Theory of functions of a complex variable,

Available on demand as hard copy or computer file from Cornell University Library.

Theory of functions of a complex variable /

Mode of access: Internet.

The sex complex; a study of the relationships of the internal secretions to the female characteristics and functions in health and disease,

Mode of access: Internet.

The sex complex; a study of the relationships of the internal secretions to the female characteristics and functions in health and disease.

"This is not the kind of book that can usefully be taken through numerous editions, so with the issue of this edition it will finish its career."

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

MSC2010: 30C45, 33C45

Nitric oxide photorelease from hydrogels and from skin containing a nitro-ruthenium complex

Nitric oxide (NO) is a gaseous molecule that has specific functions dictated by its localization and its kinetics of release. As NO-donors have a range of potential uses in the skin, much attention has been paid to the development of topical NO delivery systems. The aim of this work was to study the release rate and the skin penetration of the NO-donor cis[Ru(NO(2))(bpy)(2)(4-pic)](+) from different gel formulations and their potential as topical NO delivery systems under light stimuli. Among the formulations developed, the anionic gel retarded the nitro-ruthenium complex diffusion and also obstructed NO release after light irradiation. On the other hand, NO release before light irradiation was observed when the complex was dispersed in the cationic chitosan gel, possibly due to oxi-redox reactions between the amino groups of the polymer and the drug molecule. Finally, the non-ionic gel released the NO after light irradiation to the same extent as a drug aqueous solution at the same pH. The drug dispersed in this gel also penetrated into the stratum corneum skin layer, and the nitro-ruthenium complex present in the skin was able to release the NO after light stimuli, suggesting the potential use of this formulation as a topical NO delivery system. (C) 2010 Elsevier B.V. All rights reserved.

U-q[(sl(2)over-cap vertical bar 1)] vertex operators, screen currents, and correlation functions at an arbitrary level

Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra U-q[sl((2) over cap\1)] are constructed for arbitrary level k=alpha, where alpha not equal 0,-1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-alpha highest weight Fock-Wakimoto modules. Screen currents which commute with the action of U-q[sl((2) over cap/1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed. (C) 2000 American Institute of Physics. [S0022-2488(00)00608-3].

The human papillomavirus E7 protein is able to inhibit the antiviral and anti-growth functions of interferon-alpha

It is now well recognized that cervical cancer is caused by infection with certain human papillomavirus (HPV) subtypes and while interferon-alpha (IFN-alpha) is used to treat HPV-infected lesions, HPV appears to have developed a means to avoid the effects of IFN-alpha. Clinically, resistance appears to be associated with the expression of the E7 oncoprotein. Here we investigated the effects of expression in cells of the E7 protein from high- and low-risk papillomavirus subtypes on a range of responses to IFN-alpha. 2fTGH, a cell line dependent on IFN-alpha for growth in selection medium, grew significantly less well in the presence of E7, and the antiproliferative effects of IFN-alpha upon epithelial cells was lost upon E7 expression. The antiviral effects of IFN-alpha were abrogated in E7-expressing cells. Loss of response to IFN-alpha was found to occur in both high- and low-risk papillomaviruses. Finally, deletion of amino acids 21-24 of HPV type 16 E7 protein partially reversed repression. We conclude that E7 inhibits the functional effects of IFN-alpha and that this property is shared by all HPV subtypes tested. (C) 2000 Academic Press.

Structure optimization combining soft-core interaction functions, the diffusion equation method, and molecular dynamics

Smoothing the potential energy surface for structure optimization is a general and commonly applied strategy. We propose a combination of soft-core potential energy functions and a variation of the diffusion equation method to smooth potential energy surfaces, which is applicable to complex systems such as protein structures; The performance of the method was demonstrated by comparison with simulated annealing using the refinement of the undecapeptide Cyclosporin A as a test case. Simulations were repeated many times using different initial conditions and structures since the methods are heuristic and results are only meaningful in a statistical sense.

Some results on holomorphic generalized functions

In this note, we present three independent results within generalized complex analysis (in the Colombeau sense). The first of them deals with non-removable singularities; we construct a generalized function u on an open subset Omega of C(n), which is not a holomorphic generalized function on Omega but it is a holomorphic generalized function on Omega\S, where S is a hypersurface contained in Omega. The second result shows the existence of a holomorphic generalized function with prescribed values in the zero-set of a classical holomorphic function. The last result states the existence of a compactly supported solution to the (partial derivative) over bar operator.

A novel approach to antigen-specific deletion of CTL with minimal cellular activation using alpha 3 domain mutants of MHC class I/peptide complex

In this study, we have compared the effector functions and fate of a number of human CTL clones in vitro or ex vivo following contact with variant peptides presented either on the cell surface or in a soluble multimeric format. In the presence of CD8 coreceptor binding, there is a good correlation between TCR signaling, killing of the targets, and Fast-mediated CTL apoptosis. Blocking CD8 binding using (alpha3 domain mutants of MHC class I results in much reduced signaling and reduced killing of the targets. Surprisingly, however, Fast expression is induced to a similar degree on these CTLs, and apoptosis of CTL is unaffected. The ability to divorce these events may allow the deletion of antigen-specific and pathological CTL populations without the deleterious effects induced by full CTL activation.

Complex natural resonances of conducting planar objects buried in a dielectric half-space

A scheme is presented to incorporate a mixed potential integral equation (MPIE) using Michalski's formulation C with the method of moments (MoM) for analyzing the scattering of a plane wave from conducting planar objects buried in a dielectric half-space. The robust complex image method with a two-level approximation is used for the calculation of the Green's functions for the half-space. To further speed up the computation, an interpolation technique for filling the matrix is employed. While the induced current distributions on the object's surface are obtained in the frequency domain, the corresponding time domain responses are calculated via the inverse fast Fourier transform (FFT), The complex natural resonances of targets are then extracted from the late time response using the generalized pencil-of-function (GPOF) method. We investigate the pole trajectories as we vary the distance between strips and the depth and orientation of single, buried strips, The variation from the pole position of a single strip in a homogeneous dielectric medium was only a few percent for most of these parameter variations.

On the fast approximation of Green's functions in MPIE formulations for planar layered media

The numerical implementation of the complex image approach for the Green's function of a mixed-potential integralequation formulation is examined and is found to be limited to low values of k(0) rho (in this context k(0) rho = 2 pirho/ lambda(0), where rho is the distance between the source and the field points of the Green's function and lambda(0) is the free space wavelength). This is a clear limitation for problems of large dimension or high frequency where this limit is easily exceeded. This paper examines the various strategies and proposes a hybrid method whereby most of the above problems can be avoided. An efficient integral method that is valid for large k(0) rho is combined with the complex image method in order to take advantage of the relative merits of both schemes. It is found that a wide overlapping region exists between the two techniques allowing a very efficient and consistent approach for accurately calculating the Green's functions. In this paper, the method developed for the computation of the Green's function is used for planar structures containing both lossless and lossy media.