Some expansions associated with Bessel functions

An Expansion for the Product of Two Bessel Functions.-1.1. An expansion for the product of two Bessel functions obtained by one of us(1) led to the discovery of a different expansion for the said product multiplied by the leading terms in the power series for the Bessel functions. Two proofs of this second expansion are given here

Transport Protocol Throughput Fairness

Interest continues to grow in alternative transport protocols to the Transmission Control Protocol (TCP). These alternatives include protocols designed to give greater efficiency in high-speed, high-delay environments (so-called high-speed TCP variants), and protocols that provide congestion control without reliability. For the former category, along with the deployed base of ‘vanilla’ TCP – TCP NewReno – the TCP variants BIC and CUBIC are widely used within Linux: for the latter category, the Datagram Congestion Control Protocol (DCCP) is currently on the IETF Standards Track. It is clear that future traffic patterns will consist of a mix of flows from these protocols (and others). So, it is important for users and network operators to be aware of the impact that these protocols may have on users. We show the measurement of fairness in throughput performance of DCCP Congestion Control ID 2 (CCID2) relative to TCP NewReno, and variants Binary Increase Congestion control (BIC), CUBIC and Compound, all in “out-of-the box” configurations. We use a testbed and endto- end measurements to assess overall throughput, and also to assess fairness – how well these protocols might respond to each other when operating over the same end-to-end network path. We find that, in our testbed, DCCP CCID2 shows good fairness with NewReno, while BIC, CUBIC and Compound show unfairness above round-trip times of 25ms

Resettlement of young people leaving custody: Lessons from the literature

This literature review aims to set out the research and practice evidence about effective resettlement services for children and young adults and can be used to inform future policy and practice to ensure service delivery is evidence based. The findings of the review will help to steer the focus of Beyond Youth Custody’s research over the duration of the programme and act as a baseline to assess how our understanding has advanced in terms of what works in facilitating the transition from youth custody to the community and beyond. In addition, the review highlights some examples of good practice, as well as the emerging key principles of effective resettlement provision

Representations of SU(1,1) in Non-commutative Space Generated by the Heisenberg Algebra

SU(1,1) is considered as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the irreducible representations of the group are realized is explicitly constructed. The addition theorems are derived.Comment: Latex, 8 page

Le principe de l’anonymat du don de sperme: remarques sur son histoire et son application

International audienc

Feasibility study of an Integrated Program for Aerospace vehicle Design (IPAD). Volume 3: Support of the design process

The user requirements for computer support of the IPAD design process are identified. The user-system interface, language, equipment, and computational requirements are considered

A probabilistic approach to some results by Nieto and Truax

In this paper, we reconsider some results by Nieto and Truax about generating functions for arbitrary order coherent and squeezed states. These results were obtained using the exponential of the Laplacian operator; more elaborated operational identities were used by Dattoli et al. \cite{Dattoli} to extend these results. In this note, we show that the operational approach can be replaced by a purely probabilistic approach, in the sense that the exponential of derivatives operators can be identified with equivalent expectation operators. This approach brings new insight about the kinks between operational and probabilistic calculus.Comment: 2nd versio

Relativistic ideal Fermi gas at zero temperature and preferred frame

We discuss the limit T->0 of the relativistic ideal Fermi gas of luxons (particles moving with the speed of light) and tachyons (hypothetical particles faster than light) based on observations of our recent paper: K. Kowalski, J. Rembielinski and K.A. Smolinski, Phys. Rev. D, 76, 045018 (2007). For bradyons this limit is in fact the nonrelativistic one and therefore it is not studied herein

High orders of Weyl series for the heat content

This article concerns the Weyl series of spectral functions associated with the Dirichlet Laplacian in a $d$-dimensional domain with a smooth boundary. In the case of the heat kernel, Berry and Howls predicted the asymptotic form of the Weyl series characterized by a set of parameters. Here, we concentrate on another spectral function, the (normalized) heat content. We show on several exactly solvable examples that, for even $d$, the same asymptotic formula is valid with different values of the parameters. The considered domains are $d$-dimensional balls and two limiting cases of the elliptic domain with eccentricity $\epsilon$: A slightly deformed disk ($\epsilon\to 0$) and an extremely prolonged ellipse ($\epsilon\to 1$). These cases include 2D domains with circular symmetry and those with only one shortest periodic orbit for the classical billiard. We analyse also the heat content for the balls in odd dimensions $d$ for which the asymptotic form of the Weyl series changes significantly.Comment: 20 pages, 1 figur