All articles
199 articles
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The Role of Symmetry in Topological Insulators and Superconductors
Abstract: Topological insulators and superconductors constitute a class of quantum materials characterized by insulating bulks and symmetry-protected conducting boundaries. Symmetry principles, notably time-reversal (TRS), particle-hole (PHS), and chiral symmetry, play a fundamental role in determining the topological phases and their classification within the Altland-Zirnbauer scheme. TRS protects gapless surface states in topological insulators, while PHS stabilizes Majorana modes in topological superconductors. Symmetry-protected topology extends this framework by considering partial symmetry breaking, …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 01–05 Read article
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Symmetry Breaking in Mathematical Models: Bifurcation, Chaos, and Pattern Formation
Abstract: Symmetry breaking serves as a central organizing principle in the understanding of nonlinear systems across physics, biology, chemistry, and engineering. When a system transitions from a symmetric state to an asymmetric configuration, it often signals the onset of new structures, dynamic behaviors, or even chaotic regimes. This review explores symmetry breaking from the theoretical and mathematical perspectives of bifurcation theory, chaos theory, and pattern formation. We discuss how small parameter …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 25–30 Read article
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Symmetry Principles in Digital Twin Systems: Modeling, Integration, and Applications
Abstract: This systematic review comprehensively examines the burgeoning field of Digital Twin (DT) technology, analyzing its current state, diverse applications, and future trajectory. Through a rigorous methodology involving a systematic search of academic databases and relevant industry literature, this review synthesizes findings across a spectrum of disciplines. We identify the core components and underlying principles of DTs, distinguishing them from traditional simulation models by their dynamic, realtime data integration and bi-directional …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 06–24 Read article
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China’s Economic Performance (2020–2024): A Sectoral Index Analysis
Abstract: This study applies Laspeyres, Paasche, and Fisher ideal indices to China’s official 2020–2024 price and quantity data, quantifying sectoral inflation and real growth in agriculture, manufacturing, services, exports, and investment. Results show manufacturing experienced mild deflation (Laspeyres ≈ 98.7, implying ≈ 1.3% overall price decline) with a slight real output drop (~6.1%). A key driver was a sharp 21.4% fall in electric vehicle unit prices, despite +523% volume growth. Services …
Published in Research & Reviews : Journal of Statistics · Vol. 14, Issue 3, 2025 · pp. 26–38 Read article
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Artificial Intelligence Technology in Libraries: Transforming Information Access and Management.
Abstract: This article provides an extensive summary of the integration of AI technologies with library services. Examining current applications, benefits, challenges, and future trends, the discussion highlights the transformative potential of AI and advocates for the ethical implementation of execution strategies. As libraries evolve in the digital age, adopting AI in a responsible and informed manner will be crucial to maintaining their role as vital centers of knowledge and community engagement. …
Published in Journal of Advancements in Library Sciences · Vol. 12, Issue 2, 2025 · pp. 1–5 Read article
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Exploratory Analysis of the Statistical Characteristics of Nuclear Fuel Cost Trends
Abstract: Nuclear power reactors of the current fleet mainly use uranium as the fissile fuel material. The economics of nuclear fuels are mainly governed by the prices of uranium. This work is an analysis of monthly uranium price data available from public data sources, covering the time frame from January 1990 to April 2025. In the near term, from 2021 to 2024, monthly uranium spot prices have been between $ 35.28±6.64/lb …
Published in Research & Reviews : Journal of Statistics · Vol. 14, Issue 3, 2025 · pp. 39–49 Read article
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Algebraic Geometry and Mathematical Physics: An Interdisciplinary Exploration
Abstract: Algebraic geometry, a branch of mathematics that studies solutions to systems of polynomial equations, has profound implications in mathematical physics. This paper delves into the intersection of algebraic geometry and mathematical physics, exploring how concepts from algebraic geometry illuminate various physical phenomena. We examine applications in string theory, quantum field theory, and positive geometry, highlighting the role of algebraic structures in understanding the fabric of the universe.
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 26–29 Read article
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Comparing Results of a Study on Mathematics Instruction in English at Diploma College in Solapur District
Abstract: Study programmes at the Diploma College in Solapur include mathematics courses, which are instructed in English. Comparing the educational outcomes in the Mathematics study course with the English language of instruction is the primary objective of the paper. We concentrated on the students' proficiency in solving specific linear algebra and mathematical analysis problems. The first-year students in the Diploma study programme in Diploma College, Solapur made up the research sample. …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 12–18 Read article
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Exploring the Studies of Mathematics: Foundations, Evolution, Pedagogy and Prospects
Abstract: Mathematics, often regarded as the universal language of science and logic, has evolved through centuries as both a tool for understanding the natural world and a discipline of abstract reasoning. This study explores the multifaceted dimensions of mathematics by examining its foundations, historical evolution, pedagogical approaches, and future prospects. The foundational aspects trace back to ancient civilizations—Babylonian arithmetic, Greek geometry, and Indian and Arabic contributions to algebra— highlighting how early …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 25–31 Read article
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Studies of Mathematics: A Review of Research Trends, Themes and Implications
Abstract: This review examines contemporary research trends, thematic developments, and emerging implications within the field of mathematics education and mathematical studies. Drawing on a synthesis of recent scholarly literature, it explores how mathematics as both a discipline and a pedagogical practice continues to evolve in response to technological advancements, interdisciplinary applications, and changing educational paradigms. Major research trends reveal a growing emphasis on problem-based learning, mathematical modeling, and the integration of …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 19–24 Read article
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Dynamics of Prime Gap Sets: An Algorithmic and Set-Theoretic Approach
Abstract: In this paper, we present a theorem and an efficient algorithm for computing all prime numbers up to a given integer X. Our theorem establishes a relationship between the primes up to X and those up to (X+1)2, providing a theoretical foundation for the algorithm. The proposed method improves upon the traditional Sieve of Eratosthenes by dynamically eliminating multiples of primes using only the remaining numbers in the set, thereby …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 20–25 Read article
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The Evolution and Impact of Numbers: From Ancient Tallies to Quantum Computing: Review Article on Numbers
Abstract: Numbers are among the most fundamental constructs in human civilization, serving as the backbone of mathematics, science, technology, and virtually every aspect of daily life. They represent not only quantities and measures but also relationships, structures, and patterns that underpin the fabric of human understanding. From the earliest tallies etched on bones by prehistoric humans to the sophisticated numerical systems embedded in today’s artificial intelligence and quantum computing, the evolution …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 15–19 Read article
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Effective Use of Library Resources and Services by the End Users at PPSavani University, Surat
Abstract: This qualitative research study examines the perceptions of students and faculty regarding the utilization of library resources and services at P. P. Savani University (PPSU), Surat. While the library has modern infrastructure, an extensive print collection (25,000+ books) and digital collection (64,200+ e-journals, 18,500+ e-books), and full automation via KOHA (a widely used open-source Integrated Library System (ILS)), a nuanced understanding of user experiences is paramount to truly optimize its …
Published in Journal of Advancements in Library Sciences · Vol. 12, Issue 3, 2025 · pp. 33–38 Read article
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The Contribution of Mathematics to Make Developed India
Abstract: This research paper explores the significant contributions of mathematics to the development of India, tracing its influence from ancient innovations to modern applications across diverse sectors. India has a long-standing mathematical tradition, with foundational achievements such as the invention of zero, the decimal system, and advancements in algebra, trigonometry, and geometry, which profoundly shaped global knowledge systems. These early contributions established India as a pioneering hub of mathematical thought and …
Published in Research & Reviews : Journal of Statistics · Vol. 14, Issue 3, 2025 · pp. 08–15 Read article
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Graphs and Their Real-Life Applications in Pharmaceutical Research
Abstract: This study provides a comprehensive overview of the role of graphs in pharmacy research, emphasizing their significance as powerful tools for data visualization, interpretation, and communication. In the field of pharmacy, research often generates large volumes of complex data related to drug development, pharmacokinetics, pharmacodynamics, medication safety, and patient outcomes. Graphs serve as an essential medium to translate these data into accessible, interpretable, and actionable insights, supporting evidence-based practice and …
Published in Research & Reviews : Journal of Statistics · Vol. 14, Issue 3, 2025 · pp. 01–08 Read article
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China’s Economic Performance (2020–2024): A Sectoral Index Analysis
Abstract: This study applies Laspeyres, Paasche, and Fisher ideal indices to China’s official 2020–2024 price and quantity data, quantifying sectoral inflation and real growth in agriculture, manufacturing, services, exports, and investment. Results show manufacturing experienced mild deflation (Laspeyres ≈ 98.7, implying ≈ 1.3% overall price decline) with a slight real output drop (~6.1%). A key driver was a sharp 21.4% fall in electric vehicle unit prices, despite +523% volume growth. Services …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 14, Issue 3, 2025 Read article
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A Review Paper on The Mathematical Foundations of Artificial Intelligence
Abstract: Artificial Intelligence (AI) is deeply rooted in various branches of mathematics, which provide the theoretical foundation and practical tools for developing intelligent systems. This paper explores the crucial role of mathematics in AI, focusing on key areas such as Linear Algebra, Probability and Statistics, Optimization Techniques, Calculus, Graph Theory, and Fourier and Wavelet Transforms. Linear Algebra is fundamental for representing and manipulating data, with applications in dimensionality reduction and neural …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 7–14 Read article
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Mathematical Approaches to Nonlinear Oscillatory Systems with Damping: Exact and Approximate Solutions
Abstract: The study of nonlinear oscillatory systems with damping is a key area of research in applied mathematics, particularly in the context of dynamical systems, stability analysis, and bifurcation theory. These systems, described by second-order nonlinear differential equations, exhibit a rich variety of behaviors, including periodic, quasi-periodic, and chaotic motions. The introduction of damping—representing energy dissipation—adds a layer of complexity, making the analytical and numerical solution of such systems a challenging …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 7–11 Read article
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Extended Fixed Point Theorems in Menger PM-Type Spaces: Generalized Auxiliary Functions and Contractivity Conditions
Abstract: Background: Fixed point theory in probabilistic metric spaces, particularly Menger spaces, has been a subject of intensive research due to its applications in nonlinear analysis and mathematical modeling. Traditional approaches often impose restrictive constraints on the defining properties of Menger spaces and limit the class of auxiliary functions in contractivity conditions Methods: We extend recent fixed point theorems in Menger spaces by: (1) introducing the notion of Menger PM-type spaces …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 1–6 Read article
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Electronic Resources of University Libraries: AI-Driven Management and Optimization
Abstract: In order to maximize accessibility, utilization, and efficiency, university libraries’ growing reliance on electronic resources (ER) has prompted the creation of sophisticated management techniques. The difficulty of handling enormous volumes of data has increased as educational institutions move from conventional physical collections to massive digital repositories. A key instrument in revolutionizing library operations, artificial intelligence (AI) offers creative ways to improve retrieval methods, manage digital resources more effectively, and customize …
Published in Journal of Advancements in Library Sciences · Vol. 12, Issue 3, 2025 · pp. 8–15 Read article