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Showing papers on "Product (mathematics) published in 2001"


Book
27 Dec 2001
Abstract: Composites manufacturing: materials, product, and process engineering , Composites manufacturing: materials, product, and process engineering , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

506 citations


Journal ArticleDOI
TL;DR: An approach to architecting a product family that shares inter-changeable modules that permits the platform itself to be one of several possible options, and provides a systematic approach to generating architectures.

399 citations


Journal ArticleDOI
TL;DR: Left-invariant metrics are defined on the product G × I thus allowing the generation of transformations of the background geometry as well as the image values, and structural generation in which image values are changed supporting notions such as tissue creation in carrying one image to another.
Abstract: This paper constructs metrics on the space of images {\cal I} defined as orbits under group actions {\cal G}. The groups studied include the finite dimensional matrix groups and their products, as well as the infinite dimensional diffeomorphisms examined in Trouve (1999, Quaterly of Applied Math.) and Dupuis et al. (1998). Quaterly of Applied Math.). Left-invariant metrics are defined on the product {\cal G} \times {\cal I} thus allowing the generation of transformations of the background geometry as well as the image values. Examples of the application of such metrics are presented for rigid object matching with and without signature variation, curves and volume matching, and structural generation in which image values are changed supporting notions such as tissue creation in carrying one image to another.

379 citations


Proceedings ArticleDOI
01 May 2001
TL;DR: This paper addresses the issue of handling product line variability at the code level and various implementation approaches are examined with respect to their use in a product line context.
Abstract: Software product lines have numerous members. Thus, a product line infrastructure must cover various systems. This is the significant difference to usual software systems and the reason for additional requirements on the various assets present during software product line engineering. It is imperative that they support the description of the product line as a whole, as well as its instantiation for the derivation of individual products.Literature has already addressed how to create and instantiate generic product line assets, such as domain models and architectures to generate instance specific ones [1, 2, 3], yet little attention has been given on how to actually deal with this genericity at the code level.This paper addresses the issue of handling product line variability at the code level. To this end various implementation approaches are examined with respect to their use in a product line context.

302 citations


Journal ArticleDOI
TL;DR: In this paper, the notion of warped product CR-submanifolds in Kaehler manifolds was introduced and several fundamental properties of CR-warped products were established.
Abstract: In this paper we study warped product CR-submanifolds in Kaehler manifolds and introduce the notion of CR-warped products. We prove several fundamental properties of CR-warped products in Kaehler manifolds and establish a general inequality for an arbitrary CR-warped product in an arbitrary Kaehler manifold. We then investigate CR-warped products in a general Kaehler manifold which satisfy the equality case of the inequality. Finally we classify CR-warped products in complex Euclidean space which satisfy the equality.

274 citations


Patent
30 Mar 2001
TL;DR: In this paper, the authors present a system and methods for searching a product catalog data collection in such a manner that it is easy to search, drill down, drill-up and drill across products in the data collection using multiple, independent hierarchical category taxonomies of the products.
Abstract: The present invention relates to systems and methods for searching a product catalog data collection in such a manner that it is easy to search, drill down, drill-up and drill across products in the data collection using multiple, independent hierarchical category taxonomies of the products in the product catalog data collection.

199 citations


Patent
Bok Hyun Pack1, Young Kuk Kim1, Hyun Ju Ahn1, Han Seop Ryu1, Yeo Han Yun1 
12 Apr 2001
TL;DR: In this paper, the authors present an apparatus and method for providing and obtaining product information through a broadcast signal, in which information identifying a product item, which is in a scene to be presented from a broadcast signals, is provided together with broadcast signal and a signal receiving terminal stores the product information for a new product item and displays the stored information to a viewer.
Abstract: The present invention relates to an apparatus and method for providing and obtaining product information through a broadcast signal. In this present invention, information identifying a product item, which is in a scene to be presented from a broadcast signal, is provided together with a broadcast signal, then a signal receiving terminal stores the product information for a new product item and displays the stored information to a viewer to select one product item while or after watching an interesting broadcast program, and transmits data identifying a selected product item to a predetermined web site and receives web site address for the selected item from that site. As a result, detailed information for the selected item is acquired from a server addressed by the received web site address.

192 citations


Patent
20 Mar 2001
TL;DR: In this paper, a software development system (100) develops a product from core library of source code elements (900) the core library being categorized into components having one or more features.
Abstract: A software development system (100) develops a product from core library of source code elements (900) the core library being categorized into components having one or more features. A configurator (700) develops configuration state data based on a designated platform type and the source code elements. A graphical user interface (200) displays a visual and logical representation of the product (1000) according to the configuration state data, include visual indications of any unresolved dependencies. A product make (800) routine then generates the product from the source code elements according to the configuration state data.

188 citations


Patent
25 May 2001
TL;DR: In this article, a real-time, three-dimensional, interactive, configurable product display system and a method for configuring and displaying a product display in real time is presented.
Abstract: A real-time, three-dimensional, interactive, configurable product display system and method is disclosed. An interactive interface configures and displays products in real-time. The interface comprises a search mechanism that retrieves a product from a data repository according to predefined criteria and a three-dimensional viewer displaying a threedimensional view of the product. The interface may also include a two-dimensional viewer displaying a two-dimensional view of the product. The two-dimensional view of the product corresponds to the three-dimensional view of the product. Additionally, an interactive method is disclosed for configuring and displaying a product display in real-time. The method comprises the steps of retrieving a product from a data repository in response to input from a user, configuring the product in real-time according to instructions from the user; and displaying a three-dimensional, real-time view of the product.

181 citations


Patent
27 Jul 2001
TL;DR: In this paper, a method for controlling access to a product includes receiving a request for a product, generating a license string for the product, and transmitting that license string to a user of the product.
Abstract: A method for controlling access to a product includes receiving a request for a product, generating a license string for the product, and transmitting that license string to a user of the product. The license string is generated substantially at the time a request is received. A corresponding system is also described. In some embodiments the product functions for a trial period before requiring input of the license string. License strings may be generated that extend the trial period.

173 citations


Journal ArticleDOI
TL;DR: In this paper, necessary and sufficient conditions for separability of mixed states of n -particle systems are formulated in terms of maps which are positive on product states for n − 1 particles.

Journal ArticleDOI
TL;DR: In this paper, the authors examined multiple responses with multiple responses whose means, variances, and correlations depend on experimental factors and the experimental factors used to improve product or process quality and to make them more robust.
Abstract: Statistically designed experiments are widely used to improve product or process quality and to make them more robust Experiments with multiple responses are examined whose means, variances, and correlations depend on experimental factors Analys


Journal ArticleDOI
TL;DR: In this paper, a star product associated with an arbitrary two-dimensional Poisson structure using generalized coherent states on the complex plane is constructed for the fuzzy torus and fuzzy sphere.

Journal ArticleDOI
TL;DR: This paper provides a finite axiomatization for the propositional logic resulting from the combination of Lukasiewicz and Product Logics, together with the logic obtained by from $L \Pi$ by the adding of a constant symbol and of a defining axiom for $\frac{1}{2}$.
Abstract: In this paper we provide a finite axiomatization (using two finitary rules only) for the propositional logic (called $L\Pi$ ) resulting from the combination of Lukasiewicz and Product Logics, together with the logic obtained by from $L \Pi$ by the adding of a constant symbol and of a defining axiom for $\frac{1}{2}$ , called $L \Pi\frac{1}{2}$ . We show that $L \Pi \frac{1}{2}$ contains all the most important propositional fuzzy logics: Lukasiewicz Logic, Product Logic, Godel's Fuzzy Logic, Takeuti and Titani's Propositional Logic, Pavelka's Rational Logic, Pavelka's Rational Product Logic, the Lukasiewicz Logic with $\Delta$ , and the Product and Godel's Logics with $\Delta$ and involution. Standard completeness results are proved by means of investigating the algebras corresponding to $L \Pi$ and $L \Pi \frac{1}{2}$ . For these algebras, we prove a theorem of subdirect representation and we show that linearly ordered algebras can be represented as algebras on the unit interval of either a linearly ordered field, or of the ordered ring of integers, Z.

Journal ArticleDOI
TL;DR: In this article, a systematic procedure for the synthesis and development of manufacturing processes for creams and pastes is presented, which integrates the skills of a chemist and a chemical engineer to produce a product with specified properties.
Abstract: A systematic procedure is presented for the synthesis and development of manufacturing processes for creams and pastes. The procedure integrates the skills of a chemist and a chemical engineer to produce a product with specified properties. The desired functional and sensorial performance of the product is first identified in terms of quality factors. Then, the requisite ingredients are selected, and the process flowsheet, as well as the operating conditions, is synthesized. There are four steps in the procedure: identification of product quality factors, product formulation, flowsheet synthesis, and product and process evaluation. Design guidelines, as well as physical models describing relevant phenomena, are used to assist decision-making at each step of the procedure.

Journal ArticleDOI
TL;DR: In this paper, a new product modularization strategy is proposed across a family of products and successive generation of products, based on product functionality, product commonality and life cycle similarity.

Journal ArticleDOI
TL;DR: In this article, a questionnaire survey was conducted to explore how to effectively express product image when designing products, and the results revealed that the five most expected images perceived in micro-electronic products are: high technology, efficiency, lightness and handiness, nobility, and delicacy.

Journal ArticleDOI
TL;DR: It is shown that the minimum possible cardinality of such a set F is precisely 1+?mi=1(ki?1) for every sequence of integers k1, k2, ?, km?2

Journal ArticleDOI
TL;DR: Test findings indicate that the fuzzy AHP approach in modular product design complemented with a case example to validate its feasibility in a real company is helpful for providing key decision support information in terms of product module selection during product development stages.
Abstract: Product development stages. The analytic hierarchy process (AHP), which breaks down a complex problem into simple hierarchical decision-making processes, can be incorporated with fuzzy logic to suggest the relative strength of the factors in the corresponding criteria, thereby enabling the construction of a fuzzy judgement matrix to facilitate decision-making. This paper proposes a fuzzy AHP approach in modular product design complemented with a case example to validate its feasibility in a real company. Test findings indicate that the approach is helpful for providing key decision support information in terms of product module selection during product development stages. The significance of the contribution of this paper is the suggestion of a novel approach in modular product design, embracing a combination of computational intelligence and traditional techniques, thereby providing more alternatives and ideas for those researchers who are interested in this field of study.

Journal ArticleDOI
TL;DR: In this paper, a semi-tensor product of matrices is proposed to solve the Morgen's problem for control systems, which is shown to be a numerically solvable problem.
Abstract: This paper proposes a new matrix product, namely, semi-tensor product. It is a generalization of the conventional matrix product. Meanwhile, it is also closely related to Kronecker (tensor) product of matrices. The purpose of introducing this product is twofold: (i) treat multi-dimensional data; (ii) treat nonlinear problems in a linear way. Then the computer and numerical methods can be easily used for solving nonlinear problems. Properties and formulas are deduced. As an application, the Morgen's problem for control systems is formulated as a numerically solvable problem.

Patent
05 Jun 2001
TL;DR: In this paper, the authors present a system and method for product verification for use with products intended to be introduced into circulation and including machine readable product data, and comprising a product data storage means, at least one portable reading device for said machine-readable product data.
Abstract: The present invention provides for a system and method for product verification for use with products intended to be introduced into circulation and including machine readable product data, and comprising a product data storage means, at least one portable reading device for said machine readable product data, wherein the machine readable product data is applied to products and is arranged for inspection by the at least one portable reading device remotely from the product data storage means and at at least one point in the product circulation route, and wherein the at least one portable reading device is arranged to verify the authenticity of the machine readable product data and thereby verify the authenticity of the product itself.

Journal ArticleDOI
TL;DR: In this paper, the authors studied algebraic properties of the sequential product and showed that algebraic conditions on A∘B imply that A and B commute for the usual operator product.
Abstract: A quantum effect is an operator A on a complex Hilbert space H that satisfies 0⩽A⩽I. We denote the set of quantum effects by E(H). The set of self-adjoint projection operators on H corresponds to sharp effects and is denoted by P(H). We define the sequential product of A,B∈E(H) by A∘B=A1/2BA1/2. The main purpose of this article is to study some of the algebraic properties of the sequential product. Many of our results show that algebraic conditions on A∘B imply that A and B commute for the usual operator product. For example, if A∘B satisfies certain distributive or associative laws, then AB=BA. Moreover, if A∘B∈P(H), then AB=BA and A∘B=B or B∘A=B if and only if AB=BA=B. A natural definition of stochastic independence is introduced and briefly studied.

Posted Content
TL;DR: In this paper, the smallest powers of the quantum parameters q that occur in a product of Schubert classes in the (small) quantum cohomology of general flag varieties G/P are given.
Abstract: We give a formula for the smallest powers of the quantum parameters q that occur in a product of Schubert classes in the (small) quantum cohomology of general flag varieties G/P. We also include a complete proof of Peterson's quantum version of Chevalley's formula, also for general G/P's.

Journal ArticleDOI
TL;DR: In this article, the countable union theorem for groups acting on asymptotically nite dimensional metric spaces was proved and applied to groups with asymp- totic dimension.
Abstract: We prove a version of the countable union theorem for asymp- totic dimension and we apply it to groups acting on asymptotically nite dimensional metric spaces. As a consequence we obtain the following nite dimensionality theorems. A) An amalgamated product of asymptotically nite dimensional groups has nite asymptotic dimension: asdimAC B< 1 . B) Suppose that G 0 is an HNN extension of a group G with asdimG < 1. Then asdimG 0 <1. C) Suppose that is Davis' group constructed from a group with asdim <1. Then asdim <1. AMS Classication 20H15; 20E34, 20F69

Patent
14 Feb 2001
TL;DR: In this paper, a system, method and article of manufacture for providing product information to a user, where the user may remain anonymous, is described, and the user is allowed to access the product information on the network data site using a user identifier.
Abstract: A system, method and article of manufacture are provided for providing product information to a user, where the user may remain anonymous. A product identifier is received from a client device of a user. The product identifier is associated with a particular product. A search is made of a data store for matching the product identifier with information about the product. The product information is stored on a network data site. The user is allowed to access the product information on the network data site using a user identifier.

Journal ArticleDOI
TL;DR: It is proved that one of the four bounding schemes provides the convex envelope and that two schemes provide the concave envelope for the product of p variables overmathbb{R}_{^ + }^p.
Abstract: We analyze four bounding schemes for multilinear functions and theoretically compare their tightness. We prove that one of the four schemes provides the convex envelope and that two schemes provide the concave envelope for the product of p variables over Rp+.


Journal ArticleDOI
TL;DR: In this paper, a graded version of the convolution product on the symmetric group was introduced, and it was shown that there is a degree-preserving ring isomorphism to the Hilbert scheme of points in the complex affine plane.
Abstract: Let $\mathscr {C}(S_n)$ be the $\mathbb {Z}$-module of integer-valued class functions on the symmetric group $S_n)$. We introduce a graded version of the convolution product on $\mathscr {C}(S_n)$, and we show that there is a degree-preserving ring isomorphism $\mathscr {C}(S_n)\longrightarrow H^\ast({\rm Hilb}^n(\mathbb {A_C}^2);\mathbb {Z})$ to the cohomology of the Hilbert scheme of points in the complex affine plane.

Patent
16 Mar 2001
TL;DR: In this article, the authors present a computer-based system and method for processing orders over the Internet, which comprises the steps of identifying a customer placing a product order, displaying information relating to other orders associated with the customer, confirming details of a new product order from the customer and determining the date on which the products ordered is to be delivered to the customer.
Abstract: The present invention is a computer-based system and method for processing orders over the Internet In one embodiment, the method of the present invention comprises the steps of identifying a customer placing a product order, displaying information relating to other orders associated with the customer, receiving details of a new product order from the customer, confirming details of the new product order from the customer, determining the date on which the products ordered is to be delivered to the customer, and sending order information to at least one supplier associated with the product order Preferably, some or all of the steps of the method are performed in real-time