Showing papers on "Product (mathematics) published in 1980"
TL;DR: In this article, the authors present a set of conditions that will result in a product with a desirable combination of properties, which is a problem facing the product development community in general.
Abstract: A problem facing the product development community is the selection of a set of conditions which will result in a product with a desirable combination of properties. This essentially is a problem i...
4,109 citations
IBM1
TL;DR: This paper shows how the yield for any product can be calculated given the critical areas, defect density, and mixing parameter.
Abstract: A model with mixed Poisson statistics has been developed for calculating the yield for memory chips with redundant lines and for partially good product. The mixing process requires two parameters which are readily obtained from product data. The product is described in the model by critical areas which depend on the circuit's sensitivity to defects, and they can be determined in a systematic way. The process is represented in the model by defect densities and gross yield losses. These are measured with defect monitors independently of product type. This paper shows how the yield for any product can be calculated given the critical areas, defect density, and mixing parameter. Future yields are forecast by using expected improvements in defect densities. Examples show good agreement between actual and calculated yields.
241 citations
TL;DR: In this article, the anomalous dimension of nonsinglet structure functions is compared to a corresponding logarithmic correction factor to the nominal α S (Q 2 )/Q 2 fall off of meson form factors.
129 citations
TL;DR: Two new computational algorithms for product form networks are presented and a comprehensive treatment of these algorithms and the two important existing algorithms, convolution and mean value analysis, is given.
Abstract: In the last two decades there has been special interest in queueing networks with a product form solution. These have been widely used as models of computer systems and communication networks. Two new computational algorithms for product form networks are presented. A comprehensive treatment of these algorithms and the two important existing algorithms, convolution and mean value analysis, is given.
104 citations
TL;DR: In this paper, the transition from categorical coherence to homotopical coherence has been studied in algebraic K-theory, and a coherence theory of higher homotopy has been proposed.
79 citations
14 May 1980
TL;DR: This paper first describes the operation of the nested-block method, and derives corresponding cost formula, and presents an efficient heuristic algorithm for determining a near-optimal allocation of main-memory buffer space.
Abstract: This paper presents a new method of computing the product or join of n relations in a paged-memory environment. The method, termed the nested-block method, is an attempt to take maximum advantage of available main-memory buffer space. The problem of finding an optimal allocation of main-memory buffer space for the nested-block method of scanning n relations poses a nonlinear integer-programming problem. This paper first describes the operation of the nested-block method, and derives corresponding cost formula. It then presents an efficient heuristic algorithm for determining a near-optimal allocation of main-memory buffer space. The need to compute the product of relations arises naturally in processing n-relation queries. Conventional techniques for computing the join of relations can be complemented by the nested-block method. This paper examines these two important applications of the nested-block method.
74 citations
Journal Article•
69 citations
Journal Article•
63 citations
Patent•
08 Aug 1980
TL;DR: In this paper, a method for making a slurry containing particulate matter and fibers for a preformed insulation product comprises mixing dry particulates matter with a binder which is a liquid containing dispersed fibers.
Abstract: A method for making a slurry containing particulate matter and fibers for a preformed insulation product comprises mixing dry particulate matter with a binder which is a liquid containing dispersed fibers. An apparatus suitable for practicing the method comprises a means for disposing the particulate matter in the form of a falling curtain and a means for spraying the binder on the particulate matter.
62 citations
TL;DR: In this article, isoperimetric inequalities are used to obtain measure estimates on almost constancy sets of functions on product spaces, which are applied to produce almost unconditional or symmetric block sequences from given sequences.
Abstract: Isoperimetric inequalities are used to obtain measure estimates on almost constancy sets of functions on product spaces. These are applied to produce almost unconditional or symmetric block sequences from given sequences. Their length, which is (logn)1/2 in the general case, improves ton
a
where a cotype condition is imposed or when the given sequences arep-type attaining for somep<2. In thep-type attaining case, block sequences (1+e)-equivalent to the unit vector basis ofl
p
m
can be obtained when log logm ∼ log logn.
55 citations
Patent•
11 Jul 1980
TL;DR: In this article, an indicator for providing a time/temperature integrated indication of the temperature history of a deep-frozen product through the diffusion of water along a cellulose wick is presented.
Abstract: The disclosure concerns an indicator for providing a time/temperature integrated indication of the temperature history of a deep-frozen product through the diffusion of water along a cellulose wick. The cellulose wick is provided on itself with a water soluble, hydrate forming substance, such as sodium chloride and citric acid. The wick is covered in a plastic covering with an opening in the covering exposing the wick to water at the product, and the advance of the water front along the wick is indicated by a time/temperature indicator adjacent the wick and/or by an acid/base indicator on the wick and spaced from the indicator.
Patent•
19 Feb 1980
TL;DR: In this paper, a method of manufacturing a packaged web product and apparatus is described, where superposed web are compressed and while compressed web passes through an open-ended forming device having a closed perimeter and simultaneously enveloping the compressed, superposed webs, and thereafter transversely severing the resultant product into identical units.
Abstract: A method of manufacturing a packaged web product and apparatus therefor wherein superposed webs are compressed and while compressed webs pass through an open-ended forming device having a closed perimeter and simultaneously enveloping the compressed, superposed webs, and thereafter transversely severing the resultant product into identical units.
Book•
01 Jan 1980
TL;DR: In this article, Bergstrom's product formula in the case of real cyclic cubic fields was used for computing the class number of K6 and the signature rank of U6.
Abstract: Real cyclic cubic fields.- Real cyclic sextic fields.- The function ? and the structure of UR.- Bergstrom's product formula.- Bergstrom's product formula in the case of real cyclic sextic fields.- Formulas for computing ?A.- The class number of K6.- The signature rank of U6.- The computer program.- Numerical results.
TL;DR: In this paper, the initial vibrational product distributions have been obtained for the thermal proton abstraction reactions, Cl−+HBr→HCl(v=0,1)+Br− and Cl−−HI→H Cl(v = 0,1,2)+I−.
Abstract: Initial vibrational product distributions have been obtained for the thermal proton abstraction reactions, Cl−+HBr→HCl(v=0,1)+Br− and Cl−+HI→HCl(v=0,1,2)+I−. The experimental method utilizes detection of infrared chemiluminescence from the products of the ion–molecule reactions in a flowing afterglow. A detailed description of the apparatus design and characteristics is given. The initial relative HCl product vibrational distribution for the reaction Cl−+HI was determined to be Nv=1=1.0, Nv=2=0.85±0.05. The ratio of the total emission from Cl−+HBr to that from Cl−+HI was measured to be 39±2%. The results suggest substantial disposal of energy into product vibrations in these ion–molecule reactions.
28 May 1980
TL;DR: Two new computational algorithms for product form networks are presented and a comprehensive treatment of these algorithms and the two important existing algorithms, convolution and mean value analysis, is given.
Abstract: In the last two decades there has been special interest in queueing networks with a product form solution. These have been widely used as models of computer systems and communication networks. Two new computational algorithms for product form networks are presented. A comprehensive treatment of these algorithms and the two important existing algorithms, convolution and mean value analysis, is given.
TL;DR: In this article, the assembly work is broken down into its work elements which fasten the parts in each group, and an assignment method is proposed to assign the work elements to work stations in a single assembly line.
Abstract: This paper deals with two methods of analyzing and planning an assembly work. First, we propose a method of breaking the assembly work down into its work elements, in which all parts constituting the product are classified into unit groups based on the fastener method in assembling (e.g. bolted joints, riveted joints, shrinking and pressing fits, and so on). As a result, the assembly work is broken down into its work elements which fasten the parts in each group. At the same time, a problem of precedence relation among them arises. Secondary, we propose an assignment method in which the number of stations is determined, and the work elements are assigned to the work stations in a single assembly line as the efficiency of line balancing alters as a variable. By using the methods proposed here, we could analyze the assembly work consistently through breaking it down into work elements and assigning the work elements to work stations.
TL;DR: Conjoint analysis (or trade-off analysis) has become increasingly used in marketing as discussed by the authors, which attempts to parse the appeals of a product or concept into a set of factors, assign utility values to the separate levels of each factor, and finally, under the assumption of separability, determine the utility value of any product and concept by adding (or multiplying) the utility values of the individual level of each of the factors embodied in the product and concepts.
Abstract: Conjoint analysis (or trade-off analysis) has become increasingly used in marketing. Essentially, the techniques attempt to parse the appeals of a product or concept into a set of factors, assign utility values to the separate levels of each factor, and finally, under the assumption of separability, determine the utility value of any product or concept by adding (or multiplying) the utility values of the individual levels of each of the factors embodied in the product or concept. A good expository description of conjoint analysis is given in Green and Srinivasan (1978). For notational convenience, I present a brief description herein. Formally, if we are considering n factors, with the ith factor (i = 1, . . . , n) having mi levels, then we shall represent a bundle as an n-tuple (i1, i2, . . , ia), where
TL;DR: It is shown that the class of strongly Sperner rank-unimodal rank-symmetric partially ordered sets is closed under the operation of product.
TL;DR: In this article, Graphical methods of spin algebras are used to derive the expressions for the matrix elements of the total particle-number-conserving operators in the basis of hole-particle states.
Abstract: Graphical methods of spin algebras are used to derive the expressions for the matrix elements of the total particle-number-conserving operators in the basis of hole-particle states, adapted to the chain $\mathrm{U}({n}^{\ensuremath{'}}+{n}^{\ensuremath{'}\ensuremath{'}})\ensuremath{\supset}\mathrm{U}({n}^{\ensuremath{'}})\ensuremath{\bigotimes}\mathrm{U}({n}^{\ensuremath{'}\ensuremath{'}})$, where ${n}^{\ensuremath{'}}$ and ${n}^{\ensuremath{'}\ensuremath{'}}$ designate dimensions of particle and hole subspaces, respectively. The matrix elements are expressed as a product of segment values, each associated with one orbital level as in the particle formalism, and of an additional segment value, representing a linkage of the hole and particle subspaces. It is shown that the particle formalism segment values can be used throughout except for the link segment, whose possible values are derived. An example of hole-particle bases and of their graphical representations is given and the advantages of the hole-particle formalism in shell-model calculations are outlined. An extension of this formalism to particle-number-nonconserving operators, needed in applications involving the $m\mathrm{p}\ensuremath{-}n\mathrm{h}$ propagators with $m\ensuremath{
e}n$, $m$, $n=0$, 1, and 2, is discussed.
01 Jan 1980
TL;DR: A survey of what is known about the question of when a box product of compact spaces is paracompact can be found in this article, where the authors give a fairly complete survey, including proofs, and show how badly the Tychonoff product of uncountably many infinite discrete spaces fails to be normal.
Abstract: We give a fairly complete survey, including proofs, of what is known about the question of when a box product of compact spaces is paracompact, and show how badly a box product of compact or metrizable spaces can fail to be normal A side result is that the Tychonoff product of uncountably many infinite discrete spaces is not countably orthocompact 1980 Math Subj Class: 54B10, 54D15, 54D18, 54A35; 54E35, 54E65
Patent•
10 Oct 1980
TL;DR: A proteinaceous food product simulating cheese, comprising a blend of (a) soy protein selected from the class consisting of soy isolate, cold insoluble soy fraction, and combinations thereof, (b) gelatin, (c) a hydrocolloid gum preferably including either xanthan-locust bean gum mixtures and carrageenans, (d) fat, and (e) water.
Abstract: A proteinaceous food product simulating cheese, comprising a blend of (a) soy protein selected from the class consisting of soy isolate, cold insoluble soy fraction, and combinations thereof, (b) gelatin, (c) a hydrocolloid gum preferably including either xanthan-locust bean gum mixtures and carrageenans, (d) fat, and (e) water. Other desirable ingredients include an emulsifier, salt, chelating agent, coloring agent and flavoring.
TL;DR: In this paper, it was shown that the height of [λ] ⊗ [μ] is bounded by the product of the heights of the two vertices of a pair of vertices, and that if A and B satisfy a Capelli identity then so does A ⊆ B.
TL;DR: It is shown that for certain $(alpha,\beta ), \mu_x,y$ is absolutely continuous and so can be expressed in terms of a kernel $k(x... x) $ and the set of $(\alpha ,\beta )$ for which the product formula holds with $\mu _{x,Y} $ quasipositive is completely determined.
Abstract: The generalized Chebyshev polynomials $T_n^{(\alpha ,\beta )} (x),\,\alpha ,\,\beta > - 1$, are the polynomials orthogonal on $( - 1,1)$ with respect to the weight function $(1 - x^2 )^\alpha |x|^{2\beta + 1} $ and normalized by $T_n^{(\alpha ,\beta )} (1) = 1$. We show that for certain $(\alpha ,\beta )$ the product formula \[T_n^{(\alpha ,\beta )} (x)T_n^{(\alpha ,\beta )} (y) = \int_{ - 1}^1 {T_n^{(\alpha ,\beta )} (z)dm_{x,y} (z),\quad - 1 < x,y < 1,\quad n = 0,1,2, \cdots ,} \] holds, where $\mu _{x,y} $ is a real Borel measure which is independent of n, and explicitly determine $\mu _{x,y} $ is a real Borel measure which is independent of n. We also completely determine the set of $(\alpha ,\beta )$ for which the product formula holds with $\mu _{x,y} $ quasipositive; i.e., \[\int_{ - 1}^1 {\left|d\mu _{x,y} (z)\right| \leqq M,\quad - 1 < x,y < 1,} \] where M does not depend on x and y. For certain $( \alpha,\beta ), \mu_x,y$ is absolutely continuous and so can be expressed in terms of a kernel $k(x...
TL;DR: In this article, the authors compared the performance of ZIPMAP and PROPOSAS with respect to the solution values of the objective functions and the CPU-time requirements of the problem.
Abstract: Product positioning is concerned with the determination of new product attributes such that certain objectives can be met. Recently, Zufryden proposed a model for optimal product positioning with respect to sales. It relies on the single choice assumption, i.e. consumers choose that product closest to their ideal product perceptions. To improve solvability, Zufryden suggests to solve his model via an approximate procedure, called ZIPMAP. This procedure is compared with an exactly optimising algorithm for the same problem, called PROPOSAS. Comparisons are drawn with respect to the solution values of the objective functions and the CPU-time requirements. The results indicate a superiority of PROPOSAS for a vast number of problem types.
TL;DR: A characterization of the Dilworth numbers in terms of the dimensions of the kernels of certain linear maps on the complex vector space generated by the elements of P is given.
Abstract: The Dilworth numbers of a finite partially ordered set $P,\{ d_k ( P )|k\geqq 0 \}$, are the maximum sizes of the union of k antichains. We give a characterization of the Dilworth numbers in terms of the dimensions of the kernels of certain linear maps on the complex vector space generated by the elements of P. This is applied to prove bounds on the Dilworth numbers of product partial orders in terms of those of its factors and to prove sufficient conditions for the product of two partial orders to have the Sperner property.