scholarly journals A Simple Way for Implementing Extraction Columns of Infinite Height in Flowsheet Simulators

2019 ◽  
Vol 91 (3) ◽  
pp. 314-322
Author(s):  
Martin Kaul ◽  
Hans Hasse ◽  
Jakob Burger
Keyword(s):  
Infinite Height

PERFECTLY BOUNDED CLASSES OF ABELIAN GROUPS

2013 ◽  
Vol 12 (05) ◽  
pp. 1250208 ◽  
Author(s):  
PATRICK W. KEEF
Keyword(s):  
Abelian Groups ◽  
Direct Sums ◽  
Proper Subclass ◽  
Infinite Height ◽  
Reduced Group

Let [Formula: see text] be the class of abelian p-groups. A non-empty proper subclass [Formula: see text] is bounded if it is closed under subgroups, additively bounded if it is also closed under direct sums and perfectly bounded if it is additively bounded and closed under filtrations. If [Formula: see text], we call the partition of [Formula: see text] given by [Formula: see text] a B/U-pair. We state most of our results not in terms of bounded classes, but rather the corresponding B/U-pairs. Any additively bounded class contains a unique maximal perfectly bounded subclass. The idea of the length of a reduced group is generalized to the notion of the length of an additively bounded class. If λ is an ordinal or the symbol ∞, then there is a natural largest and smallest additively bounded class of length λ, as well as a largest and smallest perfectly bounded class of length λ. If λ ≤ ω, then there is a unique perfectly bounded class of length λ, namely the pλ-bounded groups that are direct sums of cyclics; however, this fails when λ > ω. This parallels results of Dugas, Fay and Shelah (1987) and Keef (1995) on the behavior of classes of abelian p-groups with elements of infinite height. It also simplifies, clarifies and generalizes a result of Cutler, Mader and Megibben (1989) which states that the pω + 1-projectives cannot be characterized using filtrations.

scholarly journals Dry granular avalanche impact force on a rigid wall of semi-infinite height

2017 ◽  
Vol 140 ◽  
pp. 03054 ◽  
Author(s):  
Adel Albaba ◽  
Stéphane Lambert ◽  
Thierry Faug
Keyword(s):  
Impact Force ◽  
Rigid Wall ◽  
Infinite Height ◽  
Granular Avalanche

The measurement of surface tension by means of a vertical-plate balance

1970 ◽  
Vol 23 (11) ◽  
pp. 2153 ◽  
Author(s):  
JE Lane ◽  
DO Jordan
Keyword(s):  
Surface Tension ◽  
Experimental Error ◽  
Gravitational Force ◽  
Vertical Plate ◽  
Infinite Plate ◽  
Arbitrary Cross Section ◽  
Finite Plate ◽  
Fluid Surface ◽  
Additional Force ◽  
Infinite Height

A thermodynamic analysis of the measurement of surface tension using plates with either horizontal or vertical grooves of arbitrary cross section is presented. An exact description of the behaviour of horizontal grooves in a plate of infinite width and of vertical grooves in a plate of infinite height is given. The behaviour of a plate of finite height with vertical grooves can be the same as for an infinite plate, but in most instances this is not true. An approximate analysis of a finite plate with vertical grooves is developed and the errors in the curvatures of the resulting liquid-fluid surface are evaluated. In general, it is found that a grooved plate partly immersed in liquid requires a greater force to balance it than a smooth plate of the same overall dimensions and mass and with zero contact angle against the liquid and fluid phases. The additional force required to balance the grooved plate is approximately independent of the groove orientation but increases with width (pitch) of the groove. It is shown that if the measurements are made with the bottom of the plate at the level of the liquid-fluid surface at an infinite distance from the plate, the additional force almost equals the gravitational force on the mass of liquid adhering to the plate after complete immersion and withdrawal from the liquid, the agreement improving as the groove pitch is decreased. This conclusion helps explain the good results obtained for surface tension measurements using roughened plates with scratched surfaces. The important results are checked experimentally and in most cases the agreement is within the experimental error. The only exceptions to this are the results for finite plates with vertical grooves but even then the agreement is nearly quantitative.

A Reinforced Tabu Search Approach for 2D Strip Packing

2012 ◽  
pp. 171-188
Author(s):  
Giglia Gómez-Villouta ◽  
Jean-Philippe Hamiez ◽  
Jin-Kao Hao
Keyword(s):  
Tabu Search ◽  
Search Algorithm ◽  
Fitness Function ◽  
Packing Problem ◽  
Two Dimensional ◽  
Strip Packing ◽  
Benchmark Instances ◽  
Finite Set ◽  
Infinite Height ◽  
Search Approach

This paper discusses a particular “packing” problem, namely the two dimensional strip packing problem, where a finite set of objects have to be located in a strip of fixed width and infinite height. The variant studied considers regular items, rectangular to be precise, that must be packed without overlap, not allowing rotations. The objective is to minimize the height of the resulting packing. In this regard, the authors present a local search algorithm based on the well-known tabu search metaheuristic. Two important components of the presented tabu search strategy are reinforced in attempting to include problem knowledge. The fitness function incorporates a measure related to the empty spaces, while the diversification relies on a set of historically “frozen” objects. The resulting reinforced tabu search approach is evaluated on a set of well-known hard benchmark instances and compared with state-of-the-art algorithms.

On a Genetic-Tabu Search Based Algorithm for Two-Dimensional Guillotine Cutting Problems

2012 ◽  
Vol 4 (2) ◽  
pp. 26-40 ◽  
Author(s):  
Hamza Gharsellaoui ◽  
Hamadi Hasni
Keyword(s):  
Tabu Search ◽  
Hybrid Approach ◽  
Search Method ◽  
Two Dimensional ◽  
Whole Number ◽  
Infinite Height ◽  
Tabu Search Method ◽  
Problem Instances ◽  
Cutting Problems ◽  
Guillotine Cutting

The paper deals with the purpose of one hybrid approach for solving the constrained two-dimensional cutting (2DC) problem. The authors study this hybrid approach that combines the genetic algorithm and the Tabu search method. For this problem, they assume a packing of a whole number of rectangular pieces to cut, and that all cuts are of guillotine type in one sheet of a fixed width and an infinite height. Finally, they undertake an extensive experimental study with a large number of problem instances extracted from the literature by the Hopper’s benchmarks in order to support and to prove their approach and to evaluate the performance.

Nonlinear convection in high vertical channels

1984 ◽  
Vol 143 ◽  
pp. 223-242 ◽  
Author(s):  
C. Normand
Keyword(s):  
Specific Treatment ◽  
Finite Size ◽  
Stationary Solutions ◽  
Amplitude Equation ◽  
Weakly Nonlinear ◽  
Convective Systems ◽  
Horizontal Extent ◽  
Aspect Ratios ◽  
Infinite Height ◽  
The Stability

Application of Landau's ideas to the theory of weakly nonlinear instabilities shows that the amplitude of the unstable modes behaves as the square root of the reduced control parameter ε, its critical value being ε = 0. When applied to cellular structures the theory has been improved by taking into account the slow spatial variations of the amplitude and phase of the unstable modes. Until now the case of thermo-convective instabilities in high vertical channels has not been studied using this approach. In high vertical structures the nonlinear terms disappear in the limit of an infinite height, and the supercritical behaviour requires a specific treatment. It differs from the standard analysis valid for the case of fluid layers of infinite horizontal extent, where the nonlinearities and the finite-size effects are disconnected. In the limit of high aspect ratios (height [Gt ] horizontal extent) we have derived an amplitude equation for convective systems where the nonlinear terms contain derivatives at the lowest order. As a consequence the amplitude equation cannot be put into a variational form and the stability of the stationary solutions cannot be deduced from an ordering in decreasing values of a Lyapunov functional.

The computable dimension of trees of infinite height

2005 ◽  
Vol 70 (1) ◽  
pp. 111-141 ◽  
Author(s):  
Russell Miller
Keyword(s):  
Computable Presentation ◽  
Computable Dimension ◽  
Infinite Height ◽  
Computable Presentations

AbstractWe prove that no computable tree of infinite height is computably categorical, and indeed that all such trees have computable dimension ω. Moreover, this dimension is effectively ω, in the sense that given any effective listing of computable presentations of the same tree, we can effectively find another computable presentation of it which is not computably isomorphic to any of the presentations on the list.

Recursively presented Abelian groups: Effective p-Group theory. I

1981 ◽  
Vol 46 (3) ◽  
pp. 617-624 ◽  
Author(s):  
Charlotte Lin
Keyword(s):  
Abelian Group ◽  
University Of California ◽  
Structure Theory ◽  
Primary Group ◽  
Cyclic Groups ◽  
Direct Sum ◽  
Classical Mathematics ◽  
Hebrew University ◽  
Infinite Height ◽  
Complete Theories

The study of effectiveness in classical mathematics is rapidly expanding, through recent research in algebra, topology, model theory, and functional analysis. Well-known contributors are Barwise (Wisconsin), Crossley (Monash), Dekker (Rutgers), Ershoff (Novosibirsk), Feferman (Stanford), Harrington (Berkeley), Mal′cev (Novosibirsk), Morley (Cornell), Nerode (Cornell), Rabin (Hebrew University), Shore (Cornell). Further interesting work is due to Kalantari (University of California, Santa Barbara), Metakides (Rochester), Millar (Wisconsin), Remmel (University of California, San Diego), Nurtazin (Novosibirsk). Areas investigated include enumerated algebras, models of complete theories, vector spaces, fields, orderings, Hilbert spaces, and boolean algebras.We investigate the effective content of the structure theory of p-groups. Recall that a p-group is a torsion abelian group in which the (finite) order of each element is some power of a fixed prime p. (In the sequel, “group” = “additively written abelian group”.)The structure theory of p-groups is based on the two elementary notions of order and height. Recall that the order of x is the least integer n such that nx = 0. The height of x is the number of times p divides x, that is, the least n such that x = pny for some y in the group but x ≠ pn+1y for any y. If for each n ∈ ω there is a “pnth-root” yn, so that x = pnyn, then we say that x has infinite height. In 1923, Prüfer related the two notions as criteria for direct sum decomposition, provingTheorem. Every group of bounded order is a direct sum of cyclic groups, andTheorem. Every countable primary group with no (nonzero) elements of infinite height is a direct sum of cyclic groups.

scholarly journals Exact solutions for the 2d-strip packing problem using the positions-and-covering methodology

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0245267
Author(s):  
Nestor M. Cid-Garcia ◽  
Yasmin A. Rios-Solis
Keyword(s):  
Exact Solutions ◽  
Optimal Solution ◽  
Packing Problem ◽  
Set Covering ◽  
Medium Size ◽  
Strip Packing ◽  
Fixed Weight ◽  
Np Hard Problem ◽  
Minimum Height ◽  
Infinite Height

We use the Positions and Covering methodology to obtain exact solutions for the two-dimensional, non-guillotine restricted, strip packing problem. In this classical NP-hard problem, a given set of rectangular items has to be packed into a strip of fixed weight and infinite height. The objective consists in determining the minimum height of the strip. The Positions and Covering methodology is based on a two-stage procedure. First, it is generated, in a pseudo-polynomial way, a set of valid positions in which an item can be packed into the strip. Then, by using a set-covering formulation, the best configuration of items into the strip is selected. Based on the literature benchmark, experimental results validate the quality of the solutions and method’s effectiveness for small and medium-size instances. To the best of our knowledge, this is the first approach that generates optimal solutions for some literature instances for which the optimal solution was unknown before this study.

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