Layer structures for the solutions to the perturbed simple pendulum problems

We consider the perturbed simple pendulum equation

     

Equilibrium existence results for simple dynamic games

The investigation of equilibrium existence in a salient class of multistage games is simplified and generalized by reducing them to singlestage games which correspond also to competitive economies. Thus, economic theory provides much of the motivation as well as method for the study. Working in locally convex topological vector spaces, a fixedpoint theorem of Fan is applied to show the existence of the Nash equilibria studied. En route, but also as a matter of interest in itself, certain topological foundations of the equilibrium analysis used are laid out. A particular feature of generality of the dynamic games studied is that the feasible control regions of individual players are allowed to depend on the past state-history and control-history. Another such feature is that the next-state map is allowed certain nonlinearities.     

A dynamic approach to ‘simple’ algebraic curves

Despite its low relevance for teaching in schools the desideratum “Algebraic Curves’ has always been an issue within mathematical didactics. This article aims to continue this tradition with respect to a project oriented mathematics instruction by applying current dynamic geometry software (Cabri II+).     

An iterative elastic SBFE approach for collapse load analysis of inelastic structures

The paper proposes a novel numerical approach that incorporates the use of a modified elastic compensation method, within a polygon scaled boundary finite element framework, to determine the maximum load capacity of structures at plastic collapse. The distinctive feature of the proposed scheme is its effective computational ability in performing a series of successive elastic analyses by systematically adjusting elastic material properties of structures up to failure. The quadtree structural discretization within a polygon scaled boundary finite element platform enables model construction of sophisticated geometries at modest computing effort and thus the effective analysis of large-scale structures. The approach overcomes the challenges associated with stress singularity and locking phenomena under incompressibility conditions, even in the presence of high-order nonlinear yield loci. The robustness and accuracy of the proposed scheme are validated through a number of benchmarks and available practical engineering applications in 2D and 3D spaces. These illustrate the influences of some key algorithmic parameters, and the satisfaction of a lower-bound limit given by the present analysis method for a sufficiently fine discretization.     

Sequence of operations analysis for dynamic data structures

This paper introduces a rather general technique for computing the average-case performance of dynamic data structures, subjected to arbitrary sequences of insert, delete, and search operations. The method allows us effectively to evaluate the integrated cost of various interesting data structure implementations, for stacks, dictionaries, symbol tables, priority queues, and linear lists; it can thus be used as a basis for measuring the efficiency of each proposed implementation. For each data type, a specific continued fraction and a family of orthogonal polynomials are associated with sequences of operations: Tchebycheff for stacks, Laguerre for dictionaries, Charlier for symbol tables, Hermite for priority queues, and Meixner for linear lists. Our main result is an explicit expression, for each of the above data types, of the generating function for integrated costs, as a linear integral transform of the generating functions for individual operation costs. We use the result to compute explicitly integrated costs of various implementations of dictionaries and priority queues.     

On minimizing the response of structures to dynamic loading

Zusammenfassung Eine obere Schranke wird angegeben für die Ausschläge eines elastischen Balkens unter allgemeiner dynamischer Belastung. Die Bemessung, für welche diese Schranke einen Kleinstwert annimmt, wird bestimmt und mit der Bemessung für kleinste statische Durchbiegung verglichen.

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Supported in part by the U. S. Army Research Office-Durham and in part by the United States Navy under Grant No. NONR N00014-67-A-0191-0009.     

A simple approach to dynamic stabilization of a rotating body-beam

In this paper, we use the frequency multiplier method to provide a simple proof of an exponential stabilization result, obtained in [B. Chentouf. Dynamic boundary controls of a rotating body-beam system with time-varying angular velocity, J. Appl. Math. 2 (2004) 107–126], for a rotating body-beam system with a control torque applied on the rigid body and either a dynamic boundary control moment or a dynamic boundary control force or both of them applied at the free end of the beam.     

Stochastic binary problems with simple penalties for capacity constraints violations

This paper studies stochastic programs with first-stage binary variables and capacity constraints, using simple penalties for capacities violations. In particular, we take a closer look at the knapsack problem with weights and capacity following independent random variables and prove that the problem is weakly ${\mathcal{N}\mathcal{P}}$ -hard in general. We provide pseudo-polynomial algorithms for three special cases of the problem: constant weights and capacity uniformly distributed, subset sum with Gaussian weights and strictly positively distributed random capacity, and subset sum with constant weights and arbitrary random capacity. We then turn to a branch-and-cut algorithm based on the outer approximation of the objective function. We provide computational results for the stochastic knapsack problem (i) with Gaussian weights and constant capacity and (ii) with constant weights and capacity uniformly distributed, on randomly generated instances inspired by computational results for the knapsack problem.     

An integrated approach to dynamic plant location and capacity planning

We consider a dynamic capacitated plant location problem in which capacities of opened plants are determined by acquisition and/or disposal of multiple types of facilities. We determine the opening schedule of plants, allocations of customers' demands and plans for acquisition and/or disposal of plant capacities that minimise the sum of discounted fixed costs for opening plants, delivery costs of products, and acquisition and operation costs of facilities. The dynamic capacitated plant location problem is formulated as a mixed integer linear program and solved by a heuristic algorithm based on Lagrangian relaxation and a cut and branch algorithm which uses Gomory cuts. Several solution properties of the relaxed problem are found and used to develop efficient solution procedures for the relaxed problem. A subgradient optimisation method is employed to obtain better lower bounds. The heuristic algorithm is tested on randomly generated test problems and results show that the algorithm finds good solutions in a reasonable amount of computation time.     

Correction to: Principal component analysis constrained by layered simple structures

Advances in Data Analysis and Classification - A Correction to this paper has been published: 10.1007/s11634-022-00503-9     

A dynamic programming approach for the airport capacity allocation problem

In most of the optimization models developed to manage airportsoperations, arrivals and departures capacities are treated asindependent variables: that is the number of flights allowedto take off does not affect the number of landings in any unitof time, and vice versa. This assumption is seldom verifiedin most of the congested airports, where many interactions betweenarrivals and departures take place. In this paper, we face the problem of finding the optimal trade-offbetween the number of arrivals and departures in order to reducea delay function of all the flights, using a more realisticrepresentation of the airport capacity, i.e. the capacity envelope. Under the assumption of piecewise linear convex capacity envelopesand of the exact interpolation of all the Pareto-optimal operationalpoints, we show that the problem can be formulated as a linearprogramming model. For general airport capacity envelopes, wepropose a dynamic programming formulation with a correspondingbackward solution algorithm, which is robust, easy to implementand has a linear computational complexity. The algorithm performancesare evaluated on different realistic scenarios, and the optimalsolutions are compared with those computed by a greedy algorithm,which can be seen as an approximation of the current decisionprocedures. The percentage deviation of the cost of these twosolutions ranges from 3.98 to 35.64%.     

Approximate dynamic programming for capacity allocation in the service industry

We consider a problem where different classes of customers can book different types of service in advance and the service company has to respond immediately to the booking request confirming or rejecting it. The objective of the service company is to maximize profit made of class-type specific revenues, refunds for cancellations or no-shows as well as cost of overtime. For the calculation of the latter, information on the underlying appointment schedule is required. In contrast to most models in the literature we assume that the service time of clients is stochastic and that clients might be unpunctual. Throughout the paper we will relate the problem to capacity allocation in radiology services. The problem is modeled as a continuous-time Markov decision process and solved using simulation-based approximate dynamic programming (ADP) combined with a discrete event simulation of the service period. We employ an adapted heuristic ADP algorithm from the literature and investigate on the benefits of applying ADP to this type of problem. First, we study a simplified problem with deterministic service times and punctual arrival of clients and compare the solution from the ADP algorithm to the optimal solution. We find that the heuristic ADP algorithm performs very well in terms of objective function value, solution time, and memory requirements. Second, we study the problem with stochastic service times and unpunctuality. It is then shown that the resulting policy constitutes a large improvement over an “optimal” policy that is deduced using restrictive, simplifying assumptions.     

Heuristics for selecting robust database structures with dynamic query patterns

The success of a company increasingly depends on timely information (internal or external) being available to the right person at the right time for crucial managerial decision-making. Achieving such a “right time/right place” duet depends directly on database performance. A database system has been a core component that supports modern business system such as enterprise resource planning (ERP) system that integrates and supports all enterprise processes including product designing and engineering, manufacturing, and other business functions to achieve highest efficiency and effectiveness of operations. We develop and demonstrate through a proof-of-concept case study, a new “query-driven” heuristics for database design that seeks to identify database structures that perform robustly in dynamic settings with dynamic queries. Our focus is the design of efficient structures to process read-only queries in complex environments. Our heuristics begins with detailed analysis of relationships between diverse queries and the performance of different database structures. These relationships are then used in a series of steps that identify “robust” database structures that maintain high performance levels for a wide range of query patterns. We conjecture that our heuristics can facilitate efficient operations and effective decision-making of companies in today’s dynamic environment.     

Resource capacity allocation to stochastic dynamic competitors: knapsack problem for perishable items and index-knapsack heuristic

In this paper we propose an approach for solving problems of optimal resource capacity allocation to a collection of stochastic dynamic competitors. In particular, we introduce the knapsack problem for perishable items, which concerns the optimal dynamic allocation of a limited knapsack to a collection of perishable or non-perishable items. We formulate the problem in the framework of Markov decision processes, we relax and decompose it, and we design a novel index-knapsack heuristic which generalizes the index rule and it is optimal in some specific instances. Such a heuristic bridges the gap between static/deterministic optimization and dynamic/stochastic optimization by stressing the connection between the classic knapsack problem and dynamic resource allocation. The performance of the proposed heuristic is evaluated in a systematic computational study, showing an exceptional near-optimality and a significant superiority over the index rule and over the benchmark earlier-deadline-first policy. Finally we extend our results to several related revenue management problems.     

Product line pricing for services with capacity constraints and dynamic substitution

In this paper, we address a service provider’s product line pricing problem for substitutable products in services, such as concerts, sporting events, or online advertisements. For each product, a static price is selected from a pre-defined set such that the total revenue is maximised. The products are differentiated by some of their attributes, and their availability is restricted due to individual capacity constraints. Furthermore, they are simultaneously sold during a common selling period at the end of which the service is delivered. Consumers differ from one another with respect to their willingness to pay, and, hence, their reservation prices vary depending on the product. In the event of a purchase, they choose the product that maximises their consumer surplus.     

Data structures and dynamic programming background for editing highly structured texts

The interactive editing and formatting of texts structured by a hierarchy of non-standard layout features requires a thorough study of the data structures and algorithms used. It is well known that many text processing systems in this field suffer either from bad performance or reduced quality of outputs and screen representation. The aim of this note is to demonstrate how to overcome these difficulties using dynamic programming algorithms and suitably designed data structures controlling the layout of structured texts.     

Solution of dynamic problems for perforated structures by the method of averaging

We consider transverse oscillations of a membrane with a square network of perforations whose contour is clamped and whose aperture edges are free. We apply the method of averaging in conjunction with variational methods for solving cell problems. The eigenfunctions and characteristic frequencies of oscillation are represented as asymptotic series in powers of a small parameter that characterizes the period of the lattice. The problem is solved in stages: first the cell problem, then the principal parts of the eigenfunctions and characteristic frequencies are determined from the averaged equation. To determine the first correction to the frequency we use the averaged equation for the next approximation and the selfadjoint property of the original operator.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 72–75.