Search
Search results for: PERIODIC EXPANSION ZETA FUNCTION SET OF PERIODS NON-ORIENTABLE COMPACT SURFACES
-
Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms
PublicationWe 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...
-
Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g tori
Open Research DataMorse–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...
-
Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g real projective planes.
Open Research DataMorse–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...
-
Database of algebraic periods of quasi-unipotent orientation-preserving homeomorphisms of orientable surfaces
Open Research DataThe set of algebraic periods of a map contains important information about periodic points and, in addition, is a homotopy invariant of the map. It is determined by indices of nonzero Dold coefficients which are computed purely algebraically from maps induced on homology groups of a considered space. In this dataset, we include for a given g=1,2,...,30,...
-
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
Open Research DataThe 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...
-
Minimal Sets of Lefschetz Periods for Morse-Smale Diffeomorphisms of a Connected Sum of g Real Projective Planes
PublicationThe 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...
-
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
Open Research DataAn 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...
-
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
Open Research DataAn 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...
-
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
Open Research DataAn 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...
-
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
Open Research DataAn 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...
-
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
Open Research DataAn 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...
-
Quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi^4 model
PublicationAnalytical 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
-
One-dimensional chaos in a system with dry friction: analytical approach
PublicationWe 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...
-
Some new soliton solutions to the higher dimensional Burger–Huxley and Shallow water waves equation with couple of integration architectonic
PublicationIn 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.
-
Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublicationLet 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...
-
Minimal number of periodic points for smooth self-maps of simply-connected manifolds
Open Research DataThe 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...
-
Resonant Frequencies in the Open Microstrip Structures Placed on Curved Surfaces
PublicationThe 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...
-
Correction of far-field measurements obtained in non-anechoic test site
Open Research DataThe dataset contains raw and processed measurements of radiation pattern characteristics performed in non-anechoic regime for two geometrically small antenna structures: a spline-parameterized Vivaldi structure and a compact spline-based monopole. The responses have been obtained at the selected frequencies of interest as a function of mentioned structures...
-
Radiation pattern measurements of geometrically small antennas performed in non-anechoic environments
Open Research DataThe 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...
-
Measurements of electrically small antenna radiation patterns in non-anechoic environments using TGM
Open Research DataThe dataset contains raw and processed measurements of radiation pattern characteristics performed in non-anechoic regime for four antenna structures: a spline-parameterized Vivaldi structure, a compact spline-based monopole, super-ultrawideband antenna, and a quasi-Yagi component. The responses have been obtained at the selected frequencies of interest...
-
The equivariant spectral flow and bifurcation of periodic solutions of Hamiltonian systems
PublicationWe 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...
-
The influence of the distance of the pyrometer from the surface of the radiating object on the accuracy of measurements
Open Research DataDuring 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....
-
Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #24 - #25.
Open Research DataSpecimen 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...
-
Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #28 - #29.
Open Research DataSpecimen 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...
-
Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #30 - #31.
Open Research DataSpecimen 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...
-
Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #20 - #21.
Open Research DataSpecimen 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...
-
Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #22 - #23.
Open Research DataSpecimen 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...
-
Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #28 - #29.
Open Research DataSpecimen 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...
-
Specimen running-in. Prep. to sliding friction tests. Ring-on-ring contact. Sintered alumina ceramics (98%). Paraffin oil lubrication. Specimen set #26 - #27.
Open Research DataSpecimen 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...
-
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.
Open Research DataWear 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,...
-
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.
Open Research DataWear 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,...
-
On the Nonlinear Effects of Magnetoacoustic Perturbations in Optically Thin Quasi-Isentropic Plasmas
PublicationNonlinear 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...
-
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.
Open Research DataWear 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,...
-
Two-dimensional hydrogen-like atom in a weak magnetic field
PublicationWe 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...
-
Simple Fractal Calculus from Fractal Arithmetic
PublicationNon-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...
-
A Subspace-Splitting Moment-Matching Model-Order Reduction Technique for Fast Wideband FEM Simulations of Microwave Structures
PublicationThis 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...
-
Finite element models used in diagnostics of transverse cracks in bridge approach pavement
Open Research DataTransverse 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...
-
Estimates for minimal number of periodic points for smooth self-maps of simply-connected manifolds
Open Research DataWe 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...
-
Signal Reconstruction from Sparse Measurements Using Compressive Sensing Technique
PublicationThe 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...
-
Application of sliding switching functions in backstepping based speed observer of induction machine
PublicationThe 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...
-
Fast Machine-Learning-Enabled Size Reduction of Microwave Components Using Response Features
PublicationAchieving compact size has emerged as a key consideration in modern microwave design. While structural miniaturization can be accomplished through judicious circuit architecture selection, precise parameter tuning is equally vital to minimize physical dimensions while meeting stringent performance requirements for electrical characteristics. Due to the intricate nature of compact structures, global optimization is recommended,...
-
Simulation of the weight averaging of pulse frequency modulated sensor output signal
Open Research DataThe 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...
-
The site at the cape Zidine in Lopar in the context of coastal residential and commercial complexes of Rab Island
PublicationSince 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,...
-
Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos
PublicationIn 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...
-
Experimental certification of more than one bit of quantum randomness in the two inputs and two outputs scenario
PublicationOne 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...
-
Autocorrelation function for the chosen effective potential of the diatomic silver anion
Open Research DataThe 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...
-
Non-adiabatic coupling elements between the diatomic silver anion and neutral silver dimer plus continuum electron
Open Research DataThe 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...
-
Multisine impedimetric probing of biocatalytic reactions for label-free detection of DEFB1 gene: How to verify that your dog is not human?
PublicationAlbert 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...
-
Accelerated design optimization of miniaturized microwave passives by design reusing and Kriging interpolation surrogates
PublicationElectromagnetic (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...
-
Multi-objective optimization of microwave couplers using corrected domain patching
PublicationPractical 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...