Showing papers on "Product (mathematics) published in 1998"

Local description of quantum inseparability

Abstract: We show how to decompose any density matrix of the simplest binary composite systems, whether separable or not, in terms of only product vectors. We determine for all cases the minimal number of product vectors needed for such a decomposition. Separable states correspond to mixing from one to four pure product states. Inseparable states can be described as pseudomixtures of four or five pure product states, and can be made separable by mixing them with one or two pure product states.

Application of in-situ product removal techniques to biocatalytic processes

Abstract: Biocatalytic processes for the manufacture of small, highly functionalized molecules frequently have limited productivity. A common reason for this is the presence of the reaction products that can cause inhibitory or toxic effects (making poor use of the enzyme) or promote unfavourable equilibria (giving low conversions). In each case, the product needs to be removed as soon as it is formed in order to overcome these constraints and hence increase the productivity of the biocatalytic process. Here, we review the need for in situ product removal and the process research required for its implementation.

Product design through multivariate statistical analysis of process data

Abstract: A methodology is developed for finding a window of operating conditions within which one should be able to produce a product having a specified set of quality characteristics. The only information assumed to be available is that contained within historical data on the process obtained during the production of a range of existing product grades. Multivariate statistical methods are used to build and to invert either linear or nonlinear empirical latent variable models of the existing plant operations to obtain a window of operating conditions that are capable of yielding the desired product and that are still consistent with past operating procedures and constraints. The methods and concepts are illustrated using a simulated high-pressure tubular reactor process for producing low-density polyethylene.

Quantum Entanglement and the Communication Complexity of the Inner Product Function

Abstract: We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state. We prove linear lower bounds for both exact protocols, as well as for protocols that determine the answer with bounded-error probability. Our proofs employ a novel kind of "quantum" reduction from a quantum information theory problem to the problem of computing the inner product. The communication required for the former problem can then be bounded by an application of Holevo's theorem. We also give a specific example of a probabilistic scenario where entanglement reduces the communication complexity of the inner product function by one bit.

Manufacturing system and method for assembly of computer systems in a build-to-order environment

Abstract: Parallel organized unit-by-unit manufacturing and assembly systems and methods for computer systems and other products advantageously integrate into a build-to-order environment. Responsive to orders received, kit trays are prepared that each hold parts and components needed to build an ordered product. The kit tray is transferred to a work cell where a team builds the product. The product is then tested and repaired, with information regarding any problems provided to the responsible work cell.

Concurrent design and subsequent partitioning of product and test die

Abstract: One embodiment of the present invention concerns a design methodology for generating a test die for a product die including the step of concurrently designing test circuitry and a product circuitry in a unified design. The test circuitry can be designed to provide a high degree of fault coverage for the corresponding product circuitry generally without regard to the amount of silicon area that will be required by the test circuitry. The design methodology then partitions the unified design into the test die and the product die. The test die includes the test circuitry and the product die includes the product circuitry. The product and test die may then be fabricated on separate semiconductor wafers. By partitioning the product circuitry and test circuitry into separate die, embedded test circuitry can be either eliminated or minimized on the product die. This will tend to decrease the size of the product die and decrease the cost of manufacturing the product die while maintaining a high degree of test coverage of the product circuits within the product die.

Method and device for determining the quantity of product present in a reservoir, a product reservoir and a device for processing electrical signals intended for such a determination device

Abstract: A device and a method for determining the quantity of product present in a reservoir, and more particularly determining with precision when there is a predetermined quantity of product in the reservoir. The invention applies to an ink reservoir in an image formation device, such as a printer. According to the invention, the product is connected to a predetermined potential and an electrical field is established through the product present in the reservoir. The electrical field passing through the product is measured in order to produce an electrical signal representing the electrical field, and the resulting electrical signal is processed in order to produce a signal representing the quantity of product present in the reservoir and to detect the interruption of the connection of the product to the predetermined potential, where the interruption corresponds t the predetermined quantity of product in the reservoir.

Electronic shopping system and method of defining electronic catalogue data therefor

Abstract: Product data information to be stored in a product database is defined by setting essential items necessary to define products with respect to their essential parts, and setting optional items necessary to define optional products deriving from standards product defined by their essential items. A product definition section produces product data information on standard products based on the set essential items, and produces product data information on optional products based on the set optional items. This product data information is transferred from an electronic shop client to an electronic mall server to be stored into the product database through a product registering section.

Computer-based method of structuring product configuration information and configuring a product

Abstract: A computer based method of collecting, structuring, and displaying product configuration information, and using the product configuration information to produce a computer program that validates product option selections and configures a product, is disclosed. The computer based method is used to create a Knowledge Map that contains product information objects. A product information object can be one of: a product option object, representing a customer option; a product module object, representing a collection of product parts, plans, tools, functional tests, inspections, or software; a grouping object, grouping product options or modules; or a relational object representing a relation between product objects. An input device is used to select a plurality of product information objects and position the objects in a display area. Upon selection of the objects, an operator is prompted to input specific information pertaining to the selected object. Constraints limit the selections that an operator can make, the appearance of the objects, and the configurations that can be produced from selected objects. Information pertaining to selected objects and their configuration is stored in a database. Changes can be made directly to the information stored in the database, and these changes are reflected in a corresponding display of the product information. After producing a Knowledge Map, the information is retrieved from a database to produce a set of rules that is input to a rule-based program for validating a set of product option selections and configuring a final product defined by resulting modules. The information can also be retrieved to produce object-based information to be used in the creation of an object-based program for validating a set of product options and configuring a product.

Multiplication of distributions

Abstract: Multiplication by harmonic representations of distributions, introduced by Li Banghe, is an extension of a certain product by radial (rotationally symmetric) mollifiers and therefore a strict extension of the Kaminski and Colombeau product. product Classification: 46F10 There exist several definitions of a multiplication of distributions. A popular approach to define a product for a pair of distributions is to approximate them by smooth functions, multiply these, and pass to a limit. Approximation is usually done by convolution with �-sequences, i.e. sequences or nets of smooth functions, converging to the �-distribution. The limit process should be related to the usual limit in distribution spaces, if the resulting object is required to be a distribution. Since most of these approaches extend the multiplication of continuous functions, regarded as distributions, these products cannot be defined for all pairs of distri- butions due to a well-known result of Schwartz (14). The purpose of this paper is to give a reasonable enlargement of the definition area of some of these partial mappings, namely of products equivalent to the so-called Kaminski or Colombeau product.

Method and apparatus for computer aided building specification generation

Abstract: A method and apparatus for producing a design document for a product, with the product having product elements arranged in a hierarchical manner and stored in a relational database, is described. A selection is received for at least one product element. At least one performance value associated with the selected product element is received. A text segment associated with each selected product element is retrieved from the database. Selected text segments are then used to construct the design document.

Sensor-based data recording of use conditions for product takeback

Abstract: Information on product properties and the history of product use are essential for higher levels of product recovery like the reuse of components or remanufacturing. These product recovery options are economically more attractive than materials recycling. In this paper, the ISPR (Information System for Product Recovery) is proposed. Its key component is an electronic device, the so-called EDL (Electronic Data Log), which is integrated in a product to record and store data strongly correlated with the degradation of components during the use stage of a product. The data recorded and processed during the use stage are retrieved and analyzed by the ISPR when the product is returned. The objectives for the development of the EDL, its implementation and its economical efficiency are discussed in detail.

Coupon dispenser and method for generating coupons

Abstract: A computer implemented coupon dispensing system is provided The computer implemented coupon dispensing system includes a display area, a memory arrangement, a processor, and a printer The display area includes a display screen having a plurality of product identification cells for selecting a product type The memory arrangement is configured to store information comprising product identification information, product discount information, and product location information for locating a product in a store The proecessor is coupled to the memory arrangement and the display screen and is configured to process the information stored in the memory arrangement in order to generate selected product data packets including selected product identification information, selected product discount information, and selected product location information The printer is coupled to the processor and is provided for printing coupons having selected product identification information, selected product discount information, and selected product location information A computer implemented method for dispensing coupons is provided

Generic Architecture Descriptions for Product Lines

Abstract: Two of the fundamental needs in defining an architecture for a product line are to be able to generalize or abstract from the individual products to capture the important aspects of the product line and to be able to instantiate an individual product architecture from the product line architecture In other words, having a product line implies having a generic architecture from which the individual product architectures can be derived in some manner.

Market research database containing separate product and naked product information

Abstract: A market research database includes industry code information containing industry codes (such as UPCs), naked product information containing information about naked products, package information containing information about packages, and product definition information linking naked product information, package information, and industry codes. Accordingly, the storage of information in the database is not dependent upon UPCs or other industry codes, making access to product related information difficult. The use of naked product information, together with the way of identifying products, facilitate a third normal form data-base.

The Max‐Min‐Min Principle of Product Differentiation

Abstract: We analyze two and three-dimensional variants of Hotelling's model of differentiated products. In our setup, consumers can place different importances on each product attribute; these are measured by weights on the disutility of distance in each dimension. Two firms play a two-stage game; they choose locations in stage 1 and prices in stage 2. We seek subgame-perfect equilibria. We find that all such equilibria have maximal differentiation in one dimension only; in all other dimensions they have minimum differentiation. An equilibrium with maximal differentiation in a certain dimension occurs when consumers place sufficient importance (weight) on that attribute. Thus, depending on the importance consumers place on each attribute, in two dimensions there is a max-min equilibrium, a min-max equilibrium, or both. In three dimensions, depending on the weights, there can be a max-min-min equilibrium, a min-max-min equilibrium, a min-min-max equilibrium, any two of these, or all three.

Design of Single-Product Campaign Batch Plants under Demand Uncertainty

Abstract: A new method is introduced for optimally designing multiproduct batch plants under the single-product campaign (SPC) production mode. Uncertain future product demands are described with normal probability distributions, and more than one processing unit of equal size are allowed per stage. At the expense of imposing the normality assumption for product demand uncertainty and the SPC production mode, the original two-stage stochastic optimization problem is transformed into a deterministic mixed-integer nonlinear programming problem without relying on implicit or explicit discretization of the uncertain variables. This is accomplished through the explicit solution of the inner problem and the analytical integration overall product demand realizations. This problem representation and solution strategy result in savings of orders of magnitude over existing methods in computational requirements.

Product merchandising display unit with replaceable product graphics

Abstract: A product module adaptable for interlocking engagement with other similarly constructed modules to form a composite display assembly for merchandising products therefrom, each product module including at least one elongated product channel defined by a pair of laterally spaced upstanding side walls and a substantially planar product supporting floor portion extending therebetween, each product channel including a product graphic panel which is removably attachable to the front portion of each product channel via a wide variety of different constructional arrangements. Each product graphic panel is preferably dimensioned such that when it is attached to the front portion of a particular product channel, the graphic panel will substantially overlay the product identification and graphics associated with the lead product container positioned within that particular product channel. The present product modules may also optionally include an adjustable mechanism for adjusting the fore and aft position of such module relative to the front portion of an underlying support structure upon which the modules may rest. Still other optional features associated with the present product modules function to more effectively facilitate their utilization in a wide variety of different merchandising applications.

Enhanced implement control

Abstract: A sectional rate control unit for an agricultural implement is disclosed herein. The sectional rate control unit is preferably used with a planting system including a planting implement coupled to a work vehicle. The implement includes a frame having at least one section supporting multiple row units which are configured to apply a product (e.g., seed, fertilizer, insecticide, herbicide) to the rows in a field. Each section includes a product delivery apparatus having a target delivery rate controlled by a section application control signal and at least one product channel for delivering an amount of the product to each of the row units. The control unit includes an electronic product sensor coupled to each of the sections and the product channel. The product sensor is configured to generate a product rate signal representative of the amount of the product delivered to the row units. An electronic display located in the cab is configured to generate an image in response to a display signal. The display includes operator-actuatable switches configured to independently control the state of each of the sections and the target delivery rate of each product for each of the sections. A processor circuit is configured to monitor the product rate signal from each product sensor, to calculate product rate data for each product sensor, to generate and apply a display signal to the electronic display to generate the image on the display representing the product rate data for each product in each section, and to generate and apply the section application control signal to each product delivery apparatus in response to actuations of the switches on the electronic display.

Intelligent Software for Product Formulation

Abstract: From the Publisher: An account of the applicability of expert systems, neural networks, genetic algorithms and other intelligent software in product formulation, which includes an explanation of the technology involved in and examples of, two commerical software packages specifically developed for product formulation.

Method and apparatus for attribute selection

Abstract: The invention provides a method and apparatus for selecting desired attributes for system configuration. The invention uses one or more rule sets to define rules that are met when a configuration is valid. A rule set may specify the interrelation of attribute values within a product or between two or more products. If the combination of attribute values that specify a product conform to at least one rule in each of the rule sets that apply to that product, that combination of attribute values is considered to specify a valid product. If the combination of attribute values that specify all of the products of an assembly conform to at least one rule in each of the rule sets that apply to that assembly, that combination of attribute values is considered to specify a valid assembly.

Accurate Computation of the Product-Induced Singular Value Decomposition with Applications

Abstract: We present a new algorithm for floating-point computation of the singular value decomposition (SVD) of the product $B^{\tau}C$, where $B$ and $C$ are full row rank matrices. The algorithm replaces the pair $(B,C)$ with an equivalent pair $(B',C')$ and then it uses the Jacobi SVD algorithm to compute the SVD of the explicitly computed matrix $B'^{\tau}C'$. In this way, each nonzero singular value $\sigma$ is approximated with some $\sigma+\delta\sigma$, where the relative error $|\delta\sigma|/\sigma$ is, up to a factor of the dimensions, of order \boldmath${\varepsilon}$\unboldmath $\{\min_{\Delta\in{\cal D}}\kappa_2(\Delta B)+ \min_{\Delta\in{\cal D}} \kappa_2(\Delta C)\}$, where ${\cal D}$ denotes the set of diagonal nonsingular matrices, $\kappa_2(\cdot)$ denotes the spectral condition number, and \boldmath${\varepsilon}$\unboldmath\ is the roundoff unit of floating-point arithmetic. The new algorithm is applied to the eigenvalue problem $HM x = \lambda x$ with symmetric positive definite $H$ and $M$. It is shown that each eigenvalue $\lambda$ is computed with high relative accuracy and that the relative error $|\delta\lambda|/\lambda$ of the computed approximation $\lambda+\delta\lambda$ is, up to a factor of the dimension, of order \boldmath${\varepsilon}$\unboldmath$\{\min_{\Delta\in{\cal D}}\kappa_2(\Delta H\Delta) + \min_{\Delta\in{\cal D}}\kappa_2(\Delta M\Delta)\}$. The new algorithm can also be used for accurate SVD computation of a single matrix $G$ that admits an accurate factorization $G=B^{\tau}C$.

Process for precise multichip integration and product thereof

Abstract: Process for making an integrated circuit module and product thereof including a carrier supporting a plurality of precisely aligned semiconductor circuit chips having uniform thicknesses.