that this technique in which sensitivity considerations are an integral part of the design procedure yields better results compared to other pole assignment techniques using constant gain feedback controllers. Numerical examples are presented to illustrate the application of the design procedure.
TL;DR: In this paper, the second and third order elastic constants of hexagonal boron nitride were calculated and compared with the available experimental data, and the planar bending constant, important to the semicontinuum theory for layered crystals was obtained from a simple model.
Abstract: Elementary potentials are applied to a study of hexagonal boron nitride. All second‐ and third‐order elastic constants are calculated and compared with the available experimental data. The planar bending constant, important to the semicontinuum theory for layered crystals, is obtained from a simple model.
TL;DR: For stationary random or transient data representing multicorrelated input/output data occurring in physical systems, iterative computational algorithms are developed to identify the frequency response functions of optimum constant parameter linear systems connecting this data.
TL;DR: In this article, two simple models including pairing in the dynamical equations governing the motion of the nucleus are presented and their relation to the Landau-Zener type of coupling is investigated.
Journal Article•
TL;DR: In this article, the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php).
Abstract: L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
TL;DR: In this article, the authors summarized work carried out during the period 1963-1973 into the constant and random amplitude fatigue crack propagation performance of a mild steel at ambient temperature, and derived fracture mechanics parameters for the process of propagation under a variety of mean stress intensity conditions.
TL;DR: In this article, a stabilization problem of singularly perturbed linear constant systems using a linear state feedback is analyzed, and it is shown that the stabilizability of two subsystems can assure that of the original system.
Abstract: A stabilization problem of singularly perturbed linear constant systems using a linear state feedback is analyzed. It is shown that the stabilizability of two subsystems can assure that of the original singularly perturbed system. The stabilizing controller for the singularly perturbed system is also given.
TL;DR: In this article, it was shown that if all the Jacobian determinants in the unbounded regions have the same sign, the equation f(x)= y has at least one solution and an algorithm was developed, which obtains one or more solutions in a finite number of steps.
Abstract: Nonlinear resistive networks can be characterized by the equation f(x)= y where f(x) is a continuous piecewise-linear mapping of Rn into itself. The n-dimensional Euclidean space is divided into a finite number of regions, and, in each region say region Rm, we can express f by J(m)x + w(m) where J(m) is a constant n × n Jacobian matrix and w(m) is a constant n-vector. In this paper we obtain the following results:
If all the Jacobian determinants in the unbounded regions have the same sign, the equation f(x)= y has at least one solution and an algorithm is developed, which obtains one or more solutions in a finite number of steps. The work represents a generalization of early work by Fujisawa, Kuh and Ohtsuki and relaxes the condition imposed on the function. For example, in the bounded regions, the Jacobian matrices can be singular and the sign of Jacobian determinants can be arbitrary.
TL;DR: Numerical results indicate that in studying gene differentiation between species or taxa of higher rank the authors may assume that there was no migration between the two taxa from the very beginning of separation.
Abstract: The effect of migration on genetic distance has been studied with a finite island model for the following two cases: constant migration rate and decreasing migration rate. Results based on the assumption that migration rate decreases with time are very different from those based on the assumption of constant migration rate. Numerical results indicate that in studying gene differentiation between species or taxa of higher rank we may assume that there was no migration between the two taxa from the very beginning of separation.
TL;DR: An efficient algorithm is presented for moving arbitrary list structures, using no storage other than that required to hold the original list and the copy, and is superior in execution speed to previous algorithms for the same problem.
Abstract: An efficient algorithm is presented for moving arbitrary list structures, using no storage (apart from program variables) other than that required to hold the original list and the copy. The original list is destroyed as it is moved. No mark bits are necessary, but pointers to the copy must be distinguishable from pointers to the original. The algorithm is superior in execution speed to previous algorithms for the same problem. Some variations and extensions o f the algorithm are discussed.
TL;DR: In this article, the authors extend Gnedenko's F test to situations with hypercensoring and provide guidance for its use, particularly when a log-normal distribution is the alternative.
Abstract: In this note some extensions are made to previous work by a number of authors on the development of tests for exponentiality. The most recent example is due to Fercho and Ringer in which they compare the small sample powers of a few well-known test statistics for the hypothesis of a constant failure rate. It is the primary intent of this current work to extend Gnedenko's F test to situations with hypercensoring and to provide guidance for its use, particularly when a log-normal distribution is the alternative.
TL;DR: Methods developed for the reduction in order of single-input/single-output systems are extended to the reduction of linear, constant, equal input/equal output multivariable systems.
Abstract: Methods developed for the reduction in order of single-input/single-output systems are extended to the reduction of linear, constant, equal input/equal output multivariable systems. The methods considered are the continued fraction and the Pade approximation techniques. Examples are given to illustrate the method.
01 Jul 1976
TL;DR: In this article, the authors describe a technique for solving systems of non-linear partial differential equations of the form where f(γ) and g (γ) are arbitrarily assigned functions.
Abstract: This work amalgamates and solves certain problems arising in differential equation theory and in classical differential geometry.It describes a novel technique for solving systems of non-linear partial differential equations of the formwhere f(γ) and g(γ) are arbitrarily assigned functions. The circumstances are determined under which compatible solutions exist, not only when γ is real, but also when γ is complex, and all of the corresponding solutions are found. This is done by using a geometric technique that incorporates the equipotential surfaces of constant γ. In general, these surfaces are imaginary, and a fairly extensive treatment of such surfaces in (complexified) 3-dimensional Euclidean space is included. A close association is discovered between the set of equipotential surfaces and the class of surfaces of constant radii of principal normal curvature.
TL;DR: Ionizations in almost all enzyme mechanisms can properly be treated as equilibria, provided that ionization is not accompanied by a slow, compulsory change in conformation.
Abstract: If the Michaelis constant of an enzyme-catalysed reaction is independent of pH under conditions where the catalytic constant varies with pH, it is equal to the thermodynamic dissociation constant of the enzyme-substrate complex. This is true for realistic mechanisms in which binding and catalytic steps, are clearly distinguished, as well as for the simpler mechanisms that have been considered previously. It is also true for a mechanism in which a bell-shaped pH profile for the catalytic constant results from a change of rate-limiting step with pH. The relaxation time for ionization of a typical group in unbuffered solutions at 25 degrees C is of the order of 0.1 ms at the longest, and is much shorter in buffered solutions. Thus ionizations in almost all enzyme mechanisms can properly be treated as equilibria, provided that ionization is not accompanied by a slow, compulsory change in conformation.
TL;DR: In this paper, exact solutions of the problem of steady-state diffusion and convection are presented for constant wall concentration, constant flux across the wall and a heterogeneous chemical reaction of the first order.
01 Jan 1976
TL;DR: In this article, a treatment-effect function t is defined and distribution-free confidence bounds for the function t both in the case where t has specified parametric forms and the case when t is not parameterized.
Abstract: In the usual two-sample problem one is estimating the constant additive effect of a treatment or the additive constant by which two random variables differ. However, if the treatment-effect may depend on the response level, then a more general approach to twosample problems seems appropriate. We define a treatment-effect function t and characterize distribution-free confidence bounds for the function t both in the case where t has specified parametric forms and in the case where t is not parameterized.