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All papers have been typed and translated trying to reproduce as much as possible their original aspect. We only used common fonts and the same style for the titles, the abstracts and the bibliography. [ABSTRACT FROM AUTHOR]

Weyl group multiple Dirichlet series were associated with a root system Φ and a number field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg, and Hoffstein [2]. Brubaker, Bump, and Friedberg [4] provided for when n is sufficiently large; the coefficients involve n-th order Gauss sums and reflect the combinatorics of the root system. Conjecturally, these functions coincide with Whittaker coefficients of metaplectic Eisenstein series, but they are studied in these papers by a method that is independent of this fact. The assumption that n is large is called stability and allows a simple description of the Dirichlet series. "Twisted" Dirichet series were introduced in Brubaker, Bump, Friedberg, and Hoffstein [5] without the stability assumption, but only for root systems of type A{inr}. Their description is given differently, in terms of Gauss sums associated to Gelfand-Tsetlin patterns. In this paper, we reimpose the stability assumption and study the twisted multiple Dirichlet series for general Φ by introducing a description of the coefficients in terms of the root system similar to that given in the untwisted case in [4]. We prove the analytic continuation and functional equation of these series, and when Φ = A{inr} we also relate the two different descriptions of multiple Dirichlet series given here and in [5] for the stable case. [ABSTRACT FROM AUTHOR]

In this paper we discuss upscaling of immiscible multiphase and miscible multicomponent flow and transport in heterogeneous porous media. The discussion presented in the paper summarizes the results of in Upscaled Modeling in Multiphase Flow Applications by Ginting et al. (2004) and in Upscaling of Multiphase and Multicomponent Flow by Ginting et al. (2006). Perturbation approaches are used to upscale the transport equation that has hyperbolic nature. Our numerical results show that these upscaling techniques give an improvement over the existing upscaled models which ignore the subgrid terms. [ABSTRACT FROM AUTHOR]

The paper is concerned with general optimal control problems (OCP) which are characterized by a nonsmooth ordinary state differential equation. More precisely, we assume that the right-hand side of the state equation is piecewise smooth and that the switching points, which separate these pieces, are determined as roots of a state- and control dependent (smooth) switching function. For this kind of optimal control problems necessary conditions are developed. Special attention is payed to the situation that the switching function vanishes identically along a nontrivial subarc. Such subarcs, which are called singular state subarcs, are investigated with respect to the necessary conditions and to the junction conditions. In extension to earlier results, cf. [5], in this paper the case of a zero-order switching function is considered. [ABSTRACT FROM AUTHOR]

Starting from the modelling requirements of the early design phase of the product development, the paper will show a possible strategy to overcome some limitations of current CAS/CAD systems. In fact, the styling stage involves both technical knowledge and fuzzy and dynamic aspects, which have to be taken into account for a proper management. The paper focuses on high-level modelling tools developed to deform surfaces with semantic (aesthetic) constraints, i.e. the crucial design elements for the stylist. Furthermore, the communication among the other actors of the design process is consequently facilitated. [ABSTRACT FROM AUTHOR]

In finance, the strong convergence properties of discretisations of stochastic differential equations (SDEs) are very important for the hedging and valuation of exotic options. In this paper we show how the use of the Milstein scheme can improve the convergence of the multilevel Monte Carlo method, so that the computational cost to achieve an accuracy of O(e) is reduced to O(ϵ−2) for a Lipschitz payoff. The Milstein scheme gives first order strong convergence for all one-dimensional systems (one Wiener process). However, for processes with two or more Wiener processes, such as correlated portfolios and stochastic volatility models, there is no exact solution for the iterated integrals of second order (Lévy area) and the Milstein scheme neglecting the Lévy area gives the same order of convergence as the Euler-Maruyama scheme. The purpose of this paper is to show that if certain conditions are satisfied, we can avoid the calculation of the Lévy area and obtain first convergence order by applying an orthogonal transformation. We demonstrate when the conditions of the two-dimensional problem permit this and give an exact solution for the orthogonal transformation. We present examples of pricing exotic options to demonstrate that the use of both the orthogonal Milstein scheme and the multilevel Monte Carlo give a substantial reduction in the computation cost. [ABSTRACT FROM AUTHOR]

This paper is meant to be the continuation of the previous work [1] where a coupled ODE/PDE method for the simulation of semiconductor devices was introduced. From a strictly mathematical viewpoint, analytical results on coupled PDE/ODE systems (as arising in integrated circuit simulation) can be found in [2]. In particular, in the present paper, we investigate numerically new algorithms of Domain Decomposition type for the simulation of circuits containing distributed devices (Sect. 2) as well as semiconductors in which some part is modeled with lumped parameters (Sect. 3). The results presented here have been investigated in the seminal work [3], while a more extended analysis is ongoing [4]. [ABSTRACT FROM AUTHOR]

Multiple Recursive Generators (MRGs) have become the most popular random number generators recently. They compute the next value iteratively from the previous k values using a k-th order recurrence equation which, in turn, corresponds to a k-th degree primitive polynomial under a prime modulus p. In general, when k and p are large, checking if a k-th degree polynomial is primitive under a prime modulus p is known to be a hard problem. A common approach is to check the conditions given in Alanen and Knuth [1964] and Knuth [1998]. However, as mentioned in Deng [2004], this approach has two obvious problems: (a) it requires the complete factorization of pk - 1, which can be difficult; (b) it does not provide any early exit strategy for non-primitive polynomials. To avoid (a), one can consider a prime order k and prime modulus p such that (pk - 1)/(p - 1) is also a prime number as considered in L'Ecuyer [1999] and Deng [2004]. To avoid (b), one can use a more efficient iterative irreducibility test proposed in Deng [2004]. In this paper, we survey several leading probabilistic and deterministic methods for the problems of primality testing and irreducibility testing. To test primality of a large number, it is known that probabilistic methods are much faster than deterministic methods. On the other hand, a probabilistic algorithm in fact has a very tiny probability of, say, 10-200 to commit a false positive error in the test result. Moreover, even when such an unlikely event had happened, for a speci.c choice of k and p, it can be argued that such an error has a negligible e.ect on the successful search of a primitive polynomial. We perform a computer search for large-order DX generators proposed in Deng and Xu [2003] and present many such generators in the paper for ready implementation. An extensive empirical study shows that these large-order DX generators have passed the stringent Crush battery of the TestU01 package. [ABSTRACT FROM AUTHOR]

This paper describes our method of pairing automorphic distributions.We present a third technique for obtaining the analytic properties of automorphic L-functions, in addition to the existing methods of integral representations (Rankin-Selberg) and Fourier coefficients of Eisenstein series (Langlands-Shahidi). We recently used this technique to establish new cases of the full analytic continuation of the exterior square L-functions. The paper here gives an exposition of our method in two special, yet representative cases: the Rankin-Selberg tensor product L-functions for PGL(2,Z)∖PGL(2,R), as well as for the exterior square L-functions for GL(4,Z)∖GL(4,R). [ABSTRACT FROM AUTHOR]

Numerous decision problems in management science and problems in economic theory give rise to constrained optimization of linear or nonlinear functions. If in the nonlinear case the objective function is a ratio of two functions or involves several such ratios, then the optimization problem is called a fractional program. Apart from isolated earlier results, most of the work in fractional programming were done since about 1960. The analysis of fractional programs with only one ratio has largely dominated the literature until about 1980. Since the first international conference with an emphasis on fractional programming the NATO advanced Study Institute on "Generalized Concavity in Optimization and Economics" (Schaible and Ziemba (1981)), that indicates a shift of interest from the single to the multiobjective case, see Singh and Dass (1989), Cambini, Castagnoli, Martein, Mazzoleni and Schaible (1990), Komlosi, Rapcsak and Schaible (1994), Mazzoleni (1992). It is interesting to note that some of the earliest publications in fractional programming, though not under this name, Von Neuman's classical paper on a model fo a general economic equilibrium [Von Neumann (1937)] analysis a multiobjective fractional program. Even a duality theory was proposed for this nonconcave program, and this at a time when linear programming hardly existed. However, this early paper was followed almost exclusively by articles in single objective fractional programming until the early 1980s. [ABSTRACT FROM AUTHOR]

It is well known that there are "nonclassical" situations where, in contrast to Lax's and Glimm's results, the Cauchy problem for a system of conservation laws does not possess a weak L∞-solution except for some particular initial data. To solve the Cauchy problem in this "nonclassical" situation, it is necessary to introduce new singular solutions called δ-shocks and singular shocks. The components of these solutions contain delta functions [ASh05], [B94], [DSh03]- [LW02], [S02]- [Sh04], [TZZ94]. The exact structure of such type solutions is given below in (2), (7) and Definition 1. The theory of δ-shocks and singular shocks has been intensively developed in the last 10 years. In particular, in numerous papers δ-shock type solutions of "zero-pressure gas dynamics" have been studied. Moreover, in the recent papers [PSh06], [Sh06] the theory of δ′-shocks was established, and a concept of δ(n)-shocks was introduced, n = 2, 3,. … They are new type singular solutions such that their components contain delta functions and their derivatives. [ABSTRACT FROM AUTHOR]

Many equations arising in continuum fluid dynamics do not, or at least are not known to, possess smooth solutions for general data. Therefore it is necessary to identify a larger class of "weak solutions" in order to develop a rigorous mathematical theory. Following the seminal paper of Leray [10] we introduce a class of weak solutions to the Navier-Stokes-Fourier system based on the concept of generalized derivatives (distributions). The main objective of the present paper is to illustrate the strength of the abstract theory reviewing several theoretical results on the asymptotic behavior of the weak solutions that are in good agreement with practical experiments as well as their numerical analysis.The main topics to be discussed include the following: [ABSTRACT FROM AUTHOR]

A multivariate assumed PDF approach together with finite-rate chemistry is used for the simulation of scramjet combustors. Because the combustor entrance conditions of scramjets at low flight Mach numbers (Ma ≈ 8) are close to the ignition limit of hydrogen air mixtures, detailed kinetic schemes are required and an accurate simulation of temperature and temperature fluctuations is essential. In the present paper, a lobed strut injector concept is used for hydrogen injection which enhances the mixing process by production of streamwise vorticity. The influence of the chosen combustor geometry on the mixing behaviour is investigated in this paper. Moreover a Mach 2 supersonic combustion experiment is simulated to investigate the influence of the chosen reaction mechanism and of the assumed PDF model. A detached flame is obtained and the predicted ignition length is a measure for the accuracy of the used kinetic scheme and the modeling of turbulence chemistry interaction. [ABSTRACT FROM AUTHOR]

This paper is concerned with the generation of C0 semigroup associated with the Oseen equation with rotating effect and its Lp-Lq decay estimate. The theorems presented in this paper give us one of the key steps in order to show a globally in time existence of solutions to the Navier-Stokes equations describing the motion of viscous incompressible fluid flow past a rotating rigid body. [ABSTRACT FROM AUTHOR]

In this paper we explain the notion of stochastic backward differential equations and its relationship with classical (backward) parabolic differential equations of second order. The paper contains a mixture of stochastic processes like Markov processes and martingale theory and semi-linear partial differential equations of parabolic type. Some emphasis is put on the fact that the whole theory generalizes Feynman-Kac formulas. A new method of proof of the existence of solutions is given. All the existence arguments are based on rather precise quantitative estimates. [ABSTRACT FROM AUTHOR]

This paper is an addition to the paper [3], where it was proved that the theorem about the null space of the classical Sylvester resultant matrix also holds for its continuous analogue for entire matrix function provided that a certain so-called quasi-commutativity condition is fulfilled. In the present paper we show that this quasi-commutativity condition is not only sufficient but also necessary. [ABSTRACT FROM AUTHOR]

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain. [ABSTRACT FROM AUTHOR]

A typical problem in engineering is to find a numerical solution to a partial differential equation (or a coupled set thereof), given a number of boundary conditions, and the usual approach of solving the problem starts by discretizing the domain into elementary volumes. In this paper, we focus on mesh generation suitable for the solution of field problems in arbitrary VLSI structures. We assume that the problem cannot be easily reduced to a lower dimensionality by exploiting symmetry or regularity, so that the problem-domain is intrinsically threedimensional. Also, we assume that the selected numerical technique (e.g., the finite element method) requires a three-dimensional discretization (as opposed to a surface-discretization). Surveys on mesh generation are given in [2] and [5]. The mesh generator described in this paper is based on techniques from the Delaunay-based mesh generation literature. The main benefit of these techniques is that the quality of the resulting meshes can be guaranteed, and, equally important, that the meshes are still small enough to be practically useful. An additional advantage is that computation of the mesh is efficient in practice. In general, mesh computation is much faster than solving the subsequent numerical problems. An example mesh generated by our implementation is shown in Figure 1. [ABSTRACT FROM AUTHOR]

The paper describes the application of the Newton method in conjunction with the Finite Integration Technique. Even on orthogonal grid pairs, the material matrices become nondiagonal and lead to higher algorithmic complexity. A uni-directional version of these matrices provides a computationally inexpensive alternative. The paper compares and discusses the two algorithms' order of convergence and their computational complexity. [ABSTRACT FROM AUTHOR]

This paper summarizes the recent circuit-simulation activities [Roo04]-[Sil06] at Helsinki University of Technology (TKK), Circuit Theory Laboratory (CTL). This paper is mostly based on the results of the national projects Advanced Radio Frequency SImulation and Modeling (ARFSIM 2002-2003) [Roo04], MOdeling and Simulation for Advanced Integrated Circuits and Systems (MOSAICS 2004-2005), and Accurate Models Aim for Zero Errors (AMAZE 2006-2008). All these projects have been funded by the National Technology Agency of Finland, Nokia Corporation, and AWR-APLAC Corporation; the annual volume at TKK CTL has been 4.0-5.5 man years. In these projects, APLAC circuit simulation and design tool [A06] has been used as a common platform for the circuit analysis and modeling methods developed. [ABSTRACT FROM AUTHOR]

The design of microwave and millimeter wave devices requires more and more accurate synthesis procedures to satisfy the increasingly stringent specifications of modern communication systems [1]. Most of the available synthesis techniques are based on models that do not conveniently describe the physical behavior of circuits. The goal of the present paper is to calculate the scattering matrix for the case of single and cascaded strip gratings. The strip gratings allow a complete transmission of certain frequencies and a complete reflection at other frequencies and, then, exists a simple type of frequency selective surface [2]. A wide variety of filter characteristics can be obtained by cascading multiple layers of frequencies-selective surfaces. In this paper, a new method for scattered matrix analysis is presented. This method is based on Floquet harmonics analysis. [ABSTRACT FROM AUTHOR]

In this paper, we review a number of basic results about so-called Hopf algebras. We begin by giving a historical account of the results obtained in the 1930's and 1940's about the topology of Lie groups and compact symmetric spaces. The climax is provided by the structure theorems due to Hopf, Samelson, Leray and Borel. The main part of this paper is a thorough analysis of the relations between Hopf algebras and Lie groups (or algebraic groups). We emphasize especially the category of unipotent (and prounipotent) algebraic groups, in connection with Milnor-Moore's theorem. These methods are a powerful tool to show that some algebras are free polynomial rings. The last part is an introduction to the combinatorial aspects of polylogarithm functions and the corresponding multiple zeta values. [ABSTRACT FROM AUTHOR]

One of the greatest achievements of mathematics in the 20th century is Harish-Chandra's classification of discrete series representations of semisimple Lie groups. Let G be a noncompact semisimple Lie group with a maximal compact subgroup K. Discrete series representations are those irreducible unitary representations of G which occur as subrepresentations in the Plancherel decomposition of L2(G). Harish-Chandra proved that a necessary and sufficient condition for G to have a discrete series is to have a compact Cartan subgroup. He constructed the characters of all discrete series representations. Speaking of Harish-Chandra's work on discrete series, we quote Varadarajan in his article "Harish-Chandra, His Work, and its Legacy" [Va]: "In my opinion the character problem and the problem of constructing the discrete series were the ones that defined him, by stretching his formidable powers to their limit. The Harish-Chandra formula for the characters of discrete series is the single most beautiful formula in the theory of infinite-dimensional unitary representations." Harish-Chandra "actually wrote down all the proofs in an extraordinary sequence of 8 papers [1964a]-[1966b], totaling 461 journal pages constituting one of the most remarkable series of papers in the annals of scientific research in our times—remarkable because of how long it took him to reach his goal, remarkable for how difficult the journey was and how it was punctuated by illness, remarkable for how unaided his achievement was, and finally, remarkable for the beauty and inevitability of his theorems." [ABSTRACT FROM AUTHOR]

The success in the use of lattice-Boltzmann methods for the simulation of laminar .ows has prompted the interest in extending the technique for the simulation of turbulent flows. In this paper, a square cylinder at Re = 21400 is used to investigate the suitability of lattice-Boltzmann methods to solve turbulent unsteady problems with open boundary conditions. Numerical simulations are performed with a single-relaxation-time lattice-Boltzmann method and with a large-eddy simulation turbulence model. These simulations present several not-fully-resolved issues for lattice-Boltzmann methods, which are briefly discussed in this paper. Specifically, we propose a filtered-density open-boundary condition for fluid-flow simulations with the lattice-Boltzmann equation. This filter modification of inflow boundary condition is shown to improve simulations of unsteady flows at high Reynolds numbers, in terms of calculation stability and speed, and quality of the results. [ABSTRACT FROM AUTHOR]

In the present paper we will construct an infinite series of so-called Hurwitz groups. One possible way to describe Hurwitz groups is to define them as finite homomorphic images of the Fuchsian triangle group with the signature (2, 3, 7). A reason why Hurwitz groups are interesting lies in the fact, that precisely these groups occur as the automorphism groups of compact Riemann surfaces of genus g > 1, which attain the upper bound 84(g − 1) for the order of the automorphism group. For a long time the only known Hurwitz group was the special linear group PSL2($$ \mathbb{F}_7 $$), with 168 elements, discovered by F. Klein in 1879, which is the automorphism group of the famous Kleinian quartic. In 1967 Macbeath found an infinite series of Hurwitz groups using group theoretic methods. In this paper we will give an alternative arithmetic construction of this series. [ABSTRACT FROM AUTHOR]

High altitude pulmonary hypertension (HAPH) is a genetically determined trait, associated with the diminished oxygen content at high altitudes and it usually affects native or long-term highlanders and may reflect a loss of adaptation. This paper reviews the epidemiological evidence for a genetic trait of the altitude-related illnesses, mainly HAPH, as well as the molecular evidence for the contribution of the specific candidate genes or pathways involved. We focus on our own data and experience in the research of genetics of HAPH done on the indigenous population of Pamir and Tien- Shan mountains. These data include the existence or lack of association of polymorphisms of ACE gene, β2-adrenoreceptor gene, C677T polymorphism of MTHFR gene, 838 C>A polymorphism of p27kip1, polymorphisms of eNOS gene and S/L polymorphism of 5-HTT gene. The paper closes with a discussion on what could be the future of the expansion of the existing database of the genetic risk factors and polymorphisms involved in the development of HAPH. Keywords: HAPH; hypoxic pulmonary hypertension; altitude sickness; genetic epidemiology; gene polymorphism [ABSTRACT FROM AUTHOR]

The main subject of this paper is the numerical simulation of the chemical differentiation of the Earth's mantle. This differentiation induces the generation and growth of the continents and, as a complement, the formation and augmentation of the depleted MORB mantle. Here, we present for the first time a solution of this problem by an integrated theory in common with the problem of thermal convection in a 3-D compressible spherical-shell mantle. The whole coupled thermal and chemical evolution of mantle plus crust was calculated starting with the formation of the solid-state primordial silicate mantle. No restricting assumptions have been made regarding number, size and form of the continents. It was, however, implemented that moving oceanic plateaus touching a continent are to be accreted to this continent at the corresponding place. The model contains a mantle-viscosity profile with a usual asthenosphere beneath a lithosphere, a highly viscous transition zone and a second low-viscosity layer below the 660-km mineral phase boundary. The central part of the lower mantle is highly viscous. This explains the fact that there are, regarding the incompatible elements, chemically different mantle reservoirs in spite of perpetual stirring during more than 4.49×109 a. The highly viscous central part of the lower mantle also explains the relatively slow lateral movements of CMB-based plumes, slow in comparison with the lateral movements of the lithospheric plates. The temperature- and pressure-dependent viscosity of the model is complemented by a viscoplastic yield stress, σy. The paper includes a comprehensive variation of parameters, especially the variation of the viscosity-level parameter, rn, the yield stress, σy, and the temporal average of the Rayleigh number. In the rn−σy plot, a central area shows runs with realistic distributions and sizes of continents. This area is partly overlapping with the rn−σy areas of piecewise plate-like movements of the lithosphere and of realistic values of the surface heat flow and Urey number. Numerical problems are discussed in Sect. 3. [ABSTRACT FROM AUTHOR]

In the past few years, Domain Decomposition Methods (DDM) have emerged as advanced solvers in several areas of computational mechanics. In particular, during the last decade, in the area of solid and structural mechanics, they reached a considerable level of advancement and have been shown to be more efficient than popular solvers, like advanced sparse direct solvers. The present contribution follows the lines of a series of recent publications by the authors on DDM. In these papers, the authors developed a unified theory of primal and dual methods and presented a family of DDM that were shown to be more efficient than previous methods. The present paper extends this work, presenting a new family of related DDM, thus enriching the theory of the relations between primal and dual methods. [ABSTRACT FROM AUTHOR]

Recent progress has been made to more robustly handle the increased complexity of high-order schemes by focusing on the local nature of the discretization. This locality is particularly true for many Discontinuous Galerkin formulations and is the focus of this paper. The contributions of this paper are twofold. First, novel observations regarding various flux representations in the discontinuous Galerkin formulation are highlighted in the context of overlapping Schwarz methods. Second, we conduct additional experiments using high-order elements for the indefinite Helmholtz equation to expose the impact of overlap. [ABSTRACT FROM AUTHOR]

The parareal algorithm is a method to solve time dependent problems parallel in time: it approximates parts of the solution later in time simultaneously to parts of the solution earlier in time. In this paper the relation of the parareal algorithm to space-time multigrid and multiple shooting methods is first briefly discussed. The focus of the paper is on some new convergence results that show superlinear convergence of the algorithm when used on bounded time intervals, and linear convergence for unbounded intervals. [ABSTRACT FROM AUTHOR]

Throughout this paper we denote by Lp the Banach lattice of p-integrable functions on a σ-finite measure space (X, B, μ), where 1 ≤ p ≤ ∞. We will consider those aspects of the theory of positive linear operators, which are in some way special due to the fact the operators are acting on Lp-spaces. For general information about positive operators on Banach lattices we refer to the texts [1]. [20], and [36]. Our focus on Lp-spaces does not mean that in special cases some of the results can not be extended to a larger class of Banach lattices of measurable function such as Orlicz spaces or re-arrangement invariant Banach function spaces. However in many cases the results in these extensions are not as precise or as complete as in the case of Lp-spaces. We will discuss results related to the boundedness of positive linear operators on Lp-spaces. The most important result is the so-called Schur criterion for boundedness. This criterion is the most frequently used tool to show that a concrete positive linear operator is bounded from Lp to Lq. Then we will show how this result relates to the change of density result of Weis [33]. Next the equality case of Schur's criterion is shown to be closely related to the question whether a given positive linear operator attains its norm. We discuss in detail the properties of norm attaining operators on Lp-spaces and discuss as an example the weighted composition operators on Lp-spaces. Then we return to the Schur criterion and show how it can be applied to the factorization theorems of Maurey and Nikišin. Most results mentioned in this paper have appeared before in print, but sometimes only implicitly and scattered over several papers. Also a number of the proofs presented here are new. [ABSTRACT FROM AUTHOR]

We wrote a survey [18] on lattice ordered algebras five years ago. Why do we return to f-algebras once more? We hasten to say that there is only little overlap between the current paper and that previous survey.We have three purposes for the present paper. In our previous survey we remarked that one aspect that we did not discuss, while of some historical importance to the topic, is the theory of averaging operators. That theory has its roots in the nineteenth century and predates the rise of vector lattices. Positivity is a crucial tool in averaging, and positivity has been a fertile ground for the study of averaging-like operators. The fruits of positivity in averaging have recently (see [24]) started to appear in probability theory (to which averaging operators are close kin) and statistics. In the first section of our paper, we survey the literature for our selection of old theorems on averaging operators, at the same time providing some new perspectives and results as well. [ABSTRACT FROM AUTHOR]

For centuries celestial mechanics has been an exceptional rich source of problems and results in mathematics. To some extent this is still the case. Today one can discern, rather artificially, three problem fields. The first one is the study of classical problems like perturbed Kepler motion, orbits in the threebody problem, the theory of asteroids and comets, etc. The second one is a small but relatively important field in which the astrophysicists are interested; we are referring to systems with evolution like for instance changes caused by tidal effects or by exchange of mass. The third field is what one could call ‘mathematical celestial mechanics', a subject which is part of the theory of dynamical systems. The distinction between the fields is artificial. There is some interplay between the fields and hopefully, this will increase in the future. An interesting example of a study combining the first and the third field is the paper by Brjuno [41]. A typical example of an important mathematical paper which has found already some use in classical celestial mechanics is Moser's study on the geometrical interpretation of the Kepler problem [193]. Surveys of mathematical aspects of celestial mechanics have been given in [194] and [3]. [ABSTRACT FROM AUTHOR]

This paper presents a finite element method for solving the resonance line transfer problem in moving media. The algorithm is capable of dealing with three spatial dimensions, using hierarchically structured grids which are locally refined by means of duality-based a posteriori error estimates. Application of the method to coherent isotropic scattering and complete redistribution gives a result of matrix structure which is discussed in the paper. The solution is obtained by way of an iterative procedure, which solves a succession of quasi-monochromatic radiative transfer problems. It is therefore immediately evident that any simulation of the extended frequency-dependent model requires a solution strategy for the elementary monochromatic transfer problem, which is fast as well as accurate. The present implementation is applicable to arbitrary model configurations with optical depths up to 103-104. Additionally, a combination of a discontinuous finite element method with a superior preconditioning method is presented, which is designed to overcome the extremely poor convergence properties of the linear solver for optically thick and highly scattering media. The contents of this article is as follows: IntroductionOverview: numerical methodsMonochromatic 3D radiative transferPolychromatic 3D line transferTest calculationsApplicationsMulti-model preconditioningConclusion [ABSTRACT FROM AUTHOR]

In this paper, new natural element approximations are proposed, in order to address issues associated with incompressibility as well as to increase the accuracy in the Natural Element Method (NEM). The NEM exhibits attractive features such as interpolant shape functions or auto-adaptive domain of influence, which alleviates some of the most common difficulties in meshless methods. Nevertheless, the shape functions can only reproduce linear polynomials, and in contrast to moving least squares methods, it is not easy to define interpolations with arbitrary approximation consistency. In order to treat mechanical models involving incompressible media in the framework of mixed formulations, the associated functional approximations must satisfy the well known inf-sup, or LBB condition. The first proposed approach constructs richer NEM approximation schemes by means of bubbles associated with the topological entities of the underlying Delaunay tessellation, allowing to pass the LBB and to remove pressure oscillations in the incompressible limit. Despite of its simplicity, this approach does not construct approximation with higher order consistency. The second part of the paper deals with a discussion on the construction of second-order accurate NEM approximations. For this purpose, two techniques are investigated : (a) the enrichment in the MLS framework of the bubbles with higher-order polynomials and (b) the use of a new Hermite-NEM formulation. [ABSTRACT FROM AUTHOR]

In this paper we present the application of the meshfree method of finite spheres to the solution of thin and thick plates composed of isotropic as well as functionally graded materials. For the solution of such problems it is observed that using Gaussian and adaptive quadrature schemes are computationally inefficient. In this paper a new technique, presented in [26, 21], in which the integration points and weights are generated using genetic algorithms and stored in a lookup table using normalized coordinates as part of an offline preprocessing step, is shown to provide significant reduction of computational time without sacrificing accuracy. [ABSTRACT FROM AUTHOR]

In this paper we give an introduction to modelling the natural gas value chain including production, transportation, processing, contracts, and markets. The presentation gives insight in the complexity of planning in the natural gas supply chain and how optimization can help decision makers in a natural gas company coordinate the different activities. We present an integrated view from the perspective of an upstream company. The paper starts with decribing how to model natural gas transportation and storage, and at the end we present a stochastic portfolio optimization model for the natural gas value chain in a liberalized market. [ABSTRACT FROM AUTHOR]

The paper has two main themes: The first theme is to give the reader an introduction to modern methods for systems of conservation laws. To this end, we start by introducing two classical schemes, the Lax-Friedrichs scheme and the Lax-Wendroff scheme. Using a simple example, we show how these two schemes fail to give accurate approximations to solutions containing discontinuities. We then introduce a general class of semi-discrete finite-volume schemes that are designed to produce accurate resolution of both smooth and nonsmooth parts of the solution. Using this special class we wish to introduce the reader to the basic principles used to design modern high-resolution schemes. As examples of systems of conservation laws, we consider the shallow-water equations for water waves and the Euler equations for the dynamics of an ideal gas. The second theme in the paper is how programmable graphics processor units (GPUs or graphics cards) can be used to efficiently compute numerical solutions of these systems. In contrast to instruction driven micro-processors (CPUs), GPUs subscribe to the data-stream-based computing paradigm and have been optimised for high throughput of large data streams. Most modern numerical methods for hyperbolic conservation laws are explicit schemes defined over a grid, in which the unknowns at each grid point or in each grid cell can be updated independently of the others. Therefore such methods are particularly attractive for implementation using data-stream-based processing. [ABSTRACT FROM AUTHOR]

Using graphics hardware for general-purpose computations (GPGPU) has for selected applications shown a performance increase of more than one order of magnitude compared to traditional CPU implementations. The intent of this paper is to give an introduction to the use of graphics hardware as a computational resource. Understanding the architecture of graphics hardware is essential to comprehend GPGPU-programming. This paper first addresses the fixed functionality graphics pipeline, and then explains the architecture and programming model of programmable graphics hardware. As the CPU is instruction driven, while a graphics processing unit (GPU) is data stream driven, a good CPU algorithm is not necessarily well suited for GPU implementation. We will illustrate this with some commonly used GPU algorithms. The paper winds up with examples of GPGPU-research at SINTEF within simulation, visualization, image processing, and geometry processing. [ABSTRACT FROM AUTHOR]

In the present paper we analyze algebraic structures arising in Yang-Mills theory. The paper should be considered as a part of a project started with [15] and devoted to maximally supersymmetric Yang-Mills theories. In this paper we collect those of our results which hold without the assumption of supersymmetry and use them to give rigorous proofs of some results of [15]. We consider two different algebraic interpretations of Yang-Mills theory—in terms of A∞-algebras and in terms of representations of Lie algebras (or associative algebras). We analyze the relations between these two approaches and calculate some Hochschild (co)homology of the algebras in question. [ABSTRACT FROM AUTHOR]

In this paper, Part II, of a two-part paper we apply the results of [KW], Part I, to establish, with an explicit dual coordinate system, a commutative analogue of the Gelfand-Kirillov theorem for M(n), the algebra of n × n complex matrices. The function field F(n) of M(n) has a natural Poisson structure and an exact analogue would be to show that F(n) is isomorphic to the function field of an n(n − 1)-dimensional phase space over a Poisson central rational function field in n variables. Instead we show that this the case for a Galois extension, F(n, e), of F(n). The techniques use a maximal Poisson commutative algebra of functions arising from Gelfand-Zeitlin theory, the algebraic action of an n(n − 1)/2-dimensional torus on F(n, e), and the structure of a Zariski open subset of M(n) as an n(n − 1)/2-dimensional torus bundle over an n(n + 1)/2-dimensional base space of Hessenberg matrices. [ABSTRACT FROM AUTHOR]

(a) In this paper we want to present some results and conjectures about crystalline cohomology. In particular, we shall show that many results from ℓ-adic étale cohomology have analogues, like the Lefschetz trace-formula, unipotence of monodromy, and the theory of weights. Our results are a sequel to the paper [Fa2]. However, there are some differences between the approaches taken. First of all, in [Fa2] we are mainly concerned with ℤp-valued cohomology, and show at the end how results carry over to the ℚp-adic theory (which works under much more general circumstances, but gives weaker results as we neglect p-torsion). Also, in [Fa2] the results are fairly complete, that is we show pretty much the results one can hope for. Finally, we were mostly interested in the relation between crystalline cohomology and p-adic étale cohomology. [ABSTRACT FROM AUTHOR]

The paper is concerned with a sequence of constants which appear in several problems. These problems include the minimal eigenvalue of certain positive definite Toeplitz matrices, the minimal eigenvalue of some higher-order ordinary differential operators, the norm of the Green kernels of these operators, the best constant in a Wirtinger-Sobolev inequality, and the conditioning of a special least squares problem. The main result of the paper gives the asymptotics of this sequence. [ABSTRACT FROM AUTHOR]

In this paper, we develop a mini-max theory of the action functional over the semi-infinite cycles via the chain level Floer homology theory and construct spectral invariants of Hamiltonian paths on arbitrary, especially on nonexact and nonrational, compact symplectic manifold (M, ω). To each given time dependent Hamiltonian function H and quantum cohomology class 0 ≠ a ∈ QH*(M), we associate an invariant ρ(H; a) which varies continuously over H in the C0-topology. This is obtained as the mini-max value over the semi-infinite cycles whose homology class is "dual" to the given quantum cohomology class a on the covering space $$ \tilde \Omega _0 (M) $$ of the contractible loop space Ω0(M). We call them the Novikov Floer cycles. We apply the spectral invariants to the study of Hamiltonian diffeomorphisms in sequels of this paper. We assume that (M, ω) is strongly semipositive here, to be removed in a sequel to this paper. [ABSTRACT FROM AUTHOR]

The paper [11] gives a construction of the total descendent potential corresponding to a semisimple Frobenius manifold. In [12], it is proved that the total descendent potential corresponding to K. Saito's Frobenius structure on the parameter space of the miniversal deformation of the An−1-singularity satisfies the modulo-n reduction of the KP-hierarchy. In this paper, we identify the hierarchy which is satisfied by the total descendent potential of a simple singularity of ADE type. Our description of the hierarchy is parallel to the vertex operator construction of Kac-Wakimoto [17] except that we give both some general integral formulas and explicit numerical values for certain coefficients which in the Kac-Wakimoto theory are studied on a case-by-case basis and remain, generally speaking, unknown. [ABSTRACT FROM AUTHOR]

This paper gives a broad overview of the area of searching with errors and the related field of error-correcting coding. In the vast literature regarding this problem, many papers simultaneously deal with various sorts of restrictions on the searching protocol. We partition this survey into sections, choosing the most appropriate section for each topic. [ABSTRACT FROM AUTHOR]

Although primarily a researcher in geometry, Mario Pieri wrote four papers that addressed aspects of arithmetic: 1906d A Look at the New Logico-Mathematical Direction of the Deductive Sciences 1906e On an Arithmetical Definition of the Irrationals (completed in 1905) 1906g On the Consistency of the Axioms of Arithmetic 1907a On the Axioms of Arithmetic The first three are introduced in the following paragraphs, and will be discussed in detail in the second book of the present series. Section 4.1 presents historical background for the 1906e, 1906g, and 1907a papers. The last, On the Axioms of Arithmetic, is translated in entirety in section 4.2 and discussed in detail in section 4.3. [ABSTRACT FROM AUTHOR]

This chapter contains an English translation of Pieri's 1908a memoir, Elementary Geometry Based on the Notions of Point and Sphere.1 The work had two main goals. First, it presented elementary Euclidean geometry as a hypothetical-deductive system, and showed that all its notions and postulates can be defined and formulated in terms of the notion point and the relation that holds between points a,b,c just when a,b are equidistant from c. As noted in section 5.2, this result gave rise, over decades, to a stream of related research that still continues. The paper's title reflects Pieri's extensive use of elementary set theory in developing geometry from his postulates: he defined the sphere through b centered at c as the set of all points a such that a and b are equidistant from c. Pieri's second aim was to foster more extensive use of properties of spheres in presenting elementary geometry, even in school courses. In this regard, he seems to have had less impact, even though this memoir presents many useful examples. A third aim, which Pieri had already pursued for a decade, was to promote the use of transformations in elementary geometry. Pieri introduced various geometric transformations early through definitions, and employed them extensively throughout the paper, following paths already explored in his 1900a Point and Motion memoir. Finally, Pieri followed the strategy of fusionism in developing plane and solid geometry together.2 [ABSTRACT FROM AUTHOR]

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical field-theoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g., being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations. [ABSTRACT FROM AUTHOR]