CONTROLLABILITY AND OBSERVABILITY OF MATRIX SYLVESTER SYSTEMS ON TIMESCALES

Abstract This paper presents several fundamental results concerning the controllability and observability criteria for Δ-differential matrix Sylvester system X Δ (t) = A(t) X(t) + X(t) B(t) + F 1 (t) U(t) F 2 * (t), X(t 0 ) = X 0 , with output signal Y(t)= K 1 (t)X(t)K 2 * (t) and control U(t). First, we convert the system into a corresponding Kronecker product system with the help of Kronecker product technique, and its general solution is presented in terms of two transition matrices of the systems X Δ (t) = A(t)X(t) and X Δ (t) = B * (t)X(t). Then, a set of necessary and sufficient conditions are presented for the complete controllability and complete observability of the Δ-differential Kronecker product system. 2000 Mathematics subject classification. 93B05, 93B07, 49K15

Controllability and Observability of Kronecker Product Sylvester System on Time Scales

The main objective in this paper is to present the necessary and sufficient conditions for complete controllability, complete observability associated with kronecker product Sylvester system on time scales.2000 Mathematics Subject Classification: 93B05,93B07,49K15

Development of a perfect prognosis probabilistic model for prediction of lightning over south-east India

A prediction model based on the perfect prognosis method was developed to predict the probability of lightning and probable time of its occurrence over the south-east Indian region. In the perfect prognosis method, statistical relationships are established using past observed data. For real time applications, the predictors are derived from a numerical weather prediction model. In the present study, we have developed the statistical model based on Binary Logistic Regression technique. For developing the statistical model, 115 cases of lightning that occurred over the south-east Indian region during the period 2006–2009 were considered. The probability of lightning (yes or no) occurring during the 12-hour period 0900–2100 UTC over the region was considered as the predictand. The thermodynamic and dynamic variables derived from the NCEP Final Analysis were used as the predictors. A three-stage strategy based on Spearman Rank Correlation, Cumulative Probability Distribution and Principal Component Analysis was used to objectively select the model predictors from a pool of 61 potential predictors considered for the analysis. The final list of six predictors used in the model consists of the parameters representing atmospheric instability, total moisture content in the atmosphere, low level moisture convergence and lower tropospheric temperature advection. For the independent verifications, the probabilistic model was tested for 92 days during the months of May, June and August 2010. The six predictors were derived from the 24-h predictions using a high resolution Weather Research and Forecasting model initialized with 00 UTC conditions. During the independent period, the probabilistic model showed a probability of detection of 77% with a false alarm rate of 35%. The Brier Skill Score during the independent period was 0.233, suggesting that the prediction scheme is skillful in predicting the lightning probability over the south-east region with a reasonable accuracy

Pelagic fishery resources of Lawson’s bay, Waltair

At Lawson's B;y, the gears employed are shoreseines, boatseines, hooks and lines, surface g!llnets and bottom-set nylon nets. During the period 1970 to 1974, the estimated total annual landings by all gears were 654. 8, 62?.0', 577.<)8, 542.4 and 637.3 tonnes, respectively. The ca'iches by hooks and lines alone accounted for 50-60% of the tot.l landings during the period. Seasonal abundance of fish showed correlations with hydrological and planktological conditions and the food avalable in environment. Far pelagic fi&hes, high catch rates were obtained during Novem'ber to May and to a lesser extent during July-September. Prawns were caught in greater proportions by gillnets than by boat seines, the former being employed during May-September period. The adverse effects arising out of the introduction of bottom-set gillnets in the fishery are discussed

Chitin Binding Proteins Act Synergistically with Chitinases in Serratia proteamaculans 568

Genome sequence of Serratia proteamaculans 568 revealed the presence of three family 33 chitin binding proteins (CBPs). The three Sp CBPs (Sp CBP21, Sp CBP28 and Sp CBP50) were heterologously expressed and purified. Sp CBP21 and Sp CBP50 showed binding preference to β-chitin, while Sp CBP28 did not bind to chitin and cellulose substrates. Both Sp CBP21 and Sp CBP50 were synergistic with four chitinases from S. proteamaculans 568 (Sp ChiA, Sp ChiB, Sp ChiC and Sp ChiD) in degradation of α- and β-chitin, especially in the presence of external electron donor (reduced glutathione). Sp ChiD benefited most from Sp CBP21 or Sp CBP50 on α-chitin, while Sp ChiB and Sp ChiD had major advantage with these Sp CBPs on β-chitin. Dose responsive studies indicated that both the Sp CBPs exhibit synergism ≥0.2 µM. The addition of both Sp CBP21 and Sp CBP50 in different ratios to a synergistic mixture did not significantly increase the activity. Highly conserved polar residues, important in binding and activity of CBP21 from S. marcescens (Sm CBP21), were present in Sp CBP21 and Sp CBP50, while Sp CBP28 had only one such polar residue. The inability of Sp CBP28 to bind to the test substrates could be attributed to the absence of important polar residues

Chemical Additives for Corrosion Control in Desalination Plants

The addition of chemical additives has been considered as a standard operation in water treatment systems. This chapter discusses the chemical additives used for the control of corrosion in desalination systems. Specifically, corrosion inhibitors for various metallurgies, biocides, and oxygen scavengers are covered. The pros and cons of the additive chemicals have been highlighted. The need to utilize green corrosion inhibitors based on plants and ionic liquids materials have been emphasized. This class of materials are environmentally friendly, cheap, and readily available

Ternary inhibitor system containing phosphonate, molybdate and Zn²⁺ in corrosion control of carbon steel

275-282With the objective of developing a new environmental friendly inhibitor formulation for corrosion of carbon steel in nearly neutral aqueous environments, phosphonic acid viz., N-(2-hydroxyethyl) imino-bis(methylphosphonic acid) [HEIBMPA] was chosen as the inhibitor. Zn2+ was chosen as the first synergist. A maximum inhibition efficiency of 99.3% was obtained with the binary system containing 70 ppm HEIBMPA and 80 ppm Zn2+. Molybdate ion, which is inorganic in nature but environmental friendly, was used as the second synergist. The binary inhibitor formulation containing relatively low concentrations, viz., 30 ppm HEIBMPA and 40 ppm Zn2+ offered an inhibition efficiency of only 23%. To the above combination, when 200 ppm molybdate was added, the inhibition efficiency was found to increase to 95%. The potentiostatic polarization studies revealed that this ternary inhibitor system controlled the anodic reaction predominantly. A large increase in the polarisation resistance (Rp) value indicated the formation of a non-porous protective film on the metal surface. The reflection absorption FT-IR spectrum and X-ray photoelectron spectra of the film suggested that the film consisted of [Fe(III)-HEIBMPA-molybdate] complex, [Fe(III), Zn(II)-HEIBMPA-molybdate]complex, oxides and hydroxides of iron and Zn(OH)2. A plausible mechanism of inhibition of corrosion is proposed, which explains all the above experimental results

&quot;N,N-Bis(phosphonomethyl) Glycine, Zn 2+ and Tartrate&quot; -A New Ternary Inhibitor Formulation for Corrosion Control of Carbon Steel

Abstract Studies on inhibition of corrosion of carbon steel in aqueous environment using N,N -Bis(phosphonomethyl) glycine (BPM G), zinc ions and tartrate are presented. The investigations revealed that tartrate acts as an excellent synergist in corrosion inhibition. Optimu m concentrations of all the three co mponents of the ternary formu lation are established by gravimetric studies. Potentiodynamic polarization studies indicate that the new ternary system is a mixed inhib itor. Results of the impedance studies show that a protective film is formed on the metal surface in presence of the inhibitor formu lation. Analysis of the protective film us ing X-ray photoelectron spectroscopy (XPS) and reflect ion absorption Fourier transform infrared (FTIR) spectroscopy infer the presence of Zn(OH) 2 , o xides and hydroxides of iron and the inhibitor mo lecules in the surface film probably in the form of a co mplex, [Zn(II)-BPM G-tartrate]. A plausible mechanism o f corrosion inhibit ion is proposed

Synergistic effect of NTMP, Zn²⁺ and ascorbate in corrosion inhibition of carbon steel

629-634Nitrilotris(methylenephosphonic acid) (NTMP) inhibits corrosion of carbon steel in presence of Zn2+ . However, in order to make the inhibitor more environment friendly, it is necessary to reduce the levels of Zn2+ or phosphonate or both by introducing an environment friendly organic salt as a second synergist. In this paper, the inhibitive action of ascorbate as a second synergist in the presence of relatively low concentrations of NTMP and Zn2+, is presented. Addition of just 25 ppm of ascorbate to 20 ppm each of NTMP and Zn2+, at pH=7, increased the inhibition efficiency markedly from 35 to 95%. In the pH range of 6-4, the concentration of ascorbate required to bring up the inhibition efficiency to 94%, is only 10 ppm. However, the alkaline region demanded relatively higher concentration of ascorbate. This ternary system is quite effective in a wide pH range, 4-10. This is the uniqueness of this new synergistic formulation. Potentiostatic polarization studies indicated that this synergistic formulation acts as a mixed inhibitor, predominantly cathodic in nature. A large increase in charge transfer resistance and also a decrease in double layer capacitance of the surface film, were observed from a.c. impedance studies. X-ray photoelectron spectrum of the surface film indicated the presence of the elements, viz., P, O, N, C, Zn and Fe in the film. The shifts in binding energies of these elements indicated the presence of oxides and hydroxides of iron and zinc as well as complexes of Fe(III) and Zn(II) with phosphonate and ascorbate. The reflection absorption FTIR spectrum of the surface film also supported the formation of insoluble complexes of phosphonate and ascorbate with metal ions as well as presence of Zn(OH)2 on the metal surface. A suitable mechanism of corrosion inhibition is proposed, which corroborates all the above experimental results