A Quasi-Newton Adaptive Algorithm for Generalized Symmetric Eigenvalue Problem

In this paper, we first recast the generalized symmetric eigenvalue problem, where the underlying matrix pencil consists of symmetric positive definite matrices, into an unconstrained minimization problem by constructing an appropriate cost function, We then extend it to the case of multiple eigenvectors using an inflation technique, Based on this asymptotic formulation, we derive a quasi-Newton-based adaptive algorithm for estimating the required generalized eigenvectors in the data case. The resulting algorithm is modular and parallel, and it is globally convergent with probability one, We also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices (in the pencil) on the resulting eigenstructure. Simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank-one updating algorithm of Karasalo. Further, the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems.

Equivalent rate 1/2 quasi-cyclic codes

Chen et al. [1] give a list of quasi-cyclic (2m,m) codes which have the largest minimum distance of any quasi-cyclic code, for various values ofm. We present the weight distribution of these codes. It will be seen that many of the codes found by Chen et al. [1] are equivalent in the sense of having identical weight distributions.

Do stable isotopes in carbonate cement of Mio-Pleistocene Himalayan sediments record paleoecological and paleoclimatic changes?

Non-pedogenic carbonates, such as carbonate cement and nodules in the sandstones, are quite common in the terrestrial geological record. Unlike pedogenic carbonates, their stable isotope ratios lack investigations for paleo-climatic reconstructions. The present investigation therefore, explores the possibility of use of stable isotope studies of non-pedogenic carbonates from the Mb-Pleistocene Siwalik Group of sediments exposed in the Ramnagar sub-basin of the NW Himalaya. Petrographic studies reveal the dominance of micrite fabric in carbonate nodules both of pedogenic and non-pedogenic samples irrespective of specific stratigraphic unit However, calcite as cement in the sandstones shows the dominance of micrite fabric in the younger in age sediments. Seventy-two non-pedogenic carbonate samples from the carbonate nodules and cement in the Siwalik sandstones, ranging in age between similar to 1 Ma and 12.2 Ma, were analyzed for delta C-13 and delta O-18 values. The delta C-13 values vary from -24.77 parts per thousand to -1.1 parts per thousand and delta O-18 values vary from -15.34 parts per thousand to -7.81 parts per thousand. Pedogenic and non-pedogenic carbonates ranging in age between similar to 1 Ma and 6 Ma have largely similar delta C-13 values and the range of delta C-13 values indicate the dominance of C-4 type of vegetation. However, unlike pedogenic carbonates which showed the dominance of C-3 type of vegetation pre- 7 Ma on the basis of delta C-13 -depleted isotopic values (Singh et al., 2011), delta C-13 values are largely enriched in the corresponding aged non-pedogenic carbonates revealing no information on specific type of vegetation. Likewise, paleoprecipitational reconstructions from delta O-18 values in pedogenic carbonates showed a progressive increase in aridity from similar to 12 Ma to recent excluding short term increases in rainfall/monsoon intensity at around 10 Ma, 5 Ma, and 1.8 Ma (Singh et al., 2012). On the contrary, such reconstructions are not possible from the delta O-18 values of non-pedogenic carbonates and indeed the delta O-18 values of non-pedogenic carbonates are largely depleted to as much as 6 parts per thousand from the corresponding pedogenic carbonates. Such differences in delta C-13 and delta O-18 values of non-pedogenic carbonates from pedogenic carbonates are primarily due to the dependence of the former on groundwater conditions responsible for precipitating carbonate. Further, a comparison of isotopic values between non-pedogenic and pedogenic carbonates can be interpreted that post-6 Ma and pre-6 Ma non-pedogenic carbonates were largely formed by shallow and deep groundwater conditions respectively. The result of these investigative studies therefore, suggests that the stable delta C-13 and delta O-18 values of non-pedogenic carbonates, unlike the pedogenic carbonates and irrespective of nature of calcite fabric, showed their little importance in paleoclimatic and paleoecological reconstructions. (C) 2014 Elsevier B.V. All rights reserved.

GRMHD formulation of highly super-Chandrasekhar magnetized white dwarfs: stable configurations of non-spherical white dwarfs

The topic of magnetized super-Chandrasekhar white dwarfs is in the limelight, particularly in the last few years, since our proposal of their existence. By full-scale general relativistic magnetohydrodynamic (GRMHD) numerical analysis, we confirm in this work the existence of stable, highly magnetized, significantly super-Chandrasekhar white dwarfs with mass more than 3 solar mass. While a poloidal field geometry renders the white dwarfs oblate, a toroidal field makes them prolate retaining an overall quasi-spherical shape, as speculated in our earlier work. These white dwarfs are expected to serve as the progenitors of over-luminous type Ia supernovae.