Efficient Transformation of Nitrile into Amide under Mild Condition

Transformation of various kinds of nitriles into the corresponding amides or amide salts was performed in good yields by the addition of two equiv of chlorotrimethylsilane and three equiv of water at 0℃ to room temperature. Hydrogen halide generated in situ by TMSX and water is an important reaction especially when HX is needed in requisite amount and under dry reaction conditions. As part of our endeavor to utilize HX thus generated, we have found TMSC1 and water can be used for transformation of nitriles into amides under very mild reaction conditions and with satisfactory yields. Interestingly, under the condition of hydration of nitrile, ester of carboxylic acid remains intact. Although there are several reports in the literature to bring about the same transformation, however, a new approach is still significant and needed. Moreover, most of the reported methods have not been proven in general and practical in scope. This paper reports the hydration of a series aliphatic as well as aromatic nitriles into amides at 0℃ to room temperature for only two to four hours. Solvent is not needed in this transformation. Attempts to use THF, MeNO₂, or CH₂Cl₂ as the solvent results in poor yields. Protonation of the nitrile by HCl, generated in situ from TMSC1 and half equiv of H₂O, and followed by nucleophilic attack by another equiv of H₂O to form the amide salt seems to be the possible pathway for this reaction. Ideally, the molar ratio for RCN/TMSC1/H₂O is 1:1:1.5. Use of little excess of the reagents (0.2 to 0.5 equiv) leads to completion of this reaction in 10 to 12 h. To compensate the escape of HCl generated in situ, one more equiv of HCl is generally used in this reaction. No further hydrolysis of amide to the carboxylic acid was observed in the presence of one more equiv of water.     

On the Solution of the Stokes Equation on Regions with Corners

The detailed behavior of solutions to Stokes equations on regions with corners has been historically difficult to characterize. The solutions to Stokes equations on regions with corners are known to develop singularities in the vicinity of corners; in particular, the solutions are known to have infinite oscillations along almost every ray that meet at the corner. While the nature of singularities for the differential equation have been analyzed in great detail, very little is known about the nature of singularities for the corresponding integral equations. In this paper, we observe that, when the Stokes equation is formulated as a boundary integral equation, the solutions are representable by rapidly convergent series of the form , where t is the distance from the corner and the parameters μ_j, β_j are real, and are determined via an explicit formula depending on the angle at the corner. In addition to being analytically perspicuous, these representations lend themselves to the construction of highly accurate and efficient numerical discretizations, significantly reducing the number of degrees of freedom required for the solution of the corresponding integral equations. The results are illustrated by several numerical examples. © 2020 Wiley Periodicals LLC     

Syntheses,characterizations, crystal structures,DFT/TD-DFT,luminescence behaviors and cytotoxic effect of bicompartmental Zn (II)-dicyanamide Schiff base coordination polymers: An approach to apoptosis,autophagy and necrosis type classical cell death

Two new Zn (II)-dicyanamide (dca) 1-D chain coordination polymers (CPs), [Zn (L^OMe)(μ₁-dca)(μ_1,5-dca)]_n (1) and [Zn (L^OEt)(μ₁-dca)(μ_1,5-dca)]_n (2) have been successfully synthesized from bicompartmental Schiff base ligands N,N^′-Bis(3-methoxysalicylidenimino)-1,3-diaminopropane (H₂L^OMe), N,N^′-Bis(3-ethoxysalicylidenimino)-1,3-diaminoproane (H₂L^OEt) respectively and structurally characterized using various spectroscopic protocols like ¹H NMR, IR, Raman, UV–Vis, fluorescence as well as elemental analysis, TGA, PXRD and SCXRD studies. X-ray single crystal study revealed that both the complexes have two different geometrical arrangement of Zn metal centres with distorted square pyramidal Zn(2) and trigonal prismatic geometry Zn(1). Ab-initio DFT (Density functional theory) has been executed at B3LYP (Becke, 3-parameter, Lee-Yang-Parr) using DGDVP (Diffuse gradient double valence polarised) basis set to explain FMO (Frontier molecular orbital), TD-DFT (Time-dependent density functional theory) and photovoltaic efficiency in Dye Sensitized Solar Cell (DSSC). Hirshfeld surface (HS) and 2D fingerprint plot analyses are shed more light on the non-covalent supramolecular interactions. The steady state and time-resolved fluorescence measurements have been conducted in DMSO and solid-state. CPs exhibited bi-exponential decay in DMSO as well as solid-state where fluorescence behaviors are mainly intra-ligand (π → π^*) in nature with lifetimes in the range (1.11–1.06 ns). In particular, in vitro cytotoxic activities were evaluated towards MCF7 (breast cancer) cell line, MDA-MB-231 (breast carcinoma) cell line and MCF10A (breast epithelial) cell line using MTT assay. CP 1 had lower cytotoxic effect against MCF7 (20 μM), MDA-MB-231 (15 μM) cell lines in comparison with cisplatin (42.2 ± 8, 128.2 ± 7 μM). CP 1 induced classical cell death apoptosis, autophagy and necrosis. Lower IC₅₀ value of CP 1 against MDA-MB-231 cell line provide new insights in the development of cancer therapeutics.     

Balanced group-labeled graphs

A group-labeled graph is a graph whose vertices and edges have been assigned labels from some abelian group. The weight of a subgraph of a group-labeled graph is the sum of the labels of the vertices and edges in the subgraph. A group-labeled graph is said to be balanced if the weight of every cycle in the graph is zero. We give a characterization of balanced group-labeled graphs that generalizes the known characterizations of balanced signed graphs and consistent marked graphs. We count the number of distinct balanced labellings of a graph by a finite abelian group $\Gamma$ and show that this number depends only on the order of $\Gamma$ and not its structure. We show that all balanced labellings of a graph can be obtained from the all-zero labeling using simple operations. Finally, we give a new constructive characterization of consistent marked graphs and markable graphs, that is, graphs that have a consistent marking with at least one negative vertex.     

Reconstructing obstacles by the enclosure method using the far field measurements in one step

In this work, we are concerned with the reconstruction of the obstacles by the enclosure method using the far field measurements in one step. To justify this, first we state the indicator function of the enclosure method linking directly the far field pattern to the reflected solutions corresponding to the used complex geometrical optics solutions. Second, we use layer potential techniques to derive the needed estimates of the reflected solutions. No condition on the geometry of the obstacle or on the used frequency is needed.     

Elastic constitutive laws for incompatible crystalline media: the contributions of dislocations,disclinations and G-disclinations

Linear higher-grade higher-order elastic constitutive laws for compatible (defect-free) and incompatible (containing crystal line defects) media are presented. In the proposed model, the free energy density of a body subjected to elastic deformation under the action of surface tractions, moments or hyper-traction tensors (second-order tensors whose anti-symmetric part corresponds to moments) has contributions coming from the first two gradients of displacements. Thermodynamic considerations reveal that only the symmetric component of the gradient of elastic displacement, i.e., compatible elastic strain tensor, and the anti-symmetric component of the second gradient of elastic displacement, i.e., compatible third-order elastic curvature tensor, contribute to the free energy density during compatible deformation of the body. The line crystal defect contributions are accounted for by incorporating the incompatible components of elastic strains, curvatures and symmetric 2-distortions as state variables of the free energy density. In particular, the presence of generalized disclinations (G-disclinations) is acknowledged when the medium is subjected to surface hyper-traction tensors having a non-zero symmetric component along with surface-tractions on its boundary. Mechanical dissipation analysis provides for the coupling between the Cauchy stresses and third-order symmetric hyper-stresses. The free energy density and elastic laws for a defect-free and line crystal defected medium are proposed in a linear setting. In the special case of isotropy, the cross terms between elastic strains and curvatures contribute to the free energy density through a single elastic constant. More interestingly, the Cauchy and couple stresses are found to have contributions coming from both, elastic strains and curvatures.     

A production-repairing inventory model with fuzzy rough coefficients under inflation and time value of money

In this paper, a production-repairing inventory model in fuzzy rough environment is proposed incorporating inflationary effects where a part of the produced defective units are repaired and sold as fresh units. Here, production and repairing rates are assumed as dynamic control variables. Due to complexity of environment, different costs and coefficients are considered as fuzzy rough type and these are reduced to crisp ones using fuzzy rough expectation. Here production cost is production rate dependent, repairing cost is repairing rate dependent and demand of the item is stock-dependent. Goal of the research work is to find decisions for the decision maker (DM) who likes to maximize the total profit from the above system for a finite time horizon. The model is formulated as an optimal control problem and solved using a gradient based non-linear optimization method. Some particular cases of the general model are derived. The results of the models are illustrated with some numerical examples.