The equation-transform model for Dirac–Morse problem including Coulomb tensor interaction

The approximate solutions of Dirac equation with Morse potential in the presence of Coulomb-like tensor potential are obtained by using Laplace transform (LT) approach. The energy eigenvalue equation of the Dirac particles is found and some numerical results are obtained. By using convolution integral, the corresponding radial wave functions are presented in terms of confluent hypergeometric functions.     

Dynamics of a prey-predator system under Poisson white noise excitation

The classical Lotka-Volterra （LV） model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is in- vestigated by using the stochastic averaging method. The averaged generalized It6 stochastic differential equation and Fokkerlanck-Kolmogorov （FPK） equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter e2s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo （MC） simulation.     

Multilevel Monte Carlo in approximate Bayesian computation

In the following article, we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.     

Analysis of a time-dependent scheduling problem by signatures of deterioration rate sequences

In the paper a single machine time-dependent scheduling problem is considered. The processing time p_j of each job is described by a function of the starting time t of the job, p_j=1+α_jt, where the job deterioration rate α_j?0 for j=0,1,…,n and t?0. Jobs are nonpreemptable and independent, there are no ready times and no deadlines. The criterion of optimality of a schedule is the total completion time.First, the notion of a signature for a given sequence of job deterioration rates is introduced, two types of the signature are defined and their properties are shown. Next, on the basis of these properties a greedy polynomial-time approximation algorithm for the problem is formulated. This algorithm, starting from an initial sequence, iteratively constructs a new sequence concatenating the previous sequence with new elements, according to the sign of one of the signatures of this sequence.Finally, these results are applied to the problem with job deterioration rates which are consecutive natural numbers, α_j=j for j=0,1,…,n. Arguments supporting the conjecture that in this case the greedy algorithm is optimal are presented.     

Fuzzy logic in measurements

Our main interest in this paper is to translate from “natural language” into “system theoretical language”. This is of course important since a statement in system theory can be analyzed mathematically or computationally. We assume that, in order to obtain a good translation, “system theoretical language” should have great power of expression. Thus we first propose a new frame of system theory, which includes the concepts of “measurement” as well as “state equation”. And we show that a certain statement in usual conversation, i.e., fuzzy modus ponens with the word “very”, can be translated into a statement in the new frame of system theory. Though our result is merely one example of the translation from “natural language” into “system theoretical language”, we believe that our method is fairly general.     

Bending wave intensity in a thick beam

I.IntroductionMeasurementSofbendingwaveintensityinoneortwodimensi0na1structuresbecomequitepopularandgetavarietyofindustria1app1icati0ns.Theexistingintensitytheory['-']wasderivedbasedontheclassicaIBernou11i-Eu1ertheorywhichisanapproximatetheoryforana-lyzingstructuralvibration.Inthe1ow-frequencylimitwherebendingwavelengthsaremuchlongincomparisonwiththethicknessofthestructurealongwhichtheypr0pagate(i.e.,thinstructurcs),theuse0ftheclassica1theorywi1lresu1tinanegligiblyerro/`].Forshortwave-1ength…     

Newton's method for sections on Riemannian manifolds: Generalized covariant -theory

One kind of the L-average Lipschitz condition is introduced to covariant derivatives of sections on Riemannian manifolds. A convergence criterion of Newton's method and the radii of the uniqueness balls of the singular points for sections on Riemannian manifolds, which is independent of the curvatures, are established under the assumption that the covariant derivatives of the sections satisfy this kind of the L-average Lipschitz condition. Some applications to special cases including Kantorovich's condition and the γ-condition as well as Smale's α-theory are provided. In particular, the result due to Ferreira and Svaiter [Kantorovich's Theorem on Newton's method in Riemannian manifolds, J. Complexity 18 (2002) 304–329] is extended while the results due to Dedieu Priouret, Malajovich [Newton's method on Riemannian manifolds: covariant alpha theory, IMA J. Numer. Anal. 23 (2003) 395–419] are improved significantly. Moreover, the corresponding results due to Alvarez, Bolter, Munier [A unifying local convergence result for Newton's method in Riemannian manifolds, Found. Comput. Math. to appear] for vector fields and mappings on Riemannian manifolds are also extended.     

An integer linear programming approach for approximate string comparison

We introduce a problem called maximum common characters in blocks (MCCB), which arises in applications of approximate string comparison, particularly in the unification of possibly erroneous textual data coming from different sources. We show that this problem is NP-complete, but can nevertheless be solved satisfactorily using integer linear programming for instances of practical interest. Two integer linear formulations are proposed and compared in terms of their linear relaxations. We also compare the results of the approximate matching with other known measures such as the Levenshtein (edit) distance.     

Charge-conserving electron density averaging for a set of nuclear configurations

The Löwdin-Inverse Löwdin Transformation (LILT) technique combined with the Diophantine Density Matrix Purification (DDMP) method is suggested for a charge-preserving density averaging approach for a range of nuclear configurations.     

The case for an interval-based representation of linguistic truth

This paper develops an interval-based approach to the concept of linguistic truth. A special-purpose interval logic is defined, and it is argued that, for many applications, this logic provides a potentially useful alternative to the conventional fuzzy logic.The key idea is to interpret the numerical truth value v(p) of a proposition p as a degree of belief in the logical certainty of p, in which case p is regarded as true, for example, if v(p) falls within a certain range, say, the interval [0.7, 1]. This leads to a logic which, although being only a special case of fuzzy logic, appears to be no less linguistically correct and at the same time offers definite advantages in terms of mathematical simplicity and computational speed.It is also shown that this same interval logic can be generalized to a lattice-based logic having the capacity to accommodate propositions p which employ fuzzy predicates of type 2.