Controlling an oscillating Jackson-type network having state-dependent service rates

We consider a Jackson-type network comprised of two queues having state-dependent service rates, in which the queue lengths evolve periodically, exhibiting noisy cycles. To reduce this noise a certain heuristic, utilizing regions in the phase space in which the system behaves almost deterministically, is applied. Using this heuristic, we show that in order to decrease the probability of a customers overflow in one of the queues in the network, the server in that same queue – contrary to intuition – should be shut down for a short period of time. Further noise reduction is obtained if the server in the second queue is briefly shut down as well, when certain conditions hold.     

Optimal decompositions for theK-functional for a couple of Banach lattices

Letf=g _t+h _t be the optimal decomposition for calculating the exact value of theK-functionalK(t, f; ) of an elementf with respect to a couple =(X ₀ ,X ₁) of Banach lattices of measurable functions. It is shown that this decomposition has a rather simple form in many cases where one of the spacesX ₀ andX ₁ is eitherL ^∞ orL ¹. Many examples are given of couples of lattices for which |g _t| increases monotonically a.e. with respect tot. It is shown that this property implies a sharpened estimate from above for the Brudnyi-KrugljakK-divisibility constant γ( ) for the couple. But it is also shown that certain couples do not have this property. These also provide examples of couples of lattices for which γ( ). Research supported by the Technion V. P. R. Fund.     

On a superatomic Boolean algebra which is not generated by a well-founded sublattice

Let b denote the unboundedness number of ω^ω. That is, b is the smallest cardinality of a subset such that for everyg∈ω^ω there isf ∈ F such that {n: g(n) ≤ f(n)}is infinite. A Boolean algebraB is wellgenerated, if it has a well-founded sublatticeL such thatL generatesB. We show that it is consistent with ZFC that , and there is a Boolean algebraB such thatB is not well-generated, andB is superatomic with cardinal sequence 〈ℵ₀, ℵ₁, ℵ₁, 1〉. This result is motivated by the fact that if the cardinal sequence of a Boolean algebraB is 〈ℵ₀, ℵ₀, λ, 1〉, andB is not well-generated, then λ≥b.     

Empowerment of Elementary School Teachers to Implement Science Curriculum Reforms

The authors evaluate the Science-Technology-Society (STS) views, attitudes and literacy of Israeli elementary science school teachers in three in-depth, longitudinal inservice programs. The programs were aimed at promoting teacher empowerment for the implementation, on a national scale, of a new STS-oriented elementary science curriculum reform. By using a blend of qualitative and quantitative research methods, the effectiveness of these similar but not identical programs has been determined. It was found that appropriately designed inservice science teacher training courses did induce a shift in the STS views/positions, beliefs/attitudes and literacy of elementary science teachers, and that this shift can be increased by using research-based data, obtained within an ongoing formative education process.     

LU factorizations, q = 0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relations which admit a dual system of orthogonal polynomials. For the q = 0 orthogonal limit functions we discuss interpretations on p-adic spaces. In the little 0-Jacobi case we also discuss product formulas. Dedicated to Dick Askey on the occasion of his seventieth birthday. 2000 Mathematics Subject Classification Primary—33D45, 33D80 Work done at KdV Institute, Amsterdam and supported by NWO, project number 613.006.573.     

Property (<Emphasis Type="Italic">T</Emphasis>) and rigidity for actions on Banach spaces

We study property (T) and the fixed-point property for actions on L ^p and other Banach spaces. We show that property (T) holds when L ² is replaced by L ^p (and even a subspace/quotient of L ^p ), and that in fact it is independent of 1≤p<∞. We show that the fixed-point property for L ^p follows from property (T) when 1<p< 2+ε. For simple Lie groups and their lattices, we prove that the fixed-point property for L ^p holds for any 1< p<∞ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive spaces. Bader partially supported by ISF grant 100146; Furman partially supported by NSF grants DMS-0094245 and DMS-0604611; Gelander partially supported by NSF grant DMS-0404557 and BSF grant 2004010; Monod partially supported by FNS (CH) and NSF (US).     

Cyclic reservation schemes for efficient operation of multiple-queue single-server systems

We study two new cyclic reservation schemes for the efficient operation of systems consisting of a single server and multiple queues. The schemes are the Globally Gated regime and the Cyclic-Reservation Multiple-Access (CRMA). Both procedures possess mechanisms for prioritizing the queues and lend themselves to a closed-form analysis. The combination of these two properties allows for effective and efficient operation of the systems, for which we provide a thorough delay analysis and derive simple rules for optimal operation.     

Considerations on modelling the market for softwood lumber in the United States

The analysis in this paper looks at two important elements in modelling the market for timber in the United States. First, the issue of directional causality between price and quantity and its implications in a modelling effort is investigated. Second, the extent of the geographic market for timber is discussed and a method of detecting it is suggested. The method for detecting the extent of the geographical market is tractable and can be applied in a straightforward way. Both considerations are applied to the softwood lumber market in the United States.     

The Examination Where the Student Asks the Question

The Examination where the Student Asks the Questions (ESAQ) is an innovative, system-oriented teaching/evaluation strategy ideated, developed and successfully implemented by the author, initially within the teaching of freshman chemistry (general and organic) in a four-year college. It constitutes a reflective, multidimensional response to the urgent need for effective teaching and evaluation strategies which will foster question asking, and higher order cognitive skills (HOCS). Such strategies are, ideally, relevant, challenging, and compatible with the new goals of science teaching and student performance evaluation. The core element of the ESAQ is a prearranged oral examination in which the course professor is examined by students, using home-prepared, written questions. Our experience suggests that the ESAQ can be creatively adopted and successfully implemented in different contexts of science teaching worldwide and would benefit both educators and students. The increase in the HOCS capacity of students is attainable.