Classes of biorthonormal systems

Summary The biorthogonal systems which are studied in this paper are composed of an Appel set of polynomials and of a sequence of derivatives. Conditions on one sequence are given which ensure the existence of the other. Expansion theorems in terms of derivatives and by means of summability methods are then proved. This work has been sponsored by the European Office, Air Research and Development Command, U. S. Air Force, under Contract AF 61(052)-324.     

Classes of biorthonormal systems

Summary The (A)-summability and mean-convergence of Fourier series in terms of certain biorthonormal systems have been investigated. The problem of completing a set of polynomials to a biothonormal system has been solved in the case of certain sets of type zero (Sheffer’s classification). The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research of the Air Research and Development Command, United States air Force, through its European Office, under Contract N₀ AF 61 (052)-324.     

The geometry of profinite graphs with applications to free groups and finite monoids

We initiate the study of the class of profinite graphs defined by the following geometric property: for any two vertices and of , there is a (unique) smallest connected profinite subgraph of containing them; such graphs are called tree-like. Profinite trees in the sense of Gildenhuys and Ribes are tree-like, but the converse is not true. A profinite group is then said to be dendral if it has a tree-like Cayley graph with respect to some generating set; a Bass-Serre type characterization of dendral groups is provided. Also, such groups (including free profinite groups) are shown to enjoy a certain small cancellation condition.

We define a pseudovariety of groups to be arboreous if all finitely generated free pro- groups are dendral (with respect to a free generating set). Our motivation for studying such pseudovarieties of groups is to answer several open questions in the theory of profinite topologies and the theory of finite monoids. We prove, for arboreous pseudovarieties , a pro- analog of the Ribes and Zalesski product theorem for the profinite topology on a free group. Also, arboreous pseudovarieties are characterized as precisely the solutions to the much studied pseudovariety equation .

     

Conditional-phase switch at the single-photon level

We present an experimental realization of a two-photon conditional phase switch, related to the " c-phis;" gate of quantum computation. This gate relies on quantum interference between photon pairs and generates entanglement between two optical modes through the process of spontaneous parametric down-conversion (SPDC). The interference effect serves to enhance the effective nonlinearity by many orders of magnitude, so it is significant at the quantum (single-photon) level. By adjusting the relative optical phase between the classical pump for SPDC and the pair of input modes, one can impress a large phase shift on one beam which depends on the presence or absence of a single photon in a control mode.     

Nonlinear optics with less than one photon

We demonstrate suppression and enhancement of spontaneous parametric down-conversion via quantum interference with two weak fields from a local oscillator (LO). Effectively, pairs of LO photons up-convert with high efficiency for appropriate phase settings, exhibiting an effective nonlinearity enhanced by at least 10 orders of magnitude. This constitutes a two-photon switch and promises to be applicable to a wide variety of quantum nonlinear optical phenomena.     

Charged-particle pseudorapidity density distributions from Au+Au collisions at sqrt[s(NN)]=130 GeV

The charged-particle pseudorapidity density dN(ch)/d eta has been measured for Au+Au collisions at sqrt[s(NN)] = 130 GeV at RHIC, using the PHOBOS apparatus. The total number of charged particles produced for the 3% most-central Au+Au collisions for /eta/相似文献   

Revenue deficiency under second-price auctions in a supply-chain setting

Consider a firm, called the buyer, that satisfies its demand over two periods by assigning both demands to a supplier via a second-price procurement auction; call this the Standard auction. In the hope of lowering its purchase cost, the firm is considering an alternative procedure in which it will also allow bids on each period individually, where there can be either one or two winners covering the two demands; call this the Multiple Winner auction. Choosing the Multiple Winner auction over the Standard auction can in fact result in a higher cost to the buyer. We provide a bound on how much greater the buyer’s cost can be in the Multiple Winner auction and show that this bound is tight. We then sharpen this bound for two scenarios that can arise when the buyer announces his demands close to the beginning of the demand horizon. Under a monotonicity condition, we achieve a further sharpening of the bound in one of the scenarios. Finally, this monotonicity condition allows us to generalize this bound to the T-period case in which bids are allowed on any subset of period demands.     

The Quiver of an Algebra Associated to the Mantaci-Reutenauer Descent Algebra and the Homology of Regular Semigroups

We develop the homology theory of the algebra of a regular semigroup, which is a particularly nice case of a quasi-hereditary algebra in good characteristic. Directedness is characterized for these algebras, generalizing the case of semisimple algebras studied by Munn and Ponizovksy. We then apply homological methods to compute (modulo group theory) the quiver of a right regular band of groups, generalizing Saliola’s results for a right regular band. Right regular bands of groups come up in the representation theory of wreath products with symmetric groups in much the same way that right regular bands appear in the representation theory of finite Coxeter groups via the Solomon-Tits algebra of its Coxeter complex. In particular, we compute the quiver of Hsiao’s algebra, which is related to the Mantaci-Reutenauer descent algebra.