Effect of boundary condition description on convergence of solution in a boundary-value problem

It is well known that the numerical accuracy of a series solution to a boundary-value problem by the direct method depends on the technique of approximate satisfaction of the boundary conditions and on the stage of truncation of the series. On the other hand, it does not appear to be generally recognized that, when the boundary conditions can be described in alternative equivalent forms, the convergence of the solution is significantly affected by the actual form in which they are stated. The importance of the last aspect is studied for three different techniques of computing the deflections of simply supported regular polygonal plates under uniform pressure. It is also shown that it is sometimes possible to modify the technique of analysis to make the accuracy independent of the description of the boundary conditions.

Convergence correction in colloid scattering

The error introduced in depolarisation measurements due to the convergence of the incident beam has been investigated theoretically as well as experimentally for the case of colloid scattering, where the particles are not small compared to the wavelength of light. Assuming the scattering particles to be anisotropic rods, it is shown that, when the incident unpolarised light is condensed by means of a lens with a circular aperture, the observed depolarisation ratio ϱ u is given by ϱ u = ϱ u0 + 5/3 θ2 where ϱ u0 is the true depolarisation for incident parallel light, and θ the semi-angle of convergence. Appropriate formulae are derived when the incident beam is polarised vertically and horizontally. Experiments performed on six typical colloids support the theoretical conclusions. Other immediate consequences of the theory are also discussed.

Growth and Convergence: The case of China

Growth and Convergence: The Case of China Since the initiation of economic reforms in 1978, China has become one of the world’s fast-growing economies. The rapid growth, however, has not been shared equally across the different regions in China. The prominent feature of substantial differences in incomes and growth rates across the different Chinese regions has attracted the attention of many researchers. This book focuses on issues related to economic growth and convergence across the Chinese regions over the past three decades. The book has eight chapters. Apart from an introduction chapter and a concluding chapter, all the other chapters each deal with some certain aspects of the central issue of regional growth and convergence across China over the past three decades. The whole book is organized as follows. Chapter 1 provides an introduction to the basic issues involved in this book. Chapter 2 tests economic growth and convergence across 31 Chinese provinces during 1981-2005, based on the theoretical framework of the Solow growth model. Chapter 3 investigates the relationship between openness to foreign economic activities, such as foreign trade and foreign direct investment, and the regional economic growth in the case of China during 1981-2005. Chapter 4, based on data of 31 Chinese provinces over the period 1980-2004, presents new evidence on the effects of structural shocks and structural transformation on growth and convergence among the Chinese regions. Chapter 5, by building up an empirical model that takes account of different potential effects of foreign direct investment, focuses on the impacts of foreign direct investment on China’s regional economic performance and growth. Chapter 6 reconsiders the growth and convergence problem of the Chinese regions in an alternative theoretical framework with endogenous saving behavior and capital mobility across regions. Chapter 7, by building up a theoretical model concerning comparative advantage and transaction efficiency, focuses on one of the potential mechanisms through which China achieves its fast economic growth over the past few decades. Chapter 8 concludes the book by summarizing the results from the previous chapters and suggesting directions for further studies.

Magnetic fabrics indicating Late Quaternary seismicity in the Himalayan foothills

The anisotropy of magnetic susceptibility (AMS) study was performed on soft sediment samples from a trenched fault zone across the Himalayan frontal thrust (HFT), western Himalaya. AMS orientation of K-min axes in the trench sediments is consistent with lateral shortening revealed by geometry of deformed regional structures and recent earthquakes. Well-defined vertical magnetic foliation parallel to the flexure cleavage in which a vertical magnetic lineation is developed, high anisotropy, and triaxial ellipsoids suggest large overprinting of earth-quake- related fabrics. The AMS data suggest a gradual variation from layer parallel shortening (LPS) at a distance from the fault trace to a simple shear fabric close to the fault trace. An abrupt change in the shortening direction (K-min) from NE-SW to E-W suggests a juxtaposition of pre-existing layer parallel shortening fabric, and bending-related flexure associated with an earthquake. Hence the orientation pattern of magnetic susceptibility axes helps in identifying co-seismic structures in Late Holocene surface sediments.

Convergence feedback and unstable low frequency oscillations in a simple coupled ocean‐atmosphere model

The role of convergence feedback on the stability of a coupled ocean‐atmosphere system is studied using model III of Hirst (1986). It is shown that the unstable coupled mode found by Hirst is greatly modified by the convergence feedback. If the convergence feedback strength exceeds a critical value, several new unstable intraseasonal modes are also introduced. These modes have very weak dependence on the wave number. These results may explain the behaviour of some coupled models and to some extent provide a mechanism for the observed aperiodicity of the El‐Nino and Southern Oscillation (ENSO) events.

Producing interactivity : Does media convergence promote interactivity and audience participation?

This study investigates the process of producing interactivity in a converged media environment. The study asks whether more media convergence equals more interactivity. The research object is approached through semi-structured interviews of prominent decision makers within the Finnish media. The main focus of the study are the three big ones of the traditional media, radio, television and the printing press, and their ability to adapt to the changing environment. The study develops theoretical models for the analysis of interactive features and convergence. Case-studies are formed from the interview data and they are evaluated against the models. As a result the cases arc plotted and compared on a four-fold table. The cases are Radio Rock, NRJ, Biu Brother, Television Chat, Olivia and Sanoma News. It is found out that the theoretical models can accurately forecast the results of the case studies. The models are also able to distinguish different aspects of both interactivity and convergence so that a case, which at a first glance seems not to be very interactive is in the end found out to receive second highest scores on the analysis. The highest scores are received by Big Brother and Sanoma News. Through the theory and the analysis of the research data it is found out that the concepts of interactivity and convergence arc intimately intertwined and very hard in many cases to separate from each other. Hence the answer to the main question of this study is yes, convergence does promote interactivity and audience participation. The main theoretical background for the analysis of interactivity follows the work of Came Fleeter, Spiro Kiousis and Sally McMillan. Heeler's six-dimensional definition of interactivity is used as the basis for operationalizing interactivity. The actor-network theory is used as the main theoretical framework to analyze convergence. The definition and operationalization of the actor-network theory into a model of convergence follows the work of Michel Callon. Bruno Latour and especially John Law and Felix Stalder.

A delta13C record of late Quaternary climate change from tropical peats in southern India

STABLE-ISOTOPE ratios of carbon in soils or lake sediments1-3 and of oxygen and hydrogen in peats4,5 have been found to reflect past moisture variations and hence to provide valuable palaeoclimate records. Previous applications of the technique to peat have been restricted to temperate regions, largely because tropical climate variations are less pronounced, making them harder to resolve. Here we present a deltaC-13 record spanning the past 20 kyr from peats in the Nilgiri hills, southern India. Because the site is at high altitude (>2,000 m above sea level), it is possible to resolve a clear climate signal. We observe the key climate shifts that are already known to have occurred during the last glacial maximum (18 kyr ago) and the subsequent deglaciation. In addition, we observe an arid phase from 6 to 3.5 kyr ago, and a short, wet phase about 600 years ago. The latter appears to correspond to the Mediaeval Warm Period, which previously was believed to be confined to Europe and North America6,7. Our results therefore suggest that this event may have extended over the entire Northern Hemisphere.

Stereospecific construction of multiple contiguous quaternary carbons. Total synthesis of (±)-cis,anti,cis-1,8,12,12-tetramethyl-4-oxatricyclo[6.4.0.02,6]dodecan-3-ol, a thapsane isolated from Thapsia villosa var minor

The details of the first total synthesis of a natural thapsane lg containing three contiguous quaternary carbon atoms, starting from cyclogeraniol (9) '5 described. The Claisen rearrangement of 9 with methoxypropene in the presence of a catalytic amount of propionic acid produced ketone 10. Rhodium acetate-catalyzed intramolecular cyclopropanation of a-diazo-&keto ester 12, obtained from 10 via 8-keto ester 8, furnished cyclopropyl keto ester 7. Lithium in liquid ammonia reductive cleavage of cyclopropyl compound 7 gave a 1:l mixture of hydrindanone 6 and keto1 13. Wittig methylenation of 6 furnished ester 21. Epoxidation of 21, followed by BF3-OEt2-catalyzed rearrangement of epoxide 23 afforded hemiacetal 25. Treatment of hemiacetal 25 with triethylsilane in trifluoroacetic acid furnished lactone 22, a degradation product of various thapsanes. Finally, DIBAH reduction of lactone 22 generated the thapsane

Convergence of Power Control in a Random Channel Environment

In this paper, we study the Foschini Miljanic algorithm, which was originally proposed in a static channel environment. We investigate the algorithm in a random channel environment, study its convergence properties and apply the Gerschgorin theorem to derive sufficient conditions for the convergence of the algorithm. We apply the Foschini and Miljanic algorithm to cellular networks and derive sufficient conditions for the convergence of the algorithm in distribution and validate the results with simulations. In cellular networks, the conditions which ensure convergence in distribution can be easily verified.

Combining Bayes Classification and Point Group Symmetry under Boolean Framework for Enhanced Protein Quaternary Structure Inference

Our ability to infer the protein quaternary structure automatically from atom and lattice information is inadequate, especially for weak complexes, and heteromeric quaternary structures. Several approaches exist, but they have limited performance. Here, we present a new scheme to infer protein quaternary structure from lattice and protein information, with all-around coverage for strong, weak and very weak affinity homomeric and heteromeric complexes. The scheme combines naive Bayes classifier and point group symmetry under Boolean framework to detect quaternary structures in crystal lattice. It consistently produces >= 90% coverage across diverse benchmarking data sets, including a notably superior 95% coverage for recognition heteromeric complexes, compared with 53% on the same data set by current state-of-the-art method. The detailed study of a limited number of prediction-failed cases offers interesting insights into the intriguing nature of protein contacts in lattice. The findings have implications for accurate inference of quaternary states of proteins, especially weak affinity complexes.

Phase equilibria in the system CaO-CoO-SiO2 and Gibbs energies of formation of the quaternary oxides CaCoSi2O6, Ca2CoSi2O7, and CaCoSiO4

Phase relations in the pseudoternary system CaO-CoO-SiO2 have been established at 1323 K. Three quaternary oxides were found to be stable: CaCoSi2O6 with clinopyroxene (Cpx), Ca2CoSi2O7 with melilite (Mel), and CaCoSiO4 with olivine (Ol) structures. The Gibbs energies of formation of the quaternary oxides from their component binary oxides were measured using solid-state galvanic cells incorporating yttria-stabilized zirconia as the solid electrolyte in the temperature range of 1000-1324 K. The results can be summarized as follows: CoO (rs) + CaO (rs) + 2SiO(2) (Qtz) --> CaCoSi2O6 (Cpx), Delta G(f)(0) = -117920 + 11.26T (+/-150) J/mol CoO (rs) + 2CaO (rs) + 2SiO(2) (Qtz) --> Ca2CoSi2O7 (Mel), Delta G(f)(0) = -192690 + 2.38T (+/-130) J/mol CoO (rs) + CaO (rs) + SiO2 (Qtz) --> CaCoSiO2 (Ol), Delta G(f)(0) = -100325 + 2.55T (+/-100) J/mol where rs = rock salt (NaCl) structure and Qtz = quartz. The uncertainty limits correspond to twice the standard error estimate. The experimentally observed miscibility gaps along the joins CaO-CoO and CaCoSiO4-Co2SiO4 were used to calculate the excess free energies of mixing for the solid solutions CaxCo1-xO and (CayCo1-y)CoSiO4:Delta G(E) = X(1 - X)[31975X + 26736 (1 - X)] J/mol and Delta G(E) = 23100 (+/-250) Y(1 - Y) J/mol. A T-X phase diagram for the binary CaO-CoO was computed from the thermodynamic information; the diagram agrees with information available in the literature. The computed miscibility gap along the CaCoSiO4-Co2SiO4 join is associated with a critical temperature of 1389 (+/-15) K. Stability fields for the various solid solutions and the quaternary compounds are depicted on chemical-potential diagrams for SiO2, CaO, and CoO at 1323 K.

Stereospecific construction of stereogenic vicinal quaternary carbon atoms. Enantiospecific synthesis of (+)-valerane

Stereo- and enantiospecific synthesis of (+)-valerane starting from R-carvone utilising orthoester Claisen rearrangement and intramolecular diazo ketone cyclopropanation reactions for the construction of the two vicinal quaternary carbon atoms is described. Copyright (C) 1996 Elsevier Science Ltd.

Improving the convergence rate of the inverse iteration method

Solution of generalized eigenproblem, K phi = lambda M phi, by the classical inverse iteration method exhibits slow convergence for some eigenproblems. In this paper, a modified inverse iteration algorithm is presented for improving the convergence rate. At every iteration, an optimal linear combination of the latest and the preceding iteration vectors is used as the input vector for the next iteration. The effectiveness of the proposed algorithm is demonstrated for three typical eigenproblems, i.e. eigenproblems with distinct, close and repeated eigenvalues. The algorithm yields 29, 96 and 23% savings in computational time, respectively, for these problems. The algorithm is simple and easy to implement, and this renders the algorithm even more attractive.