Technical Reports (Mathematics and Statistics)

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    Use of closed population models to estimate the number of injection drug users in Victoria, B.C.
    (2011-06-07) Xu, Yuan; Cowen, Laura L.E.
    Closed mark-recapture experiments are widely used to estimate population size even though the assumption of "closed population"' is often violated (immigrations and emigrations) compared to open population models. This work investigates various methods in closed population models (Petersen estimator, maximum likelihood estimation with mixtures, and Huggins model) to estimate the number of injection drug users (IDU) in Victoria, B.C. Model selection methods used to choose a final model as well as goodness-of-fit options are discussed. We use data from the 2003 and 2005's I-Track survey program to compare these estimators.
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    Optimization of multi-drug composition for the most efficacious action
    (2010-06-02T19:53:07Z) Bose, Chris; Bizuet, Rocky; Caudillo, Luz; Gong, Jiafen; Jain, Rashi; Romanko, Oleksandr; Samarbakhsh, Abdi; Tam, Yun K.
    In this report we consider a drug-design problem as it typically appears in Chinese medicine, where a large number of potentially active components are combined into one herbal therapy. The problem is posed by the SinoVeda Canada Inc. We focus on techniques for component-activity analysis in order to isolate the most active components, and the most active synergies between components as measured by tissue response to prepared herbal mixtures. The aim is to produce both qualitative and quantitative descriptions of the most active dose-fractions for a given herbal therapy and to aid in optimal design of herbal mixtures treating the target diseases. This report describes various techniques to achieve this goal, including multivariate linear regression, principle component analysis, subset selection and regularization.
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    Approximation by normal elements with finite spectra in simple AF-algebras
    (2010-06-01T22:05:39Z) Lin, Hauxin
    We show that normal elements in simple AF-algebras with countably many extremal traces (such as UHF-algebras and matroid algebras) can be approximated by normal elements with finite spectra. Other AF-algebras are shown to have the same property.
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    Notes on K-theory of multiplier algebras and corona algebras
    (2010-06-01T19:48:45Z) Lin, Hauxin
    We give an answer to the question when the unitary group of the corona algebra of a simple AF-algebra is connected. We also compute the K-groups of the multiplier algebras and corona algebras of certain simple C*-algebras. For example, if A_\theta is an irrational rotation C*-algebra and A is a non-stable hereditary C*-subalgebra of A_\theta \varotimes K, then we find that K_1(M(A)) = K_1(M(A)/A) = {0} and K_0(M(A)) = R.
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    Maps preserving nth powers
    (2010-05-31T20:16:19Z) Bresar, Matej; Martindale, W. S. (Wallace S.); Miers, C. Robert
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    On the anisotropic Manev problem
    (2010-05-31T15:47:42Z) Craig, Scott; Diacu, Florin; Lacomba, Ernesto A.; Perez, Ernesto
    The anisotropic Manev problem describes the motion of two bodies in an Euclidean space in which the gravitational force acts differently in each direction. The potential is the sum between the inverse and the inverse square of the distance, where the distance is defined such that it embodies the anisotropy of the space. Using McGehee coordinates, we blow up the collision singularity, paste a collision manifold to the phase space, study the flow on and near the collision manifold, and find a rich set of collision orbits having positive measure. In the zero-energy case we describe all possible connections between equilibria and/or cycles at collision and at infinity and find the main qualitative features of the flow.
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    Free-market prices tend to equilibria
    (2010-05-27T18:04:34Z) Diacu, Florin
    Ignoring the way the exchange of goods takes place and taking into account only the result of the trade, we analyze the relation between demand, supply, and prices. We prove that in a free-market economy ruled only by demand and supply there are infinitely many equilibria, all stable, and that prices tend either to one of the equilibria or to zero. Moreover, we show that if other forces act on the market then, generically, no equilibria exist.
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    Nilpotent inner derivations of the skew elements of prime rings with involution
    (2010-05-27T15:52:49Z) Martindale, W. S. (Wallace S.); Miers, C. Robert
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    Some combinatorial series identities associated with the digamma function and harmonic numbers functions with negative coefficients
    (2010-05-26T21:54:57Z) Wu, T.-C.; Tu, S.-T.; Srivastava, H.M.
    The authors develop closed-form sums of several interesting families of series associated with the Digamma (or Psi) function and harmonic numbers. A number of illustrative examples and applications of the main results are also considered.
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    Certain operational techniques and their applications in analytic and univalent function theory
    (2010-05-26T18:18:05Z) Srivastava, H.M.
    Various families of linear operators are becoming increasingly useful in Geometric Function Theory which is the study of the relationship between the analytic properties of a given function and the geometric properties of its image domain. Furthermore, an immensely useful class of special functions (namely, the generalized hypergeometric function) played a rather crucial role in Louis de Branges' proof of the celebrated Bieberbach, Robertson, and Milin conjectures in the theory of analytic and univalent functions. These latter developments in an area other than the so-called traditional areas of applications of generalized hypergeometric functions have naturally provided a new impetus for the study of such an important class of special functions. With these points in view, we first illustrate the usefulness (in the study of univalent, starlike, and convex generalized hypergeometric functions) of certain families of linear operators which are defined in terms of (for example) fractional derivatives and fractional integrals, Hadamard product or convolution, and so on. We also present a systematic discussion of some properties and theorems involving starlike functions and various families of integral operators considered here. Finally, we consider several inclusion theorems associated with the Hardy space of analytic functions, which hold true for various classes of generalized hypergeometric functions whose derivative has a positive real part. Relevant connections with recent works and developments on the subject are indicated throughout this presentation.
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    Some characterizations of univalent, starlike and convex hypergeometric functions
    (2010-05-26T18:10:15Z) Srivastava, H.M.; Owa, Shigeyoshi
    E.P. Merkes and W.T. Scott [Proc. Amer. Math. Soc. 12(1961), 885-888] proved an interesting result characterizing starlike hypergeometric functions. More recently, B.C. Carlson and D.B. Shaffer [SIAM J. Math. Anal. 15(1984), 737-745] introduced a linear operator and demonstrated how this operator can be applied systematically to the study of various interesting classes of starlike, convex, and prestarlike hypergeometric functions. The object of the present paper is to establish several characterization theorems involving univalent, starlike, and convex hypergeometric functions in the unit disk. Various inequalities involving hypergeometric series are also proved.
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    Theorem on Widder's potential transform and its applications
    (2010-05-26T15:54:18Z) Srivastava, H.M.; Yürekli, Osman
    In the present paper the authors prove a Parseval-Goldstein type theorem involving the classical Laplace transform, the Fourier sine transform, and Widder's potential transform. The theorem is then shown to yield a simple algorithm for evaluating infinite integrals. Some illustrative examples are also given.
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    Some new results for radiation-field problems
    (2010-05-26T15:42:53Z) Saigo, Magumi; Srivastava, Rekha
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    Queuing theory
    (2010-05-26T15:33:13Z) Srivastava, H.M.
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    Generalized bilevel programming problems
    (2010-05-25T22:05:32Z) Ye, J. J.; Zhu, D. L.; Zhu, Q.
    The generalized bilevel programming problem (GBLP) is a mathematical programming problem with variational inequality constraints. In this paper by error bound approach, we establish some equivalent single level formulation of the generalized bilevel programming problem. The necessary optimality condition of Kuhn-Tucker type are then given by using nonsmooth analysis.
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    Efficient algorithm for generating B-spline interpolation curves and surfaces from B-spline approximations
    (2010-05-25T21:59:17Z) Wang, Hui Ping; Hewgill, Denton E.; Vickers, Geoffrey W.
    A useful and simple algorithm is presented for interactively generating B-spline interpolation curves and surfaces from B-spline approximation solutions. The difference between the data points and the B-spline approximation is used to modify the control vertices in order to generate a succession of B-spline approximations which converge rapidly to the interpolation solution. The intermediate B-spline approximations can be viewed interactively and the most appropriate solution selected for a particular application.
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    On the validity of the BBGKY hierarchy
    (2010-05-25T19:42:16Z) Hurd, A. E.
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    Irredundance in the Queen's graph
    (2010-05-25T19:39:08Z) Cockayne, E. J.
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    New characterizations of certain starlike and convex generalized hypergeometric functions
    (2010-05-25T15:55:19Z) Srivastava, H.M.; Owa, Shigeyoshi
    Applying various properties of a certain class of linear integral operators, the authors prove a number of theorems which provide interesting characterizations of starlike and convex generalized hypergeometric functions. Several useful corollaries are also deduced.
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    Lie ideals in triangular operator algebras
    (2010-05-25T15:50:25Z) Hudson, T. D.; Marcoux, L. W.; Sourour, A. R.
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