Poisson’s ratio changes during the tensile stress of technical fabric samples due to the anisotropy of technical fabrics.This paper examines the effects of the type of weave and the anisotropic characteristics of the...Poisson’s ratio changes during the tensile stress of technical fabric samples due to the anisotropy of technical fabrics.This paper examines the effects of the type of weave and the anisotropic characteristics of the technical fabric on maximum tensile force,corresponding elongation,work-to-maximum force,elasticity modulus,and Poisson’s ratio when axial tensile forces are applied to samples cut at various angles in the direction of the weft yarns of the technical fabric.In the lab,3 cotton fabric samples of constant warp and weft density with different structural weave types(plain weave,twill weave,atlas weave)were subjected to the tensile force until they broke at the following angles:0°,15°,30°,45°,60°,75°,90°.Based on the different measured values of technical fabric stretching in the longitudinal direction and lateral narrowing,Poisson’s ratio is calculated.The Poisson’s ratio was calculated up to a relative elongation of the fabric of 8%,as the buckling of the fabric occurs according to this elongation value.According to the results presented in this paper,the type of weave of the fabric,the direction of tensile force,and the relative narrowing of the technical fabrics all play important roles in the Poisson’s ratio value.The Poisson’s ratio curve of a technical fabric under tensile stress(i.e.elongation)is primarily determined by its behaviour in the opposite direction of the elongation.The change in the value of the Poisson’s ratio is represented by a graph that first increases nonlinearly and then decreases after reaching its maximum value.展开更多
In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well...In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well as quantitative properties of solutions of certain classes of difference equations.展开更多
Let Ak be an integral operator defined by Akf（x）：=1K（x）∫Ω2k（x,y）f（y）dμ2（y）where k：Ω1× Ω2 →Ris a general nonnegative kernel, （Ω1,∑1,μ1）, （Ω2,∑2,μ2） are measure spaces with a-finite meas...Let Ak be an integral operator defined by Akf（x）：=1K（x）∫Ω2k（x,y）f（y）dμ2（y）where k：Ω1× Ω2 →Ris a general nonnegative kernel, （Ω1,∑1,μ1）, （Ω2,∑2,μ2） are measure spaces with a-finite measures and K（x）：=∫Ω2k（x,y）dμ2（y）,x∈Ω1.In this paper improvements and reverses of new weighted Hardy type inequalities with integral operators of such type are stated and proved. New Cauchy type mean is introduced and monotonicity property of this mean is proved.展开更多
In this paper we define a functional as a difference between the right-hand side and lefthand side of the refined Boas type inequality using the notation of superquadratic and subquadratic functions and study its prop...In this paper we define a functional as a difference between the right-hand side and lefthand side of the refined Boas type inequality using the notation of superquadratic and subquadratic functions and study its properties, such as exponential and logarithmic convexity. We also, state and prove improvements and reverses of new weighted Boas type inequalities. As a special case of our result we obtain improvements and reverses of the Hardy inequality and its dual inequality. We introduce new Cauchy type mean and prove monotonicity property of this mean.展开更多
文摘Poisson’s ratio changes during the tensile stress of technical fabric samples due to the anisotropy of technical fabrics.This paper examines the effects of the type of weave and the anisotropic characteristics of the technical fabric on maximum tensile force,corresponding elongation,work-to-maximum force,elasticity modulus,and Poisson’s ratio when axial tensile forces are applied to samples cut at various angles in the direction of the weft yarns of the technical fabric.In the lab,3 cotton fabric samples of constant warp and weft density with different structural weave types(plain weave,twill weave,atlas weave)were subjected to the tensile force until they broke at the following angles:0°,15°,30°,45°,60°,75°,90°.Based on the different measured values of technical fabric stretching in the longitudinal direction and lateral narrowing,Poisson’s ratio is calculated.The Poisson’s ratio was calculated up to a relative elongation of the fabric of 8%,as the buckling of the fabric occurs according to this elongation value.According to the results presented in this paper,the type of weave of the fabric,the direction of tensile force,and the relative narrowing of the technical fabrics all play important roles in the Poisson’s ratio value.The Poisson’s ratio curve of a technical fabric under tensile stress(i.e.elongation)is primarily determined by its behaviour in the opposite direction of the elongation.The change in the value of the Poisson’s ratio is represented by a graph that first increases nonlinearly and then decreases after reaching its maximum value.
基金a HKU Seed grant the Research Grants Council of the Hong Kong SAR(HKU7016/07P)
文摘In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well as quantitative properties of solutions of certain classes of difference equations.
文摘Let Ak be an integral operator defined by Akf（x）：=1K（x）∫Ω2k（x,y）f（y）dμ2（y）where k：Ω1× Ω2 →Ris a general nonnegative kernel, （Ω1,∑1,μ1）, （Ω2,∑2,μ2） are measure spaces with a-finite measures and K（x）：=∫Ω2k（x,y）dμ2（y）,x∈Ω1.In this paper improvements and reverses of new weighted Hardy type inequalities with integral operators of such type are stated and proved. New Cauchy type mean is introduced and monotonicity property of this mean is proved.
基金supported by the Croatian Ministry of Science, Education and Sports (Grant No.117-1170889-0888)supported by the Croatian Ministry of Science,Education and Sports(Grant No.082-0000000-0893)
文摘In this paper we define a functional as a difference between the right-hand side and lefthand side of the refined Boas type inequality using the notation of superquadratic and subquadratic functions and study its properties, such as exponential and logarithmic convexity. We also, state and prove improvements and reverses of new weighted Boas type inequalities. As a special case of our result we obtain improvements and reverses of the Hardy inequality and its dual inequality. We introduce new Cauchy type mean and prove monotonicity property of this mean.
