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On two theta function identities of Ramanujan
Get PDFOn page 310 of his second notebook, Ramanujan recorded two theta function identities. B. C. Berndt proved them by the method of parameterization. The purpose of this article is to give an elementary proof for those two identities and also we have obtained two theta function identities which are analogues to the identities of Ramanujan. Further, we establish two distinct formula for 3-core partitions in terms of divisor function
Developing of semi-transparent alpha-Fe2O3/Cu2O heterostructures with S-scheme photocatalytic activity and biological interests
No full textThe scarcity of water has been an outgrowing problem, while population is increasing so is the demand for the water. Hence conservation of water is most important and this material might bring in drastic changes in recycling the wastewater into portable ones. The alpha-Fe2O3/Cu2O is a desirably tailored nanomaterial synthesized using eco-friendly cost-effective hydrothermal method, where alpha-Fe2O3 and Cu2O were synthesized separately and later combined to produce an effective material. The material are characterized using advanced techniques like XPS, HR-TEM, XRD, FT-IR, BET, UV-DSR, ESR, LC-MS, ICP-AES, and UPS to understand complete morphology and functioning of the material. They are examined for various application in different fields such as dye degradation, heavy metal removal and organic pollutants elimination via photocatalysis under solar irradiation. The alpha-Fe2O3 and Cu2O had the work function of 6.10 and 5.49 eV respectively and band energy of 1.46 and 2.6 eV. Docking analysis was carried out to know the protein docking efficiency. Biocompatibility of the materials is addressed upon the HeLa cell line and alpha-Fe2O3/Cu2O exposure causes inflammation in the lung fluids in a mouse model using the Bronchoalveolar lavage (BAL) assay at high concentrations, proving that the materials can help with current and future biological applications
Parametric estimation of location and scale parameters based on ranked set sampling with unequal set sizes
No full textRanked set sampling with unequal set sizes (RSSU) are some of the important variants of ranked set sampling with equal set sizes (RSS). The sets that arise naturally in many applications are typically of different set sizes. One may prefer to use the largest sets available naturally along with the smaller sets rather than an attempt to form artificial equal-sized sets. This article develops maximum likelihood estimators for the location-scale family of distributions based on ranked set sampling with unequal set sizes (RSSU). The closed form expressions for MLE under RSSU do not exist, we have proved the existence of MLE for location and scale parameters for some standard distributions for RSSU data. It is proved that MLE based on MedRSSU are more efficient than their counterparts based on SRS for some standard distributions for location-scale parameters. It is also shown that asymptotic efficiencies of the MLE based on MedRSSU are considerably better than those of the estimators based on RSS with the same number of observations. A simulation study is conducted to compare the performances of the MLE's from RSS and MedRSSU with the corresponding SRS estimators when the underlying distributions are normal and logistic
Assessment of probiotic and antifungal activity of Lactiplantibacillus plantarum MYSAGT3 isolated from locally available herbal juice against mycotoxigenic Aspergillus species
No full textThis study investigated the antifungal activities of probiotic bacteria isolated from traditional herbal juice, which was a blend of Tulsi, Mint, Bael and Indian borage leaves. About 20 isolates were obtained from the herbal juice sample; these isolates were initially screened against fungal pathogens such as Aspergillus parasiticus, Aspergillus flavus, Aspergillus ochraceus, Aspergillus carbonarius and Aspergillus fumigatus. Of the 20 isolates obtained, MYSAGT3 and MYSAGT4 exhibited potential antifungal activity against the tested fungal pathogens. Moreover, MYSAGT3 and MYSAGT4 was found to survive acidic pH and bile conditions, but were susceptible to tested antibiotics. Both the isolates exhibited 40-60% of autoaggregation ability, >90% of cell surface hydrophobicity and tolerance to 0.4-0.6% phenol. The 16S rRNA sequencing results identified the isolates MYSAGT3 and MYSAGT4 as Lactiplantibacillus plantarum. The MYSAGT3 exhibited potent antagonistic and probiotic activity compared to MYSAGT4; hence MYSAGT3 was further used for the control of Aspergillus ochraceus. Initial antifungal activity of MYSAGT3 inhibited about 76.67% growth of Aspergillus ochraceus comparatively higher than other Aspergillus sp. tested. Co-inoculation and microdilution assay revealed the high inhibitory activity of Lactiplantibacillus plantarum MYSAGT3. Further, cell free supernatant (CFS) of Lactiplantibacillus plantarum MYSAGT3 reduced the growth of fungal hyphae and conidial germination of Aspergillus ochraceus in conidial germination assay and bio preservative activity on peanuts. The CFS characterization and Liquid chromatography-mass spectroscopy (LCMS) results showed that, the antifungal activity was due to different organic acids present in the CFS of MYSAGT3. MYSAGT3 and its CFS also reduced the growth of Aspergillus ochraceus in Poultry feeds and about 21.80% of ochratoxin A (OTA) degradation was attained after 24 h of incubation with MYSAGT3. The isolated Lactic acid bacteria are able to inhibit Aspergillus ochraceus and degrade OTA in-vitro. Hence, the results suggest Lactiplantibacillus plantarum MYSAGT3 as an efficient probiotic organism and possess antifungal properties
Synthesis, structure, thermal, magnetic, dielectric properties of Ce3+doped M-type SrFe12O19 and electrochemical determination of L-cysteine
Get PDFCerium substituted SrFe12O19 with the nano composition of Sr(1-x)CexFe12O19 (x = 0.00, 0.01, 0.05 and 0.09) have been prepared using auto-combustion technique with dual fuel. The PXRD images confirmed a single-phase hexagonal crystalline structure similar to a magnetoplumbhite for all samples. Fourier transform infra-red spec-troscopy (FT-IR), field emission-scanning electron spectroscopy (FE-SEM), elemental mapping (EDS) were used to examine for the structure and morphology of the samples. The temperature dependent hexagonal phase formation and percentage weight loss was studied by thermogravimetric and differential thermal analysis (TG-DTA). Vibrating sample magnetometer (VSM) analysis confirmed that M-SrHF's are hard magnetic in nature and super paramagnetic, these are measured at room temperature. It was found that, with the increase of the dopant Ce3+ in strontium ferrites, the values of saturation magnetization (MS), remanence magnetization (Mr), coer-civity (HC) and magnetic parameters of strontium ferrites decrease. The electrochemical behavior of the SrHF's electrode and the electro-oxidation of L-cysteine was investigated using of cyclic voltammetry (CV). The best voltammetric response has been observed for a SrHF's electrode in buffer solution at pH of 7.0 with -an acquisition and scan rate of 50 mV s-1. The dielectric properties are measured in LCR meter and described based on the Maxwell-Wagner's two layer model. The electron hopping between Sr2+ and Sr3+, as well as Fe3+ and Fe2+ ions on B-sites, drives the conduction mechanism in these ferrites, these nano hexaferrites which shows its suitability in various technological applications
Rational design of a 2D TiO2-MoO3 step-scheme heterostructure for boosted photocatalytic overall water splitting
No full textThe design of step-scheme (S-scheme) heterostructure photocatalysts is a promising strategy for the high utilization of photogenerated charge carriers. Herein, a novel S-scheme two-dimensional (2D) TiO2-MoO3 heterojunction photocatalyst is fabricated by a facile electrochemical method for high water splitting photocatalytic efficiency. According to X-ray photoelectron spectroscopy (XPS) assessment, electrons are transported from TiO2 to MoO3 upon close contact, creating an internal electric field (IEF) directed from TiO2 to MoO3. Hence, upon light irradiation, the photogenerated electrons in MoO3 move toward TiO2 under the IEF effect, as revealed by EPR analysis, implying that the S-scheme heterojunction was established in the TiO2-MoO3 heterostructure and significantly promoted the separation of electron-hole pairs to enhance efficient photocatalytic water splitting. Thanks to the 2D morphology of the TiO2-MoO3 heterojunction and the significantly improved redox capability of the charge carriers in the S-scheme system, the photocatalytic water splitting efficiency of the optimized TiO2-MoO3 is higher than those of both pure MoO3 and TiO2 and commercial TiO2-P25. This study, for the first time, presents the charge transfer pathways in the TiO2-MoO3 heterostructure photocatalyst via an S-scheme system. It will shed new light on the design and fabrication of novel step-scheme heterojunction photocatalysts for overall water splitting
Pyridine coupled pyrazole analogues as lethal weapon against MRSA: An in-vitro and in-silico approach
No full textThe treatment of Methicillin-resistant staphylococcus aureus (MRSA) infections has become challenging due to the growth of multidrug resistance in the bacteria. Here we report the synthesis of pyridine-coupled pyrazoles as an antimicrobial agent against MRSA. A series of pyridine coupled pyrazoles were synthesized and synthesized compounds were characterized using FT-IR, H-1 NMR, and Mass spectroscopy. The ADMET results of all the 14 active compounds are interpreted. To identify the potent compound the synthesized compounds screened for minimum inhibitory concentrations against MRSA and compared with standard drug vancomycin. Among the synthesized compounds 6d exhibited good antibacterial activity with MIC value 21 mu g/mL, bacterial cell membrane damage study was studied potassium efflux, and cellular content leakage assay. Anticoagulant study for the potent compound also studied and validated by molecular docking and molecular dynamics simulation studies. The docking study of the synthesized compound was carried out and the study depicted that the pyridine ring of all the analogues binds with the various amino acids in the binding pocket of the active site of the Staphylocoagulase and PBP2a protein of MRSA
Poly (o-anisidine) Encapsulated K2ZrO3 Nano-core based Gelatin Nano Composites: Investigations of Optical, Thermal, Microcrystalline and Morphological Characteristics
Get PDFA series of Gelatin/poly-o-anisidine coated K2ZrO3 polymer nanocomposite were fabricated by varying the poly-o-anisidine (POA) coated K2ZrO3 viz 0, 1, 2, and 4 wt% using the solvent casting method. From High-resolution transition electron microscopy (HRTEM) results it is cleared that the average size of the prepared nanoparticles and polymer coated nanoparticles are around 18-20 and 95-100 nm respectively, and the polymer coated nanoparticles are spherical in shape, and form a core shell. The phase purity and microcrystalline behavior of the prepared nano particles, POA coated nanoparticles and gelatin nanocomposites were analyzed by using X-ray diffraction (XRD). Scanning electron microscope SEM] and energy dispersive spectroscopy EDX] were employed for the analysis of the surface morphology and the elemental composition of the prepared nanoparticles and nanocomposites. Fourier transform infrared spectroscopy (FTIR) was used to assess the physical interactions between the components in nanocomposites. The thermal stability and effect of polymer coated nanoparticles on glass transitions temperatures were studied by using Thermo-gravimetric analysis (TGA) and differential scanning calorimetry (DSC) respectively. From UV-Visible spectroscopy studies it is clear that, with increase in POA coated K 2ZrO (3) nanoparticles concentration from 0 to 4 wt % in a gelatin matrix, the band gap energy (E-g) value drops from 4.13 to 2.16 eV, and the refractive index rises from 1.529 to 3.25
Analysis of the United States’ Liability for War Crime in Afghanistan
Get PDFThere is no statistical report about the war crime committed in Afghanistan from 1978- to 2021. This paper analyzes the United States’ liability for war crimes in Afghanistan. This issue has been in public for over 20 years but has gained relevance in 2021 due to their decision to withdraw troops from the country. The Article analyzes what the ICC deems a war crime per the Rome statute. It involves a jurisprudential overview of various decisions of the ICC to develop a working understanding of war crimes. Similarly, it inquiries into specific actions carried out by the United States Government since the war in Afghanistan. Temporally this analysis is limited to the movement of the US since 2001 and will not account for actions before this date. This temporal limitation has been imposed owing to the widespread claim that the United States’ formal involvement in the “War Against the Terror” began after the attack on 11 September 2001. Henceforth, the critical research question is whether the United States can be held responsible for carrying out war crimes in Afghanistan
Syntheses and crystal structures of 4-(4-nitrophenyl)piperazin-1-ium benzoate monohydrate and 4-(4-nitrophenyl)piperazin-1-ium 2-carboxy-4,6-dinitrophenolate
No full textCrystal structures are reported for two molecular salts containing the 4-(4-nitrophenyl)piperazin-1-ium cation. Co-crystallization from methanol/ethyl acetate solution of N-(4-nitrophenyl)piperazine with benzoic acid gives the benzoate salt, which crystallizes as a monohydrate, C10H14N3O2·C7H5O2·H2O, (I), and similar co-crystallization with 3,5-dinitrosalicylic acid yields the 2-carboxy-4,6-dinitrophenolate salt, C10H14N3O2·C7H3N2O7, (II). In the structure of (I), a combination of O—H⋯O, N—H⋯O and C—H⋯O hydrogen bonds links the components into sheets, while in the structure of (II), the supramolecular assembly, generated by hydrogen bonds of the same types as in (I), is three dimensional. Comparisons are made with the structures of some related compounds