Ticket queues with regular and strategic customers

Queueing Systems - We study a Markovian single-server ticket queue where, upon arrival, each customer can draw a number from a take-a-number machine, while the number of the customer currently...     

Coding into HOD via normal measures with some applications

We develop a new method for coding sets while preserving GCH in the presence of large cardinals, particularly supercompact cardinals. We will use the number of normal measures carried by a measurable cardinal as an oracle, and therefore, in order to code a subset A of κ, we require that our model contain κ many measurable cardinals above κ. Additionally we will describe some of the applications of this result. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Regularity of weak solutions of one-dimensional two-phase Stefan problems

Sunto Si considera il problema di Stefan unidimensionale a due fasi e si dimostra l'esistenza di soluzioni classiche sotto ipotesi minimali sui dati (continuità a tratti e limitatezza). Nelle stesse ipotesi si dimostra che tali soluzioni dipendono in modo continuo dai dati, conseguendo un risultato che è più generale anche di quello noto per le soluzioni deboli.

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Entrata in Redazione il 22 dicembre 1976.

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Work partially supported by the Italian C.N.R.     

Singular solutions of some nonlinear parabolic equations

We consider the existence and uniqueness of singular solutions for equations of the formu ₁=div(|Du|^p−2 Du)-φu), with initial datau(x, 0)=0 forx⇑0. The function ϕ is a nondecreasing real function such that ϕ(0)=0 andp>2. Under a growth condition on ϕ(u) asu→∞, (H1), we prove that for everyc>0 there exists a singular solution such thatu(x, t)→cδ(x) ast→0. This solution is unique and is called a fundamental solution. Under additional conditions, (H2) and (H3), we show the existence of very singular solutions, i.e. singular solutions such that ∫_|x|≤r u(x,t)dx→∞ ast→0. Finally, for functions ϕ which behave like a power for largeu we prove that the very singular solution is unique. This is our main result. In the case ϕ(u)=u ^q, 1≤q, there are fundamental solutions forq<p*=p-1+(p/N) and very singular solutions forp-1<q<p*. These ranges are optimal. Dedicated to Professor Shmuel Agmon     

Fejer and Hermite-Hadamard type inequalities for superquadratic functions

In this paper we use basic properties of superquadratic functions to obtain new inequalities including Fejer's type and Hermite-Hadamard type inequalities. For superquadratic functions which are also convex, we get refinements of known results.     

Chemically Crosslinked Polysaccharide of the Red Microalga Rhodella Reticulata - An Ion Exchanger for Toxic Metal Ions 1

The structure and physicochemical properties of the sulfated polysaccharides that encapsulate cells of the red microalgae have been studied in our laboratory for a number of years with the aim of evaluating their potential applications.^2-6 Exploitation of the charged groups of these heteropolymers as chelating agents could provide an environmentally friendly means of disposing of toxic metals in industrial wastes. Ion exchangers and affinity absorbents may be prepared by crosslinking polysaccharides with epichlorhydrin, for example, mucopolysaccharides can bind polyvalent ions.^7-9

     

A new proof of an inequality of Bohr for Hilbert space operators

In this note we present a new proof and an extension of the Hilbert space operators version of an inequality by Bohr.     

Multi-item lot-sizing with joint set-up costs

We consider a multi-item lot-sizing problem with joint set-up costs and constant capacities. Apart from the usual per unit production and storage costs for each item, a set-up cost is incurred for each batch of production, where a batch consists of up to C units of any mix of the items. In addition, an upper bound on the number of batches may be imposed. Under widely applicable conditions on the storage costs, namely that the production and storage costs are nonspeculative, and for any two items the one that has a higher storage cost in one period has a higher storage cost in every period, we show that there is a tight linear program with O(mT ²) constraints and variables that solves the joint set-up multi-item lot-sizing problem, where m is the number of items and T is the number of time periods. This establishes that under the above storage cost conditions this problem is polynomially solvable. For the problem with backlogging, a similar linear programming result is described for the uncapacitated case under very restrictive conditions on the storage and backlogging costs. Computational results are presented to test the effectiveness of using these tight linear programs in strengthening the basic mixed integer programming formulations of the joint set-up problem both when the storage cost conditions are satisfied, and also when they are violated.     

Some new refined Hardy type inequalities with general kernels and measures

We state and prove some new refined Hardy type inequalities using the notation of superquadratic and subquadratic functions with an integral operator A _k defined by $$ A_kf(x):=\frac{1}{K(x)} \int\limits_{\Omega_2} k(x,y)f(y)d\mu_2(y), $$ where ${k: \Omega_1 \times \Omega_2 \to \mathbb{R}}$ is a general nonnegative kernel, (Ω₁, μ ₁) and (Ω₂, μ ₂) are measure spaces and $$ K(x):=\int\limits_{\Omega_2} k(x,y)d\mu_2(y), \, x \in \Omega_1. $$ The relations to other results of this type are discussed and, in particular, some new integral identities of independent interest are obtained.