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Search results for: NONNEWTONIAN CALCULUS
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Unifying Aspects of Generalized Calculus
PublicationNon-Newtonian calculus naturally unifies various ideas that have occurred over the years in the field of generalized thermostatistics, or in the borderland between classical and quantum information theory. The formalism, being very general, is as simple as the calculus we know from undergraduate courses of mathematics. Its theoretical potential is huge, and yet it remains unknown or unappreciated.
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Some applications of fractional order calculus
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The evidential value of dental calculus in the identification process
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Simple Fractal Calculus from Fractal Arithmetic
PublicationNon-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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Advances in Calculus of Variations
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Fractional Differential Calculus
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Modelling heat transfer in heterogeneous media using fractional calculus
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Modeling Heat Transfer in Heterogeneous Media Using Fractional Calculus
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Bell-Type Inequalities from the Perspective of Non-Newtonian Calculus
PublicationA 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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Fourier transforms on Cantor sets: A study in non-Diophantine 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 middle-third Cantor set. The formalism works also for fractals that are not self-similar.
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Neural Approximators for Variable-Order Fractional Calculus Operators (VO-FC)
PublicationThe paper presents research on the approximation of variable-order fractional operators by recurrent neural networks. The research focuses on two basic variable-order fractional operators, i.e., integrator and differentiator. The study includes variations of the order of each fractional operator. The recurrent neural network architecture based on GRU (Gated Recurrent Unit) cells functioned as a neural approximation for selected...
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Fractional Calculus and Applied Analysis
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Non-classical operational calculus applied to certain linear discrete time-system
PublicationW pracy zastosowano nieklasyczny rachunek operatorów do wyznaczania odpowiedzi pewnego dyskretnego układu dynamicznego. Pokazano metodę szczególnie przydatną do wyznaczania odpowiedzi pewnych dyskretnych niestacjonarnych układów dynamicznych, przy których zastosowanie przekształcenia Z sprawia duże trudności.
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Reliability Analysis of Data Storage Using Survival Signature and Logic Differential Calculus
PublicationThe Data storage system is an important part of any information system. All the necessary data that must be available for the successful operation of the information system are stored here. Therefore, it is advisable to think about the reliability of such a data storage system. As part of reliability engineering, it is possible to perform a reliability analysis of any system. Therefore, the data storage system can be analyzed as...
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Application of non-classical operational calculus to indicate hazards in numerical solutions of engineering problems
PublicationThe article addresses the application of non- classical operational calculus to approximative solutions of engineering problems. The engineering-sound examples show that a continuous–discrete problem transformation from differential unequivocal problem to a differential wildcard problem, triggering a change in solution quality. A number of approximative methods are capable to alter both quantitative and qualitative...
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Fractional Calculus Evaluation of Hyaluronic Acid Crosslinking in a Nanoscopic Part of Articular Cartilage Model System
PublicationThis work presents a study of the mechanism of physical crosslinking of hyaluronic acid in the presence of common phospholipids in synovial joint organ systems. Molecular dynamic simulations have been executed to understand the formation of hyaluronan networks at various phospholipid concentrations. The results of the simulations suggest that the mechanisms exhibit subdiffusion characteristics. Transportation quantities derive...
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ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
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CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
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Callus of American ginseng (Panax quinquefolius) as a source of ginsenosides – medicinal secondary metabolites
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Calculus of gallbladder with other cholecystitis - Female, 75 - Tissue image [5060730012998381]
Open Research DataThis is the histopathological image of GALLBLADDER 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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Calculus of gallbladder with other cholecystitis - Female, 53 - Tissue image [3110630005636871]
Open Research DataThis is the histopathological image of GALLBLADDER 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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Calculus of gallbladder with other cholecystitis - Female, 53 - Tissue image [3110630005635611]
Open Research DataThis is the histopathological image of GALLBLADDER 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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Calculus of gallbladder with other cholecystitis - Female, 75 - Tissue image [5060730012993001]
Open Research DataThis is the histopathological image of GALLBLADDER 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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Calculus of gallbladder with other cholecystitis - Female, 69 - Tissue image [6290730011495251]
Open Research DataThis is the histopathological image of GALLBLADDER tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: VS200 Olympus slide scanner (20x magnification) and saved to DICOM format.
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Calculus of gallbladder with other cholecystitis - Female, 75 - Tissue image [506073001299141]
Open Research DataThis is the histopathological image of GALLBLADDER 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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Cell Wall Epitopes and Endoploidy as Reporters of Embryogenic Potential in Brachypodium Distachyon Callus Culture
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Elicitation of solid callus cultures of Salvia miltiorrhiza Bunge with salicylic acid and a synthetic auxin (1-naphthaleneacetic acid)
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Induction of secondary metabolite production in transformated callus of Ammi majus L. grown after electromagnetic treatment of culture medium
PublicationW pracy przedstawiono wyniki badań, których celem było zbadanie wpływu elicytacji przy użyciu ADR-4, na produkcję metabolitów wtórnych. Elicytacja ADR-4 zwiększyła 2-krotnie zawartość bergaptenu. Porównano również efektywność 3 technik ekstrakcyjnych stosowanych do izolacji feuranokumaryn, kumaryn i ich glikozydów z kalusa A.majus. Ekstrakcja przy użyciu techniki ASE okazała się najbardziej efektywna.
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Field Cultivation and in vitro Cultures, Root-Forming Callus Cultures and Adventitious Root Cultures, of Panax quinquefolium as a Source of Ginsenosides
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Callus - Female, 35 - Tissue image [6290730011488801]
Open Research DataThis is the histopathological image of SKIN 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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Modélisation d'ordre non entier des machines synchrones. Modèle fréquentiel non linéaire, identification des paramètres, calcul de la réponse temporelle.
PublicationDans les réseaux d'énergie électrique contemporains, on assiste à une diversification considérable des différentes sources d'énergie. L'énergie produite est transformée par une grande quantité de dispositifs électriques pour être finalement acheminée à diverses installations électriques. Il devient donc primordial d'améliorer les modèles des différents composants électriques afin de pouvoir prévoir les interactions entre eux et...
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If Gravity is Geometry, is Dark Energy just Arithmetic?
PublicationArithmetic 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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Variable Order Differential Models of Bone Remodelling * *This work was supported by FCT, through IDMEC, under LAETA, projects UID/EMS/50022/2013, BoneSys, joint Polish-Portuguese project Modelling and controlling cancer evolution using fractional calculus, PERSEIDS (PTDC/EMS-SIS/0642/2014) and IF/00653/2012
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Non-Newtonian Mathematics Instead of Non-Newtonian 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)),...
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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.
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Fractional Order Dynamic Positioning Controller
PublicationImproving the performance of Dynamic Positioning System in such applications as station keeping, position mooring and slow speed references tracking requires improving the position and heading control precision. These goals can be achieved through the improvement of the ship control system. Fractional-order calculus is a very useful tool which extends classical, integer-order calculus and is used in contemporary modeling and control...
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Revista Internacional de Metodos Numericos para Calculo y Diseno en Ingenieria
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Determination of the shape of the CFGFT cylindrical column based on laboratory tests
PublicationAnalyses were carried out on glass-fibre-reinforced polymer tube columns with reference to laboratory tests. The angles of the glass fibre beams were 20◦, 55◦ and 85◦. The study employed non-classical operational calculus. Various modulated harmonic signal shapes were considered for columns and tubes at buckling. The buckling loads were assessed and compared for different models.
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Chemistry and Nanochemistry 2023
e-Learning CoursesWe start from General Chemistry, including: calculus in chemistry, bonds, balancing the chemical reactions, redox reactions, electrochemistry, pH, acids, bases, salts, oxides, organic molecules, and many informations about synthesis, analysis and applications in nanochemistry.
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Modélisation des machines synchrones par des systèmes d’ordre un demi. Procédure d’identification des paramètres du schéma équivalent, analyse de sensibilité des paramètres.
PublicationCe livre présente de nouveaux modèles de machines synchrones (alternateurs à pôles saillants et alternateur à aimants permanents). Les schémas équivalents de ces modèles sont établis en utilisant la modélisation fractionnaire. Ceci permet de construire des modèles les plus compacts possibles, c’est-à-dire d’ordre réduit. Les branches (R-L) dans le schéma équivalent classique, décrivant les différentes parties de la machine où les...
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Variational Method of Finding Streamlines in Ring Cascades for Creeping Flows
PublicationThis paper presents a new, analytical method of finding streamlinesfor creeping flows inside a ring cascade which is composed of an infinite number of infinitely thin blades. An analytical solution has been obtained through minimisation of a dissipation functional by means of variational calculus method. The necessary condition for optimum of a functional gives the Stokes equation if some additional assumptions are introduced....
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Crystallization of space: Space-time 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 space-time can be generated by means of homogeneous spaces associated...
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Arithmetic Loophole in Bell's Theorem: Overlooked Threat to Entangled-State Quantum Cryptography
PublicationBell’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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Numerical Investigation of Nuclear Reactor Kinetic and Heat Transfer Fractional Model with Temperature Feedback
PublicationAbstract—In the paper, the numerical results concerning the kinetics and proposed heat exchange models in nuclear reactor based on fractional calculus are presented for typical inputs. Two fractional models are proposed and compared with the model based on ordinary derivative. The first fractional model is based on one of the generalized Cattaneo equations. The second one is based on replacing the ordinary to fractional order of...
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Comparative analysis of mechanical conditions in bone union following first metatarsophalangeal joint arthrodesis with varied locking plate positions: A finite element analysis
PublicationFirst metatarsophalangeal joint arthrodesis is a typical medical treatment performed in cases of arthritis or joint deformity. The gold standard for this procedure is arthrodesis stabilisation with the dorsally positioned plate. However, according to the authors’ previous studies, medially positioned plate provides greater bending stiffness. It is worth to compare the mechanical conditions for bone formation in the fracture callus...
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Analysis of Transformation Methods of Hydroacoustic and Optoelectronic Data Based on the Tombolo Measurement Campaign in Sopot
PublicationMeasurements in the coastal zone are carried out using various methods, including Global Navigation Satellite Systems (GNSS), hydroacoustic and optoelectronic methods. Therefore, it is necessary to develop coordinate transformation models that will enable the conversion of data from the land and marine parts to one coordinate system. The article presents selected issues related to the integration of geodetic and hydrographic data....
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Simulation of Signal Propagation Along Fractional-Order Transmission Lines
PublicationIn this paper, the simulation method of signal propagation along fractional-order (FO) transmission lines is presented. Initially, fractional calculus and the model of FO transmission line are introduced. Then, the algorithm allowing for simulation of the nonmonochromatic wave propagation along FO transmission lines is presented. It employs computations in the frequency domain, i.e., an analytical excitation is transformed to the...
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Functional delay fractional equations
PublicationIn this paper, we discuss functional delay fractional equations. A Banach fixed point theorem is applied to obtain the existence (uniqueness) theorem. We also discuss such problems when a delay argument has a form α(t) = αt, 0 < α < 1, by Rusing the method of successive approximations. Some existence results are also formulated in this case. An example illustrates the main result.
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About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof
PublicationRecently, the fractional Noether's theorem derived by G. Frederico and D.F.M. Torres in [10] was proved to be wrong by R.A.C. Ferreira and A.B. Malinowska in (see [7]) using a counterexample and doubts are stated about the validity of other Noether's type Theorem, in particular ([9],Theorem 32). However, the counterexample does not explain why and where the proof given in [10] does not work. In this paper, we make a detailed analysis...
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Systems of Nonlinear Fractional Differential Equations
PublicationUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives D(T)(q)x and D(T)(q)y. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.