An elementary proof of Euler's formula using Cauchy's method
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DOI: 10.1016/j.topol.2020.107558
Abstract: Abstract The use of Cauchy's method to prove Euler's well-known formula is an object of many controversies. The purpose of this paper is to prove that Cauchy's method applies for convex polyhedra and not only… read more here.
Keywords: elementary proof; cauchy method; euler formula; method ... See more keywords
An elementary proof of the amplitude’s exponential decrease in damped oscillations
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DOI: 10.1088/1361-6552/ad26d4
Abstract: A damped oscillation is characterized by the diminishing amplitude of an oscillating system resulting from the dissipation of energy. A crucial example of damped oscillations involves a block of mass attached to the end of… read more here.
Keywords: amplitude exponential; elementary proof; proof amplitude; decrease ... See more keywords
Elementary Proof of an Estimate for Kloosterman Sums with Primes
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DOI: 10.1134/s0001434618050085
Abstract: A new elementary proof of an estimate for incomplete Kloosterman sums modulo a prime q is obtained. Along with Bourgain’s 2005 estimate of the double Kloosterman sum of a special form, it leads to an… read more here.
Keywords: proof estimate; kloosterman; estimate; elementary proof ... See more keywords
Elementary proof of congruences involving sum of binomial coefficients
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DOI: 10.1142/s1793042118500938
Abstract: We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients. read more here.
Keywords: congruences involving; proof congruences; elementary proof; involving sum ... See more keywords
An elementary proof of the symplectic spectral theorem
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DOI: 10.1142/s1793557119500335
Abstract: The classical spectral theorem completely describes self-adjoint operators on finite-dimensional inner product vector spaces as linear combinations of orthogonal projections onto pairwise orthogonal subspaces. We prove a similar theorem for self-adjoint operators on finite-dimensional symplectic… read more here.
Keywords: elementary proof; proof symplectic; spectral theorem; theorem ... See more keywords
An elementary proof of the generalized Itô formula
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DOI: 10.1515/ms-2025-0016
Abstract: Abstract For one-dimensional semimartingales, the Itô formula can be extended from C2-functions to C1-functions with a locally absolutely continuous derivative. We propose a new, different proof of this result, which is simple, straightforward and quite… read more here.
Keywords: proof generalized; proof; elementary proof; generalized formula ... See more keywords