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Exploring the foundations of mathematics and natural sciences to uncover deeper insights into the universe, from abstract theories and computational models to discoveries in physics, earth sciences, astronomy, and life sciences.
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Journal of Mathematical and Fundamental Sciences publishes peer-reviewed research across mathematics, natural sciences, and fundamental scientific disciplines. The journal supports high-quality scholarly communication in astronomy, chemistry, earth sciences, life sciences, physics, statistics, and applied mathematics with real relevance to natural science.
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Quantum walks offer promising advantages for search algorithms over graphs. Among these, Grover’s quantum search provides a quadratic speedup with a time complexity of for unstructured search problems. Nevertheless, Grover search performs poorly on cyclic graphs due to the dynamics of the Grover walk. This study explores the behavior of Grover’s quantum walk on cyclic graphs, analyzing the probability distribution of finding the marked vertex. To analyze this behavior, we extend each vertex of the cycle by attaching semi-infinite-length paths (tails). We develop a direct analytical approach to obtain the transition matrix, whose elements are independent of. For small cycles, we observe success probabilities exceeding 0.5. In contrast, with large cycles, the effectiveness drops rapidly. We observe that the success probability approaches zero as the size of the graph increases, indicating the limitations of the quantum search in cyclic structures.
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The conventional method for poverty measurement is the poverty line, which is based only on household income and expenditure. The poverty line can be used to determine whether a given household is poor or not. However, to capture the true nature of poverty, many factors other than income and expenditure should be considered. In this study, we developed a model for developing countries under a multidimensional framework to classify poverty levels of poor households by incorporating a fuzzy approach. The poverty levels are categorized into three levels and threshold values are determined for each level. In order to generate results, we used relevant statistical data from Sri Lanka. The results of this study indicated that individual education, income, and housing characteristics are the most significant factors in determining the poverty level of individual households in Sri Lanka. Further, the developed model provides a menu of focused factors and a policy tool for policymakers to allocate and distribute subsidies for needy areas.
Read more10.5614/j.math.fund.sci.2026.57.3.3
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