Joint Similarities and Parameterizations for Dilations of Dual g -frame Pairs in Hilbert Spaces

In this paper, we give an operator parameterization for the set of dilations of a given pair of dual g-frames and the set of dilations of pairs of dual g-frames of a given g-frame. In particular, for the dilations of a given pair of dual g-frames, we introduce the concept of joint complementary g-frames and prove that the joint complementary g-frames of a pair of dual g-frames are unique in the sense of joint similarity, which then helps to obtain a sufficient condition such that the complementary g-frames of a g-frame are unique in the sense of similarity and show that the set of dilations of a given dual g-frame pair are parameterized by a set of invertible diagonal operators. For the dilations of pairs of dual g-frames, we prove that the set of dilations of pairs of dual g-frames are parameterized by a set of invertible upper triangular operators.     

Optimization of axisymmetric membrane shells

Problems of the joint optimization of the shape and distribution along the meridian of the thickness of membrane shells of revolution under the action of axisymmetric loads are considered, taking account of the constraints concerning the strength of the shell and the volume of its cavity. General formulations of problems of the optimal design of shells of revolution are given and the optimal shape of a shell and the corresponding thickness distribution are investigated. Results of the exact solution of problems of the optimal design of closed shells of revolution when there is an internal pressure are presented. The simultaneous introduction of two control functions, describing the shape of the shell and the distribution of its thickness, not only ensures a substantial reduction in the mass of a shell but also leads to significant mathematical simplifications, which enable the solution of the optimization problem being considered to be obtained in an analytical form.     

区间数的绝对值与区间值函数的极限

研究了区间数的绝对值和区间值函数的极限问题.首先,讨论了区间数的H-差的性质,得到了H-差的两个运算法则;然后,给出了区间数的绝对值概念,并讨论了区间数绝对值的性质;最后,借助区间数的H-差和绝对值的概念,建立了区间值函数极限概念的一种新的表达方式,给出了极限存在的充分必要条件,证明了极限值的唯一性及对加法运算和数乘运算的封闭性.     

Estimate of the Order of Growth of a Class of Entire Functions on the Real Axis

For a class of entire functions we study the problem of estimation of the order of growth of functions on the real axis. This problem is important for the justification of the integral representation of bounded solutions to certain partial differential equations considered in other papers of the authors. In order to obtain an estimate of the order of growth of a function on the real axis, we use the method of differential equations. The method is based, on one hand, on the construction of a system of first-order ordinary differential equations whose solution is a vector function of traces of function and its derivatives on the real axis. On the other hand, under the respective change of variables in the system of equations, we obtain an estimate of the solution to the system of equations for a large positive values of the argument. The obtained estimate is non-trivial and shows the way a complex parameter of a power series affects the order of growth of a function.     

Damageability of a material reinforced with unidirectional orthotropic fibers for an exponential function of long-term microstrength

The theory of long-term damageability of a homogeneous material is generalized to the case of an orthotropic fibrous composite material with a stochastic structure. Equations of mechanics of microinhomogeneous media of this structure form the base of the theory. The process of damage of components of a composite is modeled by the formation of stochastically located micropores. The criterion of fracture of a unit microvolume is characterized by its long-term strength determined by the dependence of the time of brittle fracture on the degree of closeness of the equivalent stress to its limit value, which characterizes the short-term strength on the basis of the Huber–von Mises criterion accepted as an arbitrary function of coordinates. Efficient deformation properties and the stress-strain state of an orthotropic fibrous composite with microdamages in components are determined on the base of stochastic equations of elasticity of orthotropic media. For given macrostresses and macrostrains and an arbitrary moment of time, balance equations of damage (porosity) of components are formulated. On the basis of the iteration method, we construct algorithms for calculating dependences of microdamage of components of an orthotropic fibrous material on time and dependences of macrostresses or macrostrains on time and obtain the corresponding curves for the case of a bounded function of the long-term microstrength, which is approximated by an exponential law.     

Configurations of ovals

We survey the known hyperovals in . We then survey the relationship of the study of configurations of ovals in called augmented fans to that of ovoids of , flocks of the quadratic cone of , flocks of a translation oval cone of and spreads of certain generalised quadrangles of order. We also consider the configurations of ovals in called herds and their relationship with flocks of the quadratic cone of.     

Geometry of a five link mechanism with two degrees of freedom

The paper is devoted to the solution of straight and inverse geometrical tasks of five link mechanism with two degrees of freedom. The solution of the mentioned problem is very important in order to determine kinematic parameters of actuators. The problem can be divided into two parts. The first part is considered when we are given the coordinates of the output link of the mechanism and the necessity arises of determining the angles of rotation of actuators. On the other hand, it is very important to determine the position of the output link when the angles of rotation of the actuators are known. Here we consider that the mechanism is composed only of five classes of rotating kinematic pairs and the actuators are situated at the junctions of frames and links of the examined mechanism. The solution of the said problem is based on utilization of homogenous coordinates. On the basis of the obtained equations of motion, one can calculate the trajectories of motion of the output link as well angles of rotation of the actuators by taking into consideration preliminary given kinematic parameters of the mechanism. Here we also obtain equations for calculating values of speed and acceleration of the links of the mechanism. The calculations differ from known methods in simplicity and high performance, which would be useful for programming actuators mounted in the joints of the linkage.     

我国医疗费用增长与医疗设备投入的相关性研究

近年来我国卫生总费用占GDP的比例增长很快,而在卫生费用结构上则发生政府投入下降和个人支出的上升。本文采集了大量的统计数据,采用统计相关性研究的方法,论证了医疗设备规模的不断扩大是导致医疗费用上升的主要因素之一;医疗设备的快速增长与医院维修费用投入的增长直接相关,而引起医疗设备维修大量投入的主要原因则是故障期内医疗设备的非正常闲置。本文通过对个人卫生费用的上升、医疗设备规模的扩大及其医疗设备维修投入费用增加相关性的分析,说明了在这种关系下,十分有必要研究医院医疗设备维修体系,以在卫生投入和患者权益上达到平衡。     

Complexity Estimation for an Algorithm of Searching for Zero of a Piecewise Linear Convex Function

It is known that the problem of the orthogonal projection of a point to the standard simplex can be reduced to solution of a scalar equation. In this article, the complexity is analyzed of an algorithm of searching for zero of a piecewise linear convex function which is proposed in [30]. The analysis is carried out of the best and worst cases of the input data for the algorithm. To this end, the largest and smallest numbers of iterations of the algorithm are studied as functions of the size of the input data. It is shown that, in the case of equality of elements of the input set, the algorithm performs the smallest number of iterations. In the case of different elements of the input set, the number of iterations is maximal and depends rather weakly on the particular values of the elements of the set. The results of numerical experiments with random input data of large dimension are presented.     

On sums of independent random variables whose distributions belong to the max domain of attraction of max stable laws

In this article we study the max domains of attraction of distributions of sums of independent random variables belonging to the max domains of attraction of max stable laws under linear normalization. These results lead to the study of the max domains of attraction of distributions of products of independent random variables belonging to the max domain of attraction of max stable laws under power normalization.     

Fixed point solutions of generalized equilibrium problems for nonexpansive mappings

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a generalized equilibrium problem in a real Hilbert space. Then, strong convergence of the scheme to a common element of the two sets is proved. As an application, problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem is solved. Moreover, solution is given to the problem of finding a common element of fixed points set of nonexpansive mappings and the set of solutions of a variational inequality problem.     

Viscosity approximation methods for generalized equilibrium problems and fixed point problems

The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a generalized equilibrium problem (for short, GEP) and the set of fixed points of a nonexpansive mapping in the setting of Hilbert spaces. By using well-known Fan-KKM lemma, we derive the existence and uniqueness of a solution of the auxiliary problem for GEP. On account of this result and Nadler’s theorem, we propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of GEP and the set of fixed points of a nonexpansive mapping. Furthermore, it is proven that the sequences generated by this iterative scheme converge strongly to a common element of the set of solutions of GEP and the set of fixed points of a nonexpansive mapping.     

Generalisierung von Kommutationsfunktionen; eine Anwendung im Computermodell einer Lebensversicherungsgesellschaft

Subject of the investigation described in this paper has been: To find the general form (as a function of time elapsed since date of entry) of the variable sum assured to be paid on death or of the variable intensity of payment of a continuous life annuity such, that the calculation of the actual value of the payments can be based on the rise of a finite number of commutation functions. It is shown that the general form of the functions sought for, contains so many parameters which can be freely chosen, that the sums assured represented by functions of time of another type can be approximated very well by appropriate choice of values of the parameters. The last statement is clarified by a demonstration of an approximation of a special type of the variable sum assured payable in case of death playing a role in a forecasting model of a life office in the ordinary branch.     

A criterion for the strong ellipticity of the equilibrium equations of an isotropic non-linearly elastic material

A new criterion for satisfying the condition of strong ellipticity of the equilibrium equations of a homogeneous isotropic elastic medium is obtained, consisting of twelve unconditional and the same number of conditional inequalities. The criterion differs from previously known criteria in the fact that it is more effective for the analytical verification of the condition of strong ellipticity. A number of sufficient criteria of the strong ellipticity of the equations of the non-linear statics of an elastic body is presented. It is shown that the method used in this paper is also effective in the case of an incompressible material. A new constitutive inequality in the non-linear theory of elasticity is proposed that, in particular, ensures the strong ellipticity of the equilibrium equations and the stability of an elastic body in a state of hydrostatic compression. A mechanical interpretation of some implications of the above mentioned inequality is given. Using the criterion obtained, the condition of strong ellipticity is verified for a number of specific models of compressible elastic materials and examples of the violation of this condition are also considered.     

模糊度定义的不一致性及其理论分析

指出模糊度定义的不一致性，并通过实例进行验证；从理论上分析模糊度定义的不一致性产生的原因，指出当模糊度理论在图像处理中应用时模糊度定义的不一致性可能会产生的影响；给出一个比较合理的模糊度定义。文中提出的问题是在工程应用过程中发现的新问题，所做的工作也只是初步的。     

Grassmann image of non-isotropic surface of pseudo-Euclidean space

We consider submanifolds of non-isotropic planes of the Grassman manifold of the pseudo-Euclidean space. We prove a theorem about the unboundedness of the sectional curvature of the submanifolds of the two-dimensional non-isotropic planes of the four-dimensional pseudo-Euclidean space with the help of immersion in the six-dimensional pseudo-Euclidean space of index 3. We also introduce a concept of the indicatrix of normal curvature and study the properties of this indicatrix and the Grassman image of the non-isotropic surface of the pseudo-Euclidean space. We find a connection between the curvature of the Grassman image and the intrinsic geometry of the plane. We suggest the classification of the points of the Grassman image.