Author name: EarthCanvas

Akshay Kumar Vyash, Ram Milan Singh ABSTRACT Dihedral groups, the symmetry groups of regular polygons, are a foundational pillar of group theory, historically pivotal in geometry, crystallography, and algebra. This paper introduces the “rotational-reflection cascade,” an innovative decomposition technique that reveals previously obscured algebraic properties of dihedral groups, particularly for large orders. We present a suite of original results on element representations, subgroup distributions, and conjugacy classes, rigorously validated through computation and enriched with visually captivating, multi-colored diagrams. These theoretical advancements fuel an extensive exploration of applications, spanning robotic motion optimization, digital art pattern synthesis, crystallographic lattice design, cryptographic key generation, and rotational dynamics in physics. By integrating precise mathematics, striking visualizations, and practical implementations, this work redefines the study of dihedral groups, offering fresh insights and broad interdisciplinary relevance. Keywords: Dihedral groups, Group theory, Symmetry, Rotational-reflection cascade, Subgroup structure, Conjugacy classes, Robotics, Digital art, Crystallography, Cryptography, Physics, Visualization.

Manoj Ughade, Rahul Vishwakarma, and Manoj Kumar Shukla ABSTRACT We develop a mathematical fixed-point framework to study stress propagation in financial networks that combines interbank exposures and liquidity-induced market impact. By defining a stress-propagation operator on the space of institution-level stress vectors, we derive a sufficient, economically interpretable inequality that guarantees the operator is a contraction in the supremum norm. Through the Banach fixed-point theorem, we obtain rigorous existence, uniqueness, and geometric convergence results for the systemic-stress equilibrium. Explicit constants, detailed proofs, sensitivity analysis, and two real-world style applications a small banking contagion network and a portfolio-liquidity feedback model are presented. Numerical illustrations confirm convergence and provide insights into systemic stability under liquidity stress. Keywords: Banach contraction principle; fixed point; financial networks; liquidity risk; market impact; systemic stability.

सुश्री इंदु सिंह ‘इंदुश्री’ (59-62) साराशं यह शोध पत्र ब्रेस्ट आयरनिंग (स्तन इस्त्री) की अमानवीय और कम रिपोर्ट की गई प्रथा का आलोचनात्मक विश्लेषण प्रस्तुत करता है। यह प्रथा, जो मुख्य रूप से पश्चिम और मध्य अफ्रीका के कुछ हिस्सों, जैसे कैमरून, नाइजीरिया, चाड और बेनिन से संबंधित है, वैश्विक प्रवास के साथ यूके जैसे विकसित देशों में भी फैल गई है। इस क्रूर प्रक्रिया में युवा, अल्पवयस्क लड़कियों के स्तन ऊतक (breast tissue) को विकसित होने से रोकने के लिए गर्म वस्तुओं (जैसे पत्थर या स्पाटुला) से दागा जाता है। चौंकाने वाली बात यह है कि इस कृत्य के पीछे का उद्देश्य लड़कियों को यौन उत्पीड़न, बलात्कार और कम उम्र में गर्भावस्था से ‘बचाना’ होता है। संयुक्त राष्ट्र के अनुसार, यह प्रथा विश्व स्तर पर लगभग 3.8 मिलियन लड़कियों को प्रभावित करती है और इसे लिंग आधारित हिंसा के तहत ‘अंडर-रिपोर्टेड क्राइम’ की श्रेणी में रखा गया है। यह विश्लेषण स्थापित करता है कि यह प्रथा पुरुषों के दुराचार पर नियंत्रण लगाने के बजाय, पितृसत्तात्मक मानसिकता के कारण पीड़ित पर ही अत्याचार करने का एक वीभत्स परिणाम है, जिसके गंभीर शारीरिक और मनोवैज्ञानिक दीर्घकालिक परिणाम होते हैं। इस शोध का निष्कर्ष है कि इस कुप्रथा के दमन के लिए वैश्विक जागरूकता और पितृसत्तात्मक संरचना के खात्मे पर ध्यान केंद्रित करना आवश्यक है। शब्‍द कुंजी: ब्रेस्टआयरनिंग, लड़कियाँ, पितृसत्तात्मक

डॉ. रानी कुमारी (43-49) साराशं भारतीय स्वतंत्रता आंदोलन में बंगाल की महिलाओं का योगदान अत्यंत महत्वपूर्ण और प्रेरणादायी रहा है। सामाजिक रूढ़ियों और पितृसत्तात्मक प्रतिबंधों को तोड़ते हुए इन महिलाओं ने न केवल राजनीतिक आंदोलन में भाग लिया बल्कि बौद्धिक, सांस्कृतिक और सामाजिक क्षेत्रों में भी उल्लेखनीय भूमिका निभाई। लीला रॉय ने महिला शिक्षा, मताधिकार, आत्मरक्षा प्रशिक्षण और क्रांतिकारी संगठनों में सक्रिय भूमिका निभाई। कल्पना दत्ता, प्रीतिलता वादेदार और नानीबाला देवी जैसी क्रांतिकारी महिलाओं ने सशस्त्र संघर्ष में प्रत्यक्ष भागीदारी की तथा ब्रिटिश सत्ता को चुनौती दी। वहीं बेगम रोकेया ने महिला शिक्षा, नारीवाद और मुस्लिम महिलाओं के अधिकारों के लिए आजीवन संघर्ष किया। बसंती देवी, सरला देवी चौधरानी, कमला दास गुप्ता और लबन्या प्रभा घोष ने समाज सुधार, असहयोग, सविनय अवज्ञा तथा भारत छोड़ो आंदोलन में सक्रिय योगदान दिया। सुनीति चौधरी, सुहासिनी गांगुली और वीना मजूमदार ने महिलाओं के संगठन, शिक्षा, सामाजिक सुधार और राष्ट्रीय आंदोलनों में अपनी महत्वपूर्ण भूमिका निभाई। इन सभी महिलाओं ने अपने त्याग, साहस और नेतृत्व से सिद्ध किया कि भारत की स्वतंत्रता केवल पुरुषों का संघर्ष नहीं था, बल्कि महिलाओं ने भी कंधे से कंधा मिलाकर स्वतंत्रता और सामाजिक परिवर्तन की दिशा में महत्वपूर्ण योगदान दिया। उनका यह योगदान आज भी प्रेरणा का स्रोत है। शब्‍द कुंजी: महिला सशक्तिकरण, बंगाल की स्वतंत्रता सेनानी, क्रांतिकारी आंदोलन, नारी शिक्षा एवं अधिकार, सामाजिक सुधार

Dr. Divya Patel, Preeti Kourav, Pooja Patel (43-49) ABSTRACT Madhya Pradesh, India’s second-largest state by area and fifth most populous, has emerged as a national exemplar in sustainable municipal solid waste (MSW) management. Over the past decade, the state has implemented a multi-tiered strategy combining large-scale infrastructure, public–private partnerships, and community-based interventions. Key developments include a 6 MW waste-to-energy facility in Rewa; Bhopal’s attainment of a 7-star Garbage Free City rating; and Indore’s Devguradia GOBARdhan plant Asia’s largest MSW-based Bio-CNG facility producing 17,000 kg of Bio-CNG per day. Plastic recycling capacity has expanded more than threefold, with approximately 2.8 lakh metric tonnes processed in 2021–22 through granulation, cement co-processing, and road construction applications. Complementing these technological advances are grassroots initiatives such as Jhabua’s waste-derived public art and Chhindwara’s extensive NADEP composting programme involving 68,000 participants across 1,900 villages. Collectively, these interventions illustrate a robust “waste-to-wealth” paradigm that integrates technological innovation, participatory governance, and supportive policy frameworks. Madhya Pradesh’s experience provides a significant case study for scalable, integrated MSW management in rapidly urbanizing regions. Keywords: Municipal solid waste, waste-to-energy, waste-to-wealth, MSW management.

Dr. Pankaj Choubey, Prof. Mamta Patel (29-42) ABSTRACT regardless of age, religion, education level, marital status, or sexual orientation. The aim of this study is to analyze the victim- offender relationship and the attitudes toward premarital sex of offenders. This study was carried out at Eleven Central Prisons in Madhya Pradesh, India. The Non-Probability sampling design used the Purposive sampling method to collect the data. The tools used for the research work were the interview schedule and the sexual attitude scale. In 46.5 percent of cases it was found that the victims were known persons and already knew the offender. The reason behind in most of the cases, the offender used to make the children the victims. 1.75 percent of the cases, the level of sexual behavior of the offenders towards premarital sex relations were very high. From this, it can be concluded that this behavior was due to context of pre-marriage, live-in relationships and love affairs with the victim. Revenge against the victim by the offenders and conflict with the victim’s family, which included temptation of the victim to marry, etc. Change in the behavior of offenders can be brought through various corrective programs being run in the prison. Vocational training, yoga, meditation and other activities change the convicts’ attitude inside the prison. Keywords: Offenders, Sexual Attitudes, Pre-Marital Sex. Live-in-relationship.

Dr. Dinesh Kumar Dahare (24-28) ABSTRACT Urban vegetation plays a vital role in regulating microclimate of adjoining areas, also mitigating heat island effects, and improving eco-sociological resilience in rapidly urbanizing cities. In Bhopal, the Capital Project Administration (CPA) has carried out extensive plantation programs for restoring green cover and enriching urban thermal relief. This research paper appraises the role of CPA plantations in reforming vegetation patterns and upgrading microclimatic parameters such as air and surface temperature, humidity, soil moisture, and wind flow. The paper synthesizes scientific mechanisms underlying vegetation–microclimate interactions and proposes a methodological framework for microclimate assessment using field monitoring, GIS-based analytics, and remote sensing. Findings from past research studies suggest that urban plantations can reduce air temperature by 1–3°C, lower surface temperatures by 3–15°C, increased relative humidity, and strengthen human thermal reassurance. The analysis pinnacles the importance of plant species selection, multi-layered plantation patterns, and maintenance strategies for Bhopal’s sub-tropical climate. Overall, the study shows that CPA’s plantation programmes have made noticeable, positive differences in the microclimate of nearby areas and contribute meaningfully to the city’s long-term environmental sustainability. Keywords: Microclimate, resilience, assessment, reassurance, sustainability.

Dr. Veena Raparthi, Dr. Durgesh Kurmi, Dr. Kethoori Venkatesh (9-23) ABSTRACT Floods in India annually result in numerous fatalities and substantial economic damage, making flood monitoring essential for understanding their patterns and characteristics to aid in mitigation efforts.  This study investigates the impact of extreme rainfall events at the Khammam district. Some areas in Khammam received over 20cm of one-day rainfall, resulting in substantial Inundation of 100 villages, cropland and 5 fatalities. The research aims to Map the flood event using Sentinel-1 SAR data and quantify the impact on different land cover classes. The study used Sentinel-1 Synthetic Aperture Radar (SAR) data and Google Earth Engine (GEE) to map and analyze flood inundation patterns. SAR is crucial for flood hazard mapping and monitoring because it can image the Earth’s surface regardless of weather conditions or time of day. The findings show that 25684 hectares of land were inundated, representing 5.7% of the study area, with croplands being the most affected (24710 hectares), followed by rangeland (138.39 hectares). Built-up areas also experienced inundation, affecting 154 hectares of infrastructure. The study highlights the vulnerability of agricultural livelihoods to extreme weather events and underscores the importance of using remote sensing technologies like SAR for accurate and timely flood monitoring. The insights from this research can inform better flood management and mitigation strategies, emphasizing the need for effective disaster management, Climate Resilient planning, and sustainable agricultural practices. Keywords: Flood Inundation, Sentinel-1 SAR, Google Earth Engine, Land Use Land Cover and Disaster Management,

Dr. Bhanu Pratap Nayak (1-8) ABSTRACT Food and nutrition security is still a major concern, especially in areas where people do not get enough protein and essential nutrients. Bamboo shoots are traditional forest foods that can help improve nutrition because they are rich in important nutrients. This study explores the nutritional value and fortification potential of bamboo shoot powder (BSP) made from Dendrocalamus strictus, a common bamboo species found widely in Central India, especially in Chhattisgarh. Fresh bamboo shoots were cleaned, boiled to remove natural toxins, dried, and made into powder. The nutritional analysis showed that D. strictus BSP contains high protein, high fibre, useful minerals, and very little fat. These qualities make it a good natural ingredient for improving the nutrition of everyday foods. Using BSP in snacks, bakery items, and other food products can help increase nutrient intake and reduce hidden hunger. Overall, D. strictus bamboo shoot powder is a safe, affordable, and nutritious option that can support better health, help local communities, and promote the sustainable use of forest resources. Keywords: Bamboo shoot powder; Dendrocalamus strictus; Food fortification; Nutritional security; Functional foods; Non-timber forest products (NTFPs)