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Search results for: singular potential
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Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3
PublicationWe consider a conservative second order Hamiltonian system \ddot{q}+ ∇V(q)=0 in R3 with a potential V having a global maximum at the origin and a line l ∩ {0} = ∅ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.
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Homoclinics for singular strong force Lagrangian systems
PublicationWe study the existence of homoclinic solutions for a class of generalized Lagrangian systems in the plane, with a C1-smooth potential with a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin.Under a strong force condition around the singular point ξ, via minimization of an action integral, we will prove the existence of at least two geometrically distinct homoclinic solutions.
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Zero-range potentials for Dirac particles: Bound-state problems
PublicationA model in which a massive Dirac particle in $\mathbb{R}^{3}$ is bound by $N\geqslant1$ spatially distributed zero-range potentials is presented. Interactions between the particle and the potentials are modeled by subjecting a particle's bispinor wave function to certain limiting conditions at the potential centers. Each of these conditions is parametrized by a $2\times2$ Hermitian matrix (or, equivalently, a real scalar and a...
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Homoclinic orbits for an almost periodically forced singular Newtonian system in R^3
Publication. This work uses a variational approach to establish the existence of at least two homoclinic solutions for a family of singular Newtonian systems in R^3 which are subjected to almost periodic forcing in time variable
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A NUMERICAL STUDY ON THE DYNAMICS OF DENGUE DISEASE MODEL WITH FRACTIONAL PIECEWISE DERIVATIVE
PublicationThe aim of this paper is to study the dynamics of Dengue disease model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative are examined for the aforementioned problem. The suggested...
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Two families of infinitely many homoclinics for singular strong force Hamiltonian systems
PublicationWe are concerned with a planar autonomous Hamiltonian system with a potential possessing a single well of infinite depth at a point X and a unique strict global maximum 0 at a point A. Under a strong force condition around the singularity X, via minimization of an action integral and using a shadowing chain lemma together with simple geometrical arguments, we prove the existence of infinitely many geometrically distinct homoclinic...
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Singular Surface Curves in the Resultant Thermodynamics of Shells
PublicationWithin six-parameter shells theory we discuss the governing equations of shells with material or non-material singular curves. By singular curve we mean a surface curve where are discontinuities in some surface fields. As an example we consider shells with junctions and shells undergoing stress-induced phase transitions.
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Generic invariant measures for iterated systems of interval homeomorphisms
PublicationIt is well known that iterated function systems generated by orientation preserving homeomorphisms of the unit interval with positive Lyapunov exponents at its ends admit a unique invariant measure on (0, 1) provided their action is minimal. With the additional requirement of continuous differentiability of maps on a fixed neighbourhood of {0,1} { 0 , 1 } , we present a metric in the space of such systems which renders it complete....
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Homoclinic and Heteroclinic Orbits for a Class of Singular Planar Newtonian Systems
PublicationThe study of existence and multiplicity of solutions of differential equations possessing a variational nature is a problem of great meaning since most of them derives from mechanics and physics. In particular, this relates to Hamiltonian systems including Newtonian ones. During the past thirty years there has been a great deal of progress in the use of variational methods to find periodic, homoclinic and heteroclinic solutions...
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Exact resultant equilibrium conditions in the non-linear theory of branching and self-intersecting shells
PublicationWe formulate the exact, resultant equilibrium conditions for the non-linear theory of branching and self-intersecting shells. The conditions are derived by performing direct through-the-thickness integration in the global equilibrium conditions of continuum mechanics. At each regular internal and boundary point of the base surface our exact, local equilibrium equations and dynamic boundary conditions are equivalent, as expected,...
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On jump conditions at non-material singular curves in the resultant shell thermomechanics
PublicationThe global, refined, resultant, two-dimensional (2D) balance laws of mass, linear and angular momenta, and energy as well as the entropy inequality were formulated by Pietraszkiewicz (2011) as exact implications of corresponding laws of 3D rational thermomechanics. In case of a shell with the regular base surface and all resultant surface fields differentiable everywhere on it and at any time instant, the local laws of the resultant...
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The exemplary Kelvin probe microscopy studies of sensitized austenitic stainless steels
Open Research DataThe dataset summarizes the results of imaging the surface potential distribution using the Kelvin probe scanning technique. Due to the fact that the potential measured in this way is proportional to the electrochemical potential of metals or intermetallic phases, it is possible to assess the nobility differences of various alloy components. In the case...
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On exact two-dimensional kinematics for the branching shells
PublicationWe construct the two-dimensional (2D) kinematics which is work-conjugate to the exact 2D local equilibrium conditions of the non-linear theory of branching shells. It is shown that the compatible shell displacements consist of the translation vector and rotation tensor fields defined on the regular parts of the shell base surface as well as independently on the singular surface curve modelling the shell branching. Several characteristic...
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Singular curves in the resultant thermomechanics of shells
PublicationSome geometric and kinematic relations associated with the curve moving on the shell base surface are discussed. The extended surface transport relation and the extended surface divergence theorems are proposed for the piecewise smooth tensor fields acting on the regular and piecewise regular surfaces. The recently formulated resultant, two-dimensionally exact, thermodynamic shell relations - the balances of mass, linear and angular...
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Adiabatic potential energy curves of the singlet Pi and Delta gerade states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the singlet Pi and Delta gerade states have been calculated for the Lithium dimer. The results of the three excited states of the symmetries singlet Pi and Delta gerade have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction...
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Adiabatic potential energy curves of the triplet Sigma ungerade plus states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the triplet Sigma ungerade plus states have been calculated for the Lithium dimer. The results of the five excited states of the symmetry triplet Sigma ungerade plus have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction...
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Adiabatic potential energy curves of the triplet Pi gerade states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the triplet Pi gerade states have been calculated for the Lithium dimer. The results of the two excited states of the symmetry triplet Pi gerade have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction of valence electrons...
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Adiabatic potential energy curves of the singlet Sigma gerade plus states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the singlet Sigma gerade plus states have been calculated for the Lithium dimer. The results of the ground state and three excited states of the symmetry singlet Sigma gerade plus have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing...
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Adiabatic potential energy curves of the singlet Sigma ungerade plus states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the singlet Sigma ungerade plus states have been calculated for the Lithium dimer. The results of the three excited states of the symmetry singlet Sigma ungerade plus have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction...
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Adiabatic potential energy curves of the triplet Sigma gerade plus states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the triplet Sigma gerade plus states have been calculated for the Lithium dimer. The results of the three excited states of the symmetry triplet Sigma gerade plus have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction...
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Adiabatic potential energy curves of the triplet Pi and Delta ungerade states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the triplet Pi and Delta ungerade states have been calculated for the Lithium dimer. The results of the three excited states of the symmetries triplet Pi and Delta ungerade have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction...
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Adiabatic potential energy curves of the singlet Pi ungerade states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the singlet Pi ungerade states have been calculated for the Lithium dimer. The results of the two excited states of the symmetry singlet Pi ungerade have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction of valence electrons...
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Potential energy curves of the doublet Sigma gerade plus states of the Lithium dimer cation
Open Research DataAdiabatic potential energy curves of the doublet Sigma gerade plus (dSg+) states have been calculated for the Lithium dimer cation (Li2+). The results of the ground state and four excited states of the symmetry doublet Sigma gerade plus have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials...
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Potential energy curves of the doublet Sigma ungerade plus states of the Lithium dimer cation
Open Research DataAdiabatic potential energy curves of the doublet Sigma ungerade plus (dSu+) states have been calculated for the Lithium dimer cation (Li2+). The results of the five excited states of the symmetry doublet Sigma ungerade plus have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing...
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Potential energy curves of the doublet Pi and Delta gerade states of the Lithium dimer cation
Open Research DataAdiabatic potential energy curves of the doublet Pi and Delta gerade (dPg and dDg) states have been calculated for the Lithium dimer cation (Li2+). The results of the four excited states of the symmetries doublet Pi and Delta gerade have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials...
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Potential energy curves of the doublet Pi and Delta ungerade states of the Lithium dimer cation
Open Research DataAdiabatic potential energy curves of the doublet Pi and Delta ungerade (dPu and dDu) states have been calculated for the Lithium dimer cation (Li2+). The results of the four excited states of the symmetries doublet Pi and Delta ungerade have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials...
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Potential energy curve, rovibrational energies and nuclear wave functions of 2 singlet Pi state in KLi dimer
Open Research DataThis data sets contains potential energy curve, energy levels and nuclear wave functions of rovibrational states of KLi dimer in 2 singlet Pi electronic state. Potential energy curve (PEC) for the electronic state was calculated in the Born-Oppenheimer approximation by the means of effective core potentials and MRCI method. Nuclear wave functions and...
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Complex Root Finding Algorithm Based on Delaunay Triangulation
PublicationA simple and flexible algorithm for finding zeros of a complex function is presented. An arbitrary-shaped search region can be considered and a very wide class of functions can be analyzed, including those containing singular points or even branch cuts. The proposed technique is based on sampling the function at nodes of a regular or a self-adaptive mesh and on the analysis of the function sign changes. As a result, a set of candidate points...
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Junctions In Shell Structures: A Review
PublicationMany shell structures used in modern technology consist of regular shell parts joined together along their common boundaries. We review different theoretical, numerical, and experimental approaches to modelling, analyses and design of the compound shell structures with junctions. Several alternative forms of boundary, continuity and jump conditions at the singular midsurface curves modelling the shell junction are reviewed. We...
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LIDAR data from a cliff measurement conducted in the vicinity of the town of Jastrzębia Góra on the Baltic Sea coast
Open Research DataMeasurement data were obtained during research related to the use of LiDAR observations to assess the stability of a coastal cliff. The collected information comes from measurements conducted in the vicinity of the town of Jastrzębia Góra on the Baltic Sea coast. The acquired point cloud constitutes a comprehensive set of data regarding the geometry...
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AFM analysis of duplex steel structure and composition
Open Research DataDue to the high content of alloying elements, duplex stainless steels are characterized by a complex structure of phase transitions. Among all types of intermetallic compounds, the sigma phase is of major interest due to its detrimental effect on both mechanical properties and corrosion behavior. It is an intermetallic phase enriched in Cr and Mo and...
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Born-Oppenheimer potential energy curves of the NaK molecule
Open Research DataAdiabatic potential energy curves (APEC) of the singlet (s) and triplet (t) Sigma+, Pi, and Delta electronic states have been calculated for the NaK molecule. All results of the presented molecular states have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction...
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Potential energy curves of LiCs dimer
Open Research DataThis data presents potential energy curves of LiCs dimer in Hund's case (a). Calculated using Born-Oppenheimer approximation with scalar relativistic effects are included via large effective core potentials. Custom basis sets, core polarization potentials and MRCI method are used to accurately describe electron correlation. Dataset consists of 22 potential...
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Potential energy curves of NaRb dimer
Open Research DataThis data presents potential energy curves of NaRb dimer in Hund's case (a). Calculated using Born-Oppenheimer approximation with scalar relativistic effects are included via large effective core potentials. Core polarization potentials and MRCI method is used to describe electron correlation. Dataset consists of 18 potential energy curves of ground...
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Probiotic strains from bee products - sequences and other data
Open Research DataThis folder contains seqences and other data necessary for evaluation of probiotic potential of bacteria islated from bee products.
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Antiviral activity of bee bread derived from polish apiaries.
Open Research DataBee bread is a product of fermentation of bee-collected pollen and revealed a high nutritional value. Other bee products, such as honey and propolis, are known for their antiviral activity, but bee bread is still under investigation, thus its antiviral potential is still unspecified. For investigation antiviral activity of bee bread samples, cytotoxicity...
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On the exact equilibrium conditions of irregular shells reinforced by beams along the junctions
PublicationThe exact, resultant equilibrium conditions for irregular shells reinforced by beams along the junctions are formulated. The equilibrium conditions are derived by performing direct integration of the global equilibrium conditions of continuum mechanics. New, exact resultant static continuity conditions along the singular curve modelling reinforced junction are presented. The results do not depend on shell thickness, internal through-the-thickness...
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Quasirelativistic potential energy curves of NaRb dimer
Open Research DataThis data presents potential energy curves of NaRb dimer, that include spin-orbit interaction, in Hund's case (c). Calculated using Born-Oppenheimer approximation with relativistic effects included via large spin-orbit effective core potentials. Custom basis sets, core polarization potentials and MRCI method are used to accurately describe electron...
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TiO2-potential zeta in water
Open Research DataData contain results from measurements of zeta potential for powdered TiO2 in a diluted aqueous solution. The measurements were performed in Zetasizer Nano ZS analyser.
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Objectivity in a Noisy Photonic Environment through Quantum State Information Broadcasting
PublicationRecently, the emergence of classical objectivity as a property of a quantum state has been explicitly derived for a small object embedded in a photonic environment in terms of a spectrum broadcast form—a specific classically correlated state, redundantly encoding information about the preferred states of the object in the environment. However, the environment was in a pure state and the fundamental problem was how generic and robust...
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Tax system in Poland - current situation and direction of changes
Open Research DataThe study conducted on a group of 259 entrepreneurs from various regions of Poland concerns the opinions of business owners on the current tax situation, as well as potential changes in the tax system.
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Adiabatic potential energy curves of the KRb molecule
Open Research DataAdiabatic potential energy curves (APEC) of the singlet (s) and triplet (t) Sigma+, Sigma-, Pi, and Delta electronic states have been calculated for the KRb molecule. Presented APECs correlate with 11 atomic asymptotes, starting from ground K(4s)+Rb(5s) atomic limit and ending on double-excited K(4p)+Rb(5p) atomic limit. All results of the presented...
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Design of a microrobotic wrist for needle laparoscopic surgery
PublicationThe paper addresses the design of a micro wrist for needle laparoscopic surgery (needlescopy) using MEMS technology and an original 3 degree of freedom, 3D architecture. Advancement in needlescopy drives the development of multi-dof micro-tools 1-2mmin diameter with 3D mobility but standard available fabricationtechniques are for 2.5D structures. The paper discusses thedevelopment steps and design solutions for the realization...
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Homoclinics for singular strong force Lagrangian systems in R^N
PublicationWe will be concerned with the existence of homoclinics for second order Hamiltonian systems in R^N (N>2) given by Hamiltonians of the form H(t,q,p)=Φ(p)+V(t,q), where Φ is a G-function in the sense of Trudinger, V is C^2-smooth, periodic in the time variable, has a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin. Under a strong force type condition aroud the singular point ξ, we prove...
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MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION
PublicationThe purpose of this work is to study the memory effect analysis of Caputo–Fabrizio time fractional diffusion equation by means of cubic B-spline functions. The Caputo–Fabrizio interpretation of fractional derivative involves a non-singular kernel that permits to describe some class of material heterogeneities and the effect of memory more effectively. The proposed numerical technique relies on finite difference approach and cubic...
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Imaging and chemical investigation of silver coating
Open Research DataThe recovery of silver from materials such as plates, still used in clinical radiography [1], or scrap jewelery is still very popular. The subject of the research, part of which was microscopic imaging, was to recreate the behavior of an electrochemically deposited silver coating. The copper electrodes were covered with a layer of silver obtained from...
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Adiabatic potential energy curves of the 3, 4 and 5^1Σ^+ excited states of LiCs molecule
Open Research DataAdiabatic potential energy curves of the 3, 4, and 5^1Σ^+ excited states have been calculated for the LiCs molecule. The results of three excited states of the symmetry Σ^+ have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction of valence electrons with atomic...
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Antifungal activity of propolis extracts, screening and kinetic data
Open Research DataThis folder contains results of our studies aiming in determination of antifungal potential of ethanolic extracts of propolis and components of this product. In details, MIC, MFC values were determined and kill time assays were performed.
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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...
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TiO2-zeta potential
Open Research DataData contain results from the measurements of zeta potential of TiO2 versus pH. Data are saved as original files and in the format of Excel file. measurements were perfomed in Zetasizer Nano ZS with using Multi-Purpose Titrator MPT-2.