Class two p groups as fixed point free automorphism groups

Suppose that AG is a solvable group with normal subgroup G where (|A|, |G|) = 1. Assume that A is a class two odd p group all of whose irreducible representations are isomorphic to subgroups of extra special p groups. If p^c ≠ r^d + 1 for any c = 1, 2 and any prime r where r^2d+1 divides |G| and if C_G(A) = 1 then the Fitting length of G is bounded by the power of p dividing |A|.

The theorem is proved by applying a fixed point theorem to a reduction of the Fitting series of G. The fixed point theorem is proved by reducing a minimal counter example. IF R is an extra spec r subgroup of G fixed by A₁, a subgroup of A, where A₁ centralizes D(R), then all irreducible characters of A₁R which are nontrivial on Z(R) are computed. All nonlinear characters of a class two p group are computed.

Formation of jets by implusive acceleration of a curved free surface

The sudden axial acceleration of a column of liquid bounded at one end by a concave free surface has been found, experimentally, to produce a jet which issues from the free surface with a speed several times that imparted to the column.

Theoretical approximations to such flows, valid for small time, are formulated subject to the assumption that the fluid is inviscid and incompressible. In a special two-dimensional case, it is found that, for vanishingly small time, the velocity at the point on the free surface from which the jet emanates is π/2 times the velocity imparted to the column. The solutions to several problems in two and three dimensions assuming that the initial curvature of the free surface is small, lead to values for this ratio dependent upon the curvature—the initial velocity in the case of axial symmetry exceeding that of the analogous two-dimensional problem by approximately 25%.

Experiments conducted upon the phenomenon give values systematically in excess of those predicted by the theory, although theory and experiment are in qualitative agreement with respect to the displacement of the free surface. It is suggested that the discrepancy is attributable to effects of finite curvature having been imperfectly accounted for in the axially-symmetric analysis.

Photographic materials on pp. 115, 120, and 121 are essential and will not reproduce clearly on Xerox copies. Photographic copies should be ordered.

Genetic engineering of microorganisms: free release into the environment

Genetic engineering now makes possible the insertion of DNA from many organisms into other prokaryotic, eukaryotic and viral hosts. This technology has been used to construct a variety of such genetically engineered microorganisms (GEMs). The possibility of accidental or deliberate release of GEMs into the natural environment has recently raised much public concern. The prospect of deliberate release of these microorganisms has prompted an increased need to understand the processes of survival, expression, transfer and rearrangement of recombinant DNA molecules in microbial communities. The methodology which is being developed to investigate these processes will greatly enhance our ability to study microbial population ecology.

A nonlinear systems model for the control mechanism of free fatty acid-glucose metabolosm in normal humans

A mathematical model is proposed in this thesis for the control mechanism of free fatty acid-glucose metabolism in healthy individuals under resting conditions. The objective is to explain in a consistent manner some clinical laboratory observations such as glucose, insulin and free fatty acid responses to intravenous injection of glucose, insulin, etc. Responses up to only about two hours from the beginning of infusion are considered. The model is an extension of the one for glucose homeostasis proposed by Charette, Kadish and Sridhar (Modeling and Control Aspects of Glucose Homeostasis. Mathematical Biosciences, 1969). It is based upon a systems approach and agrees with the current theories of glucose and free fatty acid metabolism. The description is in terms of ordinary differential equations. Validation of the model is based on clinical laboratory data available at the present time. Finally procedures are suggested for systematically identifying the parameters associated with the free fatty acid portion of the model.

Corrections to the paraxial approximation of an arbitrary free-propagation beam

A relatively simple transform from an arbitrary solution of the paraxial wave equation to the corresponding exact solution of the Helmholtz wave equation is derived in the condition that the evanescent waves are ignored and is used to study the corrections to the paraxial approximation of an arbitrary free-propagation beam. Specifically, the general lowest-order correction field is given in a very simple form and is proved to be exactly consistent with the perturbation method developed by Lax et nl. [Phys. Rev. A 11, 1365 (1975)]. Some special examples, such as the lowest-order correction to the paraxial approximation of a fundamental Gaussian beam whose waist plane has a parallel shin from the z = 0 plane, are presented. (C) 1998 Optical Society of America.

Effect of elliptical manufacture error of an axicon on the diffraction-free beam patterns

Based on the generalized Huygens-Fresnel diffraction integral theory and the stationary-phase method, we analyze the influence on diffraction-free beam patterns of an elliptical manufacture error in an axicon. The numerical simulation is compared with the beam patterns photographed by using a CCD camera. Theoretical simulation and experimental results indicate that the intensity of the central spot decreases with increasing elliptical manufacture defect and propagation distance. Meanwhile, the bright rings around the central spot are gradually split into four or more symmetrical bright spots. The experimental results fit the theoretical simulation very well. (C) 2008 Society of Photo-Optical Instrumentation Engineers.

Changes in social inequalities in disability-free life expectancy in Southern Europe: the case of the Basque Country

Background: Health expectancy is a useful tool to monitor health inequalities. The evidence about the recent changes in social inequalities in healthy expectancy is relatively scarce and inconclusive, and most studies have focused on Anglo-Saxon and central or northern European countries. The objective of this study was to analyse the changes in socioeconomic inequalities in disability-free life expectancy in a Southern European population, the Basque Country, during the first decade of the 21st century. Methods: This was an ecological cross-sectional study of temporal trends on the Basque population in 1999-2003 and 2004-2008. All-cause mortality rate, life expectancy, prevalence of disability and disability free-life expectancy were calculated for each period according to the deprivation level of the area of residence. The slope index of inequality and the relative index of inequality were calculated to summarize and compare the inequalities in the two periods. Results: Disability free-life expectancy decreased as area deprivation increased both in men and in women. The difference between the most extreme groups in 2004-2008 was 6.7 years in men and 3.7 in women. Between 1999-2003 and 2004-2008, socioeconomic inequalities in life expectancy decreased, and inequalities in disability-free expectancy increased in men and decreased in women. Conclusions: This study found important socioeconomic inequalities in health expectancy in the Basque Country. These inequalities increased in men and decreased in women in the first decade of the 21st century, during which the Basque Country saw considerable economic growth.

Double-cladding Yb3+ fiber for free-space optical communication

The experiment result of Nd:YVO4 laser pumped by laser diode that was amplified by double-cladding Yb3+ fiber is reported. Stable mode-locking pulses are obtained at repetition rate of 320 MHz and the output power is 15 mW. When laser power is amplified by Yb3+- doped double-cladding fiber amplifier, its power can get to 600 mW. Based on these, experiment of double-frequency is carried out, and green laser with power of 4 mW is obtained. (c) 2007 Wiley Periodicals, Inc.

Acoustic plasmons in extrinsic free-standing graphene

An acoustic plasmon is predicted to occur, in addition to the conventional two-dimensional (2D) plasmon, as the collective motion of a system of two types of electronic carriers coexisting in the same 2D band of extrinsic (doped or gated) graphene. The origin of this novel mode stems from the anisotropy present in the graphene band structure near the Dirac points K and K'. This anisotropy allows for the coexistence of carriers moving with two distinct Fermi velocities along the Gamma K and Gamma K' directions, which leads to two modes of collective oscillation: one mode in which the two types of carriers oscillate in phase with one another (this is the conventional 2D graphene plasmon, which at long wavelengths (q -> 0) has the same dispersion, q(1/2), as the conventional 2D plasmon of a 2D free electron gas), and the other mode found here corresponds to a low-frequency acoustic oscillation (whose energy exhibits at long-wavelengths a linear dependence on the 2D wavenumber q) in which the two types of carriers oscillate out of phase. This prediction represents a realization of acoustic

Uncovering the role of free volume in biomaterials and biological matter

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Structural and upconversion fluorescence properties of Er3+/Yb3+-codoped lead-free germanium-bismuth glass

We study the structural and infrared-to-visible upconversion fluorescence properties of Er3(+)/Yb3+-codoped lead-free germanium-bismuth glass. The structure of lead-free germanium-bismuth-lanthanum glass is investigated by peak-deconvolution of Raman spectroscopy. Intense green and red emissions centred at 525, 546, and 657nm, corresponding to the transitions H-2(11/2) -> (IT15/2)-I-4 -> S-4(3/2) -> 4I(15/2), and F-4(9/2) -> I-4(15/2), respectively, are observed at room temperature. The quadratic dependence of the 525, 546, and 657nm emissions on excitation power indicates that a two-photon absorption process occurs under 975nm excitation.