Search results for: multiaxial stretching functions

Authors: Nageeb A. H. Haroun, Sabyasachi Mondal, Precious Sibanda

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The effects of thermal radiation, Soret and Dufour parameters on mixed convection and nanofluid flow over a stretching sheet in the presence of a magnetic field are investigated. The flow is subject to temperature dependent viscosity and a chemical reaction parameter. It is assumed that the nanoparticle volume fraction at the wall may be actively controlled. The physical problem is modelled using systems of nonlinear differential equations which have been solved numerically using a spectral relaxation method. In addition to the discussion on heat and mass transfer processes, the velocity, nanoparticles volume fraction profiles as well as the skin friction coefficient are determined for different important physical parameters. A comparison of current findings with previously published results for some special cases of the problem shows an excellent agreement.

Keywords: non-isothermal wedge, thermal radiation, nanofluid, magnetic field, soret and dufour effects

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Authors: Binyam Teferi

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In this paper, a theoretical analysis of blood flow in the presence of thermal radiation and chemical reaction under the influence of time dependent magnetic field intensity has been studied. The unsteady non linear partial differential equations of blood flow considers time dependent stretching velocity, the energy equation also accounts time dependent temperature of vessel wall, and concentration equation includes time dependent blood concentration. The governing non linear partial differential equations of motion, energy, and concentration are converted into ordinary differential equations using similarity transformations solved numerically by applying ode45. MATLAB code is used to analyze theoretical facts. The effect of physical parameters viz., permeability parameter, unsteadiness parameter, Prandtl number, Hartmann number, thermal radiation parameter, chemical reaction parameter, and Schmidt number on flow variables viz., velocity of blood flow in the vessel, temperature and concentration of blood has been analyzed and discussed graphically. From the simulation study, the following important results are obtained: velocity of blood flow increases with both increment of permeability and unsteadiness parameter. Temperature of the blood increases in vessel wall as Prandtl number and Hartmann number increases. Concentration of the blood decreases as time dependent chemical reaction parameter and Schmidt number increases.

Keywords: stretching velocity, similarity transformations, time dependent magnetic field intensity, thermal radiation, chemical reaction

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Jiya Mohammed, Tsadu Shuaib, Yusuf Abdulhakeem

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The research work focuses on the cases of MHD boundary layer flow past a stretching plate with heat transfer and viscous dissipation. The non-linear of momentum and energy equation are transform into ordinary differential equation by using similarity transformation, the resulting equation are solved using Adomian Decomposition Method (ADM). An attempt has been made to show the potentials and wide range application of the Adomian decomposition method in the comparison with the previous one in solving heat transfer problems. The Pade approximates value (η= 11[11, 11]) is use on the difficulty at infinity. The results are compared by numerical technique method. A vivid conclusion can be drawn from the results that ADM provides highly precise numerical solution for non-linear differential equations. The result where accurate especially for η ≤ 4, a general equating terms of Eckert number (Ec), Prandtl number (Pr) and magnetic parameter ( ) is derived which was used to investigate velocity and temperature profiles in boundary layer.

Keywords: MHD, Adomian decomposition, boundary layer, viscous dissipation

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Authors: Smita Sonker, Uaday Singh

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Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries.

Keywords: Lipschitz classes, product matrix operator, signals, trigonometric Fourier approximation

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Authors: Jean-Marie Vilaire, Ricardo Abreu-Blaya, Juan Bory-Reyes

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The classical Beltrami system of elliptic equations generalizes the Cauchy Riemann equation in the complex plane and offers the possibility to consider homogeneous system with no terms of zero order. The theory of Douglis-valued functions, called Hyper-analytic functions, is special case of the above situation. In this note, we prove an analogue of the N. Davydov theorem in the framework of the theory of hyperanalytic functions. The used methodology contemplates characteristic methods of the hypercomplex analysis as well as the singular integral operators and elliptic systems of the partial differential equations theories.

Keywords: Beltrami equation, Douglis algebra-valued function, Hypercomplex Cauchy type integral, Sokhotski-Plemelj formulae

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Authors: Shun Horikoshi, Tohru Kawabe

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This study presents performance analysis results of SMC (Sliding mode control) with changing the chattering functions applied to slip suppression problem of electric vehicles (EVs). In SMC, chattering phenomenon always occurs through high frequency switching of the control inputs. It is undesirable phenomenon and degrade the control performance, since it causes the oscillations of the control inputs. Several studies have been conducted on this problem by introducing some general saturation function. However, study about whether saturation function was really best and the performance analysis when using the other functions, weren’t being done so much. Therefore, in this paper, several candidate functions for SMC are selected and control performance of candidate functions is analyzed. In the analysis, evaluation function based on the trade-off between slip suppression performance and chattering reduction performance is proposed. The analyses are conducted in several numerical simulations of slip suppression problem of EVs. Then, we can see that there is no difference of employed candidate functions in chattering reduction performance. On the other hand, in slip suppression performance, the saturation function is excellent overall. So, we conclude the saturation function is most suitable for slip suppression sliding mode control.

Keywords: sliding mode control, chattering function, electric vehicle, slip suppression, performance analysis

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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A method to obtain analytic approximations for special function of interest in engineering and physics is described here. Each approximate function will be valid for every positive value of the variable and accuracy will be high and increasing with the number of parameters to determine. The general technique will be shown through an application to the modified Bessel function of order zero, I₀(x). The form and the calculation of the parameters are performed with the simultaneous use of the power series and asymptotic expansion. As in Padé method rational functions are used, but now they are combined with other elementary functions as; fractional powers, hyperbolic, trigonometric and exponential functions, and others. The elementary function is determined, considering that the approximate function should be a bridge between the power series and the asymptotic expansion. In the case of the I₀(x) function two analytic approximations have been already determined. The simplest one is (1+x²/4)⁻¹/⁴(1+0.24273x²) cosh(x)/(1+0.43023x²). The parameters of I₀(x) were determined using the leading term of the asymptotic expansion and two coefficients of the power series, and the maximum relative error is 0.05. In a second case, two terms of the asymptotic expansion were used and 4 of the power series and the maximum relative error is 0.001 at x≈9.5. Approximations with much higher accuracy will be also shown. In conclusion a new technique is described to obtain analytic approximations to some functions of interest in sciences, such that they have a high accuracy, they are valid for every positive value of the variable, they can be integrated and differentiated as the usual, functions, and furthermore they can be calculated easily even with a regular pocket calculator.

Keywords: analytic approximations, mathematical-physics applications, quasi-rational functions, special functions

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Authors: Chantima Wangsomchok

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The main purposes of this study are (1) to test the students’ communicative competence within six main functions: greeting, parting, thanking, offering, requesting and suggesting, (2) to employ error analysis in the students’ communicative competence within those functions, and (3) to compare the characteristics of the error found from the investigation. The subjects of the study is 328 first-year undergraduates taking the Foundation English course in the first semester of the 2008 academic year at Suan Sunandha Rajabhat University. This study found that while the subjects showed high communicative competence in the use of the following three functions: greeting, thanking, and offering, they seemed to show poor communicative competence in suggesting, requesting and parting instead. In addition, this study found that the grammatical errors were likely to be most frequently found in the parting function. In the same way, the type of errors which were less frequently found was in the functions of thanking and requesting respectively. Instead, the students tended to have high pragmatic failure in the use of greeting and suggesting functions.

Keywords: error analysis, functions of English language, communicative competence, cognitive science

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: Deepa, Yashbir Singh, Shi Yi Wu, Michael Friebe, Joao Manuel R. S. Tavares, Hu Wei-Chih

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Cardiovascular disease can be detected by measuring the regional and global wall motion of the left ventricle (LV) of the heart; In this study, we designed a dynamic simulation tool using Computed Tomography (CT) images to assess the difference between actual and simulated left ventricular functions. Thirteen healthy subjects were involved in the study with actual and simulated left ventricular functions. In this research, we found the high correlation between actual left ventricular wall motion and simulated left ventricular wall motion. Our results confirm that our simulation tool is feasible for simulating left ventricular motion.

Keywords: cardiac imaging, left-ventricular remodeling, cardiac wall motion, myocardial functions

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Authors: Vernie C. Convicto, Henry P. Aringa, Wilson I. Barredo

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This study presents a conformational model of the helical structures of globular protein particularly ferritin in the framework of white noise path integral formulation by using Associated Legendre functions, Bessel and convolution of Bessel and trigonometric functions as modulating functions. The model incorporates chirality features of proteins and their helix-turn-helix sequence structural motif.

Keywords: globular protein, modulating function, white noise, winding probability

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Authors: M. Saeed, A. Shahidzadeh

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Interaction between teachers and learners requires applying a set of samples (examples) which helps to create coordination between the goals and methods. The main result and achievement and application of samples (examples) are that they can bring the teacher and learner to a shared understanding of the concept. mathematical concepts, and also one of the challenging issues in the discussion of the function is to find the collision points of functions of and, regarding that the example space of teachers is different in this issue, this paper aims to present an example space including several problems of the secondary school with the help of intuition and drawing various graphs of functions of and for more familiarity of teachers.

Keywords: inverse function, educational example, Mathematic example, example space

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Authors: Fawzi Srairi, Abderrahmane Dib

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Recently, the desire for a self-powered micro and nanodevices has attracted a great interest of using sustainable energy sources. Further, the ultimate goal of nanogenerator is to harvest energy from the ambient environment in which a self-powered device based on these generators is needed. With the development of nanogenerator-based circuits design and optimization, the building of new device simulator is necessary for the study and the synthesis of electromechanical parameters of this type of models. In the present article, both numerical modeling and optimization of piezoelectric nanogenerator based on zinc oxide have been carried out. They aim to improve the electromechanical performances, robustness, and synthesis process for nanogenerator. The proposed model has been developed for a systematic study of the nanowire morphology parameters in stretching mode. In addition, heuristic optimization technique, namely, particle swarm optimization has been implemented for an analytic modeling and an optimization of nanogenerator-based process in stretching mode. Moreover, the obtained results have been tested and compared with conventional model where a good agreement has been obtained for excitation mode. The developed nanogenerator model can be generalized, extended and integrated into simulators devices to study nanogenerator-based circuits.

Keywords: electrical potential, heuristic algorithms, numerical modeling, nanogenerator

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Authors: Tareq Hamadneh, Jochen Merker, Hassan Al-Zoubi

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Bernstein's expansion for exponentials in Taylor functions provides lower and upper optimization values for the range of its original function. these values converge to the original functions if the degree is elevated or the domain subdivided. Taylor polynomial can be applied so that the exponential is a polynomial of finite degree over a given domain. Bernstein's basis has two main properties: its sum equals 1, and positive for all x 2 (0; 1). In this work, we prove the existence of fixed points for exponential functions in a given domain using the optimization values of Bernstein. The Bernstein basis of finite degree T over a domain D is defined non-negatively. Any polynomial p of degree t can be expanded into the Bernstein form of maximum degree t ≤ T, where we only need to compute the coefficients of Bernstein in order to optimize the original polynomial. The main property is that p(x) is approximated by the minimum and maximum Bernstein coefficients (Bernstein bound). If the bound is contained in the given domain, then we say that p(x) has fixed points in the same domain.

Keywords: Bernstein polynomials, Stability of control functions, numerical optimization, Taylor function

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Authors: Pei Zhao, Sara Sintonen, Heikki Kynäslahti

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Digital museums and arts galleries have become popular in museum education and management. Museum and arts galleries website is one of the most effective and efficient ways. Google, a corporation specializing in Internet-related services and projects, not only puts high-resolution arts images online, but also uses augmented-reality in digital art gallery. The Google Art Project, Google’s production, provides users a platform in appreciating and learning arts. After Google Art Project, more and more countries released their own museum and arts gallery websites, like British Paining in BBC, and FINNA in Finland. Pedagogical function in these websites is one of the most important functions. In this paper, we use Google Art Project and FINNA as the case studies to investigate what kinds of pedagogical functions exist in these websites. Finally, this paper will give the recommendation to digital museums and websites development, especially the pedagogical functions development, in the future.

Keywords: arts education, cultural-heritage education, education with ICTs, pedagogical functions

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Authors: Ahlem Mougaida, Hedi Bel Hadj Salah

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Several methods are suggested to improve the numerical integration in Galerkin weak form for Meshless methods. In fact, integrating without taking into account the characteristics of the shape functions reproduced by Meshless methods (rational functions, with compact support etc.), causes a large integration error that influences the PDE’s approximate solution. Comparisons between different methods of numerical integration for rational functions are discussed and compared. The algorithms are implemented in Matlab. Finally, numerical results were presented to prove the efficiency of our algorithms in improving results.

Keywords: adaptive methods, meshless, numerical integration, rational quadrature

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Authors: Jaemyoung Lee

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We present a method to set up system functions through a near filed communication (NFC) of a smartphone. The short communication distance of the NFC which is usually less than 4 cm could prevent any interferences from other devices and establish a secure communication channel between a system and the smartphone. The proposed set-up method for system function values is demonstrated for a blacbox system in a car. In demonstration, system functions of a blackbox which is manipulated through NFC of a smartphone are controls of image quality, sound level, shock sensing level to store images, etc. The proposed set-up method for system function values can be used for any devices with NFC.

Keywords: system set-up, near field communication, smartphone, android

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Authors: Ibrahim Sani

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This paper examines the use of English discourse markers with the aim of investigating their communicative functions on Facebook as used by UMYUK members of academic staff. The paper uses the qualitative approach and relevance theory by Sperber and Wilson (1995) to highlight and examine DMs in different communicative contexts. In the course of data collection, five (5) academic staff from the five faculties of the university who are already Facebook friends of the researcher are used as the participants with their consent. The paper examines the communicative functions of English DMs among UMYUK academic staff on Facebook and reveals a number of communicative functions used in different contexts. One of the major findings indicates that 'contrastive markers' such as 'but', 'however', 'although' etc. are the dominant communicative functions employed by UMYUK academic staff on Facebook with 42% occurrence; it also shows that a single DM can function differently in the same linguistic environment.

Keywords: role, communicative, discourse markers, facebook, academic staff

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Authors: Sipu Guo, Silin Huang

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Background: Most studies investigate the link between executive function and allostatic load (AL) among adults aged 18 years and older. Studies differed regarding the specific biological indicators studied and executive functions accounted for. Specific executive functions may be differentially related to allostatic load. We investigated the comorbidities of executive functions and allostatic load via network analysis. Methods: We included 603 adolescents (49.84% girls; Mean age = 12.38, SD age = 1.79) from junior high school in rural China. Eight biological markers at T1 and four executive function tasks at T2 were used to evaluate networks. Network analysis was used to determine the network structure, core symptoms, and bridge symptoms in the AL-executive function network among rural adolescents. Results: The executive functions were related to 6 AL biological markers, not to cortisol and epinephrine. The most influential symptoms were inhibition control, cognitive flexibility, processing speed, and systolic blood pressure (SBP). SBP, dehydroepiandrosterone, and processing speed were the bridges through which AL was related to executive functions. dehydroepiandrosterone strongly predicted processing speed. The SBP was the biggest influencer in the entire network. Conclusions: We found evidence for differential relations between markers and executive functions. SBP was a driver in the network; dehydroepiandrosterone showed strong relations with executive function.

Keywords: allostatic load, executive function, network analysis, rural adolescent

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Authors: Tokuei Sako, Paul-Antoine Hervieux

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The energy-level structure of a pair of electron and positron confined in a quasi-one-dimensional nano-scale potential well has been investigated focusing on its trend in the small limit of confinement strength ω, namely, the Wigner molecular regime. An anisotropic Gaussian-type basis functions supplemented by high angular momentum functions as large as l = 19 has been used to obtain reliable full configuration interaction (FCI) wave functions. The resultant energy spectrum shows a band structure characterized by ω for the large ω regime whereas for the small ω regime it shows an energy-level pattern dominated by excitation into the in-phase motion of the two particles. The observed trend has been rationalized on the basis of the nodal patterns of the FCI wave functions.

Keywords: confined systems, positron, wave function, Wigner molecule, quantum dots

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Authors: Rogelio Luck, Yucheng Liu

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This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions e⁻⁽ᵗ⁻ ᵀ⁾, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.

Keywords: singular value decomposition, impulse response function, Green’s function , Toeplitz matrix , Hankel matrix

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Authors: Hassen M. Ouakad

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In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.

Keywords: MEMS, NEMS, fringing-fields, mid-plane stretching, Galerkin

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Authors: Yasaman Mohammadi

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Executive functions are a critical component of goal-directed behavior, encompassing a diverse set of cognitive processes such as working memory, cognitive flexibility, and inhibitory control. These functions are known to decline with age, but the precise mechanisms underlying this decline remain unclear. This paper provides an in-depth review of recent research investigating age-related changes in executive functions, drawing on insights from neuroimaging, genetics, and cognitive neuroscience. Through an interdisciplinary approach, this paper offers a nuanced understanding of the complex interplay between neural mechanisms, genetic factors, and cognitive processes that contribute to executive function decline in aging. Here, we investigate how different neuroimaging methods, like functional magnetic resonance imaging (fMRI) and positron emission tomography (PET), have helped scientists better understand the brain bases for age-related declines in executive function. Additionally, we discuss the role of genetic factors in mediating individual differences in executive functions across the lifespan, as well as the potential for cognitive interventions to mitigate age-related decline. Overall, this paper presents a comprehensive and integrative view of the current state of knowledge regarding age-related changes in executive functions. It underscores the need for continued interdisciplinary research to fully understand the complex and dynamic nature of executive function decline in aging, with the ultimate goal of developing effective interventions to promote healthy cognitive aging.

Keywords: executive functions, aging, neuroimaging, cognitive neuroscience, working memory, cognitive training

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Authors: Nazish Iftikhar, Adil Jhangeer, Tayyaba Naz

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The universe is expanding at an accelerated rate. Symmetries are useful in understanding universe’s behavior. Emmy Noether reported the relation between symmetries and conservation laws. These symmetries are known as Noether symmetries which correspond to a conserved quantity. In differential equations, conservation laws play an important role. Noether symmetries are helpful in modified theories of gravity. Time independent plane symmetric spacetime was classified by Noether`s theorem. By using Noether`s theorem, set of linear partial differential equations was obtained having A(r), B(r) and F(r) as unknown radial functions. The Lagrangian corresponding to considered spacetime in the Noether equation was used to get Noether operators. Different possibilities of radial functions were considered. Firstly, all functions were same. All the functions were considered as non-zero constant, linear, reciprocal and exponential respectively. Secondly, two functions were proportional to each other keeping third function different. Second case has four subcases in which four different relationships between A(r), B(r) and F(r) were discussed. In all cases, we obtained nontrivial Noether operators including gauge term. Conserved quantities for each Noether operators were also presented.

Keywords: Noether gauge symmetries, radial function, Noether operator, conserved quantities

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Authors: A. Baqqal, O. Abduhamid, H. Abdul-Hameed, T. Messager, G. Ayoub

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In this contribution, the effect of crystal content on the cyclic response of semi-crystalline polyethylene is studied over a large strain range. Experimental observations on a high-density polyethylene with 72% crystal content and an ultralow density polyethylene with 15% crystal content are reported. The cyclic stretching does appear a thermoplastic-like response for high crystallinity and an elastomeric-like response for low crystallinity, both characterized by a stress-softening, a hysteresis and a residual strain, whose amount depends on the crystallinity and the applied strain. Based on the experimental observations, a unified viscoelastic-viscoplastic constitutive model capturing the polyethylene cyclic response features is proposed. A two-phase representation of the polyethylene microstructure allows taking into consideration the effective contribution of the crystalline and amorphous phases to the intermolecular resistance to deformation which is coupled, to capture the strain hardening, to a resistance to molecular orientation. The polyethylene cyclic response features are captured by introducing evolution laws for the model parameters affected by the microstructure alteration due to the cyclic stretching.

Keywords: cyclic loading unloading, polyethylene, semi-crystalline polymer, viscoelastic-viscoplastic constitutive model

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Authors: T. H. Young, Y. J. Tsai

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A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work.  The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.

Keywords: stress analysis, free vibration, plate buckling, nonuniform in-plane edge shear

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Authors: Mohammedi Ferhate

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This paper deals with the generalized the notion of the function of wave a micro particle moving free, the concept of the linear operator in the representation function delta of Dirac which is a generalization of the symbol of Kronecker to the case of a continuous variation of the sizes concerned with the condition of orthonormation of the Eigen functions the use of linear operators and their Eigen functions in connection with the solution of given differential equations, it is of interest to study the properties of the operators themselves and determine which of them follow purely from the nature of the operators, without reference to specific forms of Eigen functions. The models simulation examples are also presented.

Keywords: function, operator, simulation, wave

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Authors: Sai Charan Kamana, Harsha Vardhan Nakkina, B.R. Chandavarkar

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In a highly secure and robust key generation process, a key role is played by randomness and random numbers when current real-world cryptosystems are observed. Most of the present-day cryptographic protocols depend upon the Random Number Generators (RNG), Pseudo-Random Number Generator (PRNG). These protocols often use noisy channels such as Disk seek time, CPU temperature, Mouse pointer movement, Fan noise to obtain true random values. Despite being cost-effective, these noisy channels may need additional hardware devices to continuously communicate with them. On the other hand, Hash functions are Pseudo-Random (because of their requirements). So, they are a good replacement for these noisy channels and have low hardware requirements. This paper discusses, some of the key generation methodologies, and their drawbacks. This paper explains how hash functions can be used in key generation, how to combine Key Derivation Functions with hash functions.

Keywords: key derivation, hash based key derivation, password based key derivation, symmetric key derivation

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Authors: E. V. Krishnan

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In this paper, we employ mapping methods to construct exact travelling wave solutions for a modified Korteweg-de Vries equation. We have derived periodic wave solutions in terms of Jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions.

Keywords: travelling wave solutions, Jacobi elliptic functions, solitary wave solutions, Korteweg-de Vries equation

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