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Wyniki wyszukiwania dla: GRADIENT-INDEX (GRIN)
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Gradient-Index (GRIN) Matrices Based On Mosaic Assembling Technology (MAT) For Multichannel Fiberoptic Environmental Sensors
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Overview of planar antenna loading metamaterials for gain performance enhancement: the two decades of progress
PublikacjaMetamaterials (MTMs) are artificially engineered materials with unique electromagnetic properties not occurring in natural materials. MTMs have gained considerable attention owing to their exotic electromagnetic characteristics such as negative permittivity and permeability, thereby a negative refraction index. These extraordinary properties enable many practical applications such as super-lenses, and cloaking technology, and are...
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Overview of Metamaterials-Integrated Antennas for Beam Manipulation Applications: The Two Decades of Progress
PublikacjaMetamaterials (MMs) are synthetic composite structures with superior properties not found in naturally occurring materials. MMs have gained massive attention over the last two decades because of their extraordinary properties, such as negative permittivity and permeability. These materials enable many applications in communication subsystems, especially in the field of antenna design, to enhance gain, bandwidth, and efficiency,...
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E-cohomological Conley index
PublikacjaIn this thesis we continue with developing the E-cohomological Conley index which was introduced by A.Abbondandolo. In particular, we generalize the index to non-gradient flows, we show that it an possesses additional multiplicative structure and we prove the continuation principle. Then, using continuation principle, we show how the computation of the E-cohomological Conley index can be reduced to the computation of the classical...
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Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
PublikacjaIn this paper we introduce a new compactness condition — Property-(C) — for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain...
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The cohomological span of LS-Conley index
PublikacjaIn this paper we introduce a new homotopy invariant – the cohomological span of LS-Conley index. We prove the theorems on the existence of critical points for a class of strongly indefinite functionals with the gradient of the form Lx+K(x), where L is bounded linear and K is completely continuous. We give examples of Hamiltonian systems for which our methods give better results than the Morse inequalities. We also give a formula...
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Topological invariants for equivariant flows: Conley index and degree
PublikacjaAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...
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Equivariant Morse equation
PublikacjaThe paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by x˙ = − ∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.
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Relationship between GIX, SIDX, and ROTI ionospheric indices and GNSS precise positioning results under geomagnetic storms
PublikacjaIonospheric indices give information about ionospheric perturbations, which may cause absorption, diffraction, refraction, and scattering of radio signals, including those from global navigation satellite systems (GNSS). Therefore, there may be a relationship between index values and GNSS positioning results. A thorough understanding of ionospheric indices and their relationship to positioning results can help monitor and forecast...
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Computing methods for fast and precise body surface area estimation of selected body parts
PublikacjaCurrently used body surface area (BSA) formulas give satisfactory results only for individuals with typical physique, while for elderly, obese or anorectic people accurate results cannot be expected. Particularly noteworthy are the results for individuals with severe obesity (body-mass index greater than 35 kg/m2), for which BSA estimation errors reached 80%. The main goal of our study is the development of precise BSA models for...
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Predictions of cervical cancer identification by photonic method combined with machine learning
PublikacjaCervical cancer is one of the most commonly appearing cancers, which early diagnosis is of greatest importance. Unfortunately, many diagnoses are based on subjective opinions of doctors—to date, there is no general measurement method with a calibrated standard. The problem can be solved with the measurement system being a fusion of an optoelectronic sensor and machine learning algorithm to provide reliable assistance for doctors...
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Gradient versus proper gradient homotopies
PublikacjaWe compare the sets of homotopy classes of gradient and proper gradient vector fields in the plane. Namely, we show that gradient and proper gradient homotopy classi cations are essentially different. We provide a complete description of the sets of homotopy classes of gradient maps from R^n to R^n and proper gradient maps from R^2 to R^2 with the Brouwer degree greater or equal to zero.
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Design and Optimization of Metamaterial-based Highly-isolated MIMO Antenna with High Gain and Beam Tilting Ability for 5G Millimeter Wave Applications
PublikacjaThis paper presents a wideband multiple-input multiple-output (MIMO) antenna with high gain and isolation, as well as beam tilting capability, for 5G millimeter wave (MMW) applications. A single bow-tie antenna fed by a substrate-integrated waveguide (SIW) is proposed to cover the 28 GHz band (26.5–29.5 GHz) with a maximum gain of 6.35 dB. To enhance the gain, H-shaped metamaterial (MM)-based components are incorporated into the...
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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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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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Proper gradient otopies
PublikacjaWe prove that the inclusion of the space of proper gradient local maps into the space of proper local maps induces a bijection between the sets of the respective otopy classes of these maps.
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Proper gradient otopies
PublikacjaWe prove that the inclusion of the space of proper gradient local maps into the space of proper local maps induces a bijection between the sets of the respective otopy classes of these maps.
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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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Numerical Modelling for Prediction of Compression Index from Soil Index Properties in Jimma town, Ethiopia
PublikacjaIn this study, correlations are developed to predict compression index (Cc) from index parameters so that one can be able to model Jimma soils with compression index using simple laboratory tests. Undisturbed and disturbed soil samples from twelve different locations in Jimma town were collected. Laboratory tests like specific gravity, grain size analysis, Atterberg limit, and one-dimensional consolidation test for a total of twenty-four...
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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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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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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublikacjaConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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Connected components of the space of proper gradient vector fields
PublikacjaWe show that there exist two proper gradient vector fields on Rn which are homotopic in the category of proper maps but not homotopic in the category of proper gradient maps.
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Morse inequalities via Conley index theory
PublikacjaThe relation known as the Morse inequalities can be extended to a more general setting of flows on a locally compact metric spaces (Conley index) as well as dynamical systems on Hilbert spaces (LS-index). This paper is a discourse around this extension. Except the part concerning the LS-index the material is self-contained and has a character of a survey.
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Gradient otopies of gradient local maps
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The Hopf type theorem for equivariant gradient local maps
PublikacjaWe construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of equivariant gradient otopy classes and the direct sum of countably many copies of Z.
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Saint-Venant torsion based on strain gradient theory
PublikacjaIn this study, the Saint-Venant torsion problem based on strain gradient theory is developed. A total form of Mindlin's strain gradient theory is used to acquire a general Saint-Venant torsion problem of micro-bars formulation. A new Finite Element formulation based on strain gradient elasticity theory is presented to solve the Saint-Venant torsion problem of micro-bars. Moreover, the problem is solved for both micro and macro...
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On relations between gradient and classical equivariant homotopy groups of spheres
PublikacjaWe investigate relations between stable equivariant homotopy groups of spheres in classical and gradient categories. To this end, the auxiliary category of orthogonal equivariant maps, a natural enlargement of the category of gradient maps, is used. Our result allows for describing stable equivariant homotopy groups of spheres in the category of orthogonal maps in terms of classical stable equivariant groups of spheres with shifted...
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Morse cohomology in a Hilbert space via the Conley index
PublikacjaThe main theorem of this paper states that Morse cohomology groups in a Hilbert space are isomorphic to the cohomological Conley index. It is also shown that calculating the cohomological Conley index does not require finite-dimensional approximations of the vector field. Further directions are discussed.
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Path components of the space of gradient vector fields on the two dimensional disc
PublikacjaWe present a short proof that if two gradient maps on the twodimensional disc have the same degree, then they are gradient homotopic.
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Opitmalising Human Development Index with sensitivity analysis
PublikacjaResearch background: Composite indicators are commonly used not only to measure economic development, the standard of livin g, competitiveness, fairness, effectiveness but are also willingly implemented in to many different fields. How- ever, it seems that in most cases the variable weig hting procedure is avoided or erroneous since in most cases so-called “wights by belief” are...
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Analysis of Accuracy of Modified Gradient Method in Indoor Radiolocalisation System
PublikacjaIn this paper a new method, called modified gradient method, has been proposed for position calculation on the basis of distance measurement in indoor environment. It is shown that well known method of position calculation such as Foy is inefficient in indoor environment. In this article is also described the indoor radiolocalisation system which was used for collecting distance measurements which were employed for further comparative...
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Classification of homotopy classes of equivariant gradient maps
PublikacjaNiech V będzie ortogonalną reprezentacją zwartej grupy Liego Gi niech S(V),D(V) oznaczają sferę jednostkową i kulę jednostkową V.Jeżeli F jest G-niezmienniczą funkcją rzeczywistą klasy C^1 na Vto mówimy, że grad F (gradient F) jest dopuszczalny, jeżeli(grad F)(x) jest różny od zera dla x należących do S(V). Pracapoświęcona jest homotopijnej klasyfikacji dopuszczalnychG-niezmienniczych odwzorowań gradientowych.
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The Maslov index and the spectral flow—revisited
PublikacjaWe give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an associated path of self-adjoint first-order operators. We particularly pay attention to the continuity of the latter path of operators, where we consider the gap-metric on the set of all closed operators on a Hilbert space. Finally, we obtain from Cappell,...
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Ion Exchange And Related Phenomena In Glass Periodical GRIN Matrices During The Mosaic-Assembling Technology
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Parallel simulations of electrophysiological phenomena in myocardium on large 32 and 64-bit Linux clusters.
PublikacjaW pracy podjęto badania i przeprowadzono symulacje zjawisk elektrofizjologicznych w mięśniu sercowym z wykorzystaniem wytworzonego w tym celu oprogramowania równoległego opartego na MPI. Zaimplementowano i zbadano ulepszenia kodu prowadzące do uzyskania dobrej skalowalności oraz przeprowadzono testy wydajności na najnowszych 32 i 64-bitowych klastrach linuksowych. Praca stanowi próbę równoległej implementacji znanego podejścia...
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An efficient algorithm for the longest tandem scattered subsequence problem.
PublikacjaReferat dotyczy zagadnienia wyznaczania najdłuższego podciągu podwójnego (typu x1,x2,...,xk,x1,x2,...,xk) dla zadanego ciągu znaków (y1,y2,...,yn). Podano algorytm o złożoności obliczeniowej O(n^2) i pamięciowej O(n) znajdujący optymalne rozwiązanie postawionego problemu.
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Sensitivity analysis as a tool to optimise Human Development Index
PublikacjaResearch background: Composite indicators are commonly used as an approximation tool to measure economic development, the standard of living, competitiveness, fairness, effectiveness, and many others being willingly implemented into many different research disciplines. However, it seems that in most cases, the variable weighting procedure is avoided or erroneous since, in most cases, the so-called...
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Relations between the domination parameters and the chromatic index of a graph
PublikacjaIn this paper we show bounds for the sum and the product of the domination parameters and the chromatic index of a graph. We alsopresent some families of graphs for which these bounds are achieved.
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Local material symmetry group for first- and second-order strain gradient fluids
PublikacjaUsing an unified approach based on the local material symmetry group introduced for general first- and second-order strain gradient elastic media, we analyze the constitutive equations of strain gradient fluids. For the strain gradient medium there exists a strain energy density dependent on first- and higher-order gradients of placement vector, whereas for fluids a strain energy depends on a current mass density and its gradients....
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Expedited antenna optimization with numerical derivatives and gradient change tracking
PublikacjaDesign automation has been playing an increasing role in the development of novel antenna structures for various applications. One of its aspects is electromagnetic (EM)-driven design closure, typically applied upon establishing the antenna topology, and aiming at adjustment of geometry parameters to boost the performance figures as much as possible. Parametric optimization is often realized using local methods given usually reasonable...
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Thermodynamically consistent gradient theory of damage coupled with gradient plasticity
PublikacjaPrzedstawiono termodynamicznie zgodną teorię plastycznego zniszczenia w zakresie mechaniki Newtona-Eshelbego. Poza klasycznymi równaniami ruchu w przestrzeni fizycznej sformułowano dynamiczne równania równowagi sił powiązanych z defektami w przestrzeni materialnej oraz pierwsze i drugie prawo termodynamiki w przestrzeni fizycznej i materialnej. Ogólne równania konstytutywne przyjęto jako funkcję gradientu deformacji, jego składników...
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Estimation of Selected Synchronous Generator Parameters Based on the Gradient Method
PublikacjaThe authors present a method for the estimation of synchronous generator model parameters using a gradient algorithm. The paper shows an example of model parameter estimation for a turbogenerator and hydrogenerator, based on the generator voltage time responses obtained during an active and reactive power rejection test.
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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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The homotopy type of the space of gradient vector fields on the two-dimensional disc
PublikacjaWe prove that the inclusion of the space of gradient vector fields into the space of all vector fields on D^2 non-vanishing in S^1 is a homotopy equivalence
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Measurement of complex refractive index of human blood by low-coherence interferometry
PublikacjaIn this article, the usefulness of the optical technique for measurements of blood complex refractive index has been examined. Measurement of optical properties of human blood is difficult to perform because of its nonuniform nature. However, results of my investigation have shown the usefulness of low-coherencei nterferometry for measurement complex refractive index of human blood. Furthermore, mathematical analysis of spectrum...
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Strong ellipticity within the Toupin–Mindlin first strain gradient elasticity theory
PublikacjaWe discuss the strong ellipticity (SE) condition within the Toupin–Mindlin first strain gradient elasticity theory. SE condition is closely related to certain material instabilities and describes mathematical properties of corresponding boundary-value problems. For isotropic solids, SE condition transforms into two inequalities in terms of five gradient-elastic moduli.
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Topological degree for equivariant gradient perturbations of an unbounded self-adjoint operator in Hilbert space
PublikacjaWe present a version of the equivariant gradient degree defined for equivariant gradient perturbations of an equivariant unbounded self-adjoint operator with purely discrete spectrum in Hilbert space. Two possible applications are discussed.
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Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory
PublikacjaThis article is intended to analyze forced vibrations of a piezoelectric-piezomagnetic ceramic nanoplate by a new refined shear deformation plate theory in conjunction with higher-order nonlocal strain gradient theory. As both stress nonlocality and strain gradient size-dependent effects are taken into account using the higher-order nonlocal strain gradient theory, the governing equations of the composite nanoplate are formulated....
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Prediction of the Biogenic Amines Index of Poultry Meat Using an Electronic Nose
PublikacjaThe biogenic amines index of fresh chicken meat samples during refrigerated storage was predicted based on the headspace analysis using an electronic nose equipped with an array of electrochemical sensors. The reference biogenic amines index values were obtained using dispersive liquid–liquid microextraction–gas chromatography–mass spectrometry. A prototype electronic nose with modular construction and a dedicated sample chamber...