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Wyniki wyszukiwania dla: computation
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A new approach to numerical solution of fixed-point problems and its application to delay differential equations
PublikacjaW pracy rozpatruje się pewne aproksymacje punktu stałego ciągłego operatora A odwzorowującego przestrzeń metryczną w siebie. Wspomniany punkt stały przybliża się tzw. epsilon przybliżonym punktem stałym z przestrzeni skończenie wymiarowej. Udowodnione zostało twierdzenie dające warunki konieczne i dostateczne istnienia punktu stałego w ogólnej przestrzeni metrycznej. Warunki te wyrażone są w terminach epsilon przybliżonego punktu...
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Are quantum correlations symmetric?
PublikacjaWe provide operational definition of symmetry of entanglement: An entangled state contains symmetric entanglement if its subsystems can be exchanged (swapped) by means of local operations and classical communication. We show that in general states have asymmetric entanglement. This allows to construct nonsymmetric measure of entanglement, and a parameter that reports asymmetry of entanglement contents of quantum state. We propose...
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On differential-algebraic problems
PublikacjaW pracy podano warunki dostateczne na istnienie ekstremalnych lubkwazi rozwiązań dla problemów różniczkowo-algebraicznych z nieliniowymi warunkami brzegowymi. Problem istnienia jednego rozwiązania w/w zagadnień był również dyskutowany.
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Positive solutions of three-point boundary value problems for second order impulsive differential equations with advanced arguments
PublikacjaW pracy dyskutowano problem istnienia dodatnich rozwiązań dla równań różniczkowych z impulsami rzędu drugiego i z argumentami typu wyprzedzonego. Podano warunki dostateczne na istnienie jednego lub dwóch rozwiązań dodatnich takich zagadnień.
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Positive solutions to second order four-point boundary value problems for impulsive differential equations
PublikacjaPraca dotyczy problemów brzegowych dla równań różniczkowych drugiego rzędu z impulsami. Podane zostały warunki dostateczne na istnienie trzech dodatnich rozwiązań takich problemów z czteropunktowymi warunkami brzegowymi. W badaniach korzystano z twierdzenia Leggetta-Williamsa.
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On nonlinear two-point boundary value problems for impulsive differential-algebraic problems [online]
PublikacjaSformułowano warunki dostateczne na istnienie ekstremalnych rozwiązań dla zagadnień brzegowych dla równań różniczkowo-algebraicznych z impulsami. Badano też nierówności różniczkowo-algebraiczne z impulsami przy odpowiednich warunkach brzegowych. Na przykładzie zilustrowano otrzymane wyniki.
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Positive solutions for three-point one-dimensional p-Laplacian boundary value problems with advanced arguments [online]
PublikacjaPraca dotyczy problemów istnienia dodatnich rozwiązań dla trzy-punktowych zagadnień brzegowych z wyprzedzonymi argumentami. Zastosowano twierdzenie Avery-Petersona o punkcie stałym aby uzyskać warunki dostateczne na istnienie conajmniej trzech dodatnich rozwiązań.
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On dynamic equations with deviating arguments
PublikacjaPraca dotyczy istnienia rozwiązań równań dynamicznych z odchylonymi argumentami. Podane zostały warunki dostateczne na istnienie rozwiązania. Dwa przykłady ilustrują otrzymane wyniki.
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Boundary value problems for differential equations with deviated arguments which depend on the unknown solution
PublikacjaDyskutowane są zagadnienia brzegowe dla równań różniczkowo funkcyjnych pierwszego rzędu z odchylonym argumentem zależnym od nieznanego rozwiązania. Sformułowane są warunki dostateczne isnienia quasirozwiązań i rozwiązań takich zagadnień.
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Initial value problems for neutral fractional differential equations involving a Riemann-Liouville derivative
PublikacjaBadano równania neutralne typu ułamkowego z odchylonym argumentem. Podano warunki dostateczne na istnienie jednego rozwiązania.
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Existence results to delay fractional differential equations with nonlinear boundary conditions
PublikacjaPraca dotyczy problemów brzegowych dla ułamkowych równań różniczkowych z opóźnionym argumentem. Podano warunki dostateczne na istnienie rozwiązań ekstremalnych takich zagadnień.
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Existence of solutions for a coupled system of difference equations with cousal operators
PublikacjaPraca dotyczy układów równań różnicowych. Podano warunki dostateczne na istnienie rozwiązań takich problemów. Badano również nierówności różnicowe.
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Multiacces quantum communication and product higher rank numerical range
PublikacjaIn the present paper we initiate the study of the product higher rank numerical range. The latter, being a variant of the higher rank numerical range, is a natural tool for study- ing a construction of quantum error correction codes for multiple access channels. We review properties of this set and relate it to other numerical ranges, which were recently introduced in the literature. Further, the concept is applied to the construction...
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NO-BROADCASTING OF NON-SIGNALLING BOXES VIA OPERATIONS WHICH TRANSFORM LOCAL BOXES INTO LOCAL ONES
PublikacjaWe deal with families of probability distributions satisfying non-signalling condition, called non-signalling boxes and consider a class of operations that transform local boxes into local ones (the one that admit LHV model). We prove that any operation from this class cannot broadcast a bipartite non-local box with 2 binary inputs and outputs. We consider a function called anti-Robustness which can not decrease under these operations....
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ON THE NON-LOCALITY OF TRIPARTITE NON-SINGALING BOXES EMERGING FROM WIRINGS
PublikacjaIt has been recently shown, that some of the tripartite boxes admittin g bilocal decom- position, lead to non-locality under wiring operation applied to t wo of the subsystems [R. Gallego et al. Physical Review Letters 109 , 070401 (2012)]. In the following, we study this phenomenon quantitatively. Basing on the known classes of bo xes closed un- der wirings, we introduce multipartite monotones which are count erparts of bipartite ones...
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Average distance is submultiplicative and subadditive with respect to the strong product of graphs
PublikacjaWe show that the average distance is submultiplicative and subadditive on the set of non-trivial connected graphs with respect to the strong product. We also give an application of the above-mentioned result.
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Green function diagonal for a class of heat equations
PublikacjaA construction of the heat kernel diagonal is considered as element of generalized zeta function theory, which gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expressions of the Green function in the case of finite-gap potential coefficient of the heat equation are constructed. An algorithm and program for Mathematica are presented...
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Fractional problems with advanced arguments
PublikacjaThis paper concerns boundary fractional differential problems with advanced arguments. We investigate the existence of initial value problems when the initial point is given at the end point of an interval. Nonhomogeneous linear fractional differential equations are also studied. The existence of solutions for fractional differential equations with advanced arguments and with boundary value problems has been investigated by using...
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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublikacjaIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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Monotone iterative method for first-order differential equations at resonance
PublikacjaThis paper concerns the application of the monotone iterative technique for first-order differential equations involving Stieltjes integrals conditions. We discuss such problems at resonance when the measure in the Stieltjes integral is positive and also when this measure changes the sign. Sufficient conditions which guarantee the existence of extremal, unique and quasi-solutions are given. Three examples illustrate the results.
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Mathematical analysis of a generalised p53-Mdm2 protein gene expression model
PublikacjaWe propose the generalisation of the p53-Mdm2 protein gene expression model introduced by Monk (2003). We investigate the stability of a unique positive steady state and formulate conditions which guarantee the occurrence of the Hopf bifurcation. We show that oscillatory behaviour can be caused not only by time lag in protein transcription process, but also can be present in the model without time delay. Moreover, we investigate...
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Boundary vlue problems for difference equations with causal operators
PublikacjaPraca dotyczy problemów brzegowych dla równań różnicowych.Podano warunki dostateczne na istnienie ekstremalnych rozwiązań stosując metodę iteracji monotonicznych.
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Diffusion process modeling by using fractional-order models
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Chromatic cost coloring of weighted bipartite graphs
PublikacjaGiven a graph G and a sequence of color costs C, the Cost Coloring optimization problem consists in finding a coloring of G with the smallest total cost with respect to C. We present an analysis of this problem with respect to weighted bipartite graphs. We specify for which finite sequences of color costs the problem is NP-hard and we present an exact polynomial algorithm for the other finite sequences. These results are then extended...
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W-dominance: Tradeoff-inspired dominance relation for preference-based evolutionary multi-objective optimization
PublikacjaThe paper presents a method of incorporating decision maker preferences into multi-objective meta-heuristics. It is based on tradeoffcoefficients and extends their applicability from bi-objective to multi-objective. The method assumes that a decision maker specifies a priori each objective’s importance as a weight interval. Based on this, w-dominance relation is introduced, which extends Pareto dominance. By replacing reference...
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Parallel Computations of Text Similarities for Categorization Task
PublikacjaIn this chapter we describe the approach to parallel implementation of similarities in high dimensional spaces. The similarities computation have been used for textual data categorization. A test datasets we create from Wikipedia articles that with their hyper references formed a graph used in our experiments. The similarities based on Euclidean distance and Cosine measure have been used to process the data using k-means algorithm....
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Electromagnetic Problems Requiring High-Precision Computations
PublikacjaAn overview of the applications of multiple-precision arithmetic in CEM was presented in this paper for the first time. Although double-precision floating-point arithmetic is sufficient for most scientific computations, there is an expanding body of electromagnetic problems requiring multiple-precision arithmetic. Software libraries facilitating these computations were described, and investigations requiring multiple-precision...
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Parallel computations in the volunteer based Comcute system
PublikacjaThe paper presents Comcute which is a novel multi-level implemen- tation of the volunteer based computing paradigm. Comcute was designed to let users donate the computing power of their PCs in a simplified manner, requiring only pointing their web browser at a specific web address and clicking a mouse. The server side appoints several servers to be in charge of execution of particular tasks. Thanks to that the system can survive...
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Computationally Efficient Design Optimization of Compact Microwave and Antenna Structures
PublikacjaMiniaturization is one of the important concerns of contemporary wireless communication systems, especially regarding their passive microwave components, such as filters, couplers, power dividers, etc., as well as antennas. It is also very challenging, because adequate performance evaluation of such components requires full-wave electromagnetic (EM) simulation, which is computationally expensive. Although high-fidelity EM analysis...
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Computationally efficient index generation unit using a Bloom filter
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Using GPUs for Parallel Stencil Computations in Relativistic Hydrodynamic Simulation
PublikacjaThis paper explores the possibilities of using a GPU for complex 3D finite difference computation. We propose a new approach to this topic using surface memory and compare it with 3D stencil computations carried out via shared memory, which is currently considered to be the best approach. The case study was performed for the extensive computation of collisions between heavy nuclei in terms of relativistic hydrodynamics.
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IP Core of Coprocessor for Multiple-Precision-Arithmetic Computations
PublikacjaIn this paper, we present an IP core of coprocessor supporting computations requiring integer multiple-precision arithmetic (MPA). Whilst standard 32/64-bit arithmetic is sufficient to solve many computing problems, there are still applications that require higher numerical precision. Hence, the purpose of the developed coprocessor is to support and offload central processing unit (CPU) in such computations. The developed digital...
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Windowing of the Discrete Green's Function for Accurate FDTD Computations
PublikacjaThe paper presents systematic evaluation of the applicability of parametric and nonparametric window functions for truncation of the discrete Green's function (DGF). This function is directly derived from the FDTD update equations, thus the FDTD method and its integral discrete formulation can be perfectly coupled using DGF. Unfortunately, the DGF computations require processor time, hence DGF has to be truncated with appropriate...
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Application of Barycentric Coordinates in Space Vector PWM Computations
PublikacjaThis paper proposes the use of barycentric coordinates in the development and implementationof space-vector pulse-width modulation (SVPWM) methods, especially for inverters with deformed space-vector diagrams. The proposed approach is capable of explicit calculation of vector duty cycles, independentof whether they assume ideal positions or are displaced due to the DC-link voltage imbalance. The use ofbarycentric coordinates also...
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KernelHive: a new workflow-based framework for multilevel high performance computing using clusters and workstations with CPUs and GPUs
PublikacjaThe paper presents a new open-source framework called KernelHive for multilevel parallelization of computations among various clusters, cluster nodes, and finally, among both CPUs and GPUs for a particular application. An application is modeled as an acyclic directed graph with a possibility to run nodes in parallel and automatic expansion of nodes (called node unrolling) depending on the number of computation units available....
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An Assessment of RASSCF and TDDFT Energies and Gradients on an Organic Donor−Acceptor Dye Assisted by Resonance Raman Spectroscopy
PublikacjaThe excitation energies and gradients in the ground and the first excited state of a novel donor−(π- bridge)−acceptor 4-methoxy-1,3-thiazole-based chromophore were investigated by means of MS-RASPT2/RASSCF and TDDFT in solution. Within both methods, the excitation energies strongly depend on the employed equilibrium structures, whose differences can be rationalized in terms of bond length alternation indexes. It is shown that functionals with...
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Anharmonic Infrared Spectroscopy through the Fourier Transform of Time Correlation Function Formalism in ONETEP
PublikacjaDensity functional theory molecular dynamics (DFT-MD) provides an efficient framework for accurately computing several types of spectra. The major benefit of DFTMD approaches lies in the ability to naturally take into account the effects of temperature and anharmonicity, without having to introduce any ad hoc or a posteriori corrections. Consequently, computational spectroscopy based on DFT-MD approaches plays a pivotal role in...
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Electronically Excited States in Solution via a Smooth Dielectric Model Combined with Equation-of-Motion Coupled Cluster Theory
PublikacjaWe present a method for computing excitation energies for molecules in solvent, based on the combination of a minimal parameter implicit solvent model and the equation-of-motion coupled-cluster singles and doubles method (EOM-CCSD). In this method, the solvent medium is represented by a smoothly varying dielectric function, constructed directly from the quantum mechanical electronic density using only two tunable parameters. The...
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Performance of the AMOEBA Water Model in the Vicinity of QM Solutes: A Diagnosis Using Energy Decomposition Analysis
PublikacjaThe importance of incorporating solvent polarization effects into the modeling of solvation processes has been well-recognized, and therefore a new generation of hybrid quantum mechanics/molecular mechanics (QM/MM) approaches that accounts for this effect is desirable. We present a fully self-consistent, mutually polarizable QM/MM scheme using the AMOEBA force field, in which the total energy of the system is variationally minimized...
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Dominant Pathways of Adenosyl Radical-Induced DNA Damage Revealed by QM/MM Metadynamics
PublikacjaBrominated nucleobases sensitize double stranded DNA to hydrated electrons, one of the dominant genotoxic species produced in hypoxic cancer cells during radiotherapy. Such radiosensitizers can therefore be administered locally to enhance treatment efficiency within the solid tumor while protecting the neighboring tissue. When a solvated electron attaches to 8-bromoadenosine, a potential sensitizer, the dissociation of bromide...
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Theoretical Assessment of Excited State Gradients and Resonance Raman Intensities for the Azobenzene Molecule
PublikacjaThe ground state geometries and vibrational frequencies as well as the excitation energies and excited state gradients of the S 1(nπ*) and S 2(ππ * ) states of trans - and cis -azobenzene are investigated by several DFT methods, namely B3LYP, PBE, M06-2X, CAM-B3LYP, and ω B97X. Excited state properties and in particular gradients are also assessed using the wave function based methods EOM-CCSD and RASPT2/RASSCF. Comparison with...
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Keep It Flexible: Driving Macromolecular Rotary Motions in Atomistic Simulations with GROMACS
PublikacjaWe describe a versatile method to enforce the rotation of subsets of atoms, e.g., a protein subunit, in molecular dynamics (MD) simulations. In particular, we introduce a “flexible axis” technique that allows realistic flexible adaptions of both the rotary subunit as well as the local rotation axis during the simulation. A variety of useful rotation potentials were implemented for the GROMACS 4.5 MD package. Application to the...
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DL_MG: A Parallel Multigrid Poisson and Poisson–Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution
PublikacjaThe solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential -- a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the...
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Combining the MARTINI and Structure-Based Coarse-Grained Approaches for the Molecular Dynamics Studies of Conformational Transitions in Proteins
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Physics-Based Potentials for the Coupling between Backbone- and Side-Chain-Local Conformational States in the United Residue (UNRES) Force Field for Protein Simulations
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Dynamic Formation and Breaking of Disulfide Bonds in Molecular Dynamics Simulations with the UNRES Force Field
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Application of Multiplexed Replica Exchange Molecular Dynamics to the UNRES Force Field: Tests with α and α+β Proteins
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Implementation of a Serial Replica Exchange Method in a Physics-Based United-Residue (UNRES) Force Field
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Improvement of the Treatment of Loop Structures in the UNRES Force Field by Inclusion of Coupling between Backbone- and Side-Chain-Local Conformational States
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Implementation of Molecular Dynamics and Its Extensions with the Coarse-Grained UNRES Force Field on Massively Parallel Systems: Toward Millisecond-Scale Simulations of Protein Structure, Dynamics, and Thermodynamics
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