The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscilla...The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.展开更多
A neutral difference equation with positive and negative coefficientsΔ(x n-c nx n-k )+p nx n-l -q nx n-r =0, n=0,1,2,...,is considered and a sufficient condition for the global attractivity of the ze...A neutral difference equation with positive and negative coefficientsΔ(x n-c nx n-k )+p nx n-l -q nx n-r =0, n=0,1,2,...,is considered and a sufficient condition for the global attractivity of the zero solution of this equation is obtained, which improves and extends the all known results in the literature.展开更多
In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions i...In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature.展开更多
Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjectur...Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjecture forward.展开更多
This paper gives the rules of oscillations of two classes of neutraldifferential equations with forced terms, and some oscillation criteria undercertain conditions are presented according to the equations having diffe...This paper gives the rules of oscillations of two classes of neutraldifferential equations with forced terms, and some oscillation criteria undercertain conditions are presented according to the equations having differentcharacters.展开更多
If Michelson were to answer the question posed in the title, given the line of reasoning he used in 1881, Michelson would seat at his desktop computer to calculate the expected fringeshifts for several solar speeds ar...If Michelson were to answer the question posed in the title, given the line of reasoning he used in 1881, Michelson would seat at his desktop computer to calculate the expected fringeshifts for several solar speeds around 400 km/s and various directions of motion. Present author did exactly the same in 2001 to plan his repetition of Michelson and Morley’s (MM) 1887 experiment. The paper sketchedly summarizes the procedure to calculate expected fringeshifts in the MM interferometer for solar speeds available at Miller’s epoch. In a pre-relativistic context, amplitudes of several fringeshifts may be expected in both MM and Miller experiments. However, all interferometer experiments up to 1930 were designed under the (incorrect from a modern viewpoint) assumption that fringeshifts would be smaller than one fringe-width. The inescapable conclusion is that those experiments were not appropriate to measure the true value of solar motion, always yielding a small, but lower than expected, value for solar speed. The ensuing “negative” interpretation led to the birth of relativity theory and to a new series of experiments implicitly designed to test the relativistic hypothesis of length-contraction, while the earlier “positive” experiments were designed to test a different hypothesis: whether the motion of Earth relative to some preferred frame can be measured using an interferometer of constant dimensions. With the benefit of hindsight this writer repeated the MM experiment, correcting main weaknesses identified up to the Michelson-Morley-Miller (MMM) measurements at Mount Wilson from April 1925 to February 1926. A new possible reinterpretation of the MMM data as a sequence of stationary measurements is pointed out. Our Michelson-Morley-Miller-Munera (MMMM) experiment at Bogota (Colombia) from January 2003 to June 2005 gave values for solar absolute velocity in the same range as those obtained by astronomical means. Surprisingly, our results are compatible with modern third-party MM-type experiments designed and interpreted within relativistic contexts. Thus, a so far unexplored possibility arises: can interferometric experiments distinguish between pre-relativistic and relativistic theories? Our answer is negative.展开更多
We investigate oscillation of certain second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients. We use some different techniques and apply Riccati transformation to establish...We investigate oscillation of certain second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients. We use some different techniques and apply Riccati transformation to establish new oscillatory criteria which include two necessary and sufficient conditions. Moreover, we point out that how the power γ plays its role. Some interesting examples are given to illustrate the versatility of our results.展开更多
Some sufficient conditions for the oscillation of all solutions of the delay differential equations with positive and negative coefficientsare obtained, where 0 < αi, βi <1,pi>, qi >, are constants, t = ...Some sufficient conditions for the oscillation of all solutions of the delay differential equations with positive and negative coefficientsare obtained, where 0 < αi, βi <1,pi>, qi >, are constants, t = 1,2, …, n.展开更多
This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The 'sharp' condition...This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The 'sharp' conditions of oscillation for the equation have been obtained, i.e., the conditions are sufficient and necessary when all of the coefficients are constants. These conditions are distinguished from the previous criteria in the literatures, and also weaker than those existing results.展开更多
A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are p...A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.展开更多
This paper gives probabilistic expressions of theminimal and maximal positive solutions of the partial differential equation -1/2△v(x) + γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its c...This paper gives probabilistic expressions of theminimal and maximal positive solutions of the partial differential equation -1/2△v(x) + γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its complement Dc is compact, γ(x) is a positive bounded integrable function in D, and 1 ＜α≤ 2. As an application, some necessary and sufficient conditions for a compact set to be S-polar are presented.展开更多
Some properties of integrated bisemigroup S(t) of linear operators on a Banach space X are studied. The structure of the positive and negative subspaces and the operation of integrated bisemigroup on corresponding dif...Some properties of integrated bisemigroup S(t) of linear operators on a Banach space X are studied. The structure of the positive and negative subspaces and the operation of integrated bisemigroup on corresponding differentiable subspace C-n are established. respectively. The decomposition of the infinitesimal generator A of S(t) and other interested problems are also considered. As application, an abstract boundary value problem is discussed.展开更多
Some comparison theorems of the non-existence of positive solutions are derived for a classof neutral type difference equations with positive and negative coefficients. These results extendand improve some comparison ...Some comparison theorems of the non-existence of positive solutions are derived for a classof neutral type difference equations with positive and negative coefficients. These results extendand improve some comparison criteria obtained in the literature [1] and [2].展开更多
In this paper, a new oscillating result is established for the first order neutral delay differential equation with positive and negative coefficients, which improves and generalizes several results in the literatures.
文摘The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.
基金the Science Foundation of Educational Committee of Hunan Provinc
文摘A neutral difference equation with positive and negative coefficientsΔ(x n-c nx n-k )+p nx n-l -q nx n-r =0, n=0,1,2,...,is considered and a sufficient condition for the global attractivity of the zero solution of this equation is obtained, which improves and extends the all known results in the literature.
基金the National Natural Science Foundation of China(1 0 0 71 0 1 8)
文摘In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature.
文摘Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjecture forward.
文摘This paper gives the rules of oscillations of two classes of neutraldifferential equations with forced terms, and some oscillation criteria undercertain conditions are presented according to the equations having differentcharacters.
文摘If Michelson were to answer the question posed in the title, given the line of reasoning he used in 1881, Michelson would seat at his desktop computer to calculate the expected fringeshifts for several solar speeds around 400 km/s and various directions of motion. Present author did exactly the same in 2001 to plan his repetition of Michelson and Morley’s (MM) 1887 experiment. The paper sketchedly summarizes the procedure to calculate expected fringeshifts in the MM interferometer for solar speeds available at Miller’s epoch. In a pre-relativistic context, amplitudes of several fringeshifts may be expected in both MM and Miller experiments. However, all interferometer experiments up to 1930 were designed under the (incorrect from a modern viewpoint) assumption that fringeshifts would be smaller than one fringe-width. The inescapable conclusion is that those experiments were not appropriate to measure the true value of solar motion, always yielding a small, but lower than expected, value for solar speed. The ensuing “negative” interpretation led to the birth of relativity theory and to a new series of experiments implicitly designed to test the relativistic hypothesis of length-contraction, while the earlier “positive” experiments were designed to test a different hypothesis: whether the motion of Earth relative to some preferred frame can be measured using an interferometer of constant dimensions. With the benefit of hindsight this writer repeated the MM experiment, correcting main weaknesses identified up to the Michelson-Morley-Miller (MMM) measurements at Mount Wilson from April 1925 to February 1926. A new possible reinterpretation of the MMM data as a sequence of stationary measurements is pointed out. Our Michelson-Morley-Miller-Munera (MMMM) experiment at Bogota (Colombia) from January 2003 to June 2005 gave values for solar absolute velocity in the same range as those obtained by astronomical means. Surprisingly, our results are compatible with modern third-party MM-type experiments designed and interpreted within relativistic contexts. Thus, a so far unexplored possibility arises: can interferometric experiments distinguish between pre-relativistic and relativistic theories? Our answer is negative.
基金supported by National Natural Science Foundation of China (Grant No. 11271379)Guangzhou Postdoctoral Science Research Foundation Project (Grant No. gdbsh2014003)
文摘We investigate oscillation of certain second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients. We use some different techniques and apply Riccati transformation to establish new oscillatory criteria which include two necessary and sufficient conditions. Moreover, we point out that how the power γ plays its role. Some interesting examples are given to illustrate the versatility of our results.
基金Project supported by Scientific Research Fund of Hunan Provincial Education Department (China)(granted 03C427).
文摘Some sufficient conditions for the oscillation of all solutions of the delay differential equations with positive and negative coefficientsare obtained, where 0 < αi, βi <1,pi>, qi >, are constants, t = 1,2, …, n.
基金Research supported by National Natural Science Foundation of P. R. China (10071016) by Foundation of the Education Department for Excellent Teacher of University.
文摘This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The 'sharp' conditions of oscillation for the equation have been obtained, i.e., the conditions are sufficient and necessary when all of the coefficients are constants. These conditions are distinguished from the previous criteria in the literatures, and also weaker than those existing results.
文摘A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.
基金supported by the National Natural Science Foundation of China(Grant No.10471003)Foundation for Authors Awarded Excellent Ph.D.Dissertation.
文摘This paper gives probabilistic expressions of theminimal and maximal positive solutions of the partial differential equation -1/2△v(x) + γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its complement Dc is compact, γ(x) is a positive bounded integrable function in D, and 1 ＜α≤ 2. As an application, some necessary and sufficient conditions for a compact set to be S-polar are presented.
基金the National Key Project of China the Natural Science Foundation of Shanxi
文摘Some properties of integrated bisemigroup S(t) of linear operators on a Banach space X are studied. The structure of the positive and negative subspaces and the operation of integrated bisemigroup on corresponding differentiable subspace C-n are established. respectively. The decomposition of the infinitesimal generator A of S(t) and other interested problems are also considered. As application, an abstract boundary value problem is discussed.
文摘Some comparison theorems of the non-existence of positive solutions are derived for a classof neutral type difference equations with positive and negative coefficients. These results extendand improve some comparison criteria obtained in the literature [1] and [2].
基金Supported by the NSF Education Dept. (hjkj200317) and the NSF of Hainan Province (80403).
文摘In this paper, a new oscillating result is established for the first order neutral delay differential equation with positive and negative coefficients, which improves and generalizes several results in the literatures.
