The source-item coverage of the Lotka function

The following problem has never been studied : Given A, the total number of items (e.g. articles) and T, the total number of sources (e.g. journals that contain these articles) (hence A>T), when is there a Lotka function. This revised version was published online in August 2006 with corrections to the Cover Date.     

A proposal to define a core of a scientific subject: A definition using concentration and fuzzy sets

Determining the core of a field"s literature, i.e. its "most important" sources, has been and still is an important problem in bibliometrics. In this article an exact definition of a core of a bibliography or a conglomerate is presented. The main ingredients for this definition are: fuzzy set theory, Lorenz curves and concentration measures. If one prefers a strict delineation, the fuzzy core can easily be defuzzified. The method we propose does not depend on the subjective notion of "importance". It is, moreover, completely reproducible. The method and the resulting core is also independent of the mathematical function (Lotka, Zipf, Bradford, etc.) that may be used to describe the relation between the set of sources and that of items.     

桅杆在自然风中生命链研究：第三部分 桅杆结构动力可靠性分析

本文系桅杆在自然风中生命链研究的第三部分,主要研究桅杆在非零均值随激励作用下的动力可靠性。文中依据由Ｉｔｏ微分方程得到的ＦＰＫ方程、采用结构总响应统计量分析方法,直接导出在平均风和脉动风共同作用下桅杆顶层总体称的峰值概率密度函数,为直接处理类似非零均值激励总响应的峰值概率密度函数及动力可靠性分析提供一种可行途径。     

A solution procedure for Economic Lot Scheduling Problems even in high utilisation facilities

Economic lot scheduling problem (ELSP) handles the problem of deciding what order quantities to use when different products/items are produced in the same capacity constrained production facility. It has previously been shown, and it is shown in this article, that it is possible to find a feasible solution fulfilling true feasibility conditions. However, if the utilisation of the production facility is high the production often has to start before the inventory reaches zero to avoid future shortages. Such ‘early starts’ creates an extra inventory holding cost that the traditional approximation for the inventory holding cost does not account for. This article presents an iterative solution procedure that computes the true inventory holding cost and minimises the total costs. Contrary to previous solution procedures, this procedure requires that the production is scheduled in detail. The heuristic solution procedure is illustrated by a numerical example, it is programmed in MATLAB and variants of the problem are presented.     

Global dynamics of a family of 3-D Lotka–Volterra systems

In this article, we analyse the flow of a family of three-dimensional Lotka–Volterra systems restricted to an invariant and bounded region. The behaviour of the flow in the interior of this region is simple: either every orbit is a periodic orbit or orbits move from one boundary to another. Nevertheless, the complete study of the limit sets in the boundary allows one to understand the bifurcations which take place in the region as a global bifurcation that we denote by focus-centre-focus bifurcation.     

Performance and its relation with productivity in Lotkaian systems

In general information production processes (IPPs), we define productivity as the total number of sources but we present a choice of seven possible definitions of performance: the mean or median number of items per source, the fraction of sources with a certain minimum number of items, the h-, g-, R- and h_w-index. We give an overview of the literature on different types of IPPs and each time we interpret “performance” in these concrete cases. Examples are found in informetrics (including webometrics and scientometrics), linguistics, econometrics and demography. In Lotkaian IPPs we study these interpretations of “performance” in function of the productivity in these IPPs. We show that the mean and median number of items per source as well as the fraction of sources with a certain minimum number of items are increasing functions of the productivity if and only if the Lotkaian exponent is decreasing in function of the productivity. We show that this property implies that the g-, R- and h_w-indices are increasing functions of the productivity and, finally, we show that this property implies that the h-index is an increasing function of productivity. We conclude that the h-index is the indicator which shows best the increasing relation between productivity and performance.     

非晶态固体高聚物链构象的随机几何特性

本文尝试建立无规链相似于无规行走的模型,采用随机过程及平均场近似的方法研究非晶态固体高聚物的空间几何结构,如链构象的统计分布等,所得结果表明此模型可以成立,而且还表明此模型可用来描述链构象随机几何特性的若干方面。     

Some procedures for decision making in controlling high yield processes

Statistical process control based on the cumulative counts of conforming items instead of occurrences of non-conformances has proved to be useful for the manufacture of high-quality products. In this paper we study some interesting and useful issues of using cumulative counts in practice. The general problem in the control of high-quality products is first discussed, which leads to the calculation of the probability that a process is out of control when a single non-conforming item is detected. A decision graph is introduced with which we can easily judge whether the process is out of control when a non-conforming item is observed after a number of conforming ones, accompanied by the certainty level of this judgement. Next, using the equivalence of information on one non-conforming item found in a number of inspected items to that on zero non-conforming items in a smaller sample, we give a method for choosing a new starting point to reset the cumulative count after the detection of the non-conforming item. The procedures are all statistically justified and have the practical merit of simplicity in actual applications.     

The law of limited excellence: publication productivity of Israel Prize laureates in the life and exact sciences

The present paper extends Lotka’s theorem—which we rename as “the law of limited excellence”—while empirically modelling the scientific productivity of 46 Israel Prize laureates in the life and exact sciences—a group best described as ‘Star Scientists’. By focusing on this highly selective group we expose unequal scientific productivity even amongst Israel’s most prolific scientists. Specifically, we test the invariance of Lotka’s law by focusing attention on the extreme tail of publication distributions while empirically exploring the non-linearity of its seemingly “flat” tail. By exposing the rarity of excellence even in this extreme end of publication productivity we extend the generality of Lotka’s theorem and expose that—like a fractal—the tail of excellence behaves as the entire distribution. We end this empirical contribution by suggesting a few implications for research and policy.     

Effect of Columnar Defects on Magnetization of Mesoscopic Superconductors

In this work we investigated magnetization and vortex configurations in mesoscopic superconducting samples in the presence of square columnar defects (CDs). We solved numerically the nonlinear TDGL equations for different samples to study magnetization as a function of the applied magnetic field. In calculations, we focused mainly on four samples with different numbers of CDs which have the same total surface area. In this way, the total superconducting area remained the same with increasing the number of CDs for a fixed sample size. We found that the superconducting regions still exist inside the sample at high applied magnetic fields with increasing the number of CDs but irreversible effects became increasingly prominent, when the field is returned to zero. The results are discussed in frame of surface and pinning effects in mesoscopic systems.     

An informetric model for the Hirsch-index

Summary The h-index (or Hirsch-index) was defined by Hirsch in 2005 as the number h such that, for a general group of papers, h papers received at least h citations while the other papers received no more than h citations. This definition is extended here to the general framework of Information Production Processes (IPPs), using a source-item terminology. It is further shown that in each practical situation an IPP always has a unique h-index. In Lotkaian systems h = T^1/a, where T is the total number of sources and α is the Lotka exponent. The relation between h and the total number of items is highlighted.     

Optimal control of a stochastic production–inventory system under deteriorating items and environmental constraints

In this paper, we present an optimal control model of a stochastic production–inventory with deteriorating items, emission tax and pollution abatement investment. In our model, the emission tax is levied on the firm’s environmental obsolescence rate of technology rather than the total amount of the environmental externality. Our objective is to apply Hamilton–Jacobi–Bellman (HJB) equation to solve the stochastic production–inventory system with deteriorating items, emission tax and pollution abatement investment; and derive the optimal production rate and pollution abatement investment rate that maximise the objective function value. The results are discussed with some illustrative examples for different demand rate functions, and sensitivity analysis is conducted to study the effect of changing the parameters and coefficients on the objective function value.     

Zipf's data on the frequency of Chinese words revisited

At the occasion of the 40th anniversary of George Zipf's premature dead, we reanalyse his data on the frequency of Chinese words. We find the best fitting Lotka, Zipf, Bradford and Leimkuhler distribution and show that only Lotka's function is not rejected by a Kolmogorov-Smirnov test. Using an additional term to Leimkuhler's function leads to a statistically acceptable fit. In this way we can determine a core (nucleus) of most frequently used Chinese words.     

Publish and Perish

In spite of having published more than hundred articles and three monographs, the chemist and statistician Alfred James Lotka (1880–1949) is not very well known. Because he had not experienced a conventional academic curriculum, he remained ?at the margins’ of the scientific community. In 1925 he aimed for a breakthrough with his first monograph Elements of Physical Biology. The basic idea of this study was to understand nature in terms of energy. Lotka’s mathematical approach was highly innovative, although he had borrowed certain notions from his former teacher, the physical chemist Wilhelm Ostwald. This article focuses on the very process of how a new idea developed and spread through the scientific community, and tries to determine to what extent the author—with his personality, his intentions and feelings—was part of this process. This includes looking at the emotional strain that followed the publication of Lotka’s masterpiece. Considering his anxieties, worries and distress during the period of reception, and his efforts to make sure his book was acknowledged by its audience, the article sheds light on often neglected aspects of scientific work such as identification, intention, mimicry, originality, and rivalry. The case study deals with a systematic blindness in the history of science: it takes into account the actors of science, their personality and their strategic moves, in order to come to a better understanding of the close connection between their work and their actions. In addition, the history of Lotka’s worries about the reception of his book might help us challenge the postulate of ?publish or perish“ in today’s science.     

Dirichlet problem for convection-diffusion-reaction inside a permeable cylindrical porous pellet

The present article deals with the study of convection and diffusion coupled with either zero or first order reaction inside a permeable circular cylindrical porous pellet under oscillatory flow. Unsteady Stokes equations are used for the flow outside the permeable porous pellet and Darcy’s law is used inside the pellet. We use the stream function approach in order to solve the hydrodynamic problem. Then the convection-diffusion-reaction problem is formulated and solved analytically for both zero order and first order rate of nutrient uptake. The Dirichlet boundary condition, which can be achieved by neglecting the external mass transfer resistance, is used at the surface of permeable porous pellet. Also in case of zero order, an optimality criterion, which is a relationship between the Peclet number and the Thiele modulus, is proposed to avoid the starvation everywhere inside the pellet. Based on this criterion, classification is done in order to identify the regions of nutrient sufficiency and starvation. A comparison is also made with nutrient transport inside a spherical porous pellet. It is observed that in case of zero order, for a fixed combination of other parameters, spherical pellet demands a higher value of Thiele modulus compared to the cylindrical pellet in order to force starvation. Moreover, in case of first order reaction, one does not witness starvation zones either in cylindrical pellet or in spherical pellet.     

Optimal joint replenishment policy for multiple non-instantaneous deteriorating items

In this paper, we deal with the problem of determining the optimal economic operating policy when a number of non-instantaneous deteriorating items are jointly replenished. We establish a multi-item joint replenishment model for non-instantaneous deteriorating items under constant demand rate allowing full backlogging. This problem is challenging, in particular, the cost function is a piecewise function with exponential parts, which makes the problem more complicated. To solve this problem, an approximation method is used to simplify the objective function and a bound-based heuristic algorithm is developed to solve the model. Numerical examples illustrate the effectiveness of the proposed method and the quality of the approximation. Experimental results on a real-life case study show that the proposed model can achieve substantial cost savings compared to the individual replenishment policy for non-instantaneous deteriorating items. Furthermore, sensitivity analysis of key parameters is carried out and the implications are discussed in detail.     

约束最优化问题中一个全局误差界及其应用

本文利用信赖域方法中的几个特征量(由预测下降量给出的价值函数与信赖域半径等),在目标函数的梯度向量是强单调的条件下,为约束最优化问题的可行解与最优解之间的距离提供了一个全局误差界。我们利用误差界得出了可行解点列收敛于最优解的充分条件和可行解点列收敛到KT点的必要条件。最后,还给出了可行解点列至KT点集的距离趋于零的必要条件。     

Determining Optimum Reject Allowances for Multistage Job-Lot Manufacturing

Since most manufacturing processes inevitably produce some defective items, it is common practice to produce a quantity larger than the actual order size. This excess is called a reject allowance. This article considers multistage job-lot manufacture where items are produced by a sequence of n stages (operations). It demonstrates that under appropriate conditions, the total expected cost function is uni-modal which establishes the existence of a smallest optimum reject allowance. Computation procedures are also discussed.     

ON THE USE OF BUFFER INVENTORIES TO MINIMIZE COSTS WITH AN UNRELIABLE MACHINE

In this paper, we discuss the problem of quality control with an unreliable machine which produces defects at a rate of Λ₀, per unit when in-control and a rate of Lambda; ₁, when out-of-control (where Λ₁ Λ ₀). Every h time periods, we sample n units, count the number of defects, and (using a process based on a Shewart c-chart) test the hypothesis that the machine is in control by comparing the total number of defects to an upper control limit (UCL). More important, we introduce the concept that a buffer inventory which immediately follows the unreliable machine may reduce expected total costs. This buffer serves to delay the movement of items from the unreliable machine to the next stage of the production process. In this way, we can isolate and repair most defective items before they are embedded in a product downstream or sold to customers where repair is more costly. To search for the optimal control policy, we find bounds for n, h, and UCL; given values for these variables, we show how the optimal buffer size can be determined directly. Numerical results illustrate the magnitude of potential savings.     

Trajectories in parallel optics

In our previous work we showed the ability to improve the optical system's matrix condition by optical design, thereby improving its robustness to noise. It was shown that by using singular value decomposition, a target point-spread function (PSF) matrix can be defined for an auxiliary optical system, which works parallel to the original system to achieve such an improvement. In this paper, after briefly introducing the all optics implementation of the auxiliary system, we show a method to decompose the target PSF matrix. This is done through a series of shifted responses of auxiliary optics (named trajectories), where a complicated hardware filter is replaced by postprocessing. This process manipulates the pixel confined PSF response of simple auxiliary optics, which in turn creates an auxiliary system with the required PSF matrix. This method is simulated on two space variant systems and reduces their system condition number from 18,598 to 197 and from 87,640 to 5.75, respectively. We perform a study of the latter result and show significant improvement in image restoration performance, in comparison to a system without auxiliary optics and to other previously suggested hybrid solutions. Image restoration results show that in a range of low signal-to-noise ratio values, the trajectories method gives a significant advantage over alternative approaches. A third space invariant study case is explored only briefly, and we present a significant improvement in the matrix condition number from 1.9160e+013 to 34,526.