Proof of a conjecture of Frankl and Furedi

We give a simple linear algebraic proof of the following conjecture of Frankl and Furedi [7, 9, 13]. (Frankl-Furedi Conjecture) if F is a hypergraph on X = {1, 2, 3,..., n} such that 1 less than or equal to /E boolean AND F/ less than or equal to k For All E, F is an element of F, E not equal F, then /F/ less than or equal to (i=0)Sigma(k) ((i) (n-1)). We generalise a method of Palisse and our proof-technique can be viewed as a variant of the technique used by Tverberg to prove a result of Graham and Pollak [10, 11, 14]. Our proof-technique is easily described. First, we derive an identity satisfied by a hypergraph F using its intersection properties. From this identity, we obtain a set of homogeneous linear equations. We then show that this defines the zero subspace of R-/F/. Finally, the desired bound on /F/ is obtained from the bound on the number of linearly independent equations. This proof-technique can also be used to prove a more general theorem (Theorem 2). We conclude by indicating how this technique can be generalised to uniform hypergraphs by proving the uniform Ray-Chaudhuri-Wilson theorem. (C) 1997 Academic Press.

Exact analysis of simply supported rhombic plates under uniform pressure

The simply supported rhombic plate under transverse load has received extensive attention from elasticians, applied mathematicians and engineers. All known solutions are based on approximate procedures. Now, an exact solution in a fast converging explicit series form is derived for this problem, by applying Stevenson's tentative approach with complex variables. Numerical values for the central deflexion and moments are obtained for various corner angles. The present solution provides a basis for assessing the accuracy of approximate methods for analysing problems of skew plates or domains.

Rotating anisotropic disc of uniform strength

A procedure to design a constant thickness composite disc of uniform strength by radially tailoring the anisotropic elastic constants is proposed. A special case of an isotropic disc with radially varying modulus is also examined. Analytical results are also compared with FEM calculations for two cases of radially varying anisotropy and for an isotropic disc with variable modulus. (C) 1999 Elsevier Science Ltd. All rights reserved.

On Uniform Approximate Solutions in Bending of Symmetric Laminated Plates

A layer-wise theory with the analysis of face ply independent of lamination is used in the bending of symmetric laminates with anisotropic plies. More realistic and practical edge conditions as in Kirchhoff's theory are considered. An iterative procedure based on point-wise equilibrium equations is adapted. The necessity of a solution of an auxiliary problem in the interior plies is explained and used in the generation of proper sequence of two dimensional problems. Displacements are expanded in terms of polynomials in thickness coordinate such that continuity of transverse stresses across interfaces is assured. Solution of a fourth order system of a supplementary problem in the face ply is necessary to ensure the continuity of in-plane displacements across interfaces and to rectify inadequacies of these polynomial expansions in the interior distribution of approximate solutions. Vertical deflection does not play any role in obtaining all six stress components and two in-plane displacements. In overcoming lacuna in Kirchhoff's theory, widely used first order shear deformation theory and other sixth and higher order theories based on energy principles at laminate level in smeared laminate theories and at ply level in layer-wise theories are not useful in the generation of a proper sequence of 2-D problems converging to 3-D problems. Relevance of present analysis is demonstrated through solutions in a simple text book problem of simply supported square plate under doubly sinusoidal load.

On Precoding for Constant K-User MIMO Gaussian Interference Channel With Finite Constellation Inputs

This paper considers linear precoding for the constant channel-coefficient K-user MIMO Gaussian interference channel (MIMO GIC) where each transmitter-i (Tx-i) requires the sending of d(i) independent complex symbols per channel use that take values from fixed finite constellations with uniform distribution to receiver-i (Rx-i) for i = 1, 2, ..., K. We define the maximum rate achieved by Tx-i using any linear precoder as the signal-to-noise ratio (SNR) tends to infinity when the interference channel coefficients are zero to be the constellation constrained saturation capacity (CCSC) for Tx-i. We derive a high-SNR approximation for the rate achieved by Tx-i when interference is treated as noise and this rate is given by the mutual information between Tx-i and Rx-i, denoted as I(X) under bar (i); (Y) under bar (i)]. A set of necessary and sufficient conditions on the precoders under which I(X) under bar (i); (Y) under bar (i)] tends to CCSC for Tx-i is derived. Interestingly, the precoders designed for interference alignment (IA) satisfy these necessary and sufficient conditions. Furthermore, we propose gradient-ascentbased algorithms to optimize the sum rate achieved by precoding with finite constellation inputs and treating interference as noise. A simulation study using the proposed algorithms for a three-user MIMO GIC with two antennas at each node with d(i) = 1 for all i and with BPSK and QPSK inputs shows more than 0.1-b/s/Hz gain in the ergodic sum rate over that yielded by precoders obtained from some known IA algorithms at moderate SNRs.

Non-uniform beams and stiff strings isospectral to axially loaded uniform beams and piano strings

In this paper, we derive analytical expressions for mass and stiffness functions of transversely vibrating clamped-clamped non-uniform beams under no axial loads, which are isospectral to a given uniform axially loaded beam. Examples of such axially loaded beams are beam columns (compressive axial load) and piano strings (tensile axial load). The Barcilon-Gottlieb transformation is invoked to transform the non-uniform beam equation into the axially loaded uniform beam equation. The coupled ODEs involved in this transformation are solved for two specific cases (pq (z) = k (0) and q = q (0)), and analytical solutions for mass and stiffness are obtained. Examples of beams having a rectangular cross section are shown as a practical application of the analysis. Some non-uniform beams are found whose frequencies are known exactly since uniform axially loaded beams with clamped ends have closed-form solutions. In addition, we show that the tension required in a stiff piano string with hinged ends can be adjusted by changing the mass and stiffness functions of a stiff string, retaining its natural frequencies.

Growth and electron effective mass measurements of strained Si and Si0.94Ge0.06 on relaxed Si0.62Ge0.38 buffers grown by rapid thermal chemical vapor deposition

Abstract: We report the growth and the electron cyclotron resonance measurements of n-type Si/Si0.62Ge0.38 and Si0.94Ge0.06/Si0.62Ge0.38 modulation-doped heterostructures grown by rapid thermal chemical vapor deposition. The strained Si and Si0.94Ge0.06 channels were grown on relaxed Si0.62Ge0.38 buffer layers, which consist of 0.6 mu m uniform Si0.62Ge0.38 layers and 0.5 mu m compositionally graded relaxed SiGe layers from 0 to 38% Ge. The buffer layers were annealed at 800 degrees C for 1 h to obtain complete relaxation. A 75 Angstrom Si(SiGe) channel with a 100 Angstrom spacer and a 300 Angstrom 2 X 10(19) cm(-3) n-type supply layer was grown on the top of the buffer layers. The cross-sectional transmission electron microscope reveals that the dense dislocation network is confined to the buffer layer, and relatively few dislocations terminate on the surface. The plan-view image indicates the threading dislocation density is about 4 X 10(6) cm(-2). The far-infrared measurements of electron cyclotron resonance were performed at 4 K with the magnetic field of 4-8 T. The effective masses determined from the slope of the center frequency of the absorption peak versus applied magnetic field plot are 0.203m(0) and 0.193m(0) for the two dimensional electron gases in the Si and Si0.94Ge0.06 channels, respectively. The Si effective mass is very close to that of a two dimensional electron gas in an Si MOSFET (0.198m(0)). The electron effective mass of Si0.94Ge0.06 is reported for the first time and is about 5% lower than that of pure Si.

Activities in the $FeTiO_{3}-NiTiO_{3}$ Solid Solution from Alloy-Oxide Equilibria at 1273 K

Nine tie-lines between Fe-Ni alloys and FeTiO3-NiTiO3 solid solutions were determined at 1273 K. Samples were equilibrated in evacuated quartz ampoules for periods up to 10 days. Compositions of the alloy and oxide phases at equilibrium were determined by energy-dispersive x-ray spectroscopy. X-ray powder diffraction was used to confirm the results. Attainment of equilibrium was verified by the conventional tie-line rotation technique and by thermodynamic analysis of the results. The tie-lines are skewed toward the FeTiO3 corner. From the tie-line data and activities in the Fe-Ni alloy phase available in the literature, activities of FeTiO3 and NiTiO3 in the ilmenite solid solution were derived using the modified Gibbs-Duhem technique of Jacob and Jeffes [K.T. Jacob and J.H.E. Jeffes, An Improved Method for Calculating Activities from Distribution Equilibria, High Temp. High Press., 1972, 4, p 177-182]. The components of the oxide solid solution exhibit moderate positive deviations from Raoult's law. Within experimental error, excess Gibbs energy of mixing for the FeTiO3-NiTiO3 solid solution at 1273 K is a symmetric function of composition and can be represented as: Delta G(E) = 8590 (+/- 200) X-FeTiO3 X-NiTiO3 J/mol Full spectrum of tie-lines and oxygen potentials for the three-phase equilibrium involving Fe-Ni alloys, FeTiO3-NiTiO3 solid solutions, and TiO2 at 1273 K were computed using results obtained in this study and data available in the literature.

Certain Aspects Related To Computation By Modified Crack Closure Integral(MCCI)

This paper presents the proper computational approach for the estimation of strain energy release rates by modified crack closure integral (MCCI). In particular, in the estimation of consistent nodal force vectors used in the MCCI expressions for quarter-point singular elements (wherein all the nodal force vectors participate in computation of strain energy release rates by MCCI). The numerical example of a centre crack tension specimen under uniform loading is presented to illustrate the approach.

Some studies on TiO2 films deposited by sol-gel technique

TiO2 films are extensively used in various applications including optical multi-layers, sensors, photo catalysis, environmental purification, and solar cells etc. These are prepared by both vacuum and non-vacuum methods. In this paper, we present the results on TiO2 thin films prepared by a sol-gel spin coating process in non-aqueous solvent. Titanium isopropoxide is used as TiO2 precursor. The films were annealed at different temperatures up to 3000 C for 5 hours in air. The influence of the various deposition parameters like spinning speed, spinning time and annealing temperature on the thickness of the TiO2 films has been studied. The variation of film thickness with time in ambient atmosphere was also studied. The optical, structural and morphological characteristics were investigated by optical transmittance-reflectance measurements, X-ray diffraction (XRD) and scanning electron microscopy (SEM) respectively. The refractive index and extinction coefficient of the films were determined by envelope technique and spectroscopic ellipsometry. TiO2 films exhibited high transparency (92%) in the visible region with a refractive index of 2.04 at 650 nm. The extinction coefficient was found to be negligibly small. The X-ray diffraction analysis showed that the TiO2 film deposited on glass substrate changes from amorphous to crystalline (anatase) phase with annealing temperature above 2500 C. SEM results show that the deposited films are uniform and crack free.

Characterisation of k-Variegated Graphs, k greater-than-or-equal-to 3

A graph is said to be k-variegated if its vertex set can be partitioned into k equal parts such that each vertex is adjacent to exactly one vertex from every other part not containing it. Bednarek and Sanders [1] posed the problem of characterizing k-variegated graphs. V.N. Bhat-Nayak, S.A. Choudum and R.N. Naik [2] gave the characterization of 2-variegated graphs. In this paper we characterize k-variegated graphs for k greater-or-equal, slanted 3.