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Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms
PublikacjaWe apply the representation of Lefschetz numbers of iterates in the form of periodic expansion to determine the minimal sets of Lefschetz periods of Morse–Smale diffeomorphisms. Applying this approach we present an algorithmic method of finding the family of minimal sets of Lefschetz periods for Ng, a non-orientable compact surfaces without boundary of genus g. We also partially confirm the conjecture of Llibre and Sirvent (J Diff...
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Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g tori
Dane BadawczeMorse–Smale diffeomorphisms, structurally stable and having relatively simple dynamics, constitute an important subclass of diffeomorphisms that have been carefully studied during past decades. For a given Morse–Smale diffeomorphism one can consider “Minimal set of Lefschetz periods”, which provides the information about the set of periodic points of...
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Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g real projective planes.
Dane BadawczeMorse–Smale diffeomorphisms, structurally stable and having relatively simple dynamics, constitute an important subclass of diffeomorphisms that were carefully studied during past decades. For a given Morse–Smale diffeomorphism one can consider “Minimal set of Lefschetz periods”, which provides the information about the set of periodic points of considered...
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The database of odd algebraic periods for quasi-unipotent self-maps of a space having the same homology group as the connected sum of g tori
Dane BadawczeThe dataset consists of 20 files indexed by numbers g=1,...,20. Each file provides sets of odd algebraic periods for all quasi-unipotent self-maps of a space having the same homology groups as the connected sum of g tori. Let us remark that each data set covers all algebraical restrictions that come from zeta functions for the sets of minimal Lefschetz...
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Minimal Sets of Lefschetz Periods for Morse-Smale Diffeomorphisms of a Connected Sum of g Real Projective Planes
PublikacjaThe dataset titled Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g real projective planes contains all of the values of the topological invariant called the minimal set of Lefschetz periods, computed for Morse-Smale diffeomorphisms of a non-orientable compact surface without boundary of genus g (i.e. a connected sum of g real projective planes), where g varies from 1 to...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 4 and homology groups with the sum of ranks less or equal to10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 4 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 6 and homology groups with the sum of ranks less or equal to10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 6 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 5 and homology groups with the sum of ranks less or equal to10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 5 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 8 and homology groups with the sum of ranks less or equal to 10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 8 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 7 and homology groups with the sum of ranks less or equal to10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 7 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi^4 model
PublikacjaAnalytical form of quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi^4 model is obtained through zeta function regularisation with account of all rest variables of a d-dimensional theory. Qualitative dependence of quantum corrections on parameters of the classical systems is also evaluated for a much broader class of potentials u(x) = b^2 f(bx) + C with b and C as arbitrary real constants
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One-dimensional chaos in a system with dry friction: analytical approach
PublikacjaWe introduce a new analytical method, which allows to find chaotic regimes in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered. The corresponding mathematical model is being studied. We show that the considered dynamical system is a skew product over a piecewise smooth mapping of a segment (the so-called base map). For this base map we demonstrate existence of...
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Some new soliton solutions to the higher dimensional Burger–Huxley and Shallow water waves equation with couple of integration architectonic
PublikacjaIn this paper, we retrieve some traveling wave, periodic solutions, bell shaped, rational, kink and anti-kink type and Jacobi elliptic functions of Burger’s equation and Shallow water wave equation with the aid of various integration schemes like improved -expansion scheme and Jacobi elliptic function method respectively. We also present our solutions graphically in various dimensions.
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Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublikacjaLet M be a smooth compact and simply-connected manifold with simply-connected boundary ∂M, r be a fixed odd natural number. We consider f, a C1 self-map of M, preserving ∂M . Under the assumption that the dimension of M is at least 4, we define an invariant Dr(f;M,∂M) that is equal to the minimal number of r-periodic points for all maps preserving ∂M and C1-homotopic to f. As an application, we give necessary and sufficient...
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Minimal number of periodic points for smooth self-maps of simply-connected manifolds
Dane BadawczeThe problem of finding the minimal number of periodic points in a given class of self-maps of a space is one of the central questions in periodic point theory. We consider a closed smooth connected and simply-connected manifold of dimension at least 4 and its self-map f. The topological invariant D_r[f] is equal to the minimal number of r-periodic points...
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Resonant Frequencies in the Open Microstrip Structures Placed on Curved Surfaces
PublikacjaThe paper presents the research on open microstrip structures placed on curved surfaces such as cylindrical, elliptical or spherical. The numerical analysis of investigated structures is based on expansion of electric and magnetic fields into suitable function series. Utilizing the continuity conditions the boundary problem is formulated which is solved with the use of method of moments. The investigated structures find application...
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Radiation pattern measurements of geometrically small antennas performed in non-anechoic environments
Dane BadawczeThe dataset contains unprocessed measurements of radiation pattern characteristics performed in non-anechoic regime for three geometrically small antenna structures: a spline-parameterized Vivaldi structure, a compact spline-based monopole, and a quasi-Yagi geometry with enhanced bandwidth. The responses have been obtained over broad frequency ranges...
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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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The influence of the distance of the pyrometer from the surface of the radiating object on the accuracy of measurements
Dane BadawczeDuring the COVID-19 epidemic, non-contact body temperature measurement has become very important. This dataset contain results of measurements of the four professional commercially available pyrometers. The CHY 314P, TM-F03B, TFA 31.1125 and Abatronic AB-8855 where tested in function of measuring distance from the surface of the radiating black body....
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Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #24 - #25.
Dane BadawczeSpecimen running-in procedure. Preparation to sliding friction tests in ring-on-ring contact. Sintered alumina ceramics (98%) in self-mated contact. Lubrication: paraffin oil. Sliding velocity: 0.2 m/s. Mean contact stress: 10 MPa. Test rig: PT-3 Tribometer. Specimen set #24 (upper, rotating), #25 (lower, non-rotating)CZ_PRZYS.MAT - accelerometerMOM_TAR.MAT...
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Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #28 - #29.
Dane BadawczeSpecimen running-in procedure. Preparation to sliding friction tests in ring-on-ring contact. Sintered alumina ceramics (98%) in self-mated contact. Lubrication: paraffin oil. Sliding velocity: 0.2 m/s. Mean contact stress: 10 MPa. Test rig: PT-3 Tribometer. Specimen set #28 (upper, rotating), #29 (lower, non-rotating)CZ_PRZYS.MAT - accelerometerMOM_TAR.MAT...
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Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #30 - #31.
Dane BadawczeSpecimen running-in procedure. Preparation to sliding friction tests in ring-on-ring contact. Sintered alumina ceramics (98%) in self-mated contact. Lubrication: paraffin oil. Sliding velocity: 0.2 m/s. Mean contact stress: 10 MPa. Test rig: PT-3 Tribometer. Specimen set #30 (upper, rotating), #31 (lower, non-rotating)CZ_PRZYS.MAT - accelerometerMOM_TAR.MAT...
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Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #20 - #21.
Dane BadawczeSpecimen running-in procedure. Preparation to sliding friction tests in ring-on-ring contact. Sintered alumina ceramics (98%) in self-mated contact. Lubrication: paraffin oil. Sliding velocity: 0.2 m/s. Mean contact stress: 10 MPa. Test rig: PT-3 Tribometer. Specimen set #20 (upper, rotating), #21 (lower, non-rotating)CZ_PRZYS.MAT - accelerometerMOM_TAR.MAT...
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Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #22 - #23.
Dane BadawczeSpecimen running-in procedure. Preparation to sliding friction tests in ring-on-ring contact. Sintered alumina ceramics (98%) in self-mated contact. Lubrication: paraffin oil. Sliding velocity: 0.2 m/s. Mean contact stress: 10 MPa. Test rig: PT-3 Tribometer. Specimen set #22 (upper, rotating), #23 (lower, non-rotating)CZ_PRZYS.MAT - accelerometerMOM_TAR.MAT...
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Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #28 - #29.
Dane BadawczeSpecimen running-in procedure. Preparation to sliding friction tests in ring-on-ring contact. Sintered alumina ceramics (98%) in self-mated contact. Lubrication: paraffin oil. Sliding velocity: 0.2 m/s. Mean contact stress: 10 MPa. Test rig: PT-3 Tribometer. Specimen set #28 (upper, rotating), #29 (lower, non-rotating)CZ_PRZYS.MAT - accelerometerMOM_TAR.MAT...
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Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #26 - #27.
Dane BadawczeSpecimen running-in procedure. Preparation to sliding friction tests in ring-on-ring contact. Sintered alumina ceramics (98%) in self-mated contact. Lubrication: paraffin oil. Sliding velocity: 0.2 m/s. Mean contact stress: 10 MPa. Test rig: PT-3 Tribometer. Specimen set #26 (upper, rotating), #27 (lower, non-rotating)CZ_PRZYS.MAT - accelerometerMOM_TAR.MAT...
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Wear in siding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specim. sets #20-#21, #22-#23, #24-#25, #26-#27, #28-#29,#30 - #31. Run time: 4-8h.
Dane BadawczeWear in sliding friction tests in ring-on-ring contact. Sintered alumina ceramics (98%) in self-mated contact. Lubrication: paraffin oil. Sliding velocity: 0.2 m/s. Mean contact stress: 10 MPa. Test rig: PT-3 Tribometer.Running time: 4-8h.Specimen sets:Specim. sets (# [upper, rotating] - #[lower, non-rotating]):#20-#21, #22-#23, #24-#25, #26-#27,...
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Wear in siding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specim. sets #20-#21, #22-#23, #24-#25, #26-#27, #28-#29,#30 - #31. Run time: 0-4h.
Dane BadawczeWear in sliding friction tests in ring-on-ring contact. Sintered alumina ceramics (98%) in self-mated contact. Lubrication: paraffin oil. Sliding velocity: 0.2 m/s. Mean contact stress: 10 MPa. Test rig: PT-3 Tribometer.Running time: 0 - 4h.Specimen sets:Specim. sets (# [upper, rotating] - #[lower, non-rotating]):#20-#21, #22-#23, #24-#25, #26-#27,...
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On the Nonlinear Effects of Magnetoacoustic Perturbations in Optically Thin Quasi-Isentropic Plasmas
PublikacjaNonlinear effects of planar magnetosound perturbations in a plasma are discussed. Plasma is non-adiabatic due to optically thin radiation and external heating. For these reasons, thermal instability of a plasma may appear which makes it acoustically active. The plasma is assumed to be initially homogeneous ideal gas with infinite electrical conductivity permeated by a straight magnetic field which is orthogonal to the trajectories...
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Wear in siding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specim. sets #20-#21, #22-#23, #24-#25, #26-#27, #28-#29,#30 - #31. Run time: 0-4h. High frequency burst recording.
Dane BadawczeWear in sliding friction tests in ring-on-ring contact. Sintered alumina ceramics (98%) in self-mated contact. Lubrication: paraffin oil. Sliding velocity: 0.2 m/s. Mean contact stress: 10 MPa. Test rig: PT-3 Tribometer. High frequency burst recording.Running time: 0 - 4h.Specimen sets:Specim. sets (# [upper, rotating] - #[lower, non-rotating]):#20-#21,...
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Two-dimensional hydrogen-like atom in a weak magnetic field
PublikacjaWe consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr¨odinger perturbation theory, using the Sturmian expansion of the generalized radial Coulomb Green function, we derive explicit analytical expressions for corrections to an arbitrary planar hydrogenic bound-state energy level, up to the fourth...
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Simple Fractal Calculus from Fractal Arithmetic
PublikacjaNon-Newtonian calculus that starts with elementary non-Diophantine arithmetic operations of a Burgin type is applicable to all fractals whose cardinality is continuum. The resulting definitions of derivatives and integrals are simpler from what one finds in the more traditional literature of the subject, and they often work in the cases where the standard methods fail. As an illustration, we perform a Fourier transform of a real-valued...
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A Subspace-Splitting Moment-Matching Model-Order Reduction Technique for Fast Wideband FEM Simulations of Microwave Structures
PublikacjaThis article describes a novel model-order reduction (MOR) approach for efficient wide frequency band finite-element method (FEM) simulations of microwave components. It relies on the splitting of the system transfer function into two components: a singular one that accounts for the in-band system poles and a regular part that has no in-band poles. In order to perform this splitting during the reduction process, the projection...
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Finite element models used in diagnostics of transverse cracks in bridge approach pavement
Dane BadawczeTransverse cracks in the asphalt pavement were observed on bridge structures next to single-module expansion joints with a 5 meter approach slab set at the depth of 1 m. The finite element (FE) models of the approach pavement were created to investigate the reasons of premature cracking and crack initiation mechanism over the back edge of the abutment...
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Estimates for minimal number of periodic points for smooth self-maps of simply-connected manifolds
Dane BadawczeWe consider a closed smooth connected and simply-connected manifold of dimension at least 4 and its self-map f. The topological invariant Dr[f] is equal to the minimal number of r-periodic points in the smooth homotopy class of f. We assume that r is odd and all coefficients b(k) of so-called periodic expansion of Lefschetz numbers of iterations are...
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Signal Reconstruction from Sparse Measurements Using Compressive Sensing Technique
PublikacjaThe paper presents the possibility of applying a new class ofmathematical methods, known as Compressive Sensing (CS) for recovering thesignal from a small set of measured samples. CS allows the faithful recon-struction of the original signal back from fewer random measurements bymaking use of some non-linear reconstruction techniques. Since of all thesefeatures, CSfinds its applications especially in the areas where, sensing is...
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Application of sliding switching functions in backstepping based speed observer of induction machine
PublikacjaThe paper presents an analysis of the speed observer which is based on the backstepping and sliding mode approach. The speed observer structure is based on the extended mathematical model of an induction machine. The observer structure is based on the measured phase stator currents and transformed to ( αβ ) coordinate system. The stator voltage vector components are treated as known values. Additionally, such an observer structure...
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Simulation of the weight averaging of pulse frequency modulated sensor output signal
Dane BadawczeThe aim of the research is investigation of the efficiency of weight averaging of pulse frequency modulated signal. It was shown that from the point of view of the reduction of the sampling error the best are polynomial weighing functions, for which the maximum of this component error decreases proportionally to the appropriate power of the number of...
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The site at the cape Zidine in Lopar in the context of coastal residential and commercial complexes of Rab Island
PublikacjaSince 2013, the “Archaeological topography of the island of Rab” project has approached the island’s archaeology holistically and interdisciplinary, tackling all periods and archaeological evidence present on the island. Nevertheless, mostly due to a large amount of new data, a significant segment of research is devoted to Roman residential and production complexes, located either in the island’s fields or along the coast. Thus,...
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Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos
PublikacjaIn a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents mathematical analysis showing that the system can support bursts of any period as a function of model parameters, and that these are organized in a period-incrementing structure. In continuous dynamical...
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Experimental certification of more than one bit of quantum randomness in the two inputs and two outputs scenario
PublikacjaOne of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing...
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Autocorrelation function for the chosen effective potential of the diatomic silver anion
Dane BadawczeThe process of a two-channel decay of the diatomic silver anion (Ag2-), namely the spontaneous electron ejection giving Ag2 + e- and the dissociation leading to Ag- + Ag is theoretically studied. The ground state potential energy curves (PECs) of the neutral silver dimer and anionic silver diatomic molecule are calculated using the single reference...
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Non-adiabatic coupling elements between the diatomic silver anion and neutral silver dimer plus continuum electron
Dane BadawczeThe process of a two-channel decay of the diatomic silver anion (Ag2-), namely the spontaneous electron ejection giving Ag2 + e- and the dissociation leading to Ag- + Ag is theoretically studied. The ground state potential energy curves (PECs) of the neutral silver dimer and anionic silver diatomic molecule are calculated using the single reference...
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Accelerated design optimization of miniaturized microwave passives by design reusing and Kriging interpolation surrogates
PublikacjaElectromagnetic (EM) analysis has become ubiquitous in the design of microwave components and systems. One of the reasons is the increasing topological complexity of the circuits. Their reliable evaluation—at least at the design closure stage—can no longer be carried out using analytical or equivalent network representations. This is especially pertinent to miniaturized structures, where considerable EM cross-coupling effects occurring...
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Multisine impedimetric probing of biocatalytic reactions for label-free detection of DEFB1 gene: How to verify that your dog is not human?
PublikacjaAlbert is a dog (Canis familiaris), but he does not realize this. Albert loves human food (and beer), watching movies on the internet, sleeping in bed, and more. But he should not do all these things. To convince him that, we have desinged a test procedure. The DEFB1 gene is unique to human species. Detecting its presence from saliva and in short periods may offer an advantage in the field of forensic medicine, and influence Albert’s...
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Multi-objective optimization of microwave couplers using corrected domain patching
PublikacjaPractical design of microwave components and circuits is a compromise between various, often conflicting objectives. In case of compact structures, the trade-offs are typically concerned with the circuit size and its electrical performance. Comprehensive information about the best possible trade-offs can be obtained by means of multi-objective optimization. In this paper, we propose a computationally efficient technique for identifying...
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GreedyMAX-type Algorithms for the Maximum Independent Set Problem
PublikacjaA maximum independent set problem for a simple graph G = (V,E) is to find the largest subset of pairwise nonadjacent vertices. The problem is known to be NP-hard and it is also hard to approximate. Within this article we introduce a non-negative integer valued functionp defined on the vertex set V(G) and called a potential function of agraph G, while P(G) = max{vinV(G)| p(v)} is called a potential of G. For any graph P(G) <= D(G),...
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SPECTRAL RESPONSE OF STATIONARY JACK-UP PLATFORMS LOADED BY SEA WAVES AND WIND USING PERTURBATION METHOD
PublikacjaThe paper addresses non-linear vibrations of offshore jack-up drilling platforms loaded by sea waves and wind in their stationary condition using the perturbation method. Non-linearity of dynamic equations of motion for fixed offshore platforms yields from two factors. The first is load excitation generating non-linear velocity coupling in a dynamic system. This coupling is inherent in the modified Morison equation, involving the...
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Indoor accelerated controlled corrosion degradation test of small- and large-scale specimens
PublikacjaThe work presented here is a part of a long-term project analysing the structural behaviour of ageing marine structures. An accelerated corrosion degradation set-up was developed to reproduce corroded marine structural specimens of different degrees of degradation, controlling various natural factors, i.e., temperature, oxygen content, salinity, and flow velocity. The nine stiffened plates of 1.2 m length and 30 small scale specimens...
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A study of a compact high-efficiency zero-emission power plant with oxy-fuel combustion
PublikacjaThis paper discusses the application of global trends in gas cycles technology using oxy-fuel combustion. This is followed by a demonstration of a design solution for a new cycle with two enhanced energy-converting devices, namely a wet combustion chamber and a spray-ejector condenser. The proposed gas and steam cycle unit is contained within a single turbine, whose benefits combine those offered by gas turbines (high inlet temperatures)...