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The authors propose a mathematical model for a multi-channel queueing system with feedback in which one part of calls instantaneously enters the system for repeated service and the other part either retries in some random time or finally leaves the system. The behavior of the serviced calls is randomized. Both exact and asymptotic methods are developed to calculate the characteristics of the proposed model. The results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

We study stationary Stokes equations in an unbounded domain of 3, with periodicity conditions on one part of the boundary, Dirichlet conditions on the other and a transmission condition. We show the existence and uniqueness of a solution which decays exponentially fast at infinity. We introduce an approximation process by solutions in bounded subdomains and establish asymptotically precise estimates for the truncation error. This gives rise to a practical numerical approximation method. [ABSTRACT FROM AUTHOR]

In this note, we consider a Frémond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely, we generalize the paper [12] dealing with the one-dimensional case. First, we show the existence of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the non-autonomous case by the limiting global attractor. [ABSTRACT FROM AUTHOR]

The asymptotic behavior of a Stokes flow with Fourier boundary condition on one part on the boundary and Tresca free boundary friction condition on the other, when one dimension of the fluid domain tends to zero is studied. The strong convergence of the velocity is proved, a specific Reynolds equation is obtained, and the uniqueness of the limit velocity and pressure distributions is established. [ABSTRACT FROM AUTHOR]

New Findings: What is the central question of this study?Is neuromuscular fatigability interrelated between different muscle groups from the same individual during isometric all‐out exercise?What is the main finding and its importance?Although the average decrease can vary between muscles, an individual demonstrates interrelated fatigability aetiology regardless of the muscle group tested. The inter‐individual variability provides evidence of different profiles common between muscles, which can be regarded as an individual characteristic. Neuromuscular fatigability is commonly attributed to central and peripheral origins. However, there is strong evidence of interactions between these two mechanisms. According to the idea that peripheral fatigability might be centrally regulated, one can hypothesize that neuromuscular fatigability would be correlated between different muscle groups at the individual level. Thirty‐two healthy participants (16 women and 16 men) completed two 5 min fatiguing exercises [60 isometric maximal voluntary contractions (MVCs)] with finger flexors (FFs) and ankle plantar flexors (PFs) in two randomized sessions. Neuromuscular testing was conducted before, during (every six MVCs) and directly after the fatigue procedure. The force asymptote (FA) was calculated as the asymptote of the force–time relationship. Changes (post‐ vs. pre‐fatigue) in the exercise‐evoked force (ΔDb100), voluntary activation (ΔVA) and central activation ratio (∆CAR) were also investigated. Significant correlations were found between FFs and PFs for FA, ΔDb100 and ΔVA (r = 0.65, r = 0.63 and r = 0.50, respectively). A significant negative correlation between ∆CAR and ∆Db100 was evidenced for both PFs (r = −0.82) and FFs (r = −0.57). Neuromuscular fatigability is correlated between different muscle groups at the individual level. The results support the idea that a restrained motor drive prevents large peripheral perturbations and that individuals exhibit correlated fatigability aetiology regardless of the muscle group tested. Widely different central/peripheral profiles can be found amongst individuals, and a part of the fatigability aetiology can be regarded as an individual characteristic. [ABSTRACT FROM AUTHOR]

Recently, we introduced the class of matrix games under time constraints and characterized the concept of (monomorphic) evolutionarily stable strategy (ESS) in them. We are now interested in how the ESS is related to the existence and stability of equilibria for polymorphic populations. We point out that, although the ESS may no longer be a polymorphic equilibrium, there is a connection between them. Specifically, the polymorphic state at which the average strategy of the active individuals in the population is equal to the ESS is an equilibrium of the polymorphic model. Moreover, in the case when there are only two pure strategies, a polymorphic equilibrium is locally asymptotically stable under the replicator equation for the pure-strategy polymorphic model if and only if it corresponds to an ESS. Finally, we prove that a strict Nash equilibrium is a pure-strategy ESS that is a locally asymptotically stable equilibrium of the replicator equation in n-strategy time-constrained matrix games. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the asymptotic behaviour of a wide class of incompressible quasi-Newtonian fluids flowing through a thin 3D pipe, with prescribed pressure variance at the ends. The small parameter is given by the ratio between the diameter of the cross section and the length. We prove that, if the domain satisfies a particular geometric condition at the ends, a complete asymptotic expansion can be obtained. [ABSTRACT FROM AUTHOR]

Following the work of Anily et al., we consider a variant of bin packing called bin packing with general cost structures (GCBP) and design an asymptotic fully polynomial time approximation scheme (AFPTAS) for this problem. In the classic bin packing problem, a set of one-dimensional items is to be assigned to subsets of total size at most 1, that is, to be packed into unit sized bins. However, in GCBP, the cost of a bin is not 1 as in classic bin packing, but it is a non-decreasing and concave function of the number of items packed in it, where the cost of an empty bin is zero. The construction of the AFPTAS requires novel techniques for dealing with small items, which are developed in this work. In addition, we develop a fast approximation algorithm which acts identically for all non-decreasing and concave functions, and has an asymptotic approximation ratio of 1.5 for all functions simultaneously. [ABSTRACT FROM AUTHOR]

We conjecture that the asymptotic behavior of the numbers of solid (threedimensional) partitions is identical to the asymptotics of the three-dimensional MacMahon numbers. Evidence is provided by an exact enumeration of solid partitions of all integers ≥ 68 whose numbers are reproduced with surprising accuracy using the asymptotic formula (with one free parameter) and better accuracy on increasing the number of free parameters. We also conjecture that similar behavior holds for higher dimensional partitions and provides some preliminary evidence for four- and five-dimensional partitions. [ABSTRACT FROM AUTHOR]

We continue the study of bin packing with splittable items and cardinality constraints. In this problem, a set of n items must be packed into as few bins as possible. Items may be split, but each bin may contain at most k (parts of) items, where k is some given parameter. Complicating the problem further is the fact that items may be larger than 1, which is the size of a bin. The problem is known to be strongly NP-hard for any fixed value of k. We essentially close this problem by providing an efficient polynomial-time approximation scheme (EPTAS) for most of its versions. Namely, we present an efficient polynomial time approximation scheme for k= o( n). A PTAS for k=Θ( n) does not exist unless P = NP. Additionally, we present dual approximation schemes for k=2 and for constant values of k. Thus we show that for any ε>0, it is possible to pack the items into the optimal number of bins in polynomial time, if the algorithm may use bins of size 1+ ε. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the concept of low-Mach-number approximation to multi-phase flows and apply it to the two-phase flow model of Papalexandris (J. Fluid Mech., vol. 517, 2004, p. 103) for granular materials. In our approach, the governing system of equations is first non-dimensionalized with values that correspond to a reference thermodynamic state of the phase with the smaller speed of sound. By doing so, the Mach number based on this reference state emerges as a perturbation parameter of the equations in hand. Subsequently, we expand each variable in power series of this parameter and apply singular perturbation techniques to derive the low-Mach-number equations. As expected, the resulting equations are considerably simpler than the unperturbed compressible equations. Our methodology is quite general and can be directly applied for the systematic reduction of continuum models for granular materials and for many different types of multi-phase flows. The structure of the low-Mach-number equations for two special cases of particular interest, namely, constant-density flows and the equilibrium limit is also discussed and analysed. The paper concludes with some proposals for experimental validation of the equations. [ABSTRACT FROM AUTHOR]

We suggest quantile regression methods for a class of smooth coefficient time series models. We use both local polynomial and local constant fitting schemes to estimate the smooth coefficients in a quautile framework. We establish the asymptotic properties of both the local polynomial and local constant estimators for α-mixing time series. We also suggest a bandwidth selector based on the nonparametric version of the Akaike information criterion, along with a consistent estimate of the asymptotic covariance matrix. We evaluate the asymptotic behaviors of the estimators at boundaries and compare the local polynomial quantile estimator and the local constant estimator. A simulation study is carried out to illustrate the performance of estimates. An empirical application of the model to real data further demonstrates the potential of the proposed modeling procedures. [ABSTRACT FROM AUTHOR]

A comparative analysis of the two powerful asymptotic methods, ILDM and MIM (intrinsic low‐dimensional manifolds; method of invariant manifold), is presented in the paper. The two methods are based on the general theory of integral manifolds. The ILDM method is able to handle large systems of ODEs, whereas the MIM method treats systems with a limited number of unknown variables. The MIM method allows one to conduct analytical exploration of the original system and to obtain final expressions in compact form, whereas the ILDM method is a numerical approach that yields the numerical form of the desired surface. The ILDM method works well in a region where a rough splitting of the initial system exists. Regions of the phase space where splitting does not exist are problematic for the ILDM method. In these regions the MIM method provides additional information regarding the dynamical behaviour of the system. A number of simple examples are considered and analysed. It is shown that for the Semenov model (singularly perturbed system of ODEs) the ILDM method gives a surface which appears close to the first order (with respect to the corresponding small parameter) approximation of the stable (attracting) invariant manifolds. The complementary properties of the two asymptotic approaches suggests a feasible combination of the two methods, which is the subject of a future work. [ABSTRACT FROM PUBLISHER]