Nonnegative solutions to reaction–diffusion system with cross-diffusion and nonstandard growth conditions

We establish the existence of nonnegative weak solutions to nonlinear reaction–diffusion system with cross-diffusion and nonstandard growth conditions subject to the homogeneous Neumann boundary conditions. We assume that the diffusion operators satisfy certain monotonicity condition and nonstandard growth conditions and prove that the existence of weak solutions using Galerkin's approximation technique.     

Evaluation of trace element contents in Swertia paniculata Wall.

Important mineral elements (Fe, Zn, Mn, Cu, Co, Na, K, Ca and Li) were determined in the leaves and roots of Swertia paniculata collected from three different altitudes in three seasons using atomic absorption spectroscopy. The highest concentrations of Zn, Cu, Mn, Fe, Co, Na, K, Ca and Li were found to be 193.0?±?5.6, 26.0?±?7.6, 303.0?±?8.5, 1507.0?±?2.5, 88.0?±?1.2, 345.0?±?1.2, 11622.0?±?6.4, 3461.0?±?3.5 and 48.0?±?4.5?mg?kg(-1), respectively. The overall concentration of K was found to be the highest, whereas the level of Cu was the lowest. The concentrations of Cu and Li were quite low in all samples, whereas Zn, Mn, Co and Na were found in moderate concentration and K, Ca and Fe were found in very high concentrations in all the samples tested.     

Analytical applications of mercaptan-carbon disulphide reaction: Determination of mixtures containing mercaptans

Summary A method is described for the determination of mercaptans by alkalimetric titration of trithiocarbonic acids formed through their reaction with carbon disulphide in tert.-butanol. The method has been applied to the analysis, on the same sample solution, of mixtures of mercaptans containing titrable hydrogen and those containing nontitrable hydrogen, mercaptans and alkali mercaptides, and mercaptans and mercaptopyrimidines.

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Analytische Anwendung der Merkaptan-Schwefelkohlenstoff-Reaktion: Bestimmung von Merkaptan in Gemischen

Zusammenfassung Ein Verfahren zur Merkaptanbestimmung durch alkalimetrische Titration der Trithiokohlensäure auf der Grundlage seiner Reaktion mit Schwefelkohlenstoff in tert. Butanol wurde beschrieben. Es eignet sich zur Bestimmung von Gemischen aus Merkaptanen mit titrierbarem Wasserstoff und solchen ohne titrierbaren Wasserstoff sowie von Merkaptanen und Merkaptiden, weiters von Merkaptanen und Merkaptopyrimidinen.

     

Picone’s identity for biharmonic operators on Heisenberg group and its applications

In this paper, we establish a nonlinear analogue of Picone’s identity for biharmonic operators on Heisenberg group. As an applications of Picone’s identity, we obtain Hardy-Rellich type inequality, Morse index, Caccioppoli inequality, Picone inequality for biharmonic operators on Heisenberg group.     

Determination of trace elements in Rheum moorcroftianum by AAS

Micro and macro elements such as Zn, Cu, Mn, Fe, Co, Na, K, Ca and Li were detected from Rheum moorcroftianum Royle, a plant used in folk medicines. Altitudinal and seasonal variation of these trace elements in cultivated and wild roots and leaves of R. moorcroftianum were quantified by atomic absorption spectroscopy. The highest concentrations of Zn, Cu, Mn, Fe, Co, Na, K, Ca and Li were found to be 376.0?±?0.9, 83.0?±?4.6, 322.0?±?6.0, 920.0?±?1.9, 72.0?±?1.5, 402.0?±?7.8, 10,235.0?±?7.0, 12,336.0?±?2.6 and 59.9?±?0.3 mg?kg(-1), respectively, in all the samples analysed.     

Space of invariant bilinear forms

Let \({\mathbb {F}}\) be a field, V a vector space of dimension n over \({\mathbb {F}}\). Then the set of bilinear forms on V forms a vector space of dimension \(n^2\) over \({\mathbb {F}}\). For char \({\mathbb {F}}\ne 2\), if T is an invertible linear map from V onto V then the set of T-invariant bilinear forms, forms a subspace of this space of forms. In this paper, we compute the dimension of T-invariant bilinear forms over \({\mathbb {F}}\). Also we investigate similar type of questions for the infinitesimally T-invariant bilinear forms (T-skew symmetric forms). Moreover, we discuss the existence of nondegenerate invariant (resp. infinitesimally invariant) bilinear forms.     

Synthesis, antiamoebic activity and thermal study of copper complexes of 1-formyl-2-pyrazolines

Copper complexes of 1-formyl-2-pyrazolines were prepared by the reaction of 1-formyl-2-pyrazolines with copper chloride and nitrate with methanol. The structures of copper complexes 1a–3a have been established by elemental analysis, FT-IR, UV and thermogravimetric analysis. These compounds were tested against HM1:IMSS strain of Entamoeba histolytica by the microdilution method. Complexes 2a and 3a are more active than other complexes.