Showing papers on "Product (mathematics) published in 1991"

An algorithm for associating the features of two images

Abstract: In this paper we describe an algorithm that operates on the distances between features in the two related images and delivers a set of correspondences between them. The algorithm maximizes the inner product of two matrices, one of which is the desired \`pairing matrix' and the other a \`proximity matrix' with elements exp (-r$\_{ij}^{2}$/2$\sigma ^{2}$), where r$\_{ij}$ is the distance between two features, one in each image, and $\sigma $ is an adjustable scale parameter. The output of the algorithm may be compared with the movements that people perceive when viewing two images in quick succession, and it is found that an increase in $\sigma $ affects the computed correspondences in much the same way as an increase in interstimulus interval alters the perceived displacements. Provided that $\sigma $ is not too small the algorithm will recover the feature mappings that result from image translation, expansion or shear deformation -- transformations of common occurrence in image sequences -- even when the displacements of individual features depart slightly from the general trend.

A Mathematica™ Package for Computing Operator Product Expansions

Abstract: A general purpose Mathematica™ package for computing Operator Product Expansions of composite operators in meromorphic conformal field theory is described. Given the OPEs for a set of “basic” fields, OPEs of arbitrarily complicated composites can be computed automatically. Normal ordered products are always reduced to a standard form. Two explicit examples are presented: the conformal anomaly for superstrings and a free field realization for the $\widehat{B_2}$ Kac-Moody-algebra.

Convergence estimates for product iterative methods with applications to domain decomposition

Abstract: In this paper, we consider iterative methods for the solution of symmetric positive definite problems on a space % which are defined in terms of products of operators defined with respect to a number of subspaces. The simplest algorithm of this sort has an error-reducing operator which is the product of orthogonal projections onto the complement of the subspaces. New normreduction estimates for these iterative techniques will be presented in an abstract setting. Applications are given for overlapping Schwarz algorithms with many subregions for finite element approximation of second-order elliptic problems.

Method and system for product configuration definition and tracking

Abstract: A method and system for the definition and tracking of multiple unique product configurations for configuration management in which customer contracted views of the product are defined by applying temporary changes to the base product configuration A product serial number effectivity is assigned to each unique customer specified product configuration and to the base product configuration in order to maintain multiple time-oriented versions of the product, thus supporting simultaneously both customer-specified and design-specified engineering changes to the base product A product configuration identifier provides non-redundant data storage for each unique product configuration and can refer to noncontiguous ranges of product serial numbers The configuration entry identifier in a product configuration table is used to peg detail component requirements to serially numbered products in order to correlate the product configurations as built with the product configuration as designed A component position identifier provides traceability of temporary changes made to the base product that result from customer contract specifications

Analysis of the asymmetric shortest queue problem

Abstract: In this paper we study a system consisting of two parallel servers withdifferent service rates. Jobs arrive according to a Poisson stream and generate an exponentially distributed workload. On arrival a job joins the shortest queue and in case both queues have equal lengths, he joins the first queue with probabilityq and the second one with probability 1 −q, whereq is an arbitrary number between 0 and 1. In a previous paper we showed for the symmetric problem, that is for equal service rates andq = 1/2, that the equilibrium distribution of the lengths of the two queues can be exactly represented by an infinite sum of product form solutions by using an elementary compensation procedure. The main purpose of the present paper is to prove a similar product form result for the asymmetric problem by using a generalization of the compensation procedure. Furthermore, it is shown that the product form representation leads to a numerically efficient algorithm. Essentially, the method exploits the convergence properties of the series of product forms. Because of the fast convergence an efficient method is obtained with upper and lower bounds for the exact solution. For states further away from the origin the convergence is faster. This aspect is also exploited in the paper.

Custom-made manufacturing system and custom-made manufacturing method

Abstract: The present invention relates to a manufacturing system which accepts a custom order of product from a customer and custom manufactures a product without sacrificing manufacturing efficiency. The manufacturing system includes the featuring steps of inputting the required specification of a product, creating the product design based on the design information of the product transmitted from a designing department, status data from the production department, and the input required specification, showing the created product design to the customer, selectively indicating a product to be purchased, transmitting the specification of the selected product to the production department, and producing a product based on the selected product specification.

Erratum: Negative regulation of human c-fos expression by the retinoblastoma gene product (Nature (1990) 346, (668-671))

Abstract: Nature 346, 668-671 (1990) THIS letter in the 16 August 1990 issue of Nature reported that the protein product of the retinoblastoma susceptibility gene (RB-1) can repress c-fos expression and AP-1 transcriptional activity in both serum-induced and cycling 3T3 cells. We also identified a cis- actingelement in the human c-fos promoter that can confer repression by Rb to a heterologous promoter.

Localization factor for multichannel disordered systems

Abstract: The localization factor (inverse of the localization length) is derived as a function of the transmission matrix \ensuremath{\tau} for multichannel disordered systems using a multiplicative ergodic theorem of Oseledets [Trans. Mosc. Math. Soc. 19, 197 (1968)]. The wave-transfer-matrix formalism is used in which the transfer matrices are symplectic and elements of the special unitary group SU(d,d). Modeling the disordered multichannel system via a product of random-wave-transfer matrices and applying the theorem of Oseledets as a starting point, it is shown that the multichannel localization factor (the smallest Lyapunov exponent of the random matrix product) can be expressed asymptotically as a function of any one of three matrix norms of the transmission matrix \ensuremath{\tau}. As a by-product of this analysis, we also develop expressions for the remaining Lyapunov exponents as a function of \ensuremath{\tau}. The localization factor result is compared with two others appearing in the literature.

Braided product and method of making same.

Abstract: An expandable braided product having greatly reduced tendency to splay at its ends when cut is provided by coating the braided product (10) with a thin layer of elastomeric material which provides the desired anti-splaying property, while retaining the expandable characteristic whereby the product expands laterally when compressed longitudinally and when released returns to its original size and shape.

The Composing Process for Computer Conversation

Abstract: Computer conversation provides a writing context in which both process and product are mediated via the computer terminal and the product is semipermanent This 8-month study of the use of computer

Fundamentals of Production Theory

Abstract: Activity analysis, which has only very recently been developed by Koopmans (1951) and extended by Debreu (1959) and Hlldenbrand (1966), is a general and relatively modern concept, using technological data for the thorough formal investigation and characterization of the productive relations that exist in a firm between the factor input quantities and the end product quantities. In this context, a technology is defined as the set of all production points that can be realized alternatively on the grounds of the enterprise’s technical knowledge. These production points are also termed activities or input-output-combinations. A technology is limited by the available resources in general.

A formal approach for product model information

Abstract: A formal approach to the representation of engineering and CAD information is developed, called EDM. Its intended use includes defining schemas for integrated engineering databases, a normal form for translating between CAD systems and/or engineering applications, and for archiving. A set of information structures or forms is developed for describing engineering product models. The criteria identified and used to evaluate and justify the structures include: (1) representation of function, as well as the form and physical properties of the product; (2) support for multiple levels of abstraction and for the various phases of the product life cycle; (3) representation of semantics sufficient for all uses and for determining the validity of information used in applications; and (4) extensible semantics, supporting the addition of new functional evaluations, new technologies, and new conceptual generalizations. A small set of class structures and relations is presented. expressed as predicate logic forms, and composed from domains and aggregations. These class structures support: (1) functional descriptions of a product and their accumulation within multiple hierarchies, based on shared physical property descriptions; (2) the definition of physical objects in terms of functional descriptions and their composition into higher level objects; (3) generalizations of objects and functions; (4) constraint structures that specify integrity conditions; and (5) structures able to depict engineering technologies.

Method and apparatus for forming individual pouches from a continuous web and packaging a product in the individual pouches

Abstract: The present invention includes a process and apparatus for producing highly specialized individual product pouches with high efficiency and simplicity at production speeds that are easily obtainable with present day forming machines, particularly, horizontal-type form-fill-seal machines. The subject process and apparatus advantageously form pouches from a continuous supply of flexible web material by folding the flexible web material into two side walls and a bottom gusset and performing one or more forming operations on only one of the gusset portion and lower side wall combinations at one time. Such forming operations may include any operation which physically or perspectively alters the appearance or nature of the pouches. After at least one such forming operation is conducted, a plurality of side seals are provided to define at least one specialized pouch. Preferably, during such forming operations, a separation element is inserted within the bottom gusset to effectively isolate one of the gusset portion and lower side wall combinations from the other.

Fast QR decomposition of Vandermonde-like matrices and polynomial least squares approximation

Abstract: Let f and g be functions defined at the real and distinct nodes $x_k $, and consider the inner product $( f,g ): = \sum_{k = 1}^m f ( x_k ) g ( x_k ) w_k^2 $ with positive weights $w_k^2 $. The present paper discusses the computation of orthonormal polynomials $\pi _0 ,\pi _1 , \cdots ,\pi _{n - 1} ,n\leqq m$, with respect to this inner product, and the use of these polynomials in a fast scheme for computing a QR decomposition of the transpose of Vandermonde-like matrices. Two methods are compared for computing the recurrence coefficients for the polynomials $\pi _j $ and their values at the nodes $x_k $: the Stieltjes procedure and a method in which an inverse eigenvalue problem for a tridiagonal symmetric matrix is solved by an algorithm proposed by Rutishauser, Gragg, and Harrod. The latter method is found to generally yield higher accuracy than the Stieltjes procedure if n is close to m, and roughly the same accuracy otherwise. This method for solving an inverse eigenvalue problem is applied in an alg...

Description of quantum spin using functions on the sphere S2

Abstract: An overview of isomorphic correspondences between spin algebra and algebras of functions on the sphere is given. In addition, the authors show that in one case the induced product between the spin function and another function is expressible by the action of a first-order differential operator correcting the ordinary product. This deformation leads to the geometric quantization of classical spin. The classical limit is studied for a class of correspondences.

Countable Sets and Hessenberg's Theorem

Abstract: Summary. The concept of countable sets is introduced and there are shown some facts which deal with finite and countable sets. Besides, the article includes theorems and lemmas on the sum and the product of infinite cardinals. The most important of them is Hessenberg’s theorem which says that for every infinite cardinal m the product m · m is equal to m.

Remarks on Talagrand’s deviation inequality for Rademacher functions

Abstract: Recently Talagrand [T] estimated the deviation of a function on $\{0,1\}^n$ from its median in terms of the Lipschitz constant of a convex extension of $f$ to $\ell ^n_2$; namely, he proved that $$P(|f-M_f| > c) \le 4 e^{-t^2/4\sigma ^2}$$ where $\sigma$ is the Lipschitz constant of the extension of $f$ and $P$ is the natural probability on $\{0,1\}^n$. Here we extend this inequality to more general product probability spaces; in particular, we prove the same inequality for $\{0,1\}^n$ with the product measure $((1-\eta)\delta _0 + \eta \delta _1)^n$. We believe this should be useful in proofs involving random selections. As an illustration of possible applications we give a simple proof (though not with the right dependence on $\varepsilon$) of the Bourgain, Lindenstrauss, Milman result [BLM] that for $1\le r 0$, every $n$-dimensional subspace of $L_s \ (1+\varepsilon)$-embeds into $\ell ^N_r$ with $N = c(r,s,\varepsilon)n$.

Closed cycle power system

Abstract: A closed cycle power system adaptable for use in terrestrial and extraterrestrial applications. A combustor is provided for combusting a fuel and an oxidizer at stoichiometric conditions. The resulting combustion efflux is combined with a third product to form a working fluid. The third product has the same atomic and molecular constituents as the fuel and oxidizer. An engine is provided for receiving the working fluid and driving power output therefrom. The exhaust from the engine is cooled and a controlled portion therefrom is extracted and condensed. The controlled portion is separated into its original atomic constituents for storage under high pressure and ultimate reuse as said fuel and oxidizer. The remaining portion of the exhaust is recompressed and reheated. That remaining portion becomes said third product which becomes combined with the comsution efflux to form a working fluid. The resulting stoichiometric closed loop process provides an efficient source of power.

Product application technique alters the sun protection factor.

Abstract: A number of factors may alter the efficacy of a sunscreen product being tested. Notably among these are (1) the source of ultraviolet (UV) radiation, (2) the filtration of the UV radiation source, (3) such environmental factors as swimming or sweating (4) and/or the amount of product applied. This is the first report in which the technique of product application itself is examined. We find that the act of rubbing the product into the skin appears also to remove product from the skin. In our study, different techniques of product application produced a 25% deviation in product sun protection factor. The variables associated with the application of sunscreening products are discussed.

Unstaffed checkout system

Abstract: The invention relates to an unstaffed checkout system comprising a checkout counter (1) provided with appropriate actuators, a background system (17) containing at least the product data, and a cash terminal program (15) which transmits information from the checkout counter actuators to the background system The system comprises a functional block (13) with an interface (14) compatible with the data transmitted by the cash terminal program (15) Product data relating to product identification are collected and new data are automatically added to the data for each product until the system has learned the key characteristics of each product