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In this paper, the mean square exponential convergence of semi-linear stochastic differential equations is proved by using quadratic Lyapunov function approach with stochastic process. Many theoretical rustles for convergence and mean square exponential convergence as well as mean square exponential stability of different stochastic differential systems using the necessary mathematical conditions have been proposed and supported with mathematical proofs and illustration. The presented approach provides a sufficient condition for stability of some classes of stochastic differential equations. The quadratic types of Lyapunov function gives an effective technique to ensure stable qualitative behavior to stochastic differential system in the present of system random uncertainty corresponding to Brownian motion perturbation. [ABSTRACT FROM AUTHOR]

In this article, K denotes a complete, non-trivially valued, non-Archimedean field. The study of analysis over non-Archimedean fields is called "non-Archimedean Analysis." λ - Statistical convergence is the generalised concept of statistical convergence. In the present paper, we have discussed the concepts of statistically convergent and λ-statistically convergent sequences in n-normed space and we have proved few theorems in such non-Archimedean fields. [ABSTRACT FROM AUTHOR]

In this paper we study estimator of mean residual life function in a partıally informatıve regression model, when life times are randomly censored on the right. We prove an asymptotic normality of estimators and the weakly convergence of a stochastic process to a Gaussian process in Skorohod space. [ABSTRACT FROM AUTHOR]

In the deregulated environment, the transmission grids are used optimally. This utilization of the transmission system makes some lines congested due to the capacity constraints of the line. Congestion becomes a barrier of power trading and it affects the security of the power system. Congestion Management (CM) acts as a major issue that threatens the system security and it is a most difficult task for the system operators. This paper tries to introduce a novel optimization based CM model with advanced soft computing technique. An algorithm is introduced in this paper to deal with CM, which obviously optimize the generating power of added generators with the bus system. This manages the congestion with minimum rescheduling cost. The proposed optimization algorithm termed as Whale Optimization algorithm (WOA) involves in the management of congestion optimally. Subsequently, the experimentation is performed in the test bus system of 118 bus systems. The effectiveness of proposed model is compared with the conventional methods, with respect to cost and convergence. [ABSTRACT FROM AUTHOR]

This paper presents the algorithms for the solution of the optimal control problem of wide scale linear dynamic systems. These algorithms are based on the prediction concept. For the beginning, is considered the interaction prediction approach and afterwards, the cost prediction approach is used. The convergence behavior of the proposed algorithms is thoroughly investigated. In this paper is designed a multi-input, multi-output controller by shaping the gain of an openloop response across frequency. This technique is applied to controlling the pitch axis of an aircraft. Eventually, the paper successfully investigates and demonstrates how to choose a suitable target loop shape and to compute a multivariable controller that optimally matches the target loop shape. [ABSTRACT FROM AUTHOR]

In this paper we deal with iterative methods for approximating multiple roots of nonlinear equations, it is a special case where some particular aspects must be taken into account. We are interested in local convergence studies, that is in obtaining an open ball B(α, r) where the sequence xn generated by an iterative method, starting from any initial point in it generates a sequence {xn} that remains in the ball and converges to the solution of the problem, α. Then, it is interesting to obtain the largest possible value of r, but obviously, this depends on the conditions that the nonlinear function verifies. We define a new technique to simplify the process of obtaining the functions that bound the error equation just by using a characterization of the function using Taylor's development around the root under the assumption of a bounding condition for the (m + 1)th derivative of the function f (x). This technique simplifies the usual intricate properties of divided differences that are used in already published papers about local convergence for multiple roots. Moreover, we complete the study in cases where the multiplicity m is unknown, so we estimate this factor by different strategies comparing the behavior of the corresponding estimations and how this fact affect to the original method. [ABSTRACT FROM AUTHOR]

The subject of this paper belongs to the theory of approximate metrics [23]. An approximate metric on X is a real application defined on X × X that satisfies only a part of the metric axioms. In a recent paper [23], we introduced a new type of approximate metric, named C-metric, that is an application which satisfies only two metric axioms: symmetry and triangular inequality. The remarkable fact in a C-metric space is that a topological structure induced by the C-metric can be defined. The innovative idea of this paper is that we obtain some convergence properties of a C-metric space in the absence of a metric. In this paper we investigate C-metric spaces. The paper is divided into four sections. Section 1 is for Introduction. In Section 2 we recall some concepts and preliminary results. In Section 3 we present some properties of C-metric spaces, such as convergence properties, a canonical decomposition and a C-fixed point theorem. Finally, in Section 4 some conclusions are highlighted. [ABSTRACT FROM AUTHOR]

In this paper the difference equation Δxn = unφ(xσ(n)) is considered. For a given b 2 R, and assuming the absolute convergence of the series Σun, we investigate the properties of a function j sufficient for the existence of a solution convergent to b. It is known that the continuity of j on some neighborhood of b is sufficient for the existence of such solution. The main result of this paper is the example in which we show that the continuity at the point b is not sufficient. [ABSTRACT FROM AUTHOR]

The ant colony algorithm has many advantages compared with other algorithms in path planning, but its shortcomings still cannot be ignored. For example, the convergence speed is very low at initial stage, it is easy to fall into the local optimal solution, and the solution speed is slow and so on. In order to solve these problems and reduce the search time, this paper firstly makes the assignment of the main parameters of α, β, M and ρ in the ant colony algorithm through a large number of experimental data analysis. Then an improved ant colony algorithm based on dynamic parameters and new pheromone updating mechanism is proposed in this paper. Simulation results show that the improved ant colony algorithm can not only greatly shorten the algorithm running time, but also has greater probability to get the global optimal solution, and the convergence rate of algorithm is better than traditional ant colony algorithm. It is very advantageous for solving large-scale optimization problems. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a concept of ideal lacunary statistical quasi-Cauchy sequence of order α of real numbers in the sense that a sequence (xk) of points in R is called I-lacunary statistically quasi-Cauchy of order α, if ... for each ε > 0 and for each δ > 0, where an ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. The main purpose of this paper is to investigate ideal lacunary statistical ward continuity of order α, where a function ƒ is called I- lacunary statistically ward continuous of order α if it preserves I-lacunary statistically quasi-Cauchy sequences of order α, i.e. (ƒ(xn)) is a Sθα (I)-quasi-Cauchy sequence whenever (xn) is. [ABSTRACT FROM AUTHOR]

In the present paper, we provide an information about the growth of the leading coefficients of the numerators of over-convergent subsequences of the mth row of the classical Pad´e table. [ABSTRACT FROM AUTHOR]

In this paper, we provide the mixed generalized iterative method for scalar first order non-linear initial value problem, where the forcing function is the sum of increasing, decreasing, convex and concave functions. We develop the generalized iterative coupled lower and upper solutions of mixed type. Our method will yield generalized monotone method and generalized generalized method as special cases. In these situations, we obtain linear and quadratic convergence respectively. In all other situations, we obtain super linear convergence. As an application, we provide some numerical results. [ABSTRACT FROM AUTHOR]

As well as the Padé approximations itself, multidimensional approximations of such type can be used both to expand the domain of convergence and to accelerate the rate of convergence of series. We consider the modified method of parameter continuation (MMPC) as an asymptotic technique for solving initial both and boundary value problems. MMPC implies the use of multidimensional Padé-type approximants. In this paper we consider the application of several types of multidimensional Padé-type approximants depending on the problem specificity which is being solved. The comparison with numerical calculations confirms the advantages of proposed methods and their accuracy. [ABSTRACT FROM AUTHOR]

Blockchain platform has given information system scholars research opportunities in understanding dynamics of convergence of technology and social context. The information system research issues are complex and require taxonomies to understand the similarities and uniqueness among objects. Developing taxonomies is a complex process that needs systematic approach. This paper is a research-in-progress. We proposed taxonomy for Blockchain platform using existing method of developing taxonomies in information systems. With the unprecedented growth led to several companies to develop the varieties of Blockchain platforms. The complexity in the implementation and understanding the technical protocols leading to difficulty face by researchers and practitioners to access their full potentials. To bridge the gap, we proposed a taxonomy of Blockchains distributed ledger platforms in order to provide a mechanism for researchers and practitioners to understand the phenomenon. Final of taxonomy contains five (5) dimensions with fifteen (15) characteristics. Our analysis discovered Blockchain platforms are designed with specific goals, which prescribe its features, i.e FinTech Blockchain platforms for financial domain. [ABSTRACT FROM AUTHOR]

In this paper, we consider a plane axisymmetric test problem on the convergence of the numerical solution of the model kinetic equation of Bhatnagar-Gross-Kruk (BGK) from the initial approximation for the distribution function to the known equilibrium distribution function corresponding to the state of quasi-solid gas rotation in the cylinder. [ABSTRACT FROM AUTHOR]

The most well-known technique or method in unconstrained optimization is the conjugate gradient method. It is used to get the greatest solution for the unconstrained optimization problems. This method is used in many fields especially, computer science, and engineering due to its convergence speed, simplicity, and the low memory requirements. A new modified conjugate gradient method is presented in this paper. This method is proved with the strong Wolfe-Powell (SWP) line search that it possesses sufficient descent property, and is globally convergent. Numerical results for a set of 141 test problems show the outperformance of the new proposed formula comparing with other methods using the same line search. The performance of this method is more efficient and better than the others. [ABSTRACT FROM AUTHOR]

The Adomian decomposition method is a meshless method. It has fast convergence to the exact solution for a large number of differential equation problems if the exact solution can be expressed in a closed form. On the other hand if the exact solution cannot be expressed in a closed form, the method may need a large number of iterations in order to obtain accurate solutions. In this paper we consider the shallow water equations, as these equations have a wide range of water flow applications. The Adomian decomposition method has been successfully implemented to solve the shallow water equations. However, how relevance the Adomian decomposition method is for the shallow water equations has not been investigated. Therefore, our aim in this paper is to investigate the relevance of the Adomian decomposition method for solving the shallow water equations. Our research results show that the method can be used to solve the shallow water equations for small time values, but is not relevant to be implemented for large time values. [ABSTRACT FROM AUTHOR]

A new iterative procedure is formulated in this paper known as the interval midpoint symmetric single-step IMSS2-5D procedure. In this paper, we consider this new procedure in order to describe the rate of convergence of the IMSS2-5D procedure. It is analytically proven that the IMSS2-5D procedure has a higher convergence rate than ISS2 and ISS2-5D, verifying the rate of convergence to be at least 12. Hence, computational time is reduced since this procedure is more efficient for bounding simple zeros simultaneously. Hence, it would be effective to use this procedure in determining the zeros of polynomial simultaneously. [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 (0) = min{4,4ε} (for ε > 0) - see [1]. On the other hand λ = 1 (cumulative chords) yields 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]

This paper proposes a novel parallelization of ABC Algorithm to solve Short-term Hydro-Thermal Scheduling (SHTS) problem. Parallelization is a novel way of improving the convergence of the algorithm. In case of normal ABC algorithms accelerating operation or modification can be used for better convergence and diversity. But with large number of variables the non-linearity of the search space increases and these modifications are not sufficient to give enough diversity in the crowds of swarms for finding better solutions. However, parallelization of the algorithm increases the diversity in solutions and the search capability. The performance of the proposed algorithm is experimented on two short term multi reservoir cascaded hydrothermal systems. First test case is moderately large while the second test case is a considerably large one. Experimental results demonstrate the superior performance of the proposed algorithm as compared to other recently reported ones in terms of convergence and better quality of solutions. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems for generalized expansive mapping in a cone metric space over Banach algebras without the assumption of normality of cone. Moreover, we give an example to elucidate our result. Our results are significant extension and generalizations of recent result of B. Jiang et al., (J. Comput. Anal. Appl. 21(6):1103 - 1114, 2016) and many well-known results in the literature. [ABSTRACT FROM AUTHOR]

Partitioning is a strategy that will reduce computational cost. Starting with all equations be treated as non-stiff, this strategy will divide the equations into the stiff and nonstiff subsystem. The non-convergence partitioning strategy will determine equations that caused instability, and put the equations into stiff subsystem and solved using Newton iteration backward differentiation formulae and all other equations remain in the non-stiff subsystem and solved by Adams method. This partitioning strategy will continue until instability occurs again and placed equations that caused instability into the stiff subsystem. But for van der Pol equation, the nature of the equations need to change from stiff to the non-stiff subsystem and vice versa when it is necessary. This paper will extend the non-convergence partitioning strategy by allowing equations from the stiff subsystem to be placed back in the non-stiff subsystem. [ABSTRACT FROM AUTHOR]

In this paper, we give a generalization of absolutely almost convergence, and prove interesting results. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to approximate some matrix functions by using a family of high-order Newton-type iterative methods. We analyse the semilocal convergence and the speed of convergence of these methods. Concerning stability, it is well known that even the simplified Newton method can be unstable. Despite it, we present stable versions of our family of algorithms for several matrix functions. We test numerically the methods: we check the numerical robustness and stability by considering matrices that are close to be singular and badly conditioned. We find algorithms of the family with better numerical behavior than the Newton and the Halley methods. These two algorithms are basically the iterative methods proposed in the literature to solve many of this type of problems. [ABSTRACT FROM AUTHOR]

In this paper, a parametric family of twelfth-order iterative methods for solving nonlinear systems is presented. Its local convergence is studied and quadratic polynomials are used to investigate its dynamical behavior. The study of fixed and critical points of the rational function associated allows us to obtain regions of the complex plane where the method is stable. From parameter planes and dynamical planes complementary information of the analytical results is obtained. [ABSTRACT FROM AUTHOR]

In this paper we consider different methods for formulating boundary optimal control problems of either Dirichlet or Neumann type. On one hand, standard approaches typically have the drawback of searching for the optimal controls in proper subspaces of natural trace spaces. Therefore, we consider alternative formulations with lifting functions that have several advantages. First of all, boundary controls can be determined on natural trace spaces, without additional regularity as required by standard approaches. This also leads to numerical discretizations that have the same rate of convergence for the unknowns defined on the domain and for those on the boundary. A potential drawback of the method consists in the use of control functions defined over the problem domain instead of on its boundary, thus increasing the number of degrees of freedom of the problem. This drawback can be compensated by using lifting functions with restricted support, whose boundary contains the control boundary under interest. Numerical results solving the optimality systems in an all-at-once approach show that it is possible to use restricted functions which do not substantially change the minimum value of the target functional with respect to the case of lifting functions with non-restricted support. [ABSTRACT FROM AUTHOR]

In the paper, we utilize the fractional differential transformation (FDT) to solving singular initial value problem of fractional Emden-Fowler type differential equations. The solutions of our model equations are calculated in the form of convergent series with fast computable components. The numerical results show that the approach is correct, accurate and easy to implement when applied to fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we shall tackle the numerical treatment of two-dimensional fractional sub-diffusion equations using parametric quintic spline. It is shown that this numerical scheme is solvable, stable and convergent with high accuracy which improves some earlier work. Finally, we carry out an experiment to demonstrate the efficiency of our numerical scheme. [ABSTRACT FROM AUTHOR]

In this paper, we shall construct a new numerical scheme for fourth-order fractional diffusion wave model. The solvability, stability and convergence of proposed method are established in l2 norm and it is shown that the numerical scheme improves the earlier work done. Simulation is carried out to verity the accuracy and efficiency of the numerical scheme. [ABSTRACT FROM AUTHOR]

Aiming at the problem of long computing time in image feature matching process and convergence. This paper proposes Bayes Grid Statistics for fast feature matching and convergence. Firstly, the human visual judgment system is established by using Bayes rule. The image is meshed and the probability of Bayes feature matching in the grid is calculated. Matching the correct region statistic is higher. We can through the Bayes Grid Statistics make the convergence of base matrix becomes faster. Finally, a fast and robust real-time solutions can be obtained. [ABSTRACT FROM AUTHOR]

In this paper study is conducted to identify the accurate FE idealization technique for Cut-Out analysis simulation. Case study is conducted on a 2D plate FE model constrained at one edge and in-plane loading at opposite edge. Various MSC Nastran Interface elements like RBE2, RBE3, RSPLINE and CINTC are studied in detail and FE iterations are carried out on a 2D plate model connecting dissimilar meshes with Interface elements. The best interface element is proposed based on the accuracy of the results. Parametric studies have been conducted to validate the FE results. [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]

In the present paper, we extend the notions of statistically convergence of order β and strong Cesàro summability of order β for sequences of fuzzy numbers and introduce the notions of f-statistically convergence of order β and strong Cesàro summability of order β for β ∈ (0,1] with respect to an unbounded modulus function f for double sequences of fuzzy numbers and give some inclusion theorems. [ABSTRACT FROM AUTHOR]

The error analysis for the meshless methods, especially for the Meshless Finite Difference Method (MFDM), is discussed in the paper. Both a priori and a posteriori error estimations are considered. Experimental order of convergence confirms the theoretically developed a priori error bound. The higher order extension of the MFDM - the multipoint approach may be used as a source of the improved reference solution, instead of the true analytical one, for the global and local error estimation of the solution and residual errors. Several types of a posteriori error estimators are described. A variety of performed tests confirm high quality of a posteriori error estimation based on the multipoint MFDM. [ABSTRACT FROM AUTHOR]

This paper presents the influence of the lack of ellipticity property on the solution convergence of the coupled electro-mechanical problems. This influence consists in the non-monotonic convergence which can hardly be described analytically. We recall our previous unpublished research where we demonstrate that the non-monotonicity depends very much on the energy level of the two component parts of the energy related to the coupled fields of mechanical and electric character. We further investigate the influence of this non-monotonic character of the convergence on the error estimation via equilibrated residual method. We also assess the influence of such convergence on the three-step error-controlled adaptive algorithms. We indicate the methods of practical overcoming the mentioned problems related to the lack of ellipticity. [ABSTRACT FROM AUTHOR]

In the present paper, we propose an eficient iterative numerical method of successive approximations to approximate solution of nonlinear Urisohn-Volterra fuzzy functional integral equations by fuzzy trapezoidal quadrature formula for classes of fuzzy-number-valued functions of Lipschitz type. We prove the convergence of the method and investigate the numerical stability of the present method with respect to the choice of the first iteration. The convergence of the method is tested through a numerical experiment, that confirms the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we propose an efficient iterative method to solve two-dimensional nonlinear Hammerstein fuzzy functional integral equations based on fuzzy Haar wavelets. We prove the convergence of the method by Banach's fixed point theorem and investigate the numerical stability of the presented method with respect to the choice of the first iteration. Finally, some numerical experiment confirm the theoretical results and illustrate the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

A family of the Bessel-Maitland functions are considered in this paper and some useful estimations are obtained for them. Series defined by means of these functions are considered and their behaviour on the boundaries of the convergence domains is discussed. Using the obtained estimations, necessary and sufficient conditions for the series overconvergence, as well as Hadamard type theorem are proposed. [ABSTRACT FROM AUTHOR]

This paper presents on meshing convergence analysis of finite element (FE) model to simulate enamelcement- bracket fracture. Three different materials used in this study involving interface fracture are concerned. Complex behavior ofinterface fracture due to stress concentration is the reason to have a well-constructed meshing strategy. In FE analysis, meshing size is a critical factor that influenced the accuracy and computational time of analysis. The convergence study meshing scheme involving critical area (CA) and non-critical area (NCA) to ensure an optimum meshing sizes are acquired for this FE model. For NCA meshing, the area of interest are at the back of enamel, bracket ligature groove and bracket wing. For CA meshing, area of interest are enamel area close to cement layer, the cement layer and bracket base. The value of constant NCA meshing tested are meshing size 1 and 0.4. The value constant CA meshing tested are 0.4 and 0.1. Manipulative variables are randomly selected and must abide the rule of NCA must be higher than CA. This study employed first principle stresses due to brittle failure nature of the materials used. Best meshing size are selected according to convergence error analysis. Results show that, constant CA are more stable compare to constant NCA meshing. Then, 0.05 constant CA meshing are tested to test the accuracy of smaller meshing. However, unpromising result obtained as the errors are increasing. Thus, constant CA 0.1 with NCA mesh of 0.15 until 0.3 are the most stable meshing as the error in this region are lowest. Convergence test was conducted on three selected coarse, medium and fine meshes at the range of NCA mesh of 0.15 until 3 and CA mesh area stay constant at 0.1. The result shows that, at coarse mesh 0.3, the error are 0.0003% compare to 3% acceptable error. Hence, the global meshing are converge as the meshing size at CA 0.1 and NCA 0.15 for this model. [ABSTRACT FROM AUTHOR]