Journal of Applied Science and Education (JASE)

Neutrix Convolution of Ultra-Distributions Product and Distributions on C^∞-Manifolds

Chinta Mani Tiwari — 2024-07-25

The absence of a general definition for convolutions and products of distribution is one of the issues with distribution theory. It is discovered in quantum theory and physics that certain convolutions and products such as 1/x + δ are in usea description of the term "product of distributions" and a list of sample product results using a particular delta sequence δ_n (x)=C_m n^m ρ(n² r² ) in an m-dimensional space. The Fourier transform is applied to D' (m) and the exchange formula for defining ultradistribution convolutions in Z' (m) in terms of products of distributions in D' (m). We are going to demonstrate a theorem that says that for any items f ˜ and g ˜ in Z' (m), the neutrix convolution f ˜⊗ g ˜ exists in Z' (m) if and only if the product f∘g exists in D' (m). Some convolutional findings are derived using van der Corput's neutrix calculus. Let V'(M) be a smooth m-manifold M's space of distributions, each specified by an assemblage of 'compatible' ordinary distributions (components) displayed on the charts of some C^∞ on M. Drawing on van der Corput's concept of neutrix limitations, we expand the definition of the neutrix distribution product in this context. onto the space V'(M). We establish the existence of certain theorems regarding the neutrix distribution product in the space V'(M) under various assumptions on the neutrix product of the constituents.

Comparative Study of Systematization Procedures Applied to K-level Electron Binding Energies in X-ray Spectra

Garima Misra — 2024-07-25

X-ray and photoelectron spectroscopic studies have led to the measurement of accurate K level binding energy values in atoms. Since these experiments are conducted at various laboratories all over the globe using different instruments, there is every possibility that the results deviate from reality more than the probable errors. Consequently when these energy values are used for some other applications, their results obtained will be different from what is being expected. Therefore these energy values need to be systematized and corrected for errors if any. Various systematization procedures available in X-rays spectroscopy are (i) Mosley Law (ii) Modified Mosley Plot (iii) Hagstrom doubly modified Mosley plot (iv) Iterative self-consistent doubly modified Mosley plot. A detailed comparative study of all these systematization procedures is performed as applied to the K level binding energies with a view to ascertain their applicability for the purpose.

Spam Detection Using Natural Language Processing

Aditya Srivastava — 2024-07-25

In the digital age, where digital communication is omnipresent, the issue of spam remains pervasive, undermining the quality of user experiences, compromising cybersecurity, and posing significant challenges. This research paper is a comprehensive exploration of "Spam Detection Using Natural Language Processing". We traverse a multifaceted journey through the realms of spam detection, dissecting its crucial components and implications. Our investigation commences with data collection and preprocessing, discussing the intricacies of gathering diverse datasets and transforming them into analysable forms. Feature engineering takes center stage as we unveil the pivotal role of engineered features in distinguishing spam from legitimate content. Model building and evaluation form the core of spam detection, and we scrutinize various algorithms, techniques, and metrics that drive the development of effective spam detection systems. Challenges loom large in spam detection, from imbalanced datasets and evasion tactics to the perpetual struggle for false positive-false negative equilibrium. Privacy concerns and the legal landscape add further layers of complexity. Real-world applications span the gamut, encompassing social media moderation, review systems, chat applications, and more. We unearth how spam detection safeguards user interactions, maintains quality, and secures digital ecosystems across these diverse platforms. Finally, we gaze into the horizon of spam detection's future, envisioning trends such as deep learning dominance, multimodal detection, adversarial defense, and blockchain authentication. This research paper is a compendium of insights, strategies, and prospects, providing a holistic view of spam detection in the dynamic digital age.

Function of Fractional Calculus and Relationship Between Distribution Theory and Partial Differential Equations

Shilpa Pal — 2024-07-25

Partial Differential Equations are fundamental mathematical tools used to model physical phenomena across various disciplines such as physics, engineering, and economics. Solving PDEs often involves the concept of distributions, which extends the classical notion of functions to more generalized objects. This paper provides an introduction to PDEs, outlines the basic concepts of distribution theory, and discusses their interplay in solving PDEs. and distributional derivatives its convergence with distributional solution with space D^' (Ω) its extended form with weak derivatives.

Graphene Quantum Dots: Sustainable and Greener Synthetic Approaches

Garima Joshi — 2024-07-25

Honeycomb crystal lattice graphene has proved to be a subject of a great deal of investigation over the previous decades owing to its intriguing electrical, optical and physical properties. Graphene identification imparts a significant lift and vital dimensions to nanotechnology and materials science. Graphene quantum dots (GQDs), a nanomaterial with zero dimensions (0D) demonstrated encouraging potential in biomedicine because of their really tiny and harmless nature, water solubility, outstanding biological compatibility, adjustable fluorescence, and photo resilience thereby gaining a great deal of interest in the biomedical sector. GQDs wide bandgap and their flexibility to engineer its bandgap over an extensive range and carrier selectivity play a major role in catalysis and energy applications. There are wide range possibilities for new applications due to their unique structure – related features such as optical, electrical, physiochemical qualities and exceptional biocompatibility when compared to other nanomaterials. They have gained tremendous attention along with other graphene derivatives in the last few years. Therefore, the development of GQDs became a remarkable catalyst for the utilization of graphene. Top down as well as bottom-up methodologies are applied for production of GQDs. Sustainable synthesis of GQDs has a variety of advantages, including the least cost and noncorrosive material, faster reactions, environmentally conscious resources, and simpler post-processing procedures than with synthetic methods. In this review, we have compiled a few of the green methods utilized by various research groups worldwide, for the green synthesis of GQDs and some of its biomedical applications.

Advances in Synthesis Approaches and Biological Applications of Silver Nanoparticles: A Systematic Review

Prakash Chandra Dhabas — 2024-07-25

The need for silver nanoparticlesor AgNPs is rising quickly across a wide range of industries, including healthcare, pharmaceuticals, food, cosmetics, and medicine. Owing to its many functions, it has been applied in a variety of settings, including the food industry, medical devices, housekeeping, wound dressing, orthopaedics, and diagnostics. It has also been utilised as an anticancer agent. These microscopic particles can potentially be put to use for a plenty of purposes and have the ability to alter their physical, chemical, and biological properties. Three discrete approaches emerge for preparing AgNPs: chemical, biological, and physical. Of the three approaches, the biological approach is proven to be the most straightforward, environmentally friendly, marketable, and one-step procedure; it also requires the least amount of force, high pressure, or temperature. Ag NPs have been shown to halt the expansion and proliferation of numerous bacteria by linkingAg/Ag+utilizing the biomolecules that thrive in the cells of microbes.