Search results for "Mathematica"

showing 10 items of 7971 documents

What is Mathematics: Gödel's Theorem and Around (Edition 2013)

2013

Hyper-textbook for students in mathematical logic and foundations of mathematics. Edition 2013. ATTENTION! New Edition 2015 available at https://dspace.lu.lv/dspace/handle/7/5306.

foundations of mathematicsincompleteness theoremmathematical logicGödelGoedel
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An optimization-based approach for solving a time-harmonic multiphysical wave problem with higher-order schemes

2013

This study considers developing numerical solution techniques for the computer simulations of time-harmonic fluid-structure interaction between acoustic and elastic waves. The focus is on the efficiency of an iterative solution method based on a controllability approach and spectral elements. We concentrate on the model, in which the acoustic waves in the fluid domain are modeled by using the velocity potential and the elastic waves in the structure domain are modeled by using displacement.Traditionally, the complex-valued time-harmonic equations are used for solving the time-harmonic problems. Instead of that, we focus on finding periodic solutions without solving the time-harmonic problem…

fourth-order Runge–Kuttata113Numerical AnalysisOptimization problemfluid–structure interactionta114Physics and Astronomy (miscellaneous)DiscretizationApplied Mathematicsta111Mathematical analysisSpectral element methodspectral element methodAcoustic wavecoupled problemcontrollabilityComputer Science ApplicationsControllabilityComputational MathematicsMultigrid methodRate of convergenceModeling and SimulationConjugate gradient methodMathematicsJournal of Computational Physics
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On the discreet spectrum of fractional quantum hydrogen atom in two dimensions

2019

We consider a fractional generalization of two-dimensional (2D) quantum-mechanical Kepler problem corresponding to 2D hydrogen atom. Our main finding is that the solution for discreet spectrum exists only for $\mu>1$ (more specifically $1 < \mu \leq 2$, where $\mu=2$ corresponds to "ordinary" 2D hydrogenic problem), where $\mu$ is the L\'evy index. We show also that in fractional 2D hydrogen atom, the orbital momentum degeneracy is lifted so that its energy starts to depend not only on principal quantum number $n$ but also on orbital $m$. To solve the spectral problem, we pass to the momentum representation, where we apply the variational method. This permits to obtain approximate analytica…

fractional Schrödinger equationFOS: Physical sciencesPosition and momentum space01 natural sciences010305 fluids & plasmasSchrödinger equationMomentumsymbols.namesakeKepler problem0103 physical sciencesPrincipal quantum number010306 general physicsCondensed Matter - Statistical MechanicsMathematical PhysicsMathematical physicsPhysicsQuantum PhysicsStatistical Mechanics (cond-mat.stat-mech)fractional statisticsSpectrum (functional analysis)Mathematical Physics (math-ph)Hydrogen atomCondensed Matter PhysicsAtomic and Molecular Physics and OpticsVariational methodsymbolsQuantum Physics (quant-ph)hydrogenic problemsPhysica Scripta
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On the Landis conjecture for the fractional Schrödinger equation

2023

In this paper, we study a Landis-type conjecture for the general fractional Schrödinger equation ((−P)s+q)u=0. As a byproduct, we also prove the additivity and boundedness of the linear operator (−P)s for non-smooth coefficents. For differentiable potentials q, if a solution decays at a rate exp (−∣x∣1+), then the solution vanishes identically. For non-differentiable potentials q, if a solution decays at a rate exp (−∣x∣4s−14s+), then the solution must again be trivial. The proof relies on delicate Carleman estimates. This study is an extension of the work by Rüland and Wang (2019). peerReviewed

fractional Schrödinger equationLandis conjectureunique continuation at infinityStatistical and Nonlinear PhysicsGeometry and TopologyMathematical PhysicsJournal of Spectral Theory
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On a Fractional in Time Nonlinear Schrödinger Equation with Dispersion Parameter and Absorption Coefficient

2020

This paper is concerned with the nonexistence of global solutions to fractional in time nonlinear Schr&ouml

fractional in time nonlinear Schrödinger equationPhysics and Astronomy (miscellaneous)General MathematicsMathematics::Analysis of PDEs01 natural sciencesSchrödinger equationsymbols.namesakeSettore MAT/05 - Analisi Matematicaglobal solutionDispersion (optics)absorption coefficientComputer Science (miscellaneous)Absorption (logic)0101 mathematicsNonlinear Schrödinger equationMathematical physicsPhysicslcsh:Mathematics010102 general mathematicsMathematics::Spectral Theorylcsh:QA1-939010101 applied mathematicsNonlinear systemChemistry (miscellaneous)Attenuation coefficientsymbolsdispersion parameterSymmetry
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On some properties of g-frames and g-coherent states

2010

After a short review of some basic facts on g-frames, we analyze in details the so-called (alternate) dual g-frames. We end the paper by introducing what we call {\em g-coherent states} and studying their properties.

frameFOS: Physical sciencesMathematical Physics (math-ph)coherent statesSettore MAT/07 - Fisica MatematicaMathematical Physics
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Characterizing and Quantifying Frustration in Quantum Many-Body Systems

2011

We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identifi…

frustrationmedia_common.quotation_subjectFOS: Physical sciencesGeneral Physics and AstronomyFrustrationQuantum capacityQuantum entanglement01 natural sciences010305 fluids & plasmasOpen quantum systemQuantum mechanics0103 physical sciencesQuantum operationStatistical physics010306 general physicsMathematical Physicsmedia_commonMathematicsQuantum PhysicsQuantum discordMathematical Physics (math-ph)Condensed Matter - Other Condensed MatterQuantum processQuantum algorithmCondensed Matter::Strongly Correlated ElectronsQuantum Physics (quant-ph)Other Condensed Matter (cond-mat.other)
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Nestriktās matemātikas morfoloģijas operatori: teorijas pamati un operatoru realizācija konkrētiem konjuktoru-implikatoru pāriem

2021

Maģistra darbā apskatīti matemātiskās morfoloģijas pamatoperatoru - dilācija, erozija, atvēršana, slēgšana - paplašinājumi nestriktās kopās. Vispārīga nestrikta morfoloģijas operatora definīcija realizēta konkrētiem konjunktoru-implikātoru pāriem. Operatoru realizācijā par konjunktoriem izvēlētas minimuma, reizinājuma un Lukasieviča t-normas un par implikatoriem - tām atbilstošie rezidiji un Klīnī-Dinesa implikācija. Konkrētie konjunktoru-implikatoru pāriem iegūtie operatori ilustrēti ar vizuāliem piemēriem, to realizācijai izstrādāta arī lietojumprogramma. Veikta iegūto rezultātu analīze.

fuzzy setMatemātikaopeningdilationerosionfuzzy mathematical morphology
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Mathematical Models and their Solutions for Domains of Compex Form

2014

Promocijas darbā tiek apskatīti dažādi oriģināli modeļi un to risinājumi sarežģītas formas apgabaliem. Intensīvās tērauda rūdīšanas procesi sistēmām ar ribām tiek aprakstīti ar 3D hiperbolisko, kā arī ar klasisko siltuma vadīšanas vienādojumu. Precīzā atrisinājuma iegūšanai izmantota Grīna funkciju metode un tās vispārinājums. Modernajos datoros sastopamajām sistēmām ar dubulsieniņu un dubultribu dota stacionārā un nestacionārā siltumvadīšanas problēma 2D gadījumā. Tās risinājums tiek iegūts ar konservatīvās viduvēšanas metodi, galīgo diferenču metodi un tās modifikāciju robežnosacījumiem. Piedāvāts jauns matemātiskais modelis vītola flautai, problēmas formulējumā izmantojot 1D lineāru viļņ…

galīgo diferenču metodeL-shape samplewillow fluteMathematical modellingMatemātiskā modelēšanakonservatīvā viduvēšanavītola flautaheat conduction equationssistēmas ar dubultsieniņu un dubultribuL-veida apgabalsGreen’s functionmethod of separation of variablesdouble wall with double finssiltuma vadīšanas vienādojumiGrīna funkcijamainīgo atdalīšanas metodeMatemātikawave equationviļņu vienādojumsconservative averagingMathematicsfinite difference method
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Distributed n-player approachability via time and space average consensus

2012

Abstract In this paper we consider repeated coalitional games with transferable utilities (TU) over networks. Namely, we consider a set of n players that have to distribute among themselves a vector of rewards (one for each player). In our network version there is no coordinator allocating the rewards, but the agents have to agree on a common time-averaged vector by updating the local estimates of the reward vector. The common time-averaged reward vector has to approach a suitable constraint set, called core of the game, that guarantees that no agents benefit from quitting the grand coalition. We propose a doubly (over time and space) averaging distributed algorithm. At every iteration, eac…

game theoryComputer Science::Computer Science and Game TheoryMathematical optimizationSpacetimeReward-based selectionconsensus algorithmsGeneral Medicinecontrol optimization game theoryApproachabilitySet (abstract data type)Constraint (information theory)Core (game theory)Order (business)Distributed algorithmnetwork systemMathematicsIFAC Proceedings Volumes
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