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For a first-order quasilinear equation with an asymmetrical flux function a generalized entropy solution of the Cauchy problem with exponential initial condition is constructed. We also consider initial data which coincides with exponential function in a neighborhood of infinity. All the solutions constructed in the present paper are sign-alternating and one-sided periodic with respect to spatial variable. [ABSTRACT FROM AUTHOR]

This paper deals with obtaining the best estimator for the reliability function of a two-parameter exponential distribution using the Bayesian estimation method under four different loss functions: squared error loss function, precautionary loss function, and entropy loss function. The exponential distribution prior and Gamma distribution have been assumed as the priors for the scale γ and location δ parameters, respectively. In Bayesian estimation, maximum likelihood estimators have been used as the initial estimators for the two unknown parameters, and the Tierney-Kadane approximation has been effectively employed. The estimators were compared using the Monte-Carlo simulation method based on the integral mean squared error (IMSE). [ABSTRACT FROM AUTHOR]

In the present paper, in the Hilbert space W ~ 2 (2 , 1) (0,1] of periodic complex-valued functions, an optimal quadrature formula with exponential weight function is constructed. The optimality of the formula of rectangles in the space W ~ 2 (2 , 1) (0,1] of periodic functions for ω=0 is shown. In addition, the numerical results show that the order of convergence of the optimal quadrature formula constructed in the space W ~ 2 (2 , 1) (0,1] is equal to 2. [ABSTRACT FROM AUTHOR]

The inequality of finding the upper bounds for the nonlinear functional |a3 - µa22| of the Taylor-Mclaurin series is popularly famous as the Fekete-Szegö inequality. This inequality has a rich history in the geometric function theory. Its source by Fekete-Szegö in 1933. In this paper, through the advantage of applying concepts quasi-subordinate, Sakaguchi functions and exponential functions, the authors construct a new subclass Ne,q(s, b, λ) of Non-Bazilević functions. As well as, obtained the first and two Taylor-Maclaurin coefficient estimates, sharp upper bounds of the Fekete-Szegö inequality and majorization for functions which belong to this subclass. [ABSTRACT FROM AUTHOR]

In the present paper we consider European style options with an exponential payoff function. The problem is transformed to evaluation of multidimensional integrals of the exponential function over the unit cube where the values of the parameters involved in the formula depend the values of the European options. We compare the performance of quasi-Monte Carlo methods based on lattice rules for multiple integrals up to 30 dimensions. The performance of a lattice rule depends on the choice of the generator vectors. When the integrand is sufficiently regular the lattice rules outperform not only the standard Monte Carlo methods, but also other types of methods using low discrepancy sequences. We consider "rank 1" rules whose lattices have a a single generator vector. The advantages and disadvantages of the different quasi-Monte Carlo methods for multidimensional integrals related to evaluation of European options are studied in the paper. [ABSTRACT FROM AUTHOR]

The paper deals with linear-quadratic optimal control problems with a weak control and the fixed left point in a critical case, where a matrix standing in front of a state variable in the state equation is singular for any argument value if the small parameter is equal to zero. Using the direct scheme method, consisting in immediate substituting a postulated asymptotic solution into the problem condition and obtaining problems for finding asymptotics terms, the zero order asymptotic solution is constructed under some conditions. In contrast to the paper: N. T. Hoai, J. Optim. Theory Appl., vol. 175, 324-340 (2017), where the considered problem was studied, the projector approach is applied here. This approach allows us to make the algorithm of constructing asymptotic solution clearer and to correct some inaccuracies in the paper mentioned. [ABSTRACT FROM AUTHOR]

In wireless communication, there is a rapid change in technologies from first generation to fifth generation with different modulation schemes, data rates and channel access methods. Also there is an exponential growth in number of users in the system. So it is necessary to handle more number of users without degrading the system's performance. Therefore channel access method with low power consumption and efficient spectral usage must be implemented. So our idea of research is to propose an optimum multiple access technique called Non Orthogonal Multiple Access (NOMA), which is different from conventional orthogonal access methods In NOMA based system, users can be allowed to send and receive their information simultaneously. In this paper, we explore the performance of the above mentioned emerging mechanism NOMA, which is based on power domain multiplexing at sender and Successive Interference Cancellation (SIC) decoding mechanism in receiver. The transmitted signals are generated from binary phase shift keying for two users. Also it is essential to calculate the bit error rate of the users at the receiver by considering the wireless channel characteristics with different fading effects. [ABSTRACT FROM AUTHOR]

In this paper, the (G′/G²)-expansion approach is employed to investigate the exact traveling wave solutions of the (2+1)- dimensional Boiti-Leon-Pempinelli system. The proposed approach is efficient, reliable and practically appropriate for solving the nonlinear partial differential equations analytically. Some new exact solutions are obtained in the form of rational functions, exponential functions and trigonometric functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce extra exponential, sub exponential and extorial functions arrived from exponential and extorial functions. Using these two types of functions we find solutions of higher order differential and difference equations. Our findings are validated by appropriate examples. [ABSTRACT FROM AUTHOR]

In this study, this paper presents the characteristics of pressure-related fluctuations in decaying turbulence generated by a multi-scale turbulence grid on the centerline. This study focuses on the turbulent kinetic energy related to dynamic pressure and the static pressure fluctuation RMS related to static pressure as the pressure fluctuation characteristics. As a multi-scale turbulence grid, a fractal turbulence grid used in previous studies is used. Two turbulence grids are used as the computational conditions. In the previous study, the velocity fluctuation of the multiscale grid turbulence was pointed out to follow an apparent exponential function on the centerline. In this study, the characteristics of the static pressure fluctuations on the central axis are mainly examined. The relative static pressure fluctuation intensity, which is often calculated in previous studies, is also discussed. In this study, the issue is approached by direct numerical analysis. The governing equations are discretized based on a high-order accuracy spatial discretization scheme, and the external force terms reproduce the no-slip conditions on the surface of the turbulent grid. In addition to the turbulent kinetic energy, the static pressure fluctuation RMS is shown in this study to follow an apparent exponential function on the central axis. [ABSTRACT FROM AUTHOR]

We discuss the problem of approximating the length of a curve γ in arbitrary euclidean space En, from ε -uniformly sampled reduced data Qm ={qi}mi =0, where γ (ti)=qi. The interpolation knots {ti}mi=0 are assumed in this paper to be unknown (the so-called non-parametric interpolation). We fit Qm with the piecewise-quadratic interpolant γ2 based on the so-called exponential parameterization (depending on parameter λ ∈ [0,1]) which estimates the missing knots {ti}m i=0 ≈ {ti}mi=0. The asymptotic orders βε (λ) for length estimation d(γ) ≈ d(y2) in case of λ = 0 (uniformly guessed knots) read as βε (1) = min{4,3+ε} (see [2]). This paper establishes a more general result holding for all λ ∈ [0,1] and ε -uniform samplings - see Th. 5. More specifically the respective convergence orders amount to βε (1) = min{4,3+ε} (see [2]). This paper establishes a more general result holding for all λ ∈ [0,1] and ε -uniform samplings - see Th. 5. More specifically the respective convergence orders amount to βε (λ) = min{4,4ε} for λ ∈ [0,1). Consequently βε (λ) are independent of λ ∈ [0,1) and the discontinuity in asymptotic orders βε (λ) at λ = 1 occurs, for all ε ∈ (0,1). The full proof of Th. 5 is presented in ICNAAM'14 post-conference journal publication together with more exhaustive relevant experimentation. [ABSTRACT FROM AUTHOR]

Recently, symplectic/energy-preserving exponentially-fitted methods for Hamiltonian systems with periodic/ oscillatory solutions have been attracting much interest. In this paper, we extend the energy-preserving exponentiallyfitted method for Hamiltonian systems to Poisson systems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new accumulation process, the Semi-Markov Accumulation Process (SMAP). This class of processes extends the framework of continuous-time Markov Additive Processes (MAPs) by allowing the underlying environmental component to be a semi-Markov process instead of a Markov process. Next, we follow an analytic approach to derive a Master Equation formula of the Renewal type that describes the evolution of SMAPs in time. We show that under exponential holding times, a matrix exponential form analogous to the matrix exponent of a MAP is attained. Finally, we consider an application of our results where closed-form solutions are rather easy to achieve. [ABSTRACT FROM AUTHOR]

The scope of the paper is the presentation of a new method of generating numbers from a given distribution. The method uses the inverse cumulative distribution function and a method of flattening of probabilistic distributions. On the grounds of these methods, a new construction of chaotic maps was derived, which generates values from a given distribution. The analysis of the new method was conducted on the example of a newly constructed chaotic recurrences, based on the Box-Muller transformation and the quantile function of the exponential distribution. The obtained results certify that the proposed method may be successively applicable for the construction of generators of pseudo-random numbers. [ABSTRACT FROM AUTHOR]

The paper studies the exponential stability and exponential estimation of solutions to linear discrete systems with delay x(k + 1) = A(k)x(k) + B(k)x(k - m(k)), k = 0, 1, ... where x is an n-dimensional dependent variable, A(k) and B(k) are nxn real matrices, and m(k) ∈ ℕ. Using the method of Lyapunov functions, conditions are derived for exponential stability. [ABSTRACT FROM AUTHOR]

In the present paper we present the results of a statistical analysis of some characteristics of precipitation events and propose a kind of a theoretical explanation of the proposed models in terms of mixed Poisson and mixed exponential distributions based on the information-theoretical entropy reasoning. The proposed models can be also treated as the result of following the popular Bayesian approach. [ABSTRACT FROM AUTHOR]

The present paper deals with the propagation characteristics of plane waves at the edge of an initially stressed heterogeneous dry sandy plate in which heterogeneity has been considered as exponential function of depth for both regidity and density. Characteristic equations of plane waves are derived with the aid of potential function. The dispersion relation has been obtained in a simplified form with the help of suitable boundary conditions. Numerical computation has been carried out to show the influence of wave number, sandiness parameter, heterogeneity parameter and initial stresses and depicted by means of graphs. [ABSTRACT FROM AUTHOR]

A multi-peaked analytically extended function (AEF), previously applied by the authors to modeling of lightning discharge currents, is used in this paper for representation of the electrostatic discharge (ESD) currents. In order to estimate its non-linear parameters, the Marquardt least-squares method (MLSM) is used. ESD currents' modelling is illustrated through an essential example corresponding to approximation of the IEC Standard 61000-4-2 waveshape. [ABSTRACT FROM AUTHOR]

In this study, we have applied the modified exp (Ω(ξ))-expansion function method to the Cahn-Allen equation. We have obtained some new analytical solutions such hyperbolic function solutions. Then, we have constructed the two and three dimensional surfaces for all analytical solutions obtained in this paper by using Wolfram Mathematica 9. [ABSTRACT FROM AUTHOR]

The ITS-90 Inconsistency in overlap region of the Mercury-Gallium and the Water-Argon Sub-ranges are investigated in this paper. The calibration data of thirteen SPRTs are used to determine the magnitude of the inconsistency. The result shows it no greater than 0.22mK. By mean of extending a logarithm of the platinum resistance ratio of the ITS-90 interpolation in a power series, this paper gives an inconsistency function of the form of interpolation error in the region . The function is only with approximate error less than 3.4×10-5 mK, almost no error, checked by the SPRTs. [ABSTRACT FROM AUTHOR]

Light as a stream of particles along the different lines after originating from source can understood by the specific geometry over space-time around it with periodic condition such that it describes by the string/sound wave differential equation which determines the electromagnetic wave. Due to the different reported actions about and along the photon travel line with elementary particles such as atom, electron etc, it bring to a close that the photon like ordinary mass particles do have physical observables of different for instance momentum, pressure etc. Within this paper, the photon momentum function is obtained by considering the space-time complex exponential function of light under the exponential operator subjected to it. The exponential operator over several variables of photon is the Taylor theorem for photon which in absence of any material and field space reduces to the space-time variables only. [ABSTRACT FROM AUTHOR]

Is it possible to determine the stability function of an exponentially-fitted Runge-Kutta method, without actually constructing the method itself? This question was answered in a recent paper and examples were given for one-stage methods. In this paper we summarize the results and we focus on two-stage methods. [ABSTRACT FROM AUTHOR]

The conflict driven clause learning or CDCL is one of algorithm widely used in a lot of modern SAT solvers. It is because CDCL SAT solvers are so effective in practice, thanks to its non-chronological backjumping and conflict analysis. In this paper, we will discuss about the organization of CDCL solver for SAT solving and how it can be applied for satisfiability modulo theory. We also do experiment on hard-square constraint and found that the computation time using SMT solver follows an exponential function and the precomputation time is not affectedby the increase in the number of blanks. [ABSTRACT FROM AUTHOR]

The current paper presents a semi-analytical solution for the problem of swirl decay under laminar flow in a circular duct with constant value of the radial velocity at the inlet. The swirl velocity equation is solved by the separation of variable technique. Based on the eigenvalues and eigenfunctions corresponding to the solution of main problem it is found that the slowest breakdown processes of eddy structures under laminar viscous flow are described by the exponential function. [ABSTRACT FROM AUTHOR]

With exponential type, a class of alternating group finite difference scheme based on the saul’yev asymmetric schemes is derived for solving convection-diffusion equation in this paper. The scheme has the obvious property of Parallelism. The result of stability analysis shows that the scheme is unconditionally stable. In the end of the paper, numerical experiment is given, which illustrates the scheme presented is of high accuracy. [ABSTRACT FROM AUTHOR]

One of the important things provided by the fuzzy model is the determination of the membership function. It is used in applications with the fuzzy reliability functions. These functions of distributions are with positive random variables. There are many belonging functions that have been studied by many researchers. The most used Functions are the trigonometric membership function and Trapezoidal membership function. In this paper, a beta membership function has been used, because it is more flexible in statistical applications. It is adopted in this research to study the classical method of obtaining estimation of the fuzzy reliability function of the new mixed distribution (Weibull-Raleigh-Exponential). A simulation method will be used to choose the best fuzzy value for this new mixed distribution. [ABSTRACT FROM AUTHOR]

This paper aims to suggest a new compound probability distribution represented by the Left Truncated Gumbel-Exponential distribution using the cumulative distribution function method. As the mathematical formula for the probability density and cumulative distribution functions of the new distribution was derived, in addition to its properties represented by the Noncenteral Moment, the central Moment, the kortisies coefficient, Mod and the median. As well as discussing different methods of estimating its parameters, represented by Maximum Likelihood Method and the Percentiles Estimators of Method through the simulation method. Several conclusions were also reached, including the superiority of the Percentiles Estimators method over the Maximum Likelihood Method in estimating the parameters of the proposed probability distribution. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new function which is defined by replacing polynomials into polynomial factorials in the expansion of exponential function denoted by e(k)(1)ℓ entitled as extorial function, an original and unique contribution. Required identities involving difference operators with factorials are enumerated. And these identities are applied to obtain solutions of difference and discrete partial difference equation for heat flows and current flows in RL circuit. Numerical verifications validating the above results are included. [ABSTRACT FROM AUTHOR]

Bayesian approach is actively used to develop global optimization algorithms aimed at expensive black box functions. One of the challenges in this approach is the selection of an appropriate model for the objective function. Normally, a Gaussian random field is chosen as a theoretical model. However, the problem of estimation of parameters, using objective function values, is not thoroughly researched. In this paper, we consider the behavior of maximum likelihood estimators (MLEs) of parameters of the homogeneous isotropic Gaussian random field with squared exponential covariance function. We also compare properties of exponential covariance function models. [ABSTRACT FROM AUTHOR]

In this work, by implementing the generalized (G′/G²)-expansion method, we present exact solutions of a completely integrable model namely; Whitham-Broer-Kaup (WBK) equations. The considered equation describes the small amplitude regime for dispersive long waves in shallow water. The solutions are obtained in terms of exponential functions, trigonometric functions and rational functions. Moreover, by selecting arbitrary constants appropriately in the solutions, we discovered various interesting periodic soliton structures. Also, innovative as well as distinct exact solutions raised in this paper may hold powerful applications in various fields of mathematical physics. [ABSTRACT FROM AUTHOR]

In this paper we focus on calculating an approximate solution to the one dimensional Thomas-Fermi equation in the form of an expansion using exponential basis functions. We use a self-consistent approach for finding the expansion coefficients. In practice this results in an iterative algorithm. In this way, the problem of solving a system of nonlinear equations, which is common for other similar methods for finding approximate solutions for the equation of interest, is avoided. The evaluation of this approach has been performed in two directions. First, to see the effect of using the exponential basis set, we compare the quality of found approximate solutions using the proposed algorithm with an analog self-consistent approach based on finite elements. A comparison is also conducted with the use of Padé approximation for solving the one dimensional Thomas-Fermi equation. [ABSTRACT FROM AUTHOR]

This paper proposes the bivariate version of Poisson-weighted exponential (PWE) distribution considered in Zamani and Ismail (2010). This new discrete bivariate Poisson-weighted exponential (BPWE) distribution can be used as an alternative for modeling dependent and over-dispersed count data. Several properties such as mean, variance, correlation and joint moment generating function of the new BPWE distribution are discussed. A numerical example is given and the BPWE distribution is compared to bivariate Poisson (BP) distribution. The results show that BPWE distribution provides larger log likelihood and smaller AIC, indicating that BPWE distribution is better than BP distribution and can be used as an alternative for fitting dependent and over-dispersed count data. [ABSTRACT FROM AUTHOR]

The Lindley distribution was introduced by Lindley in the context of Bayes inference.1 Its density function is obtained by mixing the exponential distribution, with scale parameter β, and the gamma distribution, with shape parameter 2 and scale parameter β. Recently, a new generalization of the Lindley distribution was proposed by Barco et al., called the inverse power Lindley distribution.2 This paper will introduce an extension of the inverse power Lindley distribution using the Marshall-Olkin method, resulting in the Marshall-Olkin Extended Inverse Power Lindley (MOEIPL) distribution. The MOEIPL distribution offers a flexibility in representing data with various shapes. This flexibility is due to the addition of a tilt parameter to the inverse power Lindley distribution. Some properties of the MOEIPL are explored, such as its probability density function, cumulative distribution function, hazard rate, survival function, and quantiles. Estimation of the MOEIPL parameters was conducted using maximum likelihood method. The proposed distribution was applied to model the wind speed in Demak, Indonesia. The results illustrate the MOEIPL distribution and arre compared to Lindley, power Lindley, inverse Lindley, inverse power Lindley, gamma, and Weibull. Model comparison using the AIC shows that MOEIPL fits the data better than the other distributions. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce and investigate a class of generalized Bernoulli polynomials and Euler polynomials based on the generating function. We unify all forms of q-exponential functions by one more parameter. We study some conditions on this parameter to related this to some classical results for q-Bernoulli numbers and polynomials. [ABSTRACT FROM AUTHOR]

The paper discusses asymptotic behaviors of the delayed matrix exponential, delayed matrix sine and delayed matrix cosine. Such functions were defined in connection with a formalization of the step method for linear systems of differential equations with a constant delay r. The above matrix functions are defined by matrix polynomials on every interval [(k - 1)τ, kτ), where k = 0, 1, . . . and τ > 0. To investigate the asymptotic behavior of the delayed matrix functions, the main branch of the Lambert function is used. [ABSTRACT FROM AUTHOR]

This paper considers a multiserver loss system with servers-orbit interaction and feedbacks motivated from call centers. Incoming calls that are blocked upon arrival join an orbit from which they independently retry after some random time. In addition, idle servers make outgoing calls to the customers either in the orbit or outside. We assume that incoming calls, outgoing calls from the orbit and outgoing calls from outside follow three distinct exponential distributions. Using a Lyapunov function approach, we derive the necessary and sufficient condition for the stability of the system. [ABSTRACT FROM AUTHOR]

In this paper, we study the performance of an Automatic Pipeline, Variable Inventory, Order-Based Production Control System (APVIOBPCS) using linear control theory. In particular, we consider a system with independent adjustments for the inventory and pipeline feedback loops and the use of triple exponential smoothing (the Holt-Winters no-trend, additive seasonality model) as a forecasting strategy. To quantify the performance of the system, we derive the transfer functions of the system and plot the frequency response of the system under a number of different parametrizations. We find that the system using Holt-Winters forecasting (the HW-model) significantly outperforms the system using simple exponential smoothing (the SES model), commonly found in the literature, under certain demand assumptions. However, we find that the HW-model is very sensitive to the demand frequency, while the SES is very robust. Thus, the performance range is substantially narrower for the SES model. Finally, we show that previous insights related to behavioral biases are not affected by the choice of forecasting strategy. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new spaces of entire functions in multivariable infinite dimensional with certain exponential growth rates determined by Young functions. These entire functions characterize, via the Kernel theorem, the symbols of Quantum Fock space operators. Then, we define the Quantum annihilation and Quantum creation derivatives. So, we prove that every Quantum operators have an integral representation. [ABSTRACT FROM AUTHOR]

In the recent development in various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In last two decades, the Tsallis version has found a lot of applications. In this paper, we consider a deformation which has two purposes. First, we introduce it as more general mathematical tool where the Tsallis exponential function is the special case. Then, we prove that it has a lot of interesting properties from mathematical point of view and possibilities in the applications. We emphasize the differential and difference properties of our deformation which are important for the formation and explanation of continuous and discrete models of numerous phenomena. [ABSTRACT FROM AUTHOR]

In this paper, we discuss control variate methods for Asian option pricing under exponential jump diffusion model for the underlying asset prices. Numerical results show that the new control variate XNCV is much more efficient than the classical control variate XCCV when used in pricing Asian options. For example, the variance reduction ratios by XCCV are no more than 120 whereas those by XNCV vary from 15797 to 49171 on average over sample sizes 1024, 2048, 4096, 8192, 16384 and 32768. [ABSTRACT FROM AUTHOR]

In this paper we present the class of numerical methods called "exponentially fitted explicit Runge-Kutta" (EFRK) schemes with the property of minimum storage requirements for systems with large dimension and whose solution is oscillatory or periodic. A study of schemes of the minimum storage family of van der Houwen with orders p < 4 that require only two storage locations per variable is carried out. Two optimal EFRK formulae are deduced taking into account accuracy and stability. The first one is a RK with three-stages and third order, and the second one with five-stages and fourthorder. Finally some numerical experiments are presented to show the behaviour of the new EFRK schemes for some periodic problems. [ABSTRACT FROM AUTHOR]

In this paper we investigate some practical aspects concerning the use of the Restricted-Denominator (RD) rational Arnoldi method for the computation of the core functions of exponential integrators for parabolic problems. We derive a useful a-posteriori bound that exploits the fast convergence of the Arnoldi method for compact operators. Some numerical experiments arising from the discretization of sectorial operators are presented. [ABSTRACT FROM AUTHOR]

Stable distributions are a class of distributions which allow skewness and heavy tail. Non-Gaussian stable random variables play the role of normal distribution in the central limit theorem, for normalized sums of random variables with infinite variance. The lack of analytic formula for density and distribution functions of stable random variables has been a major drawback to the use of stable distributions, also in the case of inference in Bayesian framework. Buckle introduced priors for the parameters of stable random variables to obtain an analytic form of posterior distribution. However, many researchers tried to solve the problem, through the Markov chain Monte Carlo methods, e.g. [8] and their references. In this paper a new class of heavy-tailed distribution is introduced, called skewed stable. This class has two main advantages: It has many inferential advantages, since it is a member of exponential family, so the Bayesian inference can be drawn similar to the exponential family of distributions and modelling skew data with stable distributions is dominated by this family. Finally, Bayesian inference for skewed stable arc compared to the stable distributions through a few simulations study. [ABSTRACT FROM AUTHOR]

Montgomery modular multiplication (MMM) plays a crucial role in the implementation of modular exponentiations of public-key cryptography. In this paper, we discuss the iterative structure and extend the iterative bound condition of MMM. It can be applied to complicated modular exponentiations. Based on the iterative condition of MMM, we can directly use non-modular additions, subtractions and even simple multiplications instead of the modular forms, which make modular exponentiation operation very efficient but more importantly iterative applicability of MMM. [ABSTRACT FROM AUTHOR]

Tuned methods of the exponentially-fitted kind are derived and applied to fourth order ordinary differential equations subject to a special kind of boundary condtions. In this paper we analyse and construct several methods of order 2. A numerical experiment is performed to sustain the derived technique. [ABSTRACT FROM AUTHOR]

This paper proffers differential quadrature scheme to obtain approximate solution of one dimensional advection diffusion equation with Dirichlet's boundary conditions. The scheme uses modified exponential cubic spline basis functions to obtain the numerical results. The method uses less computational effort and produces more accurate results. In the numerical problems, L∞ and L2 errors show the relative performance of the method for different time levels. The results shown by the method are in good approximation with the exact solution. [ABSTRACT FROM AUTHOR]

Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 1-D gas flow are analyzed in the phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the real axis. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1]. [ABSTRACT FROM AUTHOR]

Numerical calculation of photon migration in biological tissue using the radiative transfer equation (RTE) has attracted great interests in biomedical optics and imaging. Because biological tissue is a highly forward-peaked scattering medium, a normalization of scattering phase function in the RTE is crucial. This paper proposes a simple way of normalizing the phase function by the double exponential formula, which is heuristically modified from the original one. The proposed method is validated by the agreement between the numerical solution of the RTE with the proposed method and analytical solution of the RTE for the case of a highly forward-peaked scattering medium, while the numerical solutions with conventional normalization methods disagree with the analytical solution. This result suggests the proposed method is accurate in numerical calculation of the RTE. [ABSTRACT FROM AUTHOR]

As the world's oil reserves are dwindling, some researchers have been prompted to make a breakthrough to further improve the efficiency of exploration and production. One of the technologies used is heating the crude oil. This paper presents the modeling results of heat treatment on crude oil using microwave energy. Modeling is conducted by assuming that the diameter of the well is 11,16 cm, the heat source is applied on the surface of the well, and the cut-off frequency in the air and on crude oil are 1,56 GHz. and 0.91 GHz, respectively. The energy generated by the microwave radiation is converted into heat energy which is absorbed by the crude oil. Consequently, this energy increases the temperature of crude oil through a heat transfer mechanism. The results obtained showed that the temperature of crude oil is about 200°C at a depth of 62.5cm, and at a distance of 3 cm from the center of the well. Temperature along the well follows an exponential function, which is from the center of the well in the direction radially outward from the cylinder axis. It has been observed that the temperature decreases as measured from the well surface along the cylinder. [ABSTRACT FROM AUTHOR]

This paper deals with the foresight turnover with the time series. The time adjustment is made using the modified exponential and the Gompertz function. The graphic model for the data we know is represented by an asymptotic smooth curve where growth is slowest at the end of a time period, so the turnover forecast is realized with time series - Gompertz curve. We used the regression function of the model to predict future events. [ABSTRACT FROM AUTHOR]