G. H. Hardy and S. Ramanujan observed that round numbers (those with prime factors repeated many times) are very rare. We seek to make the concepts of "roundedeness" and "rarity" precise by intoducing k-round numbers. We expolit density results for numbers with specified numbers of prime divisors. We discuss alternative approaches using i) normal orders of additive functions and ii) square-full numbers.

Satyavolu Srinivas Rau has taught at Chanakya University’s School of Mathematics and Natural Science since October, 2023. He is interested in Tauberian theory applied to asymptotics of Arithmetic functions and also in mathematical structures of Quantum Field Theory. He has more than 25 years of teaching experience at the Undergraduate and Postgraduate levels including varied batches in Eritrea and Libya.They cover degree programs in Mathematics,Technology,Social Sciences and Education (!) He was associated with ICFAI,Hyderabad for more than 15 years as faculty member. He worked for 9 years at North Maharashtra University ,Jalgaon (1994-2003).Prior to that he did post doctoral work for nearly 5 years at ICTP, ISI,Bangalore and as CSIR Rssearch Associate. His PhD and MPhil degrees are from the University of Hyderabad.He is an alumnus of BITS,Pilani with MSc(Hons) in Mathematics (1981) Currently Srinivas Rau handles mathematics and statistics courses for BCA, MCA and MSc(Data Science) programs.

This paper proposes an AI-based Student Emotion Recognition and Engagement Monitoring System, which analyzes the facial emotions and other relevant factors to determine the level of student engagement during online classrooms. This system uses deep learning algorithms such as EfficientNet-B0 and MobileNetV3 to recognize facial emotions and then uses a regression-based fusion model to determine the level of student engagement by analyzing the facial features and other relevant factors such as sleep time, stress level, motivation level, and screen time. This system operates in the background and provides a summary of the level of engagement of students to the teacher only, indicating the level of class and student disengagement. From the experimental results, it is clear that the fusion of the proposed system enhances the robustness of the student engagement prediction system.

The burgeoning population, coupled with the resource demand and alterations in the climatic regime, have been posing serious challenges for the sustenance of natural resources. Natural Resource Rich Regions (NRRRs) are areas endowed with abundant natural resources, which maintain ecological balance and economic activities. These regions are pivotal for supporting the livelihoods of local communities by providing essential ecosystem services and resources. However, land degradation leading to deforestation due to unplanned developmental activities has escalated the carbon footprint, aggravated the vagaries of the climate, and posed significant challenges, especially for communities reliant on fragile, arid, and semi-arid ecosystems. The nexus of socio-economic disparity, persistent poverty, and unplanned developmental activities often poses severe challenges for realizing full economic potential with environmental sustainability. Land use (LU) changes with urbanization and agricultural expansion, leading to fragmentation, habitat loss, decline of native species, and disruption of ecological processes with a potential decline of biodiversity. The arid region in the northern part of Karnataka, located in Southern India, has been experiencing a sharp decline in the groundwater table due to frequent droughts and excessive groundwater extraction. The current study unveils actionable solutions for sustainable management of natural resource-rich regions by meticulously analyzing the nexus between rapid development, LU modifications, and their subsequent environmental ramifications. LU transitions are quantified using temporal-spatial data acquired through space-borne sensors through supervised machine learning classifiers based on the non-parametric algorithm Random Forest (RF). Land use dynamics assessment reveals that paved surfaces (area under buildings, roads) have increased from 186.22 sq. km (in 1973) to 1085.12 sq. km (in 2022). The study area has degraded forest patches, and the estimation through fragmentation metrics reveals that the intact forest has shown a decline from 3252.39 sq. km (1973) to 1508.12 sq. km (2022). The forests have continuously decreased from 2,154.20 sq. km (1973) to 1,096.34 sq. km (2022). In Northern Karnataka, the prioritization of NRRRs highlights the status of resource availability, with highly resource-rich zones represented by NRRR1 (67 grids) and NRRR2 (127 grids), followed by NRRR3 (304 grids) with moderate resource potential, and NRRR4 (522 grids) encompassing areas with comparatively scarcer resources. The prioritization of natural resource-rich regions emphasizes the need for prudent land management strategies, with holistic and integrated approaches considering social, economic, and environmental issues with degrees of sensitivity across arid regions.

Tuberculosis, a widespread pulmonary disease in the world, claims millions of lives every year. The ever-growing demand for better treatment and care, mounting costs of treatment and negligence among the patients is also a concern. In the view of modern medication and its side effects, literature suggests use of medicinal plants in the treatment of Tuberculosis. The Sacrificial fire therapy (Yajna) or the Ethnobotanical inhalation therapy is a prominent method in Ayurveda to treat pulmonary diseases. Studies have shown the sacrificial fire therapy to be effective in curing Neurological disorders too. In this process, parts of Ayurvedic medicinal plants are selected in specific proportions, sublimated, and evaporated and the components released have exhibited the potential to treat Tuberculosis. This paper explores an idea that can help against antibiotic resistance and analyses the effect on microorganisms and seems a possible option to use it as a complimentary medicine to the humankind.

Right from the dawn of civilisation, every society had this problem: How to save food for the proverbial rainy days - safe from microbes and insects out to spoil it. The ancient Indian wisdom of preserving food, both perishable and non-perishable, has survived for centuries. Based on wisdom passed through generations, our ancestors practised several food preservation methods. For several years, these methods were on the decline. However, of late they are staging a comeback with necessary modifications. Regardless of the recent advances in modern food storage technologies, the revival of low-cost, readily available, environment friendly ancient food storage methods appear to be a promising option to minimise the post- harvest losses. Understanding the science behind these traditional practices and improvising them to make them relevant in the present context is the need of the hour as borne out by the studies we conducted in different climatic conditions of India. We studied the various food preservation methods prevalent in these regions and reviewed their potential for modern times. There is no doubt that traditional storage methods, when appropriately modified, can significantly reduce losses and contribute to increased food security and poverty alleviation by increasing the returns of smallholder farmers.

Dr. Ramakrishna Pejathaya has a doctorate from the Rashtriya Sanskrit Vidyapeetha (RSVP), Tirupati, for his research on the medieval text on astronomy Siddhāntaśekhara of Śrīpati and its influence on later astronomers. He has been actively involved in teaching Jyotiṣa, Sanskrit literature, Indian Knowledge Systems and Poetics since 2007. Ramakrishna holds a Vidvat degree in Triskandha Jyotiṣa which he studied traditionally along with Sāhitya and Siddhānta Kaumudī at SMSP Sanskrit College, Udupi. He has several research papers and books to his credit. He has also produced study material for the texts Jātakālaṅkāra, Janmapatradīpakam and Bhāskarīya Bījagaṇitam. He was a co-investigator for the encyclopaedia project Jyotiṣaviśvakoṣaḥ undertaken by SMSP Sanskrit Research Centre, Udupi. The output has been published in nine volumes by the centre. He as a Principal Investigator is now in the revising process of a research project Idiomatic expressions from classical Sanskrit plays funded by Samskrit Promotion Foundation. Currently, Dr. Pejathaya serves as Associate Professor in the Centre for Indian Knowledge Systems at Chanakya University. During his service at Chinmaya Vishwavidyapeeth he was the Program Director of MA Sanskrit and the founder Director of the Centre for Avadhanām, a joint initiative of Chinmaya Vishwavidyapeeth and Indic Academy. He has designed several innovative courses. Noteworthy of them are Kauṭilya and Public Finance Administration, Puruṣārthas: Perspectives from Mahābhārata, Life Lessons from Bhagavad Gītā and Avadhāniśikṣā. He is also a member of academic bodies such as the Academic Council and Board of Studies at several institutions. Dr. Ramakrishna is one of few practitioners of the art of Avadhānam in Sanskrit and classical Kannada. He has performed more than 25 Aṣṭāvadhānas till date in different parts of the country including Udupi, Sringeri, Bengaluru, Ernakulam, Calicut, Tirupati, Somnath, Prayag Raj and Varanasi.

Hinduism is considered unique in the world of religions since it had no founder yet grew gradually over five thousand years, absorbing, assimilating, and guiding all other faiths to bear the cultural heritage of India. Hinduism has no Bible/Koran/Dhammapadam to find potential solutions for problems. Hinduism clarifies the differences and shared beliefs of different schools of thought within it, thus resembling Christianity binding human civilization with a common thread. There is no historical creator of Hinduism as in Jainism, Buddhism, and Sikhism. According to the literature (Hindu text, the Bhagvad Gita), relationships of human/nature (yagna), human/divine (tapas), and human/human (dana) are conceptualized to stitch human beings and nature through soil, soul, and society. This suggests a high level of realization to connect these three to have a harmonious relationship with nature and sustain human civilization. All religions address soils differently and portray diverse cultural patterns of understanding this valuable natural resource. According to Hindu religious belief, soil (matter, nature) is considered divine and respected as Mother. Soil is seen as a feminine donor, attributed predominantly to chthonic (Ancient Greek word: khthon, which means earth or soil). In Hinduism soil is referred as dharti/bhoo mata: Mother Earth is also related to cosmic elements. In Buddhism, the soil is described as a symbol of dust in this ephemeral world to support life. Humans belong to nature, and when they cultivate soil, it always reverberates in their mind. To relate humans with soils, two different types of religious concepts, namely natural religion and salvation religion are postulated. During the long history of human civilisation with primal religion (Primal religion has a priority where the fundamental aspect of religion is available). Being dominant, the soil is considered supernatural and controlled by an unseen power. Soils are part of religious reverence, justifying certain rituals to sustain their fertility. However, the modern-day approach to soils takes environment, ethics, and ecology as more essential aspects. Human ecology is related to human concepts of nature and destiny (religion). Hindu religion always considers land/soil as mother earth, cautioned about its use and abuse, and recommends its preservation for posterity. Given this, Hinduism and other religions such as Jainism, Buddhism, and Sikhism and their concepts indirectly believe in the environment and ecological sustenance. They are in line with the modern-day vision.