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Stock is a tradeable instrument on the stock exchange. Stock price movement is controlled by demand and supply. Demand and supply area is an area constructed by some corporate or foreign investor to accumulate and distribute stock price. They usually on purpose to discover a significant price movement by construction this area and an investor can use this as signal to buy or sell stock. They can take profit-taking optimally by technical analysis. Technical analysis is an approach to investment using historical stock data to forecast future price in T time period. Historical stock price is visualized as a candlestick and it can be predicted by mathematical functions such as moving average and stochastic. However, those method are not significant enough to identify demand and supply area. In this research, we investigate Unilever Indonesia Tbk. (UNVR) dataset to discover a supply and demand area with smoothing spline. Technically, smoothing spline can interpolate an unknown function by controlling certain value. For the dataset, we use historical price on UNVR for 312 days. Based on this research, we obtain a demand area on UNVR in the range of 3450-3720 because of repeating interpolation value over 22 days (March 18 2022 – April 19 2022). [ABSTRACT FROM AUTHOR]

This paper attempts to obtain generating functions for the polynomials defined by Chebyshev denoted as Tn (x) (Special Ultra Spherical Polynomials of the first kind) using Weisner's group-theoretic method by interpreting 'n' suitably. It is possible to derive at least three generating relations for various special functions of mathematical physics using this method introduced by Louis Weisner. In approximation theory, the roots (nodes) of Tn (x) are used as matching points for optimizing polynomial interpolation. Chebyshev polynomials are also used in many models to study them elegantly, including filters in signal processing distributed networks. [ABSTRACT FROM AUTHOR]

In this paper, we consider an alternative model for assessment of American call option with stochastic features of the underlying asset price and volatility transition. The alteration in volatility is represented by a mathematical function that takes into account various macroeconomic and microeconomic conditions, as well as factors that are not directly observable. As a result, the issue becomes a free boundary problem in a system of partial differential equations (PDEs). The volatility of an asset price is not constant and could have a jump when the market conditions are changed. Such a model helps for a more realistic description of the behavior of the asset price and provides a contemporary opportunity for a correct assessment of the American call option value. The model's parameters are adjusted and several numerical computations are provided to demonstrate the theoretical outcomes. In the problem solution are applied numerical methods. Important remarks for the stochastic features of the asset price are made in the conclusion of the present study. [ABSTRACT FROM AUTHOR]

The convex function is one of the most widely discussed functions in Mathematics. Many topics in mathematics using Young's function, one of them is the definition of Young's function that forms the basis of the Orlicz space construction. The purpose of this study is to construct a generalization of Young's function. The method used in this study is using s-convex function to define generalized Young's function. Novelty of this research is the construction of the generalized Young's function and its properties. Based on our result, it is expected to be a bridge in constructing the generalized Orlicz space. [ABSTRACT FROM AUTHOR]

Mathematics textbooks play a significant role in helping students develop problem-solving skills, which is required in this century. The main objective of the present study was to analyze how mathematical problem-solving is represented in a 10th grade mathematical textbook in Indonesia. The study focused on the topics of Function with four basic competencies. The teaching for problem-solving approach was used to analyze the book. All exercises and competency tests tasks were analyzed and classified into various problems representations such as similarity, form, closed/open, and the number of steps. The analysis result showed that the chapter offers non-routine, open-ended, and word problems in moderate numbers. However, it delivered a large number of problems required to solve using multiple steps. As a result, it was found that the chapter presented a limited foundation for students to develop their problem-solving skills. Several suggestions for further improvement of the textbook regarding the representation of problem-solving are presented. [ABSTRACT FROM AUTHOR]

With the progression of a country, the number of vehicles increases and their composition varies very rapidly. Though these are essential for mobility, these have become a major concern for the overall environment as they pose adverse impacts on it. In this study, the effect of different types of vehicles plying on the highways on the surrounding air quality is analyzed. It focuses on the vehicle composition on a specific link of national highway: N106-1 or Chittagong-Rangamati Highway, a Bangladeshi national highway connecting Chittagong with Rangamati via Raozan Upazila & Hathazari Upazila. Vehicle composition data is taken from the surveys done by the RHD Division, Bangladesh from their RMMS Database. Emission factors are taken from the literature. For relating emission factors to vehicle composition, a simple mathematical function is used with three independent variables: No. of a certain type of vehicle on that road (AADT value), length of the road section traveled by that vehicle, and their emission factors. The dependent variable is the amount of a certain type of pollutant emitted daily. Pollutants considered in this study are-Nitrogen Oxides (NOx), Sulfur Oxides (SOx), Hydrocarbons (HC), Carbon Monoxide (CO) and Suspended Particulate Matter (SPM). For this link, trucks are the main contributor of pollution and contribute to 55% of NOx pollution and 68% of SOx pollution. Trucks are also the main contributor to SPM and CO pollution. The second highest contributor varies for specific types of pollution. Bus is the second highest contributor of NOx, SOx and SPM pollution but it has comparatively less impact on HC and CO pollution. The number of auto-rickshaws is the highest (56%) on the road and they mainly contribute to HC and CO pollution. The contribution of auto-rickshaws to other pollution is relatively insignificant. Motorcars plying on this highway section need less attention than the major vehicles using this road segment. These results illustrate the severity of the current operating modes of transportation for emitting different pollutants on the regional highways near Chittagong-Rangamati. These can certainly help the policy-makers to introduce preventive policies to different modes according to their emission level to reduce the overall pollution. [ABSTRACT FROM AUTHOR]

This study aimed to describe a valid, practical, and effective Sparkol Video Scribe based animated video study to enhance ability on a matter of the limit function in mathematics education study program. The results of this study were a learning animated video media which was valid, practical, and effective. Learning media was declared valid based on the assessment of three media experts and educational experts, with a percentage of validity respectively 79.85% and 79.74% in the very proper category. The media was declare practical based on the assessment by students response with such a percentage of 82.01% which had avery practical category. The effectiveness of the media based on the n-gain score of 0.45 with the interpretation there was an increase in the medium category. This research was conducted in the Department of Mathematics Education, State University of Medan (Unimed) and has the following targets/objectives to: (1) develop learning media based on Sparkol Videoscribe to improve students' visual mathematical abilities; (2) publish reputable scientific articles like indexed proceedings or web of science; (3) produce research reports registered with Copyright; (4) produce teaching materials with ISBN that can be used by students. [ABSTRACT FROM AUTHOR]

The paper considers the method of drawing up a model of the distribution of the duration of standing of the parameters of the external climate during the probably possible year. The method is based on the formation of an array of data based on possible hourly values of the parameters of the external climate and the presentation of discrete distributions of the duration of the combination of temperatures and relative humidity of the outside air in certain intervals of their values in the form of integral characteristics. The latter are represented by a system of mathematical functions, which in turn are generalized into one equation representing a mathematical model of the distribution of the duration of standing of a combination of given values of climate parameters. The proposed method can be implemented for any geographical point, in the presence of statistical distributions of climate parameters of the standard type. The model of distribution of parameters of the external air can be useful for the analysis of operation of systems of creation of microclimate of buildings in order to choose the rational technological scheme and modes of operation. [ABSTRACT FROM AUTHOR]

The work considers the method of compiling a model for the distribution of the duration of standing parameters of the outdoor climate during the average year. The method is based on the presentation of discrete statistics on the distribution of observations of the combination of temperature and relative humidity of outdoor air at certain intervals of their values in the form of integral characteristics. The latter are represented by a system of mathematical functions, which in turn are summarized into one equation, representing a mathematical model of the distribution of the duration of the standing of a combination of specified values of climate parameters. The proposed method can be implemented for any geographical location, if there are statistical distributions of the parameters of the standard kind of climate. The outdoor air distribution model can be useful for analysing the operation of building microclimate systems in order to select a rational design and operating modes. [ABSTRACT FROM AUTHOR]

The problem of radial, torsional, and spheroidal vibrations of a deformable spherical inclusion in an infinite viscoelastic medium is considered. With the help of special functions of mathematical physics of Bessel, Hankel and Legendre, the Muller method and the Gauss method, an algorithm for solving the problem on a computer is developed. Based on the constructed complex frequency equations with complex output parameters, numerical results are obtained. The considered problems were reduced to finding those complex eigenfrequencies at which the system of equations of motion of a spherical inclusion with shortened radiation conditions has a non-zero solution in the class of infinitely differentiable functions. Detailed numerical calculations of the complex eigenfrequencies of three modes of radial, torsional, and spheroidal oscillations of spherical inhomogeneities in an infinite viscoelastic medium are performed. It is shown that the problem has a discrete complex spectrum. It is found that the eigenfrequencies of spheroidal oscillations of low-contrast inhomogeneities are divided into two groups: radially similar and torsion-like. It is revealed that at certain values of the viscoelastic density parameters, low-frequency natural oscillations occur, which are essentially some aperiodic motion, since the imaginary part of the natural frequency is large. The results obtained will allow us to predict the scattering of viscoelastic (or seismic) waves in deformable media in the presence of an inclusion. [ABSTRACT FROM AUTHOR]

It is a spherical body located in the natural vibrations of the same-sex systems, that is, in a deformed viscoelastic environment. The main emphasis is on the study of low-contrast inhomogeneitlarni in the viscoelastic environment. Deformation the issue of radial, torsional and spherical vibrations of spherical bonds is considered in an infinite viscoelastic environment. In the viscoelastic environment, the theory and methods of calculating complex natural frequencies and oscillatory patterns of viscoelastic spherical inhomogeneity are created. Such vibrations carry out radial, torsional and spheroidal classification. In the viscoelastic environment, frequency-transcendental equations of spherical inhomogeneity are formed. The general solution of the vector equation of motion of the three-dimensional theory of viscoelasticity in the displacement potentials of a spherical coordinate system is used. With the help of special functions of mathematical physics of Bessel, Hankel and Legendre, the Muller method and the Gauss method, an algorithm for solving computer problems is developed. Based on the constructed complex frequency equations with complex input parameters, numerical results are obtained. The considered problems were reduced to finding those complex eigenfrequencies at which the system of equations of motion of a spherical inclusion with shortened radiation conditions has a non-zero solution in the class of infinitely differentiable functions. Detailed numerical calculations of the complex eigenfrequencies of three modes of radial, torsional, and spheroidal oscillations of spherical inhomogeneities in an infinite viscoelastic medium are performed. It is shown that the problem has a discrete complex spectrum. It is found that the eigenfrequencies of spheroidal oscillations of low-contrast inhomogeneities are divided into two groups: radially similar and torsion-like. Due to the fact that the imaginary part of the natural frequency is large, it is established that low-frequency natural oscillations occur at certain values of the viscosity density parameters. The results obtained allow to predict the dispersion of viscoelastic (or seismic) waves in deformed environments with the participation of inclusions. [ABSTRACT FROM AUTHOR]

In the article "Struggling with physics and mathematics curricula based on the notion of function in the context of the educational reform in Poland" (AIP Conf. Proc. 2152; 2019) we analyzed the phenomenon of the lack of correlation between mathematics and physics teaching in the context of the concept of function. It is now taught the secondary school level of mathematics, but is also needed in the teaching of kinematics at the elementary school level of physics. In this paper, we present the chosen results of a pilot pedagogical remote-teaching experiment to provide a preliminary answer to several research questions on this issue: Does the attempt to integrate mathematics and physics have an impact on the understanding of functional relationships in a physics context? Specifically, does the introduction of a propaedeutic of the concept of function in mathematics lessons have an impact on the understanding and ability of analyzing motion? Similarly, do additional lessons on motion analysis affect the proficiency in representing, reading, and interpreting functional relationships? How do students process information about functional relationships in a physical context presented in a variety of representations? Is an elementary school student's intuitive understanding of the concept of functions enough to understand the analysis of motion in physics? What role do the remote experiments performed during the lesson play in learning new issues related to the concept of function in the context of motion analysis? [ABSTRACT FROM AUTHOR]

In this paper, an attempt has been made to obtain generating functions for the Chebyshev polynomials Tn (x) (Special ultra spherical polynomials of first kind) using Weisner's group-theoretic method by interpreting 'n' suitably. It is possible to derive at least three generating relations for various special functions of mathematical physics using this method introduced by Louis Weisner. In approximation theory, the roots (nodes) of Tn(x) are used as matching-points for optimizing polynomial interpolation. Chebyshev polynomials are also used in many models to study them elegantly. [ABSTRACT FROM AUTHOR]

We explore an application from the author's work in neuroscience. A code used to investigate neural development modeled 100 neurons with all-to-all excitatory connectivity. We used a simple ordinary differential equation system to model each neuron, and this 100-neuron model was used to produce a paper published in the Journal of Neurophysiology. Later a colleague used our code to continue this work, and found he could not reproduce our results. This lead us to thoroughly investigate this code and we discovered that it offered many different ways to thwart reproducibility that could be explained by round-off error arising from floating-point arithmetic. Numerical reproducibility is considered a task that directly follows from the determinism in computations. However, reproducibility has become an intense concern and and issue for research. In fact, the author developed an series of international workshops on numerical reproducibility and computational reproducibility that is now a regular offering at the annual international supercomputing conferences. We will show how this particular code provides a lack of reproducibility from the following three mechanisms: (i) the introduction of floating-point errors in an inner product; (ii) introduction of floating-point errors at each an increasing number of time steps during temporal refinement (ii); and (iii) differences in the output of library mathematical functions at the level of round-off error. This code's sensitivity makes it a very powerful tool to explore many different manifestations of numerical reproducibility. However, this code is by no means exceptional, as in neuroscience these types of models are used extensively to gain insights on the functioning of the nervous system. In addition, these types of models are widely used in many other fields of study as they just nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

The electrophysiology of cardiomyocytes is traditionally described with ordinary differential equations, the parameters of which are fitted to experimental data using the least-squares method, however, some physiological processes cannot be described by one model and require a statistical analysis of a population of models. This population and Bayes’ theorem can provide a probability density function for the model parameter values under certain experimental observations. However, the results of Bayesian approaches are fully determined by the model of the studied process. In this preliminary study, we analyze the sensitivity of Majumder2016 model, which describes the neonatal rat atrial cardiomyocyte, to variation of its parameters. In addition, we test several functions translating distance between action potential shapes into probability, that may be useful for Bayes’ approaches that fitting of model parameters to experimental observations. [ABSTRACT FROM AUTHOR]

Molecular docking algorithms predict the binding of a macromolecule (receptor) and a small molecule (ligand). Virtual screening by molecular docking has become established as a method for drug lead discovery and optimization. All docking algorithms make use of a scoring function in combination with a method of search. Presuming adequate search strategies, a scoring function's location performance will dominate behavior with respect to docking accuracy: the degree to which a predicted pose of a ligand matches experimental observation. Approaches to the development of scoring functions have varied widely, with a number of functions yielding similarly high levels of performance relating to the location issue. In this paper a survey of scoring functions for protein-ligand docking is presented. [ABSTRACT FROM AUTHOR]

We have discussed the quantum particle model for the case of a free particle solution in the one-dimensional Klein-Gordon nonlinear equations. This model was obtained through the two equations from the conservation laws of the classical physics, namely, the Hamilton-Jacobi equation for the relativistic motion and continuity equations. In this case, the Hamilton-Jacobi equation describes a part of the particle while the continuity equation describes the wave side. The derivation of this equation did not use the two postulates in the quantum mechanics, namely, the Einstein and de Broglie's postulates regarding the quantization of energy and momentum. According to this derivation, the particle side has almost most of the energy of quantum particle that accumulate at a point while the wave part has only a small portion of the energy of the quantum particle that surrounds the part of the particle. In addition, this paper also shows the form of mathematical functions that represent the particle and wave parts for a free particle solution. This form is obtained through a special solution of the free particle which is a plane-wave solution. [ABSTRACT FROM AUTHOR]

Rain Water Algorithm is a new algorithm that inspired by the pattern of physically rain water movements from air to the lowest place on the earth. It is necessary to evaluate the new algorithm with other algorithm utilizing known mathematical function that available in Comparing Continuous Optimizers (COCO) especially Black Box Optimization Benchmarking (BBOB) to analyze the performance of proposed algorithm. Optimization results exhibit that the purposed algorithm has surpass performance than others algorithms such as Genetic Algorithm (GA) and Simulated Annealing (SA). [ABSTRACT FROM AUTHOR]

The object of this paper is the study of a periodic structure formed by identical mufflers or expansion chambers by a new method called ”Interface Response Function” or ”Green’s Function”. This method is very well known in solid physics but remains unrecognized in acoustics. The objective is to investigate the acoustic attenuation performance of expansion chamber by developing analytical expressions. The present work focuses on the acoustic characteristics of wave transmission and the band structure across a cell and then to the entire network. The effect of the discontinuity between two waveguide is not taken account. The theoretical analysis is for a one-dimensional rigid waveguide. It is reported that the viscothermic effect is ignored. [ABSTRACT FROM AUTHOR]

We study the existence of infinitely many solutions for anisotropic variable exponent problem of the type {– Σi=1 N ∂xiai(x, ∂xiu) + Σi=1 N ai(x,u) = λ|u|q(x)-2u in Ω, ∂u/∂v = 0 on ∂Ω. (1) Where Ω ⊂ RN(N ≥ 3) is a bounded domain with smooth boundary ∂Ω, λ > 0,, pi,q are continuous functions on Ω̅ such that pi(x) ≥ 2,∀x ∈ Ω and i ∈ {1,2,...,N}. The main result of this paper establishes the existence of two positive constants λ0 and λ1 with λ0 ≤ λ1 such that every λ ∈ (λ1, ∞) is an eigenvalue, while no λ ∈ (0, λ0) can be an eigenvalue of the above problem. [ABSTRACT FROM AUTHOR]

In this paper we elaborate an algorithm to estimate the parameters of a ARCH(p) model. This algorithm combines quasi-maximum likelihood method, the Kalman Filter, and the simulated annealing method, without any assumptions about initial values. In the aim to generalize the results found for ARCH(1) in the recent paper of Allal and Benmoumen (2014). Simulation results demonstrate that the algorithm is viable and promising. [ABSTRACT FROM AUTHOR]

A new approach related to construction of admissible functions that do not coincide with the Lyapunov functions was proposed to investigate partial stability of solutions of systems of ordinary differential equations. An example of using admissible functions for establishing partial stability of solutions for one nonlinear system of differential equations is presented. [ABSTRACT FROM AUTHOR]

The paper aims to identify such a method of guidance and attitude control for the spacecraft motion in vicinity of objects with complex geometric shape as asteroids. Proposed methods provide both sufficient accuracy of the calculations and ease of use. The approach suggested by the authors is based on the model of point-focus concentrators and is based on the topological similarity of the gravitational field form obtained and the real form of the object. The control models are based on the locally optimal control laws. The first problem is to define particular law for every maneuvering task and correspondent coefficients that determine control program for an engine. The second problem is to define the thrust engine’s control law, which is able to stabilize a trajectory for different orbits. The paper materials are of practical value to the professionals involved in the problems solution of spacecraft control systems development when designing missions affecting maneuvering in close proximity to asteroids, comets and small planetary satellites. [ABSTRACT FROM AUTHOR]

In this research article, the Discrete Inverse Sumudu Transform (DIST) multiple shifting properties are used to design a methodology for solving ordinary differential equations. We say ”Discrete” because it acts on the Taylor or Mclaurin series of the function when any. The algorithm applied to solve the Whittaker and Zettl equations and get their exact solutions. A DIST Table for elementary functions is provided. [ABSTRACT FROM AUTHOR]

Holomorphic functions are the key tool for solutions of two dimensional problems in mathematical and theoretical physics, mechanics of continua. For the three-dimensional problems the hypercomplex analysis is an analogical one, i.e. monogenic Clifford functions or regular quaternionic functions playing the role of a three-dimensional analogue of holomorphic functions. In this paper a survey of investigations in the quaternionic analysis have been made in the North-Eastern federal university (Yakutsk state university) from the 1980s is presented. [ABSTRACT FROM AUTHOR]

In the paper for multidimensional parabolic equation we consider a problem of the right-hand side identification which is a product of two functions, one of which depends on time and the other one depends on space variables. For numerical solution of the posed inverse initial-boundary value problem, the conjugate gradient method is used in combination with the method of finite differences with a purely implicit time approximation. The results of the computational experiment for model problems with quasi-real solutions are discussed. [ABSTRACT FROM AUTHOR]

In this paper, it is introduced the operator h-preinvex function. And then it is established some new Hermite-Hadamard type inequalities for continuous functions of selfadjoint operators. [ABSTRACT FROM AUTHOR]

Lemoine's conjecture is an unsolved problem in number theory. It puzzled mathematicians for a hundred and twenty three years. Lemoine's conjecture is as follows: All odd integers greater than five can be represented as the sum of an odd prime and an even semiprime (a natural number that is the product of two (not necessarily distinct) prime numbers). Expressed algebraically: 2n + 1 = p + 2q always has a solution in primes p and q (not necessarily distinct) where n > 2 such as 23 = 13 + 2 ⋅ 5 = 17 + 2 ⋅ 3 = 19 + 2 ⋅ 2, we say the 3 has 3 ways to be present as p + 2q, which we called Lemoine's conjecture. The most common calculator provided which has arithmetic and logical functions, did not offer a special operation such as Lemoine calculator. Base on this paper and viewpoint, the authors will design this calculator when researchers want to work on the conjecture. [ABSTRACT FROM AUTHOR]

On two, initially independent (baseline) random variables X,Y stochastic dependence structure is imposed by introducing a "dependence factor" ϕ(x,y) so that their joint survival function takes on the product form ϕ(x,y) S1(x) S2(y). This form turns out to be (possibly) universal (!). The procedure is also extended to construction of bivariate stochastic processes. [ABSTRACT FROM AUTHOR]

In this article some properties of the generalized Laguerre functions (GLF) will be presented. The application of the generalized Laguerre functions for modeling of the dead time in the time domain will be shown. The speed of convergence for the approximating series with the generalized Laguerre functions will be compared with the simple Laguerre functions series. [ABSTRACT FROM AUTHOR]

In this article the question of the optimal choice of the generalization parameter ff and the time-scale parameter p for truncated series of generalized Laguerre functions (GLF) will be studied. Short introduction of the GLF identification method will be given. The impact of the optimal choice of parameters ff and p for approximating output signals of LTI dynamical systems will be presented on the examples. [ABSTRACT FROM AUTHOR]

The contribution deals with the description and demonstration of an algorithm for the generation of spatial geometry - the material structure of concrete. The term "material structure of concrete" is taken to mean a mix of randomly distributed aggregate and cement binder, the latter being used to bond the aggregate. In order for the generated material structure to be as realistic as possible, a photograph of the material which is to be created is used as the input (i.e. data source) for the algorithm. The generation process itself involves the use of spatial noise functions, which are able to generate simple patterns as well as very complex fractals. The algorithm is based on the principle that similarities can be found between a suitably placed section cut through a noise space and the abovementioned input for the algorithm - a real photograph of the material. The functionality and individual steps of the algorithm are presented via two examples of concrete generation with differently shaped aggregate grains. [ABSTRACT FROM AUTHOR]

We consider an infinite fluid queue modulated by a Markovian environment which varies slowly between two different modes of behaviour. We derive the series expansion of the stationary density of its buffer content as a function of the aggregated stationary densities of the buffer contents of the two environmental fluid queues. [ABSTRACT FROM AUTHOR]

In this paper we postulate different scenarios based on two copula models under the format C(u, v)= uv + f (u)g(v) for suitable functions f and g, see Rodríguez-Lallena & Úbeda Flores (2004) [4] and Nelsen et al. (1997) [3]. We used these copulas to model the dependence between two currencies quoted relative to the U.S. Dollar, the Canadian Dollar and the South Korean Won. We assume a Bayesian approach to estimate the copulas parameters, then we estimate the impact of losses on the South Korean Won on the Canadian Dollar. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give some combinatorial sums, identities and relations related to a family of combinatorial numbers and the Bernstein type basis functions. With the help of generating functions for the combinatorial numbers from this aforementioned family, we give some functional equations. By using these functional equations, we obtain several relationships including these combinatorial numbers and the Bernstein type basis functions. Moreover, we provide not only some identities, but also applications including combinatorial sums, integrals, the combinatorial numbers, the extended Bersntein basis functions, and the beta function. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give interpolation function for the families of numbers which are associated with not only the Apostol-Bernoulli numbers, but also the Apostol-Euler numbers and the Apostol-Genocchi numbers. We investigate some properties of these functions and these numbers. Moreover, we give some formulas including these functions and these numbers. Finally, we also give some observations related to well-known families of zeta-type functions. [ABSTRACT FROM AUTHOR]

Let S*LC represent a new subclass of analytic functions f defined in the open unit disk in the complex plane such that zf'(z)f(z) lies in the interior of the domain bounded by the limacon given by the equation (4x2+4y2-8x-5)2+8(4x2+4y2-12x-3)=0. In this paper, we investigate the geometric properties of functions in this class. [ABSTRACT FROM AUTHOR]

Let R(α,δ) denote the subclass of normalized analytic functions in the open unit disk D={z∈ℝ:|z|<1} satisfying the condition Reeiδf'(z)>α for some 0≤α<1 and cos(δ)-α>0. For f∈R(α,δ), the main aim of this paper is to obtain the upper bounds for the third Hankel determinant, |H3(1)|≤|a3|‖a2a4-a23|+|a4|‖a2a3-a4|+|a5|‖a3-a22|. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamics of the Lebesque quadratic stochastic operator on the set of all Lebesque measures of the set X = [0,1] . We consider the family of functions such that for any fixed x, y a probability measure P(x, y,.) is absolutely continuous with respect to usual Lebesque measure on X with simple Radon-Nikodym derivative. We construct the family of strictly non-Volterra quadratic stochastic and show that their dynamic behavior coincides with dynamic of strictly non-Volterra quadratic stochastic operator on 3-dimensional simplex. [ABSTRACT FROM AUTHOR]

A linear Kernel is a machine computationally efficient, also it has the ability to work by the analysis-data in the high-dimensional feature space with complex structure random. The purpose for the study in this paper is to introduce a new vision into the linear kernel machines by integrated with Hopfield Neural Network for doing the logical programming by using horn clause logic to become new network called Linear Kernel Hopfield Neural Network (LKHNN). The benefit by integrating kernel machine with Hopfield network to reduce the arithmetic burden by intelligently determining the pattern of memory embedded in high-dimensional space feature. The new network (LKHNN) able to formulation estimates for the state of neurons. The LKHNN and HNN simulation are performed using Dev C ++ program. The outcomes from simulator show the effectiveness of LKHNN in doing logic program by optimization horn clauses problem and improve efficiency to find the global solution. The robustness of LKHNN and HNN in doing logic programming by using horn clause are evaluated based on global minima ratio(zM), Hamming distance(HD) and computational time(CT). [ABSTRACT FROM AUTHOR]

This paper focuses on reconstructing the road curve by using Bezier curve fitting on a map with the aid of various parameterization approaches. A good fitting requires the Bezier curve fits closely to the road on a map without any major distortion that can be seen visually. Since the Bezier curve does not interpolate its control points, then designers had difficulties in determining the most ideal set of control points that can lead to a desired design. The parameterization method proposed by previous researchers may be very useful since the choice of control points had been automatically generated such that the curve will pass through the selected points on the road curve on a map. Differentparameterization techniques for fitting Bezier curve had been implemented in the perspective of road map fitting. One of the finding is that parameterization does not work well for a higher degree. By increasing control points, the curve is perturbed especially near both ends of the curve. The generated Bezier curve fitting may become worse if the actual road contains a lot of sharp corner. [ABSTRACT FROM AUTHOR]

This paper presents a new framework for the development of generalized composite kernels machines for discrete Hopfield neural network and to upgrading the performance of logic programming in Hopfield network by applying kernels machines in the system. We put up a new family of generalized composite kernels which exhibit great flexibility when combining the spectral and the spatial information contained in the analyze data that make use of kernels. The present an analysis based on kernels machines (Linear kernel Hopfield neural network, Polynomial kernel Hopfield neural network, and Gaussian kernel Hopfield neural network) that measure how the capacity of Hopfield network to use for solving the combinatorial problem that always occurs in Hopfield network and guaranty that the solution is optimal. This work is merely focusing on the ways to upgrade the performance of logic programming in Hopfield network. We carried out computer simulations to demonstrate the ability of kernels Hopfield neural network in enhancing the performance of the system. By applying kernels Hopfield neural network in the system, it does not only produce better quality solutions but it also can handle the network better even though the complexity increased. Besides that, the system also makes the solutions converge faster. Thus, the presence of this kernels Hopfield neural network in the system will produce solutions with better quality [ABSTRACT FROM AUTHOR]

Developing an appropriate mathematical model for assessing reliability of high reliability products is still an open issue. In order to get accurate estimation of reliability indexes, the reliability information which issued from different sources should be utilized in the process of reliability assessment when the reliability test data is scarce. An original method for evaluating reliability of high reliability products is provided in the presence of aleatory and epistemic uncertainties. The proposed approach applies the transferable belief model interpretation of the Dempster-Shafer theory to represent the contribution of each reliability active to product reliability and to evaluate the product reliability. A reliability assessment model is put forward. [ABSTRACT FROM AUTHOR]

A dynamical system d X/d t = F(X; A) is treated where F(X; A) is a polynomial (or some general type of radical contained) function in the vectors of state variables X ∈ ℝn and parameters A ∈ ℝm. We are looking for stability domains in both spaces, i.e. (a) domain ℙ ⊂ ℝm such that for any parameter vector specialization A ∈ ℙ, there exists a stable equilibrium for the dynamical system, and (b) domain 𝕊 ⊂ ℝn such that any point X* ∈ 𝕊 could be made a stable equilibrium by a suitable specialization of the parameter vector A. [ABSTRACT FROM AUTHOR]

The paper deals with first-order differential equations under the assumption that the right-hand side is a periodic function of time and continuous in the set of arguments. Pliss V.A. obtained the first results for a particular class of equations and showed that a number of theorems can not be continued. In this paper, it was possible to reduce the restrictions on the degree of smoothness of the right-hand side of the equation and obtain upper and lower bounds on the number of possible periodic solutions. [ABSTRACT FROM AUTHOR]

The additive process of forming a semicircular arched structure by means of layer-by-layer addition of material to its inner surface is simulated. The impact of this process running mode on the development of the technological stresses fields in the structure being formed under the action of gravity under properties of the material creep and aging is examined. In the framework of the linear mechanics of accreted solids a mathematical model of the process under study is offered and numerical experiments are conducted. It is shown that the stress-strain state of the additively formed heavy objects decisively depends on their formation mode. Various practically important trends and features of this dependence are studied. [ABSTRACT FROM AUTHOR]

Authors presented some composition formulae for the Marichev-Saigo-Maeda (M-S-M) fractional integral operator with the multi-index Mittag-Leffler functions. Our results are generalizes the results obtained by Choi and Agarwal [3]. Here, we record some particular cases of our main result. Finally, we obtain Laplace transforms of the composition formulae. [ABSTRACT FROM AUTHOR]

Finding parametric equation of a space curve is not easy task when its curvature functions are given. It is well known that this problem is known as fundamental theorem of a space curve. If the curvature functions are functions of arc-length, the solution of this problem is usually impossible. In this study, we discuss the answer of the problem when the curve is a general helix in Euclidean 3-space. By using slope axis of general helix, we get parametric equations of a general helix. Also, we give some examples and their figures. [ABSTRACT FROM AUTHOR]

In this paper, we established some new Hadamard-type integral inequalities for functions whose derivatives of absolute values are m- convex functions via Riemann-Liouville fractional integrals. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce the concepts of Δm-statistical convergence of order β for sequences of fuzzy numbers and strongly Δm-summable of order β for sequences of fuzzy numbers by using a modulus function f and taking supremum on metric d for 0 < β ≤ 1 and give some inclusion relations between them. [ABSTRACT FROM AUTHOR]