Construction of inverses with prescribed zero minors and applications to decentralized stabilization

We examine the following question: Suppose R is a principal ideal domain, and that F is an n × m matrix with elements in R, with n>m. When does there exist an m × n matrix G such that GF = Im, and such that certain prescribed minors of G equal zero? We show that there is a simple necessary condition for the existence of such a G, but that this condition is not sufficient in general. However, if the set of minors of G that are required to be zero has a certain pattern, then the condition is necessary as well as sufficient. We then show that the pattern mentioned above arises naturally in connection with the question of the existence of decentralized stabilizing controllers for a given plant. Hence our result allows us to derive an extremely simple proof of the fact that a necessary and sufficient condition for the existence of decentralized stabilizing controllers is the absence of unstable decentralized fixed modes, as well as to derive a very clean expression for these fixed modes. In addition to the application to decentralized stabilization, we believe that the result is of independent interest.

Acoustic emission source location in composite structure by Voronoi construction using geodesic curve evolution

Conventional analytical/numerical methods employing triangulation technique are suitable for locating acoustic emission (AE) source in a planar structure without structural discontinuities. But these methods cannot be extended to structures with complicated geometry, and, also, the problem gets compounded if the material of the structure is anisotropic warranting complex analytical velocity models. A geodesic approach using Voronoi construction is proposed in this work to locate the AE source in a composite structure. The approach is based on the fact that the wave takes minimum energy path to travel from the source to any other point in the connected domain. The geodesics are computed on the meshed surface of the structure using graph theory based on Dijkstra's algorithm. By propagating the waves in reverse virtually from these sensors along the geodesic path and by locating the first intersection point of these waves, one can get the AE source location. In this work, the geodesic approach is shown more suitable for a practicable source location solution in a composite structure with arbitrary surface containing finite discontinuities. Experiments have been conducted on composite plate specimens of simple and complex geometry to validate this method.

Cytotoxicity of half sandwich ruthenium(II) complexes with strong hydrogen bond acceptor ligands and their mechanism of action

Neutral and cationic organometallic ruthenium(II) piano stool complexes of the type [(eta(6)-cymene)R-uCl(X)(Y)] (complexes R1-R8) has been synthesized and characterized. In cationic complexes, X, Y is either a eta(2) phosphorus ligand such as 1,1-bis(diphenylphosphino)methane (DPPM) and 1,2-bis(diphenylphosphino)ethane (DPPE) or partially oxidized ligands such as 1,2-bis(diphenylphosphino)methane monooxide (DPPMO) and 1,2-bis(diphenylphosphino)ethane monooxide (DPPEO) which are strong hydrogen bond acceptors. In neutral complexes. X is chloride and Y is a monodentate phosphorous donor. Complexes with DPPM and DPPMO ligands ([(eta(6)-cymene)Ru(eta(2)-DPPM)Cl]PF6 (R2), [(eta(6)-cymene)Ru(eta(2)-DPPMO)Cl]PF6 (R3), [(eta(6)-cymene)Ru(eta(1)-DPPM)Cl-2] (R5) and [(eta(6)-cymene)Ru(eta(1)-DPPMO)Cl-2] (R6) show good cytotoxicity. Growth inhibition study of several human cancer cell lines by these complexes has been carried out. Mechanistic studies for R5 and R6 show that inhibition of cancer cell growth involves both cell cycle arrest and apoptosis induction. Using an apoptosis PCR array, we identified the sets of antiapoptotic genes that were down regulated and pro-apoptotic genes that were up regulated. These complexes were also found to be potent metastasis inhibitors as they prevented cell invasion through matrigel. The complexes were shown to bind DNA in a non intercalative fashion and cause unwinding of plasmid DNA in cell-free medium by competitive ethidium bromide binding, viscosity measurements, thermal denaturation and gel mobility shift assays.

The effect of halogen atom on the molecular quadratic nonlinearity of half sandwich complexes in the presence of an acceptor

Half sandwich complexes of the type [CpM(CO)(n)X] {X=Cl, Br, I; If, M=Fe, Ru; n=2 and if M=Mo; n=3} and [CpNiPPh3X] {X=Cl, Br, I} have been synthesized and their second order molecular nonlinearity (beta) measured at 1064 nm in CHCl3 by the hyper-Rayleigh scattering technique. Iron complexes consistently display larger beta values than ruthenium complexes while nickel complexes have marginally larger beta values than iron complexes. In the presence of an acceptor ligand such as CO or PPh3, the role of the halogen atom is that of a pi donor. The better overlap of Cl orbitals with Fe and Ni metal centres make Cl a better pi donor than Br or I in the respective complexes. Consequently, M-pi interaction is stronger in Fe/Ni-Cl complexes. The value of beta decreases as one goes down the halogen group. For the complexes of 4d metal ions where the metal-ligand distance is larger, the influence of pi orbital overlap appears to be less important, resulting in moderate changes in beta as a function of halogen substitution. (C) 2006 Elsevier B.V. All rights reserved.

Tuning the beta-turn segment in designed peptide beta-hairpins: Construction of a stable type I ' beta-turn nucleus and hairpin-helix transition promoting segments

Designed octapeptides Boc-Leu-Val-Val-Aib-(D)Xxx-Leu- Val-Val-OMe ((D)Xxx = (D)Ala, 3a; (D)Val, 3c and (D)Pro, 5a) and Boc-Leu-Phe-Val-Aib-DAla-Leu-Phe-Val-OMe (3b) have been investigated to construct models of a stable type I' beta-turn nucleated hairpin and to generate systems for investigating helix-hairpin conformational transitions. Peptide 5a, which contains a central Aib-(D)Pro segment, is shown to adopt a stable type I' beta-turn nucleated hairpin structure, stabilized by four cross-strand hydrogen bonds. The stability of the structure in diverse solvents is established by the observation of all diagnostic NOEs expected in a beta-hairpin conformation. Replacement of (D)Pro5 by (D)Ala/(D)Val (3a-c) results in sequences that form beta-hairpins in hydrogen bonding solvents like CD3OH and DMSO-d(6). However, in CDCl3 evidence for population of helical conformations is obtained. Peptide 6b (Boc-Leu-Phe-Val-Aib-Aib-Leu-Phe-Val-OMe), which contains a centrally positioned Aib-Aib segment, provides a clear example of a system, which exhibits a helical conformation in CDCl3 and a significant population of both helices and hairpins in CD3OH and DMSO-d(6). The coexistence of multiple conformations is established by the simultaneous observation of diagnostic NOEs. Control over stereochemistry of the central beta-turn permits generation of models for robust beta-hairpins and also for the construction of systems that may be used to probe helix-hairpin conformational transitions. (c) 2006 Wiley Periodicals, Inc.

A unified construction of space-time codes with optimal rate-diversity tradeoff

The problem of constructing space-time (ST) block codes over a fixed, desired signal constellation is considered. In this situation, there is a tradeoff between the transmission rate as measured in constellation symbols per channel use and the transmit diversity gain achieved by the code. The transmit diversity is a measure of the rate of polynomial decay of pairwise error probability of the code with increase in the signal-to-noise ratio (SNR). In the setting of a quasi-static channel model, let n(t) denote the number of transmit antennas and T the block interval. For any n(t) <= T, a unified construction of (n(t) x T) ST codes is provided here, for a class of signal constellations that includes the familiar pulse-amplitude (PAM), quadrature-amplitude (QAM), and 2(K)-ary phase-shift-keying (PSK) modulations as special cases. The construction is optimal as measured by the rate-diversity tradeoff and can achieve any given integer point on the rate-diversity tradeoff curve. An estimate of the coding gain realized is given. Other results presented here include i) an extension of the optimal unified construction to the multiple fading block case, ii) a version of the optimal unified construction in which the underlying binary block codes are replaced by trellis codes, iii) the providing of a linear dispersion form for the underlying binary block codes, iv) a Gray-mapped version of the unified construction, and v) a generalization of construction of the S-ary case corresponding to constellations of size S-K. Items ii) and iii) are aimed at simplifying the decoding of this class of ST codes.

Nonlinear vibration analysis of composite laminated and sandwich plates with random material properties

Nonlinear vibration analysis is performed using a C-0 assumed strain interpolated finite element plate model based on Reddy's third order theory. An earlier model is modified to include the effect of transverse shear variation along the plate thickness and Von-Karman nonlinear strain terms. Monte Carlo Simulation with Latin Hypercube Sampling technique is used to obtain the variance of linear and nonlinear natural frequencies of the plate due to randomness in its material properties. Numerical results are obtained for composite plates with different aspect ratio, stacking sequence and oscillation amplitude ratio. The numerical results are validated with the available literature. It is found that the nonlinear frequencies show increasing non-Gaussian probability density function with increasing amplitude of vibration and show dual peaks at high amplitude ratios. This chaotic nature of the dispersion of nonlinear eigenvalues is also r

Wavelength/Time Multiple-Pulses-per-Row codes: Construction and verification

Two dimensional Optical Orthogonal Codes (OOCs) named Wavelength/Time Multiple-Pulses-per-Row (W/T MPR) codes suitable for use in incoherent fiber-optic code division multiple access (FO-CDMA) networks are reported in [6]. In this paper, we report the construction of W/T MPR codes, using Greedy Algorithm (GA), with distinct 1-D OOCs [1] as the row vectors. We present the W/T MPR codes obtained using the GA. Further, we verify the correlation properties of the generated W/T MPR codes using Matlab.

Construction and use of linear regression models for processor performance analysis

Processor architects have a challenging task of evaluating a large design space consisting of several interacting parameters and optimizations. In order to assist architects in making crucial design decisions, we build linear regression models that relate Processor performance to micro-architecture parameters, using simulation based experiments. We obtain good approximate models using an iterative process in which Akaike's information criteria is used to extract a good linear model from a small set of simulations, and limited further simulation is guided by the model using D-optimal experimental designs. The iterative process is repeated until desired error bounds are achieved. We used this procedure to establish the relationship of the CPI performance response to 26 key micro-architectural parameters using a detailed cycle-by-cycle superscalar processor simulator The resulting models provide a significance ordering on all micro-architectural parameters and their interactions, and explain the performance variations of micro-architectural techniques.

Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, Wu et al. characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A sub-space based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.

Studies directed towards the synthesis of schisanartane and related complex nortriterpenoids: construction of models of the peripheral ABC and FGH segments of rubrifloradilactone C

A conceptually unifying and flexible approach to the ABC and FGH segments of the nortriterpenoid rubrifloradilactone C, each embodying a furo[3,2-b]furanone moiety, from the appropriate Morita-Baylis-Hillman adducts is delineated. (C) 2010 Elsevier Ltd. All rights reserved.

A Novel Construction of Complex Orthogonal Designs with Maximal Rate and Low-PAPR

Space-time block codes based on orthogonal designs are used for wireless communications with multiple transmit antennas which can achieve full transmit diversity and have low decoding complexity. However, the rate of the square real/complex orthogonal designs tends to zero with increase in number of antennas, while it is possible to have a rate-1 real orthogonal design (ROD) for any number of antennas.In case of complex orthogonal designs (CODs), rate-1 codes exist only for 1 and 2 antennas. In general, For a transmit antennas, the maximal rate of a COD is 1/2 + l/n or 1/2 + 1/n+1 for n even or odd respectively. In this paper, we present a simple construction for maximal-rate CODs for any number of antennas from square CODs which resembles the construction of rate-1 RODs from square RODs. These designs are shown to be amenable for construction of a class of generalized CODs (called Coordinate-Interleaved Scaled CODs) with low peak-to-average power ratio (PAPR) having the same parameters as the maximal-rate codes. Simulation results indicate that these codes perform better than the existing maximal rate codes under peak power constraint while performing the same under average power constraint.

An Eventful Synthetic Approach Towards the Biologically Potent Natural Product Ottelione A: Enantio-, Regio- and Stereoselective Construction of the Bicyclic Core

A novel synthetic approach towards the recently reported anti-tumor and anti-tuberculor natural product ottelione A from the readily available Diels-Alder adduct of cyclopentadiene and p-benzoquinone is delineated. Our short strategy, besides being enantio-, regio- and stereoselective, charts an eventful course and is inherently well-suited for adaptation towards diverse synthetic analogues of this biologically potent natural product.