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Search results for: TENSOR PRODUCT STRUCTURES
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Tensor-product versus geometric-product coding
PublicationKodowanie przy pomocy iloczynów tensorowych, a kodowanie przy pomocy iloczynów geometrycznych. Formalizm jest zilustrowany przy pomocy paru przykładów.
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Hidden Tensor Structures
PublicationAny single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and classical signal analysis. Accordingly, systems as simple as a single one-dimensional harmonic oscillator, an infinite potential well, or a classical finite-amplitude signal of finite duration...
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Teleportation of geometric structures in 3D
PublicationThe simplest quantum teleportation algorithms can be represented in geometric terms in spaces of dimensions 3 (for real state vectors) and 4 (for complex state vectors). The geometric representation is based on geometric-algebra coding, a geometric alternative to the tensor-product coding typical of quantum mechanics. We discuss all the elementary ingredients of the geometric version of the algorithm: geometric analogs of states...
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Geometric analogue of holographic reduced representation
PublicationHolographic reduced representations (HRRs) are distributed representations of cognitive structuresbased on superpositions of convolution-bound n-tuples. Restricting HRRs to n-tuples consisting of 1,one reinterprets the variable binding as a representation of the additive group of binary n-tupleswith addition modulo 2. Since convolutions are not defined for vectors, the HRRs cannot be directlyassociated with geometric structures....
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Geometric Algebra Model of Distributed Representations
PublicationFormalism based on GA is an alternative to distributed representation models developed so far-Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric products, interpretable in terms of geometry which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates...
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Marek Czachor prof. dr hab.
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Advanced Mechanics of Marine Structures I, MSc, Summer 2022-2023, [L,T], PG_00051723
e-Learning Courses1. Literature overview, definition of marine and offshore structures, ocean engineering technologies and mechanical aspects, structural systems applied, jack-up drilling platforms and structural elements. 2. Tensor algebra fundamentals, stress and small strain states of a solid, constitutive relations. 3. SDOF and MDOF dynamic systems, damping and added masses in offshore vibrations, generalised eigenvalue problem, forced vibrations...
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Dobór geotekstyliów i wyrobów pokrewnych pełniących funkcję zbrojenia w budownictwie komunikacyjnym – wybrane problemy inżynierskie
PublicationZ uwagi na odpowiedzialność uczestników procesu budowlanego za realizowane inwestycje komunikacyjne w coraz dłuższym horyzoncie czasowym, celowe wydaje się zwrócenie uwagi na zagadnienia związane z obserwowanymi niestety nadal problemami dotyczącymi umiejętności odróżniania poszczególnych rodzajów geosyntetyków oraz weryfikacji wymaganych w projekcie tzw. technicznych parametrów istotnych (np. wytrzymałość długoterminowa w przypadku...
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Applications of Tensor Analysis in Continuum Mechanics
PublicationA tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components...
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