High-order filtered scheme for front propagation problems

In this work we develop a specific application of the scheme proposed and analyzed in [1] to front propagation problems. The approach is based on the level-set method which leads in the isotropic case to a classical evolutive first order Hamilton- Jacobi equation.We will apply to this equation high-order “filtered schemes”, for these schemes the strong monotonicity property will not be satisfied. However, a weak ?-monotonicity property applies and this is enough to obtain a convergence result and a precise error estimate. In the last section we will present several examples where we solve front propagation problems by filtered scheme in two and three dimensions showing the accuracy of our method.     

Constructions of almost complex 2-tori of type (III) in the nearly Kähler 6-sphere

In this paper, we give a machinery method of constructing almost complex curve of type (III) in the nearly Kähler 6-sphere. As application, a first non-trivial example of almost complex 2-tori of type (III) will be described in terms of the Jacobi elliptic functions. In the final section, a general solution of such tori will be described in terms of the Prym-theta functions using the known results from the integrable system theory.     

Solvability of Semilinear Hemivariational Inequalities at Resonance Using Generalized Landesman–Lazer Conditions

In this paper we examine semilinear hemivariational inequalities at resonance at any eigenvalue of the negative Laplacian with Dirichlet boundary condition. Our approach is variational based on the Nonsmooth Critical Point Theory and it uses a generalized Landesman–Lazer condition. We prove two existence theorems using two different forms of the generalized Landesman–Lazer condition. In the last section we show that our Landesman-Lazer condition is more general than the ones existing in the literature.     

Solvability of Semilinear Hemivariational Inequalities at Resonance Using Generalized Landesman–Lazer Conditions

In this paper we examine semilinear hemivariational inequalities at resonance at any eigenvalue of the negative Laplacian with Dirichlet boundary condition. Our approach is variational based on the Nonsmooth Critical Point Theory and it uses a generalized Landesman–Lazer condition. We prove two existence theorems using two different forms of the generalized Landesman–Lazer condition. In the last section we show that our Landesman-Lazer condition is more general than the ones existing in the literature.     

An orthotropic plate model for decks of suspension bridges

The main purpose of the present paper is to compare two different kinds of approaches in modeling the deck of a suspension bridge: in the first approach we look at the deck as a rectangular plate and in the second one we look at the deck as a beam for vertical deflections and as a rod for torsional deformations. Throughout this paper we will refer to the model corresponding to the second approach as the beam-rod model. In our discussion, we observe that the beam-rod model contains a larger number of elastic parameters if compared with the isotropic plate model. For this reason the beam-rod model is supposed to be more appropriate to describe the behavior of the deck of a real suspension bridge. A possible strategy to make the plate model more efficient could be to relax the isotropy condition with a more general condition of orthotropy, which is expected to increase the number of elastic parameters. In this new setting, a comparison between the two approaches becomes now possible.Basic results are proved for the suggested problem, from existence and uniqueness of solutions to spectral properties. We suggest realistic values for the elastic parameters thus obtaining with both approaches similar responses in the static and dynamic behavior of the deck. This can be considered as a preliminary article since many work has still to be done with the perspective of formulating models for a complete suspension bridge which take into account not only the deck but also the action on it of cables and hangers. With this perspective, a section is devoted to possible future developments.     

Asymptotic analysis of stochastic programs

In this paper we discuss a general approach to studying asymptotic properties of statistical estimators in stochastic programming. The approach is based on an extended delta method and appears to be particularly suitable for deriving asymptotics of the optimal value of stochastic programs. Asymptotic analysis of the optimal value will be presented in detail. Asymptotic properties of the corresponding optimal solutions are briefly discussed.     

Non-linear second-order periodic systems with non-smooth potential

In this paper we study second order non-linear periodic systems driven by the ordinary vectorp-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth conditions on the potential function. Then we establish the existence of non-trivial homoclinic (to zero) solutions. Our theorem appears to be the first such result (even for smooth problems) for systems monitored by thep-Laplacian. In the last section of the paper we examine the scalar non-linear and semilinear problem. Our approach uses a generalized Landesman-Lazer type condition which generalizes previous ones used in the literature. Also for the semilinear case the problem is at resonance at any eigenvalue.     

One-Sided FKPP Travelling Waves for Homogeneous Fragmentation Processes

In this paper, we introduce an analogue of the classical one-sided FKPP equation in the context of homogeneous fragmentation processes. The main result of the present paper is concerned with the existence and uniqueness of one-sided FKPP travelling waves in this setting. In addition, we prove some analytic properties of such travelling waves. Our techniques make use of fragmentation processes with killing, an associated product martingale as well as various properties of Lévy processes. This paper is mainly concerned with general fragmentation processes, but we also devote a section to related considerations regarding fragmentations with a finite dislocation measure, where we obtain a stronger result than for fragmentation processes with an infinite jump activity over finite time horizons. Furthermore, we discuss the relation of our problem to similar questions in the setting of branching Brownian motions, which provides a motivation for our approach.     

Linear Stieltjes equation with generalized riemann integral and existence of regulated solutions

1. IntroductiollIn the last two decades the memann generalized integral, having values in B-spaces,has been increasingly studied.The development in this area mainly concerns the HenstoCk-Kurzweil (see e.g. I1, 2]),and the Dushnik and the Young integrals (see e.g. I3]). Recently there appeared in the1iterature many proper app1ications in this field ("proper" here being considered in thesense that the results are not disguises of an essentially finite dimensional frame) (see e.g.[4, 5]).In t…     

考虑横向剪切变形时圆截面悬臂梁的广义变分原理

本文通过二类变量广义变分原理导出了考虑横向剪切变形时圆截面等直悬臂梁的近似理论,给出了对应于该理论的具有两个广义位移的二类变量广义余能的算式.     

An expansion theorem for two‐dimensional elastic waves and its application

We prove an Atkinson–Wilcox‐type expansion for two‐dimensional elastic waves in this paper. The approach developed on the two‐dimensional Helmholtz equation will be applied in the proof. When the elastic fields are involved, the situation becomes much harder due to two wave solutions propagating at different phase velocities. In the last section, we give an application about the reconstruction of an obstacle from the scattering amplitude. Copyright © 2006 John Wiley & Sons, Ltd.     

ANTICIPATIVE STOCHASTIC INTEGRALS EQUATIONS DRIVEN BY SEMIMARTINGALES

In this paper, we use the Riemann sum approach to construct the anticipative stochastic integrals and consider the Cauchy problem (non-adapted initial value) for stochastic integral equations driven by discontinuous semimartingales. For general equations with Lipschitz coefficients, we prove the existence of the solutions. Apropos of semilinear equations, we find that under some conditions uniqueness of solutions will also hold.     

Solutions with internal jump for an autonomous elliptic system of FitzHugh–Nagumo type

Systems of elliptic partial differential equations which are coupled in a noncooperative way, such as the FitzHugh–Nagumo type studied in this paper, in general do not satisfy order preserving properties. This not only results in technical complications but also yields a richer solution structure. We prove the existence of multiple nontrivial solutions. In particular we show that there exists a solution with boundary layer type behaviour, and we will give evidence that this autonomous system for a certain range of parameters has a solution with both a boundary and an internal layer. The analysis uses results from bifurcation theory, variational methods, as well as some pointwise a priori estimates. The final section contains some numerically obtained results.     

On the Vertices of Simple Modules for Symmetric Groups

In this article, we are concerned with the computation of vertices of some series of simple modules for the symmetric group of n letters in odd characteristic. In the first, the second, and the third section of this work we recall some more or less general results that are needed in our proofs. The fourth section contains new ingredients (in terms of dimension) that play an important role in our proofs of the main results in the last section.     

Some geometric results arising from the Borel fixed property

In this paper, we will give some geometric results using generic initial ideals for the degree reverse lex order. The main goal of the paper is to improve on results of Bigatti, Geramita and Migliore concerning geometric consequences of maximal growth of the Hilbert function of the Artinian reduction of a set of points. When the points have the Uniform Position Property, the consequences are even more striking. Here we weaken the growth condition, assuming only that the values of the Hilbert function of the Artinian reduction are equal in two consecutive degrees, and that the first of these degrees is greater than the second reduction number of the points. We continue to get nice geometric consequences even from this weaker assumption. However, we have surprising examples to show that imposing the Uniform Position Property on the points does not give the striking consequences that one might expect. This leads to a better understanding of the Hilbert function, and the ideal itself, of a set of points with the Uniform Position Property, which is an important open question. In the last section we describe the role played by the Weak Lefschetz Property (WLP) in this theory, and we show that the general hyperplane section of a smooth curve may not have the WLP.     

Bilevel programming with discrete lower level problems

In this article, we investigate bilevel programming problems with discrete lower level and continuous upper level problems. We will analyse the structure of these problems and discuss both the optimistic and the pessimistic solution approach. Since neither the optimistic nor the pessimistic solution functions are in general lower semicontinuous, we introduce weak solution function. By using these functions we are able to discuss optimality conditions for local and global optimality.     

Hybrid genetic algorithms for bin-packing and related problems

The genetic algorithm (GA) paradigm has attracted considerable attention as a promising heuristic approach for solving optimization problems. Much of the development has related to problems of optimizing functions of continuous variables, but recently there have been several applications to problems of a combinatorial nature. What is often found is that GAs have fairly poor performance for combinatorial problems if implemented in a naive way, and most reported work has involved somewhat ad hoc adjustments to the basic method. In this paper, we will describe a general approach which promises good performance for a fairly extensive class of problems by hybridizing the GA with existing simple heuristics. The procedure will be illustrated mainly in relation to the problem ofbin-packing, but it could be extended to other problems such asgraph partitioning, parallel-machine scheduling andgeneralized assignment. The method is further extended by usingproblem size reduction hybrids. Some results of numerical experiments will be presented which attempt to identify those circumstances in which these heuristics will perform well relative to exact methods. Finally, we discuss some general issues involving hybridization: in particular, we raise the possibility of blending GAs with orthodox mathematical programming procedures.     

Symmetry and the golden ratio in the analysis of a regular pentagon

The regular pentagon had a symbolic meaning in the Pythagorean and Platonic philosophies and a subsequent important role in Western thought, appearing also in arts and architecture. A property of regular pentagons, which was probably discovered by the Pythagoreans, is that the ratio between the diagonal and the side of these pentagons is equal to the golden ratio. Here, we will study some relations existing between a regular pentagon and this ratio. First, we will focus on the group of fivefold rotational symmetry, to find the position in the complex plane of the vertices of this geometric figure. Then, we will propose an analytic method to solve the same problem based on the Cartesian coordinates, a method where we find the golden ratio without any specific geometric consideration. This study shows a comparison of the use of complex numbers, symmetries and analytic methods, applied to a subject which can be interesting for general education in mathematics. In fact, the proposed approach can convey and link several concepts, requiring only a general pre-college education, showing at the same time the richness that mathematics can offer in solving geometric problems.     

Error Estimation for Nordsieck Methods

The local discretization errors of general linear methods depend on the sequence of all stepsize ratios and the derivation of the exact formulas for the corresponding error estimates does not seem to be practical. In this paper we will describe an approach in which the estimates of local discretization errors are evaluated numerically as the computation proceeds from step to step.     

Developing a mathematical theory of computability which speaks the language of levels

In this paper, we use the modern systems theory to retrace the history of some of the important and interesting philosophical problems. And, based on the discussion, it is shown that the multilevel structure of the nature can be approached by making use of the general systems theory approach started by Mesarovic in the early 1960s. Two difficulties appearing in modern physics are listed, and studied in terms of a new mathematical theory. This theory reflects the characteristic of multilevels of the nature. Some elementary properties of the new theory are listed. Some important and fruitful leads for future research are posed in the final section.