A search algorithm for linear codes: progressive dimension growth

This paper presents an algorithm, called progressive dimension growth (PDG), for the construction of linear codes with a pre-specified length and a minimum distance. A number of new linear codes over GF(5) that have been discovered via this algorithm are also presented.      

Interactive markovian models of ‘progressive’ trends

Non‐linear Markovian models are investigated for a developing society stratified in terms of literacy or some other sociocultural attribute and characterized by two opposing features: a) progressive trends which forbid upper to lower state intergeneration transitions, and b) fertility differential in favour of lower states. The progressive trends in the models arise due to ‘attraction’ of the higher states. Two different limits are considered: one in which all upward transitions are permitted (Maximal Attractor Model) and the other in which only one‐step transitions are allowed (Adjacent Attractor Model). The nature of the critical points of the two models is examined analytically and/or numerically as appropriate to the case in question. In the first model, the society converges to the highest state in due course despite the fertility differential. The three‐state and four‐state cases of the models are considered in some detail. The main interesting result concerns the Adjacent Attractor Model. For the three‐state case, numerical computation reveals this model society locked in an endless cyclic pattern of evolution despite the existence of a progressive trend.     

Inference for a progressive stress model from Weibull distribution under progressive type-II censoring

Based on progressively type-II censored samples, this paper considers progressive stress accelerated life tests when the lifetime of an item under use condition follows the Weibull distribution with a scale parameter satisfying the inverse power law. It is assumed that the progressive stress is directly proportional to time and the cumulative exposure model for the effect of changing stress holds. Point estimation of the model parameters is obtained graphically by using Weibull probability paper plot that serves as a tool for model identification and also by using the maximum likelihood method. Interval estimation is performed by finding approximate confidence intervals (CIs) for the parameters as well as the studentized-t and percentile bootstrap CIs. Monte Carlo simulation study is carried out to investigate the precision of the estimates and compare the performance of CIs obtained. Finally, two examples are presented to illustrate our results.     

A free boundary problem arising from DCIS mathematical model

Ductal carcinoma in situ – a special cancer – is confined within the breast ductal only. We derive the mathematical ductal carcinoma in situ model in a form of a nonlinear parabolic equation with initial, boundary, and free boundary conditions. Existence, uniqueness, and stability of problem are proved. Algorithm and illustrative examples are included to demonstrate the validity and applicability of the technique in this paper. Copyright © 2016 John Wiley & Sons, Ltd.     

A mathematical programming-based scheduling framework for multitasking environments

A new paradigm along with a mixed (binary) integer-linear programming model is developed for scheduling tasks in multitasking environments, for which the number of completed tasks is not a good measure. One special case falls into the realm of deteriorating jobs. Polynomial time optimal solution algorithms are presented for this and one other special case. As the complexity of the original problem is believed to be strongly NP-hard, an efficient solution algorithm, based on tabu search, is developed to solve the problem. Small, medium, and large size problems are solved, and the solution obtained from the algorithm is compared with that of the optimal solution or the upper bound found from using the Lagrangian relaxation. Where it was measurable, the search algorithm gave quantifiably good quality solutions, and in all cases it had a much better time efficiency than the branch-and-bound enumeration method. A detailed statistical experiment, based on the split-plot design, is developed to identify the characteristics of the tabu search algorithm, thus guaranteeing a solution that is significantly better in quality. A conjecturing technique is introduced for problems with very large planning horizons. This technique had remarkable time efficiency with no apparent loss of quality.     

A multi-objective joint replenishment inventory model of deteriorated items in a fuzzy environment

In this study, a fuzzy multi-objective joint replenishment inventory model of deteriorating items is developed. The model maximizes the profit and return on inventory investment (ROII) under fuzzy demand and shortage cost constraint. We propose a novel inverse weight fuzzy non-linear programming (IWFNLP) to formulate the fuzzy model. A soft computing, differential evolution (DE) with/without migration operation, is proposed to solve the problem. The performances of the proposed fuzzy method and the conventional fuzzy additive goal programming (FAGP) are compared. We show that the solution derived from the IWFNLP method satisfies the decision maker’s desirable achievement level of the profit objective, ROII objective and shortage cost constraint goal under the desirable possible level of fuzzy demand. It is an effective decision tool since it can really reflect the relative importance of each fuzzy component.     

A note on: Optimal ordering policy for stock-dependent demand under progressive payment scheme

In a recent paper, Soni and Shah [Soni, H., Shah, N. H. (2008). Optimal ordering policy for stock-dependent demand under progressive payment scheme. European Journal of Operational Research 184(1), 91–100] developed a model to find the optimal ordering policy for a retailer with stock-dependent demand and a supplier offering a progressive payment scheme to the retailer. This note corrects some errors in the formulation of the model of Soni and Shah. It also extends their work by assuming that the credit interest rate of the retailer may exceed the interest rate charged by the supplier. Numerical examples illustrate the benefits of these modifications.     

A mathematical model for the first-pass dynamics of antibiotics acting on the cardiovascular system

We present a preliminary first-pass dynamic model for delivery of drug compounds to the lungs and heart. We use a compartmental mass-balance approach to develop a system of nonlinear differential equations for mass accumulated in the heart as a result of intravenous injection. We discuss sensitivity analysis as well as methodology for minimizing mass in the heart while maximizing mass delivered to the lungs on a first circulatory pass.     

A note on optimal ordering policies when the supplier provides a progressive interest scheme

Goyal et al. [Goyal, S.K., Teng, J.T., Chang, C.T., 2007. Optimal ordering policies when the supplier provides a progressive interest scheme. European Journal of Operational Research 179, 404–413] explore optimal ordering policies when the supplier provides a progressive interest scheme. The main purpose of this paper is fourfold:

(1)

This paper simplifies the total relevant cost per year Z(T) of Goyal et al. (2007) such that we can locate the optimal solutions of Z(T) by an easier way.     

ROI-based procedures for progressive transmission of digital images: A comparison

Nowadays, problems arise when handling large-sized images (i.e. medical image such as Computed Tomographies or satellite images) of 10, 50, 100 or more Megabytes, due to the amount of time required for transmitting and displaying, this time being even worse when a narrow bandwidth transmission medium is involved (i.e. dial-up or mobile network), because the receiver must wait until the entire image has arrived. To solve this issue, progressive transmission schemes are used. These schemes allow the image sender to encode the image data in such a way that it is possible for the receiver to perform a reconstruction of the original image from the very beginning of transmission. Despite this reconstruction being, of course, partial, it is possible to improve the reconstruction on the fly, as more and more data of the original image are received. There are many progressive transmission methods available, such as it planes, TSVQ, DPCM, and, more recently, matrix polynomial interpolation, Discrete Cosine Transform (DCT, used in JPEG) and wavelets (used in JPEG 2000). However, none of them is well suited, or perform poorly, when, in addition to progressive transmission, we want to include also ROIs (Region Of Interest) handling. In the progressive transmission of ROIs, we want not only to reconstruct the image as we receive image data, but also to be able to select which part or parts of the emerging image we think are relevant and want to receive first, and which part or parts are of no interest. In this context we present an algorithm for lossy adaptive encoding based on singular value decomposition (SVD). This algorithm turns out to be well suited for progressive transmission and ROI selection of 2D and 3D images, as it is able to avoid redundancy in data transmission and does not require any sort of data recodification, even if we select arbitrary ROIs on the fly. We compare the performing of SVD with DCT and wavelets and show the results.     

A comprehensive extension of optimal ordering policy for stock-dependent demand under progressive payment scheme

In a recent paper, Soni and Shah (2008) presented an inventory model with a stock-dependent demand under progressive payment scheme, assuming zero ending-inventory and adopting a cost-minimization objective. However, with a stock-dependent demand a non-zero ending stock may increase profits resulting from the increased demand. This work is motivated by Soni and Shah’s (2008) paper extending their model to allow for: (1) a non-zero ending-inventory, (2) a profit-maximization objective, (3) a limited inventory capacity and (4) deteriorating items with a constant deterioration rate. For the resulted model sufficient conditions for the existence and uniqueness of the optimal solution are provided. Finally, several economic interpretations of the theoretical results are also given.     

A mathematical model of silicon-based thermobiosensors

A mathematical model of a silicon glucose thermobiosensor thatdetects changes in temperature produced by a biocatalytic reactionis proposed for calculation of transient temperature and reactantconcentration profiles, time-dependencies of the output signal,and calibration curves. Mathematically the model is reducedto a one-dimensional linear initial-boundary-value problem ofthe heat-conduction equation with a thermal source F(x, t).In order to find F(x, t), a system of the second-order nonlinearpartial differential equations for glucose and oxygen concentrations,describing a combination of diffusion-membrane theory and Michaelis-Mentenenzyme reaction theory, has been solved. The computed dependenciesof transient temperature profile and sensor response to variousconditions such as oxygen buffer concentration, membrane thickness,enzyme loading, and operation mode are analysed for the optimaldesign of the tensor.     

A mathematical model of infectious diseases

In the formulation of models for the spread of communicable diseases which include removal and population dynamics, it is necessary to distinguish between removal through recovery with immunity and removal by death due to disease. This distinction must be made because of the difference in the effect on the population dynamics of the different kinds of removal and because there are significant differences in the behavior of the models. We have formulated a class of models which allow recovery with immunity for a fraction of the infective and permanent removal by death from disease for the remainder. Earlier models of this type have postulated an increased death rate for infective, but such models are restricted to exponentially distributed-infective periods. Because of the differences in behavior between models with recovery and models with permanent removal do not arise when the infective period is exponentially distributed, we have chosen to formulate a different type of model which is sufficiently general to admit qualitative differences.     

A mathematical model of inter-terminal transportation

We present a novel integer programming model for analyzing inter-terminal transportation (ITT) in new and expanding sea ports. ITT is the movement of containers between terminals (sea, rail or otherwise) within a port. ITT represents a significant source of delay for containers being transshipped, which costs ports money and affects a port’s reputation. Our model assists ports in analyzing the impact of new infrastructure, the placement of terminals, and ITT vehicle investments. We provide analysis of ITT at two ports, the port of Hamburg, Germany and the Maasvlakte 1 & 2 area of the port of Rotterdam, The Netherlands, in which we solve a vehicle flow combined with a multi-commodity container flow on a congestion based time–space graph to optimality. We introduce a two-step solution procedure that computes a relaxation of the overall ITT problem in order to find solutions faster. Our graph contains special structures to model the long term loading and unloading of vehicles, and our model is general enough to model a number of important real-world aspects of ITT, such as traffic congestion, penalized late container delivery, multiple ITT transportation modes, and port infrastructure modifications. We show that our model can scale to real-world sizes and provide ports with important information for their long term decision making.     

A mathematical model of market competition

We consider a mathematical model of decision making by a company attempting to win a market share. We assume that the company releases its products to the market under the competitive conditions that another company is making similar products. Both companies can vary the kinds of their products on the market as well as the prices in accordance with consumer preferences. Each company aims to maximize its profit. A mathematical statement of the decision-making problem for the market players is a bilevel mathematical programming problem that reduces to a competitive facility location problem. As regards the latter, we propose a method for finding an upper bound for the optimal value of the objective function and an algorithm for constructing an approximate solution. The algorithm amounts to local ascent search in a neighborhood of a particular form, which starts with an initial approximate solution obtained simultaneously with an upper bound. We give a computational example of the problem under study which demonstrates the output of the algorithm.     

A mathematical model of clarifier-thickener units

We review a recent analysis of a clarifier-thickener model for flocculated suspensions. The resulting governing PDE is a strongly degenerate convection-diffusion equation with discontinuous flux. A new numerical example illustrates how control actions speed up thickener operation significantly. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A mathematical model of retinal neovascularization

A mathematical model based on diffusion equations is presented, which directly relates the production of Vascular Endothelial Growth Factor (VEGF) in the retina to oxygen concentration and consumption, the capillary density growth to VEGF production and concentration, and the oxygen concentration to the growth of capillary density. The effects of local neovascularization on local oxygenation, which in turn affects the vascularization process resulting in biological feedback, are examined.     

A mathematical model for continuous crystallization

J. Banasiak We discuss a mixed‐suspension, mixed‐product removal crystallizer operated at thermodynamic equilibrium. We derive and discuss the mathematical model based on population and mass balance equations and prove local existence and uniqueness of solutions using the method of characteristics. We also discuss the global existence of solutions for continuous and batch mode. Finally, a numerical simulation of a continuous crystallizer in steady state is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

A mathematical model for asset pricing

Asset price dynamics is studied by using a system of ordinary differential equations which is derived by utilizing a new excess demand function introduced by Caginalp [4] for a market involving more information on demand and supply for a stock rather than their values at a particular price. Derivation is based on the finiteness of assets (rather than assuming unbounded arbitrage) in addition to investment strategies that are based on not only price momentum (trend) but also valuation considerations. For this new model and the older models which were extracted using the classical excess demand function by Caginalp and Balenovich [2] and [3], time evolutions of asset price are compared through numerical simulations.