Showing papers on "Product (mathematics) published in 1993"

Method of and system for ordering products

Abstract: In ordering products, a customer selects a product from a product list stored in a remote computer system via a communication line. A sensor detects the customer size information and transmits it to the remote computer, thus enabling the remote computer to select a product having an appropriate size. Subsequently, on a monitor display, product image is superimposed on the customer body image. The fit evaluation is automatically performed by the local computer system. Depending on the fit of the product, the customer tries different products until placing an order.

The Riemannian Structure of Euclidean Shape Spaces: A Novel Environment for Statistics

Abstract: The Riemannian metric structure of the shape space $\sum^k_m$ for $k$ labelled points in $\mathbb{R}^m$ was given by Kendall for the atypically simple situations in which $m = 1$ or 2 and $k \geq 2$. Here we deal with the general case $(m \geq 1, k \geq 2)$ by using the properties of Riemannian submersions and warped products as studied by O'Neill. The approach is via the associated size-and-shape space that is the warped product of the shape space and the half-line $\mathbb{R}_+$ (carrying size), the warping function being equal to the square of the size. When combined with parallel studies by Le of the corresponding global geodesic geometry, the results obtained here determine the environment in which shape-statistical calculations have to be acted out. Finally three different applications are discussed that illustrate the theory and its use in practice.

System for self-checkout of bulk produce items

Abstract: A retail checkout station for purchaser self-checkout is coupled to a service terminal with a video monitor directed at the checkout. The service terminal preferably services a number of checkouts. Product codes can be downloaded from a remote location to a checkout presented with a product lacking a product code barcode label, such as an item of bulk produce. A product database having product price information stored in a memory is normally indexed to product codes which are scanned in, and also is at least partly indexed by product identity information. The checkout station can have an electronic scale for determining the weight of a product. A video image of an uncoded product in the security zone is captured by a camera and displayed on a video monitor which is viewable by store personnel. A keyboard associated with the video monitor permits the store personnel to enter a product code corresponding to the product displayed on the video monitor. The service terminal function can be met by cashiers at idle checkout lanes or payment stations. The data processor accesses product price information from memory, and if necessary calculates a purchase price of the product by weight. The purchase price is added to the price of other consumer purchases for payment by the purchaser.

Removing Negative Country Images: Effects of Decomposition, Branding, and Product Experience:

Abstract: This article reports two studies on how negative country images can be removed by investigating the effects of decomposing country image into component and assembly origins, as well as the effects ...

Macrocell with flexible product term allocation

Abstract: An improved macrocell is provided for summing product term inputs to complete a sum of products. Some or all of a macrocell's product terms can be allocated to another macrocell. The macrocell OR function remains available to sum product term inputs, even when other product term inputs in the same macrocell are allocated elsewhere. Macrocells can also by daisy-chained bidirectionally, so that the delay associated with allocating product terms between multiple macrocells can be reduced.

Method of producing a bill of material for a configured product

Abstract: This invention provides a method utilizing component-to-attribute relationships resulting in a bill of materials documenting the specific structure of the configuration of an end product. Attributes and their values together with option attributes which describe the end product are input to a database. A check is made to determine if dependent attributes are required to further define the end product. A check is then made to determine if incompatible attribute combinations exist. Components are selected to satisfy the specific structure of the configuration of the end product. Part numbers and nomenclature are created to identify the configuration just created. A bill of materials is created to document the specific structure of the end product together with price/cost of the end product.

SHARED: An information model for cooperative product development

Abstract: One fundamental issue in developing collaborative engineering systems is the representation of product information which supports communication and coordination. This product information includes not only the geometric and physical properties of the product and its parts, but also information about functions, constraints and the design rationale. In this paper, we describe an information model, SHARED, which was developed for encoding product information in DICE, a distributed and integrated environment for computer-aided engineering. SHARED provides multiple levels of both functional and geometric abstractions, multiple views and techniques for maintaining consistency between the various abstractions and views. These elements are essential for a good representation model of product information. The use of the SHARED model is illustrated through an example, depicting the various representations of a product as it evolves through the design process. The SHARED model has been implemented over a distributed OODBMS as a toolkit/framework for developing environments which need to model, manipulate and communicate product information between distributed cooperating applications, while supporting coordination between them.

A generalization of Laguerre polynomials

Abstract: The authors study orthogonal polynomials on $[0, + \infty )$ with respect to an inner product involving derivatives that cannot be derived from a weight function. These polynomials can be written as a ${}_3 F_3 $ hypergeometric series and they satisfy a second-order differential equation and a five term recurrence relation. At most one zero of each polynomial is located outside $(0, + \infty )$, the interior of the interval of orthogonality. As a special case Koornwinder’s Laguerre polynomials $\{ L_n^{\alpha ,M} (x)\} _{n = 0}^{ + \infty } $ are included.

The domination numbers of the 5 x n and 6 x n grid graphs

Abstract: The k × n grid graph is the product Pk × Pn of a path of length k − 1 and a path of length n − 1. We prove here formulas found by E. O. Hare for the domination numbers of P5 × Pn and P6 × Pn. © 1993 John Wiley & Sons, Inc.

Introduction to distributive categories

Abstract: Distributive category theory is the study of categories with two monoidal structures, one of which “distributes” over the other in some manner When these are the product and coproduct, this distribution is taken to be the lawwhich asserts that the obvious canonical map has an inverse A distributive category is here taken to mean a category with finite products and binary coproducts such that this law is satisfiedIn any distributive category the coproduct of the final object with itself, 1 + 1, forms a boolean algebra Thus, maps into 1 + 1 provide a boolean logic: if each such map recognizes a unique subobject, the category is a recognizable distributive category If, furthermore, the category is such that these recognizers classify detachable subobjects (coproduct embeddings), it is an extensive distributive categoryExtensive distributive categories can be approached in various ways For example, recognizable distributive categories, in which coproducts are disjoint or all preinitials are isomorphic, are extensive Also, a category X having finite products and binary coproducts satisfying the slice equation (due to Schanuel and Lawvere) is extensive This paper describes a series of embedding theorems Any distributive category has a full faithful embedding into a recognizable distributive category Any recognizable distributive category can be "solidified" faithfully to produce an extensive distributive category Any extensive distributive category can be embedded into a toposA peculiar source of extensive distributive categories is the coproduct completion of categories with familial finite products In particular, this includes the coproduct completion of cartesian categories, which is serendipitously, therefore, also the distributive completion Familial distributive categories can be characterized as distributive categories for which every object has a finite decomposition into indecomposables

Learning and robust learning of product distributions

Abstract: In this paper we present some results about PAC-learning distributions with respect to the Kullback-Leibler Divergence. The hypothesis classes are distributions which are the product of conditional probabilities of at most k + 1 variables. We call this family of distribution classes CPCPk. Our main theorem shows that all classes in C’PCPk are robustly learnable. This generalizes ideas of Lewis and Chow et al., who investigated restricted classes in CPCPk and only proved a weak convergence result for classes in CPCP1. Our approach is to transform the learning problem to a structured combinatorial optimization problem. The second part of this paper develops efficient algorithms for such problems thereby guaranteeing efficient learnability. We show the efficient robust learnability of tree dependent distributions and develop a combinatorial algorithm for the efficient proper learnability of Markov expansions. This algrithm finds a maximal Hamiltonian path for certain classes of graphs. Moreover we discuss the efficient learnability of classes in CPCPk for k > 1. Here the combinatorial problems are more involved, but we state positive results for learning Chow(k) expansions in special cases.

Real time tank product loss detection system

Abstract: A system for detecting product loss from a fluid product storage and dispensing means including at least one storage tank comprises tank volume monitoring devices, fluid dispenser monitoring devices and computer means to analyze the data from such devices at various times as determined by the status of the various elements to determine if there are unexplained shortages of product.

Chemical process optimization method

Abstract: A method for producing two or more products from a production site such as an air separation plant to satisfy a given demand for each of the products in which energy consumption and the rate of product production are correlated so that product production may be determined from a conventional mixed integer linear programming model the solution of which will provide an optimum production schedule for producing product to meet total product demand at minimum energy cost over a given time horizon.

Monte Carlo evaluation of real-time Feynman path integrals for quantal many-body dynamics: Distributed approximating functions and Gaussian sampling

Abstract: In this paper the authors report the initial steps in the development of a Monte Carlo method for evaluation of real-time Feynman path integrals for many-particle dynamics. The approach leads to Gaussian factors. These Gaussian factors result from the use of a generalization of their new discrete distributed approximating functions (DDAFs) to continuous distributed approximating functions (CDAFs) so as to replace the exact coordinate representation free-particle propagator by a {open_quotes}CDAF-class, free-particle propagator{close_quotes} which is highly banded. The envelope of the CDAF-class free propagator is the product of a {open_quotes}bare Gaussian{close_quotes}, exp[{minus}(x{prime} {minus} x){sup 2}{sigma}{sup 2}(0)/(2{sigma}{sup 4}(0) + {h_bar}{sup 2}{tau}{sup 2}/m{sup 2})], with a {open_quotes}shape polynomial{close_quotes} in (x{prime}{minus}x){sup 2}, where {sigma}(0) is a width parameter at zero time (associated with the description of the wavepacket in terms of Hermite functions), {tau} is the time step ({tau} = t/N, where t is the total propagation time), and x and x{prime} are any two configurations of the system. The bare Gaussians are used for Monte Carlo integration of a path integral for the survival probability of a Gaussian wavepacket in a Morse potential. The approach appears promising for real-time quantum Monte Carlo studies based on the time-dependent Schroedinger equation, the time-dependent von Neumann more » equation, and related equations. 38 refs., 3 figs., 3 tabs. « less

A Bayes method for assessing product-reliability during development testing

Abstract: A fully Bayes approach is presented for analyzing product reliability during the development phase. Based on a Bayes version of the Barlow-Scheuer reliability-growth model, it is assumed that the product goes through a series of test/modification stages, where each product test yields attribute (pass-fail) data, and failure types are classified as fixable or nonfixable. Relevant information on both the failure probabilities and the reliability-growth process is used to motivate the prior joint distribution for the probability of each failure type over the specified range of testing. Results at a particular test-stage can be used to update the knowledge about the probability of each failure type (and thus product reliability) at the current test-stage as well as at subsequent test-stages, and at the end of the development phase. A relative ease of incorporation of prior information and a tractability of the posterior analysis are accomplished by using a Dirichlet distribution as the prior distribution for a transformation of the failure probabilities. >

Single axioms for groups and Abelian groups with various operations

Abstract: This paper summarizes the results of an investigation into single axioms for groups, both ordinary and Abelian, with each of following six sets of operations: {product, inverse}, {division}, {double division, identity}, {double division, inverse}, {division, identity}, and {division, inverse}. In all but two of the twelve corresponding theories, we present either the first single axioms known to us or single axioms shorter than those previously known to us. The automated theorem-proving program OTTER was used extensively to construct sets of candidate axioms and to search for and find proofs that given candidate axioms are in fact single axioms.

Method and apparatus for determining the amount of oncogene protein product in a cell sample

Abstract: An apparatus and method for determining an amount of oncogene protein product copies in a cell includes an optical conversion module for measuring an amount of optically enhanced DNA in a cell sample. A subsystem for measuring an amount of an optically enhanced oncogene protein product protein product is coupled to the DNA measuring means. A subsystem for comparing the measured DNA amount and measured oncogene protein product protein product amount produces a oncogene protein product copy measurement which is fed to an output device for producing an output indicative of the amounts of the oncogene protein product in the cells of the cell sample.

Continuous information system

Abstract: In this paper we generalise the notion of (algebraic) information system to continuous information system. Just as algebraic information systems are concrete representations of Scott domains, continuous information systems are concrete representations of continuous Scott domains. The class of continuous information systems can be generated from the subclass of qualitative information systems, in the sense that the category of continuous information systems is equivalent to the Karoubi envelope of the category of qualitative information systems. Because qualitative information systems correspond to the qualitative domains of Girard (Theoret. Comput. Sci.45, 159-192 (1986)) this implies that the category of continuous Scott domains is equivalent to the Karoubi envelope of the category of qualitative domains. We show how constructions on qualitative information systems (such as product and function space) can be "translated" to constructions on continuous information systems. Among other things, we prove that the category of qualitative information systems is weak Cartesian closed. Finally, we define two universal information systems.

The mathematics of product form queuing networks

Abstract: Markov processes that have a product form solution have become an important computer performance modeling tool. The fact that such a simple solution exists for seemingly complex Markov processes is surprising at first encounter and can be established by showing that balance equations are satisfied. In this article we attempt to provide insight as to why such a solution form exists and demonstrate that product form and companion results, such as the arrival theorem and Norton's theorem, are consequences of four properties satisfied by queues that satisfy partial balance. Notions of reverse processes, reversibility, and quasireversibility are developed to establish the four properties

Neural network and wavelet transform for scale-invariant data classification.

Abstract: Given an astrophysical observation with an arbitrary carrier frequency and an unknown scale under an additive white noise, s'(t)\ensuremath{\equiv}s(\ensuremath{\alpha}t)+n(t), its wavelet transform is W'(a,b)\ensuremath{\equiv}(s'(t),${\mathit{h}}_{\mathit{a}\mathit{b}}$(t)), as computed by the inner product with a daughter wavelet ${\mathit{h}}_{\mathit{a}\mathit{b}}$(t)\ensuremath{\equiv}h((t-b)/a)/a. W'(a,b) equals the original transform W(a,b)\ensuremath{\equiv}(s(t),${\mathit{h}}_{\mathit{a}\mathit{b}}$(t)) displaced along the radial direction W'(a,b)=W(\ensuremath{\alpha}a,\ensuremath{\alpha}b) plus noise in the time-scale joint-representation plane. A bank of wedge-shaped detectors collects those displaced transforms W'(a,b) to create a set of invariant features. These features are fed into a two-layer feed-forward artificial neural network, to interpolate discrete sampling, as demonstrated successfully for real-time-signal automatic classification. Useful wavelet applications in turbulence onset, spectrum analyses, fractal aggregates, and bubble-chamber particle-track pattern-recognition problems are indicated but are modeled, in the interest of simplicity, in a one-dimensional example.

CAD system with product assembly/disassembly planning function

Abstract: Assembly design of mechanical products is one of the most important subjects in the CAD/CAM systems of the near future. The product model (geometric model) is the input in many CAD/CAM systems in order to determine the assembly/disassembly sequence. Disassembly is executed with cooperation between the computer system and the designer. The kinematic simulation should support the designer; however, most simulation systems do not have enough functions to do this. There are many problems left, mainly caused by the lack of functionality of the kinematic simulation of mechanical products. When product designers are requested to consider product assembly and extract the fundamental assembly plan from their design solutions, the kinemati simulation and evaluation functions, to obtain the product assembly plan, are most important in CAD systems. This paper deals with a kinematic simulation system used in assembly planning that simulates physical phenomena including the effect of gravity, and a prototype simulator is developed. An evaluation method for the ease of assembly/disassembly based on the kinematic simulation system is also proposed, which gives a decision support tool. Here, the assembly sequence is considered as the reverse of the disassembly sequence, which is justified through taking the kinematic simulation into consideration. The part to be removed is decided by comparing the evaluation standard values of candidate parts when several parts can be removed at the same time. With the use of the product model presented by 3-D solid geometry, possible movements of each part in the product are calculated, and the removal possibilities from the product can be searched. When there are several ways to remove the part from the product, the best disassembly operation for the part is selected on the basis of shortest distance of part movement. In the evaluation, the effect of gravity is considered, which may cause the next assembly/disassembly operation to be difficult. The developed simulation system is also effective in detecting the necessity for jigs or fixtures in the assembly sequence. Through a case study, it is shown that the developed system is valid and effective in enabling product designers to obtain product assembly plans.