Stability and accuracy functions in a coalition game with bans,linear payoffs and antagonistic strategies

A coalition game with a finite number of players in which initial coefficients of linear payoff functions are subject to perturbations is considered. For any efficient solution which may appear in the game, appropriate measures of the quality are introduced. These measures correspond to the so-called stability and accuracy functions defined earlier for efficient solutions of a generic multiobjective combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied. Maximum norms of perturbations for which an efficient in sense of equilibrium solution preserves the property of being efficient are calculated.     

Estimates on the Speedup and Slowdown for a Diffusion in a Drifted Brownian Potential

We study a model of diffusion in a Brownian potential. This model was first introduced by T. Brox (Ann. Probab. 14:1206–1218, 1986) as a continuous time analogue of random walk in random environment. We estimate the deviations of this process above or under its typical behavior. Our results rely on different tools such as a representation introduced by Y. Hu, Z. Shi and M. Yor, Kotani’s lemma, introduced at first by K. Kawazu and H. Tanaka (J. Math. Soc. Jpn. 49:189–211, 1997), and a decomposition of hitting times developed in a recent article by A. Fribergh, N. Gantert and S. Popov (Preprint, 2008). Our results are in agreement with their results in the discrete case.     

Convergence criterion and convergence ball of the Newton-type method in Banach space

The paper is concerned with the convergence problem of third-order Newton-type methods for finding zeros of nonlinear operations in Banach spaces. Under the hypothesis that the derivative of f satisfies the weak Lipschitz condition with L-average, the convergence criterion and convergence ball are given. Furthermore, some corollaries are obtained by applying the main results to some special functions L.     

Technological progress and productivity growth in the U.S. mobile telecommunications industry

The fast growing U.S. mobile wireless industry has been experiencing dramatic technological change and substantial competition. As a result of these catalysts, we argue that wireless firms have experienced significant productivity improvement and provide new evidence that technological progress almost exclusively contributed to productivity improvements in the wireless industry by significantly expanding the production possibilities set. We employ nonparametric estimation procedures based on Data Envelopment Analysis (DEA) that utilize input-output data from a representative sample of 16 firms in the mobile wireless industry to estimate productivity change, technological change, and relative efficiency change for the period spanning the years from 2000 to 2002. Our findings show that the industry experienced a significant growth of 13% in productivity, which was primarily due to an average technological progress of 9.9% in the industry. Additionally, we find that national wireless operators experienced significantly higher productivity growth and contributed more to technological progress than regional providers. Firms that were industry pioneers as evidenced by high market share at the beginning of our sample period experienced higher productivity growth and greater technological progress compared to firms with lower initial market share. Moreover, the industry experienced significantly higher productivity growth and technical progress in the later sample period between 2001 and 2002 than in the early period between 2000 and 2001.     

On some invariants in numerical semigroups and estimations of the order bound

Let S={s _i } _i∈??? be a numerical semigroup. For s _i ∈S, let ν(s _i ) denote the number of pairs (s _i ?s _j ,s _j )∈S ². When S is the Weierstrass semigroup of a family $\{\mathcal{C}_{i}\}_{i\in\mathbb{N}}Let S={s _i } _i∈ℕ⊆ℕ be a numerical semigroup. For s _i ∈S, let ν(s _i ) denote the number of pairs (s _i −s _j ,s _j )∈S ². When S is the Weierstrass semigroup of a family {C_i}_{i ? \mathbbN}\{\mathcal{C}_{i}\}_{i\in\mathbb{N}} of one-point algebraic-geometric codes, a good bound for the minimum distance of the code C_i\mathcal{C}_{i} is the Feng and Rao order bound d _ORD (C _i ). It is well-known that there exists an integer m such that d _ORD (C _i )=ν(s _i+1) for each i≥m. By way of some suitable parameters related to the semigroup S, we find upper bounds for m and we evaluate m exactly in many cases. Further we conjecture a lower bound for m and we prove it in several classes of semigroups.     

Place and use of new technology in the teaching of mathematics: ICMI activities in the past 25 years

Looking back at the place of technology in the past ICMEs during the last decades and on the two ICMI studies devoted to technology, it is obvious that the role and use of technology has given rise to a diversity of points of view and attitudes across the world. The ICMEs and the two studies are places where researchers, teacher educators and practitioners meet. To what extent do they reflect the evolution of the trends of research and/or of integration of technology into real practice? The study will develop a general analysis of the theoretical frameworks, issues and wishes related to the use of technology in mathematics teaching from the proceedings of past ICMEs and of the two ICMI studies. Both a quantitative and a qualitative point of view will be adopted. From the great diversity of questions and approaches, the study attempts to formulate the main trends and their evolution over time within the ICMI community, as well as some pertinent issues for the coming years.     

Shape optimization of an airfoil in the presence of compressible and viscous flows

The objective of this article is to present a step-by-step problem-solving procedure of shape optimization. The procedure is carried out to design an airfoil in the presence of compressible and viscous flows using a control theory approach based on measure theory. An optimal shape design (OSD) problem governed by full Navier-Stokes equations is given. Then, a weak variational form is derived from the linearized governing equations. During the procedure, because the measure theory (MT) approach is implemented using fixed geometry versus moving geometry, a proper bijective transformation is introduced. Finally, an approximating linear programming (LP) problem of the original shape optimization problem is obtained by means of MT approach that is not iterative and does not need any initial guess to proceed. Illustrative examples are provided to demonstrate efficiency of the proposed procedure.     

Modeling the synergy level in a vertical collaborative supply chain through the IMP interaction model and DEA framework

This work develops a mathematical programming model that characterizes the main variables present in the interaction dynamics of each agent in a collaborative vertical logistical system, such as a supply chain, and measures the synergy level of such system. The model is based on the interaction model developed by the IMP (Industrial Marketing and Purchasing) group and also on the DEA (Data Envelopment Analysis) framework. The basics of these two approaches allow modeling of the characteristics of an agent as well as the collaborative relationships with other agents within the chain. The model was validated using information of supply chain of leather and its products, classified by DANE (Departamento Nacional de Estadistica—Colombia) as the sector CIIU323.     

On Universality of Critical Behavior in the Focusing Nonlinear Schrödinger Equation, Elliptic Umbilic Catastrophe and the Tritronquée Solution to the Painlevé-I Equation

We argue that the critical behavior near the point of “gradient catastrophe” of the solution to the Cauchy problem for the focusing nonlinear Schrödinger equation $i\epsilon \varPsi _{t}+\frac{\epsilon^{2}}{2}\varPsi _{xx}+|\varPsi |^{2}\varPsi =0We argue that the critical behavior near the point of “gradient catastrophe” of the solution to the Cauchy problem for the focusing nonlinear Schr?dinger equation , ε ≪1, with analytic initial data of the form is approximately described by a particular solution to the Painlevé-I equation.      

The optimal order and payment policies for deteriorating items in discount cash flows analysis under the alternatives of conditionally permissible delay in payments and cash discount

This study investigates a deteriorating inventory problem in which the supplier simultaneously offers the retailer either a conditionally permissible delay in payments or a cash discount. In the case of a conditionally permissible delay, if the retailer orders more than a predetermined quantity, then he/she has a grace period to make the full payment. Otherwise, he/she must pay the payment for goods of certain proportion first while receiving the goods and has a grace period to pay off the rest. As to a cash discount, if the retailer pays for the entire amount of the order within a certain short period, then he/she will receive a cash discount from the supplier. In additions, from a financial standpoint, all cash outflows related to the inventory control that occur at different points of time have different values. Hence, it is necessary to take account of the factor of time value of monetary when drafting the replenishment policy. In a word, this paper uses an alternate approach-discount cash flow (DCF) analysis to establish an inventory problem for deteriorating items in which the supplier provides the retailer either a conditionally permissible delay or a cash discount. We then study the necessary and sufficient conditions for finding the optimal solution. Furthermore, we establish several theoretical results to obtain the solution that provides the smallest present value of all future cash flows. Finally, several numerical examples are given to illustrate the results and obtain some managerial insights.     

Scheduling in a multi-processor environment with deteriorating job processing times and decreasing values: the case of forest fires

In forest fire fighting, time and effort required to control a fire increase if fire containment effort is delayed. The problem of scheduling multiple resources employed as parallel identical or non-identical processors in order to contain N≥2 fires may be tackled using the concept of deteriorating jobs. In this paper, the above problem is stated and a model is formulated, the criterion being to maximize the total remaining value of the burnt areas and a real-time synchronous heuristic algorithm is proposed. The heuristic algorithm’s efficiency was compared to real data provided by Greek Fire Corps from a severe wildfire near Athens in June-July, 2007.     

Wavelet improvement in turning point detection using a hidden Markov model: from the aspects of cyclical identification and outlier correction

The hidden Markov model (HMM) has been widely used in regime classification and turning point detection for econometric series after the decisive paper by Hamilton (Econometrica 57(2):357–384, 1989). The present paper will show that when using HMM to detect the turning point in cyclical series, the accuracy of the detection will be influenced when the data are exposed to high volatilities or combine multiple types of cycles that have different frequency bands. Moreover, outliers will be frequently misidentified as turning points. The present paper shows that these issues can be resolved by wavelet multi-resolution analysis based methods. By providing both frequency and time resolutions, the wavelet power spectrum can identify the process dynamics at various resolution levels. We apply a Monte Carlo experiment to show that the detection accuracy of HMMs is highly improved when combined with the wavelet approach. Further simulations demonstrate the excellent accuracy of this improved HMM method relative to another two change point detection algorithms. Two empirical examples illustrate how the wavelet method can be applied to improve turning point detection in practice.     

Retracts in Polydisk and Analytic Varieties with the <Emphasis Type="Italic">H</Emphasis><Superscript>∞</Superscript>-Extension Property

This article mainly concerns retracts in polydisk, analytic varieties with the H ^∞-extension property and the three-point Pick problem on . Arising in the study of Nevanlinna-Pick interpolation on the bidisk, Agler and McCarthy recently discovered a remarkable theorem which characterizes subsets in the bidisk with the polynomial extension property, and in this case, these subsets are retracts. To study H ^∞-extensions of holomorphic functions from subvarieties of polydisk, one naturally is concerned with retracts in polydisk. Under certain mild assumptions, it is shown that subvarieties with H ^∞-extension property are exactly retracts. Furthermore, we apply our argument to determine those retracts whose retractions are unique. In particular, a retract in having at least two different retractions is exactly a balanced disk. As an application, we give a sufficient condition of the uniqueness of the solution for the three-point Pick problem on .      

Some properties of Frobenius numbers and a fraction of symmetric semigroups in the weak limit for <Emphasis Type="Italic">n</Emphasis>=3

We generalize and prove a conjecture by V.I. Arnold on the parity of Frobenius numbers. For the case of symmetric semigroups with three generators we give an exact formula for Frobenius numbers, which is, in a sense, a sum of two Sylvester’s formulae. We prove that a fraction of symmetric semigroups vanishes in the weak limit.