Search results for: functional equations

Authors: Shailendra Natraj, Kristin Paetzold, B. R. Katzy

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The significant role of technology in strategic business decisions has created the need for executives who understand technology and recognize profitable applications to products, services and processes. The role of CTO’s is very complex within technology-based firms, which stretches from the technology aspects to the strategic goal and vision of the firm. Often the roles of CTOs scales from as functional leaders, strategic leaders or supera- functional leaders. In most of the companies the roles are unclear and fuzzy. We in our research are trying to explore each of the orientation and link between leadership types (functional, strategic and super functional) of CTOs, responsibilities, credibility and strategic and conceptual responsibilities. Approach: We conducted a comprehensive literature review with the available databank sources. Results: From the conducted literature review we could identify that most of the research work conducted so far were mainly distributed between roles and responsibilities of CTOs. The available sources pointed were limited to roles of CTOs as functional leaders. Contribution: In our findings based on the literature review, we could identify that apart from the conducted research what so far has not been focused yet are (a) The leadership types (mainly) strategic and super-functional leaders) of CTOs, (b) the responsibilities and credibility of CTOs and (c) the strategic and conceptual responsibilities of CTOs.

Keywords: CTO, chief technology officer, strategy, technology leaders

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Authors: Y. J. Zhou, G. Lu

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In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of five main parameters (radial stress, circumferential stress, radial strain, circumferential strain, and particle velocity) are obtained by using the characteristic method to transform five partial differential equations (two continuity equations, one motion equation, and two constitutive equations). Analytical expressions of the attenuation properties for spherical wave in brain tissue are analytically derived. Numerical results are obtained based on the five ordinary differential equations. The mechanical responses (particle velocity and stress) of brain are compared at different radii including 5, 6, 10, 15 and 25 mm under four different input conditions. The results illustrate that loading curves types of the particle velocity significantly influences the stress in brain tissue. The understanding of the influence by the input loading cures can be used to reduce the potentially injury to brain under head impact by designing protective structures to control the loading curves types.

Keywords: analytical method, mechanical responses, spherical wave propagation, traumatic brain injury

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Authors: Abdel-Maksoud Abdel-Kader Soliman

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The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

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Authors: Skirmante Mozuriunaite

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Contemporary metropolitan areas and large cities are dynamic, rapidly growing and continuously changing. Thus, urban transformations and mutations are not a new phenomenon, but rather a continuous process. Basic factors of urban transformation are related to development of technologies, globalisation, lifestyle, etc., which, in combination with local factors, have generated an extremely great variety of urban development conditions. This article discusses the main urbanisation processes in Lithuania during last 50 year period and social factors affecting urban functional mutations.

Keywords: dispersion, functional mutations, urbanization, urban mutations, social factors

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Authors: Saurabh Rawat, Anushree Sah

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K Maps are generally and ideally, thought to be simplest form for obtaining solution of Boolean equations. Cubical Representation of Boolean equations is an alternate pick to incur a solution, otherwise to be meted out with Truth Tables, Boolean Laws, and different traits of Karnaugh Maps. Largest possible k- cubes that exist for a given function are equivalent to its prime implicants. A technique of minimization of Logic functions is tried to be achieved through cubical methods. The main purpose is to make aware and utilise the advantages of cubical techniques in minimization of Logic functions. All this is done with an aim to achieve minimal cost solution.r

Keywords: K-maps, don’t care conditions, Boolean equations, cubes

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Authors: Maali Kachouri, Anis Jarboui

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We focus on the causal relationship between governance and information transparency as well as interrelation among the various governance mechanisms. This paper employs a simultaneous equations approach to show this relationship in the Tunisian context. Based on an 8-year dataset, our sample covers 28 listed companies over 2006-2013. Our findings suggest that internal and external governance mechanisms are interdependent. Moreover, in order to analyze the causal effect between information transparency and governance mechanisms, we found evidence that information transparency tends to increase good corporate governance practices.

Keywords: simultaneous equations approach, transparency, causal relationship, corporate governance

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Authors: Mahdi Jalili

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Functional connectivity in the human brain can be represented as a network using electroencephalography (EEG) signals. Network representation of EEG time series can be an efficient vehicle to understand the underlying mechanisms of brain function. Brain functional networks – whose nodes are brain regions and edges correspond to functional links between them – are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which graph theory metrics are sex dependent. To this end, EEGs from 24 healthy female subjects and 21 healthy male subjects were recorded in eyes-closed resting state conditions. The connectivity matrices were extracted using correlation analysis and were further binarized to obtain binary functional networks. Global and local efficiency measures – as graph theory metrics– were computed for the extracted networks. We found that male brains have a significantly greater global efficiency (i.e., global communicability of the network) across all frequency bands for a wide range of cost values in both hemispheres. Furthermore, for a range of cost values, female brains showed significantly greater right-hemispheric local efficiency (i.e., local connectivity) than male brains.

Keywords: EEG, brain, functional networks, network science, graph theory

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Authors: M. Shaban, A. Alibeigloo

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This paper studies free vibration behavior of single-walled carbon nanotubes (SWCNTs) embedded on elastic medium based on three-dimensional theory of elasticity. To accounting the size effect of carbon nanotubes, nonlocal theory is adopted to shell model. The nonlocal parameter is incorporated into all constitutive equations in three dimensions. The surrounding medium is modeled as two-parameter elastic foundation. By using Fourier series expansion in axial and circumferential direction, the set of coupled governing equations are reduced to the ordinary differential equations in thickness direction. Then, the state-space method as an efficient and accurate method is used to solve the resulting equations analytically. Comprehensive parametric studies are carried out to show the influences of the nonlocal parameter, radial and shear elastic stiffness, thickness-to-radius ratio and radius-to-length ratio.

Keywords: carbon nanotubes, embedded, nonlocal, free vibration

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Authors: Ali Kara, Asim Olgun, Sevgi Sozugecer, Sahin Ozel, Kubra Nur Yildiz, P. Sevinç, Abdurrahman Kuresh, Guliz Turhan, Duygu Gulgun

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The synthetic dyes, one of the most hazardous chemical compound classes, are important potential water pollutions since their presence in water bodies reduces light penetration, precluding the photosynthesis of aqueous flora and causing various diseases. Some the synthetic dyes are highly toxic and/or carcinogenic, and their biodegradation can produce even more toxic aromatic amines. The adsorption procedure is one of the most effective means of removing synthetic dye pollutants, and has been described in a number of previous studies by using the functional polymers. In this study, we investigated the removal of synthetic dyes from aqueous solution by using a functional polymer as an adsorbent material. The effect of initial solution concentration, pH, and contact time on the adsorption capacity of the adsorbent were studied in details. The results showed that functional polymer has a potential to be used as cost-effective and efficient adsorbent for the treatment of aqueous solutions from textile industries.

Keywords: functional polymers, synhetic dyes, adsorption, physicochemical parameters

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Authors: M. Taibeche, L. Guerbous, M. Kechouane, R. Nedjar, T. Zergoug

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It is known that Y2O3 Material is the most important among the sesquioxides within the general class of refractory ceramics. Indeed, this compound has many applications such as sintering optical windows, components for rare-earth doped lasers as well as inorganic scintillators in the detection scintillation. In particular Eu2+ and Ce3+ are favored dopants in many the scintillators due to its allowed optical 5d-4f transition. In this work, we present new results concerning structural and electronic properties of Ce-doped Y2O3, investigated by density functional theory (DFT), using the Heyd–Scuseria–Ernzerhof (HSE) hybrid functional and DFT+U two approaches. When, we compared the results from the two methods we obtain a good agreement available experimental data. Furthermore, the effect of cerium on the material has also been studied and discussed in the same framework.

Keywords: DFT, vienne ab initio simulation packages, scintillators, Heyd–Scuseria–Ernzerhof (HSE) hybrid functional

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In the paper, our purpose is to enhance the ability to solve a nonlinear differential equation which is about the motion of an incompressible fluid flow going down of an inclined plane without thermal effect with a simple and innovative approach which we have named it new method. Comparisons are made amongst the Numerical, new method, and HPM methods, and the results reveal that this method is very effective and simple and can be applied to other nonlinear problems. It is noteworthy that there are some valuable advantages in this way of solving differential equations, and also most of the sets of differential equations can be answered in this manner which in the other methods they do not have acceptable solutions up to now. A summary of the excellence of this method in comparison to the other manners is as follows: 1) Differential equations are directly solvable by this method. 2) Without any dimensionless procedure, we can solve equation(s). 3) It is not necessary to convert variables into new ones. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison to the other methods.

Keywords: viscos fluid, incompressible fluid flow, inclined plane, nonlinear phenomena

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Authors: C. S. Marques, M. J. Reis Lima, J. Oliveira, E. Teixeira-Lemos

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The growing concerns for physical wellbeing and health have been reflected in the way we choose food in our table. Nowadays, we are all more informed consumers and choose healthier foods. On the other hand, stroke, cancer and atherosclerosis may be somehow minimized by the intake of some bioactive compounds present in food, the so-called nutraceuticals and functional foods. The aim of this work was to make a revision of the published studies about the effects of some bioactive compounds, namely lycopene in human health, in the prevention of diseases, thus playing the role of a functional food. Free radical in human body can induce cell damage and consequently can be responsible for the development of some cancers and chronic diseases. Lycopene is one of the most powerful antioxidants known, being the predominant carotenoid in tomato. The respective chemistry, bioavailability, and its functional role in the prevention of several diseases will be object of this work. On the other hand the inclusion of lycopene in some foods can also be made by biotechnology and represents a way to recover the wastes in the tomato industry with nutritional positive effects in health.

Keywords: tomato, lycopene, bioavailability, functional foods, carotenoids, cancer and antioxidants

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Authors: Y. M. Aiyesimi, S. O. Abah, G. T. Okedayo

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A general analysis has been developed to study the chemical reaction effects on unsteady MHD double-diffusive free convective flow over a vertical stretching plate. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are solved numerically by using Runge-Kutta shooting technique. The effects of the chemical parameters are examined on the velocity, temperature and concentration profiles.

Keywords: chemical reaction, MHD, double-diffusive, stretching plate

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Authors: Haniye Dehestani, Yadollah Ordokhani

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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: collocation method, fractional partial differential equations, legendre-laguerre functions, pseudo-operational matrix of integration

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Authors: Daniil Karzanov

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This paper studies the effect of quarterly earnings reports on the stock price. The profitability of the stock is modeled by geometric Brownian diffusion and the Constant Elasticity of Variance model. We fit several variations of stochastic differential equations to the pre-and after-report period using the Maximum Likelihood Estimation and Grid Search of parameters method. By examining the change in the model parameters after reports’ publication, the study reveals that the reports have enough evidence to be a structural breakpoint, meaning that all the forecast models exploited are not applicable for forecasting and should be refitted shortly.

Keywords: stock market, earnings reports, financial time series, structural breaks, stochastic differential equations

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The main purpose of this paper is to present the Modified Newmark Method as a method of non-linear frame analysis by considering the effect of the axial load (second order analysis). The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. This part of the investigation is performed to generalize the established method for the assemblage structures such as frameworks. As explained, the governing differential equations are non-linear and cannot be formulated easily due to unknown axial load of the struts in the frame. By the assumption of constant axial load, the governing equations are changed to linear ones in most methods. Since the modeling and the solutions of the non-linear form of the governing equations are cumbersome, the linear form of the equations would be used in the established method. However, according to the ability of the method to reconsider the minor omitted parameters in modeling during the solution procedure, the axial load in the elements at each stage of the iteration can be computed and applied in the next stage. Therefore, the ability of the method to present an accurate approach to the solutions of non-linear equations will be demonstrated again in this paper.

Keywords: nonlinear, stability, buckling, modified newmark method

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Authors: Karolis Leonavičius, Dalius Kučiauskas, Dangiras Lukošius, Arnoldas Jasiūnas, Kostas Zdanys, Rokas Stanislovas, Emilis Gegevičius, Žana Kapustina, Juozas Nainys

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Screening throughput is a common bottleneck in many research areas, including functional genomics, drug discovery, and directed evolution. High-throughput screening techniques can be classified into two main categories: (i) affinity-based screening and (ii) functional screening. The first one relies on binding assays that provide information about the affinity of a test molecule for a target binding site. Binding assays are relatively easy to establish; however, they reveal no functional activity. In contrast, functional assays show an effect triggered by the interaction of a ligand at a target binding site. Functional assays might be based on a broad range of readouts, such as cell proliferation, reporter gene expression, downstream signaling, and other effects that are a consequence of ligand binding. Screening of large cell or gene libraries based on direct activity rather than binding affinity is now a preferred strategy in many areas of research as functional assays more closely resemble the context where entities of interest are anticipated to act. Droplet sorting is the basis of high-throughput functional biological screening, yet its applicability is limited due to the technical complexity of integrating high-performance droplet analysis and manipulation systems. As a solution, the Droplet Genomics Styx platform enables custom droplet sorting workflows, which are necessary for the development of early-stage or complex biological therapeutics or industrially important biocatalysts. The poster will focus on the technical design considerations of Styx in the context of its application spectra.

Keywords: functional screening, droplet microfluidics, droplet sorting, dielectrophoresis

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Authors: Hanaa H. Abd El Baky, Gamal S. El Baroty, Eman A. Ibrahem

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Microalgae Scenedesmus obliquus, the carotenoides (astaxanine and β-caroteine) were identified as the major bioactive constituents. In this work we prepared functional pre-biotic cakes to increase general mental health. Functional cakes were formulated by adding algal caroteinods at 2 and 4 mg/100g to flower and the cakes were storage for 20 days. Oxidative stability of both function cakes products were examined during storage periods by DPPH and TBA assays, and the results revealed that both values in function food products were significantly much low than that in untreated food products. Data of sensory evaluation revealed that treated biscuit and cakes with algae or algae extracts were significantly acceptable as control for main sensory characteristics (colour, odour/aroma, flavour, texture, the global appreciation, and overall acceptability). Thus, it could be concluded that functional biscuits and cakes (very popular and well balanced nutritional food) had good sensory and nutritional profiles and can be developed as new niche food market.

Keywords: Scenedesmus obliquus, carotenoids, functional cakes antioxidant, nutritional profiles

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: Ahmed Elsayed Ahmed, Ashraf Hafez, A. N. Ouda, Hossam Eldin Hussein Ahmed, Hala Mohamed ABD-Elkader

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Unmanned Aircraft Systems (UAS) are playing increasingly prominent roles in defense programs and defense strategies around the world. Technology advancements have enabled the development of it to do many excellent jobs as reconnaissance, surveillance, battle fighters, and communications relays. Simulating a small unmanned aerial vehicle (SUAV) dynamics and analyzing its behavior at the preflight stage is too important and more efficient. The first step in the UAV design is the mathematical modeling of the nonlinear equations of motion. In this paper, a survey with a standard method to obtain the full non-linear equations of motion is utilized,and then the linearization of the equations according to a steady state flight condition (trimming) is derived. This modeling technique is applied to an Ultrastick-25e fixed wing UAV to obtain the valued linear longitudinal and lateral models. At the end, the model is checked by matching between the behavior of the states of the non-linear UAV and the resulted linear model with doublet at the control surfaces.

Keywords: UAV, equations of motion, modeling, linearization

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Authors: M. A. Lahmer, K. Guergouri

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The ferromagnetic properties of carbon-doped ZnO (ZnO:CO) and hydrogenated carbon-doped ZnO (ZnO:CO+H) are investigated using the density functional tight binding (DFTB) method. Our results reveal that CO-doped ZnO is a ferromagnetic material with a magnetic moment of 1.3 μB per carbon atom. The presence of hydrogen in the material in the form of CO-H complex decreases the total magnetism of the material without suppressing ferromagnetism. However, the system in this case becomes quickly antiferromagnetic when the C-C separation distance was increased.

Keywords: ZnO, carbon, hydrogen, ferromagnetism, density functional tight binding

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Authors: Mohammad Vahedi Torshizi

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In this investigation, at first, bending stress, contact stress, Safety factor of bending and Safety factor of contact between sun gear and planet gear tooth was determined using mathematical equations. Also, The amount of Sun Revolution in, Speed carrier, power Transmitted of the sun, sun torque, sun peripheral speed, Enter the tangential force gears, was calculated using mathematical equations. According to the obtained results, maximum of bending stress and contact stress occurred in three plantary and low status of four plantary. Also, maximum of Speed carrier, sun peripheral speed, Safety factor of bending and Safety factor of contact obtained in four plantary and maximum of power Transmitted of the sun, Enter the tangential force gears, bending stress and contact stress was in three pantry and factors And other factors were equal in the two planets.

Keywords: bending stress, contact stress, plantary, mathematical equations

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: Yangming Zhu, Mingming Guo, Xiaozan Wang

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Introduction: The purpose of this study is to integrate functional training into physical education to test the effectiveness of functional training in improving the physical fitness (PF) and sport skills (SS) of female college students. Methods: A total of 54 female college students from East China Normal University were selected for this study (27 in the experimental group and 27 in the control group), and 13 weeks of the experimental intervention was conducted during the semester. During the experimental period, the experimental group was functionally trained for 1 hour per week. The control group performed one-hour weekly sports (such as basketball, football, etc.) as usual. Before and after the experiment, the national students' physical fitness test was used to test the PF of the experimental group and the control group, and the SS of the experimental group and the control group were tested before and after the intervention. Then using SPSS and Excel to organize and analyze the data. Results: The independent sample T-test showed that there was no significant difference in the PF and SS between the experimental group and the control group before the experiment (T PF=71.86, p PF> 0.05, Tₛₛ=82.41,pₛₛ > 0.05); After the experiment, the PF of the experimental group was significantly higher than that of the control group (T Improve=71.86, p Improve < 0.05); after the experiment, the SS of the experimental group was significantly higher than that of the control group (Tₛₛ = 1.31, pₛₛ <0.01) Conclusions: Integrating functional training into physical education can improve the PF of female college students. At the same time, the integration of functional training into physical education can also effectively improve the SS of female college students. Therefore, it is suggested that functional training be integrated into the daily physical education of female college students so as to improve their PF and SS.

Keywords: functional training, physical fitness, sport skills, female college students

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Authors: Preetham Shankapal, Jill King, Kori Murray, Corby Martin, Paula Giselman, Jason Hicks, Owen Carmicheal

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Activation of reward and satiety networks in the brain while processing palatable food cues, as well as functional connectivity during rest has been studied using functional Magnetic Resonance Imaging of the brain in various obesity phenotypes. However, functional connectivity within the reward and satiety network during food cue processing is understudied. 14 obese individuals underwent two fMRI scans during viewing of Macronutrient Picture System images. Each scan included two blocks of images of High Sugar/High Fat (HSHF), High Carbohydrate/High Fat (HCHF), Low Sugar/Low Fat (LSLF) and also non-food images. Seed voxels within seven food reward relevant ROIs: Insula, putamen and cingulate, precentral, parahippocampal, medial frontal and superior temporal gyri were isolated based on a prior meta-analysis. Beta series correlation for task-related functional connectivity between these seed voxels and the rest of the brain was computed. Voxel-level differences in functional connectivity were calculated between: first and the second scan; individuals who saw novel (N=7) vs. Repeated (N=7) images in the second scan; and between the HC/HF, HSHF blocks vs LSLF and non-food blocks. Computations and analysis showed that during food image viewing, reward network ROIs showed significant functional connectivity with each other and with other regions responsible for attentional and motor control, including inferior parietal lobe and precentral gyrus. These functional connectivity values were heightened among individuals who viewed novel HS/HF images in the second scan. In the second scan session, functional connectivity was reduced within the reward network but increased within attention, memory and recognition regions, suggesting habituation to reward properties and increased recollection of previously viewed images. In conclusion it can be inferred that Functional Connectivity within reward network and between reward and other brain regions, varies by important experimental conditions during food photography viewing, including habituation to shown foods.

Keywords: fMRI, functional connectivity, task-based, beta series correlation

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Authors: Bakur Gulua

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In this work, we consider some boundary value problems for the plate. The plate is the elastic material with voids. The state of plate equilibrium is described by the system of differential equations that is derived from three-dimensional equations of equilibrium of an elastic material with voids (Cowin-Nunziato model) by Vekua's reduction method. Its general solution is represented by means of analytic functions of a complex variable and solutions of Helmholtz equations. The problem is solved analytically by the method of the theory of functions of a complex variable.

Keywords: the elastic material with voids, boundary value problems, Vekua's reduction method, a complex variable

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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Authors: Bara Yousef

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The development of independency and functional participation is an important therapeutic goal for many children with cerebral palsy,They was many therapeutic approach have been used for treatment those children like neurodevelopment treatment, balance training strengthening and stretching exercise. More recently, therapy for children with cerebral palsy has focused on achieving functional goals using task-oriented interventions and summer camping model, which focus on activities that relevant and meaningful to the child, to learn more efficient and effective motor skills. We explore the effectiveness of using functional rehabilitation comparing with regular rehabilitation among 40 Saudi children with cerebral palsy in pediatric unit at Sultan Bin Abdul Aziz Humanitarian City-Ksa ,where 20 children randomly assign in control group who received rehabilitation based on regular therapy approach and other 20 children assign on experiment group who received rehabilitation based on functional therapy approach with an average of 45min OT treatment and 45 min PT treatment- daily within a period of 6 week. Our finding reported that children in experiment group has improved in gross motor function with an average from 49.4 to 57.6 based on GMFM 66 as primary outcome measure and improved in WeeFIM with an average from 52 to 62 while children in control group has improved with an average from 48.4 to 53.7 in GMFM and from 53 to and 58 in WeeFIM. Consequently, there has been growing interest in determining the effects of functional training programs as promising approach for these children.

Keywords: Cerebral Palsy (CP), gross motor function measure (GMFM66), pediatric Functional Independent Measure (WeeFIM), rehabilitation, disability

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Authors: N. A. Mokhtar, A. G. Hussin, Y. Z. Zubairi

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This paper proposes a new simultaneous simple linear functional relationship model by assuming equal error variances. We derive the maximum likelihood estimate of the parameters in the simultaneous model and the covariance. We show by simulation study the small bias values of the parameters suggest the suitability of the estimation method. As an illustration, the proposed simultaneous model is applied to real data of the wind direction and wave direction measured by two different instruments.

Keywords: simultaneous linear functional relationship model, Fisher information matrix, parameter estimation, circular variables

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