Showing papers on "Product (mathematics) published in 1999"

Harmonic Polylogarithms

Abstract: The harmonic polylogarithms (hpl's) are introduced They are a generalization of Nielsen's polylogarithms, satisfying a product algebra (the product of two hpl's is in turn a combination of hpl's) and forming a set closed under the transformation of the arguments x=1/z and x=(1-t)/(1+t) The coefficients of their expansions and their Mellin transforms are harmonic sums

Proximal and Dynamical Approaches to Equilibrium Problems

Abstract: The theory of equilibrium problems has emerged as an interesting branch of applied mathematics, permitting the general and unified study of a large number of problems arising in mathematical economics, optimization and operations research. Inspired by numerical methods developed for variational inequalities and motivated by recent advances in this field, we propose several ways (including an auxiliary problem principle, a selection method, as well as a dynamical procedure) to solve the following equilibrium problem: $$(GEP)Find\overline x \in CsuchthatF(\overline x ,x) + \left\langle {G(\overline x ),x - \overline x } \right\rangle \geqslant 0\forall x \in C,$$ where C is a nonempty convex closed subset of a real Hilbert space X, F: C × C → ℝ is a given bivariate function with F(x, x) = 0 for all x ∈ C and G: C → ℝ is a continuous mapping. This problem has useful applications in nonlinear analysis, including as special cases optimization problems, variation al inequalities, fixed-point problems and problems of Nash equilibria. Throughtout the paper, X is a real Hilbert space, denotes the associated inner product and | · | stands for the corresponding norm. From now on, we assume that the solution set, S, of problem (GEP) is nonempty. This corresponds to some important situations such as linear programming and semi-coercive minimization problems.

Product modularization for life cycle engineering

Abstract: Modular products consist of detachable modules, which can be manufactured, assembled, and serviced separately Some of the modules may be reusable, recyclable or re-manufacturable upon product retirement Thus, modular design can provide benefits to many aspects of product life cycle This paper presents an integrated modular design methodology for life cycle engineering The methodology consists of three phases: problem definition, interaction analysis and module formation The methodology identifies the factors related to the design objectives, relates these factors to design components through interaction analysis, and clusters components into modules Two case studies along with detailed analysis are provided to illustrate the methodology and the algorithms

Toward Identifying the Inventive Templates of New Products: A Channeled Ideation Approach:

Abstract: New product ideation might be improved by identifying and applying certain well-defined schemes derived from an historical analysis of product-based trends, termed “templates.” These templates migh...

Multicriteria optimization in product platform design

Abstract: A product platform is a set of common components, modules or parts from which a stream of derivative products can be created. Product platform design requires selection of the shared parts and assessment of the potential sacrifices in individual product performance that result from parts sharing. A multicriteria optimization problem can be formulated to study such decisions in a quantitative manner at the product performance level. Studying the Pareto sets that correspond to various derivative products leads to a systematic methodology for design decision making. Design of a nail gun platform is used to illustrate the concepts presented.

One-dimensional partially asymmetric simple exclusion process with open boundaries: orthogonal polynomials approach

Abstract: The stationary state of the partially asymmetric simple exclusion process with open boundaries is reconsidered. The so-called matrix product ansatz is employed. This enables us to construct the stationary state in the form of the product of the matrices D and E. Noticing the fact that the matrix C( = D+E) for the model is related to certain q-orthogonal polynomials, the model is analysed for a wide range of parameters. The current and the correlation length are evaluated in the thermodynamic limit. It turns out that the phase diagram for the correlation length is richer than that for the totally asymmetric case.

Method and apparatus for automated measurement of properties of perishable consumer products

Abstract: A method and apparatus for reporting dynamic properties of a product using radio frequency identification device technology. With this invention, an electronic tag is equipped with a sensor which determines dynamic properties of a product when the tag is activated. The dynamic properties of the product are then either further processed into other dynamic properties. In any event either the former or the latter dynamic properties are then transmitted from the tag. Such dynamic properties could be the temperature of a product or the expiration date of the product derived from periodic measurements of the temperature of the product.

Method for managing life cycles and system for the same

Abstract: A method and system for managing the overall life cycle of a product from its manufacture to its destruction or recycling. To the product is affixed a storage medium storing a product identifier uniquely identifying the product and information about the parts that are contained in the product. At each site that the product passes through during its life cycle, product life cycle information is recorded in the storage medium affixed to the product. When the product is to be destroyed or recycled, the information stored in the recording medium is used to determine the method for destroying or recycling. The product is then destroyed or recycled according to this method.

Identifying Product Portfolio Architecture Modularity Using Function and Variety Heuristics

Abstract: This paper proposes a method for identifying product portfolio architecture alternatives based upon customer needs , and product function. Customer needs and uses are interpreted according to the variation in performance target values across the market and within the' set of individual customer uses. Product uses are represented by function structures consisting of the functions necessary for achieving the use. These individual product use function structures are combined into a irionolithic function structure to represent the entire product portfolio. This monolith is then partitioned according to function and product variety heuristics into function clusters that anticipate product modules, candidate modularity can then be used to deliver product variety across the product portfolio given functional constraints. A portfolio of xerographic products is used as die working example.

Distributed Source Models: Standard Solutions and New Developments

Abstract: When solving the electro-magnetic inverse problem we face the solution of a linear inverse problem with discrete measurements (Bertero et al. 1985, 1988) that can be written as: $${d_i} = \int_R {{L_i}(x) \circ j(x)dR + {n_i}{\text{ }}i = 1..{N_s},}$$ (1) where L i (x) stands for the vector lead field associated to the ith sensor, that is operated on (scalar or vector product ○) with the unknown current density vector j(x). The integration of this product over the whole region R results in the ith measurement. The n i stands for the noise contribution.

Representation of weak limits and definition of nonconservative products

Abstract: The goal of this article is to show that the notion of generalized graphs is able to represent the limit points of the sequence { g(un), dun} in the weak-$\star$ topology of measures when {un} is a sequence of continuous functions of uniformly bounded variation. The representation theorem induces a natural definition for the nonconservative product g(u), du in a BV context. Several existing definitions of nonconservative products are then compared, and the theory is applied to provide a notion of solutions and an existence theory to the Riemann problem for quasi-linear, strictly hyperbolic systems.

Scaling behavior in a proportional voting process.

Abstract: We perform a statistical analysis on the proportional elections held in Brazil in October 1998. We show that the distribution of votes among candidates for the whole country follows a power law $N(v)\ensuremath{\propto}{v}^{\ensuremath{-}\ensuremath{\alpha}}$, with $\ensuremath{\alpha}=1.00\ifmmode\pm\else\textpm\fi{}0.02$, extending over two orders of magnitude. The voting distributions for several states of the federation also display scale-invariant behavior with $\ensuremath{\alpha}\ensuremath{\approx}1$. We argue that this particular voting system can be modeled as a typical multiplicative process in which the choice of the candidate is governed by a product of probabilities.

A system partitioning and optimization approach to target cascading

Abstract: This article presents a rigorous but practical methodology for addressing the target cascading process Under this concept, product design can be viewed as a four-step process: (i) specify overall product targets; (ii) propagate product targets to system, subsystem and component “sub-targets”; (iii) design system, subsystems and components to achieve their respective subtargets; and (iv) verify that the resulting product meets overall product targets The goal of the target cascading process is that systems, subsystems and components operate together in the desired way (ie, they are compatible and consistent) A mathematically rigorous decisionmaking methodology that takes advantage of hierarchical system partitioning and coordination and analytical models can be a valuable tool for both engineers and managers The main benefits of target cascading are reduction in product design-cycle time, avoidance of design iterations late in the development process, and increased likelihood that physical prototypes will be closer to production quality Target setting also allows outsourcing the design of a particular subsystem or component after providing the supplier with the corresponding set of targets

Masses of J / ψ and η c in the Nuclear Medium: QCD Sum Rule Approach

Abstract: We investigate the masses of the lowest $c\overline{c}$ states, the $J/\ensuremath{\psi}$ and ${\ensuremath{\eta}}_{c}$, in nuclear matter using QCD sum rules. Up to dimension four, the differences between the operator product expansions in vacuum and in medium arise from the density-dependent change in the gluon condensate and from a new contribution proportional to the nucleon expectation value of the twist-2 gluon operator. Both terms together give an attractive shift of about 5--10 MeV to the $J/\ensuremath{\psi}$ and ${\ensuremath{\eta}}_{c}$ masses in nuclear matter.

Product configuration display system and method with user requested physical product alterations

Abstract: A product configuration display system and method enabling the configuration and displaying of a product for purchase by a potential buyer. A product configuration display system comprises a data center having a microprocessor operably connected to a storage media. The data center is configured to be networked with at least a buyer terminal, and to receive at least one request to change a product presentation from the buyer terminal. The product configuration display system also includes at least one three-dimensional digital representation or model of a product. The three-dimensional representation of the product is stored in the storage media and is capable of illustrating multiple perspective views of the product by rotating. The product configuration display system further includes a product display module that is operably connected to the storage media. The product display module is configured to execute in the data center, and includes a definition of a product display screen that is accessible by the buyer terminal. The product display module is further configured to receive a request to change a product presentation through the product display screen. The product display module is additionally configured to display the changed product presentation in the product display screen. Changes such as color and texture can be made quickly because the same basic digitized model is used for multiple colors and textures.

Doubles of Quasi-Quantum Groups

Abstract: In [Dr1] Drinfeld showed that any finite dimensional Hopf algebra \(\) extends to a quasitriangular Hopf algebra \(\), the quantum double of \(\). Based on the construction of a so-called diagonal crossed product developed by the authors in [HN], we generalize this result to the case of quasi-Hopf algebras \(\). As for ordinary Hopf algebras, as a vector space the “quasi-quantum double”\(\) is isomorphic to \(\), where \(\) denotes the dual of \(\). We give explicit formulas for the product, the coproduct, the R-matrix and the antipode on \(\) and prove that they fulfill Drinfeld's axioms of a quasitriangular quasi-Hopf algebra. In particular \(\) becomes an associative algebra containing \(\) as a quasi-Hopf subalgebra. On the other hand, \(\) is not a subalgebra of \(\) unless the coproduct on \(\) is strictly coassociative. It is shown that the category \(\) of finite dimensional representations of \(\) coincides with what has been called the double category of \(\)-modules by S. Majid [M2]. Thus our construction gives a concrete realization of Majid's abstract definition of quasi-quantum doubles in terms of a Tannaka–Krein-like reconstruction procedure. The whole construction is shown to generalize to weak quasi-Hopf algebras with \(\) now being linearly isomorphic to a subspace of \(\).

Estimating a mixture of two product distributions

Abstract: We describe an efficient algorithm for estimating a mixture of two product distributions over binary vectors.

Macro level product development using design for modularity

Abstract: Modular design is an engineering methodology that will organize and structure a complex product, process or system into a set of distinct sub-systems and components that may be developed independently of each other and then assembled together. Modular design aims at identifying independent and standard units that could be used to create a variety of products. A structured methodology is proposed for identifying components that can be developed in parallel. In the proposed methodology the needs and product functional requirements are first established. The product is then decomposed based on its functional and physical characteristics. Next, a similarity index is introduced to measure the associativity between the basic components. Finally, a clustering technique is used to integrate the basic components into design modules based on their similarity index.

Non commutative gravity from the ADS/CFT correspondence

Abstract: The exclusion principle of Maldacena and Strominger is seen to follow from deformed Heisenberg algebras associated with the chiral rings of S_N orbifold CFTs. These deformed algebras are related to quantum groups at roots of unity, and are interpreted as algebras of space-time field creation and annihilation operators. We also propose, as space-time origin of the stringy exclusion principle, that the $ADS_3 \times S^3$ space-time of the associated six-dimensional supergravity theory acquires, when quantum effects are taken into account, a non-commutative structure given by $SU_q(1,1) \times SU_q (2)$. Both remarks imply that finite N effects are captured by quantum groups $SL_q(2)$ with $q= e^{{i \pi \over {N + 1}}}$. This implies that a proper framework for the theories in question is given by gravity on a non-commutative spacetime with a q-deformation of field oscillators. An interesting consequence of this framework is a holographic interpretation for a product structure in the space of all unitary representations of the non-compact quantum group $SU_q(1,1)$ at roots of unity.

A geometrical product specification language based on a classification of symmetry groups

Abstract: A relatively old and deeply entrenched engineering “language” universally used by draughtsmen for specifying product geometry is undergoing renovation for the modern information age. Part of the renovation process is to find a set of firm mathematical principles that can support much of the edifice that has served industry well thus far. This search has turned up a set of surprisingly powerful results based on an elegant classification of continuous subgroups of rigid motion. Among them is a compact classification of surface features and lower order kinematic pairs, their reduction to simpler geometric elements that preserve the classification and serve as datums, and a rationale for parameterizing the relative positioning of geometric objects. These results are now being enthusiastically embraced by the International Organization for Standardization (ISO) as part of the basic principles to define the next generation of a product geometry specification language. The paper tells this story.

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.

Automatically configuring product manual by binding document objects in logical structure to proper versions of component documents in a document database

Abstract: A system for automatically assembling product manuals based on a product model, a delivery model and a formal configuration specification includes a structure instantiator for instantiating a product manual structure from a model-specific configuration specification to create a logical structure for a product manual. The product manual structure incorporates product information from a product model, the product manual structure including document objects. A manual configurer is included for configuring the product manual by binding the document objects in the logical structure to proper versions of component documents stored in a document database. A manual generator is also included for generating the product manual by physically extracting the document objects from the document database to a directory, based on a delivery model. A method for automatically assembling product manuals is also included.