This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case ...This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).展开更多
On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial ...On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.展开更多
In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coeffi...In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in Aψ,w are discussed.展开更多
This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tai...This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tail dependence parameters are deduced since the copula of continuous variables is invariant under strictly increasing transformation about the random variables, which are more simple than those obtained in previous research. Then, the local monotonicity of these indices about the correlation coefficient is discussed, and it is concluded that the upper extremal dependence index increases with the correlation coefficient, but the monotonicity of the upper orthant tail dependence index is complex. Some simulations are performed by the Monte Carlo method to verify the obtained results, which are found to be satisfactory. Meanwhile, it is concluded that the obtained conclusions can be extended to any distribution family in which the generating random variable has a regularly varying distribution.展开更多
0 Introduction It is well known that there axe a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the cond...0 Introduction It is well known that there axe a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the condition to quasi-monotonicity, O-regularly varying quasi-monotonicity, etc..展开更多
A method for determining symbolic and all numerical solutions in design optimization based on monotonicity analysis and solving polynomial systems is presented in this paper. Groebner Bases of the algebraic system equ...A method for determining symbolic and all numerical solutions in design optimization based on monotonicity analysis and solving polynomial systems is presented in this paper. Groebner Bases of the algebraic system equivalent to the subproblem of the design optimization is taken as the symbolic (analytical) expression of the optimum solution for the symbolic optimization, i.e. the problem with symbolic coefficients. A method based on substituting and eliminating for determining Groebner Bases is also proposed, and method for finding all numerical optimum solutions is discussed. Finally an example is given, demonstrating the strategy and efficiency of the method.展开更多
The monotonicity of a rational Bezier curve, usually related to an explicit function, is determined by the used coordinate system. However, the shape of the curve is independent of the coordinate system. To meet the a...The monotonicity of a rational Bezier curve, usually related to an explicit function, is determined by the used coordinate system. However, the shape of the curve is independent of the coordinate system. To meet the affine invariant property, a kind of generalized mono- tonicity, called direction monotonicity, is introduced for rational Bezier curves. The direction monotonicity is applied to both planar and space curves and to both Cartesian and affine co- ordinate systems, and it includes the traditional monotonicity as a subcase. By means of it, proper affine coordinate systems may be chosen to make some rational Bezier curves monotonic. Direction monotonic interpolation may be realized for some of the traditionally nonmonotonic data as well.展开更多
In approximation of fractional order systems,a significant objective is to preserve the important properties of the original system.The monotonicity of time/frequency responses is one of these properties whose preserv...In approximation of fractional order systems,a significant objective is to preserve the important properties of the original system.The monotonicity of time/frequency responses is one of these properties whose preservation is of great importance in approximation process.Considering this importance,the issues of monotonicity preservation of the step response and monotonicity preservation of the magnitude-frequency response are independently investigated in this paper.In these investigations,some conditions on approximating filters of fractional operators are found to guarantee the preservation of step/magnitude-frequency response monotonicity in approximation process.These conditions are also simplified in some special cases.In addition,numerical simulation results are presented to show the usefulness of the obtained conditions.展开更多
In this paper,we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-Laplacian systems.By virtue of this method,we investigate t...In this paper,we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-Laplacian systems.By virtue of this method,we investigate the qualitative properties of positive solutions for the following Schrodinger system with fractional p-Laplacian{(-△)^(s)_(p)u+au^(p-1)=f(u,v),(-△)^(t)_(p)v+bv(p-1)=g(u,v),where 0<s,t<1 and 2<p<∞.We obtain the radial symmetry in the unit ball or the whole space R^(N)(N≥2),the monotonicity in the parabolic domain and the nonexistence on the half space for positive solutions to the above system under some suitable conditions on f and g,respectively.展开更多
In this note, we prove that the convergence rate of the modified Gauss-Seidel (MGS) method with preconditional I+S α is a monotonic function of preconditioning parameter α. Based on this result, to achieve better c...In this note, we prove that the convergence rate of the modified Gauss-Seidel (MGS) method with preconditional I+S α is a monotonic function of preconditioning parameter α. Based on this result, to achieve better convergence rate we suggest proforming twice preconditoning when applying the MGS method to solve a linear system whose coefficient matrix is an irreducible non-singular M-matrix.展开更多
As a prerequisite for effective prognostics, the goodness of the features affects the complexity of the prognostic methods. Comparing to features quality evaluation in diagnostics, features evaluation for prognostics ...As a prerequisite for effective prognostics, the goodness of the features affects the complexity of the prognostic methods. Comparing to features quality evaluation in diagnostics, features evaluation for prognostics is a new problem. Normally, the monotonic tendency of feature series can be used as the visual representation of equipment damage cumulation so that forecasting its future health states is easy to implement. Through introducing the concept of ranking mutual information in ordinal case, a monotonicity evaluation method of monitoring feature series is proposed. Finally, this method is verified by the simulating feature series and the results verify its effectivity. For the specific application in industry, the evaluation results can be used as the standard for selecting prognostic feature.展开更多
In this paper,we present monotonicity results of a function involving the inverse hyperbolic sine.From these,we obtain some lower bounds for the inverse hyperbolic sine.
In this paper, we present numerical studies of a recently proposed scalar nonlocal nonlinear conservation law in one space dimension. The nonlocal model accounts for nonlocal interactions over a finite horizon and enj...In this paper, we present numerical studies of a recently proposed scalar nonlocal nonlinear conservation law in one space dimension. The nonlocal model accounts for nonlocal interactions over a finite horizon and enjoys maximum principle, monotonicity-preserving and entropy condition on the continuum level. Moreover, it has a well-defined local limit given by a conventional local conservation laws in the form of partial differential equations. We discuss convergent numerical approximations that preserve similar properties on the discrete level.We also present numerical experiments to study various limiting behavior of the numerical solutions.展开更多
Let?be a real Hilbert space and?C?be a nonempty closed convex subset of H. Let T : C?→?C?be a demicontractive map satisfying?〈Tx, x〉?≥?‖x‖2 for all?x?∈ D (T). Then the Mann iterative sequence given by?xn + 1?= ...Let?be a real Hilbert space and?C?be a nonempty closed convex subset of H. Let T : C?→?C?be a demicontractive map satisfying?〈Tx, x〉?≥?‖x‖2 for all?x?∈ D (T). Then the Mann iterative sequence given by?xn + 1?= (1 - an) xn +?anT xn, where an ∈?(0, 1) n?≥?0, converges strongly to an element of F (T):= {x?∈ C : Tx = x}. This strong convergence is obtained without the compactness-type assumptions on C, which many previous results (see e.g. [1]) employed.展开更多
In this paper, we introduce the notion of EF-critical map with potential with respect to the functional EF,H（u）. By using the stress-energy tensor, we obtain some monotonicity formulas and vanishing results for thes...In this paper, we introduce the notion of EF-critical map with potential with respect to the functional EF,H（u）. By using the stress-energy tensor, we obtain some monotonicity formulas and vanishing results for these maps under conditions on H.展开更多
This paper addresses the problem of inference for a multinomial regression model in the presence of likelihood monotonicity. This paper proposes translating the multinomial regression problem into a conditional logist...This paper addresses the problem of inference for a multinomial regression model in the presence of likelihood monotonicity. This paper proposes translating the multinomial regression problem into a conditional logistic regression problem, using existing techniques to reduce this conditional logistic regression problem to one with fewer observations and fewer covariates, such that probabilities for the canonical sufficient statistic of interest, conditional on remaining sufficient statistics, are identical, and translating this conditional logistic regression problem back to the multinomial regression setting. This reduced multinomial regression problem does not exhibit monotonicity of its likelihood, and so conventional asymptotic techniques can be used.展开更多
In this paper,we study the completely monotonic property of two functions involving the functionΔ(x)=[ψ′(x)]2+ψ″(x)and deduce the double inequality x^(2)+3x+3/3x^(4)(2x+1)^(2)<Δ(x)<625x^(2)+2275x+5043/3x^(...In this paper,we study the completely monotonic property of two functions involving the functionΔ(x)=[ψ′(x)]2+ψ″(x)and deduce the double inequality x^(2)+3x+3/3x^(4)(2x+1)^(2)<Δ(x)<625x^(2)+2275x+5043/3x^(4)(50x+41)^(2),x>0which improve some recent results,whereψ(x)is the logarithmic derivative of the Gamma function.Also,we deduce the completely monotonic degree of a function involvingψ′(x).展开更多
Terrain characteristics can be accurately represented in spectrum space. Terrain spectra can quantitatively reflect the effect of topographic dynamic forcing on the atmosphere. In wavelength space, topographic spectra...Terrain characteristics can be accurately represented in spectrum space. Terrain spectra can quantitatively reflect the effect of topographic dynamic forcing on the atmosphere. In wavelength space, topographic spectral energy decreases with decreasing wavelength, in spite of several departures. This relationship is approximated by an exponential function. A power law relationship between the terrain height spectra and wavelength is fitted by the least-squares method, and the fitting slope is associated with grid-size selection for mesoscale models. The monotonicity of grid size is investigated, and it is strictly proved that grid size increases with increasing fitting exponent, indicating that the universal grid size is determined by the minimum fitting exponent. An example of landslide-prone areas in western Sichuan is given, and the universal grid spacing of 4.1 km is shown to be a requirement to resolve 90% of terrain height variance for mesoscale models, without resorting to the parameterization of subgrid-scale terrain variance. Comparison among results of different simulations shows that the simulations estimate the observed precipitation well when using a resolution of 4.1 km or finer. Although the main flow patterns are similar, finer grids produce more complex patterns that show divergence zones, convergence zones and vortices. Horizontal grid size significantly affects the vertical structure of the convective boundary layer. Stronger vertical wind components are simulated for finer grid resolutions. In particular, noticeable sinking airflows over mountains are captured for those model configurations.展开更多
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802)。
文摘This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).
文摘On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.
基金supported by the National Science Foundation of China(11271248 and 11302002)the National Science Research Project of Anhui Educational Department(KJ2012Z127)the PhD research startup foundation of Anhui Normal University
文摘In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in Aψ,w are discussed.
基金The National Natural Science Foundation of China(No.11001052,11171065)the National Science Foundation of Jiangsu Province(No.BK2011058)the Science Foundation of Nanjing University of Posts and Telecommunications(No.JG00710JX57)
文摘This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tail dependence parameters are deduced since the copula of continuous variables is invariant under strictly increasing transformation about the random variables, which are more simple than those obtained in previous research. Then, the local monotonicity of these indices about the correlation coefficient is discussed, and it is concluded that the upper extremal dependence index increases with the correlation coefficient, but the monotonicity of the upper orthant tail dependence index is complex. Some simulations are performed by the Monte Carlo method to verify the obtained results, which are found to be satisfactory. Meanwhile, it is concluded that the obtained conclusions can be extended to any distribution family in which the generating random variable has a regularly varying distribution.
基金Supported in part by Natural Science Foundation of China(No.10471130)
文摘0 Introduction It is well known that there axe a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the condition to quasi-monotonicity, O-regularly varying quasi-monotonicity, etc..
文摘A method for determining symbolic and all numerical solutions in design optimization based on monotonicity analysis and solving polynomial systems is presented in this paper. Groebner Bases of the algebraic system equivalent to the subproblem of the design optimization is taken as the symbolic (analytical) expression of the optimum solution for the symbolic optimization, i.e. the problem with symbolic coefficients. A method based on substituting and eliminating for determining Groebner Bases is also proposed, and method for finding all numerical optimum solutions is discussed. Finally an example is given, demonstrating the strategy and efficiency of the method.
基金Supported by the National Natural Science Foundation of China(6140220111326243+3 种基金612723001137117411501252)the Jiangsu Natural Science Foundation of China(BK20130117)
文摘The monotonicity of a rational Bezier curve, usually related to an explicit function, is determined by the used coordinate system. However, the shape of the curve is independent of the coordinate system. To meet the affine invariant property, a kind of generalized mono- tonicity, called direction monotonicity, is introduced for rational Bezier curves. The direction monotonicity is applied to both planar and space curves and to both Cartesian and affine co- ordinate systems, and it includes the traditional monotonicity as a subcase. By means of it, proper affine coordinate systems may be chosen to make some rational Bezier curves monotonic. Direction monotonic interpolation may be realized for some of the traditionally nonmonotonic data as well.
基金supported by the Research Council of Sharif University of Technology(G930720)
文摘In approximation of fractional order systems,a significant objective is to preserve the important properties of the original system.The monotonicity of time/frequency responses is one of these properties whose preservation is of great importance in approximation process.Considering this importance,the issues of monotonicity preservation of the step response and monotonicity preservation of the magnitude-frequency response are independently investigated in this paper.In these investigations,some conditions on approximating filters of fractional operators are found to guarantee the preservation of step/magnitude-frequency response monotonicity in approximation process.These conditions are also simplified in some special cases.In addition,numerical simulation results are presented to show the usefulness of the obtained conditions.
基金Supported by the National Natural Science Foundation of China(12101452,12071229,11771218)。
文摘In this paper,we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-Laplacian systems.By virtue of this method,we investigate the qualitative properties of positive solutions for the following Schrodinger system with fractional p-Laplacian{(-△)^(s)_(p)u+au^(p-1)=f(u,v),(-△)^(t)_(p)v+bv(p-1)=g(u,v),where 0<s,t<1 and 2<p<∞.We obtain the radial symmetry in the unit ball or the whole space R^(N)(N≥2),the monotonicity in the parabolic domain and the nonexistence on the half space for positive solutions to the above system under some suitable conditions on f and g,respectively.
文摘In this note, we prove that the convergence rate of the modified Gauss-Seidel (MGS) method with preconditional I+S α is a monotonic function of preconditioning parameter α. Based on this result, to achieve better convergence rate we suggest proforming twice preconditoning when applying the MGS method to solve a linear system whose coefficient matrix is an irreducible non-singular M-matrix.
基金the Test Technique Research Project(No.2014SZJY3101)
文摘As a prerequisite for effective prognostics, the goodness of the features affects the complexity of the prognostic methods. Comparing to features quality evaluation in diagnostics, features evaluation for prognostics is a new problem. Normally, the monotonic tendency of feature series can be used as the visual representation of equipment damage cumulation so that forecasting its future health states is easy to implement. Through introducing the concept of ranking mutual information in ordinal case, a monotonicity evaluation method of monitoring feature series is proposed. Finally, this method is verified by the simulating feature series and the results verify its effectivity. For the specific application in industry, the evaluation results can be used as the standard for selecting prognostic feature.
文摘In this paper,we present monotonicity results of a function involving the inverse hyperbolic sine.From these,we obtain some lower bounds for the inverse hyperbolic sine.
基金Supported in part by the NSF(Grant No.DMS-1558744)the AFOSR MURI Center for Material Failure Prediction Through Peridynamics and the ARO MURI(Grant No.W911NF-15-1-0562)
文摘In this paper, we present numerical studies of a recently proposed scalar nonlocal nonlinear conservation law in one space dimension. The nonlocal model accounts for nonlocal interactions over a finite horizon and enjoys maximum principle, monotonicity-preserving and entropy condition on the continuum level. Moreover, it has a well-defined local limit given by a conventional local conservation laws in the form of partial differential equations. We discuss convergent numerical approximations that preserve similar properties on the discrete level.We also present numerical experiments to study various limiting behavior of the numerical solutions.
文摘Let?be a real Hilbert space and?C?be a nonempty closed convex subset of H. Let T : C?→?C?be a demicontractive map satisfying?〈Tx, x〉?≥?‖x‖2 for all?x?∈ D (T). Then the Mann iterative sequence given by?xn + 1?= (1 - an) xn +?anT xn, where an ∈?(0, 1) n?≥?0, converges strongly to an element of F (T):= {x?∈ C : Tx = x}. This strong convergence is obtained without the compactness-type assumptions on C, which many previous results (see e.g. [1]) employed.
基金Supported by the National Natural Science Foundation of China(Grant No.11201400)Basic and Frontier Technology Reseach Project of Henan Province(Grant No.142300410433)Project for Youth Teacher of Xinyang Normal University(Grant No.2014-QN-061)
文摘In this paper, we introduce the notion of EF-critical map with potential with respect to the functional EF,H（u）. By using the stress-energy tensor, we obtain some monotonicity formulas and vanishing results for these maps under conditions on H.
文摘This paper addresses the problem of inference for a multinomial regression model in the presence of likelihood monotonicity. This paper proposes translating the multinomial regression problem into a conditional logistic regression problem, using existing techniques to reduce this conditional logistic regression problem to one with fewer observations and fewer covariates, such that probabilities for the canonical sufficient statistic of interest, conditional on remaining sufficient statistics, are identical, and translating this conditional logistic regression problem back to the multinomial regression setting. This reduced multinomial regression problem does not exhibit monotonicity of its likelihood, and so conventional asymptotic techniques can be used.
文摘In this paper,we study the completely monotonic property of two functions involving the functionΔ(x)=[ψ′(x)]2+ψ″(x)and deduce the double inequality x^(2)+3x+3/3x^(4)(2x+1)^(2)<Δ(x)<625x^(2)+2275x+5043/3x^(4)(50x+41)^(2),x>0which improve some recent results,whereψ(x)is the logarithmic derivative of the Gamma function.Also,we deduce the completely monotonic degree of a function involvingψ′(x).
基金supported by the Key Research Program of the Chinese Academy of Sciences (Grant No. KZZD-EW-05-01)the special grant (Grant No. 41375052) from the National Natural Science Foundation of Chinafunded by an open project of the State Key Laboratory of Severe Weather (Grant No. 2013LASW-A06)
文摘Terrain characteristics can be accurately represented in spectrum space. Terrain spectra can quantitatively reflect the effect of topographic dynamic forcing on the atmosphere. In wavelength space, topographic spectral energy decreases with decreasing wavelength, in spite of several departures. This relationship is approximated by an exponential function. A power law relationship between the terrain height spectra and wavelength is fitted by the least-squares method, and the fitting slope is associated with grid-size selection for mesoscale models. The monotonicity of grid size is investigated, and it is strictly proved that grid size increases with increasing fitting exponent, indicating that the universal grid size is determined by the minimum fitting exponent. An example of landslide-prone areas in western Sichuan is given, and the universal grid spacing of 4.1 km is shown to be a requirement to resolve 90% of terrain height variance for mesoscale models, without resorting to the parameterization of subgrid-scale terrain variance. Comparison among results of different simulations shows that the simulations estimate the observed precipitation well when using a resolution of 4.1 km or finer. Although the main flow patterns are similar, finer grids produce more complex patterns that show divergence zones, convergence zones and vortices. Horizontal grid size significantly affects the vertical structure of the convective boundary layer. Stronger vertical wind components are simulated for finer grid resolutions. In particular, noticeable sinking airflows over mountains are captured for those model configurations.
