A Continuous Transition Between Quantum and Classical Mechanics. II

Examples are worked out using a new equation proposed in the previous paper to show that it has new physical predictions for mesoscopic systems.     

On a Coordinate-Independent Description of String Worldsheet Theory

We rewrite the bosonic worldsheet theory in curved background in a language where it describes a single particle moving in an infinite-dimensional curved spacetime. This language is developed at a formal level without regularizing the infinite-dimensional traces. Then, we adopt DeWitt’s (Phys Rev 85:653, 1952) coordinate-independent formulation of quantum mechanics in the present context. This procedure enables us to define coordinate invariant quantum analogue of classical Virasoro generators, which we call DeWitt–Virasoro generators. This framework also enables us to calculate the invariant matrix elements of an arbitrary operator constructed out of the DeWitt–Virasoro generators between two arbitrary scalar states. Using these tools, we further calculate the DeWitt–Virasoro algebra in spin-zero representation. The result is given by the Witt algebra with additional anomalous terms that vanish for Ricci-flat backgrounds. Further analysis need to be performed to precisely relate this with the beta function computation of Friedan and others. Finally, we explain how this analysis improves the understanding of showing conformal invariance for certain pp-wave that has been recently discussed using hamiltonian framework.     

Beyond the standard model: Working group report

This report summarises the activities of the working group on ‘Physics beyond the Standard Model’. The results of investigations in incorporatingR-parity in grand unification, the possibility of a light charged Higgs boson in extension of MSSM and radiative generation of neutral vector boson self-couplings within the MSSM are described. Also given is an account of activities in neutrino physics, namely a proposal for a study of the atmospheric muon anomaly in deep underground mines, a field theoretic study of neutrino oscillations and a mechanism to generate appropriate masses of three active plus one sterile neutrino species.     

Syntheses of (−)-gabosine A, (+)-4-epi-gabosine A, (−)-gabosine E, and (+)-4-epi-gabosine E

(+)-4-epi-Gabosine A 1 and (−)-gabosine A 2 have been synthesized starting from methyl α,d-glucopyranoside and methyl α,d-mannopyranoside, respectively, by utilizing Pd(0) catalyzed Stille coupling as the key step. On the other hand, syntheses of (+)-4-epi-gabosine E 3 and (−)-gabosine E 4 have been accomplished from methyl α,d-glucopyranoside and from methyl α,d-mannopyranoside, respectively, by utilizing DMAP catalyzed Morita-Baylis-Hillman reaction as the key step. Presence of acetyl group at C-6 position of sugar derived cyclic enone prevented the aromatization of MBH adduct. A plausible mechanism is also described.     

Coordination-driven self-assembly of 2D-metallamacrocycles using a shape-selective Pt(II)2-organometallic 90° acceptor: design, synthesis and sensing study

Synthesis of a series of two-dimensional metallamacrocycles via coordination-driven self-assembly of a shape-selective Pt(II)(2)-molecular building unit incorporating carbazole-ethynyl functionality is described. An equimolar (1?:?1) combination of a Pt(II)(2)-organometallic 90° acceptor, 1, with rigid linear ditopic donors (L(a) and L(b)) afforded [4 + 4] self-assembled octanuclear molecular squares, 2 and 3, in quantitative yields, respectively [L(a) = 4,4'-bipyridine; L(b) = trans-1,2-bis(4-pyridyl)ethylene]. Conversely, a similar treatment of 1 with an amide-based unsymmetrical flexible ditopic donor, L(c), resulted in the formation of a [2 + 2] self-sorted molecular rhomboid (4a) as a single product [L(c) = N-(4-pyridyl)isonicotinamide]. Despite the possibility of several linkage isomeric macrocycles (rhomboid, triangle and square) due to the different connectivity of L(c), the formation of a single and symmetrical molecular rhomboid (4a) as the only product is an interesting observation. All the self-assembled macrocycles (2, 3 and 4a) were fully characterized by multinuclear NMR ((1)H and (31)P) and ESI-MS analysis. Further structural insights about the size and shape of the macrocycles were obtained through energy minimization using density functional theory (DFT) calculations. Decoration of the starting carbazole building unit with Pt-ethynyl functionality enriches the assemblies to be more π-electron rich and luminescent in nature. Macrocycles 2 and 3 could sense the presence of electron deficient nitroaromatics in solution by quenching of the initial intensity upon gradual addition of picric acid (PA). They exhibited the largest quenching response with high selectivity for nitroaromatics compared to several other electron deficient aromatics tested.     

Computational/In-Silico Methods: An Influential Approach for Drug Designing and Development

As the world is struggling with the pandemic. Various infectious diseases have become a threat to human health. Millions of deaths are caused by these microbial infections (bacterial, fungal, and viral infections). The process of designing and discovering new drugs is very expensive and it also consumes a good amount of time. As per available data, the process of discovery and designing takes 3–20 years to complete. There is a strong urge and demand to discover new methods to make the process of drug design and development more cost-effective. Computational methods are one the novel methods for designing and developing a drug. In this respect, in-silico parameters; ADME (Absorption, Distribution, Metabolism, and Excretion) models have been established with various levels of complication for the transmission of huge data of derivatives/ligands/drugs. Nowadays, in-silico tools are more cost-effective, faster, and simpler than transitional experimental trials. Currently, the pharmaceutical industry faces a huge erosion rate of preclinical and clinical applicants due to the unavailability of pharmacokinetics properties and huge toxicity. These can be minimized via structural modifications of drugs and can help medicinal chemists/pharmacists. In this report, various methodologies and steps have been explained via molecular docking that will lead to drug development in lesser time against various stains.     

Complete Convergence of Martingale Arrays

We study complete convergence of martingale arrays under rather weak conditions. Our results considerably strengthen many of the results available in the literature. As a tool, we establish a martingale analogue of an inequality of Hoffman-Jørgensen which was earlier known only for independent random variables.     

Recent advances in the chemistry of lignans

The recent literature on the chemistry of simple lignans has been comprehensively reviewed.