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
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
In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithm...In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithmic derivative of the ratio,and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.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 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 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
Let K(r)be the complete elliptic integrals of the first kind for r∈(0,1)and f_(p)(x)=[(1−x)^(p)K(√x)].Using the recurrence method,we find the necessary and sufficient conditions for the functions−f′_(p),ln f_(p),−(...Let K(r)be the complete elliptic integrals of the first kind for r∈(0,1)and f_(p)(x)=[(1−x)^(p)K(√x)].Using the recurrence method,we find the necessary and sufficient conditions for the functions−f′_(p),ln f_(p),−(ln f_(p))^((i))(i=1,2,3)to be absolutely monotonic on(0,1).As applications,we establish some new bounds for the ratios and the product of two complete integrals of the first kind,including the double inequalities exp[r^(2)(1−r^(2))/^(64)]/(1+r)^(1/4)<K(r)/K(√r)<exp[−r(1−r)/4],π/2 exp[θ0(1−2r^(2))]<π/2 K(r′)/K(r)<π/2(r′/r)^(p)exp[θ_(p)(1−2r^(2))],K^(2)(1/√2)≤K(r)K(r′)≤1/√2rr′K^(2)(1/√2)for r∈2(0,1)and p≥13/32,where r′=√1−r^(2) and θ_(p)=2Γ(3/4)^(4)/π^(2)−p.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
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
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
Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stabi...Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stability and continuity for such best approximation problems are discussed.展开更多
For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations,we show that the simple boun...For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations,we show that the simple bound-preserving limiter in Li et al.(SIAM J Numer Anal 56:3308–3345,2018)can enforce the strict bounds of the vorticity,if the velocity field satisfies a discrete divergence free constraint.For reducing oscillations,a modified TVB limiter adapted from Cockburn and Shu(SIAM J Numer Anal 31:607–627,1994)is constructed without affecting the bound-preserving property.This bound-preserving finite difference method can be used for any passive convection equation with a divergence free velocity field.展开更多
A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In L_(3)-valued propositional logic, a multisequent is a triple Δ∣Θ∣Γ, which i...A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In L_(3)-valued propositional logic, a multisequent is a triple Δ∣Θ∣Γ, which is true under an assignment if either some formula in Δ has truth-value t, or some formula in Θ has truth-value m, or some formula in Γ has truth-value f. There is a sound, complete and monotonic Gentzen deduction system G for sequents. Dually, there is a sound, complete and nonmonotonic Gentzen deduction system G′ for co-sequents Δ: Θ: Γ. By taking different quantifiers some or every, there are 8 kinds of definitions of validity of multisequent Δ∣Θ∣Γ and 8 kinds of definitions of validity of co-multisequent Δ: Θ: Γ, and correspondingly there are 8 sound and complete Gentzen deduction systems for sequents and 8 sound and complete Gentzen deduction systems for co-sequents. Correspondingly their monotonicity is discussed.展开更多
Chaundy and Jolliffe proved that if {a n } is a non-increasing (monotonic) real sequence with lim n →∞ a n = 0, then a necessary and sufficient condition for the uniform convergence of the series ∑∞ n=1 a n sin nx...Chaundy and Jolliffe proved that if {a n } is a non-increasing (monotonic) real sequence with lim n →∞ a n = 0, then a necessary and sufficient condition for the uniform convergence of the series ∑∞ n=1 a n sin nx is lim n →∞ na n = 0. We generalize (or weaken) the monotonic condition on the coefficient sequence {a n } in this classical result to the so-called mean value bounded variation condition and prove that the generalized condition cannot be weakened further. We also establish an analogue to the generalized Chaundy-Jolliffe theorem in the complex space.展开更多
This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of "desirable pair of upper-lower solutions", through which a...This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of "desirable pair of upper-lower solutions", through which a subset can be constructed. We then apply the Schauder's fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.展开更多
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partially supported by the National Nature Science Foundation of China(12061033)。
文摘In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithmic derivative of the ratio,and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.
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 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.
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.
文摘Let K(r)be the complete elliptic integrals of the first kind for r∈(0,1)and f_(p)(x)=[(1−x)^(p)K(√x)].Using the recurrence method,we find the necessary and sufficient conditions for the functions−f′_(p),ln f_(p),−(ln f_(p))^((i))(i=1,2,3)to be absolutely monotonic on(0,1).As applications,we establish some new bounds for the ratios and the product of two complete integrals of the first kind,including the double inequalities exp[r^(2)(1−r^(2))/^(64)]/(1+r)^(1/4)<K(r)/K(√r)<exp[−r(1−r)/4],π/2 exp[θ0(1−2r^(2))]<π/2 K(r′)/K(r)<π/2(r′/r)^(p)exp[θ_(p)(1−2r^(2))],K^(2)(1/√2)≤K(r)K(r′)≤1/√2rr′K^(2)(1/√2)for r∈2(0,1)and p≥13/32,where r′=√1−r^(2) and θ_(p)=2Γ(3/4)^(4)/π^(2)−p.
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.
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.
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.
基金Supported by National Natural Science Foundation of China, Grant (10471032)
文摘Hudzik and Kurc discussed some best approximation problems in Banach lattices by means of monotonicities. This paper deals with more general best approximation problems in Banach lattices. Existence, uniqueness, stability and continuity for such best approximation problems are discussed.
文摘For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations,we show that the simple bound-preserving limiter in Li et al.(SIAM J Numer Anal 56:3308–3345,2018)can enforce the strict bounds of the vorticity,if the velocity field satisfies a discrete divergence free constraint.For reducing oscillations,a modified TVB limiter adapted from Cockburn and Shu(SIAM J Numer Anal 31:607–627,1994)is constructed without affecting the bound-preserving property.This bound-preserving finite difference method can be used for any passive convection equation with a divergence free velocity field.
基金supported by the Open Fund of the State KeyLaboratory of Sofware Development Environment(SKLSDE-2010KF-06)Beijing University of Aeronautics and Astronautics,and by the National Basic Research Program of China(973 Program)(2005CB321901).
文摘A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In L_(3)-valued propositional logic, a multisequent is a triple Δ∣Θ∣Γ, which is true under an assignment if either some formula in Δ has truth-value t, or some formula in Θ has truth-value m, or some formula in Γ has truth-value f. There is a sound, complete and monotonic Gentzen deduction system G for sequents. Dually, there is a sound, complete and nonmonotonic Gentzen deduction system G′ for co-sequents Δ: Θ: Γ. By taking different quantifiers some or every, there are 8 kinds of definitions of validity of multisequent Δ∣Θ∣Γ and 8 kinds of definitions of validity of co-multisequent Δ: Θ: Γ, and correspondingly there are 8 sound and complete Gentzen deduction systems for sequents and 8 sound and complete Gentzen deduction systems for co-sequents. Correspondingly their monotonicity is discussed.
基金supported by National Sciences and Engineering Research Council of CanadaNational Natural Science Foundation of China (Grant No. 10471130)
文摘Chaundy and Jolliffe proved that if {a n } is a non-increasing (monotonic) real sequence with lim n →∞ a n = 0, then a necessary and sufficient condition for the uniform convergence of the series ∑∞ n=1 a n sin nx is lim n →∞ na n = 0. We generalize (or weaken) the monotonic condition on the coefficient sequence {a n } in this classical result to the so-called mean value bounded variation condition and prove that the generalized condition cannot be weakened further. We also establish an analogue to the generalized Chaundy-Jolliffe theorem in the complex space.
基金Supported by the National Natural Science Foundation of China(No.19971032)the second author is supported by Natural Science Foundation of Canadaby a Petro Canada Young Innovator Award.
文摘This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of "desirable pair of upper-lower solutions", through which a subset can be constructed. We then apply the Schauder's fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.