Heuristics for Multidimensional Packing Problems
Egeblad, Jens
minimum height container required for the items. The main contributions of the thesis are three new heuristics for strip-packing and knapsack packing problems where items are both rectangular and irregular. In the two first papers we describe a heuristic for the multidimensional strip-packing problem that...... results of this heuristic are among the best published in the literature both for two- and three-dimensional strip-packing problems for irregular shapes. In the third paper, we introduce a heuristic for two- and three-dimensional rectangular knapsack packing problems. The two-dimensional heuristic uses...... promising. A heuristic for a three-dimensional knapsack packing problem involving furniture is presented in the fourth paper. The heuristic is based on a variety of techniques including tree-search, wall-building, and sequential placement. The solution process includes considerations regarding stability and...
The Maximum Resource Bin Packing Problem
Boyar, J.; Epstein, L.; Favrholdt, L.M.;
2006-01-01
Usually, for bin packing problems, we try to minimize the number of bins used or in the case of the dual bin packing problem, maximize the number or total size of accepted items. This paper presents results for the opposite problems, where we would like to maximize the number of bins used or...... algorithms, First-Fit-Increasing and First-Fit-Decreasing for the maximum resource variant of classical bin packing. For the on-line variant, we define maximum resource variants of classical and dual bin packing. For dual bin packing, no on-line algorithm is competitive. For classical bin packing, we find...
Modified strip packing heuristics for the rectangular variable-sized bin packing problem
FG Ortmann
2010-06-01
Full Text Available Two packing problems are considered in this paper, namely the well-known strip packing problem (SPP and the variable-sized bin packing problem (VSBPP. A total of 252 strip packing heuristics (and variations thereof from the literature, as well as novel heuristics proposed by the authors, are compared statistically by means of 1170 SPP benchmark instances in order to identify the best heuristics in various classes. A combination of new heuristics with a new sorting method yields the best results. These heuristics are combined with a previous heuristic for the VSBPP by the authors to find good feasible solutions to 1357 VSBPP benchmark instances. This is the largest statistical comparison of algorithms for the SPP and the VSBPP to the best knowledge of the authors.
On Approximating Four Covering and Packing Problems
Ashley, Mary; Berman, Piotr; Chaovalitwongse, Wanpracha; DasGupta, Bhaskar; Kao, Ming-Yang; 10.1016/j.jcss.2009.01.002
2011-01-01
In this paper, we consider approximability issues of the following four problems: triangle packing, full sibling reconstruction, maximum profit coverage and 2-coverage. All of them are generalized or specialized versions of set-cover and have applications in biology ranging from full-sibling reconstructions in wild populations to biomolecular clusterings; however, as this paper shows, their approximability properties differ considerably. Our inapproximability constant for the triangle packing problem improves upon the previous results; this is done by directly transforming the inapproximability gap of Haastad for the problem of maximizing the number of satisfied equations for a set of equations over GF(2) and is interesting in its own right. Our approximability results on the full siblings reconstruction problems answers questions originally posed by Berger-Wolf et al. and our results on the maximum profit coverage problem provides almost matching upper and lower bounds on the approximation ratio, answering a...
Comparing Online Algorithms for Bin Packing Problems
Epstein, Leah; Favrholdt, Lene Monrad; Kohrt, Jens Svalgaard
2012-01-01
The relative worst-order ratio is a measure of the quality of online algorithms. In contrast to the competitive ratio, this measure compares two online algorithms directly instead of using an intermediate comparison with an optimal offline algorithm. In this paper, we apply the relative worst......-order ratio to online algorithms for several common variants of the bin packing problem. We mainly consider pairs of algorithms that are not distinguished by the competitive ratio and show that the relative worst-order ratio prefers the intuitively better algorithm of each pair....
The load-balanced multi-dimensional bin-packing problem
Trivella, Alessio; Pisinger, David
2016-01-01
bin, to the general balanced bin-packing problem. Given the difficulty for standard solvers to deal even with small size instances, a multi-level local search heuristic is presented. The algorithm takes advantage of the Fekete-Schepers representation of feasible packings in terms of particular classes...
Improved Absolute Approximation Ratios for Two-Dimensional Packing Problems
Harren, Rolf; van Stee, Rob
We consider the two-dimensional bin packing and strip packing problem, where a list of rectangles has to be packed into a minimal number of rectangular bins or a strip of minimal height, respectively. All packings have to be non-overlapping and orthogonal, i.e., axis-parallel. Our algorithm for strip packing has an absolute approximation ratio of 1.9396 and is the first algorithm to break the approximation ratio of 2 which was established more than a decade ago. Moreover, we present a polynomial time approximation scheme (mathcal{PTAS}) for strip packing where rotations by 90 degrees are permitted and an algorithm for two-dimensional bin packing with an absolute worst-case ratio of 2, which is optimal provided mathcal{P} not= mathcal{NP}.
Integrating packing and distribution problems and optimization through mathematical programming
Fabio Miguel; Mariano Frutos; Fernando Tohmé; Máximo Méndez
2016-01-01
This paper analyzes the integration of two combinatorial problems that frequently arise in production and distribution systems. One is the Bin Packing Problem (BPP) problem, which involves finding an ordering of some objects of different volumes to be packed into the minimal number of containers of the same or different size. An optimal solution to this NP-Hard problem can be approximated by means of meta-heuristic methods. On the other hand, we consider the Capacitated Vehicle Routing Proble...
A SAT Encoding for Multi-dimensional Packing Problems
Grandcolas, Stéphane; Pinto, Cédric
The Orthogonal Packing Problem (OPP) consists in determining if a set of items can be packed into a given container. This decision problem is NP-complete. Fekete et al. modelled the problem in which the overlaps between the objects in each dimension are represented by interval graphs. In this paper we propose a SAT encoding of Fekete et al. characterization. Some results are presented, and the efficiency of this approach is compared with other SAT encodings.
Multi-dimensional Bin Packing Problems with Guillotine Constraints
Amossen, Rasmus Resen; Pisinger, David
2010-01-01
The problem addressed in this paper is the decision problem of determining if a set of multi-dimensional rectangular boxes can be orthogonally packed into a rectangular bin while satisfying the requirement that the packing should be guillotine cuttable. That is, there should exist a series of face...... parallel straight cuts that can recursively cut the bin into pieces so that each piece contains a box and no box has been intersected by a cut. The unrestricted problem is known to be NP-hard. In this paper we present a generalization of a constructive algorithm for the multi-dimensional bin packing...
A Novel GRASP Algorithm for Solving the Bin Packing Problem
Abdesslem Layeb
2012-04-01
Full Text Available The Bin Packing Problem (BPP is one of the most known combinatorial optimization problems. This problem consists in packing a set of items into a minimum number of bins. There are several variants of this problem; the most basic problem is the one-dimensional bin packing problem (1-BPP. In this paper, we present a new approach based on the GRASP procedure to deal with the1-BPP problem. The first GRASP phase is based on a new random heuristics based on hybridization between First Fit and Best Fit heuristics. The second GRASP phase is based on Tabu search algorithm used for the enhancement of the solutions found in the first phase. The obtained results are very encouraging and show the feasibility and effectiveness of the proposed approach
Bin Completion Algorithms for Multicontainer Packing, Knapsack, and Covering Problems
Fukunaga, A S; 10.1613/jair.2106
2011-01-01
Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in multi-agent systems and distributed systms, and can also be found as subproblems of scheduling problems. We propose bin completion, a branch-and-bound strategy for one-dimensional, multicontainer packing problems. Bin completion combines a bin-oriented search space with a powerful dominance criterion that enables us to prune much of the space. The performance of the basic bin completion framework can be enhanced by using a number of extensions, including nogood-based pruning techniques that allow further exploitation of the dominance criterion. Bin completion is applied to four problems: multiple knapsack, bin covering, min-cost covering, and bin packing. We show that our bin completion algorithms yield new, state-of-the-art results for the multiple knapsack, bin covering,...
A Personified Annealing Algorithm for Circles Packing Problem
ZHANGDe-Fu; LIXin
2005-01-01
Circles packing problem is an NP-hard problem and is difficult to solve. In this paper, a hybrid search strategy for circles packing problem is discussed. A way of generating new configuration is presented by simulating the moving of elastic objects, which can avoid the blindness of simulated annealing search and make iteration process converge fast. Inspired by the life experiences of people,an effective personified strategy to jump out of local minima is given. Based on the simulated annealing idea and personification strategy, an effective personified annealing algorithm for circles packing problem is developed. Numerical experiments on benchmark problem instances show that the proposed algorithm outperforms the best algorithm in the literature.
Integrating packing and distribution problems and optimization through mathematical programming
Fabio Miguel
2016-06-01
Full Text Available This paper analyzes the integration of two combinatorial problems that frequently arise in production and distribution systems. One is the Bin Packing Problem (BPP problem, which involves finding an ordering of some objects of different volumes to be packed into the minimal number of containers of the same or different size. An optimal solution to this NP-Hard problem can be approximated by means of meta-heuristic methods. On the other hand, we consider the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW, which is a variant of the Travelling Salesman Problem (again a NP-Hard problem with extra constraints. Here we model those two problems in a single framework and use an evolutionary meta-heuristics to solve them jointly. Furthermore, we use data from a real world company as a test-bed for the method introduced here.
A Heuristic Algorithm for Solving Triangle Packing Problem
Ruimin Wang
2013-01-01
Full Text Available The research on the triangle packing problem has important theoretic significance, which has broad application prospects in material processing, network resource optimization, and so forth. Generally speaking, the orientation of the triangle should be limited in advance, since the triangle packing problem is NP-hard and has continuous properties. For example, the polygon is not allowed to rotate; then, the approximate solution can be obtained by optimization method. This paper studies the triangle packing problem by a new kind of method. Such concepts as angle region, corner-occupying action, corner-occupying strategy, and edge-conjoining strategy are presented in this paper. In addition, an edge-conjoining and corner-occupying algorithm is designed, which is to obtain an approximate solution. It is demonstrated that the proposed algorithm is highly efficient, and by the time complexity analysis and the analogue experiment result is found.
Solving non-standard packing problems by global optimization and heuristics
Fasano, Giorgio
2014-01-01
This book results from a long-term research effort aimed at tackling complex non-standard packing issues which arise in space engineering. The main research objective is to optimize cargo loading and arrangement, in compliance with a set of stringent rules. Complicated geometrical aspects are also taken into account, in addition to balancing conditions based on attitude control specifications. Chapter 1 introduces the class of non-standard packing problems studied. Chapter 2 gives a detailed explanation of a general model for the orthogonal packing of tetris-like items in a convex domain. A number of additional conditions are looked at in depth, including the prefixed orientation of subsets of items, the presence of unusable holes, separation planes and structural elements, relative distance bounds as well as static and dynamic balancing requirements. The relative feasibility sub-problem which is a special case that does not have an optimization criterion is discussed in Chapter 3. This setting can be exploit...
Two personification strategies for solving circles packing problem
黄文奇[1; 许如初[2
1999-01-01
Two personification strategies are presented, which yield a highly efficient and practical algorithm for solving one of the NP hard problems——circles packing problem on the basis of the quasi-physical algorithm. A very clever polynomial time complexity degree approximate algorithm for solving this problem has been reported by Dorit S.Hochbaum and Wolfgang Maass in J. ACM. Their algorithm is extremely thorough-going and of great theoretical significance. But, just as they pointed out, their algorithm is feasible only in conception and even for examples frequently encountered in everyday life and of small scale, it is the case more often than not that up to a million years would be needed to perform calculations with this algorithm. It is suggested toward the end of their paper that a heuristic algorithm of higher practical effectiveness should be sought out. A direct response to their suggestion is intented to provide.
Performance Analysis of Selective Breeding Algorithm on One Dimensional Bin Packing Problems
Sriramya, P.; Parvathavarthini, B.
2012-12-01
The bin packing optimization problem packs a set of objects into a set of bins so that the amount of wasted space is minimized. The bin packing problem has many important applications. The objective is to find a feasible assignment of all weights to bins that minimizes the total number of bins used. The bin packing problem models several practical problems in such diverse areas as industrial control, computer systems, machine scheduling, VLSI chip layout and etc. Selective breeding algorithm (SBA) is an iterative procedure which borrows the ideas of artificial selection and breeding process. By simulating artificial evolution in this way SBA algorithm can easily solve complex problems. One dimensional bin packing benchmark problems are taken for evaluating the performance of the SBA. The computational results of SBA algorithm show optimal solution for the tested benchmark problems. The proposed SBA algorithm is a good problem-solving technique for one dimensional bin packing problems.
A Novel Quantum Inspired Cuckoo Search Algorithm for Bin Packing Problem
Abdesslem Layeb
2012-05-01
Full Text Available The Bin Packing Problem (BPP is one of the most known combinatorial optimization problems. This problem consists to pack a set of items into a minimum number of bins. There are several variants of this problem; the most basic problem is the one-dimensional bin packing problem (1-BPP. In this paper, we present a new approach based on the quantum inspired cuckoo search algorithm to deal with the 1-BPP problem. The contribution consists in defining an appropriate quantum representation based on qubit representation to represent bin packing solutions. The second contribution is proposition of a new hybrid quantum measure operation which uses first fit heuristic to pack no filled objects by the standard measure operation. The obtained results are very encouraging and show the feasibility and effectiveness of the proposed approach.
Hybrid next-fit algorithm for the two-dimensional rectangle bin-packing problem
J.B.G. Frenk (Hans); G. Galambos
1987-01-01
textabstractWe present a new approximation algorithm for the two-dimensional bin-packing problem. The algorithm is based on two one-dimensional bin-packing algorithms. Since the algorithm is of next-fit type it can also be used for those cases where the output is required to be on-line (e. g. if we
Model and algorithm for container ship stowage planning based on bin-packing problem
无
2005-01-01
In a general case, container ship serves many different ports on each voyage. A stowage planning for container ship made at one port must take account of the influence on subsequent ports. So the complexity of stowage planning problem increases due to its multi-ports nature. This problem is NP-hard problem. In order to reduce the computational complexity, the problem is decomposed into two sub-problems in this paper. First, container ship stowage problem (CSSP) is regarded as "packing problem", ship-bays on the board of vessel are regarded as bins, the number of slots at each bay are taken as capacities of bins, and containers with different characteristics (homogeneous containers group) are treated as items packed. At this stage, there are two objective functions, one is to minimize the number of bays packed by containers and the other is to minimize the number of overstows. Secondly, containers assigned to each bays at first stage are allocate to special slot, the objective functions are to minimize the metacentric height, heel and overstows.The taboo search heuristics algorithm are used to solve the subproblem. The main focus of this paper is on the first subproblem. A case certifies the feasibility of the model and algorithm.
Spatial Cluster Analysis by the Bin-Packing Problem and DNA Computing Technique
Xiyu Liu; Jie Xue
2013-01-01
Spatial cluster analysis is an important data mining task. Typical techniques include CLARANS, density- and gravity-based clustering, and other algorithms based on traditional von Neumann's computing architecture. The purpose of this paper is to propose a technique for spatial cluster analysis based on sticker systems of DNA computing. We will adopt the Bin-Packing Problem idea and then design algorithms of sticker programming. The proposed technique has a better time complexity. In the case ...
A Modified Partially Mapped MultiCrossover Genetic Algorithm for Two-Dimensional Bin Packing Problem
M. Sarabian
2010-01-01
Full Text Available Problem statement: Non-oriented case of Two-Dimensional Rectangular Bin Packing Problem (2DRBPP was studied in this study. The objective of this problem was to pack a given set of small rectangles, which may be rotated by 90°, without overlaps into a minimum numbers of identical large rectangles. Our aim was to improve the performance of the MultiCrossover Genetic Algorithm (MXGA proposed from the literature for solving the problem. Approach: Four major components of the MXGA consisted of selection, crossover, mutation and replacement are considered in this study. Initial computational investigations were conducted independently on the named components using some benchmark problem instances. The new MXGA was constructed by combining the rank selection, modified Partially Mapped Crossover (PMXm, mutation with two mutation operators and elitism replacement scheme with filtration. Results: Extensive computational experiments of the new proposed algorithm, MXGA, Standard GA (SGA, Unified Tabu Search (UTS and Randomized Descent Method (RDM were performed using benchmark data sets. Conclusion: The computational results indicated that the new proposed algorithm was able to outperform MXGA, SGA, UTS and RDM.
A new class of variational equation problems
无
2003-01-01
Applying an analysis method to a group of multivariable equations, a new class of variational equations are proved. This method is more concise and more direct than the others. This result can be applied to some stochastic control models.
Protein side-chain packing problem: a maximum edge-weight clique algorithmic approach.
Dukka Bahadur, K C; Tomita, Etsuji; Suzuki, Jun'ichi; Akutsu, Tatsuya
2005-02-01
"Protein Side-chain Packing" has an ever-increasing application in the field of bio-informatics, dating from the early methods of homology modeling to protein design and to the protein docking. However, this problem is computationally known to be NP-hard. In this regard, we have developed a novel approach to solve this problem using the notion of a maximum edge-weight clique. Our approach is based on efficient reduction of protein side-chain packing problem to a graph and then solving the reduced graph to find the maximum clique by applying an efficient clique finding algorithm developed by our co-authors. Since our approach is based on deterministic algorithms in contrast to the various existing algorithms based on heuristic approaches, our algorithm guarantees of finding an optimal solution. We have tested this approach to predict the side-chain conformations of a set of proteins and have compared the results with other existing methods. We have found that our results are favorably comparable or better than the results produced by the existing methods. As our test set contains a protein of 494 residues, we have obtained considerable improvement in terms of size of the proteins and in terms of the efficiency and the accuracy of prediction. PMID:15751115
Bin packing approach for solving VLSI circuit partitioning problem using Genetic algorithm
Prof. Sharadindu Roy
2012-12-01
Full Text Available In this paper,the circuit partitioning using genetic algorithm with bin packing concept has been attempted. In this practical paper solution is easy and we can easily apply genetic operator in this type of problem. The bin packing problem is to find the minimum number of bins needed to pack a given set of objects of known sizes so they do not exceed the capacity of each bin. Complexity is both time in space, provided size of problem an as integer (count is infinite.This problem is known NP-hard. The technique of our approach is to be design module trick. We can be realizing with self standard IC chip. Obviously we have taken into account minimum power conjunction. The solution of a circuit partitioning problem is global optimum. Like circuit partitioning is the more critical step in the physical design of various circuit in VLSI.In the partitioning main objective is to minimize the number of cuts.This chapter addresses the problem of partitioning and particular the use of the genetic algorithms for circuit partitioning.The object to be partitioned in VLSI design are typically logic gates or instances of standard cell. Circuit partitioning is one of the important parts in chip designing. We let, the number of bins will be needed equal to be number of genes divided by number of bins. At first the genes will be insert in first bin until the bin is not full, when bin is full then insert second bin and so on. Our method calculates the fitness value and discards solution with low fitness value. The increase in number of crossover point does not necessarily increase the fitness, as the fitness achieved depends on crossover as well as mutation probability. Especially in the paper find minimum cut size. If we get, cut size is same on generation than change the crossover boundary. This paper shows bin packing approach for the circuit partitioning using genetic algorithm . Genetic algorithm is an evolutionary optimization technique based on Darwinian
The CLASS system and the scheduling problem
The need to process large quantities of data on the machine equipment of nuclear power plants and the high level of occurrence of recurrent technological procedures applied in maintenance will create the preconditions for the introduction of automated processing of this data and the subsequent automated control of units of centralized maintenance in nuclear power plants. For the said purposes the Research Institute for Nuclear Power Plants at Jaslovske Bohunice has selected activities suitable for automated processing and has experimentally applied to these activities the CLASS decision-making system operating with the CPM method. It is stated that the automated system for the operative control of repairs of nuclear power plants requires detailed information on conditions from which ensue the inter-relations between repairs. The choice of the most suitable sequence of operations should be left to the program which uses elements of artificial intelligence. Some aspects are discussed of the mathematical model of such a decision-making system in CLASS-AI operative control. (Z.M.)
Solving a Class of Non-Smooth Optimal Control Problems
M. H. Noori Skandari
2013-06-01
Full Text Available In this paper, we first propose a new generalized derivative for non-smooth functions and then we utilize this generalized derivative to convert a class of non-smooth optimal control problem to the corresponding smooth form. In the next step, we apply the discretization method to approximate the obtained smooth problem to the nonlinear programming problem. Finally, by solving the last problem, we obtain an approximate optimal solution for main problem.
Dynamic Multi-class Network Loading Problem
无
2005-01-01
The dynamic network loading problem (DNLP) consists in determining on a congested network, timedependent arc volumes, together with arc and path travel times, given the time varying path flow departure rates over a finite time horizon. The objective of this paper is to present the formulation of an analytical dynamic multiclass network loading model. The model does not require the assumption of the FIFO condition. The existence of a solution to the model is shown.
SPECTRUM OF DIRECTED KIRKMAN PACKING DESIGNS
ZhangYan; DuBeiliang
2003-01-01
The problem studied in this article is the directed Kirkman packing, the resolvable directed packing which requires all blocks to be of size three except that ,each resolution class should contain either one block of size two(when v=2(mod 3)) or one block of size four (when v=l (mod 3)). A directed Kirkman packing design DKPD(v) is a resolvable directed packing of a v-set by the maximum possible number of resolution classes of this type. This article investigates the spectrum of DKPD(v) and it is found that it contains all positive integers v≥3 and v≠5,6.
A dichotomous search-based heuristic for the three-dimensional sphere packing problem
Mhand Hifi
2015-12-01
Full Text Available In this paper, the three-dimensional sphere packing problem is solved by using a dichotomous search-based heuristic. An instance of the problem is defined by a set of $ n $ unequal spheres and an object of fixed width and height and, unlimited length. Each sphere is characterized by its radius and the aim of the problem is to optimize the length of the object containing all spheres without overlapping. The proposed method is based upon beam search, in which three complementary phases are combined: (i a greedy selection phase which determines a series of eligible search subspace, (ii a truncated tree search, using a width-beam search, that explores some promising paths, and (iii a dichotomous search that diversifies the search. The performance of the proposed method is evaluated on benchmark instances taken from the literature where its obtained results are compared to those reached by some recent methods of the literature. The proposed method is competitive and it yields promising results.
Numerical Algorithm for a Class of Linear Fractional Programming Problem
Hongwei Jiao; Kun Li; Jianping Wang
2013-01-01
In this study, a branch and bound algorithm is presented for globally solving a class of linear fractional programming problems. In the algorithm, a linear relaxation method is introduced to generate the linear relaxation programming problem of the investigated linear fractional programming problems. In this study, we pay more attention to the numerical experiments. Several test problems are used to verify the feasibility and computational efficiency of the proposed branch and bound algorithm.
Study on the Uneven cells Problem of the Power Battery Pack in the Automotive Application by ECM
Jiayuan, Wang; Zechang, Sun; Xuezhe, Wei; Haifeng, Dai
Uneven cells problem is a universal phenomenon in the cell grouping application. It will cause performance and safety problems if the uneven is not considered during pack design and application, especially for the automotive application. The ECM model is used for the study of the uneven cells phenomenon of the power battery pack in the automotive application. An EV model and a FCV model are used for simulating the current profiles for two representative powertrain systems. The links of the ECM are set in five conditions for separate study on the impact. The results show different impact on the SOC and voltage with the same sets of links for the two powertrain model. The cell grouping design and the balance algorithm should be adjusted according to the different application background when the uneven cells problems are considered.
Minimax theory for a class of nonlinear statistical inverse problems
Ray, Kolyan; Schmidt-Hieber, Johannes
2016-06-01
We study a class of statistical inverse problems with nonlinear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the nonlinearity. This reduces the initial nonlinear problem to a linear inverse problem with deterministic noise, which is then solved in a second step. The noise reduction step is based on wavelet thresholding and is shown to be minimax optimal (up to logarithmic factors) in a pointwise function-dependent sense. Our analysis is based on a modified notion of Hölder smoothness scales that are natural in this setting.
An Evaluable Theory for a Class of Migration Problems
G Haag; Weidlich, W.
1983-01-01
A master equation formulation for a class of migration problems describing the spatio-temporal dynamics of a system of regions is introduced. The transition probabilities are functions of trend parameters, which characterize preferences, growth pool and saturation effects. The trend parameters can be determined by regression analysis from the empirical migration matrix. The solution of meanvalue equations yields a nonlinear migration prognosis. The relation between trend parameters and motiva...
Solving a Class of Generalized Nash Equilibrium Problems
Peiyu LI; Guihua LIN
2013-01-01
Generalized Nash equilibrium problem (GNEP) is an important model that has many applications in practice.However,a GNEP usually has multiple or even infinitely many Nash equilibrium points and it is not easy to choose a favorable solution from those equilibria.This paper considers a class of GNEP with some kind of separability.We first extend the so-called normalized equilibrium concept to the stationarity sense and then,we propose an approach to solve the normalized stationary points by reformulating the GNEP as a single optimization problem.We further demonstrate the proposed approach on a GNEP model in similar product markets.
Polynomial approximations of a class of stochastic multiscale elasticity problems
Hoang, Viet Ha; Nguyen, Thanh Chung; Xia, Bingxing
2016-06-01
We consider a class of elasticity equations in {mathbb{R}^d} whose elastic moduli depend on n separated microscopic scales. The moduli are random and expressed as a linear expansion of a countable sequence of random variables which are independently and identically uniformly distributed in a compact interval. The multiscale Hellinger-Reissner mixed problem that allows for computing the stress directly and the multiscale mixed problem with a penalty term for nearly incompressible isotropic materials are considered. The stochastic problems are studied via deterministic problems that depend on a countable number of real parameters which represent the probabilistic law of the stochastic equations. We study the multiscale homogenized problems that contain all the macroscopic and microscopic information. The solutions of these multiscale homogenized problems are written as generalized polynomial chaos (gpc) expansions. We approximate these solutions by semidiscrete Galerkin approximating problems that project into the spaces of functions with only a finite number of N gpc modes. Assuming summability properties for the coefficients of the elastic moduli's expansion, we deduce bounds and summability properties for the solutions' gpc expansion coefficients. These bounds imply explicit rates of convergence in terms of N when the gpc modes used for the Galerkin approximation are chosen to correspond to the best N terms in the gpc expansion. For the mixed problem with a penalty term for nearly incompressible materials, we show that the rate of convergence for the best N term approximation is independent of the Lamé constants' ratio when it goes to {infty}. Correctors for the homogenization problem are deduced. From these we establish correctors for the solutions of the parametric multiscale problems in terms of the semidiscrete Galerkin approximations. For two-scale problems, an explicit homogenization error which is uniform with respect to the parameters is deduced. Together
Pelayo, Alvaro
2007-01-01
We define and solve the toric version of the symplectic ball packing problem, in the sense of listing all 2n-dimensional symplectic-toric manifolds which admit a perfect packing by balls embedded in a symplectic and torus equivariant fashion. In order to do this we first describe a problem in geometric-combinatorics which is equivalent to the toric symplectic ball packing problem. Then we solve this problem using arguments from Convex Geometry and Delzant theory. Applications to symplectic bl...
张德福; 陈胜达; 刘艳娟
2007-01-01
An improved heuristic recursive strategy combining with genetic algorithm is presented in this paper. Firstly, this method searches some rectangles, which have the same length or width, to form some layers without waste space, then it uses the heuristic recur sive strategies to calculate the height of the remaining packing order and uses the evolutionary capability of genetic algorithm to reduce the height. The computational results on several classes of benchmark problems have shown that the presented algorithm can compete with known evolutionary heuristics. It performs better especially for large test problems.
Jiao, Yang; Lau, Timothy; Hatzikirou, Haralampos; Meyer-Hermann, Michael; Joseph C Corbo; Torquato, Salvatore
2014-02-01
Optimal spatial sampling of light rigorously requires that identical photoreceptors be arranged in perfectly regular arrays in two dimensions. Examples of such perfect arrays in nature include the compound eyes of insects and the nearly crystalline photoreceptor patterns of some fish and reptiles. Birds are highly visual animals with five different cone photoreceptor subtypes, yet their photoreceptor patterns are not perfectly regular. By analyzing the chicken cone photoreceptor system consisting of five different cell types using a variety of sensitive microstructural descriptors, we find that the disordered photoreceptor patterns are "hyperuniform" (exhibiting vanishing infinite-wavelength density fluctuations), a property that had heretofore been identified in a unique subset of physical systems, but had never been observed in any living organism. Remarkably, the patterns of both the total population and the individual cell types are simultaneously hyperuniform. We term such patterns "multihyperuniform" because multiple distinct subsets of the overall point pattern are themselves hyperuniform. We have devised a unique multiscale cell packing model in two dimensions that suggests that photoreceptor types interact with both short- and long-ranged repulsive forces and that the resultant competition between the types gives rise to the aforementioned singular spatial features characterizing the system, including multihyperuniformity. These findings suggest that a disordered hyperuniform pattern may represent the most uniform sampling arrangement attainable in the avian system, given intrinsic packing constraints within the photoreceptor epithelium. In addition, they show how fundamental physical constraints can change the course of a biological optimization process. Our results suggest that multihyperuniform disordered structures have implications for the design of materials with novel physical properties and therefore may represent a fruitful area for future
Jiao, Yang; Lau, Timothy; Hatzikirou, Haralampos; Meyer-Hermann, Michael; Corbo, Joseph C.; Torquato, Salvatore
2014-02-01
Optimal spatial sampling of light rigorously requires that identical photoreceptors be arranged in perfectly regular arrays in two dimensions. Examples of such perfect arrays in nature include the compound eyes of insects and the nearly crystalline photoreceptor patterns of some fish and reptiles. Birds are highly visual animals with five different cone photoreceptor subtypes, yet their photoreceptor patterns are not perfectly regular. By analyzing the chicken cone photoreceptor system consisting of five different cell types using a variety of sensitive microstructural descriptors, we find that the disordered photoreceptor patterns are "hyperuniform" (exhibiting vanishing infinite-wavelength density fluctuations), a property that had heretofore been identified in a unique subset of physical systems, but had never been observed in any living organism. Remarkably, the patterns of both the total population and the individual cell types are simultaneously hyperuniform. We term such patterns "multihyperuniform" because multiple distinct subsets of the overall point pattern are themselves hyperuniform. We have devised a unique multiscale cell packing model in two dimensions that suggests that photoreceptor types interact with both short- and long-ranged repulsive forces and that the resultant competition between the types gives rise to the aforementioned singular spatial features characterizing the system, including multihyperuniformity. These findings suggest that a disordered hyperuniform pattern may represent the most uniform sampling arrangement attainable in the avian system, given intrinsic packing constraints within the photoreceptor epithelium. In addition, they show how fundamental physical constraints can change the course of a biological optimization process. Our results suggest that multihyperuniform disordered structures have implications for the design of materials with novel physical properties and therefore may represent a fruitful area for future
Positive solutions for classes of multiparameter elliptic semipositone problems
Sumalee Unsurangsie
2007-06-01
Full Text Available We study positive solutions to multiparameter boundary-value problems of the form egin{gather*} - Delta u =lambda g(u+mu f(uquad ext{in } Omega \\ u =0 quad ext{on } partial Omega , end{gather*} where $lambda >0$, $mu >0$, $Omega subseteq R^{n}$; $ngeq 2$ is a smooth bounded domain with $partial Omega $ in class $C^{2}$ and $Delta $ is the Laplacian operator. In particular, we assume $g(0>0$ and superlinear while $f(0<0$, sublinear, and eventually strictly positive. For fixed $mu$, we establish existence and multiplicity for $lambda $ small, and nonexistence for $lambda $ large. Our proofs are based on variational methods, the Mountain Pass Lemma, and sub-super solutions.
A Personified Annealing Algorithm for Circles Packing Problem%求解圆形packing问题的拟人退火算法
张德富; 李新
2005-01-01
Circles packing problem is an NP-hard problem and is difficult to solve. In this paper, a hybrid search strategy for circles packing problem is discussed. A way of generating new configuration is presented by simulating the moving of elastic objects, which can avoid the blindness of simulated annealing search and make iteration process converge fast. Inspired by the life experiences of people,an effective personified strategy to jump out of local minima is given. Based on the simulated annealing idea and personification strategy, an effective personified annealing algorithm for circles packing problem is developed. Numerical experiments on benchmark problem instances show that the proposed algorithm outperforms the best algorithm in the literature.
An evolutionary approach to the problem of three-dimensional geometric objects packing
Крижанівський, В'ячеслав Борисович; Шавурська, Ганна Павлівна
2014-01-01
A problem of optimal placement of three-dimensional geometric objects is considered. The position of geometric objects is determined by solving linear programming problems. A search in linear programming problems set is implemented using a genetic algorithm. Designed and implemented a software product that allows you to examine the behavior of genetic algorithms depending on the population size, selection operators of pair of "parents", the type of crossover, selection operator of individuals...
George Cristian Gruia
2013-05-01
Full Text Available In the aviation industry, propeller motor engines have a lifecycle of several thousand hours of flight and the maintenance is an important part of their lifecycle. The present article considers a multi-resource, priority-based case scheduling problem, which is applied in a Romanian manufacturing company, that repairs and maintains helicopter and airplane engines at a certain quality level imposed by the aviation standards. Given a reduced budget constraint, the management’s goal is to maximize the utilization of their resources (financial, material, space, workers, by maintaining a prior known priority rule. An Off-Line Dual Maximum Resource Bin Packing model, based on a Mixed Integer Programming model is thus presented. The obtained results show an increase with approx. 25% of the Just in Time shipping of the engines to the customers and approx. 12,5% increase in the utilization of the working area.
Kumar, Saravana
2013-01-01
The higher education sector is undergoing tremendous change, driven by complex driving forces including financial, administrative, and organisational and stakeholder expectations. It is in this challenging environment, educators are required to maintain and improve the quality of teaching and learning outcomes while contending with increasing class sizes. Despite mixed evidence on the effectiveness of large classes on student outcomes, large classes continue to play an important part in higher education. While large classes pose numerous challenges, they also provide opportunities for innovative solutions. This paper provides an overview of these challenges and highlights opportunities for innovative solutions. PMID:24358851
Jia-qi Mo; Wan-tao Lin
2006-01-01
A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems is studied using the theory of differential inequalities.
Minimizers of a Class of Constrained Vectorial Variational Problems: Part I
Hajaiej, Hichem
2014-04-18
In this paper, we prove the existence of minimizers of a class of multiconstrained variational problems. We consider systems involving a nonlinearity that does not satisfy compactness, monotonicity, neither symmetry properties. Our approach hinges on the concentration-compactness approach. In the second part, we will treat orthogonal constrained problems for another class of integrands using density matrices method. © 2014 Springer Basel.
Online Stochastic Packing Applied to Display Ad Allocation
Feldman, Jon; Henzinger, Monika; Korula, Nitish; Mirrokni, Vahab S.; Stein, Cliff
2010-01-01
Inspired by online ad allocation, we study online stochastic packing linear programs from theoretical and practical standpoints. We first present a near-optimal online algorithm for a general class of packing linear programs which model various online resource allocation problems including online variants of routing, ad allocations, generalized assignment, and combinatorial auctions. As our main theoretical result, we prove that a simple primal-dual training-based algorithm achieves a (1 - o(...
Optimized packings with applications
Pintér, János
2015-01-01
This volume presents a selection of case studies that address a substantial range of optimized object packings (OOP) and their applications. The contributing authors are well-recognized researchers and practitioners. The mathematical modelling and numerical solution aspects of each application case study are presented in sufficient detail. A broad range of OOP problems are discussed: these include various specific and non-standard container loading and object packing problems, as well as the stowing of hazardous and other materials on container ships, data centre resource management, automotive engineering design, space station logistic support, cutting and packing problems with placement constraints, the optimal design of LED street lighting, robust sensor deployment strategies, spatial scheduling problems, and graph coloring models and metaheuristics for packing applications. Novel points of view related to model development and to computational nonlinear, global, mixed integer optimization and heuristic st...
Quasiperiodic packing densities
The problem of the packing density on quasiperiodic lattices is discussed in a systematic way using projection techniques. For compact domains a direct construction is presented using a Voronoi construction on a quasilattice in perpendicular space defined by the forbidden volume of the packed objects. A generalized inflation law, valid for arbitrary shapes of the acceptance domain using the properties of linear mappings of the hyperlattice on itself which commute with the symmetry group, is used to show that the packing densities and the whole structure of the projected quasilattice are periodic under scale transformations. We find the optimal compact acceptance domains and packing densities for several icosahedral problems. For the packing of spheres on the primitive lattice, an icosahedron and the truncated triacontahedron give equal densities but different quasilattices. For the packing of icosahedra one finds only the second lattice and a very high density. For the fcc and bcc lattices the maximum density acceptance domain is a triacontahedron and the densities are considerably lower. The results of Henley for including correlations to increase the density are reformulated in terms of a graph problem in perpendicular space. Including only the graphs equivalent to his, we find the same packing density for the two primitive and for the fcc lattice. It is shown that a generalization leads to an interesting and very complex problem in graph theory which we are unable to solve
An object oriented C++ class library for solving electromagnetic time domain problems
The author has developed a C++ class library to solve three dimensional electromagnetic transient problems. All the data and method for solving field are defined as classes and users can build their specific application using these classes of the library. In the first part of this paper, the algorithms and class structure of the library are described. Three application examples are shown in the rest part. Showing these examples the ease of merging with the advanced computer environment and the enhancability of the library to a specific problem are shown
An object oriented C++ class library for solving electromagnetic time domain problems
The author has developed a C++ class library to solve three dimensional electromagnetic transient problems. All the data and method for solving field are defined as classes and users can build their specific application using these classes of the library. In the first part of this paper, the algorithms and class structure of the library are described. Three application examples are shown in the rest part. Showing these examples the ease of merging with the advanced computer environment and the enhancability of the library to a specific problem are shown. copyright 1997 American Institute of Physics
Renormalization problem in a class of nonrenormalizable theories
A possible way to approach the simplest nonrenormalizable theory - phi4 theory in more than four space-time dimensions - is described. The problems of extension to other nonrenormalizable theories are discussed and the conclusions reached so far are compared with the corresponding ones for renormalizable theories. For more details, Comm. Math. Phys. or DESY 75/12 should be consulted. (BJ)
Doyle Scott
2011-10-01
Full Text Available Abstract Background Supervised classifiers for digital pathology can improve the ability of physicians to detect and diagnose diseases such as cancer. Generating training data for classifiers is problematic, since only domain experts (e.g. pathologists can correctly label ground truth data. Additionally, digital pathology datasets suffer from the "minority class problem", an issue where the number of exemplars from the non-target class outnumber target class exemplars which can bias the classifier and reduce accuracy. In this paper, we develop a training strategy combining active learning (AL with class-balancing. AL identifies unlabeled samples that are "informative" (i.e. likely to increase classifier performance for annotation, avoiding non-informative samples. This yields high accuracy with a smaller training set size compared with random learning (RL. Previous AL methods have not explicitly accounted for the minority class problem in biomedical images. Pre-specifying a target class ratio mitigates the problem of training bias. Finally, we develop a mathematical model to predict the number of annotations (cost required to achieve balanced training classes. In addition to predicting training cost, the model reveals the theoretical properties of AL in the context of the minority class problem. Results Using this class-balanced AL training strategy (CBAL, we build a classifier to distinguish cancer from non-cancer regions on digitized prostate histopathology. Our dataset consists of 12,000 image regions sampled from 100 biopsies (58 prostate cancer patients. We compare CBAL against: (1 unbalanced AL (UBAL, which uses AL but ignores class ratio; (2 class-balanced RL (CBRL, which uses RL with a specific class ratio; and (3 unbalanced RL (UBRL. The CBAL-trained classifier yields 2% greater accuracy and 3% higher area under the receiver operating characteristic curve (AUC than alternatively-trained classifiers. Our cost model accurately predicts
Wang Geng
2006-01-01
A class of nonlinear two-species competitive singularly perturbed initial-boundary-value problems for reaction-diffusion systems are studied. Under suitable assumptions, by using the stretched variable, the formal asymptotic expansion for the problems is constructed. The uniform validity of the solution for initial-boundary-value problems is obtained by using the theory of differential inequalities.
A CLASS OF NONLINEAR SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS
莫嘉琪
2003-01-01
A class of nonlinear singularly perturbed problems for reaction diffusion equations are considered.Under suitable conditions,by using the theory of differential inequalities,the asymptotic behavior of solutions for the initial boundary value problems are studied,reduced problems of which possess two intersecting solutions.
Local solution for a class of mixed boundary value problems
A local method is developed for solving locally partial differential equations with mixed boundary conditions. The method is based on a heuristic idea, properties of diffusion processes, stopping times and the Ito formula for semimartingales. According to the heuristic idea, the diffusion process used for solving locally a partial differential with mixed boundary conditions is stopped when it reaches a Neumann boundary and then restarted inside the domain of definition of this equation at a point depending on the Neumann conditions. The proposed method is illustrated and its accuracy assessed by two simple numerical examples solving locally mixed boundary value problems in one and two space dimensions
A CLASS OF SINGULARLY PERTURBED INITIAL BOUNDARY PROBLEM FOR REACTION DIFFUSION EQUATION
Xie Feng
2003-01-01
The singularly perturbed initial boundary value problem for a class of reaction diffusion equation isconsidered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solu-tion are showed by using the fixed-point theorem.
An Analysis on the Problem of Students’ Engagement in English Class
陈瑜
2015-01-01
Students’ engagement in English class is a common problem facing by English teachers.This study analyzes the factors which influence students’ classroom engagement, tries to find out possible solutions to solve this problem from the perspective of SLA theory and teaching approaches and gives implications for future teaching.
ADOPTING THE PROBLEM BASED LEARNING APPROACH IN A GIS PROJECT MANAGEMENT CLASS
Problem Based Learning (PBL) is a process that emphasizes the need for developing problem solving skills through hands-on project formulation and management. A class adopting the PBL method provides students with an environment to acquire necessary knowledge to encounter, unders...
McCoy, Bradley
2011-04-01
General studies science classes at many universities, such as physical science, earth science, or astronomy, stress memorization and repetition of concepts. This approach leaves students with little appreciation for how science is used to explain phenomena from general principles. We present a novel instructional technique for an earth science class in which the students are instructed in the use of a general problem solving strategy, adapted from well-known quantitative problem solving strategies, in order to train the students in how to apply physical principles. Using the Epistemological Beliefs Assessment for Physical Science, we have found that explicit training in problem solving significantly improves students' epistemology.
Does the non-identity problem block a class of arguments against cloning?
Green, Richard
2004-01-01
One class of argument against cloning human beings in the contemporary literature focuses on the bad consequences that will befall the clone or "later-twin." In this paper I consider whether this line of argumentation can be blocked by invoking Parfit's non-identity problem. I canvass two general strategies for solving the non-identity problem: a consequentialist strategy and non-consequentialist, rights based strategy. I argue that while each general strategy offers a plausible solution to the non-identity problem as applied to the cases most frequently discussed in the non-identity problem literature, neither provides a reason for putting aside the non-identity problem when applied to cloning. I conclude (roughly) that the non-identity problem does serve to block this class of argument against cloning. PMID:15468498
Problem-Based Inquiry on World Water Problems in Large Undergraduate Classes
Halvorson, Sarah J.; Wescoat, James L., Jr.
2002-01-01
This paper reports on the design and implementation of a project-based course--World Water Problems--that was introduced within the framework of introductory undergraduate geography education. The aims of the course were twofold: (1) to cultivate in students a world geographic perspective on water problems; and (2) to conduct an original research…
Barış ÇETİN
2013-04-01
Full Text Available The aim this study is to determine the undesired behaviors of students that class teachers faced in the classroom and their solutions. The sample of the study consists of 37 class teachers working in the provinces of Gumushane, Canakkale, Erzurum, Istanbul, Tekirdag, Kocaeli, Kutahya, Bursa, Samsun, Eskisehir, and Mus in Turkey in the fall term of 2011-2012 academic year. As a result, the undesired behaviors of students that teachers faced in the classroom have been determined as not obeying the class rules, swearing, talking without permission, shyness, hyperactivity and lack of attention, and problems caused by watching violent TV programs (such as threatening. Solutions to these problems have been stated as: punishments and awards, warning, ignoring, behaving more sincerely towards students, including students by means of activities, guidance service, giving assignment, making students sit in front of the class, and playing games.
Nazan Karaoğlu; Sevgi Pekcan; Burak Cem Soner; Muzaffer Şeker; Rahmi Örs
2011-01-01
Introduction: It is stated that students cannot carry their knowledge on basic medical sciences that they gained with classical education to clinical classes and clinical practice and problem based learning (PBL) can compensate this drawback. It was aimed to evaluate the effect of PBL scenario written on this topic on level of knowledge about childhood poisoning of third class students who completed the most of theoretical pharmacology education.Materials and Method: A questionnaire form prep...
Online Mixed Packing and Covering
Bhaskar, Umang
2012-01-01
In many problems, the inputs arrive over time, and must be dealt with irrevocably when they arrive. Such problems are online problems. A common method of solving online problems is to first solve the corresponding linear program, and then round the fractional solution online to obtain an integral solution. We give algorithms for solving linear programs with mixed packing and covering constraints online. We first consider mixed packing and covering linear programs, where packing constraints are given offline and covering constraints are received online. The objective is to minimize the maximum multiplicative factor by which any packing constraint is violated, while satisfying the covering constraints. No prior sublinear competitive algorithms are known for this problem. We give the first such --- a polylogarithmic-competitive algorithm for solving mixed packing and covering linear programs online. We also show a nearly tight lower bound. Our techniques for the upper bound use an exponential penalty function in...
Random sequential packing of cubes
Sikiric, Mathieu Dutour
2011-01-01
In this volume very simplified models are introduced to understand the random sequential packing models mathematically. The 1-dimensional model is sometimes called the Parking Problem, which is known by the pioneering works by Flory (1939), Renyi (1958), Dvoretzky and Robbins (1962). To obtain a 1-dimensional packing density, distribution of the minimum of gaps, etc., the classical analysis has to be studied. The packing density of the general multi-dimensional random sequential packing of cubes (hypercubes) makes a well-known unsolved problem. The experimental analysis is usually applied to t
MO Jia-qi; WANG Hui; LIN Wan-tao
2005-01-01
A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, first, the outer solution of the original problem was obtained. Secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer was constructed. Finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems was studied, and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation were discussed.
Class and Home Problems: Humidification, a True "Home" Problem for p. Chemical Engineer
Condoret, Jean-Stephane
2012-01-01
The problem of maintaining hygrothermal comfort in a house is addressed using the chemical engineer's toolbox. A simple dynamic modelling proved to give a good description of the humidification of the house in winter, using a domestic humidifier. Parameters of the model were identified from a simple experiment. Surprising results, especially…
Regular Totally Separable Sphere Packings
Reid, Samuel
2015-01-01
The topic of totally separable sphere packings is surveyed with a focus on regular constructions, uniform tilings, and contact number problems. An enumeration of all regular totally separable sphere packings in $\\mathbb{R}^2$, $\\mathbb{R}^3$, and $\\mathbb{R}^4$ which are based on convex uniform tessellations, honeycombs, and tetracombs, respectively, is presented, as well as a construction of a family of regular totally separable sphere packings in $\\mathbb{R}^d$ that is not based on a convex...
A class of neutral functional differential equations and the abstract Cauchy problem
In this paper we establish the basic equivalence between the generalized solutions of a certain class of Neutral Functional Differential Equations and the trajectories of the associated abstract Cauchy problem. These results have applications in several fields including Mathematical Biology, Ecology and Control Theory. (author)
Hydrostatic Pressure Project: Linked-Class Problem-Based Learning in Engineering
Davis, Freddie J.; Lockwood-Cooke, Pamela; Hunt, Emily M.
2011-01-01
Over the last few years, WTAMU Mathematics, Engineering and Science faculty has used interdisciplinary projects as the basis for implementation of a linked-class approach to Problem-Based Learning (PBL). A project that has significant relevance to engineering statics, fluid mechanics, and calculus is the Hydrostatic Pressure Project. This project…
A first passage problem and its applications to the analysis of a class of stochastic models
Lev Abolnikov
1992-01-01
Full Text Available A problem of the first passage of a cumulative random process with generally distributed discrete or continuous increments over a fixed level is considered in the article as an essential part of the analysis of a class of stochastic models (bulk queueing systems, inventory control and dam models.
On a class of non-self-adjoint periodic boundary value problems with discrete real spectrum
Boulton, Lyonell; Levitin, Michael; Marletta, Marco
2010-01-01
In [arXiv:0801.0172] we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the associated resolvent operator.
Global solutions to a class of CEC benchmark constrained optimization problems
Zhou, Xiaojun
2012-01-01
This paper aims to solve a class of CEC benchmark constrained optimization problems that have been widely studied by nature-inspired optimization algorithms. Global optimality condition based on canonical duality theory is derived. Integrating the dual solutions with the KKT conditions, we are able to obtain the approximate solutions or global solutions easily.
Sevening, Diane; Baron, Mark
2002-01-01
Study compared students' achievement gains and attitudes using traditional (lecture-based) teaching methods and problem-based learning (PBL) techniques in an addiction studies class. Results showed students did not respond well to PBL and preferred a lecture-based format. Pretest mean scores indicated the PBL group entered the course at a higher…
2011-08-16
In this podcast for kids, the Kidtastics talk about how to pack a lunch safely, to help keep you from getting sick. Created: 8/16/2011 by National Center for Emerging and Zoonotic Infectious Diseases (NCEZID). Date Released: 8/16/2011.
2011-08-22
In this podcast for kids, the Kidtastics talk about packing a lunch that's not boring and is full of the power and energy kids need to make it through the day. Created: 8/22/2011 by National Center for Emerging and Zoonotic Infectious Diseases (NCEZID). Date Released: 8/22/2011.
Optimal Packed String Matching
Ben-Kiki, Oren; Bille, Philip; Breslauer, Dany;
2011-01-01
In the packed string matching problem, each machine word accommodates – characters, thus an n-character text occupies n/– memory words. We extend the Crochemore-Perrin constantspace O(n)-time string matching algorithm to run in optimal O(n/–) time and even in real-time, achieving a factor – speedup...
Formulation space search approach for the teacher/class timetabling problem
Kochetov Yuri
2008-01-01
Full Text Available We consider the well known NP-hard teacher/class timetabling problem. Variable neighborhood search and tabu search heuristics are developed based on idea of the Formulation Space Search approach. Two types of solution representation are used in the heuristics. For each representation we consider two families of neighborhoods. The first family uses swapping of time periods for teacher (class timetable. The second family bases on the idea of large Kernighan-Lin neighborhoods. Computation results for difficult random test instances show high efficiency of the proposed approach. .
L1-norm packings from function fields
LI; Hongli
2005-01-01
In this paper, we study some packings in a cube, namely, how to pack n points in a cube so as to maximize the minimal distance. The distance is induced by the L1-norm which is analogous to the Hamming distance in coding theory. Two constructions with reasonable parameters are obtained, by using some results from a function field including divisor class group, narrow ray class group, and so on. We also present some asymptotic results of the two packings.
Degraeve, Zeger; Peeters, Marc
2000-01-01
In this paper we present a new method for solving the linear programming relaxation of the Cutting Stock Problem. The method is based on the relationship between column generation and Lagrange relaxation. We have called our method the Hybrid Simplex Method/Subgradient Optimization Procedure. We test our procedure on generated data sets and compare it with the classical column generation approach.
Mo Jiaqi
2007-01-01
A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptotic solution of the initial boundary value problems is studied.
Haack, Constance
This study was an exploration of students' use of scaffolded problems as part of their homework in an introductory calculus-based physics class. The study included consideration of the possible relationship of students' meaningful and rote learning approaches. The sample was comprised of 48 students who had completed all study instruments. Of this number, 23 did homework assignments that included scaffolded problems that had been divided into multiple steps that simplify, highlight, and organize the knowledge associated with the problem solving process. The other 25 students did non-scaffolded homework assignments. The Mechanics Baseline Test, given at the beginning of the study, measured students' prior knowledge of physics concepts. The Learning Approach Questionnaire, also given at the beginning of the study, measured students' meaningful and rote approaches to learning. Student responses to 6 qualitative physics problems and their selection of concepts associated with 4 quantitative physics problems was a gauge of their understanding of physics concepts. These 10 problems were distributed between 2 classroom examinations given during the study. At the end of the study 4 students who had done scaffolded homework problems and 4 students who had done non-scaffolded homework problems participated in think aloud protocols. They verbalized their thoughts as they attempted to solve 2 physics problems. Characterizations of individual problem solving approaches emerged from the think aloud protocols. An analysis of statistical data showed that students who did scaffolded problems attained significantly greater understanding of physics concepts than students who did non-scaffolded assignments. There were no significant differences by learning approaches, and no significant interactions. This indicates that scaffolded homework problems may benefit students regardless of learning orientation. Think aloud protocols revealed patterns of difference between students who had
Sahay Rishi R.
2013-01-01
Full Text Available A second order Mond-Weir type dual is presented for a non-differentiable multiobjective optimization problem with square root terms in the objective as well as in the constraints. Optimality and duality results are presented. Classes of generalized higher order η - bonvex and related functions are introduced to study the optimality and duality results. A fractional case is presented at the end.
Improving classification of mature microRNA by solving class imbalance problem
Wang, Ying; Li, Xiaoye; Tao, Bairui
2016-05-01
MicroRNAs (miRNAs) are ~20–25 nucleotides non-coding RNAs, which regulated gene expression in the post-transcriptional level. The accurate rate of identifying the start sit of mature miRNA from a given pre-miRNA remains lower. It is noting that the mature miRNA prediction is a class-imbalanced problem which also leads to the unsatisfactory performance of these methods. We improved the prediction accuracy of classifier using balanced datasets and presented MatFind which is used for identifying 5‧ mature miRNAs candidates from their pre-miRNA based on ensemble SVM classifiers with idea of adaboost. Firstly, the balanced-dataset was extract based on K-nearest neighbor algorithm. Secondly, the multiple SVM classifiers were trained in orderly using the balance datasets base on represented features. At last, all SVM classifiers were combined together to form the ensemble classifier. Our results on independent testing dataset show that the proposed method is more efficient than one without treating class imbalance problem. Moreover, MatFind achieves much higher classification accuracy than other three approaches. The ensemble SVM classifiers and balanced-datasets can solve the class-imbalanced problem, as well as improve performance of classifier for mature miRNA identification. MatFind is an accurate and fast method for 5‧ mature miRNA identification.
Improving classification of mature microRNA by solving class imbalance problem.
Wang, Ying; Li, Xiaoye; Tao, Bairui
2016-01-01
MicroRNAs (miRNAs) are ~20-25 nucleotides non-coding RNAs, which regulated gene expression in the post-transcriptional level. The accurate rate of identifying the start sit of mature miRNA from a given pre-miRNA remains lower. It is noting that the mature miRNA prediction is a class-imbalanced problem which also leads to the unsatisfactory performance of these methods. We improved the prediction accuracy of classifier using balanced datasets and presented MatFind which is used for identifying 5' mature miRNAs candidates from their pre-miRNA based on ensemble SVM classifiers with idea of adaboost. Firstly, the balanced-dataset was extract based on K-nearest neighbor algorithm. Secondly, the multiple SVM classifiers were trained in orderly using the balance datasets base on represented features. At last, all SVM classifiers were combined together to form the ensemble classifier. Our results on independent testing dataset show that the proposed method is more efficient than one without treating class imbalance problem. Moreover, MatFind achieves much higher classification accuracy than other three approaches. The ensemble SVM classifiers and balanced-datasets can solve the class-imbalanced problem, as well as improve performance of classifier for mature miRNA identification. MatFind is an accurate and fast method for 5' mature miRNA identification. PMID:27181057
Vegh, Laszlo A
2011-01-01
A well-studied nonlinear extension of the minimum-cost flow problem is to minimize the objective \\sum_{ij\\in E} C_{ij}(f_{ij}) over feasible flows f, where on each arc ij of the network, C_{ij} is a convex function. We give a strongly polynomial algorithm for finding an exact optimal solution for a broad class of such problems. The key characteristic of this class is that an optimal solution can be computed exactly provided its support. The class includes convex quadratic objectives and also certain market equilibria problems, such as Fisher's market with linear or with spending constraint utilities. Thereby we give the first strongly polynomial algorithms for separable quadratic minimum-cost flows and for Fisher's market with spending constraint utilities, settling open questions posed e.g. in [Hochbaum,94] and in [Vazirani,10], respectively. The running time is O(m^4\\log m) for quadratic costs, O(n^2(m+n\\log n)\\log n+n^4) for Fisher's markets with linear utilities and O(m^2(m+n\\log n)\\log m+m(n^3+m)) for sp...
Analysis and formulation of a class of complex dynamic optimization problems
Kameswaran, Shivakumar
The Direct Transcription approach, also known as the direct simultaneous approach, is a widely used solution strategy for the solution of dynamic optimization problems involving differential-algebraic equations (DAEs). Direct transcription refers to the procedure of approximating the infinite dimensional problem by a finite dimensional one, which is then solved using a nonlinear programming (NLP) solver tailored to large-scale problems. Systems governed by partial differential equations (PDEs) can also be handled by spatially discretizing the PDEs to convert them to a system of DAEs. The objective of this thesis is firstly to ensure that direct transcription using Radau collocation is provably correct, and secondly to widen the applicability of the direct simultaneous approach to a larger class of dynamic optimization and optimal control problems (OCPs). This thesis aims at addressing these issues using rigorous theoretical tools and/or characteristic examples, and at the same time use the results for solving large-scale industrial applications to realize the benefits. The first part of this work deals with the analysis of convergence rates for direct transcription of unconstrained and final-time equality constrained optimal control problems. The problems are discretized using collocation at Radau points. Convergence is analyzed from an NLP/matrix-algebra perspective, which enables the prediction of the conditioning of the direct transcription NLP as the mesh size becomes finer. Several convergence results are presented along with tests on numerous example problems. These convergence results lead to an adjoint estimation procedure given the Lagrange multipliers for the large-scale NLP. The work also reveals the role of process control concepts such as controllability on the convergence analysis, and provides a very important link between control and optimization inside the framework of dynamic optimization. As an effort to extend the applicability of the direct
On the efficient solvability of a simple class of nonlinear knapsack problems
SE Visagie
2008-06-01
Full Text Available In this paper the efficient solvability of a class of nonlinear knapsack problems are investigated by means of the problem's necessary and sufficient conditions. It is shown that, from the general theory, it is impossible to determine sufficient conditions for a solution to be globally optimal. Furthermore, it is shown that even for the smallest possible instance of this problem it is, in general, possible to have an arbitrary large number of solutions for which the necessary conditions hold. These results are then generalised to larger instances of the problem. A possible solution approach is applied to sets of randomly generated problems that utilises the necessary conditions together with the branch-and-bound technique in an attempt to limit the search space. This approach solves mixed 0/1 knapsack problems in order to find all possible solutions satisfying the necessary conditions. Due to the large number of solutions satisfying the necessary conditions the proposed solution approach takes substantially longer than existing branch-and-bound algorithms together with linear enveloping when applied to the same set of problems. This result renders the proposed approach not very efficient.
Enhancing Higher Order Thinking Skills In A Marine Biology Class Through Problem-Based Learning
Richard M. Magsino
2014-10-01
Full Text Available The purpose of this research was to examine students' perspectives of their learning in marine biology in the collaborative group context of Problem-based Learning (PBL. Students’ higher order thinking skills (HOTS using PBL involves the development of their logical thinking and reasoning abilities which stimulates their curiosity and associative thinking. This study aimed to investigate how critical thinking skills, particularly analysis, synthesis and evaluation were enhanced in a marine biology class through PBL. Qualitative research approach was used to examine student responses in a questionnaire involving 10 open-ended questions that target students’ HOTS on a problem presented in a marine biology class for BS Biology students. Using axial coding as a qualitative data analysis technique by which grounded theory can be performed, the study was able to determine how students manifest their higher reasoning abilities when confronted with a marine biology situation. Results show student responses yielding affirmative remarks on the 10 questions intended to know their level of analysis (e.g., analyzing, classifying, inferring, discriminating and relating or connecting, synthesis (e.g., synthesizing and collaborating, and evaluation (e.g., comparing, criticizing, and convincing of information from the presented marine biology problem. Consequently, students were able to effectively design experiments to address the presented issue through problem-based learning. Results of the study show that PBL is an efficient instructional strategy embedded within a conventional curriculum used to develop or enhance critical thinking in marine biology.
Finite element formulation and solution of a class of contact-impact problems in contimuum mechanics
Contact-impact phenomena are of importance in many areas of science and technlology, e.g. in nuclear reactor technology where the solution of structural problems involving contact-impact effects is crucial to the design of safe reactor systems. In recent years large-scale computational capabilities have been developed for many areas of structural analysis, the primary technique being the finite element method. At the same time, very few developments have occurred which address themselves to complicated structural problems involving contact-impact effects, and those developments which have been made are of limited generality. The reasons for this lack of development are simple: contact-impact phenomena are inherently nonlinear and the resulting problems are difficult. In this paper the results are described of a research program to develop a finite element formulation and solution procedure for contact-impact problems of a particular class which are termed Hertzian problems. Briefly, Hertzian problems are characterized by the conditions that the contact surface is approximately planar and that the contacting structures have undergone 'small' straining in the neighborhood of the contact surface. (Auth.)
Saravana Kumar
2013-01-01
The higher education sector is undergoing tremendous change, driven by complex driving forces including financial, administrative, and organisational and stakeholder expectations. It is in this challenging environment, educators are required to maintain and improve the quality of teaching and learning outcomes while contending with increasing class sizes. Despite mixed evidence on the effectiveness of large classes on student outcomes, large classes continue to play an important part in highe...
Class attendance and cardiology examination performance: a study in problem-based medical curriculum
Bamuhair SS; Al Farhan AI; Althubaiti A; ur Rahman S; Al-Kadri HM
2016-01-01
Samira S Bamuhair,1 Ali I Al Farhan,1,2 Alaa Althubaiti,1 Saeed ur Rahman,1,2 Hanan M Al-Kadri1,3 1College of Medicine, King Saud Bin Abdulaziz University for Health Sciences, 2Department of Family Medicine and Primary Health Care, 3Department of Obstetrics and Gynecology, King Abdulaziz Medical City, Riyadh, Saudi Arabia Background and aims: Information on the effect of students' class attendance on examination performance in a problem-based learning medical curriculum is limited. T...
A Class of Singular Control Problems and the Smooth Fit Principle
Guo, Xin; Tomecek, Pascal
2007-01-01
This paper analyzes a class of singular control problems for which value functions are not necessarily smooth. Necessary and su±cient conditions for the well-known smooth ¯t principle, along with the regularity of the value functions, are given. Explicit solutions for the optimal policy and for the value functions are provided. In particular, when payo® functions satisfy the usual Inada conditions, the boundaries between action and no-action regions are smooth and strictly monotonic as postul...
Research on the Optimal Parallel Algorithms of Broadcast—Class Problems
李晓峰; 寿标; 等
1998-01-01
Speedup is considered as the criterion of determining whether a parallel algorithm is optimal.But broadcast-class problems,existing only on parallel computer system,have no sequential algorithms at all.Speedup standard becomes invalid here.Through this research on broadcast algorithms under several typical prallel computation models,a model-independent evaluation standard min C2 is developed,which can be not only used to determine an optimal broadcasting algorithm,but also normalized to apply to any parallel algorithm.As a new idea,min C2 will lead to a new way in this field.
Mond Weir Dual and Wolf Dual in a Class of Nonsmooth Programming Problems
TANG Li-ping
2010-01-01
Full Text Available In this paper duality in a class of nonsmooth programming problem with equality and inequality constraints is considered. Weak duality, strong duality, converse duality and strict converse duality are researched in Mond Weir dual under strict invexity of . Weak duality and strong duality are researched in Wolf dual under invexity of and restricted converse duality and strict converse duality are researched under strict invexity. Some corresponding duality theorems are proved without any constraints. Our results generalize and improve some known results.
A multiplicity result for a class of quasilinear elliptic and parabolic problems
M. R. Grossinho
1997-04-01
Full Text Available We prove the existence of infinitely many solutions for a class of quasilinear elliptic and parabolic equations, subject respectively to Dirichlet and Dirichlet-periodic boundary conditions. We assume that the primitive of the nonlinearity at the right-hand side oscillates at infinity. The proof is based on the construction of upper and lower solutions, which are obtained as solutions of suitable comparison equations. This method allows the introduction of conditions on the potential for the study of parabolic problems, as well as to treat simultaneously the singular and the degenerate case.
Error estimates for a certain class of elliptic optimal control problems
Mali, Olli
2014-01-01
In this paper, error estimates are presented for a certain class of optimal control problems with elliptic PDE-constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state equation. The functional a posteriori error estimates developed by Repin in late 90's are applied to estimate the cost function value from both sides without requiring the exact solution of the state equation. Moreover, a lower bound for the minimal cost fun...
The pack contains teaching material to supply factual information about nuclear energy for those teaching physics or chemistry or general science for GCE examinations. It is intended for use either in class teaching or in some forms of resource-based learning systems. The material comprises: illustrated booklets and accompanying filmstrips on (1) energy from atoms, (2) ionising radiation and its detection, (3) nuclear reactors, and (4) the uses of radioisotopes; wallcharts on (1) nuclear fuel cycle, (2) radioactivity at work, and (3) nuclear reactors for producing electricity; glossary of atomic terms; and teachers' guide. (U.K.)
A class of singular Ro-matrices and extensions to semidefinite linear complementarity problems
Sivakumar K.C.
2013-01-01
Full Text Available For ARnxn and qRn, the linear complementarity problem LCP(A, q is to determine if there is xRn such that x ≥ 0; y = Ax + q ≥ 0 and xT y = 0. Such an x is called a solution of LCP(A,q. A is called an Ro-matrix if LCP(A,0 has zero as the only solution. In this article, the class of R0-matrices is extended to include typically singular matrices, by requiring in addition that the solution x above belongs to a subspace of Rn. This idea is then extended to semidefinite linear complementarity problems, where a characterization is presented for the multplicative transformation.
We develop two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in combination with the Feynman-Kleinert approximation of the density operator. These dynamics are used to improve the Feynman-Kleinert implementation of the classical Wigner approximation for the evaluation of quantum time correlation functions known as Feynman-Kleinert linearized path-integral. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics is made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that these dynamics provide a great improvement over the classical Wigner approximation, in which purely classical dynamics are used. In a special case, our first method becomes identical to centroid molecular dynamics
The pursuit of perfect packing
Weaire, Denis
2008-01-01
Coauthored by one of the creators of the most efficient space packing solution, the Weaire-Phelan structure, The Pursuit of Perfect Packing, Second Edition explores a problem of importance in physics, mathematics, chemistry, biology, and engineering: the packing of structures. Maintaining its mathematical core, this edition continues and revises some of the stories from its predecessor while adding several new examples and applications. The book focuses on both scientific and everyday problems ranging from atoms to honeycombs. It describes packing models, such as the Kepler conjecture, Voronoï decomposition, and Delaunay decomposition, as well as actual structure models, such as the Kelvin cell and the Weaire-Phelan structure. The authors discuss numerous historical aspects and provide biographical details on influential contributors to the field, including emails from Thomas Hales and Ken Brakke. With examples from physics, crystallography, engineering, and biology, this accessible and whimsical bo...
Jing Bian
2016-01-01
Full Text Available In the era of big data, feature selection is an essential process in machine learning. Although the class imbalance problem has recently attracted a great deal of attention, little effort has been undertaken to develop feature selection techniques. In addition, most applications involving feature selection focus on classification accuracy but not cost, although costs are important. To cope with imbalance problems, we developed a cost-sensitive feature selection algorithm that adds the cost-based evaluation function of a filter feature selection using a chaos genetic algorithm, referred to as CSFSG. The evaluation function considers both feature-acquiring costs (test costs and misclassification costs in the field of network security, thereby weakening the influence of many instances from the majority of classes in large-scale datasets. The CSFSG algorithm reduces the total cost of feature selection and trades off both factors. The behavior of the CSFSG algorithm is tested on a large-scale dataset of network security, using two kinds of classifiers: C4.5 and k-nearest neighbor (KNN. The results of the experimental research show that the approach is efficient and able to effectively improve classification accuracy and to decrease classification time. In addition, the results of our method are more promising than the results of other cost-sensitive feature selection algorithms.
Class attendance and cardiology examination performance: a study in problem-based medical curriculum
Bamuhair SS
2016-02-01
Full Text Available Samira S Bamuhair,1 Ali I Al Farhan,1,2 Alaa Althubaiti,1 Saeed ur Rahman,1,2 Hanan M Al-Kadri1,3 1College of Medicine, King Saud Bin Abdulaziz University for Health Sciences, 2Department of Family Medicine and Primary Health Care, 3Department of Obstetrics and Gynecology, King Abdulaziz Medical City, Riyadh, Saudi Arabia Background and aims: Information on the effect of students' class attendance on examination performance in a problem-based learning medical curriculum is limited. This study investigates the impact of different educational activities on students' academic performance in a problem-based learning curriculum. Methods: This is a retrospective cohort study conducted on the cardiology block at the College of Medicine, King Saud Bin Abdulaziz University for Health Sciences, Riyadh, Saudi Arabia. All students who undertook the cardiology block during the academic year 2011–2012 were included. The students' attendance was measured using their overall attendance percentage. This percentage is a product of their attendance of many activities throughout the block. The students' performance was assessed by the final mark obtained, which is a product of many assessment elements. Statistical correlation between students' attendance and performance was established. Results: A total of 127 students were included. The average lecture attendance rate for the medical students in this study was found to be 86%. A significant positive correlation was noted between the overall attendance and the accumulated students' block mark (r=0.52; P<0.001. Students' attendance to different education activities was correlated to their final mark. Lecture attendance was the most significant predictor (P<0.001, that is, 1.0% increase in lecture attendance has predicted a 0.27 increase in students' final block mark. Conclusion: Class attendance has a positive effect on students' academic performance with stronger effect for lecture attendance compared to
Hajaiej, Hichem
2011-01-01
We prove the existence of minimizers of a class of multi-constrained variational problems in which the non linearity involved does not sat- isfy compactness, monotonicity, neither symmetry properties.
The pursuit of perfect packing
Weaire, Denis
2000-01-01
In 1998 Thomas Hales dramatically announced the solution of a problem that has long teased eminent mathematicians: what is the densest possible arrangement of identical spheres? The Pursuit of Perfect Packing recounts the story of this problem and many others that have to do with packing things together. The examples are taken from mathematics, physics, biology, and engineering, including the arrangement of soap bubbles in foam, atoms in a crystal, the architecture of the bee''s honeycomb, and the structure of the Giant''s Causeway. Using an informal style and with key references, the book also includes brief accounts of the lives of many of the scientists who devoted themselves to problems of packing over many centuries, together with wry comments on their efforts. It is an entertaining introduction to the field for both specialists and the more general public.
求解0-1背包问题的二进制狼群算法%A binary wolf pack algorithm for solving 0-1 knapsack problem
吴虎胜; 张凤鸣; 战仁军; 汪送; 张超
2014-01-01
狼群算法（wolf pack algorithm，WPA）源于狼群在捕食及其猎物分配中所体现的群体智能，已被成功应用于复杂函数求解。在此基础上，通过定义运动算子，对人工狼位置、步长和智能行为重新进行二进制编码设计，提出了一种解决离散空间组合优化问题的二进制狼群算法（binary wolf pack algorithm，BWPA）。该算法保留了狼群算法基于职责分工的协作式搜索特性，选取离散空间的经典问题---0-1背包问题进行仿真实验，具体通过10组经典的背包问题算例和 BWPA 算法与经典的二进制粒子群算法、贪婪遗传算法、量子遗传算法在求解3组高维背包问题时的对比计算，例证了算法具有相对更好的稳定性和全局寻优能力。%The wolf pack algorithm (WPA),inspired by swarm intelligence of wolf pack in their prey hun-ting behaviors and distribution mode,has been proposed and successfully applied in complex function optimiza-tion problems.Based on the designing of the move operator,the artificial wolves’position,step-length and in-telligent behaviors are redesigned by binary coding,and a binary wolf pack algorithm (BWPA)is proposed to solve combinatorial optimization problems in discrete spaces.BWPA preserves the feature of cooperative search-ing based on job distribution of the wolf pack and is applied to 10 classic 0-1 knapsack problems.Moreover,the 3 high-dimensional 0-1 knapsack problems are tested.All results show that BWPA has better global convergence and computational robustness and outperforms the binary particle swarm optimization algorithm,the greedy genetic al-gorithm and the quantum genetic algorithm,especially for high-dimensional knapsack problems.
Singleton, Jr., Robert [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Israel, Daniel M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Doebling, Scott William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Woods, Charles Nathan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kaul, Ann [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Walter, Jr., John William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Rogers, Michael Lloyd [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-05-09
For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.
Ng, Albert H.
2011-01-24
To incorporate protein polarization effects within a protein combinatorial optimization framework, we decompose the polarizable force field AMOEBA into low order terms. Including terms up to the third-order provides a fair approximation to the full energy while maintaining tractability. We represent the polarizable packing problem for protein G as a hypergraph and solve for optimal rotamers with the FASTER combinatorial optimization algorithm. These approximate energy models can be improved to high accuracy [root mean square deviation (rmsd) < 1 kJ mol -1] via ridge regression. The resulting trained approximations are used to efficiently identify new, low-energy solutions. The approach is general and should allow combinatorial optimization of other many-body problems. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011 Copyright © 2011 Wiley Periodicals, Inc.
Ng, Albert H; Snow, Christopher D
2011-05-01
To incorporate protein polarization effects within a protein combinatorial optimization framework, we decompose the polarizable force field AMOEBA into low order terms. Including terms up to the third-order provides a fair approximation to the full energy while maintaining tractability. We represent the polarizable packing problem for protein G as a hypergraph and solve for optimal rotamers with the FASTER combinatorial optimization algorithm. These approximate energy models can be improved to high accuracy [root mean square deviation (rmsd) < 1 kJ mol(-1)] via ridge regression. The resulting trained approximations are used to efficiently identify new, low-energy solutions. The approach is general and should allow combinatorial optimization of other many-body problems. PMID:21264879
Nazan Karaoğlu
2011-08-01
Full Text Available Introduction: It is stated that students cannot carry their knowledge on basic medical sciences that they gained with classical education to clinical classes and clinical practice and problem based learning (PBL can compensate this drawback. It was aimed to evaluate the effect of PBL scenario written on this topic on level of knowledge about childhood poisoning of third class students who completed the most of theoretical pharmacology education.Materials and Method: A questionnaire form prepared by researchers was applied to randomly chosen PBL groups without writing names and on the basis of voluntariness before and after a case of childhood poisoning which was applied as the second PBL scenario in the second midterm of 2009-2010 academic years. Numbers, percentages, chi-square and student’s t-test were used for evaluation of the questionnaire form comprised of demographic data, open-closed ended questions for measuring attitudes and level of knowledge against case of poisoning and statements as making a priority ranking.Results: In the study group, 89 students took part in pre-test and 96 students took part in post-test. In the answers to the list including the substances that are the most common causes of admission according to data of Refik Saydam National Poison Center (e.g. lotion, bath foam, cosmetics, water color and calamine lotions, the substances that the students stated to be toxic in pre-test were answered correctly in the post-test (p<0.05. Number of correct answers increased significantly for knowledge about commonly used drugs in clinical practice like anti-depressants, calcium canal blockers, oral antidiabetics that were marked as non-toxic by the students although they are toxic (p<0.05. While mean knowledge score for these 40 items was 17.52±5.82 in pre-test, it increased to 27.89±8.79 in post-test (p<0.001.Conclusion: Results of this study indicate that PBL scenario applied to the students who learned pharmacology
Multi-class Fork-Join queues & The stochastic knapsack problem
Ding, Sihan
2011-01-01
Multi-class Fork-Join queues are extension of single-class Fork-Join queues. In a multi-class Fork-Join queuing system, different types of jobs arrive, and then split into several sub-jobs. Those sub-jobs go to parallel processing queues. Then, the synchronization is required before the departure of a job. We found very few scientific efforts in analyzing the multi-class Fork-Join queues. In this thesis, we analyzed the expected sojourn time and the expected synchronization time. Since it is ...
Ge, Xun; Thomas, Michael K.; Greene, Barbara A.
2006-01-01
This study utilized elements of technology-rich ethnography to create a rich description of a multi-user virtual environment in a high school computer programming class. Of particular interest was the transition that took place in classroom culture from one characterized by a well-defined problem solving approach to one more indicative of open…
Long, Ting; Qin, Danian
2014-01-01
One major challenge of developing problem-based learning (PBL) curricula in medical schools in China is to meet the requirements of sufficient qualified PBL tutors. Since 2011, we have developed a modified group teaching approach where an experienced faculty tutor facilitates several small PBL student groups in a large class. Although our study…
"Hoffman v. Monsanto": Courts, Class Actions, and Perceptions of the Problem of GM Drift
McLeod-Kilmurray, Heather
2007-01-01
"Hoffman v. Monsanto" raises questions about the civil litigation system. Are courts appropriate institutions, and are class actions the appropriate procedure, for resolving disputes about genetically modified organisms (GMOs)? After addressing the institutional question, this article focuses on procedure. Although class actions are designed to…
Dembo, Richard; Wareham, Jennifer; Poythress, Norman; Meyers, Kathleen; Schmeidler, James
2008-01-01
The authors report the results of latent class analyses and latent class transition analyses of antisocial behavior risk factors among 137 youths participating in a juvenile diversion program. The study examined the youths' latent classifications using baseline and 1-year follow-up measures of family, peer, education, and mental health risk…
Packing, coding, and ground states
Cohn, Henry
2016-01-01
These are the lecture notes from my 2014 PCMI graduate summer school lectures. In these lectures, we'll study simple models of materials from several different perspectives: geometry (packing problems), information theory (error-correcting codes), and physics (ground states of interacting particle systems). These perspectives each shed light on some of the same problems and phenomena, while highlighting different techniques and connections. One noteworthy phenomenon is the exceptional symmetr...
Towards optimal packed string matching
Ben-Kiki, Oren; Bille, Philip; Breslauer, Dany;
2014-01-01
-time, achieving a factor α speedup over traditional algorithms that examine each character individually. Our macro-level algorithm only uses the standard AC0 instructions of the word-RAM model (i.e. no integer multiplication) plus two specialized micro-level AC0 word-size packed-string instructions. The main word-size...... string-matching instruction wssm is available in contemporary commodity processors. The other word-size maximum-suffix instruction wslm is only required during the pattern pre-processing. Benchmarks show that our solution can be efficiently implemented, unlike some prior theoretical packed string...... matching work.(b) We also consider the complexity of the packed string matching problem in the classical word-RAM model in the absence of the specialized micro-level instructions wssm and wslm. We propose micro-level algorithms for the theoretically efficient emulation using parallel algorithms techniques...
The advantages of hydraulic packing extraction
Today's competitive environment, coupled with industry's desire to improve the efficiency of plant maintenance and operations, has management continually seeking ways to save time, money, and, at nuclear plants, radiation exposure. One area where a tremendous improvement in efficiency can be realized is valve packing removal. For example, industry experience indicates that up to 70% of the time it takes to repack a valve can be spent just removing the old packing. In some case, the bonnets of small valves are removed to facilitate packing removal and prevent stem and stuffing box damage that can occur when using packing removal picks. In other cases, small valves are simply removed and discarded because it costs less to replace the valves than to remove the packing using conventional methods. Hydraulic packing extraction greatly reduces packing removal time and will not damage the stem nor stuffing box, thus eliminating the need for bonnet removal or valve replacement. This paper will review some of the more common problems associated with manual packing extraction techniques. It will explain how hydraulic packing extraction eliminates or greatly reduces the impact of each of the problem areas. A discussion will be provided of some actual industry operating experiences related to success stories using hydraulic packing extraction. The paper will also briefly describe the operating parameters associated with hydraulic packing extraction tools. Throughout the paper, actual operating experiences from the nuclear power, fossil power, petrochemical, and refinery industries will be used to support the conclusion that hydraulic packing extraction is an alternative that can save time, money, and exposure
A simplified implementation of the analytical discrete ordinates (ADO) method in radiative transfer with polarization is presented in this work. The class of problems that can be solved with the simplified ADO approach consists of problems defined in plane-parallel geometry and driven by external illumination in the form of obliquely incident parallel rays. Numerical results of benchmark quality are tabulated for the albedo problem with polarization and Lambert reflection. The new results improve on a tabulation made available in a previous work by the authors that was based on the (less accurate) spherical harmonics method.
Hard sphere packings within cylinders.
Fu, Lin; Steinhardt, William; Zhao, Hao; Socolar, Joshua E S; Charbonneau, Patrick
2016-02-23
Arrangements of identical hard spheres confined to a cylinder with hard walls have been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest configurations, called close packings, of hard spheres of diameter σ in a cylinder of diameter D is a purely geometric problem that grows increasingly complex as D/σ increases, and little is thus known about the regime for D > 2.873σ. In this work, we extend the identification of close packings up to D = 4.00σ by adapting Torquato-Jiao's adaptive-shrinking-cell formulation and sequential-linear-programming (SLP) technique. We identify 17 new structures, almost all of them chiral. Beyond D ≈ 2.85σ, most of the structures consist of an outer shell and an inner core that compete for being close packed. In some cases, the shell adopts its own maximum density configuration, and the stacking of core spheres within it is quasiperiodic. In other cases, an interplay between the two components is observed, which may result in simple periodic structures. In yet other cases, the very distinction between the core and shell vanishes, resulting in more exotic packing geometries, including some that are three-dimensional extensions of structures obtained from packing hard disks in a circle. PMID:26843132
The stability of several classes of constructions containing elastic elements has been studied. A nonlinear mathematical model of a vibration equipment device intended for the intensification of technological processes, for example, the stirring process, has been considered as an example
王鹏; 黄帅; 朱舟全
2014-01-01
As is well-known, it is difficult to solve a circle packing problem with equilibrium constraints. Therefore we aim to find a new algorithm that can further enhance search capability, efficiency and success rate. To solve the circle packing problem, we propose an improved artificial bee colony ( IABC) algorithm by introducing the trend extrapolation and a fine-tuning operator into the artificial bee colony so as to reduce its randomness in the search process and improve its search efficiency. The IABC algorithm uses different adaptability degrees of food sources at different places to produce the direction of trend extrapolation and direct the search, thus reducing its randomness. To verify the effectiveness of the IABC algorithm, we apply it to solving the circle packing problem with equilibrium constraints and simulate it with the MATLAB software. The simulation results, given in Figs. 4, 5 and 6 and Tables 3 and 4, and their analysis show preliminarily that our IABC algorithm has better search capability and efficiency than both the genetic algorithm and the particle swarm optimization ( PSO) algorithm. The IABC algorithm can find optimal solutions quickly without taking much computing time, indicating its efficiency in solving a circle packing problem with equilibrium constraints.%圆形packing问题是一个著名的NP难题，求解该问题具有很高的理论与实用价值。首先将趋势外推原理和微调算子引入人工蜂群算法，对其搜索的随机性进行有效的引导优化，然后将改进后的人工蜂群算法应用于带平衡约束的圆形布局的参数优化，并在文后采用3个典型实例进行了数值实验。结果表明新算法解决带平衡约束的圆形packing问题具有较强的寻优能力和较高的寻优效率，是一种实用的方法。
A Class of Single Machine Scheduling Problems with Variable Processing Time
无
2001-01-01
In this paper, single machine scheduling problems with variableprocessing time are raised. The criterions of the problem considered are minimizing scheduling length of all jobs, flow time and number of tardy jobs and so on. The complexity of the problem is determined.
Does Post Septoplasty Nasal Packing Reduce Complications?
Bijan Naghibzadeh
2011-01-01
Full Text Available The main issues in nasal surgery are to stabilize the nose in the good position after surgery and preserve the cartilages and bones in the favorable situation and reduce the risk of deviation recurrence. Also it is necessary to avoid the synechia formation, nasal valve narrowing, hematoma and bleeding. Due to the above mentioned problems and in order to solve and minimize them nasal packing, nasal splint and nasal mold have been advised. Patients for whom the nasal packing used may faced to some problems like naso-pulmonary reflex, intractable pain, sleep disorder, post operation infection and very dangerous complication like toxic shock syndrome. We have two groups of patients and three surgeons (one of the surgeons used post operative nasal packing in his patients and the two others surgeons did not.Complications and morbidities were compared in these two groups. Comparing the two groups showed that the rate of complication and morbidities between these two groups were same and the differences were not valuable, except the pain and discomfort post operatively and at the time of its removal. Nasal packing has several risks for the patients while its effects are not studied. Septoplasty can be safely performed without postoperative nasal packing. Nasal packing had no main findings that compensated its usage. Septal suture is one of the procedures that can be used as alternative method to nasal packing. Therefore the nasal packing after septoplasty should be reserved for the patients with increased risk of bleeding.
Stabilized quasi-reversibility method for a class of nonlinear ill-posed problems
Nguyen Huy Tuan
2008-06-01
Full Text Available In this paper, we study a final value problem for the nonlinear parabolic equation $$displaylines{ u_t+Au =h(u(t,t,quad 0
We present an experimental protocol that allows one to tune the packing fraction η of a random pile of ferromagnetic spheres from a value close to the lower limit of random loose packing ηRLP≅0.56 to the upper limit of random close packing ηRCP≅0.64. This broad range of packing fraction values is obtained under normal gravity in air, by adjusting a magnetic cohesion between the grains during the formation of the pile. Attractive and repulsive magnetic interactions are found to affect stongly the internal structure and the stability of sphere packing. After the formation of the pile, the induced cohesion is decreased continuously along a linear decreasing ramp. The controlled collapse of the pile is found to generate various and reproducible values of the random packing fraction η
Nodal Solutions for a Class of Fourth-Order Two-Point Boundary Value Problems
Xu Jia; Han XiaoLing
2010-01-01
We consider the fourth-order two-point boundary value problem , , , where is a parameter, is given constant, with on any subinterval of , satisfies for all , and , , for some . By using disconjugate operator theory and bifurcation techniques, we establish existence and multiplicity results of nodal solutions for the above problem.
Gianluca Sgueo
2008-01-01
Full Text Available The Italian financial laws for 2008 introduce, in Article 2, item 445, the first organic discipline of class actions in the Italian order. The decision made by the Italian legislator is, therefore, meaningful in relation not only to the effects produced in the legal system but also to the possible repercussions in contractual relations between citizens, companies and local and national public authorities. The article, ideally structured in three parts, puts together a historical reconstruction of the facts before the approval of the law with a detailed analysis of its contents in the light of the most relevant jurisprudential cases. The core of this brief research consists of the analysis of the perspectives as well as their problems, since the analysis of the concrete data tries to discover (possible solutions for such problems.La legge finanziaria italiana per il 2008 introduce, all’articolo 2, comma 445, la prima disciplina organica dell’azione di classe nell’ordinamento italiano. La scelta compiuta dal Legislatore italiano è comunque significativa, sia quanto agli effetti prodotti sul sistema giuridico, sia quanto alle possibili ripercussioni nei rapporti contrattuali tra cittadini, imprese e autorità pubbliche, locali e nazionali. L’articolo, idealmente strutturato in tre parti, combina una ricostruzione storica degli avvenimenti antecedenti all’approvazione della norma di legge in commento con un’analisi più approfondita di quella, alla luce della casistica giurisprudenziale più significativa. È proprio l’analisi delle prospettive e dei problemi Che costituisce il cardine di questa breve ricerca, poiché dall’analisi dei dati concreti tenta di rinvenir e le (possibili soluzioni agli stessi.
Villas Boas Junior, Manoel; Strauss, Edilberto, E-mail: junior@lmp.ufrj.b [Instituto Federal de Educacao, Ciencia e Tecnologia do Ceara/ Universidade do Estado do Ceara, Itaperi, CE (Brazil). Mestrado Integrado em Computacao Aplicada; Nicolau, Andressa dos Santos; Schirru, Roberto, E-mail: andressa@lmp.ufrj.b [Coordenacao dos Programas de Pos-Graduacao de Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear; Mello, Flavio Luis de [Universidade Federal do Rio de Janeiro (POLI/UFRJ), RJ (Brazil). Escola Politecnica. Dept. de Engenharia Eletronica e Computacao
2011-07-01
This article presents a computational model of the diagnostic system of transient. The model makes use of segmentation techniques applied to support decision making, based on identification of classes and optimized by Particle Swarm Optimization algorithm (PSO). The method proposed aims to classify an anomalous event in the signatures of three classes of the design basis transients postulated for the Angra 2 nuclear plant, where the PSO algorithm is used as a method of separation of classes, being responsible for finding the best centroid prototype vector of each accident/transient, ie equivalent to Voronoi vector that maximizes the number of correct classifications. To make the calculation of similarity between the set of the variables anomalous event in a given time t, and the prototype vector of variables of accident/transients, the metrics of Manhattan, Euclidean and Minkowski were used. The results obtained by the method proposed were compatible with others methods reported in the literature, allowing a solution that approximates the ideal solution, ie the Voronoi vectors. (author)
An Optimal Algorithm for a Class of Parallel Machines Scheduling Problem
常俊林; 邵惠鹤
2004-01-01
This paper considers the parallel machines scheduling problem where jobs are subject to different release times. A constructive heuristic is first proposed to solve the problem in a modest amount of computer time. In general, the quality of the solutions provided by heuristics degrades with the increase of the probiem's scale. Combined the global search ability of genetic algorithm, this paper proposed a hybrid heuristic to improve the quality of solutions further. The computational results show that the hybrid heuristic combines the advantages of heuristic and genetic algorithm effectively and can provide very good solutions to some large problems in a reasonable amount of computer time.
Development of an effective valve packing program
Hart, K.A.
1996-12-01
Current data now shows that graphite valve packing installed within the guidance of a controlled program produces not only reliable stem sealing but predictable running loads. By utilizing recent technological developments in valve performance monitoring for both MOV`s and AOV`s, valve packing performance can be enhanced while reducing maintenance costs. Once known, values are established for acceptable valve packing loads, the measurement of actual valve running loads via the current MOV/AOV diagnostic techniques can provide indication of future valve stem sealing problems, improper valve packing installation or identify the opportunity for valve packing program improvements. At times the full benefit of these advances in material and predictive technology remain under utilized due to simple past misconceptions associated with valve packing. This paper will explore the basis for these misconceptions, provide general insight into the current understanding of valve packing and demonstrate how with this new understanding and current valve diagnostic equipment the key aspects required to develop an effective, quality valve packing program fit together. The cost and operational benefits provided by this approach can be significant impact by the: elimination of periodic valve repacking, reduction of maintenance costs, benefits of leak-free valve operation, justification for reduced Post Maintenance Test Requirements, reduced radiation exposure, improved plant appearance.
Replacement of the cooling tower packing at the Goesgen-Daeniken AG nuclear power plant
In 2005 the asbestos cement cooling tower packing was replaced by plastic material. Two years later, the packing showed strong deformations, deposits of solids and weight gain. At the end of 2007 parts of the packing collapsed into the cooling tower basin. Investigations were made, revealing that the thickness of the packing foil was too low and that packing geometry and biofilms on the surface of the packing favoured deposition of solids. Successful measures were taken to solve the problems. (orig.)
Savoye, Philippe
2009-01-01
In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.
Solvability of a class of second-order quasilinear boundary value problems
Qing-liu YAO
2009-01-01
The second-order quasilinear boundary value problems are considered when the nonlinear term is singular and the limit growth function at the infinite exists. With the introduction of the height function of the nonlinear term on a bounded set and the consideration of the integration of the height function, the existence of the solution is proven. The existence theorem shows that the problem has a solution ff the integration of the limit growth function has an appropriate value.
Second-order cone programming formulations for a class of problems in structural optimization
Makrodimopoulos, A.; A. Bhaskar; Keane, A.J.
2010-01-01
This paper provides efficient and easy to implement formulations for two problems in structural optimization as second-order cone programming (SOCP) problems based on the minimum compliance method and derived using the principle of complementary energy. In truss optimization both single and multiple loads (where we optimize the worst-case compliance) are considered. By using a heuristic which is based on the SOCP duality we can consider a simple ground structure and...
A Special Class of Univalent Functions in Hele-Shaw Flow Problems
Paula Curt
2011-01-01
Full Text Available We study the time evolution of the free boundary of a viscous fluid for planar flows in Hele-Shaw cells under injection. Applying methods from the theory of univalent functions, we prove the invariance in time of Φ-likeness property (a geometric property which includes starlikeness and spiral-likeness for two basic cases: the inner problem and the outer problem. We study both zero and nonzero surface tension models. Certain particular cases are also presented.
Nasini, Stefano
2015-01-01
The thesis deals with the theoretical and practical study of mathematical programming methodologies to the analysis complex networks and their application in economic and social problems. More specifically, it applies models and methods for solving linear and integer programming problems to network models exploiting the matrix structure of such models, resulting in efficient computational procedures and small processing time. As a consequence, it allows the study of larger and more complex n...
Hutcheson, Brian
2007-01-01
In this article, the author introduces the concept of flat pack toys. Flat pack toys are designed using a template on a single sheet of letter-sized card stock paper. Before being cut out and built into a three-dimensional toy, they are scanned into the computer and uploaded to a website. With the template accessible from the website, anyone with…
Oberhofer, Margret; Colpaert, Jozef
2015-01-01
TLC Pack stands for Teaching Languages to Caregivers and is a course designed to support migrants working or hoping to work in the caregiving sector. The TLC Pack resources range from A2 to B2 level of the Common European Framework of Reference for Languages (CEFR), and will be made available online in the six project languages: Dutch, English,…
Some Results Connected with the Class Number Problem in Real Quadratic Fields
Aleksander GRYTCZUK; Jaroslaw GRYTCZUK
2005-01-01
We investigate arithmetic properties of certain subsets of square-free positive integers and obtain in this way some results concerning the class number h(d) of the real quadratic field Q(√d). In particular, we give a new proof of the result of Hasse, asserting that in this case h(d) = 1 is possible only if d is of the form p, 2q or qr, where p, q, r are primes and q ≡ r ≡ 3(mod4).
On perfect packings in dense graphs
Balogh, József; Treglown, Andrew
2011-01-01
We say that a graph G has a perfect H-packing if there exists a set of vertex-disjoint copies of H which cover all the vertices in G. We consider various problems concerning perfect H-packings: Given positive intergers n, r, D, we characterise the edge density threshold that ensures a perfect K_r-packing in any graph G on n vertices and with minimum degree at least D. We also give two conjectures concerning degree sequence conditions which force a graph to contain a perfect H-packing. Other related embedding problems are also considered. Indeed, we give a degree sequence condition which forces a graph to contain a copy of K_r, thereby strengthening the minimum degree version of Turan's theorem. We also characterise the edge density threshold that ensures a graph G contains k vertex-disjoint cycles.
New Class of Solutions for Water Infiltration Problems in Unsaturated Soils
Barari, Amin; Omidvar, M; Momeni, M;
2010-01-01
This paper presents the results of approximate analytical solutions to Richards’ equation, which governs the problem of unsaturated flow in porous media. The existing methods generally fall within the category of numerical and analytical methods, often having many restrictions for practical...
Positive Solutions for a Class of Coupled System of Singular Three-Point Boundary Value Problems
Naseer Ahmad Asif; Rahmat Ali Khan
2009-01-01
Existence of positive solutions for a coupled system of nonlinear three-point boundary value problems of the type , , , , , , , is established. The nonlinearities , are continuous and may be singular at , and/or , while the parameters , satisfy . An example is also included to show the applicability of our result.
Design problems and resolvent for class 1E battery of nuclear power plant
The quantity and capacity of DC and 220 V AC uninterrupted systems have been added since the control systems use DCS. It is very difficulty for design on calculation capacity and bear time during short circuit of battery and mechanics calculation of battery bracket. These problems have been solved by tests and calculations. These are good experiments for new project on battery design. (author)
Cowden, Chapel D.; Santiago, Manuel F.
2016-01-01
Interdisciplinary approaches to research in the sciences have become increasingly important in solving a wide range of pressing problems at both global and local levels. It is imperative then that science majors in higher education understand the need for exploring information from a wide array of disciplines. With this in mind, interdisciplinary…
The Problem of Coherence in English for Business and Technology (EBT) Writing Classes.
Chandrasegaran, Antonia
1993-01-01
In business correspondence and technical communications, lack of coherence can cause serious misunderstanding. This paper examines how the problem of generating coherence is addressed in English for Business and Technology textbooks. It proposes a cognitive approach to skill building and presents a teaching procedure for doing so. (Contains two…
On second- order symmetric duality for a class of multiobjective fractional programming problem
Deo Brat Ojha
2012-06-01
Full Text Available This article is concerned with a pair of second-order symmetric duals in the context of non-differentiable multiobjective fractional programming problems. We establish the weak and strong duality theorems for the new pair of dual models. Discussion on some special cases shows that results in this paper extend previous work in this area.
Bouchaud, Jean-Philippe; Didier SORNETTE
1994-01-01
The ability to price risks and devise optimal investment strategies in thé présence of an uncertain "random" market is thé cornerstone of modern finance theory. We first consider thé simplest such problem of a so-called "European call option" initially solved by Black and Scholes using Ito stochastic calculus for markets modelled by a log-Brownien stochastic process. A simple and powerful formalism is presented which allows us to generalize thé analysis to a large class of stochastic processe...
Problem-Based Learning in 9th Grade Chemistry Class: `Intermolecular Forces'
Tarhan, Leman; Ayar-Kayali, Hulya; Urek, Raziye Ozturk; Acar, Burcin
2008-05-01
This research study aims to examine the effectiveness of a problem-based learning (PBL) on 9th grade students’ understanding of intermolecular forces (dipole-dipole forces, London dispersion forces and hydrogen bonding). The student’s alternate conceptions about intermolecular bonding and their beliefs about PBL were also measured. Seventy-eight 9th grade students were stratified by cognitive levels and then randomly assigned to experimental (PBL, 40 students) and control (lecture-style teaching, 38 students) groups. Following a preparatory lesson where activation and remediation of existing knowledge occur, a pre-test was given, and no significant difference was found between the two groups of students ( p > .05). After the instruction was completed, a post-test and also a questionnaire related to the quality of the problem, the teacher’s role and group functioning were administered. Results from the post-test of both groups ( p achievement, remedying formation of alternate conceptions and also social skills.
Enhancing Higher Order Thinking Skills In A Marine Biology Class Through Problem-Based Learning
Richard M. Magsino
2014-01-01
The purpose of this research was to examine students' perspectives of their learning in marine biology in the collaborative group context of Problem-based Learning (PBL). Students’ higher order thinking skills (HOTS) using PBL involves the development of their logical thinking and reasoning abilities which stimulates their curiosity and associative thinking. This study aimed to investigate how critical thinking skills, particularly analysis, synthesis and evaluation were enhanced ...
SIMPLY OPTIMAL - BEYOND EOQ FOR A POPULAR CLASS OF INVENTORY PROBLEMS
W. Van Wijck
2012-01-01
Full Text Available
ENGLISH ABSTRACT: True optimal solution s to real life problems are normally only achievable at the expense of great complexity. Every now and then however, one is almost stunned by the simplicity of a good solution to a practical problem. This paper discusses a relatively simple method for determining the joint optimum order quantity and reorder point for the case where service level is specified as a desired fraction of demand to be satisfied directly from stock. Separate solutions were derived for complete backorders and lost sales, and the method is equally applicable to fixed order quantity and periodic review inventory problems . Demand during the lead time is assumed to be normally distributed . The intent of the paper is to focus on the findings and the application of the method, rather than the mathematical derivation of the formulae itself.
AFRIKAANSE OPSOMMING: Ware optimale oplossings vir werklike praktiese probleme is gewoonlik net bereikbaar ten koste van groot kompleksiteit. Elke nou en dan staan 'n mens egter bykans verstom omtrerit die eenvoud van 'n voortreflike oplossing vir 'n bepaalde probleem. Hierdie artikel bespreek 'n relatief eenvoudige metode om die gesamentlike optimale bestel-grootte en veiligheidsvoorraad te bepaal, vir die geval waar dienspeil uitgedruk word as die proporsie van voorraad-items wat op eerste aanvraag direk uit voorraad op hande voorsien word. Aparte oplossings is gevind vir die gevalle van volledige agterstallige bestellings en volledige verlore verkope , en die metode is ewe toepaslik vir vaste bestel-hoeveelheid- en periodieke hersiening-voorraad-stelsels. Die normaal-verdeling is as die statistiese verdeling van aanvraag gedurende die leityd aanvaar, Die artikel fokus op toepassing en bevindings eerder as op die wiskundige afleiding van die formules.
Yan Sun
2015-01-01
Under some conditions concerning the first eigenvalues corresponding to the relevant linear operator, we obtain sharp optimal criteria for the existence of positive solutions for p-Laplacian problems with integral boundary conditions. The main methods in the paper are constructing an available integral operator and combining fixed point index theory. The interesting point of the results is that the nonlinear term contains all lower-order derivatives explicitly. Finally, we give some examples ...
Mukhacheva E.A.
2000-01-01
Full Text Available Two algorithms for the one-dimensional cutting problem, namely, a modified branch-and-bound method (exact method and a heuristic sequential value correction method are suggested. In order to obtain a reliable assessment of the efficiency of the algorithms, hard instances of the problem were considered and from the computational experiment it seems that the efficiency of the heuristic method appears to be superior to that of the exact one, taking into account the computing time of the latter. A detailed description of the two methods is given along with suggestions for their improvements.
Lohiya, D; Lohiya, Daksh; Sethi, Meetu
1999-01-01
A search for a problem free cosmology within the framework of a finite range theory of gravitation is suggested. We profile a toy model that uses a multicomponent non-minimally coupled scalar tensor theory to achieve this objective. In an SO(2) invariant theory for example, we outline a program that can accommodate a coasting Milne universe with a distribution of non - topological soliton solutions [NTS's]. The interior of these solutions would be domains where effective gravitational effects would be indistinguishable from those expected in standard Einstein theory. For a large class of non - minimal coupling terms and the scalar effective potential, the effective cosmological constant identically vanishes in the region exterior to the NTS's and dynamically approaches a small value in the interior region. We describe features of a problem free cosmology that follows.
Aliev, A R
2011-01-01
The boundary-value problem on semi-axis for one class operator-differential equations of the fourth order, the main part of which has the multiple characteristic is investigated in this paper in Sobolev type weighted space. Correctness and unique solvability of the boundary-value problem is proved, and the solvability conditions are expressed in terms of the operator coefficients of the equation. Estimations of the norms of the operators of intermediate derivatives, closely connected with the solvability conditions, have been carried out. The connection between the exponent of the weight and the lower border of the spectrum of the main operator, participating in the equation, is determined in the results of the paper.
元野; 李一军; 王延青; 王晓博
2013-01-01
带有冲突关系装箱问题的优化目标是在满足货物冲突关系的前提下，使用数量最少的货箱完成货物装箱的目的。本文分析了冲突装箱问题的数学模型，提出了基于图着色模型的启发式算法进行求解。首先，使用冲突图来描述货物之间的冲突关系；其次，基于冲突图，采取图着色的方式将货物进行分组，并且组内的货物之间不存在冲突关系；最后，采取改进FFD算法对每组的货物进行装箱操作。实验表明，本文提出的启发式算法能够快速有效地找到问题的可行解，为此类装箱问题的求解提供了新思路。%The objection of bin packing problem with conflicts (BPPC)is to minimize the number of bins used to accommodate all the items , and also has to satisfy the conflict constraints among the items .This paper summaries the mathematical model of BPPC , and proposes a heuristic algorithm based on graph coloring model to solve it . Firstly, a conflict graph structure is used to represent the conflict relationship among the items , and then, based on the conflict graph , the algorithm will finish a coloring procedure to group all the items and ensure that there is no items with conflict relationship in each group , and lastly , an improved FFD algorithm is used to complete the packing operation for the items in each group .The experiments show that the algorithm of this paper could find a feasible solution of BPPC quickly and efficiently , and provide a new approach for this kind of bin packing problems .
Strohfeldt, Katja; Khutoryanskaya, Olga
2015-11-25
Objective. To introduce a new approach to problem-based learning (PBL) used in a medicinal chemistry practical class for pharmacy students. Design. The chemistry practical class was based on independent studies by small groups of undergraduate students (4-5), who designed their own practical work, taking relevant professional standards into account. Students were guided by feedback and acquired a set of skills important for health-care professionals. The model was tailored to the application of PBL in a chemistry practical class setting for a large student cohort (150 students). The achievement of learning outcomes was based on the submission of relevant documentation, including a certificate of analysis, in addition to peer assessment. Some of the learning outcomes also were assessed in the final written examination. Assessment. The practical was assessed at several time points using detailed marking schemes in order to provide the students with feedback. Students were required to engage with the feedback to succeed in the practical. Conclusion. A novel PBL chemistry laboratory course for pharmacy students was successful in that self-reflective learning and engagement with feedback were encouraged, and students enjoyed the challenging learning experience. Essential skills for health-care professionals were also promoted. PMID:26839430
Storage and treatment of SNF of Alfa class nuclear submarines: current status and problems
Available in abstract form only. Full text of publication follows: The current status and main problems associated with storage, defueling and following treatment of spent nuclear fuel (SNF) of Nuclear Submarines (NS) with heavy liquid metal cooled reactors are considered. In the final analysis these solutions could be realized in the form of separate projects to be funded through national and bi- and multilateral funding in the framework of the international collaboration of the Russian Federation on complex utilization of NS and rehabilitation of contaminated objects allocated in the North-West region of Russia. (authors)
Packing configuration performance for small stem diameters
The extensive use of graphite packing and its excellent track record for large isolating valves in CANDU, Primary Heat Transfer (PHT) systems has resulted in an increased application of graphite packing on the conventional side. Many of these applications are in air operated valves (AOVs) where the packing sets are used on small stem diameters (<1 inch) with frequent short-cycling strokes (± 10% of full stroke). The direct application of the proven packing configurations for large isolated valves to control valve application has generated problems such as stiction, packing wear and, in isolated cases, stem stall. To address this issue, a test program was conducted at AECL, CRL by MED branch. The testing showed that by reconfiguring the packing sets and using PTFE wafers reductions in stem friction of 50% at ambient conditions, a 3 fold at hot conditions are achievable. The test program also demonstrated benefits gained in packing wear with different stem roughness finishes and the potential need to exercise small stems valves that see less than full stroke cycling. The paper describes the tests results and provides field support experience. (author)
Reliability and decomposition techniques to solve certain class of stochastic programming problems
Minguez, R., E-mail: Roberto.Minguez@unican.e [Environmental Hydraulics Institute ' IH Cantabria' , Universidad de Cantabria, Cantabria (Spain); Conejo, A.J.; Garcia-Bertrand, R. [Department of Electrical Engineering, University of Castilla-La Mancha, Ciudad Real (Spain)
2011-02-15
Reliability based techniques has been an area of active research in structural design during the last decade, and different methods have been developed. The same has occurred with stochastic programming, which is a framework for modeling optimization problems involving uncertainty. The discipline of stochastic programming has grown and broadened to cover a wide range of applications, such as agriculture, capacity planning, energy, finance, fisheries management, production control, scheduling, transportation, water management, etc., and because of this, techniques for solving stochastic programming models are of great interest for the scientific community. This paper presents a new approach for solving a certain type of stochastic programming problems presenting the following characteristics: (i) the joint probability distributions of random variables are given, (ii) these do not depend on the decisions made, and (iii) random variables only affect the objective function. The method is based on mathematical programming decomposition procedures and first-order reliability methods, and constitutes an efficient method for optimizing quantiles in high-dimensional settings. The solution provided by the method allows us to make informed decisions accounting for uncertainty.
Student Perceptions about Group Based Problem Solving Process in Online and In-Class Settings
Salih Birişçi
2013-12-01
Full Text Available The aim of this study, through qualitative measures, was to systematically examine the perspectives and meanings formed by the teachers about teaching and learning. This study took place in the spring semester of the 2010-2011 academic year of Artvin Çoruh University. The sample size was 27. The participants were divided in two groups – Group 1 with group work taking place in an online test (D1, N=12; Group 2 with group work taking place in a classroom experiment (D2, N=12. After six weeks implementation, semi-structured interviews were conducted in order to determine students’ thoughts on problem solving and group work with success on attitudes towards mathematics. Positive change in students’ attitudes towards mathematics occurred in both the D1 and D2 groups. According to the application, the students stated that they developed increased interest towards mathematics and it turned into enjoyable.Key Words: Problem solving, group study, online learning, student views
Li, Hong; Zhang, Li; Jiao, Yong-Chang
2016-07-01
This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.
WANG Yan-ping
2014-01-01
Based on the theory of constructivism, this article analyzes the open problems colloquial English large size class teach-ing of higher vocational public English and points out the countermeasures of colloquial English large-scale class teaching of high-er vocational public English.
Online Variable-Sized Bin Packing with Conflicts
Epstein, Leah; Favrholdt, Lene Monrad; Levin, Asaf
2011-01-01
We study a new kind of on-line bin packing with conflicts, motivated by a problem arising when scheduling jobs on the Grid. In this bin packing problem, the set of items is given at the beginning, together with a set of conflicts on pairs of items. A conflict on a pair of items implies that they...
Extended Kalman Filter with a Fuzzy Method for Accurate Battery Pack State of Charge Estimation
Saeed Sepasi
2015-06-01
Full Text Available As the world moves toward greenhouse gas reduction, there is increasingly active work around Li-ion chemistry-based batteries as an energy source for electric vehicles (EVs, hybrid electric vehicles (HEVs and smart grids. In these applications, the battery management system (BMS requires an accurate online estimation of the state of charge (SOC in a battery pack. This estimation is difficult, especially after substantial battery aging. In order to address this problem, this paper utilizes SOC estimation of Li-ion battery packs using a fuzzy-improved extended Kalman filter (fuzzy-IEKF for Li-ion cells, regardless of their age. The proposed approach introduces a fuzzy method with a new class and associated membership function that determines an approximate initial value applied to SOC estimation. Subsequently, the EKF method is used by considering the single unit model for the battery pack to estimate the SOC for following periods of battery use. This approach uses an adaptive model algorithm to update the model for each single cell in the battery pack. To verify the accuracy of the estimation method, tests are done on a LiFePO4 aged battery pack consisting of 120 cells connected in series with a nominal voltage of 432 V.
Statistical inference for disordered sphere packings
Jeffrey Picka
2012-01-01
Full Text Available This paper gives an overview of statistical inference for disordered sphere packing processes. These processes are used extensively in physics and engineering in order to represent the internal structure of composite materials, packed bed reactors, and powders at rest, and are used as initial arrangements of grains in the study of avalanches and other problems involving powders in motion. Packing processes are spatial processes which are neither stationary nor ergodic. Classical spatial statistical models and procedures cannot be applied to these processes, but alternative models and procedures can be developed based on ideas from statistical physics.Most of the development of models and statistics for sphere packings has been undertaken by scientists and engineers. This review summarizes their results from an inferential perspective.
Webb, D J
2012-01-01
Psychologists have long known that an expert in a field not only knows significantly more individual facts/skills than a novice but also has these facts/skills organized into a mental hierarchy that links the individual facts (at the bottom of the hierarchy) together with larger more-encompassing ideas (at the top of the hierarchy). In the Spring quarter of 2012, UC Davis offered 4 sections (about 180 students each) of the first quarter of introductory physics, Physics 9A, covering Newtonian mechanics. One of these sections is a "treatment" group and had the entire 10-week quarter's set of ideas introduced, largely qualitatively, in the first 6 weeks followed by the 4 weeks where students learn to use those ideas to solve the algebraically complicated problems that physicists prize. The other three sections were organized as usual. The treatment group and one of the other sections were taught by the author and were identical (same homework, discussion, lecture, and lab) except for the organization of the cont...
Wang, Zizhuo; Ye, Yinyu
2011-01-01
We present a dynamic learning algorithm for a class of single-product revenue management problems. In these problems, a retailer sells a single product with limited on-hand inventory over a finite selling season. Customer demand arrives according to a Poisson process, the rate of which is influenced by a single action taken by the retailer (such as price adjustment, sales commission, advertisement intensity, etc.). The relation between the action and the demand rate is not known in advance. The retailer will learn the optimal action policy "on the fly" as she maximizes her total expected revenue based on observed demand reactions. Using the pricing problem as an example, we propose a dynamic "learning-while-doing" algorithm to achieve a near optimal performance. Furthermore, we prove that the convergence rate of our algorithm is almost the fastest among all possible algorithms in terms of asymptotic "regret" (the relative loss comparing to the full information optimal solution). Our result closes the performa...
Xu, Jiuping; Li, Jun
2002-09-01
In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables' expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.
Muu, Lê D.; Oettli, Werner
1988-01-01
A unifled approach to branch-and-bound and cutting plane methods for solving a certain class of nonconvex optimization problems is proposed. Based on this approach an implementable algorithm is obtained for programming problems with a bilinear objective function and jointly convex constraints.
Pesaran, Ahmad
2016-06-14
This presentation describes the thermal design of battery packs at the National Renewable Energy Laboratory. A battery thermal management system essential for xEVs for both normal operation during daily driving (achieving life and performance) and off-normal operation during abuse conditions (achieving safety). The battery thermal management system needs to be optimized with the right tools for the lowest cost. Experimental tools such as NREL's isothermal battery calorimeter, thermal imaging, and heat transfer setups are needed. Thermal models and computer-aided engineering tools are useful for robust designs. During abuse conditions, designs should prevent cell-to-cell propagation in a module/pack (i.e., keep the fire small and manageable). NREL's battery ISC device can be used for evaluating the robustness of a module/pack to cell-to-cell propagation.
Biological species have produced many simple but efficient rules in their complex and critical survival activities such as hunting and mating. A common feature observed in several biological motion strategies is that the predator only moves along paths in a carefully selected or iteratively refined subspace (or manifold), which might be able to explain why these motion strategies are effective. In this paper, a unified linear algebraic formulation representing such a predator–prey relationship is developed to simplify the construction and refinement process of the subspace (or manifold). Specifically, the following three motion strategies are studied and modified: motion camouflage, constant absolute target direction and local pursuit. The framework constructed based on this varying subspace concept could significantly reduce the computational cost in solving a class of nonlinear constrained optimal trajectory planning problems, particularly for the case with severe constraints. Two non-trivial examples, a ground robot and a hypersonic aircraft trajectory optimization problem, are used to show the capabilities of the algorithms in this new computational framework. (paper)
Liu, Quan; Chen, Lin
2011-01-01
In this paper,we consider the restless bandit problem, which is one of the most well-studied generalizations of the celebrated stochastic multi-armed bandit problem in decision theory. However, it is known be PSPACE-Hard to approximate to any non-trivial factor. Thus the optimality is very difficult to obtain due to its high complexity. A natural method is to obtain the greedy policy considering its stability and simplicity. However, the greedy policy will result in the optimality loss for its intrinsic myopic behavior generally. In this paper, by analyzing one class of so-called standard reward function, we establish the closed-form condition about the discounted factor \\beta such that the optimality of the greedy policy is guaranteed under the discounted expected reward criterion, especially, the condition \\beta = 1 indicating the optimality of the greedy policy under the average accumulative reward criterion. Thus, the standard form of reward function can easily be used to judge the optimality of the greed...
Graham, Alan; Graham, Louise
2003-01-01
Describes a very successful attempt to teach fractions to year 5 pupils based on pupils making their own fraction pack. Children decided for themselves how to make the fractional slices used in the activity using colored cardboard sheets and templates of a paper circle consisting of 24 equal slices. (Author/NB)
Optimal online bounded space multidimensional packing
Epstein, L.; Stee, R. van
2003-01-01
We solve an open problem in the literature by providing an online algorithm for multidimensional bin packing that uses only bounded space. We show that it is optimal among bounded space algorithms for any dimension $d>1$. Its asymptotic performance ratio is $(Pi_{infty})^d$, where $Pi_{infty}approx1
Teaching Large Evening Classes
Wambuguh, Oscar
2008-01-01
High enrollments, conflicting student work schedules, and the sheer convenience of once-a-week classes are pushing many colleges to schedule evening courses. Held from 6 to 9 pm or 7 to 10 pm, these classes are typically packed, sometimes with more than 150 students in a large lecture theater. How can faculty effectively teach, control, or even…
Marzena Pytel-Kudela
2006-01-01
Full Text Available The analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations in Hilbert spaces are studied using theory of bi-linear forms in respectively rigged Hilbert spaces triples. Theorems specifying the existence of a dissolving operator for a class of adiabatically perturbed nonautonomous partial differential equations are stated. Some applications of the results obtained are discussed.
Chung I-Fang
2008-10-01
Full Text Available Abstract Background The Signal-to-Noise-Ratio (SNR is often used for identification of biomarkers for two-class problems and no formal and useful generalization of SNR is available for multiclass problems. We propose innovative generalizations of SNR for multiclass cancer discrimination through introduction of two indices, Gene Dominant Index and Gene Dormant Index (GDIs. These two indices lead to the concepts of dominant and dormant genes with biological significance. We use these indices to develop methodologies for discovery of dominant and dormant biomarkers with interesting biological significance. The dominancy and dormancy of the identified biomarkers and their excellent discriminating power are also demonstrated pictorially using the scatterplot of individual gene and 2-D Sammon's projection of the selected set of genes. Using information from the literature we have shown that the GDI based method can identify dominant and dormant genes that play significant roles in cancer biology. These biomarkers are also used to design diagnostic prediction systems. Results and discussion To evaluate the effectiveness of the GDIs, we have used four multiclass cancer data sets (Small Round Blue Cell Tumors, Leukemia, Central Nervous System Tumors, and Lung Cancer. For each data set we demonstrate that the new indices can find biologically meaningful genes that can act as biomarkers. We then use six machine learning tools, Nearest Neighbor Classifier (NNC, Nearest Mean Classifier (NMC, Support Vector Machine (SVM classifier with linear kernel, and SVM classifier with Gaussian kernel, where both SVMs are used in conjunction with one-vs-all (OVA and one-vs-one (OVO strategies. We found GDIs to be very effective in identifying biomarkers with strong class specific signatures. With all six tools and for all data sets we could achieve better or comparable prediction accuracies usually with fewer marker genes than results reported in the literature using the
Damped Arrow-Hurwicz algorithm for sphere packing
Degond, Pierre; Ferreira, Marina A.; Motsch, Sébastien
2016-01-01
We consider algorithms that, from an arbitrarily sampling of $N$ spheres (possibly overlapping), find a close packed configuration without overlapping. These problems can be formulated as minimization problems with non-convex constraints. For such packing problems, we observe that the classical iterative Arrow-Hurwicz algorithm does not converge. We derive a novel algorithm from a multi-step variant of the Arrow-Hurwicz scheme with damping. We compare this algorithm with classical algorithms ...
Saravana Kumar
2013-02-01
Full Text Available The higher education sector is undergoing tremendous change, driven by complex driving forces including financial, administrative, and organisational and stakeholder expectations. It is in this challenging environment, educators are required to maintain and improve the quality of teaching and learning outcomes while contending with increasing class sizes. Despite mixed evidence on the effectiveness of large classes on student outcomes, large classes continue to play an important part in higher education. While large classes pose numerous challenges, they also provide opportunities for innovative solutions. This paper provides an overview of these challenges and highlights opportunities for innovative solutions.
Effect of packing method on the randomness of disc packings
Zhang, Z. P.; Yu, A. B.; Oakeshott, R. B. S.
1996-06-01
The randomness of disc packings, generated by random sequential adsorption (RSA), random packing under gravity (RPG) and Mason packing (MP) which gives a packing density close to that of the RSA packing, has been analysed, based on the Delaunay tessellation, and is evaluated at two levels, i.e. the randomness at individual subunit level which relates to the construction of a triangle from a given edge length distribution and the randomness at network level which relates to the connection between triangles from a given triangle frequency distribution. The Delaunay tessellation itself is also analysed and its almost perfect randomness at the two levels is demonstrated, which verifies the proposed approach and provides a random reference system for the present analysis. It is found that (i) the construction of a triangle subunit is not random for the RSA, MP and RPG packings, with the degree of randomness decreasing from the RSA to MP and then to RPG packing; (ii) the connection of triangular subunits in the network is almost perfectly random for the RSA packing, acceptable for the MP packing and not good for the RPG packing. Packing method is an important factor governing the randomness of disc packings.
Andersen, Henrik; Ritter, Thomas
Ever seen a growth strategies fail because it was not connect ed to the firm’s customer base? Or a customer relationship strategy falters just because it was the wrong thing to do with that given customer? This article presents the six pack model, a tool that makes growth profitable and predictab....... Not all customers can and should grow – thus a firm needs to classify its customers in order to implement the right customer strategy.......Ever seen a growth strategies fail because it was not connect ed to the firm’s customer base? Or a customer relationship strategy falters just because it was the wrong thing to do with that given customer? This article presents the six pack model, a tool that makes growth profitable and predictable...
Argo packing friction research update
This paper focuses on the issue of valve packing friction and its affect on the operability of motor- and air-operated valves (MOVs and AOVs). At this time, most nuclear power plants are required to perform postmaintenance testing following a packing adjustment or replacement. In many cases, the friction generated by the packing does not impact the operability window of a valve. However, to date there has not been a concerted effort to substantiate this claim. To quantify the effects of packing friction, it has become necessary to develop a formula to predict the friction effects accurately. This formula provides a much more accurate method of predicting packing friction than previously used factors based strictly on stem diameter. Over the past 5 years, Argo Packing Company has been developing and testing improved graphite packing systems at research facilities, such as AECL Chalk River and Wyle Laboratories. Much of this testing has centered around reducing and predicting friction that is related to packing. In addition, diagnostic testing for Generic Letter 89-10 MOVs and AOVs has created a significant data base. In July 1992 Argo asked several utilities to provide running load data that could be used to quantify packing friction repeatability and predictability. This technical paper provides the basis to predict packing friction, which will improve calculations for thrust requirements for Generic Leter 89-10 and future AOV programs. In addition, having an accurate packing friction formula will improve packing performance when low running loads are identified that would indicate insufficient sealing force
Separable subgroups have bounded packing
Yang, Wen-yuan
2010-01-01
In this note, we prove that separable subgroups have bounded packing in ambient groups. The notion bounded packing was introduced by Hruska-Wise \\cite{HrWi} and in particular, our result confirms a conjecture in \\cite{HrWi} which states each subgroup of a virtually polycyclic group has the bounded packing property.
Direct contact condensation in packed beds
Li, Yi; Klausner, James F.; Mei, Renwei; Knight, Jessica [Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611 (United States)
2006-12-15
A diffusion driven desalination process was recently described where a very effective direct contact condenser with a packed bed is used to condense water vapor out of an air/vapor mixture. A laboratory scale direct contact condenser has been fabricated as a twin tower structure with two stages, co-current and countercurrent. Experiments have been operated in each stage with respective saturated air inlet temperatures of 36, 40 and 43{sup o}C. The temperature and humidity data have been collected at the inlet and exit of the packed bed for different water to air mass flow ratios that vary between 0 and 2.5. A one-dimensional model based on conservation principles has been developed, which predicts the variation of temperature, humidity, and condensation rate through the condenser stages. Agreement between the model and experiments is very good. It is observed that the countercurrent flow stage condensation effectiveness is significantly higher than that for the co-current stage. The condensation heat and mass transfer rates were found to decrease when water blockages occur within the packed bed. Using high-speed digital cinematography, it was observed that this problem can occur at any operating condition, and is dependent on the packing surface wetting characteristics. This observation is used to explain the requirement for two different empirical constants, depending on packing diameter, suggested by Onda for the air side mass transfer coefficient correlation. (author)
Dense Packings of Polyhedra: Platonic and Archimedean Solids
Torquato, S
2009-01-01
We formulate the problem of generating dense packings of nonoverlapping, non-tiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem, which we call the Adaptive Shrinking Cell (ASC) scheme. This novel optimization problem is solved here (using a variety of multi-particle initial configurations) to find the dense packings of each of the Platonic solids in three-dimensional Euclidean space R3 , except for the cube, which is the only Platonic solid that tiles space. We find the densest known packings of tetrahedra, icosahedra, dodecahedra, and octahedra with densities 0:823:::, 0:836:::, 0:904:::, and 0:947:::, respectively. It is noteworthy that the densest tetrahedral packing possesses no long-range order. Unlike the densest tetrahedral packing, which must not be a Bravais lattice packing, the densest packings of the other non-tiling Platonic solids that we obtain are their previously known optimal (Bravais) lattice packings. We also derive a simp...
Ishkhanyan, A M
2014-01-01
We derive 15 classes of time-dependent two-state models solvable in terms of the confluent Heun functions. These classes extend over all the known families of 3- and 2-parametric models solvable in terms of the Gauss hypergeometric and the Kummer confluent hypergeometric functions to more general four-parametric classes involving three-parametric detuning modulation functions. The classes suggest a variety of families of field configurations possessing useful properties not covered by the previously known analytic models. In the case of constant detuning the field configurations defined by the derived classes describe excitations of two-state quantum systems by symmetric or asymmetric pulses of controllable width and edge-steepness. The particular classes out of the derived fifteen that provide constant detuning pulses of finite area are identified and the factors controlling the corresponding pulse shapes are discussed in detail. The positions of the pulse edges for the case of step-wise edges are determined...
Reference book for design of valve packings, sealing high temperature water
Mockups of stuffing boxes for valves in the 1/4 to 1 in. (0.6-2.54cm) pipe size range and ASA 900 and up pressure class were tested to determine how temperature, stuffing box dimensions, packing compressive stress and stem surface finish affect water leak rate, packing friction torque and packing volume loss (creep). One brand of wire-reinforced asbestos braid on graphite-and-asbestos core packing was used in all tests. The theory of leakage through porous media was reviewed with emphasis on application to packed stuffing boxes, and a mathematical framework for relating leakage and packing friction to stuffing box dimensions and compressive stress was developed. The tests gave empirical relationships (1) for leak rate vs temperature, packing compressive stress, stem diameter and packing size, (2) for packing friction torque vs the above variables and (3) for packing creep vs temperature and stress. Packing stress affected leakage far more than any other variable, the leak rate being inversely proportional to stress to the 7.3 power at a packing temperature of 350 deg F (175 deg C). Factors which increase packing compression (density) have a strong reducing effect on leakage and a moderate to zero effect on packing friction torque. Surface finish had no visible effect on leakage, torque or creep. Empirical results and theory have been combined to show how stuffing boxes can be designed for a given leakage rate. Suggestions for decreasing leakage from existing high temperature stuffing boxes are included. (author)
OVERCOMING THE METER BARRIER AND THE FORMATION OF SYSTEMS WITH TIGHTLY PACKED INNER PLANETS (STIPs)
Boley, A. C. [Department of Physics and Astronomy, The University of British Columbia, 6224 Agricultural Road, Vancouver, B.C. V6T 1Z1 (Canada); Morris, M. A. [Center for Meteorite Studies, Arizona State University, P.O. Box 876004, Tempe, AZ 88287-6004 (United States); Ford, E. B. [Center for Exoplanets and Habitable Worlds, The Pennsylvania State University, 525 Davey Laboratory, University Park, PA 16802 (United States)
2014-09-10
We present a solution to the long outstanding meter barrier problem in planet formation theory. As solids spiral inward due to aerodynamic drag, they will enter disk regions that are characterized by high temperatures, densities, and pressures. High partial pressures of rock vapor can suppress solid evaporation, and promote collisions between partially molten solids, allowing rapid growth. This process should be ubiquitous in planet-forming disks, which may be evidenced by the abundant class of Systems with Tightly packed Inner Planets discovered by the NASA Kepler Mission.
Adcock, Amanda C.; Merwin, Rhonda M.; Wilson, Kelly G.; Drake, Chad E.; Tucker, Christina I.; Elliott, Camden
2010-01-01
The present study examines whether facilitated acquisition occurs in contexts when 1 stimulus in a class is emotionally evocative and the other stimuli are arbitrary or neutral. Undergraduates with high and low grade-point averages (GPA) completed a matching-to-sample task that resulted in the formation of 3 stimulus equivalence classes. Each…
黎自强; 田茁君; 王奕首; 岳本贤
2012-01-01
带平衡约束圆形Packing问题属于NP-hard问题,求解困难.提出一种求解该问题的快速启发式并行蚁群算法.首先提出一种启发式方法:在轮盘赌选择定序的概率公式中增加质量因子和外围逆时针排列定位待布圆,并用它构造出多样性种群个体(相交圆数不超过3的布局方案).然后将蚁群优化与并行搜索相结合,使种群个体快速收敛到最优解或迭代出存在少量干涉的近似最优解(1～3个相交圆).若为后者,则基于物理模型用最速下降法将其快速调整成最优解.所采用的启发式方法、并行蚁群搜索机制和快速调整策略有机结合提高了算法的搜索精度和效率.数值实验表明该算法在性能指标上优于已存在的算法.%Circles packing problem with equilibrium constraints is difficult to solve due to its NP-hard nature. A fast heuristic parallel ant colony algorithm is proposed for this problem. Both circular radius and mass are taken as the probability factors of the roulette selection and the circles are located by arranging round existing circles in peripheral with counter-clockwise movement. Its diverse population individuals (no more than 3 circles are overlapped in each one) are constructed through the proposed heuristic method. The ant colony optimization combined with parallel search mechanism is adopted to obtain an optimal solution or an approximate optimal solution with 1-3 overlapping circles. The steepest descent method based on physical model is used to adjust the approximate optimal solution into the optimal one without overlapping. The combination of heuristic strategy, ant colony search mechanism in parallel, and fast adjustment strategy can improve the computational precision and efficiency of the proposed algorithm. The experiment results show that the proposed algorithm is superior to the existing algorithms in performance.
Pottmann, Helmut
2015-03-03
This paper is an overview of architectural structures which are either composed of polyhedral cells or closely related to them. We introduce the concept of a support structure of such a polyhedral cell packing. It is formed by planar quads and obtained by connecting corresponding vertices in two combinatorially equivalent meshes whose corresponding edges are coplanar and thus determine planar quads. Since corresponding triangle meshes only yield trivial structures, we focus on support structures associated with quad meshes or hex-dominant meshes. For the quadrilateral case, we provide a short survey of recent research which reveals beautiful relations to discrete differential geometry. Those are essential for successfully initializing numerical optimization schemes for the computation of quad-based support structures. Hex-dominant structures may be designed via Voronoi tessellations, power diagrams, sphere packings and various extensions of these concepts. Apart from the obvious application as load-bearing structures, we illustrate here a new application to shading and indirect lighting. On a higher level, our work emphasizes the interplay between geometry, optimization, statics, and manufacturing, with the overall aim of combining form, function and fabrication into novel integrated design tools.
Li, Shuai; Li, Yangming; Wang, Zheng
2013-03-01
This paper presents a class of recurrent neural networks to solve quadratic programming problems. Different from most existing recurrent neural networks for solving quadratic programming problems, the proposed neural network model converges in finite time and the activation function is not required to be a hard-limiting function for finite convergence time. The stability, finite-time convergence property and the optimality of the proposed neural network for solving the original quadratic programming problem are proven in theory. Extensive simulations are performed to evaluate the performance of the neural network with different parameters. In addition, the proposed neural network is applied to solving the k-winner-take-all (k-WTA) problem. Both theoretical analysis and numerical simulations validate the effectiveness of our method for solving the k-WTA problem. PMID:23334164
Dense packing on uniform lattices
Eloranta, Kari
2009-01-01
We study the Hard Core Model on the graphs ${\\rm {\\bf \\scriptstyle G}}$ obtained from Archimedean tilings i.e. configurations in $\\scriptstyle \\{0,1\\}^{{\\rm {\\bf G}}}$ with the nearest neighbor 1's forbidden. Our particular aim in choosing these graphs is to obtain insight to the geometry of the densest packings in a uniform discrete set-up. We establish density bounds, optimal configurations reaching them in all cases, and introduce a probabilistic cellular automaton that generates the legal configurations. Its rule involves a parameter which can be naturally characterized as packing pressure. It can have a critical value but from packing point of view just as interesting are the noncritical cases. These phenomena are related to the exponential size of the set of densest packings and more specifically whether these packings are maximally symmetric, simple laminated or essentially random packings.
Trout, Joseph; Bland, Jared
2013-03-01
In this pilot project, one hour of lecture time was replaced with one hour of in-class assignments, which groups of students collaborated on. These in-class assignments consisted of problems or projects selected for the calculus-based introductory physics students The first problem was at a level of difficulty that the majority of the students could complete with a small to moderate amount of difficulty. Each successive problem was increasingly more difficult, the last problem being having a level of difficulty that was beyond the capabilities of the majority of the students and required some instructor intervention. The students were free to choose their own groups. Students were encouraged to interact and help each other understand. The success of the in-class exercises were measured using pre-tests and post-tests. The pre-test and post-test were completed by each student independently. Statistics were also compiled on each student's attendance record and the amount of time spent reading and studying, as reported by the student. Statistics were also completed on the student responses when asked if they had sufficient time to complete the pre-test and post-test and if they would have completed the test with the correct answers if they had more time. The pre-tests and post-tests were not used in the computation of the grades of the students.
Packing solutions for power plants
Asbestos packings are being replaced in more and more countries with alternative products. This paper discusses modern packing solutions for valves and pumps in power plants. Die-moulded packing rings made of expanded graphite foil are described m detail, with recommendations for correct installation. Application examples for spring-loaded valves and cover lid seals are given. As an alternative for repair and service use, a braided expanded graphite packing reinforced with Inconel wire is described. Proposals for sealing various pump applications in power plants are also made. (Author)
Ciamarra, Massimo Pica; Coniglio, Antonio
2008-09-19
We measure the number Omega(phi) of mechanically stable states of volume fraction phi of a granular assembly under gravity. The granular entropy S(phi)=logOmega(phi) vanishes both at high density, at phi approximately equal to phi_rcp, and a low density, at phi approximately equal to phi_rvlp, where phi_rvlp is a new lower bound we call random very loose pack. phi_rlp is the volume fraction where the entropy is maximal. These findings allow for a clear explanation of compaction experiments and provide the first first-principle definition of the random loose volume fraction. In the context of the statistical mechanics approach to static granular materials, states with phi
Joint FAO/IAEA/WHO Expert Committee approved the use of radiation treatment of foods. Nowadays food packaging are mostly made of plastics, natural or synthetic, therefore effect of irradiation on these materials is crucial for packing engineering for food irradiation technology. By selecting the right polymer materials for food packaging it can be ensured that the critical elements of material and product performance are not compromised. When packaging materials are in contact with food at the time of irradiation that regulatory approvals sometimes apply. The review of the R-and-D and technical papers regarding material selection, testing and approval is presented in the report. The most information come from the USA where this subject is well elaborated, the International Atomic Energy Agency (IAEA) reports are reviewed as well. The report can be useful for scientists and food irradiation plants operators. (author)
Narrow sieves for parameterized paths and packings
Björklund, Andreas; Kaski, Petteri; Koivisto, Mikko
2010-01-01
We present randomized algorithms for some well-studied, hard combinatorial problems: the k-path problem, the p-packing of q-sets problem, and the q-dimensional p-matching problem. Our algorithms solve these problems with high probability in time exponential only in the parameter (k, p, q) and using polynomial space; the constant bases of the exponentials are significantly smaller than in previous works. For example, for the k-path problem the improvement is from 2 to 1.66. We also show how to detect if a d-regular graph admits an edge coloring with $d$ colors in time within a polynomial factor of O(2^{(d-1)n/2}). Our techniques build upon and generalize some recently published ideas by I. Koutis (ICALP 2009), R. Williams (IPL 2009), and A. Bj\\"orklund (STACS 2010, FOCS 2010).
Rich, Hans Walter [Kernkraftwerk Goesgen-Daeniken AG, Daeniken (Switzerland)
2012-07-01
In 2005 the asbestos cement cooling tower packing was replaced by plastic material. Two years later, the packing showed strong deformations, deposits of solids and weight gain. At the end of 2007 parts of the packing collapsed into the cooling tower basin. Investigations were made, revealing that the thickness of the packing foil was too low and that packing geometry and biofilms on the surface of the packing favoured deposition of solids. Successful measures were taken to solve the problems. (orig.)
Kawai, Yusuke; Yamada, Yoshio
2016-07-01
This paper deals with a free boundary problem for diffusion equation with a certain class of bistable nonlinearity which allows two positive stable equilibrium states as an ODE model. This problem models the invasion of a biological species and the free boundary represents the spreading front of its habitat. Our main interest is to study large-time behaviors of solutions for the free boundary problem. We will completely classify asymptotic behaviors of solutions and, in particular, observe two different types of spreading phenomena corresponding to two positive stable equilibrium states. Moreover, it will be proved that, if the free boundary expands to infinity, an asymptotic speed of the moving free boundary for large time can be uniquely determined from the related semi-wave problem.
School meal sociality or lunch pack individualism?
Andersen, Sidse Schoubye; Holm, Lotte; Baarts, Charlotte
2015-01-01
the social life of a school class, and how these arrangements involve strategies of both inclusion and exclusion. Two types of school meals are compared in the intervention study: a hot meal based on Nordic ingredients and the normal Danish school meal arrangement in which children bring lunch packs...... to school. The study discusses commensality by examining and comparing lunchtime interactions within the same group of children in the two contrasting meal situations. The results fail to confirm the conventional view that shared meals have greater social impacts and benefits than eating individualized...
Automating the packing heuristic design process with genetic programming.
Burke, Edmund K; Hyde, Matthew R; Kendall, Graham; Woodward, John
2012-01-01
The literature shows that one-, two-, and three-dimensional bin packing and knapsack packing are difficult problems in operational research. Many techniques, including exact, heuristic, and metaheuristic approaches, have been investigated to solve these problems and it is often not clear which method to use when presented with a new instance. This paper presents an approach which is motivated by the goal of building computer systems which can design heuristic methods. The overall aim is to explore the possibilities for automating the heuristic design process. We present a genetic programming system to automatically generate a good quality heuristic for each instance. It is not necessary to change the methodology depending on the problem type (one-, two-, or three-dimensional knapsack and bin packing problems), and it therefore has a level of generality unmatched by other systems in the literature. We carry out an extensive suite of experiments and compare with the best human designed heuristics in the literature. Note that our heuristic design methodology uses the same parameters for all the experiments. The contribution of this paper is to present a more general packing methodology than those currently available, and to show that, by using this methodology, it is possible for a computer system to design heuristics which are competitive with the human designed heuristics from the literature. This represents the first packing algorithm in the literature able to claim human competitive results in such a wide variety of packing domains. PMID:21609273
Tseng, Fen-Yu; Shieh, Jeng-Yi; Kao, Tze-Wah; Wu, Chau-Chung; Chu, Tzong-Shinn; Chen, Yen-Yuan
2016-02-01
Although medical humanities courses taught by teachers from nonmedical backgrounds are not unusual now, few studies have compared the outcome of medical humanities courses facilitated by physicians to that by teaching assistants majored in the liberal arts. The objectives of this study were to (1) analyze the satisfaction of medical students with medical humanities problem-based learning (PBL) classes facilitated by nonmedical teaching assistants (TAF) majored in the liberal arts, and those facilitated by the attending physicians (APF) and (2) examine the satisfaction of medical students with clinical medicine-related and clinical medicine-unrelated medical humanities PBL classes.A total of 123 medical students, randomly assigned to 16 groups, participated in this study. There were 16 classes in the course: 8 of them were TAF classes; and the others were APF classes. Each week, each group rotated from 1 subject of the 16 subjects of PBL to another subject. All of the 16 groups went through all the 16 subjects in the 2013 spring semester. We examined the medical students' satisfaction with each class, based on a rating score collected after each class was completed, using a scale from 0 (the lowest satisfaction) to 100 (the highest satisfaction). We also conducted multivariate linear regression analysis to examine the association between the independent variables and the students' satisfaction.Medical students were more satisfied with the TAF (91.35 ± 7.75) medical humanities PBL classes than APF (90.40 ± 8.42) medical humanities PBL classes (P = 0.01). Moreover, medical students were more satisfied with the clinical medicine-unrelated topics (92.00 ± 7.10) than the clinical medicine-related topics (90.36 ± 7.99) in the medical humanities PBL course (P = 0.01).This medical humanities PBL course, including nonmedical subjects and topics, and nonmedical teaching assistants from the liberal arts as class facilitators, was satisfactory. This
Dembo, Richard; Briones, Rhissa; Gulledge, Laura; Karas, Lora; Winters, Ken C.; Belenko, Steven; Greenbaum, Paul E.
2012-01-01
Reflective of interest in mental health and substance abuse issues among youths involved with the justice system, we performed a latent class analysis on baseline information collected on 100 youths involved in two diversion programs. Results identified two groups of youths: Group 1: a majority of the youths, who had high levels of delinquency,…
Ceulemans, Eva; Van Mechelen, Iven; Leenen, Iwin
2007-01-01
Hierarchical classes models are quasi-order retaining Boolean decomposition models for N-way N-mode binary data. To fit these models to data, rationally started alternating least squares (or, equivalently, alternating least absolute deviations) algorithms have been proposed. Extensive simulation studies showed that these algorithms succeed quite…
Random packing of digitized particles
Korte, de A.C.J.; Brouwers, H.J.H.
2012-01-01
The random packing of regularly and irregularly shaped particles has been studied extensively. Within this paper, packing is studied from the perspective of digitized particles. These digitized particles are developed for and used in cellular automata systems, which are employed for the simple mathe
Fast searching in packed strings
Bille, Philip
2011-01-01
the time. However, most strings are stored in a computer in a packed representation with several characters in a single word, giving us the opportunity to read multiple characters simultaneously. In this paper we study the worst-case complexity of string matching on strings given in packed...
Fast Searching in Packed Strings
Bille, Philip
2009-01-01
. However, most strings are stored in a computer in a packed representation with several characters in a single word, giving us the opportunity to read multiple characters simultaneously. In this paper we study the worst-case complexity of string matching on strings given in packed representation. Let m...
UNIFORM PACKING DIMENSION RESULTS FOR MULTIPARAMETER STABLE PROCESSES
无
2007-01-01
In this article, authors discuss the problem of uniform packing dimension of the image set of multiparameter stochastic processes without random uniform H(o)lder condition, and obtain the uniform packing dimension of multiparameter stable processes.If Z is a stable (N, d, α)-process and αN ≤ d, then the following holds with probability 1 Dim Z(E) = α DimE for any Borel setE ∈ B(R+N),where Z(E) = {x: (E) t ∈ E, Z(t) = x}. Dim(E) denotes the packing dimension of E.
Steck, Todd R; Dibiase, Warren; Wang, Chuang; Boukhtiarov, Anatoli
2012-01-01
Use of open-ended Problem-Based Learning (PBL) in biology classrooms has been limited by the difficulty in designing problem scenarios such that the content learned in a course can be predicted and controlled, the lack of familiarity of this method of instruction by faculty, and the difficulty in assessment. Here we present the results of a study in which we developed a team-based interdisciplinary course that combined the fields of biology and civil engineering across three years. We used PBL scenarios as the only learning tool, wrote the problem scenarios, and developed the means to assess these courses and the results of that assessment. Our data indicates that PBL changed students' perception of their learning in content knowledge and promoted a change in students' learning styles. Although no statistically significant improvement in problem-solving skills and critical thinking skills was observed, students reported substantial changes in their problem-based learning strategies and critical thinking skills. PMID:23653774
Todd R. Steck
2012-02-01
Full Text Available Use of open-ended Problem-Based Learning (PBL in biology classrooms has been limited by the difficulty in designing problem scenarios such that the content learned in a course can be predicted and controlled, the lack of familiarity of this method of instruction by faculty, and the difficulty in assessment. Here we present the results of a study in which we developed a team-based interdisciplinary course that combined the fields of biology and civil engineering across three years. We used PBL scenarios as the only learning tool, wrote the problem scenarios, and developed the means to assess these courses and the results of that assessment. Our data indicates that PBL changed students’ perception of their learning in content knowledge and promoted a change in students’ learning styles. Although no statistically significant improvement in problem-solving skills and critical thinking skills was observed, students reported substantial changes in their problem-based learning strategies and critical thinking skills.
Kocyigit, Sinan; Zembat, Rengin
2013-01-01
This study aimed to investigate the effects of authentic tasks on preschool preservice teachers' attitudes towards the course and problem solving skills. The study was designed in accordance with the pretest-posttest control group model. The data were collected by using the "Problem Solving Skills Inventory", the "Course…
Random close packing fractions of lognormal distributions of hard spheres
Farr, Robert S.
2013-01-01
We apply a recent one-dimensional algorithm for predicting random close packing fractions of polydisperse hard spheres [Farr and Groot, J. Chem. Phys. 133, 244104 (2009)] to the case of lognormal distributions of sphere sizes and mixtures of such populations. We show that the results compare well to two much slower algorithms for directly simulating spheres in three dimensions, and show that the algorithm is fast enough to tackle inverse problems in particle packing: designing size distributi...
Aihong Ren
2013-01-01
Full Text Available We propose a hybrid algorithm based on estimation of distribution algorithm (EDA and Nelder-Mead simplex method (NM to solve a class of nonlinear bilevel programming problems where the follower’s problem is linear with respect to the lower level variable. The bilevel programming is an NP-hard optimization problem, for which EDA-NM is applied as a new tool aiming at obtaining global optimal solutions of such a problem. In fact, EDA-NM is very easy to be implementedsince it does not require gradients information. Moreover, the hybrid algorithm intends to produce faster and more accurate convergence. In the proposed approach, for fixed upper level variable, we make use of the optimality conditions of linear programming to deal with the follower’s problem and obtain its optimal solution. Further, the leader’s objective function is taken as the fitness function. Based on these schemes, the hybrid algorithm is designed by combining EDA with NM. To verify the performance of EDA-NM, simulations on some test problems are made, and the results demonstrate that the proposed algorithm has a better performance than the compared algorithms. Finally, the proposed approach is used to solve a practical example about pollution charges problem.
Batard, Thomas; Bertalmío, Marcelo
2016-01-01
We extend two existing variational models from the Euclidean space to a vector bundle over a Riemannian manifold. The Euclidean models , dedicated to regularize or enhance some color image features, are based on the concept of nonlocal gradient operator acting on a function of the Euclidean space. We then extend these models by generalizing this operator to a vector bundle over a Riemannian manifold with the help of the parallel transport map associated to some class of covariant derivatives....
Khabbazibasmenj, Arash; Vorobyov, Sergiy A; Haardt, Martin
2012-01-01
Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying belongs to the class of difference-of-convex functions (DC) programming problems. DC programming problems occur as well in other signal processing applications and are typically solved using different modifications of the branch-and-bound method. This method, however, does not have any polynomial time complexity guarantees. In this paper, we show that a class of DC programming problems, to which the sum-rate maximization in two-way MIMO relaying belongs, can be solved very efficiently in polynomial time, and develop two algorithms. The objective function of the problem is represented as a product of quadratic ratios and parameterized so that its convex part (versus the concave part) contains only one (or two) optimization variables. One of the algorithms is called POlynomial-Time DC (POTDC) and is based on semi-definite programming (SDP) relaxation, linearization, and an iterative search over a single para...
An abstract class of bifurcation problems is investigated from the essential spectrum of the associated Frechet derivative. This class is a very general framework for the theory of one-dimensional, steady-profile traveling- shock-wave solutions to a wide family of kinetic integro-differential equations from nonequilibrium statistical mechanics. Such integro-differential equations usually admit the Navier--Stokes system of compressible gas dynamics or the MHD systems in plasma dynamics as a singular limit, and exhibit similar viscous shock layer solutions. The mathematical methods associated with systems of partial differential equations must, however, be replaced by the considerably more complex Bifurcation Theory setting. A hierarchy of bifurcation problems is considered, starting with a simple bifurcation problem from a simple eigenvalue. Sections are entitled as follows: introduction and background from mechanics; the mathematical problem: principal results; a generalized operational calculus, and the derivation of the generalized Lyapunov--Schmidt equations; and methods of solution for the Lyapunov--Schmidt and the functional differential equations. 1 figure
LI Tong; TENG Chun-xian; LI Hao-bai
2002-01-01
In the paper, it is discussed that the method on how to transform the multi-person bilevel multi-objective decision making problem into the equivalent generalized multi-objective decision making problem by using Kuhn-Tucker sufficient and necessary condition. In order to embody the decision maker's hope and transform it into single-objective decision making problem with the help of e-constraint method.Then we can obtain the global optimal solution by means of simulated annealing algorithm.
Packing of protein structures in clusters with magic numbers
Lindgård, Per-Anker; Bohr, Henrik
1997-01-01
Recently we have proposed a model for folding proteins into packed `clusters'. We have constructed a local homology measure for protein fold classes by projecting consecutively secondary structures onto a lattice. Taking into account hydrophobic forces we have found a mechanism for formation of...... abundances. In this paper we demonstrate that the results are robust to variations in the coordination number of the model....
Luo Hua; An Yulian
2010-01-01
An exact multiplicity result of positive solutions for the boundary value problems , , , is achieved, where is a positive parameter. Here the function is and satisfies , for for some . Moreover, is asymptotically linear and can change sign only once. The weight function is and satisfies , for . Using bifurcation techniques, we obtain the exact number of positive solutions of the problem under consideration for lying in various intervals in . Moreover, we indic...
Rakkapao, S.; Pengpan, T.; Srikeaw, S.; Prasitpong, S.
2014-01-01
This study aims to investigate the use of the predict-observe-explain (POE) approach integrated into large lecture classes on forces and motion. It is compared to the instructor-led problem-solving method using model analysis. The samples are science (SC, N = 420) and engineering (EN, N = 434) freshmen, from Prince of Songkla University, Thailand. Research findings from the force and motion conceptual evaluation indicate that the multimedia-supported POE method promotes students’ learning better than the problem-solving method, in particular for the velocity and acceleration concepts. There is a small shift of the students’ model states after the problem-solving instruction. Moreover, by using model analysis instructors are able to investigate students’ misconceptions and evaluate teaching methods. It benefits instructors in organizing subsequent instructional materials.
This study aims to investigate the use of the predict–observe–explain (POE) approach integrated into large lecture classes on forces and motion. It is compared to the instructor-led problem-solving method using model analysis. The samples are science (SC, N = 420) and engineering (EN, N = 434) freshmen, from Prince of Songkla University, Thailand. Research findings from the force and motion conceptual evaluation indicate that the multimedia-supported POE method promotes students’ learning better than the problem-solving method, in particular for the velocity and acceleration concepts. There is a small shift of the students’ model states after the problem-solving instruction. Moreover, by using model analysis instructors are able to investigate students’ misconceptions and evaluate teaching methods. It benefits instructors in organizing subsequent instructional materials. (paper)
On Packing Densities of Set Partitions
Goyt, Adam M.; Pudwell, Lara K.
2013-01-01
We study packing densities for set partitions, which is a generalization of packing words. We use results from the literature about packing densities for permutations and words to provide packing densities for set partitions. These results give us most of the packing densities for partitions of the set $\\{1,2,3\\}$. In the final section we determine the packing density of the set partition $\\{\\{1,3\\},\\{2\\}\\}$.
Liu, Quan; Wang, Kehao; Chen, Lin
2011-01-01
In this paper,we consider the restless bandit problem, which is one of the most well-studied generalizations of the celebrated stochastic multi-armed bandit problem in decision theory. However, it is known be PSPACE-Hard to approximate to any non-trivial factor. Thus the optimality is very difficult to obtain due to its high complexity. A natural method is to obtain the greedy policy considering its stability and simplicity. However, the greedy policy will result in the optimality loss for it...
On the tree packing conjecture
Balogh, József; Palmer, Cory
2012-01-01
The Gy\\'arf\\'as tree packing conjecture states that any set of $n-1$ trees $T_{1},T_{2},..., T_{n-1}$ such that $T_i$ has $n-i+1$ vertices pack into $K_n$. We show that $t=1/10n^{1/4}$ trees $T_1,T_2,..., T_t$ such that $T_i$ has $n-i+1$ vertices pack into $K_{n+1}$ (for $n$ large enough). We also prove that any set of $t=1/10n^{1/4}$ trees $T_1,T_2,..., T_t$ such that no tree is a star and $T_i$ has $n-i+1$ vertices pack into $K_{n}$ (for $n$ large enough). Finally, we prove that $t=1/4n^{1/...
Gorski, Paul C.
2012-01-01
A rich history of scholarship has demonstrated the ways in which popular stereotypes of disenfranchised communities, including people living in poverty, affect individual biases and preconceptions. Less attention has been paid to the ways in which such stereotypes help frame policy and practice responses regarding social problems, such as the…
Lyons, Gregory L; Huber, Heartley B; Carter, Erik W; Chen, Rui; Asmus, Jennifer M
2016-07-01
Although enhancing the social competence of students with severe disabilities has long remained a prominent focus of school-based intervention efforts, relatively little attention has focused on identifying the most critical social and behavioral needs of students during high school. We examined the social skills and problem behaviors of 137 adolescents with severe disabilities from the vantage point of both special educators and parents. We sought to identify areas of potential intervention need, explore factors associated with social skill and problem behavior ratings, and examine the extent to which teachers and parents converged in their assessments of these needs. Our findings indicate teachers and parents of high school students with severe disabilities rated social skills as considerably below average and problem behaviors as above average. In addition, lower social skills ratings were evident for students with greater support needs, lower levels of overall adaptive behavior, and a special education label of autism. We found moderate consistency in the degree to which teachers and parents aligned in their assessments of both social skills and problem behavior. We offer recommendations for assessment and intervention focused on strengthening the social competence of adolescents with severe disabilities within secondary school classrooms, as well as promising avenues for future research. PMID:27351700
Lyons, Gregory L.; Huber, Heartley B.; Carter, Erik W.; Chen, Rui; Asmus, Jennifer M.
2016-01-01
Although enhancing the social competence of students with severe disabilities has long remained a prominent focus of school-based intervention efforts, relatively little attention has focused on identifying the most critical social and behavioral needs of students during high school. We examined the social skills and problem behaviors of 137…
Lower bounds for 1-, 2- and 3-dimensional on-line bin packing algorithms
G. Galambos; A. van Vliet (André)
1994-01-01
textabstractIn this paper we discuss lower bounds for the asymptotic worst case ratio of on-line algorithms for different kind of bin packing problems. Recently, Galambos and Frenk gave a simple proof of the 1.536 ... lower bound for the 1-dimensional bin packing problem. Following their ideas, we p
Ghasem Alizadeh Afrouzi
2006-10-01
Full Text Available In this paper, we establish an equivalent statement to minimax inequality for a special class of functionals. As an application, we prove the existence of three solutions to the Dirichlet problem $$displaylines{ -u''(x+m(xu(x =lambda f(x,u(x,quad xin (a,b,cr u(a=u(b=0, }$$ where $lambda>0$, $f:[a,b]imes mathbb{R}o mathbb{R}$ is a continuous function which changes sign on $[a,b]imes mathbb{R}$ and $m(xin C([a,b]$ is a positive function.
Problems and Countermeasures in Development of University Class Organization%大学班级组织发展面临的问题及对策
夏敏
2012-01-01
University class is the common teaching organization and management form of university. The development of university class organization is helpful to create the favorable organization atmosphere for the growth of college stfidents, and the realization of the educational objective and higher educational functions. At present, under the influence of university enrolment expansion, educational reform development, and educational concept changes, the form, scope, system and contents of university class organization have been continuously challenged by external development so that the class functions have been weakened, and the management efficiency has been lowered. To change the concept of Class organizational development, to innovate the form of class organization, to broaden the scope of organizational management, and to strengthen the organizational system construction and information construction are the necessary countermeasures for solving the problems of Chinese university class organizational development currently.%大学班级是高校普遍的教学组织和管理形式。大学班级组织的发展有助于创建大学生成长的良好组织氛围，促进教育目标和高等教育功能的实现。当前，大学班级组织在高校扩招、教育改革发展、教育理念变革的影响下，班级组织形式、范围、制度、内容不断受到外部发展的挑战，班级功能弱化，管理效率降低。转变班级组织发展观念，创新班级组织形式，拓宽组织管理范围，加强组织制度建设和信息化建设是应对当前中国大学班级组织发展问题的必要对策。
Zhang, Can
2011-01-01
This paper studies a time optimal control problem with control constraints of the rectangular type for the linear multi-input time-varying ordinary di?erential equations. The aims of this study are to establish certain necessary and sufficient conditions for the optimal time and time optimal control, and to build up an al- gorithm for the optimal time and time optimal control.
A New Algorithm Based on the Homotopy Perturbation Method For a Class of Singularly Perturbed Boundary Value Problems
2013-12-01
Full Text Available . In this paper, a new algorithm is presented to approximate the solution of a singularly perturbed boundary value problem with leftlayer based on the homotopy perturbation technique and applying the Laplace transformation. The convergence theorem and the error bound of the proposed method are proved. The method is examined by solving two examples. The results demonstrate the reliability and efficiency of the proposed method.
Many-dimensional non-strictly hyperbolic systems of conservation laws with a radially degenerate flux function are considered. For such systems the set of entropies is defined and described, the concept of generalized entropy solution of the Cauchy problem is introduced, and the properties of generalized entropy solutions are studied. The class of strong generalized entropy solutions is distinguished, in which the Cauchy problem in question is uniquely soluble. A condition on the initial data is described that ensures that the generalized entropy solution is strong and therefore unique. Under this condition the convergence of the 'vanishing viscosity' method is established. An example presented in the paper shows that a generalized entropy solution is not necessarily unique in the general case
Dosimetry effects of film packing
Full text: Dosimetric artefacts in film based dosimetry have been addressed by a number of authors. We have investigated the influence on film dose results, of a number of materials that are commonly packed against the film including, solid water, paper, air and plastic. The results indicate that variations in optical density occur due to the character and relative quantity of the packing material as well as the film itself. Kodak X-omat V and GAFChromic film samples were placed in a solid water cassette with packing sheets of various materials placed in contact with the film. Photon and electron exposures were carried out with various film orientation and beam qualities. Results have been obtained for solid water, paper and air. An example of the relative change in film density as a function of depth due to four paper sheets packed adjacent to a film aligned with the central axis of a 6MV photon beam is shown. Other results indicate dose variation can be attributed to Cerenkov radiation. Packing materials in contact or in close proximity with dosimetric film, contribute to optical density variations of the order of several percent. Careful consideration of these effects is necessary when using film in high accuracy dosimetry. Copyright (2001) Australasian College of Physical Scientists and Engineers in Medicine
Webb, D J
2012-01-01
Four sections of introductory physics for physical scientists and engineers (about 180 students each) are compared. One section, treatment group, was organized so that students worked to learn the classical ideas connecting forces and motion over the first 6 weeks of the 10 week quarter and then used the final 4 weeks to apply those principles to algebraically complicated problems. The other sections learned ideas at essentially the same time as calculations over the entire 10 weeks of the quarter. The treatment group and one of the control sections were taught by the same instructor, had identical curricular materials and this instructor was blind to the comparison measure, the final exam. After controlling for GPA as well as for incoming conceptual understanding, the treatment group was found (with greater than 99% confidence) to perform better on the final exam than the control group taught by the same instructor and, by a similar measure, the treatment group performed significantly better than any other s...
Sleeping distance in wild wolf packs
Knick, S.T.; Mech, L.D.
1980-01-01
Sleeping distances were observed among members of 13 wild wolf (Canis lupus) packs and 11 pairs in northeastern Minnesota to determine if the distances correlated with pack size and composition. The study utilized aerial radio-tracking and observation during winter. Pack size and number of adults per pack were inversely related to pack average sleeping distance and variability. No correlation between sleeping distance and microclimate was observed. Possible relationships between social bonding and our results are discussed.
Planet Packing in Circumbinary Systems
Kratter, Kaitlin M
2013-01-01
The recent discovery of planets orbiting main sequence binaries will provide crucial constraints for theories of binary and planet formation. The formation pathway for these planets is complicated by uncertainties in the formation mechanism of the host stars. In this paper, we compare the dynamical states of single and binary star planetary systems. Specifically, we pose two questions: (1) What does it mean for a circumbinary system to be dynamically packed? (2) How many systems are required to differentiate between a population of packed or sparse planets? We determine when circumbinary systems become dynamically unstable as a function of the separation between the host-stars and the inner planet, and the first and second planets. We show that these represent unique stability constraints compared to single-star systems. We find that although the existing Kepler data is insufficient to distinguish between a population of packed or sparse circumbinary systems, a more thorough study of circumbinary TTVs combine...
Rash, James
2014-01-01
NASA's space data-communications infrastructure-the Space Network and the Ground Network-provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft. The Space Network operates several orbiting geostationary platforms (the Tracking and Data Relay Satellite System (TDRSS)), each with its own servicedelivery antennas onboard. The Ground Network operates service-delivery antennas at ground stations located around the world. Together, these networks enable data transfer between user spacecraft and their mission control centers on Earth. Scheduling data-communications events for spacecraft that use the NASA communications infrastructure-the relay satellites and the ground stations-can be accomplished today with software having an operational heritage dating from the 1980s or earlier. An implementation of the scheduling methods and algorithms disclosed and formally specified herein will produce globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary algorithms, a class of probabilistic strategies for searching large solution spaces, is the essential technology invoked and exploited in this disclosure. Also disclosed are secondary methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithms themselves. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure within the expected range of future users and space- or ground-based service-delivery assets. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally. The generalized methods and algorithms are applicable to a very broad class of combinatorial
Safin, V.A.
1982-01-01
The packing element of a packer is proposed which consists of an elastic core and outer layer made of plastic sealing material. It is distinguished by the fact that in order to facilitate removal of the packing element from the site of installation, the outer layer has a sublayer made of polymer material which is chemically inactive in relationship to the material of the core, for example polytetrafluoroethylene. The element is also distinguished by the fact that the outer layer together with the sublayer is attached to the core through a nonhardening and nondrying glue composition, for example, based on rubber, rosin, lanolin, vaseline oil and zinc oxide.
Cylinder valve packing nut studies
Blue, S.C. [Martin Marietta Energy Systems, Inc., Paducah, KY (United States)
1991-12-31
The design, manufacture, and use of cylinder valve packing nuts have been studied to improve their resistance to failure from stress corrosion cracking. Stress frozen photoelastic models have been analyzed to measure the stress concentrations at observed points of failure. The load effects induced by assembly torque and thermal expansion of stem packing were observed by strain gaging nuts. The effects of finishing operations and heat treatment were studied by the strain gage hole boring and X-ray methods. Modifications of manufacturing and operation practices are reducing the frequency of stress corrosion failures.
A Geometric-Structure Theory for Maximally Random Jammed Packings
Tian, Jianxiang; Xu, Yaopengxiao; Jiao, Yang; Torquato, Salvatore
2015-11-01
Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density ϕMRJ, among other packing properties of frictionless particles, still poses many theoretical challenges, even for congruent spheres or disks. Using the geometric-structure approach, we derive for the first time a highly accurate formula for MRJ densities for a very wide class of two-dimensional frictionless packings, namely, binary convex superdisks, with shapes that continuously interpolate between circles and squares. By incorporating specific attributes of MRJ states and a novel organizing principle, our formula yields predictions of ϕMRJ that are in excellent agreement with corresponding computer-simulation estimates in almost the entire α-x plane with semi-axis ratio α and small-particle relative number concentration x. Importantly, in the monodisperse circle limit, the predicted ϕMRJ = 0.834 agrees very well with the very recently numerically discovered MRJ density of 0.827, which distinguishes it from high-density “random-close packing” polycrystalline states and hence provides a stringent test on the theory. Similarly, for non-circular monodisperse superdisks, we predict MRJ states with densities that are appreciably smaller than is conventionally thought to be achievable by standard packing protocols.
Pack cementation coatings for alloys
He, Yi-Rong; Zheng, Minhui; Rapp, R.A. [Ohio State Univ., Columbus, OH (United States)
1996-08-01
The halide-activated pack cementation process was modified to produce a Ge-doped silicide diffusion coating on a Cr-Cr{sub 2}Nb alloy in a single processing step. The morphology and composition of the coating depended both on the composition of the pack and on the composition and microstructure of the substrate. Higher Ge content in the pack suppressed the formation of CrSi{sub 2} and reduced the growth kinetics of the coating. Ge was not homogeneously distributed in the coatings. In cyclic and isothermal oxidation in air at 700 and 1050{degrees}C, the Ge-doped silicide coating protected the Cr-Nb alloys from significant oxidation by the formation of a Ge-doped silica film. The codeposition and diffusion of aluminum and chromium into low alloy steel have been achieved using elemental Al and Cr powders and a two-step pack cementation process. Sequential process treatments at 925{degrees}C and 1150{degrees}C yield dense and uniform ferrite coatings, whose compositions are close to either Fe{sub 3}Al or else FeAl plus a lower Cr content, when processed under different conditions. The higher content of Al in the coatings was predicted by thermodynamic calculations of equilibrium in the gas phase. The effect of the particle size of the metal powders on the surface composition of the coating has been studied for various combinations of Al and Cr powders.
Nearly-Linear Time Packing and Covering LP Solvers
Allen-Zhu, Zeyuan; Orecchia, Lorenzo
2014-01-01
Packing and covering linear programs (PC-LPs) form an important class of linear programs (LPs) across computer science, operations research, and optimization. In 1993, Luby and Nisan constructed an iterative first-order algorithm for approximately solving PC-LPs in $\\textit{nearly-linear time}$, independently of the program's $\\textit{width}$, i.e., the largest value in the program's description. Unfortunately, all existing nearly-linear-time algorithms for solving PC-LPs require time at leas...
Valve packing manual. A maintenance application guide
Since 1970, AECL Chalk River Mechanical Equipment Development (MED) branch has invested over 175 person years in testing related to improving valve packing performance. Successful developments, including, 'live-loading', reduced packing heights, and performance-based packing qualification testing have been implemented. Since 1986, MED and the Integrated Valve Actuator Program Task Force - Valve Packing Steering Committee (IVAP-VPSC) have been involved in the development of combination die-formed graphite packing for use in CANDU plants. Many reports, articles, and specifications have been issued. Due to the large amount of test data and reports, a more user-friendly document has been prepared for everyday use. The Valve Packing Manual is based on many years of MED research and testing, as well as operating experience from CANDU nuclear generating stations (NGS). Since 1986, packing research and testing has been funded by the CANDU Owners Group (COG), the Electric Power Research Institute (EPRI), and participating valve packing manufacturers. The Valve Packing Manual (VPM) provides topical summaries of all work related to valve packing done since 1985. It includes advances in configuration design, stem packing friction, materials specifications, and installation procedures. This paper provides an overview on the application of the VPM with a focus on qualification testing, packing configuration, and stem packing friction. (author)
GÃƒÂ³Ã…ÂºdÃ…Âº A.
2000-03-01
Full Text Available This paper is a continuation of the work on the new approach to the packing problems of randomly embedded granular material proposed by GÃƒÂ³Ã…ÂºdÃ…Âº and Pietrow. In previous paper a quantum mechanical approach (QMA to packing was introduced and 2and 3-dimensional packing experiments for circles (spheres were generated on this basis. Packing fractions were calculated to test the ability to build 2 and 3-dimensional beds with correct properties. In this paper we continue testing the QMA model.