Showing papers on "Product (mathematics) published in 1986"

Optimal Lot-Sizing Algorithms for Complex Product Structures

Abstract: Lot sizing of products that have complex bills of materials plays an important role in the efficient operations of modern manufacturing and assembly processes. In this paper we develop algorithms for optimal lot sizing of products with a complex product structure. We convert the classical formulation of the general structure problem into a simple but expanded assembly structure with additional constraints, and solve the transformed problem by a branch-and-bound based procedure. The algorithm uses a Lagrangean relaxation and subgradient optimization procedure to generate tight lower bounds on the optimal solutions. In computational experiments, a code based on this method was able to solve single end product problems with up to 40 stages in the product structure. The model is extended to handle problems with multi-end items in the product structure, but with less favorable computational results.

Method and mechanism for producing cushioning dunnage product

Abstract: OF THE DISCLOSURE A mechanism and method for producing relatively low density pad-like cushioning dunnage product from sheet-like stock material. The mechanism takes the sheet-like stock material from a multi-ply roll thereof and changes it into a pad-like cushioning dunnage product having lateral pillow-like portions connected together along the generally central portion of the product. The mechanism includes a converging member which in conjunction with a forming frame coacting with the converging member, causes inward rolling of the lateral edges of the stock material into generally rolled form which is then adapted to be received in a connector operable to connect the rolled edge stock material forming the pillow-like portions, into the pad-like cushioning dunnage product. A novel separating mechanism for separating the sheets of stock material as they move from the stock roll toward the forming frame and the converging member is provided, together with a transversely extending roller disposed ahead of the separating mechanism whereby the point of commencement of entry of the multi-ply sheet-like stock material toward the separating mechanism remains constant irrespective of the diameter of the stock roll. A novel alternate, multi-ply stock roll com-prising a thicker gauge but lesser width web with a plurality of wider webs or sheets is also provided. The idea is to generally improve the con-struction of the dunnage producing mechanism, and to improve its operation as well as to provide a pad-like dunnage product possessing substantial resiliency per unit volume, and which is securely attached along the abutting rolled edges of the pillow-like portions of the produced cushioning product, so that the pad-like material tends to more positively remain in pad-like form during its use as a packing.

Calderón-Zygmund theory for product domains: Hp spaces

Abstract: This article deals with the boundedness properties of singular integrals that generalize the double Hilbert transform on product domains. The action of these operators on Hardy spaces and on L(log L) is discussed.

Computing the singular value decompostion of a product of two matrices

Abstract: An algorithm is developed for computing the singular value decomposition of a product of two general matrices without explicitly forming the product. The algorithm is based on an earlier Jacobi-like method due to Kogbetliantz and uses plane rotations applied to the two matrices separately. A triangular variant of the basic algorithm is developed that reduces the amount of work required.

Logarithmic depth circuits for algebraic functions

Abstract: This paper describes circuits for computation of a large class of algebraic functions on polynomials, power series, and integers, for which, it has been a long standing open problem to compute in depth less than $\Omega (\log n)^2 $.Algebraic circuits assume unit cost for elemental addition and multiplication. This paper describes $O(\log n)$ depth algebraic circuits which given as input the coefficients of n degree polynomials (over an appropriate ring), compute the product of $n^{O(1)} $ polynomials, the symmetric functions, as well as division and interpolation of real polynomials. Also described are $O(\log n)$ depth algebraic circuits which are given as input the first n coefficients of a power series (over an appropriate ring) compute the product of $n^{O(1)} $ power series, as well as division, reciprocal and reversion of real power series.Furthermore this paper describes boolean circuits of depth $O(\log n(\log \log n))$ which, given n-bit binary numbers, compute the product of n numbers and integ...

Une Caracterisation Volumique de Certains Espaces Normes de Dimension Finie

Abstract: We give a geometric characterization of finite dimensional normed spacesE, with a 1-unconditional basis, such that their volumetric product is minimal.

Is the Walden product useful

Abstract: Considerations sur la validite de l'utilisation du produit de Walden (conductivite-viscosite) dans l'interpretation de la conductance ionique limite

POS register system with combined optical scanner and weighing machine

Abstract: A point-of-sale register system includes an electronic cash register connected to a central inventory control unit to serve as a terminal device of a point-of-sale system: an optical scanner, which is electrically connected to the cash register, for optically scanning a bar code mounted on a product; and a weighing machine for weighing a product. The optical scanner includes a receiving section for receiving a product to be weighed thereon. The optical scanner is connected to the weighing machine so that the weight of the product placed on the optical scanner is transmitted to a measuring device of the weighing machine for measurement of the weight of the product. If a bar code is on the product which is placed on the receiving section of the optical scanner, the optical scanner scans the bar code of the product.

A new construction of noncrossed product algebras

Abstract: New examples of noncrossed product division algebras are obtained, using methods different from all previous noncrossed product constructions The examples are division algebras over intersections of />-Henselian valued fields, and they have Schur index /?"' and exponent p" for any prime number p and any integers m>n>2(n>3if^ = 2) The basic tools used in the construction are valuation theory and Galois cohomology; no generic methods are applied and there is no pi theory Along the way, local-global principles are proved for central simple algebras over intersections of p-Henselian valued fields The first examples of central simple division algebras which are not crossed products were obtained by Amitsur in (Am) in 1972 Amitsur thereby settled a question that had been one of the outstanding open problems in the theory of algebras for at least thirty years His examples were the generic division algebras UD(Q, n) of index n over Q (the rational numbers) for any natural number n such that p2 , p an odd prime, or 8|« All subsequent constructions of noncrossed products in (SS, 83,-883, R'» R°> an^ Ti) have heretofore been based on Amitsur's specialization argument, and they are all generic division algebras or extensions of generic division algebras The centers of these noncrossed product algebras are not known, nor are the Brauer groups, nor the absolute Galois groups of the centers We present here a new method of constructing noncrossed product algebras In our approach, the noncrossed product is realized as the underlying division algebra D of a tensor product of suitably chosen cyclic algebras over a field F = L, n L2, where each L, is a pth root Henselian valued field We prove local global principles relating the splitting fields of D to those of D ®F Lt, i = 1, 2 It is shown that the />-part of the Brauer group of F is completely determined by that of Ll and L2 Computations for central simple F-algebras thus become very tractable For exam- ple, we not only show that D is not a crossed product, but also calculate exactly how large r must be so that the matrix ring Mr{D) is a crossed product, and how large s must be so that MS(D) is a tensor product of cyclic algebras Indeed, the structure of the Brauer group of F is so nice that we were somewhat surprised that noncrossed products could possibly exist over F

Flexible, internally pressurizable package, method of using same and liquid product packaged therein

Abstract: Disclosed is a flexible package made of plastic and capable of standing by itself, comprising a generally cylindrically-shaped body, comprised of a flexible plastic film; a first cover part at one end of the cylindrically-shaped body; and a second cover part at the opposite end of the cylindrically-shaped body, wherein the cover parts are bonded to the plastic film by heat-sealing. Also disclosed is a packaged liquid product, in particular a product under gas pressure, and a method for producing the packaged product.

Product testing system

Abstract: A product testing system comprises a housing with at least one opening therein, the housing having an internal, environmentally controlled chamber. Products to be tested are mounted to a product carrier. The latter is carried, in turn, by a product carrier transfer assembly. By means of the vehicle and transfer assembly, the product carrier may be oriented to be received within the housing opening with the products exposed to the environmentally controlled internal housing chamber. In one embodiment, the vehicle traverses a path adjacent one or more housings, and the product carrier transfer assembly rotates, elevates and laterally moves the product carrier to position it in an opening in the housing.

On groups which are the product of two solvable subgroups

Abstract: All the groups in this article are finite. A group G is said to be factorizable if G = AB with A,B proper subgroups of G . The general problem is to obtain information on structure of a factorizabl...

Computation of system balancing transformations

Abstract: An algorithm is presented in this paper for computing state space balancing transformations directly from a state space realization. The algorithm requires no "squaring up." Various algorithmic aspects are discussed in detail. Applications to numerous other closely-related problems are also mentioned. The key idea throughout involves determining a contragredient transformation through computing the singular value decomposition of a certain product of matrices without explicitly forming the product.

A Hilbert transform product theorem

Abstract: The usual product theorem for Hilbert transforms states that under certain conditions x(t)y(t), the Hilbert transform of a product of two signals x(t) and y(t), is equal to x(t)y^(t), a result having repeated use in simplifying calculations involving modulated waveforms. Several sufficient conditions for the theorem to hold are well-known and appear in the literature. Here, using a time-domain approach, we derive a necessary and sufficient condition for the validity of the theorem and show as an example two signals which have the desired property but which do not satisfy any of the earlier sufficient conditions.

Prime Implicants, Minimum Covers, and the Complexity of Logic Simplification

Abstract: We show that any Boolean function f which can be expressed in a sum-of-products form using m product terms can contain as many as 2m− 1 implicants but no more.

Orthogonal Information Structures: a Model to Evaluate the Information Provided by a Second Opinion

Abstract: The paper discusses the value of information when a numberof independent sources provide information related to acommon set of states of nature.The starting point is the Information Economic model ofInformation Structures. The model is augmented to representindependence of informational sources by means oforthogonality of the information structures.A new mathematical operator, orthogonal product, is definedand its properties are probed. It is shown that thisoperator maintains some mathematical properties such asclosure, association, unity element, null element, etc. Itis demonstrated how the orthogonal product represents thenotion of multi-source information.The paper proves that an orthogonal product is generallymore informative than its multipliers, namely, if cost isnot considered a constraining factor, then there is a nonnegativevalue to obtaining a second opinion.The paper concludes with a numerical example and adiscussion on the applicability of the model oforthogonality.

Device and method for conveying and orienting randomized circular product-carrying pucks

Abstract: Device and a method are taught for specifically orienting and conveying products in a common direction of travel. The products are individually mounted on a plurality of identical, circular, product-carrying pucks. Each circular puck has a flat conveyor-contacting bottom surface and at least one circular peripheral surface contactable by corresponding circular peripheral surfaces of other pucks when located in a random surge thereof. Each puck is surmounted by a product support. Between its bottom surface and its product support, each puck has a peripheral slide surface parallel to the desired direction of travel of the oriented puck and at least one peripheral rotation-producing surface, the slide and rotation-producing surfaces being inset from the circular peripheral surface. A conveyor is provided having in association therewith at least one external contact surface to engage the rotation-producing surface of each puck and an alignment rail having an alignment edge to contact the slide surface of each puck. Each puck is conveyed past the at least one contact surface which cooperates with the at least one rotation-producing surface to cause rotation of the puck until the alignment edge of the alignment rail contacts the puck slide surface to stop rotation of the puck in the desired orientation and to maintain this orientation of the puck as it is conveyed to the next work station.

Fitted product with attached dust ruffle

Abstract: FITTED PRODUCT WITH ATTACHED DUST RUFFLE A unitary fitted product having a dust ruffle secured to a peripheral boundary thereof.

Twenty Years of P-Adic Model Theory

Abstract: Publisher Summary This chapter discusses the instructive development of p-adic model theory. The use of p-adic numbers is to allow free use of rational commutative algebra in the systematic study of congruences. The observation that the product formula resembles the function-theoretic principle that the sum of the residues is zero is the source of some of the most powerful ideas in modern number theory. There is an important topological difference between the number field case and the general function field case. Quantifier elimination was the original method of Tarski. It was later eclipsed by the methods of model-completeness and saturated models, but with the emphasis on complexity of computation, it was again prominent.