Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

Bimodules over nest algebras and Deddens'

We generalise Dedden's Theorem for nest algebras to nest algebra bimodules. We define an object which extends the Jacobson radical of a nest algebra, and characterose it generalising a theorem of Erdos.

Detection of glucocorticoid bioactivity in bovine urine samples using a reporter gene assay.

The illegal use of anabolic substances in the meat producing industry is an ongoing problem due to the continual production of new synthetic compounds and/or the practice of low-level cocktail administration to avoid detection by the surveillance schemes of EU member states National Plan surveillance systems.

We present a highly sensitive reporter gene assay and sample extraction procedure based on a two step solid phase extraction and high performance liquid chromatography, developed for the detection of glucocorticoid abuse in bovine urine. The assay is capable of detecting compounds with glucocorticoid bioactivity and is extremely sensitive with an EC50 of 0.79 ng mL-1 for dexamethasone. New or unknown compounds with glucocorticoid bioactivity and low-level cocktail mixtures are detectable by this assay.

Cross-reactivity data for a range of 11ß-hydroxyglucocorticoids has been provided. This assay shows low interference from the 11-keto prohormones and other steroidal hormones. The assay may be suitable for application in other matrices such as hair. In conclusion this screening assay offers advantages over existing analytical techniques.

Robust Dynamic Pricing Over Infinite Horizon in The Presence of Model Uncertainty( 2* Journal)

This paper studies a problem of dynamic pricing faced by a retailer with limited inventory, uncertain about the demand rate model, aiming to maximize expected discounted revenue over an infinite time horizon. The retailer doubts his demand model which is generated by historical data and views it as an approximation. Uncertainty in the demand rate model is represented by a notion of generalized relative entropy process, and the robust pricing problem is formulated as a two-player zero-sum stochastic differential game. The pricing policy is obtained through the Hamilton-Jacobi-Isaacs (HJI) equation. The existence and uniqueness of the solution of the HJI equation is shown and a verification theorem is proved to show that the solution of the HJI equation is indeed the value function of the pricing problem. The results are illustrated by an example with exponential nominal demand rate.

Mosaic monosomy 14: clinical features and recognizable facies

A 1-year-old child with clinical features of monosomy 14 is reported. She has dysmorphic facial features including ocular colobomata, dolichocephaly and microcephaly, retinal pigmentation, severe seizures, fair curly hair and tapering fingers. There was severe mental retardation. This is the first reported case of severe mosaic monosomy 14, with up to 30% mosaicism. A recognizable facial gestalt is present in children with 14q deletions or partial monosomy 14, as well as susceptibility to infection, feeding difficulties, seizures and retinal pigmentation. (C) 2004 Lippincott Williams Wilkins.

SK1 of graded division algebras

The reduced Whitehead group $\SK$ of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the ungraded case are then established by the following two theorems: It is proved that $\SK$ of a tame valued division algebra over a henselian field coincides with $\SK$ of its associated graded division algebra. Furthermore, it is shown that $\SK$ of a graded division algebra is isomorphic to $\SK$ of its quotient division algebra. The first theorem gives the established formulas for the reduced Whitehead group of certain valued division algebras in a unified manner, whereas the latter theorem covers the stability of reduced Whitehead groups, and also describes $\SK$ for generic abelian crossed products.

Reducing Uncertainty in Aeroelastic Flutter Boundaries Using Experimental Data

Flutter prediction as currently practiced is usually deterministic, with a single structural model used to represent an aircraft. By using interval analysis to take into account structural variability, recent work has demonstrated that small changes in the structure can lead to very large changes in the altitude at which
utter occurs (Marques, Badcock, et al., J. Aircraft, 2010). In this follow-up work we examine the same phenomenon using probabilistic collocation (PC), an uncertainty quantification technique which can eficiently propagate multivariate stochastic input through a simulation code,
in this case an eigenvalue-based fluid-structure stability code. The resulting analysis predicts the consequences of an uncertain structure on incidence of
utter in probabilistic terms { information that could be useful in planning
flight-tests and assessing the risk of structural failure. The uncertainty in
utter altitude is confirmed to be substantial. Assuming that the structural uncertainty represents a epistemic uncertainty regarding the
structure, it may be reduced with the availability of additional information { for example aeroelastic response data from a flight-test. Such data is used to update the structural uncertainty using Bayes' theorem. The consequent
utter uncertainty is significantly reduced across the entire Mach number range.

Optical source model for the 23.2-23.6 nm radiation from the multielement germanium soft X-ray laser

Distributions of source intensity in two dimensions (designated the source model), averaged over a single laser pulse, based on experimental measurements of spatial coherence, are considered for radiation from the unresolved 23.2/23.6 nm spectral lines from the germanium collisional X-ray laser. The model derives from measurements of the visibility of Young slit interference fringes determined by a method based on the Wiener-Khinchin theorem. Output from amplifiers comprising three and four target elements have similar coherence properties in directions within the horizontal plane corresponding to strong plasma refraction effects and fitting the coherence data shows source dimensions (FWHM) are similar to 26 mu m (horizontal), significantly smaller than expected by direct imaging, and similar to 125 mu m (vertical: equivalent to the height of the driver excitation). (C) 1999 Elsevier Science B.V. All rights reserved.

Coherence and bandwidth measurements of harmonics generated from solid surfaces irradiated by intense picosecond laser pulses

We present measurements of the transverse and longitudinal coherence lengths of the fourth harmonic of a 1053-nm, 2.5-ps laser generated during high-intensity (up to 10(19) W cm(-2)) interactions with a solid target. Coherence lengths were measured by use of a Young's double-slit interferometer. The effective source size, as defined by the Van Cittert-Zernicke theorem, was found to be 10-12 mu m, and the coherence time was observed to be in the range 0.02-0.4 ps.

A sequential algorithm for sparse support vector classifiers

Support vector machines (SVMs), though accurate, are not preferred in applications requiring high classification speed or when deployed in systems of limited computational resources, due to the large number of support vectors involved in the model. To overcome this problem we have devised a primal SVM method with the following properties: (1) it solves for the SVM representation without the need to invoke the representer theorem, (2) forward and backward selections are combined to approach the final globally optimal solution, and (3) a criterion is introduced for identification of support vectors leading to a much reduced support vector set. In addition to introducing this method the paper analyzes the complexity of the algorithm and presents test results on three public benchmark problems and a human activity recognition application. These applications demonstrate the effectiveness and efficiency of the proposed algorithm.


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Efficient differentiation into skin cells of bone marrow cells recovered in a pellet after density gradient fractionation

We had previously demonstrated the participation of whole bone marrow cells from adult mice in the reconstitution of skin, including the epidermis and hair follicles. To get an insight into cell populations that give rise to the epithelial components of the reconstituted skin, we fractionated bone marrow cells derived from green fluorescent protein-transgenic mice by density gradient. Unexpectedly, we found that a substantial amount of mononucleated cells (approximately 30%) was recovered in the pellet fraction and that the cells in the pellet fraction preferentially differentiated into epithelial components of skin, rather than the cells in the mononuclear cell fraction. The pellet fraction contained more CD45-negative (thus uncommitted to the hematopoietic cell lineage) cells than the mononuclear cell fraction. These results indicate that density gradient fractionation results in significant loss of specific progenitor cells into the usually discarded pellet fraction.

NO3- transport across the plasma membrane of Arabidopsis thaliana root hairs:Kinetic control by pH and membrane voltage

High-affinity nitrate transport was examined in intact root hair cells of Arabidopsis thaliana using electrophysiological recordings to characterise the response of the plasma membrane to NO₃^-challenge and to quantify transport activity. The NO₃^--associated membrane current was determined using a three-electrode voltage clamp to bring membrane voltage under experimental control and to compensate for current dissipation along the longitudinal cell axis. Nitrate transport was evident in the roots of seedlings grown in the absence of a nitrogen source, but only 4-6 days postgermination. In 6-day-old seedlings, additions of 5-100 μm NO₃^-to the bathing medium resulted in membrane depolarizations of 8-43 mV, and membrane voltage (V_m) recovered on washing NO₃^-from the bath. Voltage clamp measurements carried out immediately before and following NO₃^-additions showed that the NO₃^--evoked depolarizations were the consequence of an inward-directed current that appeared across the entire range of accessible voltages (-300 to +50 mV). Both membrane depolarizations and NO₃^--evoked currents recorded at the free-running voltage displayed quasi-Michaelian kinetics, with apparent values for K_m of 23 ± 6 and 44 ± 11 μm, respectively and, for the current, a maximum of 5.1 ± 0.9 μA cm^-2. The NO₃^-current showed a pronounced voltage sensitivity within the normal physiological range between -250 and -100 mV, as could be demonstrated under voltage clamp, and increasing the bathing pH from 6.1 to 7.4-8.0 reduced the current and the associated membrane depolarizations 3- to 8-fold. Analyses showed a well-defined interaction between the kinetic variables of membrane voltage, pH_o and [NO₃^-]_o. At a constant pH_o of 6.1, depolarization from -250 to -150 mV resulted in an approximate 3-fold reduction in the maximum current but a 10% rise in the apparent affinity for NO₃^-. By contrast, the same depolarization effected an approximate 20% fall in the K_m for transport as a function in [H⁺]_o. These, and additional characteristics of the transport current implicate a carrier cycle in which NO₃^-binding is kinetically isolated from the rate-limiting step of membrane charge transit, and they indicate a charge-coupling stoichiometry of 2(H⁺) per NO₃^-anion transported across the membrane. The results concur with previous studies showing a high-affinity NO₃^-transport system in Arabidopsis that is inducible following a period of nitrogen-limiting growth, but they underline the importance of voltage as a kinetic factor controlling NO₃^-transport at the plant plasma membrane. © 1995 Springer-Verlag New York Inc.

Hardware elliptic curve cryptographic processor over GF(p)

A novel hardware architecture for elliptic curve cryptography (ECC) over GF(p) is introduced. This can perform the main prime field arithmetic functions needed in these cryptosystems including modular inversion and multiplication. This is based on a new unified modular inversion algorithm that offers considerable improvement over previous ECC techniques that use Fermat's Little Theorem for this operation. The processor described uses a full-word multiplier which requires much fewer clock cycles than previous methods, while still maintaining a competitive critical path delay. The benefits of the approach have been demonstrated by utilizing these techniques to create a field-programmable gate array (FPGA) design. This can perform a 256-bit prime field scalar point multiplication in 3.86 ms, the fastest FPGA time reported to date. The ECC architecture described can also perform four different types of modular inversion, making it suitable for use in many different ECC applications. © 2006 IEEE.

A multi-fibre multi-layer representative volume element (M2RVE) for prediction of matrix and interfacial damage in composite laminates

Multiscale micro-mechanics theory is extensively used for the prediction of the material response and damage analysis of unidirectional lamina using a representative volume element (RVE). Th is paper presents a RVE-based approach to characterize the materi al response of a multi-fibre cross-ply laminate considering the effect of matrix damage and fibre-matrix interfacial strength. The framework of the homogenization theory for periodic media has been used for the analysis of a 'multi-fibre multi-layer representative volume element' (M2 RVE) representing cross-ply laminate. The non-homogeneous stress-strain fields within the M2RVE are related to the average stresses and strains by using Gauss theorem and the Hill-Mandal strain energy equivalence principle. The interfacial bonding strength affects the in-plane shear stress-strain response significantl y. The material response predicted by M2 RVE is in good agreement with the experimental results available in the literature. The maximum difference between the shear stress predicted using M2 RVE and the experimental results is ~15% for the bonding strength of 30MPa at the strain value of 1.1%