A Differential Game Described by a Hyperbolic System

An antagonistic differential game of hyperbolic type with a separable linear vector pay-off function is considered. The main result is the description of all ε-Slater saddle points consisting of program strategies, program ε-Slater maximins and minimaxes for each ε ∈ R^N > for this game. To this purpose, the considered differential game is reduced to find the optimal program strategies of two multicriterial problems of hyperbolic type. The application of approximation enables us to relate these problems to a problem of optimal program control, described by a system of ordinary differential equations, with a scalar pay-off function. It is found that the result of this problem is not changed, if the players use positional or program strategies. For the considered differential game, it is interesting that the ε-Slater saddle points are not equivalent and there exist two ε-Slater saddle points for which the values of all components of the vector pay-off function at one of them are greater than the respective components of the other ε-saddle point.

On a Variational Approach to some Quasilinear Problems

We prove some multiplicity results concerning quasilinear elliptic equations with natural growth conditions. Techniques of nonsmooth critical point theory are employed.

Automata–based Method for Solving Systems of Linear Constraints in {0,1}

We consider a finite state automata based method of solving a system of linear Diophantine equations with coefficients from the set {-1,0,1} and solutions in {0,1}.

Operational Methods in the Environment of a Computer Algebra System

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.

Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity

We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.

Explicit Solutions of Nonlocal Boundary Value Problems, Containing Bitsadze-Samarskii Constraints

MSC 2010: 44A35, 35L20, 35J05, 35J25

Symbolic Solving of Partial Differential Equation Systems and Compatibility Conditions

An algorithm is produced for the symbolic solving of systems of partial differential equations by means of multivariate Laplace–Carson transform. A system of K equations with M as the greatest order of partial derivatives and right-hand parts of a special type is considered. Initial conditions are input. As a result of a Laplace–Carson transform of the system according to initial condition we obtain an algebraic system of equations. A method to obtain compatibility conditions is discussed.

Indication strength of coenological similarity patterns based on genus-level taxon lists and prevalence distribution

Several methods and indicators can be used to evaluate the coenological state of a given habitat, the ones which can be created simply, quickly, standardizably and reliably and which can be used to exactly quantify the state of a given habitat in point of numbers can be of outstanding practical importance in ecology. One possible method is the examination of the genera which can be found in a given habitat in great abundance and have little number of species and various ecological characteristics. For this purpose one of the most appropriate groups is that of ground-dwelling oribatid mites (Acari: Oribatida). In our research, joining the bioindication methodological project of the “Adaptation to Climate Change” Research Group of the Hungarian Academy of Sciences, the indication strength of genus-level taxon lists and the effects of the main pattern-generating factors creating similarity patterns were analysed with the help of data series on oribatid mites collected by us and originating from literature. Our aim was to develop a method with the help of which the difference expressed with distance functions between two oribatid mite genus lists originating from any sources can correspond to spatial and temporal scales. Our results prove that these genus lists are able to express the spatial distance of the habitats. With the help of this base of comparison changes in disturbed or transformed habitats can be expressed by means of oribatid mite communities, with spatial and temporal distances.

Buraco negros, correspondência AdS/BCFT e fluido/gravidade

Einstein’s equations with negative cosmological constant possess the so-called anti de Sitter space, AdSd+1, as one of its solutions. We will later refer to this space as to the "bulk". The holographic principle states that quantum gravity in the AdSd+1 space can be encoded by a d−dimensional quantum field theory on the boundary of AdSd+1 space, invariant under conformal transformations, a CFTd. In the most famous example, the precise statement is the duality of the type IIB string theory in the space AdS5 × S 5 and the 4−dimensional N = 4 supersymmetric Yang-Mills theory. Another example is provided by a relation between Einstein’s equations in the bulk and hydrodynamic equations describing the effective theory on the boundary, the so-called fluid/gravity correspondence. An extension of the "AdS/CFT duality"for the CFT’s with boundary was proposed by Takayanagi, which was dubbed the AdS/BCFT correspondence. The boundary of a CFT extends to the bulk and restricts a region of the AdSd+1. Neumann conditions imposed on the extension of the boundary yield a dynamic equation that determines the shape of the extension. From the perspective of fluid/gravity correspondence, the shape of the Neumann boundary, and the geometry of the bulk is sourced by the energy-momentum tensor Tµν of a fluid residing on this boundary. Clarifying the relation of the Takayanagi’s proposal to the fluid/gravity correspondence, we will study the consistence of the AdS/BCFT with finite temperature CFT’s, or equivalently black hole geometries in the bulk.

Stable oxygen isotope ratios, calcium carbonate and opal content in late Pliocene sediments of DSDP Hole 75-532 in the Southeast Atlantic (Table 1)

Site 532 on the Walvis Ridge was sampled at 4000- to 800-year intervals from 2.24 to 2.60 Ma, spanning the three large glacial advances of the late Pliocene. An age model was created by correlating the oxygen isotope record to Site 607 with linear interpolations between tie-lines. The resultant age model differs from that in the site reports by more than 800,000 years, due to misidentification of a magnetic boundary. Sedimentation rates varied by an order of magnitude at this site, with minimum accumulation during glacial events. Interglacial intervals were charactrized by high marine production and high summer precipitation on land, while glacials had very low production and arid continental climate. During the large glacial events (Stages 96-100) conditions of low production and continental aridity reached their greatest intensity, but there is no evidence of a permanent mode shift in either marine or terrestrial records. Calcite concentration has a strong variation at obliquity frequencies, with maxima during interglacials, but occasionally shows a large amplitude at precessional frequencies as well, so that high concentrations occur in a few glacial intervals. As a result, color variation is not a reliable guide to glacial-scale cycles at this site. Composition of the phytoplankton assemblage is diverse and highly variable, and we have not been able to distinguish a clear indicator of upwelling-related production. Spectral analysis reveals obliquity and precessional signals in the pollen data, while several diatom records contain combination tones, indicating that these data represent a complicated response to both local and high-latitude forcing.

10Be and barium concentrations of sediment core GeoB1008-3

Particle reactive elements are scavenged to a higher degree at ocean margins than in the open ocean due to higher fluxes of biogenic and terrigenous particles. In order to determine the influence of these processes on the depositional fluxes of 10Be and barium we have performed high-resolution measurements on sediment core GeoB1008-3 from the Congo Fan. Because the core is dominated by terrigenous matter supplied by the Congo River, it has a high average mass accumulation rate of 6.5 cm/kyr. Biogenic 10Be and Ba concentrations were calculated from total concentrations by subtracting the terrigenous components of10Be and Ba, which are assumed to be proportional to the flux of Al2O3. The mean Ba/Al weight ratio of the terrigenous component was determined to be 0.0045. The unusualy high terrigenous 10Be concentrations of 9.1 * 10**9 atoms/g Al2O3 are either due to input of particles with high10Be content by the Congo River or due to scavenging of oceanic 10Be by riverine particles. The maxima of biogenic 10Be and Ba concentrations coincide with maxima of the paleoproductivity rates. Time series analysis of the 10Be and of Ba concentration profiles reveals a strong dominance of the precessional period of 24 kyr, which also controls the rates of paleoproductivity in this core. During the maxima of productivity the flux of biogenic Ba is enhanced to a larger extent than that of biogenic 10Be. Applying a model for coastal scavenging, we ascribe the observed higher sensitivity of Ba to biogenic particle fluxes to the fact that the ocean residence time of Ba is approximately 10 times longer than that of 10Be.

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes

In this paper we consider the a posteriori and a priori error analysis of discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes. In particular, we discuss the question of error estimation for linear target functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement. The theoretical results are illustrated by a series of numerical experiments.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes I: A Priori Error Analysis

We consider the a priori error analysis of hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form under weak assumptions on the mesh design and the local finite element spaces employed. In particular, we prove a priori hp-error bounds for linear target functionals of the solution, on (possibly) anisotropic computational meshes with anisotropic tensor-product polynomial basis functions. The theoretical results are illustrated by a numerical experiment.

Receção estética do texto e promoção da educação literária : trabalho colaborativo interdisciplinar

Dissertação apresentada à Escola Superior de Educação do Instituto Politécnico de Castelo Branco para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Supervisão e Avaliação Escolar.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity

We consider the a posteriori error analysis and hp-adaptation strategies for hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes with anisotropically enriched elemental polynomial degrees. In particular, we exploit duality based hp-error estimates for linear target functionals of the solution and design and implement the corresponding adaptive algorithms to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement and isotropic and anisotropic polynomial degree enrichment. The superiority of the proposed algorithm in comparison with standard hp-isotropic mesh refinement algorithms and an h-anisotropic/p-isotropic adaptive procedure is illustrated by a series of numerical experiments.