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Wyniki wyszukiwania dla: NON-DIOPHANTINE ARITHMETIC
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Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
PublikacjaFractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.
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Non-Diophantine Arithmetics in Mathematics, Physics and Psychology
PublikacjaFor a long time, all thought there was only one geometry — Euclidean geometry. Nevertheless, in the 19th century, many non-Euclidean geometries were discovered. It took almost two millennia to do this. This was the major mathematical discovery and advancement of the 19th century, which changed understanding of mathematics and the work of mathematicians providing innovative insights and tools for mathematical research and applications...
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If Gravity is Geometry, is Dark Energy just Arithmetic?
PublikacjaArithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, R^4 and (−L/2,L/2)^4, are considered where different types of arithmetic and calculus coexist simultaneously. In all the examples there exists a non-Diophantine arithmetic that makes the space globally Minkowskian, and thus the laws of physics are formulated in terms...
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Non-Newtonian Mathematics Instead of Non-Newtonian Physics: Dark Matter and Dark Energy from a Mismatch of Arithmetics
PublikacjaNewtonian physics is based on Newtonian calculus applied to Newtonian dynamics. New paradigms such as ‘modified Newtonian dynamics’ (MOND) change the dynamics, but do not alter the calculus. However, calculus is dependent on arithmetic, that is the ways we add and multiply numbers. For example, in special relativity we add and subtract velocities by means of addition β1⊕β2=tanh(tanh−1(β1)+tanh−1(β2)), although multiplication β1⊙β2=tanh(tanh−1(β1)⋅tanh−1(β2)),...
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Simple Fractal Calculus from Fractal Arithmetic
PublikacjaNon-Newtonian calculus that starts with elementary non-Diophantine arithmetic operations of a Burgin type is applicable to all fractals whose cardinality is continuum. The resulting definitions of derivatives and integrals are simpler from what one finds in the more traditional literature of the subject, and they often work in the cases where the standard methods fail. As an illustration, we perform a Fourier transform of a real-valued...
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Marek Czachor prof. dr hab.
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JOURNAL OF NON-CRYSTALLINE SOLIDS
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Bell-Type Inequalities from the Perspective of Non-Newtonian Calculus
PublikacjaA class of quantum probabilities is reformulated in terms of non-Newtonian calculus and projective arithmetic. The model generalizes spin-1/2 singlet state probabilities discussed in Czachor (Acta Physica Polonica:139 70–83, 2021) to arbitrary spins s. For s → ∞ the formalism reduces to ordinary arithmetic and calculus. Accordingly, the limit “non-Newtonian to Newtonian” becomes analogous to the classical limit of a quantum theory
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Relativity of arithmetic as a fundamental symmetry of physics
PublikacjaArithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters ‘plus’ or ‘times’ one has certain freedom of interpreting this operation. This leads to some freedom in definitions of derivatives, integrals and, thus, practically all equations occurring in...
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Information Processing and Fechner’s Problem as a Choice of Arithmetic
PublikacjaFechner’s law and its modern generalizations can be regarded as manifestations of alternative forms of arithmetic, coexisting at stimulus and sensation levels. The world of sensations may be thus described by a generalization of the standard mathematical calculus.
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Implementation of Addition and Subtraction Operations in Multiple Precision Arithmetic
PublikacjaIn this paper, we present a digital circuit of arithmetic unit implementing addition and subtraction operations in multiple-precision arithmetic (MPA). This adder-subtractor unit is a part of MPA coprocessor supporting and offloading the central processing unit (CPU) in computations requiring precision higher than 32/64 bits. Although addition and subtraction operations of two n-digit numbers require O(n) operations, the efficient...
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FPGA implementation of the multiplication operation in multiple-precision arithmetic
PublikacjaAlthough standard 32/64-bit arithmetic is sufficient to solve most of the scientific-computing problems, there are still problems that require higher numerical precision. Multiple-precision arithmetic (MPA) libraries are software tools for emulation of computations in a user-defined precision. However, availability of a reconfigurable cards based on field-programmable gate arrays (FPGAs) in computing systems allows one to implement...
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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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Crystallization of space: Space-time fractals from fractal arithmetic
PublikacjaFractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated...
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Scaling of numbers in residue arithmetic with the flexible selection of scaling factor
PublikacjaA scaling technique of numbers in resudue arithmetic with the flexible selection of the scaling factor is presented. The required scaling factor can be selected from the set of moduli products of the Residue Number System (RNS) base. By permutation of moduli of the number system base it is possible to create many auxilliary Mixed-Radix Systems associated with the given RNS with respect to the base, but they have different sets...
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Arithmetic Loophole in Bell's Theorem: Overlooked Threat to Entangled-State Quantum Cryptography
PublikacjaBell’s theorem is supposed to exclude all local hidden-variable models of quantum correlations. However,an explicit counterexample shows that a new class of local realistic models, based on generalized arith-metic and calculus, can exactly reconstruct rotationally symmetric quantum probabilities typical oftwo-electron singlet states. Observable probabilities are consistent with the usual arithmetic employedby macroscopic observers...
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Non-relational Databases 2022/2023
Kursy OnlineThis course discusses the three types of non-relational databases (i.e. document, graph, key-value). The course is aimed at students in the 7th semester of computer science.
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Non-relational Databases 2023/2024
Kursy OnlineThis course discusses the three types of non-relational databases (i.e. document, graph, key-value). The course is aimed at students in the 7th semester of computer science.
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Implementation of Coprocessor for Integer Multiple Precision Arithmetic on Zynq Ultrascale+ MPSoC
PublikacjaRecently, we have opened the source code of coprocessor for multiple-precision arithmetic (MPA). In this contribution, the implementation and benchmarking results for this MPA coprocessor are presented on modern Zynq Ultrascale+ multiprocessor system on chip, which combines field-programmable gate array with quad-core ARM Cortex-A53 64-bit central processing unit (CPU). In our benchmark, a single coprocessor can be up to 4.5 times...
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Open-Source Coprocessor for Integer Multiple Precision Arithmetic
PublikacjaThis paper presents an open-source digital circuit of the coprocessor for an integer multiple-precision arithmetic (MPA). The purpose of this coprocessor is to support a central processing unit (CPU) by offloading computations requiring integer precision higher than 32/64 bits. The coprocessor is developed using the very high speed integrated circuit hardware description language (VHDL) as an intellectual property (IP) core. Therefore,...
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Justyna Borucka dr inż. arch.
OsobyJustyna Borucka jest adiunktem na Wydziale Architektury Politechniki Gdańskiej, koordynatorem programu Erasmus i współpracy zagranicznej, a od 2016 roku prodziekanem ds. rozwoju. Jest również członkiem Zarządu Stowarzyszenia Architektów Polskich (SARP Oddział Wybrzeże). Jej badania koncentrują się na teorii architektury i strategii odnowy miejskiej ze szczególnym wpływem interdyscyplinarnych relacji współczesnej architektury i...
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FPGA realization of fir filter in residue arithmetic
Publikacjaw pracy zaprezentowano realizację fpga przepływowego filtru fir o stałych współczynnikach w arytmetyce resztowej z użyciem 8 5-bitowych modułów o łącznym zakresie liczbowym 37.07 bita. zastosowano formębezpośrednią fir. mnożenia wykonywane są przy użyciu odczytu z pamięci. sumowania w każdym z kanałów są realizowane przy zastosowaniu wielopoziomowej struktury sumatora opartego o 4-operandowe sumatory csa. w stopniu końcowym wykonywane...
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Pipelined division of signed numbers with the use of residue arithmetic in FPGA
PublikacjaAn architecture of a pipelined signed residue divider for small number ranges is presented. The divider makes use of the multiplicative division algorithm where initially the reciprocal of the divisor is calculated and subsequently multiplied by the dividend. The divisor represented in the signed binary form is used to compute the approximated reciprocal in the residue form by the table look-up. In order to reduce the needed length...
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The description of non-linear interactions of wave and non-wave modes in a non-adiabatic plasma flow
PublikacjaThe method of derivation of non-linear equations for interacting modes is explained and applied to a plasma's flow affected by a magnetic field. It is based on the linear projecting of the total perturbation field into specific variations of variables in individual modes of a flow. The method may be applied in many examples of fluid flows with different mechanisms of non-adiabaticity. It is of special importance in complex flows...
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Waves Along Fractal Coastlines: From Fractal Arithmetic to Wave Equations
PublikacjaBeginning with addition and multiplication intrinsic to a Koch-type curve, we formulate and solve wave equation describing wave propagation along a fractal coastline. As opposed to examples known from the literature, we do not replace the fractal by the continuum in which it is embedded. This seems to be the first example of a truly intrinsic description of wave propagation along a fractal curve. The theory is relativistically...
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Non-coding RNA
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Non-ferrous Metals
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Zarządzanie organizacjami non profit - lato 2022
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Zarządzanie organizacjami non profit - lato 2023
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FPGA realization of high-speed multi-stage FIR filter in residue arithmetic
PublikacjaW pracy przedstawiono implementację szybkiego wielostopniowego, kaskadowego filtru FIR w technologii FPGA. Zastosowanie arytmetyki resztowej pozwala na uzyskanie dużych częstotliwości próbkowania w zwiżaku z użyciem małych mnożników. Zalety wynikające z uzycia arytmetyki resztowej sa w pewnym stopniu ograniczne koniecznością wykonania skalowania przy kaskadowym połaczeniu filtrów FIR, tak aby uniknąć nadmiaru arytmetycznego. W...
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Fpga implementation of the two-stage high-speed fir filter in residue arithmetic
Publikacjaw pracy przedstawiono implementację szybkiego, dwustopniowego kaskadowego filtru fir w technologii fpga z użyciem arytmetyki resztowej. zastosowanie arytmetyki resztowej pozwala na uzyskanie dużych częstotliwości potokowania w związku z użyciem małych mnożników. zalety arytmetyki resztowej są ograniczane w pewnym stopniu koniecznością wykonywania skalowania po pierwszym stopniu filtru celem uniknięcia nadmiaru arytmetycznego. w...
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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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Non-isolating bondage in graphs
PublikacjaA dominating set of a graph $G = (V,E)$ is a set $D$ of vertices of $G$ such that every vertex of $V(G) \setminus D$ has a neighbor in $D$. The domination number of a graph $G$, denoted by $\gamma(G)$, is the minimum cardinality of a dominating set of $G$. The non-isolating bondage number of $G$, denoted by $b'(G)$, is the minimum cardinality among all sets of edges $E' \subseteq E$ such that $\delta(G-E') \ge 1$ and $\gamma(G-E')...
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Zarządzanie organizacjami non profit 23/24 STC
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Non-isolating 2-bondage in graphs
PublikacjaA 2-dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of V(G)D has at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. The non-isolating 2-bondage number of G, denoted by b_2'(G), is the minimum cardinality among all sets of edges E' subseteq E such that delta(G-E') >= 1 and gamma_2(G-E') > gamma_2(G)....
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Journal of Non-Oxide Glasses
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Non-coding RNA Research
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JOURNAL OF NON-EQUILIBRIUM THERMODYNAMICS
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Non-Coding RNA Investigation
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Mariusz Kaczmarek dr hab. inż.
OsobyReceived M.Sc., Eng. in Electronics in 1995 from Gdansk University of Technology, Ph.D. in Medical Electronics in 2003 and habilitation in Biocybernetics and Biomedical Engineering in 2017. He was an investigator in about 13 projects receiving a number of awards, including four best papers, practical innovations (7 medals and awards) and also the Andronicos G. Kantsios Award and Siemens Award. Main research activities: the issues...
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Non-linear FEM analysis of pounding-involved response of buildings under non-uniform earthquake excitation
PublikacjaThe aim of the paper is to show the results of the study investigating the influence of non-uniform earthquake excitation, due to spatial seismic effects connected with the propagation of seismic wave, on the pounding-involved response of two buildings. The three-dimensional non-linear FEM analysis has been conducted using the detailed models of colliding structures. Acceleration records for different structural supports have been...
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Nonlinear Excitation of the Non-Wave Perturbations by the Magnetoacoustic Waves in the Non-Isentropic Plasma
PublikacjaNonlinear excitation of slow modes by the planar magnetosonic perturbations in a plasma is discussed. Plasma is an open system due to radiation and external heating. This may stipulate enhancement of wave perturbations and hence the acoustical activity of plasma. Plasma is assumed to be a homogeneous ideal gas with infinite electrical conductivity. The straight magnetic field is orthogonal to the velocity of fluid’s...
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INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
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Special Issue: “Non-Destructive Testing of Structures”
PublikacjaThe Special Issue “Non-Destructive Testing of Structures” has been proposed to present recent developments in the field of diagnostics of structural materials and components in civil and mechanical engineering. The papers highlighted in this editorial concern various aspects of non-invasive diagnostics, including such topics as condition assessments of civil and mechanical structures and connections of structural elements, the...
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Non-destructive Testing of Wooden Elements
PublikacjaExamining the condition of wooden elements is crucial from the perspective of proper structure performance. If the deterioration in the internal wood condition, which displays no symptoms visible from the outside, is detected, the further spread of the deterioration can be prevented. Test results often point to the necessity of conducting repairs and, renovations, replacing the structure of wooden beams, or even substituting a...
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Discrete identification of continuous non-linear and non-stationary dynamical systems that is insensitive to noise correlation and measurement outliers
PublikacjaThe paper uses specific parameter estimation methods to identify the coefficients of continuous-time models represented by linear and non-linear ordinary differential equations. The necessary approximation of such systems in discrete time in the form of utility models is achieved by the use of properly tuned `integrating filters' of the FIR type. The resulting discrete-time descriptions retain the original continuous parameterization...
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Pipelined division of signed numbers with the use of residue arithmetic for small number range with the programmable gate array
PublikacjaIn this work an architecture of the pipelined signed residue divider for the small number range is presented. Its operation is based on reciprocal calculation and multiplication by the dividend. The divisor in the signed binary form is used to compute the approximated reciprocal in the residue form by the table look-up. In order to limit the look-up table address an algorithm based on segmentation of the divisor into two segments...
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Mixed neuroendocrine non-neuroendocrine neoplasm (MiNEN) - Male, 65 - Tissue image [3200630011574561]
Dane BadawczeThis is the histopathological image of STOMACH tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Mixed neuroendocrine non-neuroendocrine neoplasm (MiNEN) - Male, 65 - Tissue image [3200630011576491]
Dane BadawczeThis is the histopathological image of STOMACH tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Mixed neuroendocrine non-neuroendocrine neoplasm (MiNEN) - Male, 65 - Tissue image [3200630011579601]
Dane BadawczeThis is the histopathological image of LYMPH NODES tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.