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Search results for: NONDIOPHANTINE ARITHMETIC

Fourier transforms on Cantor sets: A study in nonDiophantine arithmetic and calculus
PublicationFractals 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 middlethird Cantor set. The formalism works also for fractals that are not selfsimilar.

NonDiophantine Arithmetics in Mathematics, Physics and Psychology
PublicationFor a long time, all thought there was only one geometry — Euclidean geometry. Nevertheless, in the 19th century, many nonEuclidean 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...

If Gravity is Geometry, is Dark Energy just Arithmetic?
PublicationArithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are nonunique. The examples of fourdimensional 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 nonDiophantine arithmetic that makes the space globally Minkowskian, and thus the laws of physics are formulated in terms...

NonNewtonian Mathematics Instead of NonNewtonian Physics: Dark Matter and Dark Energy from a Mismatch of Arithmetics
PublicationNewtonian 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)),...

Simple Fractal Calculus from Fractal Arithmetic
PublicationNonNewtonian calculus that starts with elementary nonDiophantine 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 realvalued...

Marek Czachor prof. dr hab.
People 
JOURNAL OF NONCRYSTALLINE SOLIDS
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BellType Inequalities from the Perspective of NonNewtonian Calculus
PublicationA class of quantum probabilities is reformulated in terms of nonNewtonian calculus and projective arithmetic. The model generalizes spin1/2 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 “nonNewtonian to Newtonian” becomes analogous to the classical limit of a quantum theory

Relativity of arithmetic as a fundamental symmetry of physics
PublicationArithmetic 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...

Information Processing and Fechner’s Problem as a Choice of Arithmetic
PublicationFechner’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.

Implementation of Addition and Subtraction Operations in Multiple Precision Arithmetic
PublicationIn this paper, we present a digital circuit of arithmetic unit implementing addition and subtraction operations in multipleprecision arithmetic (MPA). This addersubtractor 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 ndigit numbers require O(n) operations, the efficient...

FPGA implementation of the multiplication operation in multipleprecision arithmetic
PublicationAlthough standard 32/64bit arithmetic is sufficient to solve most of the scientificcomputing problems, there are still problems that require higher numerical precision. Multipleprecision arithmetic (MPA) libraries are software tools for emulation of computations in a userdefined precision. However, availability of a reconfigurable cards based on fieldprogrammable gate arrays (FPGAs) in computing systems allows one to implement...

IP Core of Coprocessor for MultiplePrecisionArithmetic Computations
PublicationIn this paper, we present an IP core of coprocessor supporting computations requiring integer multipleprecision arithmetic (MPA). Whilst standard 32/64bit 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...

Crystallization of space: Spacetime fractals from fractal arithmetic
PublicationFractals 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 spacetime can be generated by means of homogeneous spaces associated...

Scaling of numbers in residue arithmetic with the flexible selection of scaling factor
PublicationA 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 MixedRadix Systems associated with the given RNS with respect to the base, but they have different sets...

Arithmetic Loophole in Bell's Theorem: Overlooked Threat to EntangledState Quantum Cryptography
PublicationBell’s theorem is supposed to exclude all local hiddenvariable models of quantum correlations. However,an explicit counterexample shows that a new class of local realistic models, based on generalized arithmetic and calculus, can exactly reconstruct rotationally symmetric quantum probabilities typical oftwoelectron singlet states. Observable probabilities are consistent with the usual arithmetic employedby macroscopic observers...

Nonrelational Databases 2022/2023
eLearning CoursesThis course discusses the three types of nonrelational databases (i.e. document, graph, keyvalue). The course is aimed at students in the 7th semester of computer science.

Nonrelational Databases 2023/2024
eLearning CoursesThis course discusses the three types of nonrelational databases (i.e. document, graph, keyvalue). The course is aimed at students in the 7th semester of computer science.

Implementation of Coprocessor for Integer Multiple Precision Arithmetic on Zynq Ultrascale+ MPSoC
PublicationRecently, we have opened the source code of coprocessor for multipleprecision 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 fieldprogrammable gate array with quadcore ARM CortexA53 64bit central processing unit (CPU). In our benchmark, a single coprocessor can be up to 4.5 times...

OpenSource Coprocessor for Integer Multiple Precision Arithmetic
PublicationThis paper presents an opensource digital circuit of the coprocessor for an integer multipleprecision 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,...

Justyna Borucka dr inż. arch.
PeopleJustyna Borucka is an Assistant Professor at the Faculty of Architecture, Gdańsk University of Technology, Coordinator of Erasmus Programme and International Cooperation and since 2016 a ViceDean for Development. She is also board member of Polish Architects Association (SARP o.Wybrzeże). Her research focused on theory of architecture and strategies for urban renewal with the special impact of interdisciplinary relationships...

FPGA realization of fir filter in residue arithmetic
Publicationw pracy zaprezentowano realizację fpga przepływowego filtru fir o stałych współczynnikach w arytmetyce resztowej z użyciem 8 5bitowych 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 4operandowe sumatory csa. w stopniu końcowym wykonywane...

Pipelined division of signed numbers with the use of residue arithmetic in FPGA
PublicationAn 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 lookup. In order to reduce the needed length...

The description of nonlinear interactions of wave and nonwave modes in a nonadiabatic plasma flow
PublicationThe method of derivation of nonlinear 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 nonadiabaticity. It is of special importance in complex flows...

Waves Along Fractal Coastlines: From Fractal Arithmetic to Wave Equations
PublicationBeginning with addition and multiplication intrinsic to a Kochtype 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...

Noncoding RNA
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Nonferrous Metals
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Zarządzanie organizacjami non profit  lato 2022
eLearning Courses 
Zarządzanie organizacjami non profit  lato 2023
eLearning Courses 
Fpga implementation of the twostage highspeed fir filter in residue arithmetic
Publicationw 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...

FPGA realization of highspeed multistage FIR filter in residue arithmetic
PublicationW 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...

ON THE NONLOCALITY OF TRIPARTITE NONSINGALING BOXES EMERGING FROM WIRINGS
PublicationIt has been recently shown, that some of the tripartite boxes admittin g bilocal decom position, lead to nonlocality 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...

Nonisolating bondage in graphs
PublicationA 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 nonisolating bondage number of $G$, denoted by $b'(G)$, is the minimum cardinality among all sets of edges $E' \subseteq E$ such that $\delta(GE') \ge 1$ and $\gamma(GE')...

Zarządzanie organizacjami non profit 23/24 STC
eLearning Courses 
Nonisolating 2bondage in graphs
PublicationA 2dominating 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 2domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2dominating set of G. The nonisolating 2bondage number of G, denoted by b_2'(G), is the minimum cardinality among all sets of edges E' subseteq E such that delta(GE') >= 1 and gamma_2(GE') > gamma_2(G)....

Journal of NonOxide Glasses
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Noncoding RNA Research
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JOURNAL OF NONEQUILIBRIUM THERMODYNAMICS
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NonCoding RNA Investigation
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Nonlinear FEM analysis of poundinginvolved response of buildings under nonuniform earthquake excitation
PublicationThe aim of the paper is to show the results of the study investigating the influence of nonuniform earthquake excitation, due to spatial seismic effects connected with the propagation of seismic wave, on the poundinginvolved response of two buildings. The threedimensional nonlinear FEM analysis has been conducted using the detailed models of colliding structures. Acceleration records for different structural supports have been...

Mariusz Kaczmarek dr hab. inż.
PeopleReceived 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...

Nonlinear Excitation of the NonWave Perturbations by the Magnetoacoustic Waves in the NonIsentropic Plasma
PublicationNonlinear 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...

INTERNATIONAL JOURNAL OF NONLINEAR MECHANICS
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Special Issue: “NonDestructive Testing of Structures”
PublicationThe Special Issue “NonDestructive 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 noninvasive diagnostics, including such topics as condition assessments of civil and mechanical structures and connections of structural elements, the...

Nondestructive Testing of Wooden Elements
PublicationExamining 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...

Pipelined division of signed numbers with the use of residue arithmetic for small number range with the programmable gate array
PublicationIn 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 lookup. In order to limit the lookup table address an algorithm based on segmentation of the divisor into two segments...

Discrete identification of continuous nonlinear and nonstationary dynamical systems that is insensitive to noise correlation and measurement outliers
PublicationThe paper uses specific parameter estimation methods to identify the coefficients of continuoustime models represented by linear and nonlinear 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 discretetime descriptions retain the original continuous parameterization...

Mixed neuroendocrine nonneuroendocrine neoplasm (MiNEN)  Male, 65  Tissue image [3200630011576491]
Open Research DataThis is the histopathological image of STOMACH tissue sample obtained in Medical University Gdańsk and deposited in ZMDLGUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.

Mixed neuroendocrine nonneuroendocrine neoplasm (MiNEN)  Male, 65  Tissue image [3200630011574561]
Open Research DataThis is the histopathological image of STOMACH tissue sample obtained in Medical University Gdańsk and deposited in ZMDLGUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.

Mixed neuroendocrine nonneuroendocrine neoplasm (MiNEN)  Male, 65  Tissue image [3200630011579601]
Open Research DataThis is the histopathological image of LYMPH NODES tissue sample obtained in Medical University Gdańsk and deposited in ZMDLGUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.