Search results for: functional random differential equation

Authors: Ramzi B. Albadarneh

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In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given.

Keywords: conformable fractional derivative, finite difference formula, fractional derivative, finite difference formula

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Authors: Ofosuhene O. Apenteng, Noor Azina Ismail

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Recently tourism is a major foreign exchange earner in the World. In this paper, we propose the mathematical model to study the impact of tourists on the spread of HIV incidences using compartmental differential equation models. Simulation studies of reproduction number are used to demonstrate new insights on the spread of HIV disease. The periodogram analysis of a time series was used to determine the speed at which the disease is spread. The results indicate that with the persistent flow of tourism into a country, the disease status has increased the epidemic rate. The result suggests that the government must put more control on illegal prostitution, unprotected sexual activity as well as to emphasis on prevention policies that include the safe sexual activity through the campaign by the tourism board.

Keywords: HIV/AIDS, mathematical transmission modeling, tourists, stability, simulation

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Authors: Seyedeh Samaneh Hosseini Yousefi

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Space does not play role just in mentioning the place or locations. It also takes part in people attendance and social structures. Urban space is of substantial aspects of city which is a public sphere for free and unlimited appearance of citizens. Along with such appearances and regarding physical, environmental and functional conditions, different personal and social behaviors can be seen and analyzed toward people. The main principle of an urban space is including social relations and communications. In this survey, urban space has been referred to one in which physical, environmental and functional attractions cause pause and staying of people. Surveys have shown that urban designers have discussed about place more than architects or planners. With attention to mutual relations between urban space, society and civilization, proper policy making and planning are essential due to achieving an ideal urban space. The survey has been decided to analyze the effect of functional and physical structure of urban spaces on citizens' social behaviors. Hence, Valiasr crossroads, Tehran identified public space, has been selected in which analytic-descriptive method utilized. To test the accuracy of assumptions, statistical test has been accomplished by SPSS. Findings have shown that functional structure affects social behaviors, relations, integration and participation more than physical structure does.

Keywords: citizens' social behavior, functional structure, physical structure, urban space

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Authors: Wafa Slaibi Alsharafat

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Genetic algorithms (GA) are random algorithms as random numbers that are generated during the operation of the algorithm determine what happens. This means that if GA is applied twice to optimize exactly the same problem it might produces two different answers. In this project, we propose an evolutionary algorithm and Genetic Algorithm (GA) to be implemented in symmetric encryption and decryption. Here, user's message and user secret information (key) which represent plain text to be transferred into cipher text.

Keywords: GA, encryption, decryption, crossover

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: Faith-Michael E. Uzoka, Boluwaji A. Akinnuwesi, Taiwo Amoo, Flora Aladi, Stephen Fashoto, Moses Olaniyan, Joseph Osuji

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The overarching aim of this study is to develop a soft-computing system for the differential diagnosis of tropical diseases. These conditions are of concern to health bodies, physicians, and the community at large because of their mortality rates, and difficulties in early diagnosis due to the fact that they present with symptoms that overlap, and thus become ‘confusable’. We report on the first phase of our study, which focuses on the development of a fuzzy cognitive map model for early differential diagnosis of tropical diseases. We used malaria as a case disease to show the effectiveness of the FCM technology as an aid to the medical practitioner in the diagnosis of tropical diseases. Our model takes cognizance of manifested symptoms and other non-clinical factors that could contribute to symptoms manifestations. Our model showed 85% accuracy in diagnosis, as against the physicians’ initial hypothesis, which stood at 55% accuracy. It is expected that the next stage of our study will provide a multi-disease, multi-symptom model that also improves efficiency by utilizing a decision support filter that works on an algorithm, which mimics the physician’s diagnosis process.

Keywords: medical diagnosis, tropical diseases, fuzzy cognitive map, decision support filters, malaria differential diagnosis

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: explicit group method, finite difference, helmholtz equation, rotated grid, standard grid

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Suleiman Bashir Adamu, Lawan Sani Taura

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We study the role of boundary conditions via -symmetric quantum mechanics, where denotes parity operator and denotes time reversal operator. Using the one-dimensional Schrödinger Hamiltonian for a free particle in an infinite square well, we introduce symmetric boundary conditions. We find solutions of the 1D Klein-Gordon equation for a free particle in an infinite square well with Hermitian boundary and symmetry boundary conditions, where in both cases the energy eigenvalues and eigenfunction, respectively, are obtained.

Keywords: Eigenvalues, Eigenfunction, Hamiltonian, Klein- Gordon equation, PT-symmetric quantum mechanics

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Authors: Atousa Ataieyan, Salvador A. Gomez-Lopera, Gennaro Sepede

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Today, due to the growing urban population and consequently, the increasing water demand in cities, the amount of contaminants entering the water resources is increasing. This can impose harmful effects on the quality of the downstream water. Therefore, predicting the concentration of discharged pollutants at different times and distances of the interested area is of high importance in order to carry out preventative and controlling measures, as well as to avoid consuming the contaminated water. In this paper, the concentration distribution of an injected conservative pollutant in a square reservoir containing four symmetric blocks and three sources using Finite Volume Method (FVM) is simulated. For this purpose, after estimating the flow velocity, classical Advection-Diffusion Equation (ADE) has been discretized over the studying domain by Backward Time- Backward Space (BTBS) scheme. Then, the discretized equations for each node have been derived according to the initial condition, boundary conditions and point contaminant sources. Finally, taking into account the appropriate time step and space step, a computational code was set up in MATLAB. Contaminant concentration was then obtained at different times and distances. Simulation results show how using BTBS differentiating scheme and FVM as a numerical method for solving the partial differential equation of transport is an appropriate approach in the case of two-dimensional contaminant transfer in an advective-diffusive flow.

Keywords: BTBS differentiating scheme, contaminant concentration, finite volume, mass transfer, water pollution

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Authors: Nurul Izzati Abd Karim, Samira Albati Kamaruddin, Rozaimi Che Hasan

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The appropriate petrophysical relationship is needed for Soil Water Content (SWC) estimation especially when using Ground Penetrating Radar (GPR). Ground penetrating radar is a geophysical tool that provides indirectly the parameter of SWC. This paper examines the performance of few published petrophysical relationships to obtain SWC estimates from in-situ GPR common- offset survey measurements with gravimetric measurements at peat soil area. Gravimetric measurements were conducted to support of GPR measurements for the accuracy assessment. Further, GPR with dual frequencies (250MHhz and 700MHz) were used in the survey measurements to obtain the dielectric permittivity. Three empirical equations (i.e., Roth’s equation, Schaap’s equation and Idi’s equation) were selected for the study, used to compute the soil water content from dielectric permittivity of the GPR profile. The results indicate that Schaap’s equation provides strong correlation with SWC as measured by GPR data sets and gravimetric measurements.

Keywords: common-offset measurements, ground penetrating radar, petrophysical relationship, soil water content

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Authors: Nilay K. Doshi

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A theoretical probe describing the excited energy states of the electron density surrounding a nanoparticle (NP) is presented. An electromagnetic (EM) wave interacts with a NP much smaller than the incident wavelength. The plasmon that oscillates locally around the NP comprises of excited conduction electrons. The system is based on the Jellium model of a cluster of metal atoms. Hohenberg-Kohn (HK) equations and the variational Kohn-Sham (SK) scheme have been used to obtain the NP electron density in the ground state. Furthermore, a time-dependent density functional (TDDFT) theory is used to treat the excited states in a density functional theory (DFT) framework. The non-interacting fermionic kinetic energy is shown to be a functional of the electron density. The time dependent potential is written as the sum of the nucleic potential and the incoming EM field. This view of the quantum oscillation of the electron density is a part of the localized surface plasmon resonance.

Keywords: electron density, energy, electromagnetic, DFT, TDDFT, plasmon, resonance

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Authors: Lule Basha, Eralda Gjika

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The exchange rate is one of the most important economic variables, especially for a small, open economy such as Albania. Its effect is noticeable in one country's competitiveness, trade and current account, inflation, wages, domestic economic activity, and bank stability. This study investigates the fluctuation of Albania’s exchange rates using monthly average foreign currency, Euro (Eur) to Albanian Lek (ALL) exchange rate with a time span from January 2008 to June 2021, and the macroeconomic factors that have a significant effect on the exchange rate. Initially, the Random Forest Regression algorithm is constructed to understand the impact of economic variables on the behavior of monthly average foreign currencies exchange rates. Then the forecast of macro-economic indicators for 12 months was performed using time series models. The predicted values received are placed in the random forest model in order to obtain the average monthly forecast of the Euro to Albanian Lek (ALL) exchange rate for the period July 2021 to June 2022.

Keywords: exchange rate, random forest, time series, machine learning, prediction

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Authors: Hedia El Ourabi, Marc Alexandre Tomiuk, Ahmed Khalil Ben Ayed

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The aim of this study is to investigate the effects of the labeling cues traceability (T), health claim (HC), and verification of health claim (VHC) on consumer affective response and sensory appeal toward a wide array of functional food carriers (FFC). Predominantly, research in the food area has tended to examine the effects of these information cues independently on cognitive responses to food product offerings. Investigations and findings of potential interaction effects among these factors on effective response and sensory appeal are therefore scant. Moreover, previous studies have typically emphasized single or limited sets of functional food products and categories. In turn, this study considers five food product categories enriched with omega-3 fatty acids, namely: meat products, eggs, cereal products, dairy products and processed fruits and vegetables. It is, therefore, exhaustive in scope rather than exclusive. An investigation of the potential simultaneous effects of these information cues on the affective responses and sensory appeal of consumers should give rise to important insights to both functional food manufacturers and policymakers. A mixed (2 x 3) x (2 x 5) between-within subjects factorial ANOVA design was implemented in this study. T (two levels: completely traceable or non-traceable) and HC (three levels: functional health claim, or disease risk reduction health claim, or disease prevention health claim) were treated as between-subjects factors whereas VHC (two levels: by a government agency and by a non-government agency) and FFC (five food categories) were modeled as within-subjects factors. Subjects were randomly assigned to one of the six between-subjects conditions. A total of 463 questionnaires were obtained from a convenience sample of undergraduate students at various universities in the Montreal and Ottawa areas (in Canada). Consumer affective response and sensory appeal were respectively measured via the following statements assessed on seven-point semantic differential scales: ‘Your evaluation of [food product category] enriched with omega-3 fatty acids is Unlikeable (1) / Likeable (7)’ and ‘Your evaluation of [food product category] enriched with omega-3 fatty acids is Unappetizing (1) / Appetizing (7).’ Results revealed a significant interaction effect between HC and VHC on consumer affective response as well as on sensory appeal toward foods enriched with omega-3 fatty acids. On the other hand, the three-way interaction effect between T, HC, and VHC on either of the two dependent variables was not significant. However, the triple interaction effect among T, VHC, and FFC was significant on consumer effective response and the interaction effect among T, HC, and FFC was significant on consumer sensory appeal. Findings of this study should serve as impetus for functional food manufacturers to closely cooperate with policymakers in order to improve on and legitimize the use of health claims in their marketing efforts through credible verification practices and protocols put in place by trusted government agencies. Finally, both functional food manufacturers and retailers may benefit from the socially-responsible image which is conveyed by product offerings whose ingredients remain traceable from farm to kitchen table.

Keywords: functional foods, labeling cues, effective appeal, sensory appeal

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Authors: Joon-Hoon Park

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In this paper the rationalized Haar transform is applied for distributed parameter system identification and estimation. A distributed parameter system is a dynamical and mathematical model described by a partial differential equation. And system identification concerns the problem of determining mathematical models from observed data. The Haar function has some disadvantages of calculation because it contains irrational numbers, for these reasons the rationalized Haar function that has only rational numbers. The algorithm adopted in this paper is based on the transform and operational matrix of the rationalized Haar function. This approach provides more convenient and efficient computational results.

Keywords: distributed parameter system, rationalized Haar transform, operational matrix, system identification

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Authors: A. Khernane, N. Khelil, L. Djerou

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The aim of this work is to study the numerical implementation of the Hilbert uniqueness method for the exact boundary controllability of Euler-Bernoulli beam equation. This study may be difficult. This will depend on the problem under consideration (geometry, control, and dimension) and the numerical method used. Knowledge of the asymptotic behaviour of the control governing the system at time T may be useful for its calculation. This idea will be developed in this study. We have characterized as a first step the solution by a minimization principle and proposed secondly a method for its resolution to approximate the control steering the considered system to rest at time T.

Keywords: boundary control, exact controllability, finite difference methods, functional optimization

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Authors: Razieh Khalafi

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Myocardial infarction (MI) or acute myocardial infarction (AMI), commonly known as a heart attack, occurs when blood flow stops to part of the heart causing damage to the heart muscle. An ECG can often show evidence of a previous heart attack or one that's in progress. The patterns on the ECG may indicate which part of your heart has been damaged, as well as the extent of the damage. In chaos theory, the correlation dimension is a measure of the dimensionality of the space occupied by a set of random points, often referred to as a type of fractal dimension. In this research by considering ECG signal as a random walk we work on forecasting the oncoming heart attack by analyzing the ECG signals using the correlation dimension. In order to test the model a set of ECG signals for patients before and after heart attack was used and the strength of model for forecasting the behavior of these signals were checked. Results shows this methodology can forecast the ECG and accordingly heart attack with high accuracy.

Keywords: heart attack, ECG, random walk, correlation dimension, forecasting

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Authors: Katsumi Hirata

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To develop the useful acoustic environmental recognition system, the method of estimating 3D-position of a stationary random acoustic source using bispectral analysis of 4-point detected signals is proposed. The method uses information about amplitude attenuation and propagation delay extracted from amplitude ratios and angles of auto- and cross-bispectra of the detected signals. It is expected that using bispectral analysis affects less influence of Gaussian noises than using conventional power spectral one. In this paper, the basic principle of the method is mentioned first, and its validity and features are considered from results of the fundamental experiments assumed ideal circumstances.

Keywords: 4-point detection, a stationary random acoustic source, auto- and cross-bispectra, estimation of 3D-position

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Authors: Kritika Bansal, Akwinder Kaur, Shruti Gujral

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In this paper, the approach of denoising is solved by using a new hybrid technique which associates the different denoising methods. Wavelet thresholding and anisotropic diffusion filter are the two different filters in our hybrid techniques. The Wavelet thresholding removes the noise by removing the high frequency components with lesser edge preservation, whereas an anisotropic diffusion filters is based on partial differential equation, (PDE) to remove the speckle noise. This PDE approach is used to preserve the edges and provides better smoothing. So our new method proposes a combination of these two filtering methods which performs better results in terms of peak signal to noise ratio (PSNR), coefficient of correlation (COC) and equivalent no of looks (ENL).

Keywords: denoising, anisotropic diffusion filter, multiplicative noise, speckle, wavelets

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Authors: Cunyu Zhang

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Based on Systemic Functional Linguistics, this paper aims to explore the complex aspectuality system of English. This study shows that the complex aspectuality is classified into complex viewpoint aspect which refers to the homogeneous or heterogeneous ways continuously viewing on the same situation by the speaker and complex situation aspect which is the combined configuration of the internal time schemata of situation. Through viewpoint shifting and repeating, the complex viewpoint aspect is formed in two combination ways. Complex situation aspect is combined by the way of hypotactic verbal complex and the limitation of participant and circumstance in a clause.

Keywords: aspect series, complex situation aspect, complex viewpoint aspect, systemic functional linguistics

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Authors: Malika El Kyal, Ahmed Machmoum

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We prove the superlinear convergence of asynchronous multi-splitting methods applied to differential equations. This study is based on the technique of nested sets. It permits to specify kind of the convergence in the asynchronous mode.The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, ODE

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Authors: G. C. Tikkiwal, Mukesh Upadhyay

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During the surveillance operations at war or peace time, the Radar operator gets a scatter of targets over the screen. This may be a tracked vehicle like tank vis-à-vis T72, BMP etc, or it may be a wheeled vehicle like ALS, TATRA, 2.5Tonne, Shaktiman or moving the army, moving convoys etc. The radar operator selects one of the promising targets into single target tracking (STT) mode. Once the target is locked, the operator gets a typical audible signal into his headphones. With reference to the gained experience and training over the time, the operator then identifies the random target. But this process is cumbersome and is solely dependent on the skills of the operator, thus may lead to misclassification of the object. In this paper, we present a technique using mathematical and statistical methods like fast fourier transformation (FFT) and principal component analysis (PCA) to identify the random objects. The process of classification is based on transforming the audible signature of target into music octave-notes. The whole methodology is then automated by developing suitable software. This automation increases the efficiency of identification of the random target by reducing the chances of misclassification. This whole study is based on live data.

Keywords: radar target, FFT, principal component analysis, eigenvector, octave-notes, DSP

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Authors: Ammara Mehmood, Aneela Zameer, Muhammad Asif Zahoor Raja, Muhammad Faisal Fateh

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In this work, the strength of bio-inspired computational intelligence based technique is exploited for parameter estimation for the periodic signals using Continuous Differential Evolution (CDE) by defining an error function in the mean square sense. Multidimensional and nonlinear nature of the problem emerging in sinusoidal signal models along with noise makes it a challenging optimization task, which is dealt with robustness and effectiveness of CDE to ensure convergence and avoid trapping in local minima. In the proposed scheme of Continuous Differential Evolution based Signal Parameter Estimation (CDESPE), unknown adjustable weights of the signal system identification model are optimized utilizing CDE algorithm. The performance of CDESPE model is validated through statistics based various performance indices on a sufficiently large number of runs in terms of estimation error, mean squared error and Thiel’s inequality coefficient. Efficacy of CDESPE is examined by comparison with the actual parameters of the system, Genetic Algorithm based outcomes and from various deterministic approaches at different signal-to-noise ratio (SNR) levels.

Keywords: parameter estimation, bio-inspired computing, continuous differential evolution (CDE), periodic signals

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Authors: Tamer M. El-Messery

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By-products from sunflower oil extraction, such as sunflower cakes, are rich sources of proteins with desirable functional properties for the food industry. However, challenges such as sensory drawbacks and the presence of phenolic compounds have hindered their widespread use. In this study, sunflower protein concentrates were obtained from sunflower cakes using different ant-greening solvents (ascorbic acid (ASC) and N-acetylcysteine (NAC)), and their functional properties were evaluated. The color of extracted proteins ranged from dark green to yellow, where the using of ASC and NAC agents enhanced the color. The protein concentrates exhibited high solubility (>70%) and antioxidant activity, with hydrophobicity influencing emulsifying activity. Emulsions prepared with these proteins showed stability and microencapsulation efficiency. Incorporation of protein concentrates into low-fat whipping cream formulations increased overrun and affected color characteristics. Rheological studies demonstrated pseudoplastic behavior in whipped cream, influenced by shear rates and protein content. Overall, sunflower protein isolates showed promising functional properties, indicating their potential as valuable ingredients in food formulations.

Keywords: functional properties, sunflower protein concentrates, antioxidant capacity, ant-greening agents, low-fat whipping cream

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Authors: L. Bikulciene, E. Venskaityte, G. Jarusevicius

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Non-stationary and nonlinear signals generated by living complex systems defy traditional mechanistic approaches, which are based on homeostasis. Previous our studies have shown that the evaluation of the interactions of physiological signals by using special analysis methods is suitable for observation of physiological processes. It is demonstrated the possibility of using deep physiological model, based interpretation of the changes of the human body’s functional states combined with an application of the analytical method based on matrix theory for the physiological signals analysis, which was applied on high risk cardiac patients. It is shown that evaluation of cardiac signals interactions show peculiar for each individual functional changes at the onset of hemodynamic restoration procedure. Therefore we suggest that the alterations of functional state of the body, after patients overcome surgery can be complemented by the data received from the suggested approach of the evaluation of functional variables interactions.

Keywords: cardiac diseases, complex systems theory, ECG analysis, matrix analysis

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Authors: Rizwan Rizwan

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This paper provides an overview of Federated Learning (FL) and its application in enhancing data security, privacy, and efficiency. FL utilizes three distinct architectures to ensure privacy is never compromised. It involves training individual edge devices and aggregating their models on a server without sharing raw data. This approach not only provides secure models without data sharing but also offers a highly efficient privacy--preserving solution with improved security and data access. Also we discusses various frameworks used in FL and its integration with machine learning, deep learning, and data mining. In order to address the challenges of multi--party collaborative modeling scenarios, a brief review FL scheme combined with an adaptive gradient descent strategy and differential privacy mechanism. The adaptive learning rate algorithm adjusts the gradient descent process to avoid issues such as model overfitting and fluctuations, thereby enhancing modeling efficiency and performance in multi-party computation scenarios. Additionally, to cater to ultra-large-scale distributed secure computing, the research introduces a differential privacy mechanism that defends against various background knowledge attacks.

Keywords: federated learning, differential privacy, gradient descent strategy, convergence, stability, threats

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Authors: BenedictI Ita, Etido P. Inyang

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In this work, the resolutions of the N-dimensional Schrödinger equation with the screened modified Kratzerplus inversely quadratic Yukawa potential (SMKIQYP) have been obtained with the Greene-Aldrich approximation scheme using the Nikiforov-Uvarov method. The eigenvalues and the normalized eigenfunctions are obtained. We then apply the energy spectrum to study four (HCl, N₂, NO, and CO) diatomic molecules. The results show that the energy spectra of these diatomic molecules increase as quantum numbers increase. The energy equation was also used to calculate the partition function and other thermodynamic properties. We predicted the partition function of CO and NO. To check the accuracy of our work, the special case (Modified Kratzer and screened Modified Kratzer potentials) of the collective potential energy eigenvalues agrees excellently with the existing literature.

Keywords: Schrödinger equation, Nikiforov-Uvarov method, modified screened Kratzer, inversely quadratic Yukawa potential, diatomic molecules

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Authors: Somar Boubou, Tatsuo Narikiyo, Michihiro Kawanishi

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In this work, we address the problem of 3D object recognition with depth sensors such as Kinect or Structure sensor. Compared with traditional approaches based on local descriptors, which depends on local information around the object key points, we propose a global features based descriptor. Proposed descriptor, which we name as Differential Histogram of Normal Vectors (DHONV), is designed particularly to capture the surface geometric characteristics of the 3D objects represented by depth images. We describe the 3D surface of an object in each frame using a 2D spatial histogram capturing the normalized distribution of differential angles of the surface normal vectors. The object recognition experiments on the benchmark RGB-D object dataset and a self-collected dataset show that our proposed descriptor outperforms two others descriptors based on spin-images and histogram of normal vectors with linear-SVM classifier.

Keywords: vision in control, robotics, histogram, differential histogram of normal vectors

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Authors: Joseph Amponsah

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This research proposes an equation to predict and determine the momentum source equation term after factoring in the radial friction between the fluid and the blades and the impeller's propulsive power. This research aims to look at how CFD software can be used to predict the effect of flows in nuclear reactor stirred tanks through a momentum source equation and the concentration distribution of tracers that have been introduced in reactor tanks. The estimated findings, including the dimensionless concentration curves, power, and pumping numbers, dimensionless velocity profiles, and mixing times 4, were contrasted with results from tests in stirred containers. The investigation was carried out in Part I for vessels that were agitated by one impeller on a central shaft. The two types of impellers employed were an ordinary Rushton turbine and a 6-bladed 45° pitched blade turbine. The simulations made use of numerous reference frame techniques and the common k-e turbulence model. The impact of the grid type was also examined; unstructured, structured, and unique user-defined grids were looked at. The CFD model was used to simulate the flow field within the Rushton turbine nuclear reactor stirred tank. This method was validated using experimental data that were available close to the impeller tip and in the bulk area. Additionally, analyses of the computational efficiency and time using MRF and SM were done.

Keywords: Ansys fluent, momentum equation, CFD, prediction

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Authors: Helmi Temimi

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In this paper, we study the super-convergence properties of the discontinuous Galerkin (DG) method applied to one-dimensional mth-order ordinary differential equations without introducing auxiliary variables. We found that nth−derivative of the DG solution exhibits an optimal O (hp+1−n) convergence rates in the L2-norm when p-degree piecewise polynomials with p≥1 are used. We further found that the odd-derivatives and the even derivatives are super convergent, respectively, at the upwind and downwind endpoints.

Keywords: discontinuous, galerkin, superconvergence, higherorder, error, estimates

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