Search Results - "Legatiuk, Dmitrii"

Mathematical Modelling by Help of Category Theory: Models and Relations between Them by Legatiuk, Dmitrii

“…The growing complexity of modern practical problems puts high demand on mathematical modelling. Given that various models can be used for modelling one…”
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Cauchy Formulae and Hardy Spaces in Discrete Octonionic Analysis by Kraußhar, Rolf Sören, Legatiuk, Dmitrii

“…In this paper, we continue the development of a fundament of discrete octonionic analysis that is associated to the discrete first order Cauchy–Riemann…”
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Brownian Motion, Martingales and Itô Formula in Clifford Analysis by Bernstein, Swanhild, Legatiuk, Dmitrii

“…Clifford analysis has been the field of active research for several decades resulting in various methods to solve problems in pure and applied mathematics…”
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Formalising Autonomous Construction Sites with the Help of Abstract Mathematics by Legatiuk, Dmitrii, Luckey, Daniel

“…With the rapid development of modern technologies, autonomous or robotic construction sites are becoming a new reality in civil engineering. Despite various…”
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Coupling of Complex Function Theory and Finite Element Method for Crack Propagation Through Energetic Formulation: Conformal Mapping Approach and Reduction to a Riemann–Hilbert Problem by Legatiuk, Dmitrii, Weisz-Patrault, Daniel

“…In this paper we present a theoretical background for a coupled analytical–numerical approach to model a crack propagation process in two-dimensional bounded…”
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Operator Calculus Approach to Comparison of Elasticity Models for Modelling of Masonry Structures by Gürlebeck, Klaus, Legatiuk, Dmitrii, Webber, Kemmar

“…The solution of any engineering problem starts with a modelling process aimed at formulating a mathematical model, which must describe the problem under…”
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Discrete Hardy Spaces for Bounded Domains in Rn by Cerejeiras, Paula, Kähler, Uwe, Legatiuk, Anastasiia, Legatiuk, Dmitrii

“…Discrete function theory in higher-dimensional setting has been in active development since many years. However, available results focus on studying discrete…”
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Editorial on the special issue “Current topics in applied hypercomplex analysis” by Legatiuk, Dmitrii, Bock, Sebastian, Kaehler, Uwe

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Metaization concepts for monitoring-related information by Theiler, Michael, Ibáñez, Stalin, Legatiuk, Dmitrii, Smarsly, Kay

“…In recent years, structural health monitoring (SHM) has become a widely used state-of-the-art method for analyzing and assessing the condition of civil…”
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Conceptual modelling: Towards detecting modelling errors in engineering applications by Gürlebeck, Klaus, Legatiuk, Dmitrii, Nilsson, Henrik, Smarsly, Kay

“…Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer “simple” objects,…”
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Categorical approach to modelling and to coupling of models by Gürlebeck, Klaus, Hofmann, Dirk, Legatiuk, Dmitrii

“…Solution of any engineering problem starts with a modelling process, which typically involves a choice among different kinds of models. To create a realistic…”
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Discrete Hardy Spaces for Bounded Domains in $${\mathbb {R}}^{n} by Cerejeiras, Paula, Kähler, Uwe, Legatiuk, Anastasiia, Legatiuk, Dmitrii

“…Discrete function theory in higher-dimensional setting has been in active development since many years. However, available results focus on studying discrete…”
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Interpolation of monogenic functions by using reproducing kernel Hilbert spaces by Cerejeiras, Paula, Kähler, Uwe, Legatiuk, Dmitrii

“…In this paper, we present results on interpolation of monogenic functions in the unit ball of Rd+1 using reproducing kernels and randomly chosen interpolation…”
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Three-dimensional interpolation with monogenic polynomials by Gürlebeck, Klaus, Legatiuk, Dmitrii

“…One of the open problems in hypercomplex analysis is the interpolation of monogenic functions by monogenic polynomials. We consider the case of monogenic…”
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Modeling and evaluation of cyber‐physical systems in civil engineering by Legatiuk, Dmitrii, Dragos, Kosmas, Smarsly, Kay

“…A cyber‐physical system (CPS) is a coupled system integrating computing, networking, and physical processes. Through actuation, cyber‐physical systems control…”
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Mathematical modelling by help of category theory: models and relations between them by Legatiuk, Dmitrii

“…The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one…”
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Methoden zur Identifikation von Zugvorbeifahrten aus kontinuierlichen Messdaten by Abrahamczyk, Lars, Jaouadi, Zouhour, Kähler, Uwe, Legatiuk, Dmitrii

“…Tragwerke des Konstruktiven Ingenieurbaus sind in der Regel Unikate. Systematische Untersuchungen dienen daher dem Ziel, Umwelteinflüsse und Einwirkungen auf…”
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Weyl calculus perspective on the discrete Stokes' formula in octonions by Kraußhar, Rolf Sören, Legatiuk, Dmitrii

“…Octonions are 8-dimensional hypercomplex numbers which form the biggest normed division algebras over the real numbers. Motivated by applications in…”
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Error Estimates for the Coupling of Analytical and Numerical Solutions by Gürlebeck, Klaus, Kähler, Uwe, Legatiuk, Dmitrii

“…In this paper we present error estimates for a continuous coupling of an analytical and a numerical solution for a boundary value problem with a singularity. A…”
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Brownian motion, martingales and It\^o formula in Clifford analysis by Bernstein, Swanhild, Legatiuk, Dmitrii

“…Clifford analysis has been the field of active research for several decades resulting in various methods to solve problems in pure and applied mathematics…”
Get full text