Department of Mathematics

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Now showing 1 - 20 of 180
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    Localized Diffusion of Substances Absorbed Through the Skin
    (1974-05) James, Makungu; Marty, J. P.; Wepierre, J.
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    Comparative Study of Absorption and Distribution of Dexamethasone-3H after Percutaneous or Oral Administration in Mice and Rats]
    (1975-12) James, Makungu; Marty, J. P.; Wepierre, J.
    Percutaneous absorption of dexamethasone in alcoholic solution in mice and rats was low. Permeability constant measured on mice was included between 1.05 and 1.39.10(-5) cm/h. Under the site of application, a retention appeared in subcutaneous tissue and skeletal muscles which explained local pharmacological action. In other tissues (plasma, liver, kidney, adrenals and muscles), level of corticoid remained very low. On the contrary after oral administration, dexamethasone was present everywhere, concentration was the highest in liver and kidney.
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    Exact Analytic Formula for the Correlation Times for Single Domain Ferromagnetic Particles.
    (Elsevier, 1993) Coffey, William T.; Crothers, D. S. F.; Kalmykov, Yuri P.; Massawe, Estomih S.; Waldron, J. T.
    Exact solutions for the longitudinal relaxation time T∥ and the complex susceptibility χ∥(ω) of a thermally agitated single domain ferromagnetic particle are presented for the simple uniaxial (Maier-Saupe) potential of the crystalline anisotropy considered by Brown [Phys. Rev. 130 (1963) 1677].
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    Effective-Eigenvalue Approach to the Nonlinear Langevin Equation for the Brownian motion in a Tilted Periodic Potential: Application to the Josephson Tunneling Junction
    (1993) Coffey, William T.; Kalmykov, Yuri P.; Massawe, Estomih S.
    The concept of the effective eigenvalue appears to have been originally introduced into the study of relaxation problems in statistical physics by Leontovich.’ It was later developed and applied (sometimes implicitly) to a variety of stochastic problems in laser polar fluids,’ polymers,8 nematic liquid crystals? lo etc. In the present context, namely the theory of the Brownian motion, the method constitutes a truncation procedure which allows one using simple assumptions to obtain closed-form approximations to the solution of certain infinite hierarchies of differential-difference equations in the time variables. These magnetic domains, equations govern the time behavior of the statistical averages characterizing the relaxation of nonlinear stochastic systems. Thus, their solution is needed to calculate observable quantities such as the relaxation times and dynamic susceptibilities of the system.
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    The Effective Eigenvalue Method and Its Application to Stochastic Problems in Conjunction with the Nonlinear Langevin Equation
    (1993) Coffey, William T.; Kalmykov, Yuri P.; Massawe, Estomih S.
    The concept of the effective eigenvalue appears to have been originally introduced into the study of relaxation problems in statistical physics by Leontovich.’ It was later developed and applied (sometimes implicitly) to a variety of stochastic problems in laser polar fluids,’ polymers,8 nematic liquid crystals? lo etc. In the present context, namely the theory of the Brownian motion, the method constitutes a truncation procedure which allows one using simple assumptions to obtain closed-form approximations to the solution of certain infinite hierarchies of differential-difference equations in the time variables. These magnetic domains, equations govern the time behavior of the statistical averages characterizing the relaxation of nonlinear stochastic systems. Thus, their solution is needed to calculate observable quantities such as the relaxation times and dynamic susceptibilities of the system
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    Effective-Eigenvalue Approach to the Nonlinear Langevin Equation for the Brownian motion in a Tilted Periodic Potential. II. Application to the Ring-Laser Gyroscope
    (1993) Coffey, William T.; Kalmykov, Yuri P.; Massawe, Estomih S.
    The effective-eigenvalue method is used to obtain an approximate solution for the mean beat-signal spectrum for the ring-laser gyroscope in the presence of quantum noise. The accuracy of the effective-eigenvalue method is demonstrated by comparing the exact and approximate calculations. It shows clearly that the effective-eigenvalue method yields a simple and concise analytical description of the solution of the problem under consideration.
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    Exact Solution for the Correlation Times of Dielectric Relaxation of a Single Axis Rotator with Two Equivalent Sites
    (1993) Coffey, William T.; Kalmykov, Yuri P.; Massawe, Estomih S.; Waldron, J. T.
    It is shown how exact formulas for the longitudinal and transverse dielectric correlation times and complex polar&ability tensor, of a single axis rotator with two equivalent sites may be found. This is accomplished by writing the Laplace transforms of the dipole autocorrelation functions as three term recurrence relations and solving them in terms of continued fractions. The solution of these recurrence relations, in the zero frequency limit, yields the correlation times in terms of modified Bessel functions of the first kind. The previous result of Lauritzen and Zwanzig for the longitudinal relaxation time, based on an asymptotic expansion of the SturmLiouville equation, is regained in the limit of high potential barriers.
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    Exact Analytic Formula for the Correlation Time of a Single-Domain Ferromagnetic Particle
    (1994) Coffey, William T.; Crothers, D. S. F.; Kalmykov, Yuri P.; Massawe, Estomih S.; Waldron, J. T.
    Exact solutions for the longitudinal relaxation time T∥ and the complex susceptibility χ∥(ω) of a thermally agitated single-domain ferromagnetic particle are presented for the simple uniaxial potential of the crystalline anisotropy considered by Brown [Phys. Rev. 130, 1677 (1963)]. This is accomplished by expanding the spatial part of the distribution function of magnetic-moment orientations on the unit sphere in the Fokker-Planck equation in Legendre polynomials. This leads to the three-term recurrence relation for the Laplace transform of the decay functions. The recurrence relation may be solved exactly in terms of continued fractions. The zero-frequency limit of the solution yields an analytic formula for T∥ as a series of confluent hypergeometric (Kummer) functions which is easily tabulated for all potential-barrier heights. The asymptotic formula for T∥ of Brown is recovered in the limit of high barriers. On conversion of the exact solution for T∥ to integral form, it is shown using the method of steepest descents that an asymptotic correction to Brown’s high-barrier result is necessary. The inadequacy of the effective-eigenvalue method as applied to the calculation of T∥ is discussed.
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    Simulated Annealing Algorithm for the resource Levelling Problem
    (1996) Mushi, Allen R.; O'hEigeartaigh, M.
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    Stochastic Algorithm for the resource Levelling Problem
    (1997) Mushi, Allen R.; O'hEigeartaigh, M.
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    On the Koebe and Bieberbach Constants for Hyperbolic Domains
    (1999) Rugeihyamu, Sylvester E.
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    The Resource Levelling Problem (RLP) Mixed-Integer Programming Formulations
    (Uhandisi Journal, 1999) Mushi, Allen R.; O'hEigeartaigh, M.
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    Tabu Search Approach to the Assembly Line Balancing Problem Type2
    (1999) Mushi, Allen R.; Ndunguru, A.; Alphonce, C.
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    Tabu Search Algorithm for the RLP
    (The International Journal of Management and Systems, 2000) Mushi, Allen R.; O'hEigeartaigh, M.
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    On the Koebe and Bieberbach Constants for a Hyperbolic Planar Domain
    (Springer, 2000-12-01) Rugeihyamu, Sylvester E.
    We discuss domain constants related to the classical Bieberbach and Koebe theorems. We find a class of simply connected domains for which the value of these constants is extremal and investigate the relationship between the geometry of a sequence of hyperbolic domains and the associated sequence of domain constants.
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    On the Bieberbach and Koebe Constants of a Simply Connected Domain
    (Gordon and Breach Science Publishers, 2001-11-01) Carroll, Tom; Rugeihyamu, Sylvester E.
    The classical Bieberbach coefficient estimate and Koebe 1/4-theorem for univalent functions in the unit disk may be formulated, in terms of a naturally defined Bieberbach constant n(D) and Koebe constant C(D), as n(D)≤2 and C(D) ≥ 1/4 for each simply connected domain D. We show that these inequalities have the same extremal domains, by means of a variation on the classical argument that yields the Bieberbach and Koebe Theorems, and describe how this is related to work of Flinn and Herron and of Pommerenke. Such extremal domains satisfy n(D)C(D)=1/2. An example of a simply connected domain for which n(o:D)C(D)≠1/2 is constructed, thereby proving that equality does not always hold in the inequality n(D)C(D) ≥½, due to Osgood. In passing, we raise an interesting question on the relationship between the second coefficient of a univalent function f and the radius of the largest disk about f(0) that is covered by f
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    On the stability of a forced-free boundary layer flow with viscous heating
    (2002-07) Mureithi, Eunice; Mason, David P.
    The inviscid instability of an accelerating forced-free convection boundary layer with viscous dissipation is investigated. The boundary layer equations for the flow with free-stream velocity U∞xn admit self-similar solutions for n=1 only. The “overshooting” of the free-stream value, characteristic of accelerating buoyant boundary layers, is found to increase with increasing viscous heating. The scaled temperature profile is also found to exceed its plate value close to the plate where the viscous dissipation effects are strongest. For Eckert number Ec=0 only one single inviscid unstable mode exists. For the flow with viscous dissipation, three unstable modes have been identified. The secondary modes may be associated with the combined effect of thermal buoyancy and viscous heating. There is evidence of these modes crossing at relatively higher wavenumbers. The disturbance growth rate is found to increase with increasing buoyancy and viscous heating.
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    On the Bieberbach and Koebe Constants for Sector Domains and Sector Disks
    (Springer, 2003-12-01) Rugeihyamu, Sylvester E.
    We discuss domain constants related to the classical Bieberbach and Koebe theorems. We find a class of simply connected domains for which the product of these constants behave like extremal domain and gives a better result on Osgood’s inequalities.