Showing papers on "Product (mathematics) published in 1994"

Physicians Desk Reference

Abstract: Section 1 Manufacturers Index...1 Section 2 Name Index...101 Section 3 Product Category Index...201 Section 4 Product Identification Section...303 Section 5 Product Information...401 Section 6 Diagnostic Product Information...2645

Integration analysis of product decompositions

Abstract: This paper describes a methodology for the analysis of product design decompositions The technique is useful for developing an understanding of the "system engineering" needs which arise because of complex interactions between components of a design This information can be used to define the product architecture and to organize the development teams The method involves three steps: 1) decomposition of the system into elements, 2) documentation of the interactions between the elements, and 3) clustering the elements into architectural and team chunks By using this approach, development teams can better understand the complex interactions within the system, thus simplifying the development process for large and complex projects arranged in chunks The choice of product architecture has broad implications for product performance, product change, product variety, and manufacturability Product architecture is also strongly coupled to the firm's development capability, manufacturing specialties, and product strategy Selecting the proper architecture of the product is an extremely influential decision which must be made during the concept development and system-level design phases of the project; the architecture defines the sub-systems upon which the team will work for the bulk of the development effort In product development, analysis of the product decomposition provides valuable insight into the structure of the problem and the choice of architecture The integration analysis presented in this paper considers the interactions which occur between the elements of the decomposition The building blocks (called chunks) which result from integration analysis can be used to define the product architecture and to structure the development teams Examples of architecture and team structure can be found in any highly engineered product In the automobile industry, development programs include hundreds or thousands of team members It would be impractical to design the entire vehicle at once (too complex); nor would it be possible to develop the thousands of components one at a time (too slow) The vehicle is decomposed into a few major systems: body, powertrain, chassis, interior, climate control, electrical, and trim Each of these major systems is in turn decomposed into a large number of sub-systems, resulting in hundreds of interconnected pieces with names like: passenger restraint system, fuel delivery system, remote entry system, etc Finally, these sub-systems are decomposed into component parts which are designed and tested individually and together The decomposition of the vehicle into sub-systems and components facilitates the rapid development of the individual pieces, yet this strategy does not address the needs for integration of the components' functions during the development process

Noncommutative symmetric functions

Abstract: This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables. This allows us to endow the resulting algebra with a Hopf structure, which leads to a new method for computing in descent algebras. It also gives unified reinterpretation of a number of classical constructions. Next, we study the noncommutative analogs of symmetric polynomials. One arrives at different constructions, according to the particular kind of application under consideration. For example, when a polynomial with noncommutative coefficients in one central variable is decomposed as a product of linear factors, the roots of these factors differ from those of the expanded polynomial. Thus, according to whether one is interested in the construction of a polynomial with given roots or in the expansion of a product of linear factors, one has to consider two distinct specializations of the formal symmetric functions. A third type appears when one looks for a noncommutative generalization of applications related to the notion of characteristic polynomial of a matrix. This construction can be applied, for instance, to the noncommutative matrices formed by the generators of the universal enveloping algebra $U(gl_n)$ or of

Method and apparatus for storing and selectively retrieving product data by correlating customer selection criteria with optimum product designs based on embedded expert judgments

Abstract: A machine and method are provided for selecting product or service design, such as a social expression product. The machine and method each (i) stores a plurality of product or service designs and a plurality of descriptors for each of the plurality of product or service designs, each of the descriptors representing an application scale; (ii) stores an expert-predetermined optimum applicability value for each combination of the application scales and the product or service designs; (iii) presents, to a customer, selection criteria options for one or more application scales; (iv) stores customer preference values for one or more application scales used for describing the product/service design, the customer preference values to be predetermined by expert judgment and assigned to application scales where such values correspond to the selection criteria options chosen by the customer; (v) quantitatively correlates, by means of a correlation algorithm, each of the customer preference values with corresponding expert-predetermined optimum applicability values to calculate an average suitability rating for each of the product or service designs based on the customer-chosen selection criteria options; and (vi) displays for the customer a group of identified product or service designs based on the average suitability ratings for those identified product or service designs. In the case of a product, the apparatus and method solicit the customer to select one of the identified product designs, verify the selection and possibly modify the selected product design. The selected or modified product design may then be dispensed to the customer.

Finite transition systems: semantics of communicating systems

Abstract: Transition systems the synchronous product of transition systems transition system logics verification of properties of transition systems fixpoints in transition systems software tools.

A Balancing Act: Optimizing a Product's Properties

Abstract: Progress/June 1994 51 HE QUALITY COMMUNITY HAS LARGELY ignored a major issue in product improvement: how to improve products from the standpoint of property tradeoffs. The problem is one of optimizing property balance. It arises because, as one property is improved, it is often at the expense of one or more other properties. The trade-off problem is particularly chronic in formulation-related products, such as adhesives, rubber, plastics, inks, paints, and alloys. It is not uncommon to have to balance as many as 20 properties for such formulation products. For example, the abrasion resistance of a rubber shoe sole formulation might be improved by adding certain fillers. But this change might also result in more complex production processes and higher production costs. The problem becomes considerably more complex when several components of the formulation are being varied. Balance problems can be solved by using a modified formula of E.C. Harrington’s desirability function and combining it with response surface methodology (RSM) to form a methodology called desirability optimization methodology (DOM). Computer implementation of DOM further enhances its power.

Homotopies exploiting Newton polytopes for solving sparse polynomial systems

Abstract: This paper is concerned with the problem of finding all isolated solutions of a polynomial system The BKK bound, defined as the mixed volume of the Newton polytopes of the polynomials in the system, is a sharp upper bound for the number of isolated solutions in $\mathbb{C}_0^n ,\mathbb{C}_0 = \mathbb{C} \backslash \{ 0\} $, of a polynomial system with a sparse monomial structure First an algorithm is described for computing the BKK bound Following the lines of Bernshtei˘n’s proof, the algorithmic construction of the cheater’s homotopy or the coefficient homotopy is obtained The mixed homotopy methods can be combined with the random product start systems based on a generalized Bezout number Applications illustrate the effectiveness of the new approach

Analysis of the photon spectrum in inclusive B → X s γ decays

Abstract: Using a combination of the operator product and heavy quark expansions, we resum the leading nonperturbative contributions to the inclusive photon spectrum in $B\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$ decays. The shape of the spectrum is determined by a universal structure function, which describes the distribution of the light-cone momentum of the $b$ quark inside the $B$ meson. The moments of this function are proportional to forward matrix elements of higher-dimension operators. As a by-product, we obtain the bound ${\ensuremath{\lambda}}_{1}l0$ for one of the parameters of the heavy quark effective theory. An integral over the $B\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$ structure function is related to the shape function that governs the fall off of the lepton spectrum close to the end point in $B\ensuremath{\rightarrow}{X}_{u}\ensuremath{\ell}\overline{\ensuremath{ u}}$ decays. A measurement of the photon spectrum in rare $B$ decays can therefore help to obtain a model-independent determination of ${V}_{\mathrm{ub}}$.

Information distribution system

Abstract: A system to control the use of an informational product is disclosed. The informational product is stored on a storage medium and executed by a first processor. The informational product is operatable in a plurality of modes. The system comprises three manufacture modules. The first manufacture module, executed by the first processor, generates a registration code for a user of the informational product, the registration code being a function of the identity of the first processor, the identity of the user and the identity of the informational product. The second manufacture module, executed by the first processor, accepts as input an authorization code, verifies the authorization code and, if the verification is successful, changes the operational mode of the informational product. The second manufacture module also stores a user record in the informational product. The third manufacture module examines the user record each time the informational product is activated. The third module determines the operational mode of the informational product as a function of the operational mode stored in the user record and the identity of the processor on which the third module is executed. The third module returns to the informational product the user record.

Derandomization, Witnesses for Boolean Matrix Multiplication and Construction of Perfect Hash Functions

Abstract: Small sample spaces with almost independent random variables are applied to design efficient sequential deterministic algorithms for two problems. The first algorithm, motivated by the attempt to design efficient algorithms for the All Pairs Shortest Path problem using fast matrix multiplication, solves the problem of computing witnesses for the Boolean product of two matrices. That is, if A and B are two n by n matrices, and C = AB is their Boolean product, the algorithm finds for every entry C>sub /sub sub /sub sub /sub< = 1. Its running time exceeds that of computing the product of two n by n matrices with small integer entries by a polylogarithmic factor. The second algorithm is a nearly linear time deterministic procedure for constructing a perfect hash function for a given n-subset of {1,?,m}.

Home shopping video catalog

Abstract: This invention is an apparatus and method for shopping at home The apparatus comprises a video catalog in which a plurality of product images are established, each product image being coordinated with a corresponding product identification in an order form The video catalog and the order form are distributed to prospective customers The customers may view the video catalog and product images, and select the corresponding identification of desired product(s) in the order form Then, to place an order, the customer transmits the order form with the product identification(s) to the merchandiser, by phone, mail or electronic transmission, for example Then, the merchandiser may arrange for payment of the order by the customer, and delivery of the corresponding product(s) to the customer

Inequalities for the trace of matrix product

Abstract: To obtain estimates of solutions of Lyapunov and Riccati equations which frequently occur in the stability analysis and optimal control design in linear control theory, many researchers have attempted to determine upper and lower bounds for the product of two matrices in terms of the trace of one matrix and the eigenvalues of the other. Baksalary and Puntanen claimed ("An inequality for the trace of matrix product", ibid., vol. 37, no. 2, p. 239-40, 1992) that they had obtained a better estimate for the trace of the product of two matrices. The purpose of this note is to point out that their main result is incorrect and a counterexample is presented. >

Conserved Currents, Consistency Relations and Operator Product Expansions in the Conformally Invariant O(N) Vector Model

Abstract: We discuss conserved currents and operator product expansions (OPE's) in the context of a $O(N)$ invariant conformal field theory. Using OPE's we find explicit expressions for the first few terms in suitable short-distance limits for various four-point functions involving the fundamental $N$-component scalar field $\phi^{\alpha}(x)$, $\alpha=1,2,..,N$. We propose an alternative evaluation of these four-point functions based on graphical expansions. Requiring consistency of the algebraic and graphical treatments of the four-point functions we obtain the values of the dynamical parameters in either a free theory of $N$ massless fields or a non-trivial conformally invariant $O(N)$ vector model in $2

Method and apparatus for communicating with a product label

Abstract: A method and apparatus for communicating with a product label. A host computer transfers information to be communicated to one or more product labels to a radio frequency transmitter. The information is transmitted to a transceiver built into the product label. The information can be intended for each of a plurality of product labels, or for a particular one of the product labels. If the particular one of the labels is one which has not communicated recently with the host computer, the information can used to locate the particular label through the use of other product labels.

Algebraic q‐integration and Fourier theory on quantum and braided spaces

Abstract: An algebraic theory of integration on quantum planes and other braided spaces is introduced. In the one‐dimensional case a novel picture of the Jackson q‐ integral as indefinite integration on the braided group of functions in one variable x is obtained. Here x is treated with braid statistics q rather than the usual bosonic or Grassmann ones. It is shown that the definite integral ∫x∞−x∞ can also be evaluated algebraically as multiples of the integral of a q‐Gaussian, with x remaining as a bosonic scaling variable associated with the q‐deformation. Further composing the algebraic integration with a representation then leads to ordinary numbers for the integral. Integration is also used to develop a full theory of q‐Fourier transformation F The braided addition Δx=x⊗1+1⊗x and braided‐antipode S is used to define a convolution product, and prove a convolution theorem. It is also proven that F2=S. The analogous results are proven on any braided group, including integration and Fourier transformation on quantum planes associated to general R matrices, including q‐Euclidean and q‐Minkowski spaces.

Integration analysis of product decompositions

Abstract: This paper describes a methodology for the analysis of product design decompositions. The technique is useful for developing an understanding of the "system engineering" needs which arise because of complex interactions between components of a design. This information can be used to define the product architecture and to organize the development teams. The method involves three steps: 1) decomposition of the system into elements, 2) documentation of the interactions between the elements, and 3) clustering the elements into architectural and team chunks. By using this approach, development teams can better understand the complex interactions within the system, thus simplifying the development process for large and complex projects. arranged in chunks. The choice of product architecture has broad implications for product performance, product change, product variety, and manufacturability. Product architecture is also strongly coupled to the firm's development capability, manufacturing specialties, and product strategy. Selecting the proper architecture of the product is an extremely influential decision which must be made during the concept development and system-level design phases of the project; the architecture defines the sub-systems upon which the team will work for the bulk of the development effort. In product development, analysis of the product decomposition provides valuable insight into the structure of the problem and the choice of architecture. The integration analysis presented in this paper considers the interactions which occur between the elements of the decomposition. The building blocks (called chunks) which result from integration analysis can be used to define the product architecture and to structure the development teams. Examples of architecture and team structure can be found in any highly engineered product. In the automobile industry, development programs include hundreds or thousands of team members. It would be impractical to design the entire vehicle at once (too complex); nor would it be possible to develop the thousands of components one at a time (too slow). The vehicle is decomposed into a few major systems: body, powertrain, chassis, interior, climate control, electrical, and trim. Each of these major systems is in turn decomposed into a large number of sub-systems, resulting in hundreds of interconnected pieces with names like: passenger restraint system, fuel delivery system, remote entry system, etc. Finally, these sub-systems are decomposed into component parts which are designed and tested individually and together. The decomposition of the vehicle into sub-systems and components facilitates the rapid development of the individual pieces, yet this strategy does not address the needs for integration of the components' functions during the development process.

Method and apparatus for storing and selectively retrieving and delivering product data based on embedded expert judgements

Abstract: An improved apparatus and method of storing and selectively retrieving and delivering product data is disclosed. Product data files, product lists, product directories and allowable customer data entry sets are stored in a data storage device. The customer is asked to specify one or more criteria relating to a product need or desire and one or more allowable customer data entry sets are selected that best correspond to these criteria. The customer data entry sets are connected to product directories and the directories are in turn connected to product lists that reference the data files of products having anticipated common uses. The product directories correspond to connected customer data entry sets with different degrees of specificity and the product lists correspond to connected product directories with different degrees of specificity or applicability. The apparatus is thus able to retrieve and display a variety of products in response to any given customer input and is also able to respond to many different kinds of customer entered criteria.

Spectroscopic ellipsometry study of the diluted magnetic semiconductor system Zn(Mn,Fe,Co)Se.

Abstract: Single-crystal films of (001)${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathit{A}}_{\mathit{x}}$Se (A=Mn, Fe, Co) (0\ensuremath{\le}x0.14) grown by molecular-beam epitaxy on (001)GaAs have been studied by spectroscopic ellipsometry in the 3.5--5.5 eV photon-energy range. Using fits of the ${\mathit{E}}_{1}$ and ${\mathit{E}}_{1}$+${\mathrm{\ensuremath{\Delta}}}_{1}$ peaks with a standard analytic expression, we find that the linewidths increase with x for all samples, the energies increase with x for ${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$Se and ${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$Se, and the energies decrease with x for ${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se. A model describing the effects of the sp-d exchange interaction on the L point band-gap energy is developed and applied. We find that the strength of the energy correction due to this interaction, which is proportional to the product of the square of the exchange integrals and the magnetic susceptibility of the material, is largest in Mn-doped and smallest in Co-doped ZnSe. While the sp-d exchange interaction model is consistent with the composition dependence of the ${\mathit{E}}_{1}$ and ${\mathit{E}}_{1}$+${\mathrm{\ensuremath{\Delta}}}_{1}$ band-gap energies in ${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se, it does not describe the behavior observed in ${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$Se and ${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$Se. We show that an sp-d hybridization model, which includes the location of the energy levels of the magnetic impurity d levels, can account for the composition dependence of ${\mathit{E}}_{1}$ and ${\mathit{E}}_{1}$+${\mathrm{\ensuremath{\Delta}}}_{1}$ band-gap energies of all three materials.

Quantization of Kähler manifolds. III

Abstract: We use Berezin's dequantization procedure to define a formal *-product on the algebra of smooth functions on the unit disk in ℂ. We prove that this formal *-product is convergent on a dense subalgebra of the algebra of smooth functions.

Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product

Abstract: We investigate the asymptotic properties of orthogonal polynomials for a class of inner products including the discrete Sobolev inner products $\langle h,g \rangle = \int hg\, d\mu + \sum_{j=1}^m \sum_{i=0}^{N_j} M_{j,i} h^{(i)}(c_j) g^{(i)}(c_j)$, where $\mu$ is a certain type of complex measure on the real line, and $c_j$ are complex numbers in the complement of $\supp(\mu)$. The Sobolev orthogonal polynomials are compared with the orthogonal polynomials corresponding to the measure $\mu$.

Self check-out system and POS system

Abstract: In a check-out system, in which a purchaser himself who intends to purchase commercial products performs a check-out processing, having a commercial product casted portion, a stocker for stocking the commercial products, a transport unit for transporting the commercial product from the commercial product casted portion to the stocker, and a commercial product identifying unit located between the commercial product casted portion and the stocker for identifying the commercial product transported from the commercial product casted portion, the commercial product casted portion is provided with a commercial product code inputting unit for inputting a commercial product code, and a commercial product detecting unit for detecting that the commercial product is put on the transport path, and the commercial product identifying unit is provided with a commercial product code reading unit for reading the commercial product code of the commercial product being transported; and a first mode in which when the commercial product detecting unit detects that the commercial product is put on the transport path, the commercial product of interest is started to be transported, and in accordance with the identification result provided by the commercial product identifying unit, the commercial product is selectively transported to either the stocker or the commercial product casted portion, and a second mode in which after the commercial product code has been input by the commercial product code inputting unit, the commercial product of interest is started to be transported, and also in accordance with the identification result provided by the commercial product identifying unit, the commercial product is selectively transported to either the stocker or the commercial product casted portion are provided.

System and method of verifying the legitimacy of a product against forgery

Abstract: A product, such as a credit card, passport, or bank note, is secured against forgery or fraud by the provision of a unique pattern of overlying individual fibers which are embedded in a transparent base material, and such that the fibers form differing geometrical configurations which are optically scannable through a surface of the transparent base material. The product is thus made unique and impossible to forge, and its authenticity may be verified by initially scanning the geometrical configurations, with the scanned information being converted into digital data which may be compressed and encrypted, and then stored in a permanent memory. Following the distribution of the product, an inspector may scan the product and compare the obtained data with the stored data to thereby verify the authenticity of the product.

Learning with Product Units

Abstract: Product units provide a method of automatically learning the higher-order input combinations required for efficient learning in neural networks. However, we show that problems are encountered when using backpropagation to train networks containing these units. This paper examines these problems, and proposes some atypical heuristics to improve learning. Using these heuristics a constructive method is introduced which solves well-researched problems with significantly less neurons than previously reported. Secondly, product units are implemented as candidate units in the Cascade Correlation (Fahlman & Lebiere, 1990) system. This resulted in smaller networks which trained faster than when using sigmoidal or Gaussian units.

The Max-Min-Min Principle of product Differentiation

Abstract: We analyze two and three-dimensional variants of Hostelling's model of differentiated products. In our setup, consumers can place different importance on each product attribute; this is measured by a weight in the disutility of distance in each dimension.

Using simulated annealing to select least-cost assembly sequences

Abstract: Applies simulated annealing (SA) to find the probable least cost assembly sequence for a mechanical product from among the thousands of feasible sequences. The sequences are represented by the assembly sequence network introduced by De Fazio and Whitney (1987). Candidate sequences are selected one at a time by the SA algorithm and their cost is estimated by designing a minimum unit cost concept assembly system using a dynamic programming algorithm. Alternate sequences are selected by perturbing the path through the sequence network in a way similar to a genetic algorithm. This method differs from that normally used to select least cost sequences, in which an engineer edits the thousands of sequences using judgment and experience, and then obtains the costs of a few that survive editing. Here, the search for a least cost sequence is done without prior editing. In the examples studied, there appear to be a large number of sequences that are technically quite different but of similar cost. >