How hard is it to tell which is a Condorcet committee?

This paper establishes the computational complexity status for a problem of deciding on the quality of a committee. Starting with individual preferences over alternatives, we analyse when it can be determined efficiently if a given committee C$C$ satisfies a weak (resp. strong) Condorcet criterion–i.e., if C$C$ is at least as good as (resp. better than) every other committee in a pairwise majority comparison. Scoring functions used in classic voting rules are adapted for these comparisons. In particular, we draw the sharp separation line between computationally tractable and intractable instances with respect to different voting rules. Finally, we show that deciding if there exists a committee which satisfies the weak (resp. strong) Condorcet criterion is computationally hard.     

Strategic interactions in traditional franchise systems: Are franchisors always better off?

The effects of price competition and advertising spillover on franchisees’ decision to cooperate and on franchisor’s contractual preferences are investigated. We show that the franchisees’ decision to cooperate or not depends on the type of franchise contracts. Under exclusive territory contracts, any mode of play between franchisees give the same profits to the franchisees and franchisor. Contracts that allow price competition and well targeted local advertising offer a good ground for horizontal cooperation, which may or may not benefit the franchisor depending on whether the prices are strategic substitutes or strategic complements. Contracts in which price competition is allowed and the burden of advertising decisions is totally transferred to the franchisor lead to cooperation between franchisees at the expense of the franchisor. Franchisees do not cooperate to the benefit of the franchisor if local advertising is predatory and price competition is not allowed in the contract, but franchisees are given the responsibility to undertake local advertising. Also, the franchisor endorses cooperation between franchisees when local advertising has a public good nature, but such a cooperation may never occur when the impact of local advertising on demand is significant. We finally show that while some contracts always dominate others, the choice of a franchise contract may also depend on local competition and/or the franchise goodwill.     

How hard is half-space range searching?

We investigate the complexity ofhalf-space range searching: givenn points ind-space, build a data structure that allows us to determine efficiently how many points lie in a query half-space. We establish a tradeoff between the storagem and the worst-case query timet in the Fredman/Yao arithmetic model of computation. We show thatt must be at least on the order of $$\frac{{(n/\log n)^{1 - (d - 1)/d(d + 1)} }}{{m^{1/d} }}$$ Although the bound is unlikely to be optimal, it falls reasonably close to the recent upper bound ofO(n/m ^1/d ) established by Matou?ek. We also show that it is possible to devise a sequence ofn inserts and half-space range queries that require a total time ofn ^2-O(1/d) . Our results imply the first nontrivial lower bounds for spherical range searching in any fixed dimension. For example, they show that, with linear storage, circular range queries in the plane require Ω(n ^1/3) time (modulo a logarithmic factor).     

Why are enterprise resource planning systems indispensable to supply chain management?

Supply chain design is becoming a core competency, and the enterprise resource planning (ERP) system is expected to be an integral component of supply chain management (SCM). Installing an ERP system is, however, expensive and risky. IT managers must decide how to use their limited resources and invest in the right product. Can an ERP system directly improve SCM competency? This study proposes a conceptual framework featuring the ERP benefits and SCM competencies, and examines the impacts of the former on the latter. The results confirm the operational, managerial, and strategic benefits of ERP for the SCM competencies, but not the IT infrastructure and organizational benefits as significant predictors of them. Moreover, more than 80% of respondents think it necessary to first adopt an ERP system as the backbone of company operations before deploying other enterprise systems (ES), such as the SCM system.     

The kidney exchange problem: How hard is it to find a donor?

The most effective treatment for kidney failure that is currently known is transplantation. However, the supply of kidneys from cadaveric donors does not meet the fast-growing demand and the kidney from a willing living donor (genetically or emotionally relative of the patient) is often not suitable for immunological reasons. Therefore in several countries attempts have started to organize exchanges of kidneys between incompatible patient-donor pairs. On the theoretical side, game-theoretical models have been proposed to analyze various optimality criteria for such exchanges and various search schemes have been tested. One possibility to model patients’ preferences is to take into account in the first step the suitability of the donated kidney and in the second step the length of the obtained cycle of exchanges. Although the core of such a cooperative game is always nonempty and one solution can be found by the famous Top Trading Cycles algorithm, in this paper we show that many questions concerning the structure of the core are difficult to answer.     

Transcendental solutions of systems of complex differential equations北大核心CSCD

Using maximum modulus principle, we investigate the problem of the existence of the transcendental meromorphic solutions of system of complex algebraic differential equations, and obtain a result which the system only the algebraic solution under certain conditions. Examples show that our results are sharp. ©, 2015, Chinese Academy of Sciences. All right reserved.     

Are plastic yielding and work hardening sensitive to the boundary conditions?

The plane strain shear of a single crystal strip with one active slip system placed in a mixed device with one clamped and one free boundary is considered. Since dislocations pile up against only the clamped boundary, the plastic yielding and work hardening differ essentially from those of a hard device, showing clearly their sensitivity to the boundary conditions. An analytical solution to this problem within continuum dislocation theory is found explicitly which exhibits the energetic and dissipative thresholds for dislocation nucleation, the Bauschinger translational work hardening, and the size effects. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

How Many Diagonal Rectangles Are Needed to Cover an Orthogonal Polygon?

We show that any orthogonal polygon of n vertices can be covered with at most ``diagonal rectangles' where ω=1 (n=8,12,16) and ω=0 (otherwise). An orthogonal polygon is a polygon whose edges are horizontal or vertical. A diagonal rectangle (of an orthogonal polygon) is a rectangle whose opposite corners are vertices of the orthogonal polygon. The result is sharp and settles a question of Mamoru Watanabe [11]. Received July 25, 1999, and in revised form March 1, 2000. Online publication May 16, 2000.     

Integrability conditions of a resonant saddle in Liénard-like complex systems

We consider a complex differential system with a resonant saddle that remind the classical Liénard systems in the real plane. For such systems we determine the conditions of analytic integrability of the resonant saddle.     

Trend to equilibrium of renormalized solutions to reaction–cross-diffusion systems

The convergence to equilibrium of renormalized solutions to reaction–cross-diffusion systems in a bounded domain under no-flux boundary conditions is studied. The reactions model complex balanced chemical reaction networks coming from mass-action kinetics and thus do not obey any growth condition, while the diffusion matrix is of cross-diffusion type and hence nondiagonal and neither symmetric nor positive semi-definite, but the system admits a formal gradient-flow or entropy structure. The diffusion term generalizes the population model of Shigesada, Kawasaki and Teramoto to an arbitrary number of species. By showing that any renormalized solution satisfies the conservation of masses and a weak entropy–entropyproduction inequality, it can be proved under the assumption of no boundary equilibria that all renormalized solutions converge exponentially to the complex balanced equilibrium with a rate which is explicit up to a finite dimensional inequality.     

Symmetry and monotonicity of positive solutions to Schr?dinger systems with fractional p-Laplacians

In this paper,we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-Laplacian systems.By virtue of this method,we investigate the qualitative properties of positive solutions for the following Schrodinger system with fractional p-Laplacian{(-△)^s_pu+au^p-1=f(u,v),(-△)^t_pv+bv(p-1)=g(u,v),where 0N(N≥2),the monotonicity in the parabolic domain and the nonexistence on the half space for positive solutions to the above system under some suitable conditions on f and g,respectively.     

Existence of complex ℓ2 solutions of linear delay systems of difference equations

We give sufficient conditions for the existence of complex ?₂ solutions of a non-homogeneous system of linear difference equations and of two general classes of delay systems of linear difference equations. In some cases, bounds of the established solutions are also given. As a consequence of the space ?₂ where we work, information can be obtained about the asymptotic behavior of the established solutions and, the asymptotic stability of the zero equilibrium point of the systems under consideration. The method we use is a functional-analytic one.