On Fitting a Surface

This article deals with the problem of fitting the surface f=g (x) h(y) to the set of points (x/sub i/,y/sub j/,f/j). Functions g(x) and h(y) are supposed to be expressible in terms of orthonormal sets of functions. The desired coefficients of these functions are determined as characteristic vectors corresponding to the largest characteristic root of two materials having common characteristic roots

Reliability of a Modular Standby Redundant System with Unrecoverable Failures

This paper considers a stand by redundant system consisting of two identical modules. Each module is compose of N distinct components in series. The failure of a module may be attributed due to the failure of any of its N components. The ith components of a module has an arbitrary repair time CDF, G./sub i/ (t). The stand by module has been assumed to have a nonzero hazard rate even when unpowered. The failure of an on-line module is identified through a sensing device which has a probability 'c' of successfully recovering a fault in the on-line module. Expressions for the distribution of the Time to First System Failure (TFSF), the expected TFSF, and the reliability of the system have been derived by using the theory of Markov renewal processes

Mesomorphic properties of alkoxybenzylidene- aminoacetophenones

Liquid crystal phase transitions in compounds of alkoxybenzylidene-aminoacetophene serie

Sub-grid scale representation of vegetation in global land surface schemes: implications for estimation of the terrestrial carbon sink

Terrestrial ecosystem models commonly represent vegetation in terms of plant functional types (PFTs) and use their vegetation attributes in calculations of the energy and water balance as well as to investigate the terrestrial carbon cycle. Sub-grid scale variability of PFTs in these models is represented using different approaches with the "composite" and "mosaic" approaches being the two end-members. The impact of these two approaches on the global carbon balance has been investigated with the Canadian Terrestrial Ecosystem Model (CTEM v 1.2) coupled to the Canadian Land Surface Scheme (CLASS v 3.6). In the composite (single-tile) approach, the vegetation attributes of different PFTs present in a grid cell are aggregated and used in calculations to determine the resulting physical environmental conditions (soil moisture, soil temperature, etc.) that are common to all PFTs. In the mosaic (multi-tile) approach, energy and water balance calculations are performed separately for each PFT tile and each tile's physical land surface environmental conditions evolve independently. Pre-industrial equilibrium CLASS-CTEM simulations yield global totals of vegetation biomass, net primary productivity, and soil carbon that compare reasonably well with observation-based estimates and differ by less than 5% between the mosaic and composite configurations. However, on a regional scale the two approaches can differ by > 30%, especially in areas with high heterogeneity in land cover. Simulations over the historical period (1959–2005) show different responses to evolving climate and carbon dioxide concentrations from the two approaches. The cumulative global terrestrial carbon sink estimated over the 1959–2005 period (excluding land use change (LUC) effects) differs by around 5% between the two approaches (96.3 and 101.3 Pg, for the mosaic and composite approaches, respectively) and compares well with the observation-based estimate of 82.2 ± 35 Pg C over the same period. Inclusion of LUC causes the estimates of the terrestrial C sink to differ by 15.2 Pg C (16%) with values of 95.1 and 79.9 Pg C for the mosaic and composite approaches, respectively. Spatial differences in simulated vegetation and soil carbon and the manner in which terrestrial carbon balance evolves in response to LUC, in the two approaches, yields a substantially different estimate of the global land carbon sink. These results demonstrate that the spatial representation of vegetation has an important impact on the model response to changing climate, atmospheric CO₂ concentrations, and land cover

On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems

We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum Acyclic Subgraph and Maximum Betweenness, we prove inapproximability of $14/15+\epsilon$ and $1/2+\epsilon$. An OCSP is said to be approximation resistant if it is hard to approximate better than taking a uniformly random ordering. We prove that the Maximum Non-Betweenness Problem is approximation resistant and that there are width-$m$ approximation-resistant OCSPs accepting only a fraction $1 / (m/2)!$ of assignments. These results provide the first examples of approximation-resistant OCSPs subject only to P $\neq$ \NP

Electric Quadrupole Moments of Metastable States of Ca+, Sr+, and Ba+

Electric quadrupole moments of the metastable nd3/2 and nd5/2 states of Ca+, Sr+, and Ba+ are calculated using the relativistic all-order method including all single, double, and partial triple excitations of the Dirac-Hartree-Fock wave function to provide recommended values for the cases where no experimental data are available. The contributions of all non-linear single and double terms are also calculated for the case of Ca+ for comparison of our approach with the CCSD(T) results. The third-order many body perturbation theory is used to evaluate contributions of high partial waves and the Breit interaction. The remaining omitted correlation corrections are estimated as well. Extensive study of the uncertainty of our calculations is carried out to establish accuracy of our recommended values to be 0.5% - 1% depending on the particular ion. Comprehensive comparison of our results with other theoretical values and experiment is carried out. Our result for the quadrupole moment of the 3d5/2 state of Ca+ ion, 1.849(17)ea_0^2, is in agreement with the most precise recent measurement 1.83(1)ea_0^2 by Roos et al. [Nature 443, 316 (2006)].Comment: 7 page

Rachis cracking in grapes

Studies on cracking of rachis of grapes have shown th at out of 87 cultivars under study, 16 were prone to it. Berry quality was not affected by the malady. Data on chemical composition of leaves suggested that the abnormality is not due to nutritional imbalance.Risse in TraubenstielenBei 16 von 87 untersuchten Rebensorten traten mehr oder weniger häufig Längsrisse in den Traubenstielen auf. Die Qualität der Beeren wurde durch die Erkrankung nicht beeinflußt. Aufgrund der Befunde über den Mineralstoffgehalt der Blätter ist zu vermuten, daß die Abnormität nicht durch eine unausgewogene Ernährung, sonde rn durch andere Faktoren verursacht wird

A Hypergraph Dictatorship Test with Perfect Completeness

A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based \PCP construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are $o(1).$ Their test makes $q\geq3$ queries and has amortized query complexity $1+O(\frac{\log q}{q})$ but has an inherent loss of perfect completeness. In this paper we give an adaptive hypergraph dictatorship test that achieves both perfect completeness and amortized query complexity $1+O(\frac{\log q}{q})$.Comment: Some minor correction

Dissolution Potentials of Sodium & Potassium Chlorides, Bromides & Iodides & of Ammonium Halides

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