The give-up problem for blocked regional lists with multi-winners

The current electoral law for the Italian Parliament prescribes blocked, linearly ordered lists of candidates for each party within each constituency. The peculiarity of the Italian electoral system is that a party can present the same candidate in different constituencies. There are several seats at stake in each constituency; these seats are allocated to the parties proportionally to the total number of votes they get. If the blocked list mechanism-which assigns the seats obtained by a party in a constituency to the first candidates of the corresponding ordered list-causes some candidates to win in more than one constituency, they may retain only one of the seats, giving up all the remaining ones. Thus, the problem arises for a party to find a suitable “schedule of give-ups” that produces the final set of winners for that party. In order to do this, we assume that such decision is centralized and based on some models of global (inter-regional) preferences over the set of candidates. In this paper, we introduce two classes of models to formulate the “give-up problem”, i.e., utility and ordinal models, and we show that for both of them some natural formulations of the problem can be efficiently solved by network flows techniques.     

Symmetry of two‐parameter homogeneous transition function

In this paper, we study a very interesting problem, that is, symmetry of the two parameters s,t>0 for a two‐parameter homogeneous transition function and obtain some important and interesting results.     

Portfolio insurance under a risk-measure constraint

We study the problem of portfolio insurance from the point of view of a fund manager, who guarantees to the investor that the portfolio value at maturity will be above a fixed threshold. If, at maturity, the portfolio value is below the guaranteed level, a third party will refund the investor up to the guarantee. In exchange for this protection, the third party imposes a limit on the risk exposure of the fund manager, in the form of a convex monetary risk measure. The fund manager therefore tries to maximize the investor’s utility function subject to the risk-measure constraint. We give a full solution to this non-convex optimization problem in the complete market setting and show in particular that the choice of the risk measure is crucial for the optimal portfolio to exist. Explicit results are provided for the entropic risk measure (for which the optimal portfolio always exists) and for the class of spectral risk measures (for which the optimal portfolio may fail to exist in some cases).     

Portfolio insurance under a risk-measure constraint

We study the problem of portfolio insurance from the point of view of a fund manager, who guarantees to the investor that the portfolio value at maturity will be above a fixed threshold. If, at maturity, the portfolio value is below the guaranteed level, a third party will refund the investor up to the guarantee. In exchange for this protection, the third party imposes a limit on the risk exposure of the fund manager, in the form of a convex monetary risk measure. The fund manager therefore tries to maximize the investor’s utility function subject to the risk-measure constraint. We give a full solution to this non-convex optimization problem in the complete market setting and show in particular that the choice of the risk measure is crucial for the optimal portfolio to exist. Explicit results are provided for the entropic risk measure (for which the optimal portfolio always exists) and for the class of spectral risk measures (for which the optimal portfolio may fail to exist in some cases).     

Harvesting discrete nonlinear age and stage structured populations

A natural extension of age structured Leslie matrix models is to replace age classes with stage classes and to assume that, in each time period, the transition from one stage class to the next is incomplete; that is, diagonal terms appear in the transition matrix. This approach is particularly useful in resource systems where size is more easily measured than age. In this linear setting, the properties of the models are known; and these models have been applied to the analysis of population problems. A more applicable setting is to assume that the reproduction, survival, and transition parameters in the model are density dependent. The behavior of such models is determined by the form of this density dependence. Here, we focus on models in which the parameters depend on the value of an aggregated variable, defined to be the weighted sum of the number of individuals in each stage class. In forestry models, for example, this aggregated variable may represent a basal area index; in fisheries models, it may represent a spawning stock biomass. Current age structured nonlinear stock-recruitment fisheries models are a special case of the models considered here. Certain results that apply to age structured models can be extended to this broader class of models. In particular, the questions addressed relate to the minimum number of age classes that need to be harvested to obtain maximum sustainable yield policies and to managing resources under nonequilibrium and stochastic conditions. Application of the model to problems in fisheries, forestry, pest, and wildlife management is also discussed.The author would like to thank R. G. Haight for comments and discussions relating to the material presented here. This work was supported by NSF Grant DMS-85-11717.     

Total probability of two‐parameter generalized transition function

In this paper, we research some properties of the total probability of a two‐parameter generalized transition function and obtain some important and interesting results.     

The Lie Theory of Two-Variable Hypergeometric Functions

We develop a Lie-algebraic method that associates with each of the 34 distinct second-order hypergeometric functions in two variables a canonical system of partial differential equations. The special functions arise by partial separation of variables in these simple systems. Some consequences are a demonstration that all such functions appear as solutions of the 4-variable wave equation and a classification of the possible imbeddings. In each case the functions are characterized by first- and second-order operators in the enveloping algebra of the conformal symmetry algebra for the wave equation. In some cases the 3-variable wave and heat equations and the 2-variable Helmholtz equation also arise. This intimate relationship between Horn functions and some fundamental equations of mathematical physics shows that these functions are more interesting than was previously recognized and permits use of the powerful tools of Lie theory and separation of variables to obtain properties of the functions.     

Demi-groupes bornés (bounded semi-groups)

The bounded semi-groups, defined and studied in this paper, form an interesting class half-way between commutative semi-groups, that are quite particular, and any noncommutative semi-groups, that are quite general. This class contains the artinian semi-groups and, more generally, semi-groups verifying Gabriel's (H) condition. The main theorem of the paper deals with tertiary and uniresiduated ideals, which appear in a theory of sets ordered in lattices. We establish that, in a bounded semi-group, the notions tertiary and uniresiduated coincide. This leads to ask several open questions.     

Weakly Cauchy Filters and Quasi-Uniform Completeness

It is well-known that the notion of a Smyth complete quasi-uniform space provides an appropriate notion of completeness to study many interesting quasi-metric spaces which appear in theoretical computer science. We observe that several of these spaces actually possess a stronger form of completeness based on the use of weakly Cauchy filters in the sense of H. H. Corson and we develop a theory of completion and completeness for this kind of filters. In parallel, we also study a more general notion of completeness based on the use of certain stable filters. Thus our results extend and generalize important theorems of Á. Császár, J. R. Isbell and N. R. Howes on uniform completeness.     

Stability properties of a flow process in graphs

We study a flow process in infinite graphs where vertices with large resources tend to attract resources from neighbors. The initial resources are random. An interesting question is whether in each finite region all motion stops after a finite time. Under certain assumptions, we prove that this is true. For some other cases, we prove a weaker stability result. We pay attention mostly to the case of Z², but several results can be easily generalized to Z^d.     

Stability and bifurcation in a harvested one-predator–two-prey model with delays

It is known that one-predator–two-prey system with constant rate harvesting can exhibit very rich dynamics. If such a system contains time delayed component, it can have more interesting behavior. In this paper we study the effects of the time delay on the dynamics of the harvested one-predator–two-prey model. It is shown that time delay can cause a stable equilibrium to become unstable. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhães. An example is given and numerical simulations are finally performed for justifying the theoretical results.     

Dominance,bargaining power and service platform performance

In this paper we study the relationship between a firm (hotel) and a service platform (Ctrip.com). We start with a newsvendor hotel facing two kinds of customers. D-customers order the room directly from the hotel front desk; C-customers order the room through Ctrip.com. Ctrip.com charges the hotel while introducing its members to the hotel. The hotel decides how many rooms are allotted to Ctrip.com to achieve optimal profit. We consider the situation where one party’s demand cannot be observed by another, and study the commonly used wholesale price contract. Interestingly, the contract can always coordinate the system. We then investigate the influence of bargaining power on the profit division under situations where Ctrip.com and hotel, respectively, dominate the system, and find that increasing (or decreasing) a party’s bargaining power without considering the other does not necessarily benefit (or damage) the first party. Further, we discuss how the parties choose dominance and appropriate bargaining power to make a trade-off for better cooperation. An interesting phenomenon is that bargaining power for each party can be identical when any party dominates the system. We also propose a threshold at which the wholesale price contracts can always be the Pareto optimal for the channel.     

On the origin of quasi-stationary states in models of wave–particle interaction

In presence of long-range interactions, physics is very peculiar and a wide range of striking phenomena appear, like the emergence of long-live quasi-stationary states (QSSs). Wave–particle interaction (plasmas, Free Electron Lasers, etc.) represents an interesting example of a long-range system and provides a unique experimental ground to investigate the aforementioned universal features. In this paper we apply a general approach, based on the statistical mechanics of the Vlasov equation, to study the QSSs in a typical model of wave–particle interaction. Using Lynden-Bell “violent relaxation” theory, we characterize a first-order phase transition with truly non-equilibrium features. We analyze in some detail the coexistence region and the non-Gaussian momentum distributions.     

A critical comparison of the various plausible inter-echelon gaming processes in supply chain models

An increasing number of supply-chain models are related to the following structure: (i) a manufacturer supplies a product to a retailer—who fixes a retail price and then retails the product to the consumers; (ii) the effect of the retail price on sales volume is dictated by a deterministic demand curve known to both parties. Results from these models depend very much on the ‘gaming process’ that is assumed to govern how the manufacturer and the retailer interact with each other. This paper reviews and compares some basic characteristics of seven seemingly plausible gaming processes; including the two most common ones: the manufacturer-Stackelberg and the fixed-markup-retailer processes. Our results show that: (i) each of the seven processes appear to be no less plausible than the other six; (ii) all seven processes possess some implausible characteristics; (iii) the relationships among the processes are confusing and do not appear to be intuitively logical; (iv) the relationships among these processes are further complicated by the way they are affected by the form of the assumed demand curve. Our results show that in supply-chain modelling more attention should be given to: (i) the proper selection of an appropriate gaming process assumption; (ii) how the model's results change under different gaming processes; (iii) the incorporation of information asymmetry that will allow these gaming-process assumptions to become more realistic.     

An analysis of setup cost reduction in a two stage system with power investment function

Recently, a framework for analyzing investment decisions as they relate to setup cost reduction in two stage production processes has appeared in the literature. Closed form results were developed for the case of logarithmic investment function. This paper extends the results to the case of power investment function. We present an algorithm for calculating the optimal values of the decision variables. A numerical example is utilized to reveal some interesting aspects of this system.     

Periodicity of Balancing Numbers

The balancing numbers originally introduced by Behera and Panda [2] as solutions of a Diophantine equation on triangular numbers possess many interesting properties. Many of these properties are comparable to certain properties of Fibonacci numbers, while some others are more interesting. Wall [14] studied the periodicity of Fibonacci numbers modulo arbitrary natural numbers. The periodicity of balancing numbers modulo primes and modulo terms of certain sequences exhibits beautiful results, again, some of them are identical with corresponding results of Fibonacci numbers, while some others are more fascinating. An important observation concerning the periodicity of balancing numbers is that, the period of this sequence coincides with the modulus of congruence if the modulus is any power of 2. There are three known primes for which the period of the sequence of balancing numbers modulo each prime is equal to the period modulo its square, while for the Fibonacci sequence, till date no such prime is available.     

Bidimensional allocation of seats via zero-one matrices with given line sums

In some proportional electoral systems with more than one constituency the number of seats allotted to each constituency is pre-specified, as well as, the number of seats that each party has to receive at a national level. “Bidimensional allocation” of seats to parties within constituencies consists of converting the vote matrix V into an integer matrix of seats “as proportional as possible” to V, satisfying constituency and party totals and an additional “zero-vote zero-seat” condition. In the current Italian electoral law this Bidimensional Allocation Problem (or Biproportional Apportionment Problem—BAP) is ruled by an erroneous procedure that may produce an infeasible allocation, actually one that is not able to satisfy all the above conditions simultaneously. In this paper we focus on the feasibility aspect of BAP and, basing on the theory of (0,1)-matrices with given line sums, we formulate it for the first time as a “Matrix Feasibility Problem”. Starting from some previous results provided by Gale and Ryser in the 60’s, we consider the additional constraint that some cells of the output matrix must be equal to zero and extend the results by Gale and Ryser to this case. For specific configurations of zeros in the vote matrix we show that a modified version of the Ryser procedure works well, and we also state necessary and sufficient conditions for the existence of a feasible solution. Since our analysis concerns only special cases, its application to the electoral problem is still limited. In spite of this, in the paper we provide new results in the area of combinatorial matrix theory for (0,1)-matrices with fixed zeros which have also a practical application in some problems related to graphs.     

Investigating purchasing-sequence patterns for financial services using Markov, MTD and MTDg models

In the past, several authors have found evidence for the existence of a priority pattern of acquisition for durable goods, as well as for financial services. Its usefulness lies in the fact that if the position of a particular customer in this acquisition sequence is known, one can predict what service will be acquired next by that customer. In this paper, we analyse purchase sequences of financial services to identify cross-buying patterns, which might be used to discover cross-selling opportunities as part of customer relationship management (CRM). Hereby, special attention is paid to transitions, which might encourage bank-only or insurance-only customers to become financial-services customers. We introduce the mixture transition distribution (MTD) model as a parsimonious alternative to the Markov model for use in the analysis of marketing problems. An interesting extension on the MTD model is the MTDg model, which is able to represent situations where the relationship between each lag and the current state differs. We illustrate the MTD and MTDg model on acquisition sequences of customers of a major financial-services company and compare the fit of these models with that of the corresponding Markov model. Our results are in favor of the MTD and MTDg models. Therefore, the MTD as well as the MTDg transition matrices are investigated to reveal cross-buying patterns. The results are valuable to product managers as they clarify the customer flows among product groups. In some cases, the lag-specific transition matrices of the MTDg model give better insight into the acquisition patterns than the general transition matrix of the MTD model.     

Radial spreading and stability of a thin rotating liquid droplet

Thin-film flows are involved in many coating processes, where it is desirable to achieve thin and homogeneous fluid layers. In the present investigations, we treat droplets, spreading on rotating solid substrates. Micro-scale effects appear, firstly, at the wetting front, where the film height tends to zero. Secondly, micro-scale effects may appear at other locations, where the free liquid/gas-interface approaches the solid substrate, as e.g. at film rupture. For such situations, molecular effects need to be considered, e.g. in form of the disjoining pressure (DJP), to get physically-correct solutions. Otherwise, the spreading can be modeled within the frame of continuum mechanics, augmented by the (empirical) law of Tanner to capture the contact-line dynamics. We present, on the one hand, an overview of several interesting issues, as (i) spreading with and without considering the DJP, (ii) spreading after central rupture, including hysteresis effects, and (iii) non-isothermal spreading, including temperature-dependent surface tension (Marangoni effect) and temperature-dependent density (Rayleigh-Bénard effect). On the other hand, we present results for the instability of the contact line, for which the contact line gets corrugated (under isothermal conditions). This instability goes along with a transition from (rotationally-symmetric) two-dimensional to three-dimensional behavior. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dichromatic Polynomials and Potts Models Summed Over Rooted Maps

We consider the sum of dichromatic polynomials over non-separable rooted planar maps, an interesting special case of which is the enumeration of such maps. We present some known results and derive new ones. The general problem is equivalent to the q-state Potts model randomized over such maps: it remains an open question whether this model exhibits a phase transition or critical behaviour.