Search results for: linear differential inclusion

Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Qasim M. Kriri

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Few Saudi Arabia production companies face financial profit issues until this moment. This work presents a linear integer programming model that solves a production problem of a Saudi Food Company in Saudi Arabia. An optimal solution to the above-mentioned problem is a Linear Programming solution. In this regard, the main purpose of this project is to maximize profit. Linear Programming Technique has been used to derive the maximum profit from production of natural juice at Saudi Food Co. The operations of production of the company were formulated and optimal results are found out by using Lindo Software that employed Sensitivity Analysis and Parametric linear programming in order develop Linear Programming. In addition, the parameter values are increased, then the values of the objective function will be increased.

Keywords: parameter linear programming, objective function, sensitivity analysis, optimize profit

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Authors: Shruti Motiwale, Xianlin Zhou, Reuben H. Kraft

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Military and sports personnel are often required to wear heavy helmets for extended periods of time. This leads to excessive cyclic loads on the neck and an increased chance of injury. Computational models offer one approach to understand and predict the time progression of disc degeneration under severe cyclic loading. In this paper, we have applied an analytic non-linear damage evolution model to estimate damage evolution in an intervertebral disc due to cyclic loads over decade-long time periods. We have also proposed a novel strategy for inclusion of recovery in the damage model. Our results show that damage only grows 20% in the initial 75% of the life, growing exponentially in the remaining 25% life. The analysis also shows that it is crucial to include recovery in a damage model.

Keywords: cervical spine, computational biomechanics, damage evolution, intervertebral disc, continuum damage mechanics

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Authors: Frederic Fovet

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Inclusive provisions have been statutorily mandated in North America for now over two decades. Despite a growing body of literature around inclusive practices, many in-service teachers continue to express difficulties when it comes to tangible implementation of inclusion in the everyday classroom. While there is debate around the various forms inclusion can take (UDL, differentiation, personalization, etc.), there appears to be a more significant hurdle in getting in-service teachers to fully embrace inclusion both as a goal and a practice. This paper investigates teachers’ degree of awareness around the Social Model of Disability. It argues that teachers often lack basic awareness of disability studies, more particularly of the Social Model of Disability, and that this has a direct impact on their capacity to conceptualize and embrace inclusion. The paper draws from the researcher’s experience as a graduate instructor with in-service teachers, as well as from his experience as a consultant working with schools and school boards. The methodology chosen here is phenomenology, and it draws on tools such as auto-ethnography. The paper opens a discussion around the reform and transformation of pre-service teacher training. It argues that disability studies should be integrated into teacher training as it plays a key role in having teachers develop a theoretical understanding of disability as a social construct.

Keywords: disability, K-12, inclusion, social model, in-service teachers

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Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: Palwinder Singh, Munish Sandhir, Tejinder Singh

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The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions.

Keywords: Ordinary differential equations (ODE), Taylor’s Series Method, Euler’s Method, Runge-Kutta Fourth Order Method

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Authors: Nicola Rubino

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This paper presents an analysis of a group of commodity exporting countries' nominal exchange rate movements in relationship to the US dollar. Using a series of Unrestricted Self-exciting Threshold Autoregressive models (SETAR), we model and evaluate sixteen national CPI price differentials relative to the US dollar CPI. Out-of-sample forecast accuracy is evaluated through calculation of mean absolute error measures on the basis of two-hundred and fifty-three months rolling window forecasts and extended to three additional models, namely a logistic smooth transition regression (LSTAR), an additive non linear autoregressive model (AAR) and a simple linear Neural Network model (NNET). Our preliminary results confirm presence of some form of TAR non linearity in the majority of the countries analyzed, with a relatively higher goodness of fit, with respect to the linear AR(1) benchmark, in five countries out of sixteen considered. Although no model appears to statistically prevail over the other, our final out-of-sample forecast exercise shows that SETAR models tend to have quite poor relative forecasting performance, especially when compared to alternative non-linear specifications. Finally, by analyzing the implied half-lives of the > coefficients, our results confirms the presence, in the spirit of arbitrage band adjustment, of band convergence with an inner unit root behaviour in five of the sixteen countries analyzed.

Keywords: transition regression model, real exchange rate, nonlinearities, price differentials, PPP, commodity points

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Authors: Parvina Ismayilova

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Inclusion is like cultural diversity because, in the modern world, it is understood as everything that allows you to immerse yourself in the environment with the opportunity to expand your experience. In a narrow sense, inclusion is more associated with "inclusive education" and "inclusive technologies" - that is, it is a principle that allows people with disabilities to interact with the outside world. Technological progress allows people to unite, ensuring that they are seen and heard.

Keywords: diversity, disability, inclusivity, equality

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Authors: Weihua Ruan, Kuan-Chou Chen

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This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Hamilton-Jacobi-Bellman equations, infinite-horizon differential games, continuous and discrete state variables, political-economy models

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Authors: Martin K. Steiger, Lukas Heisler, Hans-Georg Brachtendorf

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Deep neural networks and their variants form the backbone of many AI applications. Based on the so-called residual networks, a continuous formulation of such models as ordinary differential equations (ODEs) has proven advantageous since different techniques may be applied that significantly increase the learning speed and enable controlled trade-offs with the resulting error at the same time. For the evaluation of such models, high-performance numerical differential equation solvers are used, which also provide the gradients required for training. However, whether classical gradient-based methods are even applicable or which one yields the best results has not been discussed yet. This paper aims to redeem this situation by providing empirical results for different applications.

Keywords: deep neural networks, gradient-based learning, image processing, ordinary differential equation networks

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Authors: Y. M. Aiyesimi, G. T. Okedayo, O. W. Lawal

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The analysis has been carried out to study unsteady MHD thin film flow of a third grade fluid down an inclined plane with heat transfer when the slippage between the surface of plane and the lower surface of the fluid is valid. The governing nonlinear partial differential equations involved are reduced to linear partial differential equations using regular perturbation method. The resulting equations were solved analytically using method of separation of variable and eigenfunctions expansion. The solutions obtained were examined and discussed graphically. It is interesting to find that the variation of the velocity and temperature profile with the slip and magnetic field parameter depends on time.

Keywords: non-Newtonian fluid, MHD flow, thin film flow, third grade fluid, slip boundary condition, heat transfer, separation of variable, eigenfunction expansion

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Authors: Chao-Qing Dai

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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: Barbora Chmelikova

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Current financial markets offer a wide range of financial products to the consumers. However, access to the financial products is not always provided or guaranteed, particularly in less developed countries. For this reason, financial inclusion is an important component in the modern society. This paper investigates financial inclusion and what financial products are held by university students majoring in finance fields. The OECD methodology was used to examine the awareness and use of financial products. The study was conducted via online questionnaire at Masaryk University in the Czech Republic among finance students. The results show that the students use current and savings accounts more than any other financial products.

Keywords: financial inclusion, financial products, personal finance, university students

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Authors: Win Ko Ko, A. N. Temnov

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The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations.

Keywords: nonlinear oscillations, two-layered liquid, instability region, hydrodynamic coefficients, resonance frequency

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Authors: Pedro A. Medina-Rios, Marly Yolie Quintana-Daza

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Having the opportunity to communicate in a social, academic and work context is very relevant for any individual and more for a deaf person when oral language is not their natural language, and written language is their second language. Currently, in Colombia, there is not a specialized dictionary for our best knowledge in sign language archiving. Archival is one of the areas that the deaf community has a greater chance of performing. Nourishing new signs in dictionaries for deaf people extends the possibility that they have the appropriate signs to communicate and improve their performance. The aim of this work was to illustrate the importance of designing pedagogical and technological strategies of knowledge management, for the academic inclusion of deaf people through proposals of lexicon in Colombian sign language (LSC) in the area of archival. As a method, the analytical study was used to identify relevant words in the technical area of the archival and its counterpart with the LSC, 30 deaf people, apprentices - students of the Servicio Nacional de Aprendizaje (SENA) in Documentary or Archival Management programs, were evaluated through direct interviews in LSC. For the analysis tools were maintained to evaluate correlation patterns and linguistic methods of visual, gestural analysis and corpus; besides, methods of linear regression were used. Among the results, significant data were found among the variables socioeconomic stratum, academic level, labor location. The need to generate new signals on the subject of the file to improve communication between the deaf person, listener and the sign language interpreter. It is concluded that the generation of new signs to nourish the LSC dictionary in archival subjects is necessary to improve the labor inclusion of deaf people in Colombia.

Keywords: archival, inclusion, deaf, thesaurus

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Authors: Suparman

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Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation of piecewise linear regression models. The method used to estimate the parameters of picewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters of picewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.

Keywords: regression, piecewise, Bayesian, reversible Jump MCMC

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Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo

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Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.

Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation

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Authors: Sina Mahdavi, Faeze Noruzpur, Aysuda Noruzpur

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This paper proposes a high linear, low power and wideband Variable Gain Amplifier (VGA) with a direct current (DC) gain range of -10.2dB to 60.7dB. By applying the proposed idea to the folded cascade amplifier, it is possible to achieve a 71dB DC gain, 35MHz (-3dB) bandwidth, accompanied by high linearity and low sensitivity as well. It is noteworthy that the proposed idea can be able to apply on every differential amplifier, too. Moreover, the total power consumption and unity gain bandwidth of the proposed VGA is 1.41mW with a power supply of 1.8 volts and 4.37GHz, respectively, and 0.8pF capacitor load is applied at the output nodes of the amplifier. Furthermore, the proposed structure is simulated in whole process corners and different temperatures in the region of -60 to +90 ºC. Simulations are performed for all corner conditions by HSPICE using the BSIM3 model of the 180nm CMOS technology and MATLAB software.

Keywords: variable gain amplifier, low power, low voltage, folded cascade, amplifier, DC gain

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Authors: Selahattin Gultekin

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Today, in engineering departments, mathematics courses such as calculus, linear algebra and differential equations are generally taught by mathematicians. Therefore, during mathematicians’ classroom teaching there are few or no applications of the concepts to real world problems at all. Most of the times, students do not know whether the concepts or rules taught in these courses will be used extensively in their majors or not. This situation holds true of for all engineering and science disciplines. The general trend toward these mathematic courses is not good. The real-life application of mathematics will be appreciated by students when mathematical modeling of real-world problems are tackled. So, students do not like abstract mathematics, rather they prefer a solid application of the concepts to our daily life problems. The author highly recommends that mathematical modeling is to be taught starting in high schools all over the world In this paper, some mathematical concepts such as limit, derivative, integral, Taylor Series, differential equations and mean-value-theorem are chosen and their applications with graphical representations to real problems are emphasized.

Keywords: applied mathematics, engineering mathematics, mathematical concepts, mathematical modeling

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Authors: Afaf Manzoor, Abdul Hameed

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Hopes to attend school is the most effective means to overcome the burden of disability and become a self-reliant, productive citizen. The objectives of the study were to develop a valid and reliable scale to measure hopes of out of school children with disabilities and find an association between hopes and various demographic factors such as type of disability, gender, socio-economic status, and locale, etc. Child Hope theory by Snyder (2003) was used as a framework to develop a measure for the hopes of children. According to this theory, hope is defined as a set of cognition that includes self- perception which establish routes to achieve desired goals (pathways) and motivation for achieving the goals (agency). By applying this theory, inclusion hope scale was developed and validated. The data were collected from 361 out of school children with disabilities living in three districts (Lahore, Sheikupura, Kasur) of Lahore Division by using the cluster sampling technique. Findings of the study indicated that children with intellectual challenges were more hopeless as compared to other types of disabilities. Similarly, children living in urban areas have better hopes for inclusion in school. However, no gender disparity was found in terms of being hopeful to attend schools. The study also includes recommendations to improve hopes for educational inclusion among out of school children with disabilities.

Keywords: out of school children, disability, hopes, inclusion

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Authors: M. Berrehail, F. Benamira

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We study the quantum motion of a particle in the presence of a time- dependent linear potential using an operator invariant that is quadratic in p and linear in q within the framework of the Lewis-Riesenfeld invariant, The special invariant operator proposed in this work is demonstrated to be an Hermitian operator which has an Airy wave packet as its Eigenfunction

Keywords: airy wave packet, ivariant, time-dependent linear potential, unitary transformation

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Authors: Mary Chriselda A

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This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

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Authors: Malika Elkyal

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We consider an iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm does not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Accordingly, we note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, differential algebraic equations

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Authors: George Kamil Kamal Abdelnor

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Every major educational institution has incorporated diversity, equity, and inclusion (DEI) principles into its administrative, hiring, and pedagogical practices. Yet these DEI principles rarely incorporate explicit language or critical thinking about disability. Despite the fact that according to the World Health Organization, one in five people worldwide is disabled, making disabled people the larger minority group in the world, disability remains the neglected stepchild of DEI. Drawing on disability studies and crip theory frameworks, the underlying causes of this exclusion of disability from DEI, such as stigma, shame, invisible disabilities, institutionalization/segregation/delineation from family, and competing models and definitions of disability are examined. This paper explores both the ideological and practical shifts necessary to include disability in university DEI initiatives. It offers positive examples as well as conceptual frameworks such as 'divers ability' for so doing. Using Georgetown University’s 2020-2022 DEI initiatives as a case study, this paper describes how curricular infusion, accessibility, identity, community, and diversity administration infused one university’s DEI initiatives with concrete disability-inclusive measures. It concludes with a consideration of how the very framework of DEI itself might be challenged and transformed if disability were to be included.

Keywords: cognitive disability, cognitive diversity, disability, higher education disability, Standardized Index of Diversity of Disability (SIDD), differential and diversity in disability, 60+ population diversity, equity, inclusion, crip theory, accessibility

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Authors: Suha Alawadhi, Malak Alrasheed

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In the recent past, public participation in governments has been declined to a great extent, as citizens have been isolated from community life and their ability to articulate demands for good government has been noticeably decreased. However, the Internet has introduced new forms of interaction that could enhance different types of relationships, including government-public relationship. In fact, technology-enabled government has become a catalyst for enabling social inclusion. This exploratory study seeks to investigate public perceptions in Kuwait regarding the use of social media networks in government where social capital is built to achieve social inclusion. Social capital has been defined as social networks and connections amongst individuals, that are based on shared trust, ideas and norms, enable participants of a network to act effectively to pursue a shared objective. The quantitative method was used to generate empirical evidence. A questionnaire was designed to address the research objective and reflect the identified constructs: social capital dimensions (bridging, bonding and maintaining social capital), social inclusion, and social equality. In this pilot study, data was collected from a random sample of 61 subjects. The results indicate that all participants have a positive attitude towards the dimensions of social capital (bridging, bonding and maintaining), social inclusion and social equality constructs. Tests of identified constructs against demographic characteristics indicate that there are significant differences between male and female as they perceived bonding and maintaining social capital, social inclusion and social equality whereas no difference was identified in their perceptions of bridging social capital. Also, those who are aged 26-30 perceived bonding and maintaining social capital, social inclusion and social equality negatively compared to those aged 20-25, 31-35, and 40-above whose perceptions were positive. With regard to education, the results also show that those holding high school, university degree and diploma perceived maintaining social capital positively higher than with those who hold graduate degrees. Moreover, a regression model is proposed to study the effect of bridging, bonding, and maintaining social capital on social inclusion via social equality as a mediator. This exploratory study is necessary for testing the validity and reliability of the questionnaire which will be used in the main study that aims to investigate the perceptions of individuals towards building social capital to achieve social inclusion.

Keywords: government, social capital, social inclusion, social networks

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Authors: T. Vamsee Kiran, A. Gopi

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The undesired torque and flux ripple may occur in conventional direct torque control (DTC) induction motor drive. DTC can improve the system performance at low speeds by continuously tuning the regulator by adjusting the Kp, Ki values. In this differential evolution (DE) is proposed to adjust the parameters (Kp, Ki) of the speed controller in order to minimize torque ripple, flux ripple, and stator current distortion.The DE based PI controller has resulted is maintaining a constant speed of the motor irrespective of the load torque fluctuations.

Keywords: differential evolution, direct torque control, PI controller

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Authors: Tai-Ping Chang

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In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton’s principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin’s method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping.

Keywords: chaotic motion, damping, Lyapunov exponents, single-walled carbon nanotube

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Authors: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: Seyedehsomayeh Hosseini

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Much attention has been paid over centuries to understanding and solving the problem of minimization of functions. Compared to linear programming and nonlinear unconstrained optimization problems, nonlinear constrained optimization problems are much more difficult. Since the procedure of finding an optimizer is a search based on the local information of the constraints and the objective function, it is very important to develop techniques using geometric properties of the constraints and the objective function. In fact, differential geometry provides a powerful tool to characterize and analyze these geometric properties. Thus, there is clearly a link between the techniques of optimization on manifolds and standard constrained optimization approaches. Furthermore, there are manifolds that are not defined as constrained sets in R^n an important example is the Grassmann manifolds. Hence, to solve optimization problems on these spaces, intrinsic methods are used. In a nondifferentiable problem, the gradient information of the objective function generally cannot be used to determine the direction in which the function is decreasing. Therefore, techniques of nonsmooth analysis are needed to deal with such a problem. As a manifold, in general, does not have a linear structure, the usual techniques, which are often used in nonsmooth analysis on linear spaces, cannot be applied and new techniques need to be developed. This paper presents necessary and sufficient conditions for a strict local minimum of extended real-valued, nonsmooth functions defined on Riemannian manifolds.

Keywords: Riemannian manifolds, nonsmooth optimization, lower semicontinuous functions, subdifferential

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Authors: Tulin Coskun

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We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators.

Keywords: analytic functions, approximation of analytic functions, Linear k-positive operators, Korovkin type theorems

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