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    Crossed out modular equations of degree 11 of Ramanujan

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    In this paper, we confirm two modular equations of degree 11 of S. Ramanujan which were crossed out by him on page 244 of his second notebook

    Leap Eccentric Connectivity Index of Subdivision Graphs

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    The second degree of a vertex in a simple graph is defined as the number of its second neighbors. The leap eccentric connectivity index of a graph M, L xi(c)(M), is the sum of the product of the second degree and the eccentricity of every vertex in M. In this paper, some lower and upper bounds of L xi(c)(S(M)) in terms of the numbers of vertices and edges, diameter, and the first Zagreb and third leap Zagreb indices are obtained. Also, the exact values of L xi(c)(S(M)) for some well-known graphs are computed

    A Simple Method for Fabrication of Self-sharpened Silicon Tips for Atomic Force Microscopy Applications

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    A simple and high yield method is presented for the bulk generation of atomic force microscopy (AFM) probes with self-sharpened silicon tips. The experimental setup includes a controlled chemical etching environment at a constant temperature with continuous recirculation and filtration. A KOH solution is considered cost-effective as the etchant and stabilized to the required concentration (55%, v/v) and temperature (40 degrees C), so as to provide an etch rate of 40 nm min(-1) and yield a smooth etch profile. A high density of silicon tips is fabricated, with yield up to 90%, and a consistent tip radius of approximate to 12.73 +/- 1.51 nm. These tips can be successfully integrated with AFM cantilevers, resulting in AFM probes. Further, such AFM-probes are well characterized using laser Doppler vibrometry and scanning electron microscopy. The result shows a resonance frequency of 1.2-1.4 MHz and a high-quality factor of approximate to 708.8. In addition, the AFM probes produced images are comparable in quality to those obtained from commercially available probes

    Redesigning Mysore University Library into Green Library: A Viability Study

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    Green Library concept is gaining importance in this decade. Though existing university libraries cannot be re-build according to the LEED or IGBC standard, by adopting few technologies libraries can be redesigned to reach the Green library standard. The present article discusses on the implementation of Green Library concepts on the various sections of Mysore University Library. This study has suggested few methods towards implementation of Eco friendly atmosphere in the library

    Crystal-structure studies of 4-phenyl­piperazin-1-ium 4-eth­­oxy­benzoate monohydrate, 4-phenyl­piperazin-1-ium 4-meth­­oxy­benzoate monohydrate, 4-phenyl­piperazin-1-ium 4-methyl­benzoate monohydrate and 4-phenyl­piperazin-1-ium tri­fluoro­acetate 0.12-hydrate

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    In this study, four new piperazinium salts, namely, 4-phenyl­piperazin-1-ium 4-eth­oxy­benzoate monohydrate, C9H9O3·C10H15N2·H2O (I); 4-phenyl­piperazin-1-ium 4-meth­oxy­benzoate monohydrate, C10H15N2·C8H7O3·H2O (II); 4-phenyl­piperazin-1-ium 4-methyl­benzoate monohydrate, C10H15N2·C8H7O2·H2O (III); and 4-phenyl­piperazin-1-ium tri­fluoro­acetate 0.12 hydrate, C10H15N2·C2F3O2·0.12H2O (IV), have been synthesized. The single-crystal structures of these compounds reveal that all of them crystallize in the triclinic P[\overline{1}] space group and the crystal packing of (I)–(III) is built up of ribbons formed by a combination of hydrogen bonds of type N—H⋯O, O—H⋯O and other weak inter­actions of type C—H⋯O and C—H⋯π, leading to a three-dimensional network. In the crystal of (IV), the cations and the anions are connected by C—H⋯O, N—H⋯O and C—H⋯F hydrogen bonds and by C—H⋯π inter­actions, forming sheets which in turn inter­act to maintain the crystal structure by linking through the oxygen atoms of water mol­ecules and van der Waals inter­actions, giving the whole structure

    India and Afghanistan’s Time-Tested Friendship in the Shadow of History

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    Afghanistan is a key state from a geopolitical and geostrategic perspective. "Central Asia, the Middle East, and South Asia" may all be reached through Afghanistan. The world powers attempted to expand their sphere of influence in Afghanistan to gain more sway over this region, but their efforts failed, as history attests. It has been established that Afghanistan is the resting place of invaders. India made every effort to grow its influence in Afghanistan. Afghanistan has occasionally been identified as the hub of Indian civilization. India and Afghanistan have a close bond, and based on shared history and culture, India has been and will continue to be a dependable partner in Afghanistan's development and reconstruction endeavors. The main goals of India's development assistance have been to improve the institutions and people of Afghanistan's ability to govern themselves, provide public services, construct socio-economic infrastructure, ensure people's safety, and support their ability to earn a living. Afghanistan's connectivity and free and open access to transit for all goods have been reaffirmed, and India and Afghanistan have also agreed to identify goods and methods to improve bilateral commerce. The study employed a normative approach and examined the relationship between India and Afghanistan which relied on historical and cultural ties. The study is a glance that highlighted the contribution of India toward the reconstruction of Afghanistan for two decades

    India is an Incredible Place for Education: A Cursory Glance

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    India, from ancient times, has been a center of higher learning as it is one of the oldest civilizations in the world. Historically, Universities and libraries were a big part of the Indus Valley Civilization. The two famous ancient universities of India and the oldest universities in the world are Takshashila (Taxila)and Nalanda. Nalanda was established in the fifth century AD in Bihar, India, and survived circa 1200 AD. It was devoted to Buddhist studies and trained students in fine arts, medicine, mathematics, astronomy, politics, and the art of war. Ancient Taxila or Takshashila, in ancient Gandhara, was an early Hindu and Buddhist center of learning

    Impact of Online Banking on Financial Performance of Commercial Banks in Afghanistan

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    This study's primary objective was to examine the effects of online banking on Kabul commercial banks' financial performance. While addressing financial performance and online banking, the following question can be pondered. What is the impact of online banking on the financial performance of commercial banks in Afghanistan? Furthermore, the primary data were examined by using SPSSv.24's descriptive and regression methods. In addition, different regression assumptions, estimating methods, specification checks, and other tests were performed on econometric models. According to the findings of random effect regression analysis, capital sufficiency and cost-effect were closely related to banks' financial performance. The study finds that online banking boosts the financial performance of commercial banks in Afghanistan. Inversely, there is no statistically significant correlation between the financial success of banks in Afghanistan and online banking or bank size. Additionally, there is a plethora of literature and studies on contemporary online banking and financial performance in different countries, However, there is no study on the implication of online banking on the financial performance of financial banks in Afghanistan. Furthermore, the present study found no banking law in Afghanistan to deal with financial technology, digital currency, and online banking. Hence, the present study is expected to enrich the knowledge of online banking and financial performance in the commercial bank of Afghanistan

    The regioselective synthesis of 2,5- and 4,5-disubstituted thiazoles via the cyclization of 2-oxo-2-(amino)ethanedithioates with isocyanides

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    The regioselective synthesis of 2-(methylthio)-N-aryl/alkylthiazole-5-carboxamides and ethyl-5-(aryl/alkyl carbamoyl)thiazole-4-carboxylates was carried out via the base-induced cyclization of methyl-2-oxo-2-(amino)ethanedithioates with TosMIC and ethyl isocyanoacetate, respectively, with high yields. The regioisomeric products were confirmed based on X-ray diffraction studies. An advantage of the present method is the wide-ranging isocyanide reactivity compared to earlier protocols, while the catalyst-free nature and rapid reaction times are noteworthy features

    Structural, Optical, Spectral, Thermal and Third-Order Nlo Behaviour of 4-Chlorobenzhydrazide Trichloro Acetate Single Crystal

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    Hirshfeld surface analysis and molecular structure determination of 4-chlorobenzhydrazide trichloro acetate (4CBTCA) single crystals has been grown by the slow evaporation method at room temperature. The title compound was confirmed by single and powder X-ray diffraction studies. The determination of the single crystal structure establishes that the title compound associate with the triclinic system with the space group P 1¯¯¯. Powder XRD affirmed the crystalline nature of the crystal. The molecular structure and existence of the vibrations were revealed by NMR experiments. The identity of distinct functional groups of title of the compound was determined by FT-IR and FT-Raman spectral analyses. UV–Vis–NIR analysis was performed to examine the optical property of the grown crystal, and the maximum absorbance wavelength is realized at 390 nm. This study discusses the 4-chlorobenzhydrazide trichloro acetate crystal and demonstrates blue and green emissions at 440 and 544 nm. The thermal behaviour of the (4CBTCA) was studied by thermo-gravimetric analysis (TGA), differential thermal analysis (DTA) and differential scanning calorimetry (DSC). Third-order nonlinear refractive index and nonlinear absorption coefficient have been determined by the third-order NLO studies

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