A Galois correspondence for countable short recursively saturated models of PA

In this paper we investigate the properties of automorphism groups of countable short recursively saturated models of arithmetic. In particular, we show that Kaye's Theorem concerning the closed normal subgroups of automorphism groups of countable recursively saturated models of arithmetic applies to automorphism groups of countable short recursively saturated models as well. That is, the closed normal subgroups of the automorphism group of a countable short recursively saturated model of PA are exactly the stabilizers of the invariant cuts of the model which are closed under exponentiation. This Galois correspondence is used to show that there are countable short recursively saturated models of arithmetic whose automorphism groups are not isomorphic as topological groups. Moreover, we show that the automorphism groups of countable short arithmetically saturated models of PA are not topologically isomorphic to the automorphism groups of countable short recursively saturated models of PA which are not short arithmetically saturated (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical solution for a class of learning by doing models with multiplicative uncertainty

We find the closed form optimal solution for a class of learning by doing models, where multiplicative uncertainty is introduced in a piecewise linear cost reduction function. Previous literature does not find the closed form optimal solution for these models. We consider a monopolist, facing a linear demand function. The optimal policy for the resulting problem is shown to be piecewise linear and continuous. The optimal output increases with unit cost for certain values of the latter. Numerical examples are provided.     

Open versus closed loop capacity equilibria in electricity markets under perfect and oligopolistic competition

We consider two game-theoretic models of the generation capacity expansion problem in liberalized electricity markets. The first is an open loop equilibrium model, where generation companies simultaneously choose capacities and quantities to maximize their individual profit. The second is a closed loop model, in which companies first choose capacities maximizing their profit anticipating the market equilibrium outcomes in the second stage. The latter problem is an equilibrium problem with equilibrium constraints. In both models, the intensity of competition among producers in the energy market is frequently represented using conjectural variations. Considering one load period, we show that for any choice of conjectural variations ranging from perfect competition to Cournot, the closed loop equilibrium coincides with the Cournot open loop equilibrium, thereby obtaining a ‘Kreps and Scheinkman’-like result and extending it to arbitrary strategic behavior. When expanding the model framework to multiple load periods, the closed loop equilibria for different conjectural variations can diverge from each other and from open loop equilibria. We also present and analyze alternative conjectured price response models with switching conjectures. Surprisingly, the rank ordering of the closed loop equilibria in terms of consumer surplus and market efficiency (as measured by total social welfare) is ambiguous. Thus, regulatory approaches that force marginal cost-based bidding in spot markets may diminish market efficiency and consumer welfare by dampening incentives for investment. We also show that the closed loop capacity yielded by a conjectured price response second stage competition can be less or equal to the closed loop Cournot capacity, and that the former capacity cannot exceed the latter when there are symmetric agents and two load periods.     

On converse Lyapunov theorems for fluid network models

We consider the class of closed generic fluid network (GFN) models, which provides an abstract framework containing a wide variety of fluid networks. Within this framework a Lyapunov method for stability of GFN models was proposed by Ye and Chen. They proved that stability of a GFN model is equivalent to the existence of a functional on the set of paths that is decaying along paths. This result falls short of a converse Lyapunov theorem in that no state-dependent Lyapunov function is constructed. In this paper we construct state-dependent Lyapunov functions in contrast to path-wise functionals. We first show by counterexamples that closed GFN models do not provide sufficient information that allow for a converse Lyapunov theorem. To resolve this problem we introduce the class of strict GFN models by forcing closed GFN models to satisfy a concatenation and a semicontinuity condition. For the class of strict GFN models we define a state-dependent Lyapunov function and show that a converse Lyapunov theorem holds. Finally, it is shown that common fluid network models, like general work-conserving and priority fluid network models as well as certain linear Skorokhod problems define strict GFN models.     

Stability and General Logics

In this paper we make an attempt to study classes of models by using general logics. We do not believe that L_ww is always the best logic for analyzing a class of models. Let K be a class of models and L a logic. The main assumptions we make about K and C are that K has the L-amalgamation property and, later in the paper, that K does not omit L-types. We show that, if modified suitably, most of the results of stability theory hold in this context. The main difference is that existentially closed models of K play the role that arbitrary models play in traditional stability theory. We prove e. g. a structure theorem for the class of existentially closed models of K assuming that K is a trivial superstable class with ndop.     

Countable infinite existentially closed models of universally axiomatizable theories

In the present article, we obtain a new criterion for amodel of a universally axiomatizable theory to be existentially closed. The notion of a maximal existential type is used in the proof and for investigating properties of countable infinite existentially closed structures. The notions of a prime and a homogeneous model, which are classical for the general model theory, are introduced for such structures. We study universal theories with the joint embedding property admitting a single countable infinite existentially closed model. We also construct, for every natural n, an example of a complete inductive theory with a countable infinite family of countable infinite models such that n of them are existentially closed and exactly two are homogeneous.     

与比率有关的捕食——被捕食生态模型

本文讨论了一类生态模型的有效性，种群不灭性，闭轨和同窗轨的存在性，平衡点的稳定性，并定义了向量场同胚映射。     

Optimal Exercise Strategies for Operational Risk Insurance via Multiple Stopping Times

In this paper we demonstrate how to develop analytic closed form solutions to optimal multiple stopping time problems arising in the setting in which the value function acts on a compound process that is modified by the actions taken at the stopping times. This class of problem is particularly relevant in insurance and risk management settings and we demonstrate this on an important application domain based on insurance strategies in Operational Risk management for financial institutions. In this area of risk management the most prevalent class of loss process models is the Loss Distribution Approach (LDA) framework which involves modelling annual losses via a compound process. Given an LDA model framework, we consider Operational Risk insurance products that mitigate the risk for such loss processes and may reduce capital requirements. In particular, we consider insurance products that grant the policy holder the right to insure k of its annual Operational losses in a horizon of T years. We consider two insurance product structures and two general model settings, the first are families of relevant LDA loss models that we can obtain closed form optimal stopping rules for under each generic insurance mitigation structure and then secondly classes of LDA models for which we can develop closed form approximations of the optimal stopping rules. In particular, for losses following a compound Poisson process with jump size given by an Inverse-Gaussian distribution and two generic types of insurance mitigation, we are able to derive analytic expressions for the loss process modified by the insurance application, as well as closed form solutions for the optimal multiple stopping rules in discrete time (annually). When the combination of insurance mitigation and jump size distribution does not lead to tractable stopping rules we develop a principled class of closed form approximations to the optimal decision rule. These approximations are developed based on a class of orthogonal Askey polynomial series basis expansion representations of the annual loss compound process distribution and functions of this annual loss.     

过渡过程中谐振过电压模型及分析

该文详细分析且建立了过渡过程中谐振过电压在非同期合闸情况下所代表的泛函微分方程的数学模型,所给出模型为迄今国内外首次出现的,同时得到与实际背景相吻合的理论结果.     

A Reduced Model with Thinning-Dependence Structure

The class of reduced form models is a very important class of credit risk models, and the modelling of the default dependence structure is essential in the reduced form models. This paper models dependent defaults under a thinning-dependent structure in the reduced form framework. In our tractable model, the joint survival probability for correlated defaults can be derived, and hence the CDS premium rates (with or without counterparty risk) are given in closed form. The numerical result shows that the thinning-dependent structure is effective to model the default dependence.     

Exact solution for thick laminated closed cylindrical shells with two clamped edges

This study discards assumptions about displacement models and stress distribution and quotes the δ-function to establish the state equation for closed orthotropic cylindrical shells with two clamped edges. An identical exact solution is presented for the statics of thin, moderately thick, and thick laminated closed cylindrical shells with two clamped edges. Numerical results are obtained and compared with those calculated using SAP5.     

Instability of spikes in the presence of conservation laws

We show that spikes are unstable in a class of scalar reaction–diffusion equations coupled to a general conservation law. Our class includes the Keller–Segel model for chemotaxis, phase-field models and models for chemical reactions in closed chemical reactors.     

Instability of spikes in the presence of conservation laws

We show that spikes are unstable in a class of scalar reaction–diffusion equations coupled to a general conservation law. Our class includes the Keller–Segel model for chemotaxis, phase-field models and models for chemical reactions in closed chemical reactors.     

First-passage-time and busy-period distributions of discrete-time Markovian queues:Geom(n)/Geom(n)/1/N

This paper gives simple explicit solutions of various first-passage-time distributions for a general class of discrete-time queueing models under arbitrary initial conditions, state-dependent transition probabilities and the finite waiting room. Explicit closed form expressions are obtained in terms of roots. These expressions are then used to get numerical as well as graphical results. Explicit closed-form expressions are also deduced for the continuous-time models including the busy-period distributions. The analysis is then extended to cover the case of two absorbing states.     

Rainflow analysis in Coastal Engineering using switching second order Markov models

The paper deals with the use of Markov and switching Markov chain models of turning points to reproduce random sets of sea states. The advantages of these models are emphasized and compared with existing models based on wave height records, indicating that long and short range and period cycles are included, while the wave height records ignore this important information from the point of view of damage accumulation. Existing models for first order Markov processes are extended to the case of second order processes and closed formulas are given to derive the rainflow matrices of these processes. Finally, one illustrative example of application is given.     

MULTIQ: A Queueing Model for FMSs with Several Pallet Types

Analytical modelling of the work flow through flexible manufacturing systems (FMSs), based on closed queueing network models, has been successfully applied to the early stages of design and analysis of FMSs. This paper describes the advantages of using multiple job-class closed queueing networks for modelling realistic situations occurring in FMSs. The general modelling of FMSs by closed queueing networks is first reviewed. The way Solberg's CAN-Q—a single job-class queueing-based package—deals with several part types is clarified. A new model called MULTIQ, allowing multiple pallet types, each of which is used by several part types, is proposed. Results are derived using the data from an existing FMS. The use of the MULTIQ model for optimization purposes is suggested by some examples.     

双渠道闭环供应链的三种回收模式的建模分析

针对生产商负责网上直销、零售商负责网下零售、且具有回收再制造功能的双渠道闭环供应链,首先分析了生产商负责产品回收和零售商负责产品回收下生产商和零售商之间的博弈行为,建立了刻画两种回收模式的两层规划模型;进而假定生产商委托第三方企业负责回收,分析了生产商、零售商和第三方回收企业之间的博弈行为,建立了对应此一主两从博弈结构的带均衡约束的两层规划模型.对所得模型进行了模型求解,得到了三种回收模式下双渠道闭环分散式供应链的最优直销价、零售价和回收再制造率决策.通过数值算例对上述三种回收模式进行了比较分析,并对刻画网上直销吸引力的相关参数进行了灵敏度分析.研究发现,生产商负责回收时的回收再制造率最高;网上直销具有激发潜在需求(正效应)和吸引零售市场需求发生转移(负效应)的双重效应等.     

Random sets. A survey of results and applications

A survey of current directions in the theory of random closed sets is presented; these include: the central limit theorem, the law of large numbers for Minkowski sums and unions of random sets, semi-Markov random closed sets, Boolean models and statistical estimation of their parameters, specification of distributions and associated problems of capacity theory. Weak convergence of random closed sets is defined and its application to limit theorems for graphs and epi-graphs of random processes and problems of stochastic optimization is described. Other connections with the theory of random processes (level sets, multivalued and controllable random processes) are also discussed.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 12, pp. 1587–1599, December, 1991.     

Likelihood-based inference for bivariate latent failure time models with competing risks under the generalized FGM copula

Many existing latent failure time models for competing risks do not provide closed form expressions of sub-distribution functions. This paper suggests a generalized FGM copula models with the Burr III failure time distribution such that the sub-distribution functions have closed form expressions. Under the suggested model, we develop a likelihood-based inference method along with its computational tools and asymptotic theory. Based on the expressions of the sub-distribution functions, we propose goodness-of-fit tests. Simulations are conducted to examine the performance of the proposed methods. A real data from the reliability analysis of the radio transmitter-receivers are analyzed to illustrate the proposed methods. The computational programs are made available in the R package GFGM.copula.     

Completeness theorem for topological class models

A topological class logic is an infinitary logic formed by combining a first-order logic with the quantifier symbols O and C. The meaning of a formula closed by quantifier O is that the set defined by the formula is open. Similarly, a formula closed by quantifier C means that the set is closed. The corresponding models are a topological class spaces introduced by Ćirić and Mijajlović (Math Bakanica 1990). The completeness theorem is proved. This research was supported by the Ministry of Science, Technology and Development, Republic of Serbia, through Mathematical Institute, under grant 144013.