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Wyniki wyszukiwania dla: EQUIVARIANT GRADIENT MAPS
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Degree product formula in the case of a finite group action
PublikacjaLet V, W be finite dimensional orthogonal representations of a finite group G. The equivariant degree with values in the Burnside ring of G has been studied extensively by many authors. We present a short proof of the degree product formula for local equivariant maps on V and W.
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Otopy Classification of Gradient Compact Perturbations of Identity in Hilbert Space
PublikacjaWe prove that the inclusion of the space of gradient local maps into the space of all local maps from Hilbert space to itself induces a bijection between the sets of the respective otopy classes of these maps, where by a local map we mean a compact perturbation of identity with a compact preimage of zero.
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Sea surface temperature distribution during upwelling along the Polish Baltic coast
PublikacjaAmong over 150 maps of sea surface temperature in the Polish Baltic coastal region derived from satellite data during the warm period of the year (April-October) in 2000-2002, 41 cases were noted where its distribution showed characteristic features indicating the occurrence of coastal upwelling. The fundamental parameters of range, probability of occurrence and temperature modification caused by water from deeper sea layers...
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The equivariant spectral flow and bifurcation of periodic solutions of Hamiltonian systems
PublikacjaWe define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ring of the latter. This G-equivariant spectral flow shares all common properties of the integer valued classical spectral flow, and it can be non-trivial even if the classical spectral flow vanishes. Our main theorem uses the G-equivariant spectral flow...
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Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity
PublikacjaIn this paper we consider existence and uniqueness of the three-dimensional static boundary-value problems in the framework of so-called gradient-incomplete strain-gradient elasticity. We call the strain-gradient elasticity model gradient-incomplete such model where the considered strain energy density depends on displacements and only on some specific partial derivatives of displacements of first- and second-order. Such models...
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Journal of Maps
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Ellipticity of gradient poroelasticity
PublikacjaWe discuss the ellipticity properties of an enhanced model of poroelastic continua called dilatational strain gradient elasticity. Within the theory there exists a deformation energy density given as a function of strains and gradient of dilatation. We show that the equilibrium equations are elliptic in the sense of Douglis–Nirenberg. These conditions are more general than the ordinary and strong ellipticity but keep almost all...
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Koło Naukowe Gradient 2024
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On nonlinear dilatational strain gradient elasticity
PublikacjaWe call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient elasticity: indeed, in it, the...
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Software for calculation of noise maps implemented on the supercomputer
PublikacjaThis paper presents investigation results relevant to the implementation of the algorithms for the calculation of noise maps. The aim of the implementation of the algorithms on the computer cluster is explained. Selected implementation details of the software called the noise propagation model are described. The interaction of the software with the data acquisition system is presented. Noise maps obtained by exploitation of the...
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On structural physical approximations and entanglement breaking maps
PublikacjaVery recently, a conjecture saying that the so-called structural physical approximations (SPAs) to optimal positive maps (optimal entanglement witnesses) give entanglement breaking (EB) maps (separable states) has been posed (Korbicz et al 2008 Phys. Rev. A 78 062105). The main purpose of this contribution is to explore this subject. First, we extend the set of entanglement witnesses supporting the conjecture. Then, we ask whether...
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AI in the creation of the satellite maps
PublikacjaSatellite and aerial imagery acquisition is a very useful source of information for remote monitoring of the Earth’s surface. Modern satellite and aerial systems provide data about the details of the site topography, its characteristics due to different criteria (type of terrain, vegetation cover, soil type and moisture content), or even information about emergency situations or disasters. The paper proposes and discusses the process...
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Creating Acoustic Maps Employing Supercomputing Cluster
PublikacjaThe implemented online urban noise pollution monitoring system is presented with regard to its conceptual assumptions and technical realization. A concept of the noise source parameters dynamic assessment is introduced. The idea of noise modeling, based on noise emission characteristics and emission simulations, was developer and practically utilized in the system. Furthermore, the working system architecture and the data acquisition...
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A Note on Reduced Strain Gradient Elasticity
PublikacjaWe discuss the particular class of strain-gradient elastic material models which we called the reduced or degenerated strain-gradient elasticity. For this class the strain energy density depends on functions which have different differential properties in different spatial directions. As an example of such media we consider the continual models of pantographic beam lattices and smectic and columnar liquid crystals.
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Periodic Points for Sphere Maps Preserving MonopoleFoliations
PublikacjaLet S^2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S^2→S^2 preserving these foliations, more and less regular. We prove that in both cases f has at least |deg(f)| fixed points, where deg(f) is a topological degree of f. In particular, the lower growth rate of the number of fixed points of the iterations of f is at least log|deg(f)|. This confirms the Shub’s conjecture in...
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Improving depth maps of plants by using a set of five cameras
PublikacjaObtaining high-quality depth maps and disparity maps with the use of a stereo camera is a challenging task for some kinds of objects. The quality of these maps can be improved by taking advantage of a larger number of cameras. The research on the usage of a set of five cameras to obtain disparity maps is presented. The set consists of a central camera and four side cameras. An algorithm for making disparity maps called multiple...
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The Hopf theorem for gradient local vector fields on manifolds
PublikacjaWe prove the Hopf theorem for gradient local vector fields on manifolds, i.e., we show that there is a natural bijection between the set of gradient otopy classes of gradient local vector fields and the integers if the manifold is connected Riemannian without boundary.
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Data visualization of marine objects on digital maps
PublikacjaThe paper presents the implementation of two multithreaded applications for data visualization of marine objects written in C#, designed to run on operator consoles with 32-bit or 64-bit Windows 7 OS. The article describes the most important functionality and features of the developed C# .NET user controls for data visualization on digital maps and in the configurable tables.
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Lefschetz periodic point free self-maps of compact manifolds
PublikacjaLet f be a self-map of a compact connected manifold M. We characterize Lefschetz periodic point free continuous self-maps of M for several classes of manifolds and generalize the results of Guirao and Llibre [J.L.G. Guirao, J. Llibre, On the Lefschetz periodic point free continuous self-maps on connected compact manifolds,
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Music Mood Visualization Using Self-Organizing Maps
PublikacjaDue to an increasing amount of music being made available in digital form in the Internet, an automatic organization of music is sought. The paper presents an approach to graphical representation of mood of songs based on Self-Organizing Maps. Parameters describing mood of music are proposed and calculated and then analyzed employing correlation with mood dimensions based on the Multidimensional Scaling. A map is created in which...