A Dirichlet character analogue of Ramanujan's formula for odd zeta values

In 2001, Kanemitsu, Tanigawa, and Yoshimoto studied the following generalized Lambert series, $$\sum_{n=1}^{\infty} \frac{n^{N-2h} }{\exp(n^N x)-1},$$ for $N \in \mathbb{N}$ and $h\in \mathbb{Z}$ with some restriction on $h$. Recently, Dixit and the last author pointed out that this series has already been present in the Lost Notebook of Ramanujan with a more general form. Although, Ramanujan did not provide any transformation identity for it. In the same paper, Dixit and the last author found an elegant generalization of Ramanujan's celebrated identity for $\zeta(2m+1)$ while extending the results of Kanemitsu et al. In a subsequent work, Kanemitsu et al. explored another extended version of the aforementioned series, namely, $$\sum_{r=1}^{q}\sum_{n=1}^{\infty} \frac{\chi(r)n^{N-2h}{\exp\left(-\frac{r}{q}n^N x\right)}}{1-\exp({-n^N x})},$$ where $\chi$ denotes a Dirichlet character modulo $q$, $N\in 2\mathbb{N}$ and with some restriction on the variable $h$. In the current paper, we investigate the above series for {\it any} $N \in \mathbb{N}$ and $h \in \mathbb{Z}$. We obtain a Dirichlet character analogue of Dixit and the last author's identity and there by derive a two variable generalization of Ramanujan's identity for $\zeta(2m+1)$. Moreover, we establish a new identity for $L(1/3, \chi)$ analogous to Ramanujan's famous identity for $\zeta(1/2)$.Comment: 24 pages, comments are welcome

Evaluation of analgesic and anti-inflammatory activity of ethanolic extract of Enhydra fluctuans on male wistar rats

Enhydra fluctuations an edible semi-aquatic vegetable plant are widely used in the traditional system of medicine. Ethanolic extract of Enhydra fluctuans was screened for analgesic & anti-inflammatory activity. Analgesic activity was evaluated by the hot plate method and anti-inflammatory activity was evaluated by formalin induce paw edema in Wistar rats (male). Ethanolic extract dose of 300 mg/kg reduce formalin induce paw inflammation and also increased the pain threshold in rats evidenced by hot plate method. The experimental results concluded that Enhydra fluctuans have significant analgesic and anti-inflammatory activity may due to flavonoid and phenolic compound content

Antimicrobial resistance pattern, clustering mechanisms and correlation matrix of drug-resistant Escherichia coli in black Bengal goats in West Bengal, India

A cross-sectional study covering four agro-climatic zones of West Bengal, India, was carried out to understand the risk-factors, antimicrobial resistance mechanism and clustering of the resistance characteristics of Escherichia coli isolated from healthy (170) and diarrhoeic (74) goats reared under intensive (52) and semi-intensive (192) farming practices. Of the 488 E. coli isolates, the majority, including the extended spectrum (n: 64, 13.11%) and AmpC β-lactamase (ACBL) (n: 86, 17.62%) producers, were resistant to tetracycline (25.2%), followed by enrofloxacin (24.5%), cefotaxime (21.5%) and amikacin (20.5%). Statistical modelling revealed that the isolates from diarrhoeic animals (p < 0.001) are likely to be more ACBL-positive than those from the healthy counterparts. Similarly, cefotaxime (p < 0.05) and enrofloxacin-resistance (p < 0.01) were significantly higher in diarrhoeic goats and in goats reared intensively. The isolates (n = 35) resistant to multiple drugs revealed the presence of β-lactamase [blaCTXM-1-(21), blaSHV-(7), blaTEM-(3), blaCMY-6-(1), blaCITM-(3)]; quinolone [qnrB-(10), qnrS-(7), aac(6’)-Ib-cr-(3)]; tetracycline [tetA-(19), tetB-(4)] and sulphonamide resistance determinants [sul1-(4)]; multiple plasmids, especially those belonging to the IncF and IncI1 replicon types; and active acrAB efflux pumps. Further, two isolates harbored the carbapenem resistance (blaNDM-5) gene and eight were strong biofilm producers. This first ever study conducted to unravel the status of AMR in goat farming reveals that not only the intensive farming practices but also certain clinical ailments such as diarrhoea can increase the shedding of the drug-resistant isolate. The emergence of multi-drug resistant (MDR) E. coli in goats, particularly those that are carbapenem resistant, is a cause for concern that indicates the spread of such pathogens even in the livestock sub-sector generally considered as naive

Multidimensional chemical control of CRISPR–Cas9

Cas9-based technologies have transformed genome engineering and the interrogation of genomic functions, but methods to control such technologies across numerous dimensions-including dose, time, specificity, and mutually exclusive modulation of multiple genes-are still lacking. We conferred such multidimensional controls to diverse Cas9 systems by leveraging small-molecule-regulated protein degron domains. Application of our strategy to both Cas9-mediated genome editing and transcriptional activities opens new avenues for systematic genome interrogation

Molecular decoding using luminescence from an entangled porous framework

Chemosensors detect a single target molecule from among several molecules, but cannot differentiate targets from one another. In this study, we report a molecular decoding strategy in which a single host domain accommodates a class of molecules and distinguishes between them with a corresponding readout. We synthesized the decoding host by embedding naphthalenediimide into the scaffold of an entangled porous framework that exhibited structural dynamics due to the dislocation of two chemically non-interconnected frameworks. An intense turn-on emission was observed on incorporation of a class of aromatic compounds, and the resulting luminescent colour was dependent on the chemical substituent of the aromatic guest. This unprecedented chemoresponsive, multicolour luminescence originates from an enhanced naphthalenediimide–aromatic guest interaction because of the induced-fit structural transformation of the entangled framework. We demonstrate that the cooperative structural transition in mesoscopic crystal domains results in a nonlinear sensor response to the guest concentration

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Not AvailableArtificial intelligence (AI) is the branch of science that deals with the development of machines to mimic human intelligence. Machine learning (ML) is subdomain of AI where the machine can learn automatically from data without being explicitly programmed. Agriculture is constantly pressed upon to produce more with less resource. AI and ML techniques have the capacity to optimize resource utilization by analysing agricultural data. It has changed the present- day face of farming by predicting various input parameters and forecasting post-harvest life of a crop. This chapter discusses the different AI and ML techniques available and how they have been used in different phases of the agriculture life cycle. This chapter includes vast range areas in agriculture that requires AI and ML It includes soil, irrigation, and disease managements. Importance of AI in the field of plant phenomics also included in this chapter. The probable use of geographic information system(GIS) and remote sensing coupled with AI are discussed in this chapter.Not Availabl

Weakly Coordinating, Ketone-Directed Cp*Co(III)-Catalyzed C–H Allylation on Arenes and Indoles

Weakly coordinating, ketone-directed, regioselective monoallylation of arenes and indoles is reported using a stable and cost-effective high-valent cobalt­(III)-catalyst to access several important molecular building blocks. The allylation proceeds smoothly with a variety of substrates in the presence of various electron-rich and -deficient substituents. The method was applied to the formal synthesis of an ancisheynine alkaloid, a highly conjugated azatetracene, and isochroman. The mechanistic study reveals that the allylation reaction follows a base-assisted intermolecular electrophilic substitution pathway