Transition Metal Free Chemoselective Reduction of α,β‐Unsaturated Ketones to Saturated Ketones Using Tosyl Hydrazide as a Hydrogen Donor

An efficient, inexpensive and simple method for the reduction of various α,β‐unsaturated ketones to corresponding saturated ketones using tosyl hydrazide as a hydrogen donor in DMF using calcium oxide powder has been reported. A variety of enones underwent reduction without forming undesirable side products. High chemoselectivity, broad functional group tolerance and good yields are the noteworthy features of this protocol.     

Ramanujan-type congruences modulo powers of 5 and 7

Let b _? (n) denote the number of ?-regular partitions of n. In 2012, using the theory of modular forms, Furcy and Penniston presented several infinite families of congruences modulo 3 for some values of ?. In particular, they showed that for α, n ≥ 0, b ₂₅ (3^2α+3 n+2 · 3^2α+2-1) ≡ 0 (mod 3). Most recently, congruences modulo powers of 5 for c5(n) was proved by Wang, where c _N (n) counts the number of bipartitions (λ₁,λ₂) of n such that each part of λ₂ is divisible by N. In this paper, we prove some interesting Ramanujan-type congruences modulo powers of 5 for b25(n), B25(n), c25(n) and modulo powers of 7 for c49(n). For example, we prove that for j ≥ 1, \({c_{25}}\left( {{5^{2j}}n + \frac{{11 \cdot {5^{2j}} + 13}}{{12}}} \right) \equiv 0\) (mod 5 ^j+1), \({c_{49}}\left( {{7^{2j}}n + \frac{{11 \cdot {7^{_{2j}}} + 25}}{{12}}} \right) \equiv 0\) (mod 7 ^j+1) and b ₂₅ (3^2α+3 · n+2 · 3^2α+2-1) ≡ 0 (mod 3 · 5^2j-1).     

Co<Subscript>2</Subscript>(OH)<Subscript>3</Subscript>Cl xerogels with 3D interconnected mesoporous structures as a novel high-performance supercapacitor material

Co₂(OH)₃Cl xerogel interconnected mesoporous structures have been prepared by a facile one pot sol-gel process and heat treated at 200 and 400 °C. All samples are studied for their morphology, structure, and electrochemical stability upon cycling. The specific capacitance of the as-prepared Co₂(OH)₃Cl from single electrode study is 450 F/g, when the electrodes are cycled in 3 M KOH at a specific current 2 A/g. Interestingly, capacity retention after 500 and 1000 cycles is about 92 and 75 %, respectively. Sample heated at 200 °C exhibits 308 F/g at 2 A/g and that heated at 400 °C shows only 32 F/g at 0.2 A/g. With an increase in preparation temperature, amorphous Co₂(OH)₃Cl is converted to crystalline Co₃O₄ phases with lower electrochemical performance. In full cell study, as-prepared Co₂(OH)₃Cl showed a capacity of about 49 F/g as asymmetric capacitor and 32 F/g as symmetric capacitor at 2 A/g current density. Co₂(OH)₃Cl being a novel porous material with merits of homogeneous porosity, high surface area, and an interconnected three dimensional (3D) structure exhibits considerably high capacitance. With a significant specific capacity and electrochemical stability, the synthesized material is a novel potential candidate for supercapacitors.

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Graphical abstract ?

     

Congruences for 7 and 49-regular partitions modulo powers of 7

Let \(b_{k}(n)\) denote the number of k-regular partitions of n. In this paper, we prove Ramanujan-type congruences modulo powers of 7 for \(b_{7}(n)\) and \(b_{49}(n)\). For example, for all \(j\ge 1\) and \(n\ge 0\), we prove that

$$\begin{aligned} b_{7}\Bigg (7^{2j-1}n+\frac{3\cdot 7^{2j-1}-1}{4}\Bigg )\equiv 0\pmod {7^{j}} \end{aligned}$$

and

$$\begin{aligned} b_{49}\Big (7^{j}n+7^{j}-2\Big )\equiv 0\pmod {7^{j}}. \end{aligned}$$

     

Discovery of Novel Coumarin Derivatives as Potential Dual Inhibitors against α-Glucosidase and α-Amylase for the Management of Post-Prandial Hyperglycemia via Molecular Modelling Approaches

Coumarin derivatives are proven for their therapeutic uses in several human diseases and disorders such as inflammation, neurodegenerative disorders, cancer, fertility, and microbial infections. Coumarin derivatives and coumarin-based scaffolds gained renewed attention for treating diabetes mellitus. The current decade witnessed the inhibiting potential of coumarin derivatives and coumarin-based scaffolds against α-glucosidase and α-amylase for the management of postprandial hyperglycemia. Hyperglycemia is a condition where an excessive amount of glucose circulates in the bloodstream. It occurs when the body lacks enough insulin or is unable to correctly utilize it. With open-source and free in silico tools, we have investigated novel 80 coumarin derivatives for their inhibitory potential against α-glucosidase and α-amylase and identified a coumarin derivative, CD-59, as a potential dual inhibitor. The ligand-based 3D pharmacophore detection and search is utilized to discover diverse coumarin-like compounds and new chemical scaffolds for the dual inhibition of α-glucosidase and α-amylase. In this regard, four novel coumarin-like compounds from the ZINC database have been discovered as the potential dual inhibitors of α-glucosidase and α-amylase (ZINC02789441 and ZINC40949448 with scaffold thiophenyl chromene carboxamide, ZINC13496808 with triazino indol thio phenylacetamide, and ZINC09781623 with chromenyl thiazole). To summarize, we propose that a coumarin derivative, CD-59, and ZINC02789441 from the ZINC database will serve as potential lead molecules with dual inhibition activity against α-glucosidase and α-amylase, thereby discovering new drugs for the effective management of postprandial hyperglycemia. From the reported scaffold, the synthesis of several novel compounds can also be performed, which can be used for drug discovery.     

Development of electroless Ni-Zn-P/nano-TiO2 composite coatings and their properties

Ni-Zn-P-TiO₂ composite coatings were successfully obtained on low carbon steel by electroless plating technique. Deposits were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy-dispersive analysis (EDS) studies. The hardness and microstructure of as plated and heat treated Ni-Zn-P and Ni-Zn-P-TiO₂ composite coatings were analyzed. The change in microstructure and higher hardness was noticed for heat treated composite. The corrosion resistance behavior of as plated and heat treated Ni-Zn-P and Ni-Zn-P-TiO₂ coatings was investigated by anodic polarization, Tafel plots and electrochemical impedance spectroscopic (EIS) studies in 3.5 wt% NaCl solution. The composite coating exhibited enhanced corrosion resistance property over Ni-Zn-P coating.     

On overpartition pairs into odd parts modulo powers of 2

In 2012, Lin (Electron. J. Combin. 19(2) (2012) #P17) investigated the 2 and 3-divisibility properties for ${\overline{pp}}_o\left(n\right)$, the number of overpartition pairs into odd parts. Using modular forms, he proved that for a fixed positive integer $k$, ${\overline{pp}}_o\left(n\right)$ is almost always divisible by $2^k$. In this paper, we prove several congruences for ${\overline{pp}}_o\left(n\right)$ modulo higher powers of 2 in an elementary way.     

On 3-Regular Tripartitions

Abstract In this article,we investigate the arithmetic behavior of the function D_3(n)which counts the number of 3-regular tripartitions of n.For example,we show that forα≥1 and n≥0,■and ■