二阶共振周期边值问题多解的存在性

借助于与给定共振的非线性周期边值问题相关的非共振的线性边值问题来构造算子,利用范数形式的锥拉伸-压缩不动点定理,得到了非线性周期边值问题非负解的存在性定理.     

源于DNA的非线性波动方程组的Cauchy问题(英文)

本文首先证明源于DNA的非线性波动方程组的周期边值问题局部古典解的存在性和唯一性.其次通过周期边值问题序列证明这个方程组的Cauchy问题存在唯一的局部古典解.     

一般周期Riemann边值问题关于跳跃曲线的稳定性

本文研究了一般周期Riemann边值问题关于跳跃曲线的稳定性.利用解析函数边值理论和不等式分析理论,获得了一般周期Riemann边值问题的解及其关于跳跃曲线的误差估计.     

一类具有p-Laplacian算子的分数阶微分方程反周期边值问题解的存在唯一性

该文研究了一类具有p-Laplacian算子的非线性Caputo分数阶微分方程反周期边值问题解的存在唯一性.首先,利用分数阶微分方程和反周期边值条件给出了该边值问题的Green函数,然后利用p-Laplacian算子的性质和Banach压缩映射原理得到该边值问题解的存在唯一性结论,最后给出两个例子验证结论的合理性.值得一提的是此文研究的微分方程的反周期边值条件是带有Caputo分数阶微分.     

一阶脉冲时滞积分微分方程边值问题

本文研究了一类一阶脉冲时滞积分微分方程边值问题解的性质. 利用迭代分析方法, 得到了该类边值问题解的存在性、唯一性和平凡解一致稳定的充分条件, 推广了已有积分微分方程周期边值问题解的结论.     

一阶脉冲时滞积分微分方程边值问题

本文研究了一类一阶脉冲时滞积分微分方程边值问题解的性质.利用迭代分析方法,得到了该类边值问题解的存在性、唯一性和平凡解一致稳定的充分条件,推广了已有积分微分方程周期边值问题解的结论.     

奇异超线性半正定二阶周期边值问题的正解

基于格林函数理论,主要利用Lerray-Schauder抉择定理和上下解方法针对半正定条件下,奇异超线性二阶周期边值问题正解的存在性进行推理证明,获取了奇异超线性二阶周期边值问题的一个正解.     

单准周期的Riemann边值问题

本文研究了光滑封闭曲线情况下的加法与乘法单准周期Riemann边值问题,运用保角变换的方法,获得了单准周期函数的一些性质,并且对解在无穷远处作适当要求下给出了单准周期边值问题的解法.     

一类一阶周期边值问题解的存在性

考虑一类一阶常微分方程的周期边值问题,利用Schaefer不动点定理得到了边值问题解存在的一个充分条件,推广了相关文献中已有的结果.     

奇异二阶周期边值问题正解的存在性

利用不动点指数理论研究奇异二阶周期边值问题.在有关其线性算子方程对应的第一特征值的条件下得到边值问题正解的存在性,推广和改进了最近文献的结果.     

The generalized hierarchical product of graphs

A generalization of both the hierarchical product and the Cartesian product of graphs is introduced and some of its properties are studied. We call it the generalized hierarchical product. In fact, the obtained graphs turn out to be subgraphs of the Cartesian product of the corresponding factors. Thus, some well-known properties of this product, such as a good connectivity, reduced mean distance, radius and diameter, simple routing algorithms and some optimal communication protocols, are inherited by the generalized hierarchical product. Besides some of these properties, in this paper we study the spectrum, the existence of Hamiltonian cycles, the chromatic number and index, and the connectivity of the generalized hierarchical product.     

城市老旧居住小区交通环境评价指标与评价方法

定量的评判城市老旧居住小区整体交通环境质量并进而科学有效的提出老旧小区交通环境更新与改善措施,对城市老旧居住小区交通环境进行了调查,明确了老旧居住小区存在的突出交通问题,并提出了城市老旧居住小区交通环境评价的指标体系,包括行人跨路出行指数、无人行道路段长度占比、停车泊位供需比、路内非法停车占比、平均停车步行距离、泊位数量户数比、人均步行空间、无障碍通道、盲道设置比例、非机动车泊位供需比、地面停放车辆数小区面积比、外部穿行交通周转量小区面积比等。并给出了具体指标的计算方法与获得办法。以长沙市四个典型老旧居住小区为例,对评价方法进行了论证,并得到城市老旧居住小区存在的一般问题,包括人车混杂、人车交织现象严重,停车泊位短缺、车辆乱停乱放,交通设施、特别是弱势群体交通设施缺乏。给出的评价指标、评价方法与结论可为城市老旧小区改造更新,特别是其中很重要的交通环境更新提供决策依据。     

Rolling-ball method for estimating the boundary of the support of a point-process intensity

We suggest a generalisation of the convex-hull method, or ‘DEA’ approach, for estimating the boundary or frontier of the support of a point cloud. Figuratively, our method involves rolling a ball around the cloud, and using the equilibrium positions of the ball to define an estimator of the envelope of the point cloud. Constructively, we use these ideas to remove lines from a triangulation of the points, and thereby compute a generalised form of a convex hull. The radius of the ball acts as a smoothing parameter, with the convex-hull estimator being obtained by taking the radius to be infinite. Unlike the convex-hull approach, however, our method applies to quite general frontiers, which may be neither convex nor concave. It brings to these contexts the attractive features of the convex hull: simplicity of concept, rotation-invariance, and ready extension to higher dimensions. It admits bias corrections, which we describe and illustrate through implementation.     

Analysis of the Stress State of the Surface Layer of a Polymeric Mass upon Filling of Bulky Compression Molds

The stress state of the surface layer of a polymeric mass during filling of bulky compression molds is analyzed. It is shown that, at particular rheological characteristics of the mass, temperature, and filling rates, cracking of the surface layer occurs, which leads to defects in the finished products. A physical analysis of this process makes it possible to conclude that the cracks arise due to the normal stresses operating in the front region of the moving polymeric mass. It is found that, under certain flow conditions, areas with a pressure lower than the atmospheric one appear on the surface of the polymer. If the tensile stresses arising in these local regions are higher than the tensile strength of the mass, the continuity of the composition is broken in the direction determined by the greatest rate of the normal deformation. To confirm the reliability of the crack-formation mechanism proposed, the distribution of the pressure and normal stresses over the free surface is calculated based on a numerical method. These calculations show that, by comparing the stress level achieved in the front region with the tensile-strength characteristics of the polymeric composition, it is possible to predict, with a sufficient accuracy, the possibility of crack formation in the surface layer of such a mass under given flow conditions and thus to solve the question on flawless manufacturing of products.     

Quality rating of a metal matrix-diamondcomposite from its thermal conductivity and electric resistance

The efficiency of hot-pressed diamond-containing composite materials (DCM) for various tool applications is greatly affected by microdefects, namely, the residual porosity of the metal matrix, damaged diamond grains, and imperfect diamond-matrix interfaces. An instrumental evaluation of these microdefects, predetermining the quality of a tool equipped with DCM, is rather difficult due to the small size, the nonstandard shape, and the strong heterogeneity of specimens. Proposed here is an alternative, nondestructive technique of DCM quality rating, which includes the measurement of electric resistance and thermal conductivity of diamond-containing composites and processing the obtained data by the methods of composite mechanics. It exploits the fact that diamond, being a dielectric, possesses an extremely high thermal conductivity, which allows estimating the residual porosity of a sintered metal matrix from the ratio of specific electric resistances, one being measured and another predicted by a theory. These data, in turn, are utilized to predict the thermal conductivity ofDCMwith an imperfect matrix. Matching with experiments, after solving the inverse problem gives the thermal resistance of diamond-matrix interface, which, within the frame work of the given model, simulates the damage of both the diamond grains and their bonds with the matrix. Thus, the numerical rating of quality is given in terms of two dimensionless parameters. The first one, 0 < K < 1, reflects the quality of the sintered metal matrix, whereas the second one, 0 < R <1, is an aggregate measure of the integrity of diamond grains and the perfection degree of composite interfaces. The quite satisfactory agreement observed between the theory and experiment confirms the efficiency of the technique and the reliability of the data obtained. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 361–374, May–June, 2006.     

Calculation of damage and of force relaxation in amorpho-crystalline polymers

The dynamics of damage and of the relaxing force in amorpho-crystalline polymers under constant strain are calculated using the formulas for the probability of rupture of a deformed polymer molecule and a model representation of amorphous interlayers. The main parameters of the model are the maximum and minimum possible deformations of molecular chains, the energy of rupture activation, the function of the chain length distribution, the temperature, the macroscopic strain, and the relative dimensions of the amorphous interlayer. The conformity of the theoretical model and the association of the relaxation spectrum with the internal molecular and structural characteristics of the material are established.Zhambyl Technical Institute of Light and Food Industry, Taraz, Kazakhstan. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 499–508, July–August, 1999.     

Gaussian Versus Optimal Integration of Analytic Functions

We consider error estimates for optimal and Gaussian quadrature formulas if the integrand is analytic and bounded in a certain complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented. This method is applied to Szeg?-type weight functions and ellipses as regions of analyticity. In this situation, the error constants for the Gaussian formulas are close to the obtained lower bounds, which proves the quality of the Gaussian formulas and also of the lower bounds. In the sequel, different regions of analyticity are investigated. It turns out that almost exclusively for ellipses, the Gaussian formulas are near-optimal. For classes of simply connected regions of analyticity, which are additionally symmetric to the real axis, the asymptotic of the worst ratio between the error constants of the Gaussian formulas and the optimal error constants is calculated. As a by-product, we prove explicit lower bounds for the Christoffel-function for the constant weight function and arguments outside the interval of integration. September 7, 1995. Date revised: October 25, 1996.     

Development of the Tangent Modulus from the Euler-Problem to Nonsmooth Materials

History and development of the tangent modulus from the origins to the recent nonsmooth damaging versions are presented. Load history and stability analyses of structures of nonlinear reversible or irreversible materials are based on the concept of tangent modulus. Generally, instantaneously changing tangent modulus is needed and the solution yields iteration process. In the case of inelastic problems, the switch from loading to unloading of the material behaviour results in nonsmooth material functions. Nonsmooth, generally saw-tooth like behaviour happens in composite, laminated or rock type materials, or in the interaction of concrete and the reinforcement, too. Recently, damage and localization are in the focus of structural analyses, extending the tangent modulus to the negative cases, as well. Consequently, an overview of the history and development of the tangent modulus containing the recent modifications seems to be necessary. On the other hand, the more than a century long history of the tangent modulus is a marvellous study of the parallel development of mechanics and mathematics, by following the mutual inspiring effect of them through the activity of such pioneers like P.D. Panagiotopoulos in creating Nonsmooth Mechanics.     

The limiting state of a rigidly fixed nonlinearly elastic multilayer rod

The loss of the load-carrying capacity of a nonlinearly elastic multilayer rod is investigated. The rod, whose layers have various thickness and are made of different materials, is rigidly fixed at both its ends. Rigid contact conditions between the layers are assumed. The problem posed is solved by using the variational method of mixed type in combination with the Rayleigh-Ritz method. The initial analysis is reduced to the solution of the Cauchy problem for a nonlinear ordinary differential equation solved for the first derivative. As the initial condition, the maximum initial eccentricity of the rod is assumed. In the case of zero eccentricity, the Shanley critical force for an axially compressed rod is determined. For a three-layer rod whose outer layers have equal thickness and are made of the same material, numerically, for various degrees of nonlinearity, the effect of physicomechanical and geometric parameters on the critical load of buckling instability is determined. It is found that, by matching the heterogeneity of the rod, it is possible to raise its load-carrying capacity. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 347–360, May–June, 2006.     

Some curious properties and loci problems associated with cubics and other polynomials

The article begins with a well-known property regarding tangent lines to a cubic polynomial that has distinct, real zeros. We were then able to generalize this property to any polynomial with distinct, real zeros. We also considered a certain family of cubics with two fixed zeros and one variable zero, and explored the loci of centroids of triangles associated with the family. Some fascinating connections were observed between the original family of the cubics and the loci of the centroids of these triangles. For example, we were able to prove that the locus of the centroid of certain triangles associated with the family of cubics is another cubic whose zeros are in arithmetic progression. Motivated by this, in the last section of the article, we considered families of cubic polynomials whose zeros are in arithmetic progression, along with the loci of the special points of certain triangles arising from such families. Special points include the centroid, circumcentre, orthocentre, and nine-point centre of the triangles. Throughout the article, we used the computer algebra system, Mathematica®, to form conjectures and facilitate calculations. Mathematica® was also used to create various animations to explore and illustrate many of the results.