scholarly journals Compactness of order intervals in a locally solid linear lattice

2022 ◽  
Author(s):  
Zbigniew Lipecki
Keyword(s):  
Linear Lattice ◽  
Order Intervals

scholarly journals Zero-sum flows of the linear lattice

2015 ◽  
Vol 31 ◽  
pp. 108-120 ◽  
Author(s):  
Ghassan Sarkis ◽  
Shahriar Shahriari ◽  
PCURC
Keyword(s):  
Linear Lattice ◽  
Zero Sum

scholarly journals Time Dynamics of Solitons Photogenerated in Disordered Linear Lattice

2000 ◽  
Vol 138 ◽  
pp. 584-585 ◽  
Author(s):  
Yoshinori Tabata ◽  
Noritaka Kuroda
Keyword(s):  
Linear Lattice ◽  
Time Dynamics

Parameter values for lot size and quality level via CAE simulation, statistical method, and mathematical programming

2021 ◽  
pp. 095440542093787
Author(s):  
Angus Jeang ◽  
Chien-Ping Chung
Keyword(s):  
Inventory Management ◽  
Quality Level ◽  
Response Functions ◽  
Lot Size ◽  
Optimal Process ◽  
Production Inventory ◽  
Production Quantity ◽  
Parameter Values ◽  
Back Order ◽  
Order Intervals

Because of the stochastic nature of production systems, it is necessary to first build an uncertainty model for subsequent real applications. Moreover, process parameter planning, quality design, and production inventory management are interdependent elements. In this research, a computer simulation model via computer-aided engineering (CAE) was developed to determine the optimal process parameters, lot size, and back order intervals for an integrated process design and inventory management system with simultaneous quality and cost considerations. Based on the estimated process time and costs obtained using CAE, the derived production rate and unit cost were then used for production inventory applications. In consideration of the uncertainty factor, the response surface method (RSM) was employed to analyze the output, namely the total costs incurred in employing the proposed approach, as well as the inputs, which include the cutting parameters, production quantity, and back order intervals. After the RSM was used to obtain the response functions, which represent the output of the collective interests, the mathematical programming (MP) was formulated based on the response functions to determine the optimal process parameters, process quality levels, production order quantities, and back order intervals. The total cost per set time unit was minimized by determining the required quality level, process parameter values, Economic Production Quantity (EPQ), and back order intervals. A cutting example was chosen to demonstrate the proposed approach. Two cases were used for comparison: the Integrated Case (the proposed approach herein) and the Disintegrated Case.

Macroscopic imprints of ductile deformation

2021 ◽  
pp. 86-102
Author(s):  
Jean-Luc Bouchez ◽  
Adolphe Nicolas
Keyword(s):  
Plastic Deformation ◽  
Shear Strain ◽  
Sensu Stricto ◽  
Ductile Deformation ◽  
Structural Level ◽  
Linear Lattice ◽  
Crystalline Plasticity ◽  
Planar Structures ◽  
Heterogeneous Deformation ◽  
Folded Structures

The fundamentals of structural geology are presented, namely, folds, planar structures (cleavage or schistosity, foliation) and linear ones (lineations), regarded as emblematic for geologists. Ductile imprints of folds, affecting stratified formations, combined with brittle imprints, often remain modest in terms of strain intensity. Folding is essentially inhomogeneous and often results from the buckling (bending) of the layers (or stratification) as a consequence of layer parallel compression. Folded structures are frequently accompanied by fractures. Hence they may be classified as brittle–ductile. They are mostly encountered at low depths and constitute the upper structural level of the Earth’s crust. Ductile deformation sensu stricto appears at the lower structural level. The macroscopic aspects of ductile deformations and their implications will be examined. The principal operating mechanism, crystalline plasticity, represents the mechanical aspect of deformation, sometime assisted by chemical aspects (pressure-solution). While homogeneous deformation constitutes our principal concern, heterogeneous deformation is often present, particularly when examined at fine scales. At low shear strain (γ‎ < 0.7, or θ‎ ~35°, equivalent to ~30% shortening), plastic deformation generally leads to a planar and a linear anisotropy strengthening with increasing deformation. At higher shear strain, any pre-existing planar structure becomes so stretched that it cannot be recognized. The new structure may be purely planar, purely linear or plano-linear. Lattice fabrics, appearing in rocks subjected to plastic deformation and resulting from deformation mechanisms at the grain-scale, are examined in detail in Chapter 6.

Positive Forms on Nuclear *-Algebras and Their Integral Representations

1990 ◽  
Vol 42 (3) ◽  
pp. 410-469 ◽  
Author(s):  
Alain Bélanger ◽  
Erik G. F. Thomas
Keyword(s):  
Integral Representation ◽  
Positive Cone ◽  
Approximate Identity ◽  
Integral Representations ◽  
Regularity Conditions ◽  
Direct Integral ◽  
Positive Form ◽  
Representations Of Algebras ◽  
Almost All ◽  
Order Intervals

Abstract.The main result of this paper establishes the existence and uniqueness of integral representations of KMS functionals on nuclear *- algebras. Our first result is about representations of *-algebras by means of operators having a common dense domain in a Hilbert space. We show, under certain regularity conditions, that (Powers) self-adjoint representations of a nuclear *-algebra, which admit a direct integral decomposition, disintegrate into representations which are almost all self-adjoint. We then define and study the class of self-derivative algebras. All algebras with an identity are in this class and many other examples are given. We show that if is a self-derivative algebra with an equicontinuous approximate identity, the cone of all positive forms on is isomorphic to the cone of all positive invariant kernels on These in turn correspond bijectively to the invariant Hilbert subspaces of the dual space This shows that if is a nuclear -space, the positive cone of has bounded order intervals, which implies that each positive form on has an integral representation in terms of the extreme generators of the cone. Given a continuous exponentially bounded one-parameter group of *-automorphisms of we can define the subcone of all invariant positive forms satisfying the KMS condition. Central functionals can be viewed as KMS functionals with respect to a trivial group action. Assuming that is a self-derivative algebra with an equicontinuous approximate identity, we show that the face generated by a self-adjoint KMS functional is a lattice. If is moreover a nuclear *-algebra the previous results together imply that each self-adjoint KMS functional has a unique integral representation by means of extreme KMS functionals almost all of which are self-adjoint.

Trust Your Data or Not—StQP Remains StQP: Community Detection via Robust Standard Quadratic Optimization

2020 ◽  
Author(s):  
Immanuel M. Bomze ◽  
Michael Kahr ◽  
Markus Leitner
Keyword(s):  
Community Detection ◽  
Optimization Problem ◽  
Quadratic Optimization ◽  
Quadratic Optimization Problem ◽  
Standard Quadratic Optimization ◽  
Uncertainty Sets ◽  
Indefinite Quadratic Form ◽  
Indefinite Quadratic ◽  
Order Intervals ◽  
Copositive Matrix

We consider the robust standard quadratic optimization problem (RStQP), in which an uncertain (possibly indefinite) quadratic form is optimized over the standard simplex. Following most approaches, we model the uncertainty sets by balls, polyhedra, or spectrahedra, more generally, by ellipsoids or order intervals intersected with subcones of the copositive matrix cone. We show that the copositive relaxation gap of the RStQP equals the minimax gap under some mild assumptions on the curvature of the aforementioned uncertainty sets and present conditions under which the RStQP reduces to the standard quadratic optimization problem. These conditions also ensure that the copositive relaxation of an RStQP is exact. The theoretical findings are accompanied by the results of computational experiments for a specific application from the domain of graph clustering, more precisely, community detection in (social) networks. The results indicate that the cardinality of communities tend to increase for ellipsoidal uncertainty sets and to decrease for spectrahedral uncertainty sets.

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