Lineability criteria,with applications

Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed with richer structures, then the more stringent notions of dense-lineability, maximal dense-lineability and spaceability arise naturally. In this paper, several lineability criteria are provided and applied to specific topological vector spaces, mainly function spaces. Sometimes, such criteria furnish unified proofs of a number of scattered results in the related literature. Families of strict-order integrable functions, hypercyclic vectors, non-extendable holomorphic mappings, Riemann non-Lebesgue integrable functions, sequences not satisfying the Lebesgue dominated convergence theorem, nowhere analytic functions, bounded variation functions, entire functions with fast growth and Peano curves, among others, are analyzed from the point of view of lineability.     

MLE,Information, Ancillary Complement,and Conditional Inference with Illustrations

Fisher’s (Proceedings of Royal Society Series A 144, 285–307 1934, 1956) example remains a classic where the maximum likelihood estimator (T) was non-sufficient, had less than full information, but an ancillarity complement (S) helped in recovering the full information \(\mathcal {I}_{(T,S)}(\theta )\). In the absence of other readily accessible easy-to-grasp examples of similar nature, we begin with general calculations for useful information entities, both unconditional (\(\mathcal {I}_{T}(\theta )\)) and conditional (\(\mathcal {I}_{T\mid S}(\theta )\)). These have led us to propose a number of new illustrations in the spirit of the original example. Then, we introduce a multivariate data extension of the original example with an illustration. We wrap up this investigation with an example of a non-sufficient MLE T that has (i) the full Fisher information, and (ii) has an ancillary complement S.     

Functional BKR Inequalities,and their Duals,with Applications

The inequality conjectured by van den Berg and Kesten (J. Appl. Probab. 22, 556–569, 1985), and proved by Reimer (Comb. Probab. Comput. 9, 27–32, 2000), states that for A and B events on S, a finite product of finite sets, and P any product measure on S,

The Deterministic,Two-Product,Inventory System with Capacity Constraint

This paper considers the standard deterministic inventory system for two products with a capacity constraint and describes how to find the optimal policy amongst all policies which have fixed order quantities. This involves the idea of staggered initial orders and periodic policies, and includes the classical Lagrange multiplier technique and the equal order intervals method as special cases. It is shown that the usual Lagrange multiplier technique will never produce the optimal policy (in the class described above) except in the trivial case, when the capacity constraint is satisfied by the optimal unconstrained policy.     

Entropy,Periodicity, and Graphs with Zero Euler Characteristic

Let G be a graph which contains exactly one simple closed curve. We prove that a continuous map f : G → G has zero topological entropy if and only if there exist at most k ≤ |(Edg(G) End(G) 3)/2] different odd numbers n1,...,nk such that Per(f) is contained in ∪i=1^k ∪j=0^∞ ni2^j, where Edg(G) is the number of edges of G and End(G) is the number of end points of G.     

Cobordisms,Manifolds with Torus Action,and Functional Equations

The paper is devoted to applications of functional equations to well-known problems of compact torus actions on oriented smooth manifolds. These include the problem of Hirzebruch genera of complex cobordism classes that are determined by complex, almost complex, and stably complex structures on a fixed manifold. We consider actions with connected stabilizer subgroups. For each such action with isolated fixed points, we introduce rigidity functional equations. This is based on the localization theorem for equivariant Hirzebruch genera. We consider actions of maximal tori on homogeneous spaces of compact Lie groups and torus actions on toric and quasitoric manifolds. The arising class of equations contains both classical and new functional equations that play an important role in modern mathematical physics.     

Continuous-time, stage-structured, multiple-species model with applications to amphibians

Since the 1980s, biologists have noticed a major decline in amphibian population. The reason this is so alarming is because amphibians have been seen as a “Canary in the mine” when it comes to the world’s environmental changes. With global warming and CO₂ emissions all over the news, we have become more aware of how we are impacting our world. If the decline of amphibians is a precursor to what is happening with the environment, then we need to find a good model to give us estimates on what is going to happen in the future. Here we used a predator-prey-competition model to help investigate how three amphibians might interact when confined to the same area.     

SPG-reguli, SPG-systems, BLT-sets and sets with the BLT-property

This paper is a survey on SPG-reguli, SPG-systems, BLT-sets and sets with the BLT-property. It is shown how from these sets generalized quadrangles, partial geometries and semi-partial geometries can be constructed. Many examples are given and open problems are stated. There are also some new results.     

Project management with time,cost, and quality considerations

In the project management literature, quantitative models were developed for project crashing to determine the appropriate activities for crashing at minimal cost. In this paper, we suggest that the project quality may be affected by project crashing and develop linear programming models to study the tradeoffs among time, cost, and quality. Each of the three models developed optimizes one of these entities by assigning desired bounds on the other two. An illustrative example with a project network consisting of 13 nodes, 14 activities, and 2 dummy activities is provided. The computational study includes tabulation of the interrelationships among time, cost, and quality.     

A problem with a nonlocal,with respect to time,condition for multidimensional hyperbolic equations

We study a boundary-value problem for a hyperbolic equation with a nonlocal with respect to time-variable integral condition. We obtain sufficient conditions for unique solvability of the nonlocal problem. The proof is based on reduction of the nonlocal first-type condition to the second-type one. This allows to reduce the nonlocal problem to an operator equation. We show that unique solvability of the operator equation implies the existence of a unique solution to the problem.     

S-modular games,with queueing applications

The notion ofS-modularity was developed by Glasserman and Yao [9] in the context of optimal control of queueing networks.S-modularity allows the objective function to be supermodular in some variables and submodular in others. It models both compatible and conflicting incentives, and hence conveniently accommodates a wide variety of applications. In this paper, we introduceS-modularity into the context ofn-player noncooperative games. This generalizes the well-known supermodular games of Topkis [22], where each player maximizes a supermodular payoff function (or equivalently, minimizes a submodular payoff function). We illustrate the theory through a variety of applications in queueing systems.Supported in part by NSF Grant MSS-92-16490, and by Columbia's Center for Telecommunications Research.     

Lorentz spaces,with mixed norms

We study Lorentz spaces, with mixed or iterated norms. The usual Lorentz spaces enable us to clarify the concept of weak-type; the spaces with mixed norms enable us to clarify and to classify four extended notions of weak-type in product space. We give also an interpolation theorem, of the Marcinkiewicz type.     

Elliptic Integral Inequalities, with Applications

The authors study monotoneity and convexity of certain combinations of elliptic integrals and obtain sharp inequalities for them. Applications are provided. November 23, 1994. Date revised: February 5, 1997.