On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.

Bounded-input/bounded-output stability of linear multidimensional time- varying systems

The present study of the stability of systems governed by a linear multidimensional time-varying equation, which are encountered in spacecraft dynamics, economics, demographics, and biological systems, gives attention the lemma dealing with L(inf) stability of an integral equation that results from the differential equation of the system under consideration. Using the proof of this lemma, the main result on L(inf) stability is derived according; a corollary of the theorem deals with constant coefficient systems perturbed by small periodic terms. (O.C.)

Experimental Verification of the Lateral Periodicity of Axially Periodic Incoherent Fields Using the Lau Effect

General' objects, which are specially prepared to possess restricted spatial frequency spectra, have been used in the conventional Lau experiment to obtain experimental proof for the existence of lateral periodicity arising from axial periodicity, for a subclass of axially periodic wavefields in an incoherent situation.

On the alleged equivalence of certain field theories

Abstract. We critically examine some recent claims that certain field theories with and without boson kinetic energy terms are equivalent. We point out that the crucial element in these claims is the finiteness or otherwise of the boson wavefunction renormalisation constant. We show that when this constant is finite, the equivalence proof offered in the literature fails in a direct way. When the constant is divergent, the claimed equivalence is only a consequence of improper use of divergent quantities.

Heme is a positive regulator of cytochrome P-450 gene transcription

Inhibitors of heme biosynthesis such as CoCl2, 3-amino-1,2,4-triazole, and thioacetamide block the 3-methylcholanthrene-mediated induction of cytochrome P-450 (c + d) messenger RNAs and their transcription in rat liver. This effect is specific, since the messenger RNA levels for albumin and glutathione transferase (Ya + Yc) and their transcription are not significantly influenced under conditions of heme depletion. Exogenous administration of heme at very low doses (50 μg/100 g body wt) is able to completely counteract the effects of the heme biosynthetic inhibitors on cytochrome P-450 (c + d) messenger RNA levels and their transcription. This constitutes a direct proof for the role of heme as a positive regulator of cytochrome P-450 gene transcription.

Splittings of free groups, normal forms and partitions of ends

Splittings of a free group correspond to embedded spheres in the 3-manifold M = # (k) S (2) x S (1). These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of crossings of partitions of ends corresponding to normal spheres, using a graph of trees representation for normal forms. In particular, we give a constructive proof of a criterion determining when a conjugacy class in pi (2)(M) can be represented by an embedded sphere.

Completeness of the Coulomb wave functions in quantum mechanics

We give an explicit, direct, and fairly elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses only some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory; therefore it would form useful supplementary reading for a graduate course on quantum mechanics.

Phase-shift randomness in one-dimensional disordered conductors in the quasi-metallic domain

An invariant imbedding method yields exact analytical results for the distribution of the phase theta (L) of the reflection amplitude and for low-order resistance moments (pn) for a disordered conductor of length L in the quasi-metallic regime L<proof of the validity of the random-phase assumption for studying scaling of resistance in one dimension is thus obtained.

Microstructure and Properties of the Spray-Formed and Extruded 7075 Al Alloy

In the present investigation, a very good combination of strength and ductility, 630MPa 0.2% proof stress and 14.8% elongation to fracture in tensile test, has been obtained for the 7075 Al alloy after optimizing the processing parameters for spray forming, hot extruding the spray deposit, and peak aging the samples taken from the extruded rod. The spray deposits contained some porosity but it was almost eliminated on hot extrusion. Electron probe microanalysis revealed that even though spray forming was carried out in an open atmosphere, it did not affect the oxygen content and its distribution in the material on spray forming, because the atomizing argon gas provided a protective cover to molten droplets and prevented their oxidation. The chemical composition of the spray-formed material was found to be almost the same as the raw material, and the major alloying elements were found to be uniformly distributed in the extruded rod.

Spectral Invariance of SG Pseudo-Differential Operators on L-P(R-n)

We prove the spectral invariance of SG pseudo-differential operators on L-P(R-n), 1 < p < infinity, by using the equivalence of ellipticity and Fredholmness of SG pseudo-differential operators on L-p(R-n), 1 < p < infinity. A key ingredient in the proof is the spectral invariance of SC pseudo-differential operators on L-2(R-n).

Estradiol - 17β induces polyaromatic hydrocarbon-inducible cytochrome P-450 in chicken liver

A cDNA clone has been isolated from a chicken liver library prepared against messenger RNA isolated after chronic estradiol-17β treatment. The clone, pP-450 IA - 61, has an insert of 900nt and the sequence shows high homology to CYPIA2 subfamily from four other species. A single injection of estradiol-17β to immature chicken results in a striking induction of mRNA hybridizing to labeled pP-450IA - 61. The probe also hybridizes to mRNA induced by 3 — methylcholanthrene in chicken. These results offer direct proof for the similarity in the mode of action at the transcriptional level of polyaromatic hydrocarbons and estrogenic compounds.

In-Network Computation in Random Wireless Networks: A PAC Approach to Constant Refresh Rates with Lower Energy Costs

We propose a method to compute a probably approximately correct (PAC) normalized histogram of observations with a refresh rate of Theta(1) time units per histogram sample on a random geometric graph with noise-free links. The delay in computation is Theta(root n) time units. We further extend our approach to a network with noisy links. While the refresh rate remains Theta(1) time units per sample, the delay increases to Theta(root n log n). The number of transmissions in both cases is Theta(n) per histogram sample. The achieved Theta(1) refresh rate for PAC histogram computation is a significant improvement over the refresh rate of Theta(1/log n) for histogram computation in noiseless networks. We achieve this by operating in the supercritical thermodynamic regime where large pathways for communication build up, but the network may have more than one component. The largest component however will have an arbitrarily large fraction of nodes in order to enable approximate computation of the histogram to the desired level of accuracy. Operation in the supercritical thermodynamic regime also reduces energy consumption. A key step in the proof of our achievability result is the construction of a connected component having bounded degree and any desired fraction of nodes. This construction may also prove useful in other communication settings on the random geometric graph.

pi.-Facial selectivities in cycloadditions to norbornyl- and norbornenyl-fused p-benzoquinones

The stereochemistry of the Diels-Alder cycloaddition of several dienes to the facially perturbed dienophiles 2,3-norbornenobenzoquinone (3) and 2,3-norbornanobenzoquinone (4) has been examined. Unambiguous structural proof for the adducts formed has been obtained from complementary 'H and I3C NMR spectral data and in two cases through X-ray crystal structure determination. While 1,3-~yclopentadiene1, ,3-~yclohexadienea, nd cyclooctatetraene exhibit preference for addition to 3 from the bottom side, the stereochemical outcome is reversed in their response to 4.1,3-DiphenyIisobenzofuran and 1,2,3,4-tetrachloro-5,5-dimethoxycyclopentadieenneg aged 3 from the top side with marked selectivity, which is further enhanced in their reaction with 4. The observed stereoselectivities seem to be essentially controlled by steric interactons at the transition state. Model calculations provide support for this interpretation.

On the Nash-Williams′ Lemma in Graph Reconstruction Theory

A generalization of Nash-Williams′ lemma is proved for the Structure of m-uniform null (m − k)-designs. It is then applied to various graph reconstruction problems. A short combinatorial proof of the edge reconstructibility of digraphs having regular underlying undirected graphs (e.g., tournaments) is given. A type of Nash-Williams′ lemma is conjectured for the vertex reconstruction problem.

Design, modelling and simulation of vibratory micromachined gyroscopes

Among various MEMS sensors, a rate gyroscope is one of the most complex sensors from the design point of view. The gyro normally consists of a proof mass suspended by an elaborate assembly of beams that allow the system to vibrate in two transverse modes. The structure is normally analysed and designed using commercial FEM packages such as ANSYS or MEMS specific commercial tools such as Coventor or Intellisuite. In either case, the complexity in analysis rises manyfolds when one considers the etch hole topography and the associated fluid flow calculation for damping. In most cases, the FEM analysis becomes prohibitive and one resorts to equivalent electrical circuit simulations using tools like SABER in Coventor. Here, we present a simplified lumped parameter model of the tuning fork gyro and show how easily it can be implemented using a generic tool like SIMULINK. The results obtained are compared with those obtained from more elaborate and intense simulations in Coventor. The comparison shows that lumped parameter SIMULINK model gives equally good results with fractional effort in modelling and computation. Next, the performance of a symmetric and decoupled vibratory gyroscope structure is also evaluated using this approach and a few modifications are made in this design to enhance the sensitivity of the device.