SummaryWe have examined the special sequence of integrals from 0 to π/4 of even integer powers of the tangent. Each member of this sequence admits an explicit evaluation through a downward recurrence ...terminating at ±π/4. Its very first step embodies an automatic proof of sequence convergence to zero, confirming intuitive anticipation based on the fact that the tangent is strictly less than one when its argument lies interior to 0,π/4). As a direct consequence of this convergence, the limiting recurrence provides a fresh access to the historically acclaimed Gregory-Leibniz series for π4 It should moreover please the reader to realize that entirely similar reasoning applies to the special sequence having odd tangent powers, in which case one recovers the Newton-Mercator-Hudde alternating harmonic series 4 for log (2). Indeed, in the resulting counterpart to (5), each denominator within the sum advances by one unit, 2n−1→2n, whereas the final term becomes ∫0π/4 tan (φ) dφ= log (2)/2, with an obligatory minus sign still in abeyance.
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Abstract
The iterates of Fuzzy Neutrosophic Soft Circulant Matrices (FNSCMs) under the max-min product is examined right now. It is indicated that on the off chance that the first row of a FNSCM is ...in decreasing order, at that point the iterates of the circulant converge and on the off chance that the first row is in increasing order, at that point the iterates oscillate.
This article examines convergence by providing a systematic literature review using scientometric method. Despite the steady growth of convergence literature, we still have an incomplete ...understanding of convergence concepts as well as the processes of industry convergence (IC). Our systematic review highlights several key findings. First, our review highlights six clusters of research on convergence. Second, our analysis suggests that the process of convergence does not necessarily progress in the three- to four-step supply-side process as postulated in the literature, i.e., from scientific convergence, technology convergence, market convergence, and finally to IC. Although existing literature suggests that IC occurs as a result of supply-side convergence, we expand on this proposition and put forth market-driven convergence processes. Third, we provide a typology of the convergence concepts to bring clarity and avoid indiscriminate use of the various convergence concepts. Finally, our article offers new debates on the literature of convergence, providing scholars with research directions that extend beyond the standard convergence processes. Our systematic review is relevant to scholars and managers as the study highlights a taxonomy of convergence scholarship, a typology of convergence concepts, and a re-evaluation of the IC process model to drive the research forward.
A plethora of problems from diverse disciplines such as Mathematics, Mathematical: Biology, Chemistry, Economics, Physics, Scientific Computing and also Engineering can be formulated as an equation ...defined in abstract spaces using Mathematical Modelling. The solutions of these equations can be found in closed form only in special case. That is why researchers and practitioners utilize iterative procedures from which a sequence is being generated approximating the solution under some conditions on the initial data.
This type of research is considered most interesting and challenging. This is our motivation for the introduction of this special issue on Iterative Procedures.
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