单因环的性质、等价条件和结构

一个有单位元的结合环，如果其元素不是单位就是零因子，则称其为单因环。它是很广泛的一个环类．本文讨论了单因环的住质、等价条件和结构；还讨论了它同其它环诸如正则环、局部环和循环环的关系，从而较深刻地刻划了这种环。     

The Effect of Inhomogeneity of Elastic Properties on the Stress State in Composite Cylindrical Panels

The effect of inhomogeneity of elastic properties in the circumferential direction on the distribution of stress and displacement fields in orthotropic cylindrical panels is studied. The mechanical properties of the panels and the load acting on them are constant in the axial direction, which makes it possible to neglect the influence of the curvilinear ends. From the initial relations of a three-dimensional problem of the elasticity theory of inhomogeneous anisotropic bodies, a resolving system of partial differential equations is obtained, whose solution is presented in the form of truncated Fourier series, so that the conditions of free support of the rectilinear ends are satisfied. This allows us to separate the variables and to get a system of ordinary high-order differential equations, which is integrated by a stable numerical method. The problem on the stress-strain state of an orthotropic composite panel with a varying relative volume content of reinforcing elements in the circumferential direction is solved. The effect of the change in the reinforcement density on the stresses and displacements of the panel is studied.     

关于NF-环的构造

研究了无限的ＮＦ－环及有限的ＮＦ－环，并且给出了有限ＮＦ－环的构造．     

Shear Strength of Cement-Based Composite Beams

Beams of cement-based composites reinforced with different types of meshes usually do not have stirrups. With good anchoring of the longitudinal tensile reinforcement, such beams break after the development of a critical inclined crack caused by the principal tensile stresses. In this paper, the mechanics of development of such cracks is studied. The results of theoretical investigation based on the structural mechanics of laminates are compared with the results of experimental testing of cement-based composite beams reinforced with punched steel grids.     

格序环的一个根的结构

从不同角度刻画了格序环Ｒ的Ｐ－根和ｌ－Ｂ根，并对ｌ－Ｑ根环进行了讨论．揭示了Ｒ及Ｒ上的全矩阵环Ｒｎ的ｌ－Ｑ根，ｌ－Ｑ理想，素ｌ－理想，半素ｌ－理想之间的关系．     

结合环类中的E-单环

在全部结合环类中，对幂等根Ｅ，定义了Ｅ－单环．本文给出Ｅ－单环的一个刻画．     

凸体的p次径向平均体的几个性质

本文证明了凸体的p次径向平均体的线性不变性和椭球的p次径向平均体仍是椭球,并且获得了p次径向平均体相应于Blaschke-Santaló不等式的一个反向不等式．     

Bending of a Composite Material Strip with Curved Structure in the Geometrically Nonlinear Statement

To date, bending problems for strips or plates made of composite materials with curved structure have been investigated only in the linear statement. However, in many cases, the necessity arises to investigate the corresponding bending problems in the geometrically nonlinear statement. Therefore, in the present paper, some bending problems for a composite strip with a periodically curved structure is investigated in such a statement using the exact nonlinear equations of elasticity theory in Lagrangian coordinates. The numerical results are obtained by employing the FEM with the use of the Newton-Raphson and the Modified Newton-Raphson algorithms.     

Properties of the Fiber Cone of Ideals in Local Rings

Abstract

For an ideal I of a Noetherian local ring (R, m ) we consider properties of I and its powers as reflected in the fiber cone F(I) of I. In particular,we examine behavior of the fiber cone under homomorphic image R → R/J = R′ as related to analytic spread and generators for the kernel of the induced map on fiber cones ψ _J  : F _R (I) → F _R′(IR′). We consider the structure of fiber cones F(I) for which ker ψ _J  ≠ 0 for each nonzero ideal J of R. If dim F(I) = d > 0,μ(I) = d + 1 and there exists a minimal reduction J of I generated by a regular sequence,we prove that if grade(G ₊(I)) ≥ d ? 1,then F(I) is Cohen-Macaulay and thus a hypersurface.     

Influence of Different Factors on the Stiffness and Strength of Multilayer Composite Elements

In the paper, the bending stiffness and strength of multilayer structural elements in relation to the mechanical properties of layers and their number layout and sizes are investigated and the corresponding correlations are established. It is found that the most rational structure of a multilayer element in bending is a symmetric three-layer structure formed from two materials with the thickness of the core less than the half-thickness of the element. The values of normal stresses in the layers of a multilayer beam in bending depends on its bending stiffness and the position of layers relative to the neutral axis. The influence of the number of layers on the stiffness of the structural element and on the magnitude of normal stresses is insignificant.     

On the Prime Ideal Structure of Bhargava Rings

Let D be an integral domain with quotient field K. A Bhargava ring over D is defined to be 𝔹 _x (D): = {f ∈ K[X] | ? a ∈ D, f(xX + a) ∈ D[X]}, where x ∈ D. A Bhargava ring over D is a subring of the ring of integer-valued polynomials over D. In this article, we study the prime ideal structure and calculate the Krull and valuative dimension of Bhargava rings over a general domain D.     

Calculation and Experimental Study of a Two-Way Reinforced Rubber-Cord Composite in Tension

A rubber-cord composite, reinforced in two directions with fibers of polyamide cord, under large tensile deformations is investigated based on calculations of a rubber-cord composite material and on tensile tests of specimens made of the casing of a diagonal truck tire. A method of the experimental tensile testing of rubber-cord composite specimens is described. The calculations are based on the carcass theory of composite materials. The calculated and experimental parameters of the macroscopic strains of the rubber tire cord and of its structure in a deformed configuration are given. The manifestation of edge effects in relation to the reinforcement angle is described.     

Effect of Water on the Physicomechanical Properties of Composites Containing Low-Density Polyethylene and Linen Yarn Production Waste

The effect of the amount of absorbed water on the physicomechanical indices (tensile modulus and tensile strength) of composites based on low-density polyethylene (LDPE) and linen yarn production waste (LW), both with and without coupling agents (stearic acid - SA and diphenylmetane diisocyanate - DIC), is studied. It is shown that the strength properties depend considerably on the time of water sorption and on the blend composition. The tensile strength decreases with increased amount of absorbed water (with increased time of exposure to distilled water) and with increased content of LW in the composite. Somewhat different results are obtained for systems containing SA and DIC modifiers. The modifiers, intensifying the interfacial interaction, retard the process of water sorption, therefore the drop in the strength indices is not so significant. Of special interest is the behavior of systems with DIC. In some cases, a slight increase in strength (after a two to five day exposure to water) is observed, which is probably caused by cross-linking of the free diisocyanate in the system under the action of moisture.     

A Note on Constants of Integral Derivations in Semiprime Rings

Let R be a semiprime ring with extended centroid C and with Q its Martindale symmetric ring of quotients. Suppose that δ: R → R is a C-integral derivation. For a subring A of Q, let A^(δ) denote the subring of constants of δ in A. We prove that R^(δ) and Q^(δ) satisfy the same polynomial identities with coefficients in C. In particular, R^(δ) is not nil of bounded index.     

Effect of the Thermosensitivity and Reinforcement Structure on the Load-Carrying Capacity of Metal-Composite Gas-Turbine Disks

The direct problem of calculating three-layered reinforced rotating disks with account of thermosensitivity of their substructural elements is formulated. Based on this problem and a strength criterion for the substructural elements of the disk, the inverse problem on determining its load-carrying capacity at a given profile of the disk and reinforcement structure of the load-carrying layer is stated. The calculation results for a magnesium-steel disk with a fixed geometry and different reinforcement structures are presented. It is shown that the thermosensitivity of the substructural elements lowers considerably the load-carrying capacity at elevated temperatures. The isotropic steel and quasi-isotropic reinforced disks, most often used in practice, are inefficient compared with spirally and radially reinforced ones; for magnesium-steel disks, the best are the structures with a radial and radially circumferential reinforcement.     

A Probabilistic Model of the Fatigue Life of Composite Materials for Fatigue-Curve Approximations

A simple mathematical model for the fatigue life of composite materials in which the basic load is taken up by parallel rigid components (fiber strands) is offered. Based on the Markov chain theory, the model allows us to obtain an S-type curve for the growth of internal stresses and to calculate the relationship between the parameters of static strength distribution and the S-N fatigue curve (Wholer curve). The model is too simple and does not provide a numerical coincidence with experimental fatigue-test data, but, when used with additional parameters, it agrees with experiments and can be applied to the model of nonlinear regression in describing the fatigue curve and its variation as the parameters of static strength change.     

A Note on the Graded K-Theory of Certain Graded Rings

Following ideas of Quillen we prove that the graded K-theory of a ? ⁿ -graded ring with support contained in a pointed cone is entirely determined by the K-theory of the subring of degree 0 elements.     

Stable Subsets and the Existence of a Unit in (Semi)-Prime Rings

Criteria for the existence of a unit in a semiprime, prime, or simple ring and criteria for an idempotent of an arbitrary ring or of a semiprime ring to be central are obtained. In particular, it is shown that a strictly prime ring R in which r Rr for any r R is a ring with unit. In this connection, examples of prime (and even simple) rings are presented such that r Rr rR for any r R but there is no unit. The problem of whether a given ring R has a left unit was reduced earlier by the author to the semiprime case, namely, R has a left unit if and only if r Rr for any element r of the prime radical P(R) and the ring R P(R) has a left unit.     

Experimental studies on the adhesion strength of a polymer-metal bond depending on the contact zone geometry

Theoretical investigation of the stress-strain state at special points of constructions, e.g., in adhesion joints, has demonstrated that the stress state in the contact zone strongly depends on the configuration of the zone. In order to verify these results, some experiments were carried out. Cylindrical polymer specimens having a circular groove at one of its ends were cemented to steel mushrooms and tested for abruption in tension and cantilever bending. The experiments showed that the adhesive strength depended on the profile of the joint and had a maximum at the optimum value of the angle of the joint and a minimum when the groove was absent. The ratio between the maximum and minimum strength values was 1.5 in tension and 2.5 in bending. The greater effect in the latter case can be explained by the high gradient of the stresses in bending. The experimental results confirmed the possibility of controlling the adhesive strength by changing the contact geometry in accord with the stress-strain calculations.Institute of the Mechanics of Continuous Media, Russian Academy of Sciences, Perm', Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 493–498, July–August, 1999.     

新型轻质复合材料夹芯结构振动阻尼性能研究进展

作为新一代先进轻质超强韧结构材料,复合材料格栅和点阵夹芯结构受到了国内外学者的广泛关注.目前关于该类结构材料的设计制备以及相关力学性能研究已取得了大量的研究成果.然而对该类结构振动阻尼性能的研究则处于起步阶段.该文综述了纤维增强树脂基复合材料简单层合结构以及各类夹芯结构振动阻尼性能的研究现状.首先阐述其阻尼机理, 然后分别概述了复合材料简单层合板的微观和宏观阻尼模型、复合材料粘弹性阻尼夹层结构和新型夹层结构的阻尼预报工作,最后总结归纳现有关于该类结构阻尼特性研究工作中已取得的成果和不足之处,并对其未来发展进行了展望.