1,929 research outputs found
A bifurcated circular waveguide problem
No full textThis is a pre-copy-editing, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The definitive publisher-authenticated version A D Rawlins. A bifurcated circular waveguide problem. J.I.M.A. 54 (1995) 59-81. Oxford University press is available online at: http://imamat.oxfordjournals.org/cgi/reprint/54/1/59.pdfA rigorous and exact solution is obtained for the problem of the radiation of sound from a semi-infinite rigid duct inserted axially into a larger acoustically lined tube of infinite length. The solution to this problem is obtained by the Wiener-Hopf technique. The transmission and reflection coefficients, when the fundamental mode propagates in the semi-infinite tube, are obtained. The present results could be of use for exhaust design, and as a possible instrument for impedance measurement
A note on Wiener-Hopf matrix factorisation
No full textThis is a pre-copy-editing, author-produced PDF of an article accepted for publication in Quarterly Journal of Mechanics and Applied Mathematics following peer review. The definitive publisher-authenticated version Rawlins, A D (1985). A note on Wiener-Hopf matrix factorisation. Quarterly Journal of Mechanics and Applied Mathematics. 38 (3) 433-437 is available online at: http://qjmam.oxfordjournals.org/cgi/reprint/38/3/433.pdfIn this paper the most general class of 2 x 2 matrices is determined which permit a
Wiener-Hopf factorization by the procedure of Rawlins and Williams (1). According
to this procedure, the factorization problem is reduced to a matrix Hilbert problem
on a half-line, where the matrix involved in the Hilbert problem is required to have
zero diagonal elements
The method of finite-product extraction and an application to Wiener-Hopf theory
No full textCopyright @ The Author, 2011. The publisher version of the article can be accessed at the link below.In this work we describe a simple method for finding approximate representations for special functions which are entire transcendental functions that can be represented by infinite products. This method replaces the infinite product by a finite polynomial and Gamma functions. This approximate representation is shown in the case of Bessel functions to be very accurate over a large range of parameter values. These approximate expressions can be useful for finding the roots of a transcendental equation and the Wiener-Hopf factorization of functions involving such Bessel functions.The method is shown to be potentially useful for other transcendental andWiener-Hopf problems, which involve other entire functions that have infinite product representations
A note on point source diffraction by a wedge
No full textThe object of this paper is to give new expressions for the wave field produced when a time harmonic point source is diffracted by a wedge with Dirichlet or Neumann boundary conditions on its faces. The representation of the total field is expressed in terms of quadratures of elementary functions, rather than Bessel functions, which is usual in the literature. An analogous expression is given for the three-dimensional free-space Green's function
A Green's function for diffraction by a rational wedge
No full textIn this paper we derive an expression for the point source Green's function for the
reduced wave equation, valid in an angular sector whose angle is equal to a rational
multiple of 77. This Green's function can be used to find new expressions for the field
produced by the diffraction of a spherical wave by a wedge whose angle can be
expressed as a rational multiple of n. The expressions obtained will be in the form of
source terms and real integrals representing the diffracted field. The general result
obtained is used to derive a new representation for the solution of the problem of diffraction by a mixed hard-soft half plane
The Wiener-Hopf-Hilbert technique applied to problems in diffraction
No full textThis thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.A number of diffraction problems which have practical applications are examined using the Wiener-Hopf-Hilbert technique. Each problem is formulated as a matrix Wiener-Hopf equation, the solution of which requires the factor~sation of a matrix kernel. Since the determinant of the matrix kernel has poles in the cut plane, the
Wiener-Hopf-Hilbert technique is modified to allow the usual arguments to follow through. In each case an explicit matrix factorisation is carried out and asymptotic
expressions for the field scattered to infinity are obtained. The first problem solved is that of diffraction by a semi-infinite plane with different face impedances. The solution includes the case of an incident surface wave as well as an incident plane wave for an arbitrary angle of incidence. Graphs of the far-field are provided for various values of the half-plane impedance parameters. The second
problem examined is diffraction by a half-plane in a moving fluid. This is solved
without restriction on the impedance parameters of the half-plane and includes both the leading edge and trailing edge situations. The final problem is of radiation from an inductive wave-guide. Expressions are obtained for the field radiated at the waveguide mouth and the field reflected in the duct region.This work is funded by the UK Engineering and Physical Sciences Research Council (EPSRC
Wellcome Witnesses to Twentieth Century Medicine: Volume 1
No full textAnnotated and edited transcript of four Witness Seminars. Introduction by E M Tansey First published by the Wellcome Trust, 1997. ©The Trustee of the Wellcome Trust, London, 1997.In Volume One (Occasional Publication no. 4, 1997).All volumes are freely available online at: www.history.qmul.ac.uk/research/modbiomed/wellcome_witnesses/Annotated and edited transcript of four Witness Seminars. Introduction by E M Tansey.Annotated and edited transcript of four Witness Seminars. Introduction by E M Tansey.Annotated and edited transcript of four Witness Seminars. Introduction by E M Tansey.Annotated and edited transcript of four Witness Seminars. Introduction by E M Tansey.Four Witness Seminar transcripts of meetings held between 1993 and 1996: ‘Technology Transfer in Britain: The case of Monoclonal Antibodies’ (E M Tansey and P P Catterall, eds); ‘Self and Non-Self: A History of Autoimmunity’ (E M Tansey, S V Willhoft and D A Christie, eds); ‘Endogenous Opiates’ (E M Tansey and D A Christie, eds); ‘The Committee on Safety of Drugs’ (E M Tansey and L A Reynolds, eds). Introduction by E M Tansey, ‘What is a Witness Seminar’, separate index for each meeting. Tansey E M, Catterall P P, Christie D A, Willhoft S V, Reynolds L A. (eds) (1997) Wellcome Witnesses to Twentieth Century Medicine, volume 1. London: The Wellcome Trust.The Wellcome Trust is a registered charity, no. 210183
Diffraction by a half-plane in a moving fluid
No full textIn the following work we solve the problem of the diffraction of a plane sound wave by an impedance half-plane in a moving fluid. Expressions for the total far field are derived for both the leading edge and trailing edge situations. In the trailing edge situation the problem has the added complication of a trailing vortex sheet or wake. Hence a Kutta-Joukowski edge condition is imposed to ensure that the fluid velocity is finite at the edge and to obtain a unique solution to the problem
Ummah Futures Halal Investment Cooperative
No full text"Ummah Futures" is an equity-based community investment cooperative that will collect fixed monthly investments from up to 20 members of the Nur-Ul-Islam Center's Ummah (community), located in Cooper City, Florida, towards the goals of wealth creation, asset accumulation and economic brotherhood by stimulating cooperative business activities and investments according to Islamic economic and social principles. Muslims are forbidden to engage in interest or support investing in haram (Islamically unlawful) business activities (i.e. the sale of alcohol). There will be two levels of monthly investment over a 36-months period, they are: 1) 300 per month. Future funding will be derived from the increase of new memberships and the success (or lack thereof) of equity investments made by the co-op. The co-op's initial 20 members, investing at the higher tier, will invest $216,000 over the 36 months period and the return on the investment that the co-op will target is 5% plus the member's principle investment. Moreover, participants in the plan will be encouraged to reinvest their earnings back into the plan.
The success of the project will be evaluated by determining (a) how many participants complete the investment program; (b) the number of new participants enrolling in the program; (c) the increase in earnings; (d) the number of new employment or contracted opportunities created for members, (e) the number of members trained in cooperative structure and Islamic economic principles, and; (f) the effect of that training in the social and economic relations of the investors. (Author abstract)Rawlins, W. E. (2005). Ummah Futures Halal Investment Cooperative. Retrieved from http://academicarchive.snhu.eduMaster of Science (M.S.)School of Community Economic Developmen
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