Subjects -> MATHEMATICS (Total: 1118 journals)     - APPLIED MATHEMATICS (92 journals)    - GEOMETRY AND TOPOLOGY (23 journals)    - MATHEMATICS (819 journals)    - MATHEMATICS (GENERAL) (45 journals)    - NUMERICAL ANALYSIS (26 journals)    - PROBABILITIES AND MATH STATISTICS (113 journals) MATHEMATICS (819 journals)                  1 2 3 4 5 | Last

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 Applied Mathematics - A Journal of Chinese UniversitiesJournal Prestige (SJR): 0.17 Number of Followers: 2      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1993-0445 - ISSN (Online) 1005-1031 Published by Springer-Verlag  [2658 journals]
• The rate of convergence on fractional power dissipative operator on some
sobolev type spaces

Abstract: In [3], Chen, Deng, Ding and Fan proved that the fractional power dissipative operator is bounded on Lebesgue spaces Lp(ℝn), Hardy spaces Hp(ℝn) and general mixed norm spaces, which implies almost everywhere convergence of such operator. In this paper, we study the rate of convergence on fractional power dissipative operator on some sobolev type spaces.
PubDate: 2021-09-01

• On complete convergence in Marcinkiewicz-Zygmund type SLLN for random
variables

Abstract: We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions. Consequently, we get the results for many dependent structures, such as END, ϱ*-mixing, ϱ−-mixing and φ-mixing, etc.
PubDate: 2021-09-01

• Quantile inference for nonstationary processes with infinite variance
innovations

Abstract: Based on the quantile regression, we extend Koenker and Xiao (2004) and Ling and McAleer (2004)’s works from finite-variance innovations to infinite-variance innovations. A robust t-ratio statistic to test for unit-root and a re-sampling method to approximate the critical values of the t-ratio statistic are proposed in this paper. It is shown that the limit distribution of the statistic is a functional of stable processes and a Brownian bridge. The finite sample studies show that the proposed t-ratio test always performs significantly better than the conventional unit-root tests based on least squares procedure, such as the Augmented Dick Fuller (ADF) and Philliphs-Perron (PP) test, in the sense of power and size when infinite-variance disturbances exist. Also, quantile Kolmogorov-Smirnov (QKS) statistic and quantile Cramer-von Mises (QCM) statistic are considered, but the finite sample studies show that they perform poor in power and size, respectively. An application to the Consumer Price Index for nine countries is also presented.
PubDate: 2021-09-01

• A multiplicative Gauss-Newton minimization algorithm: Theory and
application to exponential functions

Abstract: Multiplicative calculus (MUC) measures the rate of change of function in terms of ratios, which makes the exponential functions significantly linear in the framework of MUC. Therefore, a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC. Taking this as motivation, this paper lays mathematical foundation of well-known classical Gauss-Newton minimization (CGNM) algorithm in the framework of MUC. This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization (MGNM) method along with its convergence properties. The proposed method is generalized for n number of variables, and all its theoretical concepts are authenticated by simulation results. Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions. From simulation results, it has been observed that proposed MGNM method converges for 12972 points, out of 19600 points considered while optimizing multiplicatively-linear exponential function, whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points, respectively. Furthermore, for a given set of initial value, the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods. A similar pattern is observed for multiplicatively-non-linear exponential function. Therefore, it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.
PubDate: 2021-09-01

• Fractal interpolation: a sequential approach

Abstract: Fractal interpolation is a modern technique to fit and analyze scientific data. We develop a new class of fractal interpolation functions which converge to a data generating (original) function for any choice of the scaling factors. Consequently, our method offers an alternative to the existing fractal interpolation functions (FIFs). We construct a sequence of α-FIFs using a suitable sequence of iterated function systems (IFSs). Without imposing any condition on the scaling vector, we establish constrained interpolation by using fractal functions. In particular, the constrained interpolation discussed herein includes a method to obtain fractal functions that preserve positivity inherent in the given data. The existence of $${{\cal C}^r} - \alpha - {\rm{FIFs}}$$ is investigated. We identify suitable conditions on the associated scaling factors so that α-FIFs preserve r-convexity in addition to the $${{\cal C}^r} - {\rm{smoothness}}$$ of original function.
PubDate: 2021-09-01

• Fractional sum and fractional difference on non-uniform lattices and
analogue of Euler and Cauchy Beta formulas

Abstract: As is well known, the definitions of fractional sum and fractional difference of f (z) on non-uniform lattices x(z) = c1z2 + c2z + c3 or x(z) = c1qz + c2q−z + c3 are more difficult and complicated. In this article, for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways. The analogue of Euler’s Beta formula, Cauchy’ Beta formula on non-uniform lattices are established, and some fundamental theorems of fractional calculas, the solution of the generalized Abel equation on non-uniform lattices are obtained etc.
PubDate: 2021-09-01

• Laguerre reproducing kernel method in Hilbert spaces for unsteady
stagnation point flow over a stretching/shrinking sheet

Abstract: This paper investigates the nonlinear boundary value problem resulting from the exact reduction of the Navier-Stokes equations for unsteady magnetohydrodynamic boundary layer flow over the stretching/shrinking permeable sheet submerged in a moving fluid. To solve this equation, a numerical method is proposed based on a Laguerre functions with reproducing kernel Hilbert space method. Using the operational matrices of derivative, we reduced the problem to a set of algebraic equations. We also compare this work with some other numerical results and present a solution that proves to be highly accurate.
PubDate: 2021-09-01

• Degree sum conditions for hamiltonian index

Abstract: In this note, we show a sharp lower bound of $$\min \left\{{\sum\nolimits_{i = 1}^k {{d_G}({u_i}):{u_1}{u_2} \ldots {u_k}}} \right.$$ is a path of (2-)connected G on its order such that (k-1)-iterated line graphs Lk−1(G) are hamiltonian.
PubDate: 2021-09-01

• Weak optimal inverse problems of interval linear programming based on KKT
conditions

Abstract: In this paper, weak optimal inverse problems of interval linear programming (IvLP) are studied based on KKT conditions. Firstly, the problem is precisely defined. Specifically, by adjusting the minimum change of the current cost coefficient, a given weak solution can become optimal. Then, an equivalent characterization of weak optimal inverse IvLP problems is obtained. Finally, the problem is simplified without adjusting the cost coefficient of null variable.
PubDate: 2021-09-01

• Numerical solution of stochastic Itô-Volterra integral equations based on
Bernstein multi-scaling polynomials

Abstract: In this paper, first, Bernstein multi-scaling polynomials (BMSPs) and their properties are introduced. These polynomials are obtained by compressing Bernstein polynomials (BPs) under sub-intervals. Then, by using these polynomials, stochastic operational matrices of integration are generated. Moreover, by transforming the stochastic integral equation to a system of algebraic equations and solving this system using Newton’s method, the approximate solution of the stochastic Itô-Volterra integral equation is obtained. To illustrate the efficiency and accuracy of the proposed method, some examples are presented and the results are compared with other methods.
PubDate: 2021-09-01

• On a new fractional-order Logistic model with feedback control

Abstract: In this paper, we formulate and analyze a new fractional-order Logistic model with feedback control, which is different from a recognized mathematical model proposed in our very recent work. Asymptotic stability of the proposed model and its numerical solutions are studied rigorously. By using the Lyapunov direct method for fractional dynamical systems and a suitable Lyapunov function, we show that a unique positive equilibrium point of the new model is asymptotically stable. As an important consequence of this, we obtain a new mathematical model in which the feedback control variables only change the position of the unique positive equilibrium point of the original model but retain its asymptotic stability. Furthermore, we construct unconditionally positive nonstandard finite difference (NSFD) schemes for the proposed model using the Mickens’ methodology. It is worth noting that the constructed NSFD schemes not only preserve the positivity but also provide reliable numerical solutions that correctly reflect the dynamics of the new fractional-order model. Finally, we report some numerical examples to support and illustrate the theoretical results. The results indicate that there is a good agreement between the theoretical results and numerical ones.
PubDate: 2021-09-01

• Correction to: Analysis method and algorithm design of biological sequence
problem based on generalized k-mer vector

PubDate: 2021-06-22

• Correction to: Existence and exponential stability of almost-periodic
solutions for MAM neural network with distributed delays on time scales

PubDate: 2021-06-22

• Correction to: Tracy-Widom distribution, Airy2 process and its sample path
properties

PubDate: 2021-06-22

• Correction to: Log-logistic parameters estimation using moving extremes
ranked set sampling design

PubDate: 2021-06-22

• Correction to: A Novel Bat Algorithm based on Cross Boundary Learning and
Uniform Explosion Strategy

PubDate: 2021-06-22

• Log-logistic parameters estimation using moving extremes ranked set
sampling design

Abstract: In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. In the current paper, a modification of ranked set sampling (RSS) called moving extremes RSS (MERSS) is considered for the estimation of the scale and shape parameters for the log-logistic distribution. Several traditional estimators and ad hoc estimators will be studied under MERSS. The estimators under MERSS are compared to the corresponding ones under SRS. The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.
PubDate: 2021-03-01

• Numerical solutions of two-dimensional nonlinear integral equations via
Laguerre Wavelet method with convergence analysis

Abstract: In this paper, the approximate solutions for two different type of two-dimensional nonlinear integral equations: two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method. To do this, these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form. By solving these systems, unknown coefficients are obtained. Also, some theorems are proved for convergence analysis. Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.
PubDate: 2021-03-01

• Stability results for a nonlinear two-species competition model with
size-structure

Abstract: We formulate a system of integro-differential equations to model the dynamics of competition in a two-species community, in which the mortality, fertility and growth are size-dependent. Existence and uniqueness of nonnegative solutions to the system are analyzed. The existence of the stationary size distributions is discussed, and the linear stability is investigated by means of the semigroup theory of operators and the characteristic equation technique. Some sufficient conditions for asymptotical stability / instability of steady states are obtained. The resulting conclusion extends some existing results involving age-independent and age-dependent population models.
PubDate: 2021-03-01

• Existence and exponential stability of almost-periodic solutions for MAM
neural network with distributed delays on time scales

Abstract: This paper is concerned with multidirectional associative memory neural network with distributed delays on almost-periodic time scales. Some sufficient conditions on the existence, uniqueness and the global exponential stability of almost-periodic solutions are established. An example is presented to illustrate the feasibility and effectiveness of the obtained results.
PubDate: 2021-03-01

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