Search results for: the exponential partial Bell polynomials

Authors: Teoman Ozer, Ozlem Orhan

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This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

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Authors: Kreangkri Ratchagit

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This paper is concerned with exponential stability of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the exponential stability of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of LMIs. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: exponential stability, hybrid systems, timevarying delays, Lyapunov-Krasovskii functional, Leibniz-Newton’s formula

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Authors: Youssef. K. A. Abdalhafid, Ezaldin A. M. Mohammed, Masoud M. M. Zatout

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This study described the changes in the liver of Uromastyx acanthinura (Bell, 1825) males and females during hibernation and activity seasons. The results revealed that, hibernation causes increase fatty liver and pigment cells with abundant damage, comparing with nearly normal structure and less fatty liver after the hibernation with almost normal pattern. Genomic DNA showed apparent separation during hibernation. Also, caspase 3 and caspase 7 activity reached a high level in the liver tissue during hibernation comparing with activity season.

Keywords: histological liver, DNA fragmentation, hibernation, caspase 3 and caspase 7

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Authors: Soner Nandappa D., Ahmed Mohammed Naji

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In a graph G = (V, E), the distance from a vertex v to a vertex u is the length of shortest v to u path. The eccentricity e(v) of v is the distance to a farthest vertex from v. The diameter diam(G) is the maximum eccentricity. The k-distance neighborhood of v, for 0 ≤ k ≤ e(v), is Nk(v) = {u ϵ V (G) : d(v, u) = k}. In this paper, we introduce a new distance degree based topological polynomial of a graph G is called a k- distance neighborhood polynomial, denoted Nk(G, x). It is a polynomial with the coefficient of the term k, for 0 ≤ k ≤ e(v), is the sum of the cardinalities of Nk(v) for every v ϵ V (G). Some properties of k- distance neighborhood polynomials are obtained. Exact formulas of the k- distance neighborhood polynomial for some well-known graphs, Cartesian product and join of graphs are presented.

Keywords: vertex degrees, distance in graphs, graph operation, Nk-polynomials

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Authors: Ananya G., B. Varshitha, Shwetha S., Kavitha S. N., Praveen Kumar Gupta

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Teleportation is the ability to travel by just reappearing at some other spot. Though teleportation has never been achieved, quantum teleportation is possible. Quantum teleportation is a process of transferring the quantum state of a particle onto another particle, under the circumstance that one does not get to know any information about the state in the process of transformation. This paper presents a brief overview of quantum teleportation, discussing the topics like Entanglement, EPR Paradox, Bell's Theorem, Qubits, elements for a successful teleport, some examples of advanced teleportation systems (also covers few ongoing experiments), applications (that includes quantum cryptography), and the current hurdles for future scientists interested in this field. Finally, major advantages and limitations to the existing teleportation theory are discussed.

Keywords: teleportation, quantum teleportation, quantum entanglement, qubits, EPR paradox, bell states, quantum particles, spooky action at a distance

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Authors: Hla Hla Khaing, Yit Jian Liang, Nant Nyein Moe Htay, Jiang Fan

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Partial shadowing is one of the problems that are always faced in terrestrial applications of solar photovoltaic (PV). The effects of partial shadow on the energy yield of conventional mono-crystalline and multi-crystalline PV modules have been researched for a long time. With deployment of new thin-film solar PV modules in the market, it is important to understand the performance of new PV modules operating under the partial shadow in the tropical zone. This paper addresses the impacts of different partial shadowing on the operating characteristics of four different types of solar PV modules that include multi-crystalline, amorphous thin-film, CdTe thin-film and CIGS thin-film PV modules.

Keywords: partial shade, CdTe, CIGS, multi-crystalline (mc-Si), amorphous silicon (a-Si), bypass diode

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Authors: Hemant Kumar Pathak

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In 1994, Matthews (S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197) introduced the concept of a partial metric as a part of the study of denotational semantics of data flow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In fact, (complete) partial metric spaces constitute a suitable framework to model several distinguished examples of the theory of computation and also to model metric spaces via domain theory. In this paper, we introduce the concept of almost partial Hausdorff metric. We prove a fixed point theorem for multi-valued mappings on partial metric space using the concept of almost partial Hausdorff metric and prove an analogous to the well-known Nadler’s fixed point theorem. In the sequel, we derive a homotopy result as an application of our main result.

Keywords: fixed point, partial metric space, homotopy, physical sciences

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Authors: N. Smaoui, B. Chentouf

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The boundary stabilization problem of the rotating disk-beam system is a topic of interest in research studies. This system involves a flexible beam attached to the center of a disk, and the control and stabilization of this system have been extensively studied. This research focuses on the case where the center of mass is fixed in an inertial frame, and the rotation of the center is non-uniform. The system is represented by a set of nonlinear coupled partial differential equations and ordinary differential equations. The boundary stabilization problem of this system via a delayed boundary control is considered. We assume that the boundary control is either of a force type control or a moment type control and is subject to the presence of a constant time-delay. The aim of this research is threefold: First, we demonstrate that the rotating disk-beam system is well-posed in an appropriate functional space. Then, we establish the exponential stability property of the system. Finally, we provide numerical simulations that illustrate the theoretical findings. The research utilizes the semigroup theory to establish the well-posedness of the system. The resolvent method is then employed to prove the exponential stability property. Finally, the finite element method is used to demonstrate the theoretical results through numerical simulations. The research findings indicate that the rotating disk-beam system can be stabilized using a boundary control with a time delay. The proof of stability is based on the resolvent method and a variation of constants formula. The numerical simulations further illustrate the theoretical results. The findings have potential implications for the design and implementation of control strategies in similar systems. In conclusion, this research demonstrates that the rotating disk-beam system can be stabilized using a boundary control with time delay. The well-posedness and exponential stability properties are established through theoretical analysis, and these findings are further supported by numerical simulations. The research contributes to the understanding and practical application of control strategies for flexible structures, providing insights into the stability of rotating disk-beam systems.

Keywords: rotating disk-beam, delayed force control, delayed moment control, torque control, exponential stability

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Authors: Owolabi Kolade Matthew

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In this work, we investigate both the analytical and numerical studies of the dynamical model comprising of three species system. We analyze the linear stability of stationary solutions in the one-dimensional multi-system modeling the interactions of two predators and one prey species. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. The analysis results presented have established the possibility of the three interacting species to coexist harmoniously, this feat is achieved by combining the local and global analyzes to determine the global dynamics of the system. In the presence of diffusion, a viable exponential time differencing method is applied to multi-species nonlinear time-dependent partial differential equation to address the points and queries that may naturally arise. The scheme is described in detail, and justified by a number of computational experiments.

Keywords: asymptotically stable, coexistence, exponential time differencing method, global and local stability, predator-prey model, nonlinear, reaction-diffusion system

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Authors: Satyanarayana Engu, Ahmed Mohd, V. Murugan

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We study the large time asymptotics of solutions to the Cauchy problem for a forced Burgers equation (FBE) with the initial data, which is continuous and summable on R. For which, we first derive explicit solutions of FBE assuming a different class of initial data in terms of Hermite polynomials. Later, by violating this assumption we prove the existence of a solution to the considered Cauchy problem. Finally, we give an asymptotic approximate solution and establish that the error will be of order O(t^(-1/2)) with respect to L^p -norm, where 1≤p≤∞, for large time.

Keywords: Burgers equation, Cole-Hopf transformation, Hermite polynomials, large time asymptotics

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Authors: Benalia Nadia, Bensiali Nadia, Zerzouri Noura

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This paper presents an analysis of the effects of parameters np and nq for exponential load on the transmission line voltage profile, transferred power and transmission losses for different shunt compensation size. For different values for np and nq in which active and reactive power vary with it is terminal voltages as in exponential form, variations of the load voltage for different sizes of shunt capacitors are simulated with a simple two-bus power system using Matlab SimPowerSystems Toolbox. It is observed that the compensation level is significantly affected by the voltage sensitivities of loads.

Keywords: static load model, shunt compensation, transmission system, exponentiel load model

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Authors: J. Juan Peña, J. Morales, J. García-Ravelo, J. García-Martínes

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It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sq is itself a generalization of Shannon entropy S. In this work, from a deformation through a scaling function applied to the differential operator, it is possible to generate a q-deformed calculus as well as a q-deformed arithmetic, which not only allows generalizing the exponential and logarithmic functions but also any other standard function. The updated q-deformed differential operator leads to an updated integral operator under which the functions are integrated together with a weight function. For each differentiable function, it is possible to identify its q-deformed partner, which is useful to generalize other algebraic relations proper of the original functions. As an application of this proposal, in this work, a generalization of exponential and logarithmic functions is studied in such a way that their relationship with the thermodynamic functions, particularly the entropy, allows us to have a q-deformed expression of these. As a result, from a particular scaling function applied to the differential operator, a q-deformed arithmetic is obtained, leading to the generalization of the Tsallis entropy.

Keywords: q-calculus, q-deformed arithmetic, entropy, exponential functions, thermodynamic functions

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Authors: Cletus Abhulimen, L. A. Ukpebor

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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

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Authors: Jose Juan Peña, J. Morales, J. García-Ravelo

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In the search of potential models applied in the theoretical treatment of diatomic molecules, some of them have been constructed by using standard hyperbolic functions as well as from the so-called q-deformed hyperbolic functions (sc q-dhf) for displacing and modifying the shape of the potential under study. In order to transcend the scope of hyperbolic functions, in this work, a kind of generalized q-deformed hyperbolic functions (g q-dhf) is presented. By a suitable transformation, through the q deformation parameter, it is shown that these g q-dhf can be expressed in terms of their corresponding standard ones besides they can be reduced to the sc q-dhf. As a useful application of the proposed approach, and considering a class of exactly solvable multi-parameter exponential-type potentials, some new q-deformed quantum interactions models that can be used as interesting alternative in quantum physics and quantum states are presented. Furthermore, due that quantum potential models are conditioned on the q-dependence of the parameters that characterize to the exponential-type potentials, it is shown that many specific cases of q-deformed potentials are obtained as particular cases from the proposal.

Keywords: diatomic molecules, exponential-type potentials, hyperbolic functions, q-deformed potentials

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Authors: Qasim Khan, Furkan Ahmad, Asfar A. Khan, M. Saad Alam, Faiz Ahmad

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In this paper, partial discharge analysis is performed in cavities artificially created in insulation. The setup is according with Cigre-II Method. Circular Samples created from Perspex Sheet with different configuration with changing number of cavities. Assessment of insulation health can be performed by Partial Discharge measurement as this has been found to be important means of condition monitoring. The experiments are done using MPD 540, which is a modern partial discharge measurement system. By analyzing the PD activity obtained for various voids/cavities, it is observed that the PD voltages show variation for cavity’s diameter, depth even for its ratios. This can be employed for scrutiny of insulation system.

Keywords: partial discharges, condition monitoring, insulation defects, degradation and corrosion, PMMA

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Authors: Sheena K. J., Jyoti Badge, Sayed Mohammed Zeeshan

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A Comparative Study of Exponential and Logistic Population Growth Models in India India is the second most populous city in the world, just behind China, and is going to be in the first place by next year. The Indian population has remarkably at higher rate than the other countries from the past 20 years. There were many scientists and demographers who has formulated various models of population growth in order to study and predict the future population. Some of the models are Fibonacci population growth model, Exponential growth model, Logistic growth model, Lotka-Volterra model, etc. These models have been effective in the past to an extent in predicting the population. However, it is essential to have a detailed comparative study between the population models to come out with a more accurate one. Having said that, this research study helps to analyze and compare the two population models under consideration - exponential and logistic growth models, thereby identifying the most effective one. Using the census data of 2011, the approximate population for 2016 to 2031 are calculated for 20 Indian states using both the models, compared and recorded the data with the actual population. On comparing the results of both models, it is found that logistic population model is more accurate than the exponential model, and using this model, we can predict the future population in a more effective way. This will give an insight to the researchers about the effective models of population and how effective these population models are in predicting the future population.

Keywords: population growth, population models, exponential model, logistic model, fibonacci model, lotka-volterra model, future population prediction, demographers

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Authors: Patricia Sanz-Cordoba, Bernd Theilen

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This article analyzes the conditions where decentralization and partial tax harmonization in a coalition of asymmetric jurisdictions plays a role in the fight of fiscal competition (i.e. the race to bottom). Starting from a centralized economies, we use the ZM-W model to analyze the fiscal competition and coordination among three countries. We find that the asymmetry of jurisdictions facilitates partial tax harmonization between jurisdictions when these asymmetries are not too large. Furthermore, when the asymmetries are large enough, the level of labor tax plays an important role in the decision of decentralize capital tax. Accordingly, decentralization is achievable when labor tax is low. This result indicates that decentralization and partial tax harmonization between jurisdictions can be possible results in order to fight the negative externalities from fiscal competition, and more in the European Union countries where the asymmetries are substantial.

Keywords: centralization, decentralization, fiscal competition, partial tax harmonization

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Authors: Abdulrahman Abdulrahman

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The specific energy equation has many applications in practical channels, such as exponential channels. In this paper, the governing equation of alternate depth ratio for exponential channels, in general, was investigated towards obtaining analytical solution for the alternate depth ratio in three exponential channel shapes, viz., rectangular, triangular, and parabolic channels. The alternate depth ratio for rectangular channels is quadratic; hence it is very simple to solve. While for parabolic and triangular channels, the alternate depth ratio is cubic and quartic equations, respectively, analytical solution for these equations may be achieved easily for a given Froud number. Different examples are solved to prove the efficiency of the proposed solution. Such analytical solution can be easily used in natural rivers and most of practical channels.

Keywords: alternate depth, analytical solution, specific energy, parabolic channel, rectangular channel, triangular channel, open channel flow

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Authors: Messis A., Adjebli A., Ayeche R., Talbi M., Tighilet K., Louardiane M.

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Cancers are the second cause of death worldwide. Prevalence and incidence of cancers is getting increased by aging and population growth. This study aims to predict and modeling the evolution of breast, Colorectal, Lung, Bladder and Prostate cancers over the period of 2014-2019. In this study, data were analyzed using time series analysis with double exponential smoothing method to forecast the future pattern. To describe and fit the appropriate models, Minitab statistical software version 17 was used. Between 2014 and 2019, the overall trend in the raw number of new cancer cases registered has been increasing over time; the change in observations over time has been increasing. Our forecast model is validated since we have good prediction for the period 2020 and data not available for 2021 and 2022. Time series analysis showed that the double exponential smoothing is an efficient tool to model the future data on the raw number of new cancer cases.

Keywords: cancer, time series, prediction, double exponential smoothing

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Authors: Waheed Zahra, Mohamed El-Beltagy, Ashraf El Mhlawy, Reda Elkhadrawy

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In this paper, we consider singular perturbation reaction-diffusion boundary value problems, which contain a small uncertain perturbation parameter. To solve these problems, we propose a numerical method which is based on an exponential spline and Shishkin mesh discretization. While interval analysis principle is used to deal with the uncertain parameter, sensitivity analysis has been conducted using different methods. Numerical results are provided to show the applicability and efficiency of our method, which is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, shishkin mesh, two small parameters, exponential spline, interval analysis, sensitivity analysis

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Authors: Ksenija Dumičić, Anita Čeh Časni, Berislav Žmuk

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The aim of this paper is to select the most accurate forecasting method for predicting the future values of the unemployment rate in selected European countries. In order to do so, several forecasting techniques adequate for forecasting time series with trend component, were selected, namely: double exponential smoothing (also known as Holt`s method) and Holt-Winters` method which accounts for trend and seasonality. The results of the empirical analysis showed that the optimal model for forecasting unemployment rate in Greece was Holt-Winters` additive method. In the case of Spain, according to MAPE, the optimal model was double exponential smoothing model. Furthermore, for Croatia and Italy the best forecasting model for unemployment rate was Holt-Winters` multiplicative model, whereas in the case of Portugal the best model to forecast unemployment rate was Double exponential smoothing model. Our findings are in line with European Commission unemployment rate estimates.

Keywords: European Union countries, exponential smoothing methods, forecast accuracy unemployment rate

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Authors: K. P. Mredula, D. C. Vakaskar

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The article traces developments and evolution of various algorithms developed for solving partial differential equations using the significant combination of wavelet with few already explored solution procedures. The approach depicts a study over a decade of traces and remarks on the modifications in implementing multi-resolution of wavelet, finite difference approach, finite element method and finite volume in dealing with a variety of partial differential equations in the areas like plasma physics, astrophysics, shallow water models, modified Burger equations used in optical fibers, biology, fluid dynamics, chemical kinetics etc.

Keywords: multi-resolution, Haar Wavelet, partial differential equation, numerical methods

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Authors: O. W. Lawal, L. O. Ahmed, Y. K. Ali

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The unsteady MHD Poiseuille flow of a third grade fluid between two parallel horizontal nonconducting porous plates is studied with heat transfer. The two plates are fixed but maintained at different constant temperature with the Joule and viscous dissipation taken into consideration. The fluid motion is produced by a sudden uniform exponential decaying pressure gradient and external uniform magnetic field that is perpendicular to the plates. The momentum and energy equations governing the flow are solved numerically using Maple program. The effects of magnetic field and third grade fluid parameters on velocity and temperature profile are examined through several graphs.

Keywords: exponential decaying pressure gradient, MHD flow, Poiseuille flow, third grade fluid

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Authors: Prayas Sharma

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This paper proposed a generalized class of estimators, an exponential class of estimators based on the adaption of Sharma and Singh (2015) and Solanki and Singh (2013), and a simple difference estimator for estimating unknown population mean in the case of Poisson distributed population in simple random sampling without replacement. The expressions for mean square errors of the proposed classes of estimators are derived from the first order of approximation. It is shown that the adapted version of Solanki and Singh (2013), the exponential class of estimator, is always more efficient than the usual estimator, ratio, product, exponential ratio, and exponential product type estimators and equally efficient to simple difference estimator. Moreover, the adapted version of Sharma and Singh's (2015) estimator is always more efficient than all the estimators available in the literature. In addition, theoretical findings are supported by an empirical study to show the superiority of the constructed estimators over others with an application to earthquake data of Turkey.

Keywords: auxiliary attribute, point bi-serial, mean square error, simple random sampling, Poisson distribution

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Authors: Fatemah A. Alqallaf, Debasis Kundu

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The aim of this paper is to introduce a bivariate inverse generalized exponential distribution which has a singular component. The proposed bivariate distribution can be used when the marginals have heavy-tailed distributions, and they have non-monotone hazard functions. Due to the presence of the singular component, it can be used quite effectively when there are ties in the data. Since it has four parameters, it is a very flexible bivariate distribution, and it can be used quite effectively for analyzing various bivariate data sets. Several dependency properties and dependency measures have been obtained. The maximum likelihood estimators cannot be obtained in closed form, and it involves solving a four-dimensional optimization problem. To avoid that, we have proposed to use an EM algorithm, and it involves solving only one non-linear equation at each `E'-step. Hence, the implementation of the proposed EM algorithm is very straight forward in practice. Extensive simulation experiments and the analysis of one data set have been performed. We have observed that the proposed bivariate inverse generalized exponential distribution can be used for modeling dependent competing risks data. One data set has been analyzed to show the effectiveness of the proposed model.

Keywords: Block and Basu bivariate distributions, competing risks, EM algorithm, Marshall-Olkin bivariate exponential distribution, maximum likelihood estimators

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Authors: Abdelhadi Elharfi

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A problem of boundary feedback (exponential) stabilization of an overhead crane model represented by a PDE is considered. For any $r>0$, the exponential stability at the desired decay rate $r$ is solved in semi group setting by a collocated-type stabiliser of a target system combined with a term involving the solution of an appropriate PDE.

Keywords: feedback stabilization, semi group and generator, overhead crane system

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Authors: V. V. Singh

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In this paper we have focused on the study of a Linux operating system connected in a LAN (local area network). We have considered two different topologies STAR topology (subsystem-1) and BUS topology (subsystem-2) which are placed at two different places and connected to a server through a hub. In both topologies BUS topology and STAR topology, we have assumed 'n' clients. The system has two types of failure partial failure and complete failure. Further the partial failure has been categorized as minor partial failure and major partial failure. It is assumed that minor partial failure degrades the subsystem and the major partial failure brings the subsystem to break down mode. The system can completely failed due to failure of server hacking and blocking etc. The system is studied by supplementary variable technique and Laplace transform by taking different types of failure and two types of repairs. The various measures of reliability like availability of system, MTTF, profit function for different parametric values has been discussed.

Keywords: star topology, bus topology, hacking, blocking, linux operating system, Gumbel-Hougaard family copula, supplementary variable

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Authors: Salah Alrabeei, Mohammad Yousuf

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The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. Modeling option pricing by Black-School models with jumps guarantees to consider the market movement. However, only numerical methods can solve this model. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, the exponential time differencing (ETD) method is applied for solving partial integrodifferential equations arising in pricing European options under Merton’s and Kou’s jump-diffusion models. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). A partial fraction form of Pad`e schemes is used to overcome the complexity of inverting polynomial of matrices. These two tools guarantee to get efficient and accurate numerical solutions. We construct a parallel and easy to implement a version of the numerical scheme. Numerical experiments are given to show how fast and accurate is our scheme.

Keywords: Integral differential equations, , L-stable methods, pricing European options, Jump–diffusion model

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Authors: Sewon Kim, Changyeop Lee

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A new concept of in-furnace partial oxidation combustion is successfully applied in this research. The burner is designed such that liquid fuel is prevaporized in the furnace then injected into a fuel rich combustion zone so that a partial oxidation reaction occurs. The effects of equivalence ratio, thermal load, injection distance and fuel distribution ratio on the NOx and CO are experimentally investigated. This newly developed burner showed very low NOx emission level, about 15 ppm when light oil is used as a fuel.

Keywords: burner, low NOx, liquid fuel, partial oxidation

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Authors: Gilbert Makanda

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The problem of free convection from a perforated spinning cone with viscous dissipation, temperature-dependent viscosity, and partial slip was studied. The boundary layer velocity and temperature profiles were numerically computed for different values of the spin, viscosity variation, inertia drag force, Eckert, suction/blowing parameters. The partial differential equations were transformed into a system of ordinary differential equations which were solved using the fourth-order Runge-Kutta method. This paper considered the effect of partial slip and spin parameters on the swirling velocity profiles which are rarely reported in the literature. The results obtained by this method was compared to those in the literature and found to be in agreement. Increasing the viscosity variation parameter, spin, partial slip, Eckert number, Darcian drag force parameters reduce swirling velocity profiles.

Keywords: free convection, suction/injection, partial slip, viscous dissipation

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