Polynomial Time Approximation Scheme for Symmetric Rectilinear Steiner Arborescence Problem

The Symmetric Rectilinear Steiner Arborescence (SRStA) problem is defined as follows: given a set of terminals in the positive quadrant of the plane, connect them using horizontal and vertical lines such that each terminal can be reached from the origin via a y-monotone path and the total length of all the line segments is the minimum possible. Finding an SRStA has applications in VLSI design, in data structures used in some optimization algorithms and in dynamic server problems. In this paper, we provide a polynomial time approximation scheme for the SRStA problem, improving the previous best approximation ratio of 3 for this problem.     

Identities Involving Partial Mock Theta Functions of Order Five

In this paper we have given transformations for the partial mock theta functions of order five and also some identities between these partial mock theta functions analogous to the identities given by Ramanujan.     

Homogeneous operators and projective representations of the Möbius group: A survey

This paper surveys the existing literature on homogeneous operators and their relationships with projective representations ofPS L(2, ℝ) and other Lie groups. It also includes a list of open problems in this area.     

Small Molecule Soluble Epoxide Hydrolase Inhibitors in Multitarget and Combination Therapies for Inflammation and Cancer

The enzyme soluble epoxide hydrolase (sEH) plays a central role in metabolism of bioactive lipid signaling molecules. The substrate-specific hydrolase activity of sEH converts epoxyeicosatrienoic acids (EETs) to less bioactive dihydroxyeicosatrienoic acids. EETs exhibit anti-inflammatory, analgesic, antihypertensive, cardio-protective and organ-protective properties. Accordingly, sEH inhibition is a promising therapeutic strategy for addressing a variety of diseases. In this review, we describe small molecule architectures that have been commonly deployed as sEH inhibitors with respect to angiogenesis, inflammation and cancer. We juxtapose commonly used synthetic scaffolds and natural products within the paradigm of a multitarget approach for addressing inflammation and inflammation induced carcinogenesis. Structural insights from the inhibitor complexes and novel strategies for development of sEH-based multitarget inhibitors are also presented. While sEH inhibition is likely to suppress inflammation-induced carcinogenesis, it can also lead to enhanced angiogenesis via increased EET concentrations. In this regard, sEH inhibitors in combination chemotherapy are described. Urea and amide-based architectures feature prominently across multitarget inhibition and combination chemotherapy applications of sEH inhibitors.     

Bismuth-Oxide-Decorated Graphene Oxide Hybrids for Catalytic and Electrocatalytic Reduction of CO2

Global warming challenges are fueling the demand to develop an efficient catalytic system for the reduction of CO₂, which would contribute significantly to the control of climate change. Herein, as-synthesized bismuthoxide-decorated graphene oxide (Bi₂O₃@GO) was used as an electro/thermal catalyst for CO₂ reduction. Bi₂O₃@GO is found to be distributed uniformly, as confirmed by scanning electron and transmission electron microscopic analysis. The X-ray diffraction (XRD) pattern shows that the Bi₂O₃ has a β-phase with 23.4 m² g⁻¹ BET surface area. Significantly, the D and G bands from Raman spectroscopic analysis and their intensity ratio (I_D/I_G) reveal the increment in defective sites on GO after surface decoration. X-ray photoelectron spectroscopic (XPS) analysis shows clear signals for Bi, C, and O, along with their oxidation states. An ultra-low onset potential (−0.534 V vs. RHE) for the reduction of CO₂ on Bi₂O₃@GO is achieved. Furthermore, potential-dependent (−0.534, −0.734, and −0.934 vs. RHE) bulk electrolysis of CO₂ to formate provides Faradaic efficiencies (FE) of approximately 39.72, 61.48, and 83.00 %, respectively. Additionally, in time-dependent electrolysis at a potential of −0.934 versus RHE for 3 and 5 h, the observed FEs are around 84.20 % and 87.17 % respectively. This catalyst is also used for the thermal reduction of CO₂ to formate. It is shown that the thermal reduction provides a path for industrial applications, as this catalyst converts a large amount of CO₂ to formate (10 mm ).     

Solvent-free synthesis and 1,3-dipolar cycloaddition reactions of N-methyl-C-(2-furyl) nitrone in a ball mill and anticancer activities of the new cycloadducts

An efficient method of mechanochemistry for the synthesis of N-methyl-C-(2-furyl) nitrone and intermolecular 1,3-dipolar cycloaddition reactions with activated alkenes and electron deficient alkynes has been studied by employing ball milling technique. This method is found to accelerate significantly the reaction rate and improved yields of isoxazolidine and isoxazoline derivatives. A comparative study with the corresponding solvent-free microwave-induced reaction showed the superiority of the ball milling method. Significant anticancer activity of the new molecules have made this protocol more attractive. All the new isoxazolidine and isoxazoline derivatives have been screened for anticancer activities and were found to be active.     

Synthesis of some novel annelated 1,2,3‐selena/thiadiazoles and 2h‐diazaphospholes

A number of annelated heterocyclic indene derivatives having 1,2,3‐selena/thiadiazole and 2H‐1,2,3‐diazaphosphole rings have been synthesized by exploiting the α‐ketomethylene functionality in some novel 1‐methyl‐piperidin‐4‐ones and 1‐oxo‐tetrahydrothiopyran‐4‐ones and were characterized by their physical and spectral data.