Third Order Lagrangians, Weyl Invariants and Classical Trace Anomaly in Six Dimensions

We have proceeded the analogy (represented in our previous works) of the Einstein tensor and the alternative form of the Einstein field equations for the generic coefficients of the eight terms in the third order of the Lovelock Lagrangian. We have found the constraint between the coefficients into two forms, an independent and a dimensional dependent versions. Each form has three degrees of freedom, and not only the exact coefficients of the third order Lovelock Lagrangian do satisfy the two forms of the constraints, but also the two independent cubic of the Weyl tensor satisfy the independent constraint in six dimensions and yield the dimensional dependent version identically independent of the dimension. Then, we have introduced the most general effective expression for a total third order type Lagrangian with the homogeneity degree number three which includes the previous eight terms plus the new three ones among the all seventeen independent terms. We have proceeded the analogy for this combination, and have achieved the relevant constraint. We have shown that the expressions given in the literature as the third Weyl-invariant combination in six dimensions do satisfy this constraint. Thus, we suggest that these constraint relations to be considered as the necessary consistency conditions on the numerical coefficients that a Weyl-invariant in six dimensions should satisfy. Finally, we have calculated the “classical” trace anomaly (an approach that was presented in our previous works) for the introduced total third order type Lagrangian and have achieved a general expression with four degrees of freedom in more than six dimensions (three degrees in six dimensions). Then, we have demonstrated that the resulted expression contains exactly the relevant coefficient of the Schwinger–DeWitt proper time method (that linked with the relevant heat kernel coefficient) in six dimensions, as a particular case. Of course, this result is a necessary consistency check, nevertheless our approach can be regarded as an alternative (perhaps simpler, and classical) derivation of the trace anomaly which also gives a general expression with the relevant degrees of freedom.     

Identifizierung organischer Säuren durch thermische Analyse und Bestimmung des Säuregehaltes in Anhydriden

Zusammenfassung Ein thermisches Analysenverfahren wurde ausgearbeitet, das die Identifizierung einiger organischer Säuren nebeneinander und zugleich deren sehr empfindliche Bestimmung in kleinen Einwaagen ermöglicht. Die dazu entwickelte Anlage verwendet einen Gaschromatographendetektor.

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Identification of organic acids through thermoanalysis and determination of the acid content of anhydrides

Summary A thermoanalytic procedure has been developed which permits to identify several organic acids in the presence of one another, and at the same time to determine them in very small samples. The apparatus employs a gaschromatograph-detector.

     

A Green Approach for the Synthesis of Silver Nanoparticles Using Root Extract of <Emphasis Type="Italic">Chelidonium majus:</Emphasis> Characterization and Antibacterial Evaluation

In this study, silver nanoparticles (Ag-NPs) have been synthesized using extract of Chelidonium majus root in aqueous solution at room temperature. The root extract was able to reduce Ag⁺ to Ag⁰ and stabilized the nanoparticles Different physico-chemical techniques including UV–Vis spectroscopy, transmission electron microscopy and powder X-ray diffraction (PXRD) were used for the characterization of the biosynthesized Ag-NPs obtained. The surface plasmon resonance band appeared at 431 nm is an evidence for formation of Ag-NPs. TEM imaging revealed that the synthesized Ag-NPs have an average diameter of around 15 nm and with spherical shape. Moreover the crystalline structure of synthesized nanoparticles was confirmed using XRD pattern. Furthermore antimicrobial activities of synthesized Ag-NPs were evaluated against Escherichia coli -ATCC 25922 and Pseudomonas aeruginosa ATCC 2785 bacteria strain.     

Facile Biosynthesis of Silver Nanoparticles Using <Emphasis Type="Italic">Descurainia sophia</Emphasis> and Evaluation of Their Antibacterial and Antifungal Properties

The objective of the present study was to evaluate efficiency of silver nanoparticles (Ag-NPs) biosynthesis using Descurainia sophia as a novel biological resource. The resulting synthesized Ag-NPs were characterized using UV visible spectroscopy, X-ray diffraction, transmission electron microscopy and dynamic light scattering (DLS). The UV–Vis spectra gave surface plasmon resonance at ~420 nm. TEM images revealed formation spherical shaped Ag-NPs with size ranged from to 1–35 nm. DLS confirmed uniformity of the synthesized Ag-NPs with an average size of ~30 nm. Following, the antibacterial and antifungal activities of the synthesized Ag-NPs were investigated. The concentration 25 µg/ml of the Ag-NPs showed maximum inhibitory effect on mycelium growth of Rhizoctonia solani (More than 86 % inhibition), followed by 15 µg/ml (55 % inhibition) and 10 µg/ml (63 % inhibition). The minimum inhibitory concentration and minimum bactericidal concentration of Ag-NPs against Agrobacterium tumefaciens (strain GV3850) and A, rhizogenes (strain 15843) were 4 and 8 µg/ml, respectively. The Ag-NPs were stable in vitro for 3 months without any precipitation or decrease of antifungal effects. Finally, it could be concluded that D. sophia can be used as an effective method for biosynthesis of nanoparticles, especially Ag-NPs.     

BTX Removal from Polluted Water Through Bioleaching Processes

In this study, benzene, toluene, and xylenes (BTX) removal from contaminated water by physical, chemical, and biological processes was studied. Results showed that air sparging in polluted water can reduce monoaromatic compounds from 140,000 to about 5 microg/l in only 1 h process with a gassing rate of 0.33 VVM. This method cannot be considered as a green technology as pollutants are only transferred from the liquid phase to the gas phase The ultimate objective of this research was thus to evaluate the efficiency of a strategy involving BTX adsorption by granular-activated charcoal (GAC) and subsequent regeneration of this support by a bioleaching process. Analysis of such processes requires the building of analytical tools able to accurately determine the contents of the contaminants in samples containing biomass to make possible the calculation of reliable material balances. Current investigation showed that BTX are readily trapped by GAC particles with low further release in the liquid medium whereas they remain at least partially available for in situ biodegradation. BTX adsorption onto the GAC was shown to reach maximum solute retention close to 350, 250, and 150 (as mg/g GAC) for xylenes, toluene, and benzene, respectively. This approach, which could afford efficient biological active carbon regeneration, is very promising for the removal of BTX compounds from water without any further environment damage.     

Multi‐component reaction‐functionalized chitosan complexed with copper nanoparticles: An efficient catalyst toward A3 coupling and click reactions in water

A novel bio‐nanocomposite nanocatalyst with highly dispersed particles is synthesized through covalent functionalization of chitosan biopolymer by the multicomponent reaction (MCR) strategy. Surface functionalization of chitosan through MCR is led to the grafting of carboxamide type ligands with a high affinity toward complexation with copper nanoparticles. The catalytic activity of the synthesized catalyst was explored in various transformations such as A³ coupling and click reactions in water. Reusability and non‐hazardous nature of the catalyst, mild reaction conditions, operational simplicity, high yielding, and using water as a solvent are the main advantages of this catalytic protocol.     

γ‐Fe2O3@Cu3Al‐LDH‐TUD as a new Amphoteric,Highly Efficient and Recyclable Heterogeneous Catalyst for the Solvent‐free Synthesis of Dihydropyrano[3,2‐c]pyrazoles and dihydropyrano[3,2‐c]chromens

Thiourea dioxide was immobilized on γ‐Fe₂O₃@Cu₃Al‐LDH magnetic nanoparticles to prepare the γ‐Fe₂O₃@Cu₃Al‐LDH‐TUD MNPs. The structure and properties of these magnetic nanoparticles were established by FT‐IR, EDX, SEM, XRD, and hystogram of particle size analytical methods. The results obtained from these analytical methods confirmed the successful immobilization of the thiourea dioxide onto the magnetic support. The synthesized magnetic nanoparticles (MNPs) exhibited high catalytic activity in one‐pot three‐component reactions under mild and solvent‐free conditions for the synthesis of diverse ranges of dihydropyrano[3,2‐c]pyrazoles and dihydropyrano[3,2‐c]chromens. All the reactions proceeded smoothly to furnish the respective products in excellent yields. Simple isolation of the products, avoidance of harmful organic solvents, versatility of the catalyst and its easy magnetic separation and reusability with no significant loss of activity are the main advantages of the present method.     

The strong persistence property and symbolic strong persistence property

Czechoslovak Mathematical Journal - Let I be an ideal in a commutative Noetherian ring R. Then the ideal I has the strong persistence property if and only if (Ik+1: RI) = Ik for all k, and I has...