Sample rotation theory with missing data

This paper studies how the sample rotation method is applied to the case where item non-response occurs in surveys. The two cases where the response to the first occasion is complete or incomplete are considered. Using ratio imputation method, the estimators of the current population mean are proposed, which are valid under uniform response regardless of the model and under the ratio model regardless of the response mechanism. Under uniform response, the variances of the proposed estimators are derived. Interestingly, although their expressions are similar, the estimator for the case of incomplete response on the first occasion can have smaller variance than the one for the case of complete response on the first occasion under uniform response. The linearized jackknife variance estimators are also given. These variance estimators prove to be approximately design-unbiased under uniform response. It should be noted that similar property on variance estimators has not been discussed in literature.     

Axisymmetric contact of anisotropic shells of rotation with rigid and elastic foundations

A class of problems are investigated on determining the stressed-strained state of anisotropic shells of rotation that are in axisymmetric one-sided contact with rigid and elastic surfaces. The shells are under the action of surface and contour loads. For some combinations of these quantities the shell may break away from the surface. To determine the contact zone, the method of successive approximations is utilized. In contrast to most investigations in which the contact zone is first determined, the method proposed makes use of a special quantity characterizing the size of the contact zone. The load on contours is determined from the solution to the problem on the stressed state of the shell and the condition specified on the boundary of the contact zone. Some examples of solving concrete problems are given. Bibliography: 5 titles. Translated fromObchyslyuval’ na ta Prykladna Matematyka, No. 76, 1992, pp 70–74.     

Applications of subordination to functions with bounded boundary rotation

Classes of analytic functions with bounded boundary rotation are considered. For these classes, we use subordination techniques to obtain known as well as new results related to Marx-Strohhäcker-type problems.     

Applications of coordinatization in modular lattice theory: The legacy of J. von Neumann

This paper reviews current work based on von Neumann's coordinization theorem.     

Directions in lattice theory

Dedicated to Bjarni Jónsson on his 70th birthday     

Efficient numerical methods in non-uniform sampling theory

Summary. We present a new ``second generation" reconstruction algorithm for irregular sampling, i\@.e\@. for the problem of recovering a band-limited function from its non-uniformly sampled values. The efficient new method is a combination of the adaptive weights method which was developed by the two first named authors and the method of conjugate gradients for the solution of positive definite linear systems. The choice of "adaptive weights" can be seen as a simple but very efficient method of preconditioning. Further substantial acceleration is achieved by utilizing the Toeplitz-type structure of the system matrix. This new algorithm can handle problems of much larger dimension and condition number than have been accessible so far. Furthermore, if some gaps between samples are large, then the algorithm can still be used as a very efficient extrapolation method across the gaps. Received December 22, 1993     

Determinant theory for lattice matrices

The determinant theory for matrices over a pseudo-complemented distributive lattice is presented. Previous results on this topic are special cases of the theorems proved in this paper.     

An extension of Boolean lattice theory

Mathematische Annalen -     

Permutability of rules in lattice theory

Lattice theory with the meet and join operations is formulated as a system of rules of inference. The order of application of these rules can be permuted so that a subterm property follows: If an atomic formula is derivable from given atomic formulas by the rules, it has a derivation all terms of which are terms in the given formulas or the conclusion. A direct decision method for universal formulas in lattice theory with the meet and join operations follows.     

On the lattice discrepancy of bodies of rotation with boundary points of curvature zero

This article gives an asymptotic result for the lattice point discrepancy of a large body of rotation in , whose boundary is piecewise smooth and contains points of vanishing Gaussian curvature. Received: 2 November 2006     

集对Fuzzy格及其在格表示论中的应用

用幂集格构造了集对 Ｆｕｚｚｙ 格（这与用整数对构造有理数集有相似之处）,并用它证明了完整的软代数表示定理,即定义了到自身的映射且有最大元和最小元的格为软代数的充要条件是它与某个集对 Ｆｕｚｚｙ 格的子格同构．这样,与分配格在幂集 Ｂｏｏｌｅ 格中表示相对应,软代数在集对 Ｆｕｚｚｙ 格中有表示,在理论上是很完美的     

On the theory of layered anisotropic cylindrical shells stiffened with ribs

The deformation, stability and vibration equations for anisotropic cylindrical shells stiffened with individual longitudinal and circumferential ribs are derived without introducing the hypothesis of nondeformable normals. The more general assumption adopted for layered materials (for example, glass-reinforced plastics) of a linear variation of the displacements over the thickness of the shell and the height of the ribs is used; in this case for the points of contact of the shell and the ribs after deformation the common normals form broken lines. The solution of the problem of the stability of a cylindrical shell stiffened with circumferential ribs is examined. For a shell with different, arbitrarily located ribs the problem is reduced to a homogeneous algebraic system of equations equal in number to three times the number of ribs.Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 647–654, July–August, 1974.     

A new refined theory of anisotropic shells

A new refined theory of anisotropic thin shells is constructed with allowance for the effects associated with all the transverse strains and stresses neglected in constructing the classical theory.Institute of Mathematics and Mechanics, Academy of Sciences of the Armenian SSR, Erevan. Translated from Mekhanika Polimerov, No. 5, pp. 884–896, September–October, 1970.     

Applications of graph theory

Graph theory is rapidly moving into the mainstream of mathematics mainly because of its applications in diverse fields. In this paper, we discuss certain ways of applying graph theoretical techniques to solve various problems and present the review of some of the applications. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)