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Search results for: TENSOR CALCULUS
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SENSORS
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e-mentor
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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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Journal of Sensors and Sensor Systems
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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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SENSORS AND ACTUATORS B-CHEMICAL
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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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Application of electrochemical sensors and sensor matrixes for measurement of odorous chemical compounds
PublicationIn this paper describes the principle of operation of the electrochemical sensors and the sensor matrixes comprised of electrochemical sensors intended for measurement of odorous compounds. Critical comparison of these sensors’ advantages and disadvantages has been made. The fields of economy contributing to release of odours and the potential sources of their emission have been identified. Commercially available electrochemical...
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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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Chapter 11 – Application of Chemical Sensors and Sensor Matrixes to Air Quality Evaluation
PublicationIndoor and outdoor air quality is one of the key factors influencing human health. However, air quality evaluation is not easy task. Air is a complex system, which is subjected to changes even within short period of time. Progress in analytical methods and analytical tools provides increasingly more reliable information on the condition and quality of indoor and outdoor air. This progress, however, generates an increase in the...
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On the sensitivity, selectivity, sensory information and optimalsize of resistive chemical sensors
PublicationWykorzystano pojęcia teorii informacji do określenia możliwości poprawy selektywności i czujności rezystancyjnych sensorów gazu. Podano ogólne rozważania dotyczące limitu selektywnoœci dla tych sensorów. Porównano iloraz sygnału do szumów oraz pojemność kanału informacyjnego dla sensorów chemicznych wykorzystujących jako sygnał zjawiska fluktuacyjne z klasycznymi sensorami charakteryzowanymi jedną wartością. Ogólne rozważania wsparto...
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IEEE SENSORS JOURNAL
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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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A measurement method for capacitive sensors based on a versatile direct sensor-to-microcontroller interface circuit
PublicationIn the paper, there is presented a new time-domain measurement method for determining the capacitance values of capacitive sensors, dedicated, among others, to capacitive relative humidity sensors. The method is based on a versatile direct sensor-to-microcontroller interface for microcontrollers with internal analog comparators (ACs) and with precision voltage reference sources, e.g. digital-to-analog converters (DACs). The reference...
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Fractional Calculus and Applied Analysis
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ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
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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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A measurement method for lossy capacitive relative humidity sensors based on a direct sensor-to-microcontroller interface circuit
PublicationA new time-domain measurement method for determining the capacitance and resistance values of lossy relative humidity capacitive sensors is presented. The method is based on a direct sensor-to-microcontroller interface for microcontrollers with internal analog comparators and timers. The interface circuit consists only of four reference resistors (two reference resistors if a microcontroller includes a voltage reference source),...
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Sztuczny sensor smaku a zmysł smaku
PublicationOmówiono klasy smaku i działanie zmysłu smaku, który odgrywa ogromną rolę w ocenie jakości żywności metodami organoleptycznymi. Metody te nie są w pełni obiektywne, stąd poszukuje się sztucznego sensora smaku. Przedstawiono szereg rozwiązań prowadzących do opracowania sensora smaku na większą skalę. Omówiono wybrane potencjometryczne i woltamperometryczne sensory smaku, a także ich handlowe modele.
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CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
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SENSORS AND ACTUATORS A-PHYSICAL
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Sensor Review
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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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Time-domain measurement methods for R, L and C sensors based on aversatile direct sensor-to-microcontroller interface circuit
PublicationtIn the paper new time-domain measurement methods for determining values of resistive (R), inductive(L) and capacitive (C) sensors based on a versatile direct sensor-to-microcontroller interface for microcon-trollers with internal analog-to-digital converters (ADCs) and analog comparators (ACs) are presented.The interface circuit consists of a reference resistor Rrworking as a voltage divider, a given R, L or C sensorand a microcontroller...
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BIOINFO Sensor Networks
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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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Tensor Decomposition for Imagined Speech Discrimination in EEG
PublicationMost of the researches in Electroencephalogram(EEG)-based Brain-Computer Interfaces (BCI) are focused on the use of motor imagery. As an attempt to improve the control of these interfaces, the use of language instead of movement has been recently explored, in the form of imagined speech. This work aims for the discrimination of imagined words in electroencephalogram signals. For this purpose, the analysis of multiple variables...
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Penser l'éducation
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ACS Sensors
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Photonic Sensors
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Telfor Journal
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Sensors International
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Measurement: Sensors
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SENSORS AND MATERIALS
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On Invariants of Fluid Mechanics Tensors
PublicationThis paper presents physical interpretations of the first and second invariants of tensors of fluid mechanics. Some examples of elementary applications and meanings are also given.
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Fibre-Optic pH Sensor
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Electrocatalytic nitrogen dioxide sensor.
PublicationOpisano konstrukcję i właściwości elektrokatalitycznego czujnika gazów na bazie domieszkowanego samarem tlenku ceru. Pomiary przeprowadzono w mieszaninie syntetycznego powietrza i dwutlenku azotu. Kształt odpowiedzi prądowo - napięciowej zależy od stężenia NO2.
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IET Wireless Sensor Systems
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International Journal of Sensor Networks
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ACM Transactions on Sensor Networks
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Sensor Letters
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