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Search results for: LOGIC DIFFERENTIAL CALCULUS
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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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Fractional Differential Calculus
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CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
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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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Homoclinics for singular strong force Lagrangian systems in R^N
PublicationWe will be concerned with the existence of homoclinics for second order Hamiltonian systems in R^N (N>2) given by Hamiltonians of the form H(t,q,p)=Φ(p)+V(t,q), where Φ is a G-function in the sense of Trudinger, V is C^2-smooth, periodic in the time variable, has a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin. Under a strong force type condition aroud the singular point ξ, we prove...
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On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces
PublicationIn this paper, we investigate the properties of the Fenchel–Moreau conjugate of G-function with respect to the coupling function c(x, A) = |A[x]2 |. We provide conditions that guarantee that the conjugate is also a G-function. We also show that if a G-function G is twice differentiable and its second derivative belongs to the Orlicz space generated by the Fenchel–Moreau conjugate of G then the modular generated by G is twice differentiable...
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The Palais–Smale condition for the Hamiltonian action on a mixed regularity space of loops in cotangent bundles and applications
PublicationWe show that the Hamiltonian action satisfies the Palais-Smale condition over a “mixed regular- ity” space of loops in cotangent bundles, namely the space of loops with regularity H^s, s ∈ (1/2, 1), in the baseand H^{1−s} in the fiber direction. As an application, we give a simplified proof of a theorem of Hofer-Viterbo on the existence of closed characteristic leaves for certain contact type hypersufaces in cotangent bundles.
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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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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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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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Rengel Cane Sia Doctoral Candidate
PeopleI'm Rengel, born and raised in the Philippines. As an undergraduate I did kinetic modeling on Copper-catalyzed atom transfer radical addition (ATRA). Then I was inspired to do both theoretical and experimental studies, which led me to propose my master's thesis on Synthesis, Computational, Electrochemical, and Photoconductivity Studies on Naphthalene and its derivatives. This led to a master's degree in Chemistry in the Mindanao...
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Physics-guided neural networks (PGNNs) to solve differential equations for spatial analysis
PublicationNumerous examples of physically unjustified neural networks, despite satisfactory performance, generate contradictions with logic and lead to many inaccuracies in the final applications. One of the methods to justify the typical black-box model already at the training stage and lead to many inaccuracies in the final applications. One of the methods to justify the typical black-box model already at the training stage involves extending...
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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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Topological invariants for equivariant flows: Conley index and degree
PublicationAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...
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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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Numerical Methods for Partial Differential Equations
e-Learning CoursesCourse description: This course focuses on modern numerical techniques for linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations (PDEs), and integral equations fundamental to a large variety of applications in science and engineering. Topics include: formulations of problems in terms of initial and boundary value problems; finite difference and finite element discretizations; boundary element approach;...
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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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Elements of logic and epistemology
e-Learning CoursesThis course serves as an introduction to the problems of epistemology and logic.
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Analysis of Learning Outcomes in Medical Education with the Use of Fuzzy Logic
PublicationThe national curricula of the EU member states are structured around learning outcomes, selected according to Bloom’s Taxonomy. The authors of this paper claim that using Bloom’s Taxonomy to phrase learning outcomes in medical education in terms of students’ achievements is difficult and unclear. This paper presents an efficient method of assessing course learning outcomes using Fuzzy Logic.
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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.
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Logic
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The Implementation of Fuzzy Logic in Forecasting Financial Ratios
PublicationThis paper is devoted to the issue of forecasting financial ratios. The objective of the conducted research is to develop a predictive model with the use of an innovative methodology, i.e., fuzzy logic theory, and to evaluate its effectiveness. Fuzzy logic has been widely used in machinery, robotics and industrial engineering. This paper introduces the use of fuzzy logic for the financial analysis of enterprises. While many current...
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Different types of solvability conditions for differential operators
PublicationSolvability conditions for linear differential equations are usually formulated in terms of orthogonality of the right-hand side to solutions of the homogeneous adjoint equation. However, if the corresponding operator does not satisfy the Fredholm property such solvability conditions may be not applicable. For this case, we obtain another type of solvability conditions, for ordinary differential equations on the real axis, and...
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Description Logic As A Common Software Engineering Artifacts Language
PublicationDescription logic is proposed as a powerful language able to support chosen software engineering process tasks like: requirements engineering, software architecture definition, software design and configuration management. To do this there is presented a correspondence between description logic and UML. Description logic based integrated software engineering process framework is proposed which owing to automatic knowledge inferring...
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On the Peano Theorem for Some Functional Differential Equations on Time Scale
PublicationThe Peano Theorem for some functional differential equations on time scale is proved. Assumptions are of Caratheodory type. Two counter examples for false Peano theorems in the literature are presented.
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Some applications of fractional order calculus
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A fuzzy logic model for forecasting exchange rates
PublicationThis article is devoted to the issue of forecasting exchange rates. The objective of the conducted research is to develop a predictive model with the use of an innovative methodology - fuzzy logic theory - and to evaluate its effectiveness in times of prosperity and during the financial crisis. The model is based on sets of rules written by the author in the form of IF-THEN, where expert knowledge is stored. This model is the result...
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Fuzzy logic in controlling flexible manufacturing cell
PublicationIn the present work a controlling method based on fuzzy rule base is proposed. Practical approaches are developed and focused on real time problems related to flexible manufacturing cell. Techniques for design and implementation of fuzzy systems in the framework of control production and quality states are presented. Keywords: controlling, manufacturing system, fuzzy logic, turning, burnishingW artykule przedstawiono propozycję...
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Restrained differential of a graph
PublicationGiven a graph $G=(V(G), E(G))$ and a vertex $v\in V(G)$, the {open neighbourhood} of $v$ is defined to be $N(v)=\{u\in V(G) :\, uv\in E(G)\}$. The {external neighbourhood} of a set $S\subseteq V(G)$ is defined as $S_e=\left(\cup_{v\in S}N(v)\right)\setminus S$, while the \emph{restrained external neighbourhood} of $S$ is defined as $S_r=\{v\in S_e : N(v)\cap S_e\neq \varnothing\}$. The restrained differential of a graph $G$ is...
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Description logic based generator of data-centric applications
PublicationThe knowledge stored in Ontology Management Systems (OMS) that originally has the form of expressions, can be seen as a user application specification or as knowledge provided by an expert. The generator of applications discussed in this paper is defined as a program that automatically generates an application that meets a certain specification stored in OMS. It is shown that it is possible to build a user interface for data management...
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Description logic based generator of data-centric applications
PublicationThe knowledge stored in Ontology Management Systems (OMS) that originally has the form of expressions, can be seen as a user application specification or as knowledge provided by an expert. The generator of applications discussed in this paper is defined as a program that automatically generates an application that meets a certain specification stored in OMS. It is shown that it is possible to build a user interface for data management...
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LOGIC 2024/2025
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Method of Decision-Making Logic Discovery in the Business Process Textual Data
PublicationGrowing amount of complexity and enterprise data creates a need for novel business process (BP) analysis methods to assess the process optimization opportunities. This paper proposes a method of BP analysis while extracting the knowledge about Decision-Making Logic (DML) in a form of taxonomy. In this taxonomy, researchers consider the routine, semi-cognitive and cognitive DML levels as functions of BP conceptual aspects of Resources,...
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The evidential value of dental calculus in the identification process
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5. Logic and epistemology
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Application of fuzzy logic to determine the odour intensity of model gas mixtures using electronic nose
PublicationThe paper presents the possibility of application of fuzzy logic to determine the odour intensity of model, ternary gas mixtures (α-pinene, toluene and triethylamine) using electronic nose prototype. The results obtained using fuzzy logic algorithms were compared with the values obtained using multiple linear regression (MLR) model and sensory analysis. As the results of the studies, it was found the electronic nose prototype along...
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Processing and querying description logic ontologies using cartographic approach
PublicationLogika opisowa (ang. description logic) jest formalizem reprezentacji wiedzy, który w ostatnich latach uzyskał dużą popularność pomiędzy inżynierami wiedzy. Po krótkim wprowadzeniu do formalizmu logiki opisowej artykuł prezentuje system wnioskowania opracowany na Politechnice Gdańskiej w ramach projektu PIPS 6 Programu Ramowego UE. System wnioskujący jest oparty na nowatorskiej metodzie kartograficznej, której podstawy również...
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Survey on fuzzy logic methods in control systems of electromechanical plants
PublicationРассмотрены алгоритмы управления электромеханическими системами с использованием теории нечеткой логики, приводятся основные положения их синтеза, рассматриваются методы анализа их устойчивости на основе нечетких функций Ляпунова. Эти алгоритмы чаще всего реализуются в виде различных регуляторов, применение которых целесообразно в системах, математическая модель которых не известна, не детерминирована или является строго нелинейной,...
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Elements of logic and epistemology
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A New, Reconfigurable Circuit Offering Functionality of AND and OR Logic Gates for Use in Algorithms Implemented in Hardware
PublicationThe paper presents a programmable (using a 1-bit signal) digital gate that can operate in one of two OR or AND modes. A circuit of this type can also be implemented using conventional logic gates. However, in the case of the proposed circuit, compared to conventional solutions, the advantage is a much smaller number of transistors necessary for its implementation. Circuit is also much faster than its conventional counterpart. The...
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Boundary problems for fractional differential equations
PublicationIn this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.
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Analysis of odour interactions in model gas mixtures using electronic nose and fuzzy logic
PublicationMeasurement and monitoring of air quality in terms of odour nuisance is an important problem. Although the source of these nuisances is different (e.g. wastewater treatment plants, municipal landfills), their common feature is that they are a complex mixture of odorants with different odour thresholds. An additional problem is occurrence of the odour interactions between mixture components. From a practical point of view, it would...
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Combining MUSHRA Test and Fuzzy Logic in the Evaluation of Benefits of Using Hearing Prostheses
PublicationAssessing the effectiveness of hearing aid fittings based on the benefits they provide is crucial but intricate. While objective metrics of hearing aids like gain, frequency response, and distortion are measurable, they do not directly indicate user benefits. Hearing aid performance assessment encompasses various aspects, such as compensating for hearing loss and user satisfaction. The authors suggest enhancing the widely used...
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Computer animation system based on rough sets and fuzzy logic
PublicationA fuzzy logic inference system was created, based on the analysis of animated motion features. The objective of the system is to facilitate the creation of high quality animation by analyzing personalized styles contained in numerous animations. Sequences portraying a virtual character acting with a differentiating personalized style (natural or exaggerated) and various levels of fluidity were prepared and subjectively evaluated....
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JOURNAL OF DIFFERENTIAL EQUATIONS
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Advances in Calculus of Variations
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Role patterns in IT projects teams - design of a selection module using fuzzy logic techniques
PublicationPresented paper introduces an approach based on usage of role patterns and modelling by the use of fuzzy logic tool for selection process with limitation to the area of IT projects environment. The article shows a concept of role patterns structures and their further usage in process of forming a fuzzy model dedicated to candidate assessment process support
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Fuzzy logic and production planning.
PublicationReferat prezentuje efektywność logiki rozmytej w projektowaniu procesów produkcyjnych. Przedstawiono algorytm i przesłanki zastosowania logiki rozmytej opartej o informacje eksperckie.
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Fuzzy logic in financial management
PublicationW rozdziale tym przedstawiono rozważania na temat możliwości prognozowania sytuacji finansowej gospodarstw domowych przy zastosowaniu logiki rozmytej. Autor zaproponował model składający się ze zmiennych wejściowych opartych na informacjach demograficznych i finansowych konsumentów - na przykład: wiek, wykształcenie, liczba dzieci, wynagrodzenie, stopień zabezpieczenia finansowego.
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Voltage and Reactive Power Load Flow Optimization in the Power System Using Fuzzy Logic
PublicationThe paper presents issues related to voltage control in the power system. An original method of reactive power flow optimization is considered, which leads to improved voltages in the power system and reduced active power losses. The optimization method is based on a procedure that employs fuzzy logic and is supported by a gradient search algorithm. The method has been implemented in PLANS software and verified.