IRIS Università degli Studi di Bolognahttps://cris.unibo.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Wed, 19 Jan 2022 02:14:04 GMT2022-01-19T02:14:04Z10631Hypergeometric Identities Related to Roberts Reductions of Hyperelliptic Integralshttp://hdl.handle.net/11585/793517.1Titolo: Hypergeometric Identities Related to Roberts Reductions of Hyperelliptic Integrals
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11585/793517.12020-01-01T00:00:00ZEvaluation of harmonic sums with integralshttp://hdl.handle.net/11585/661496.1Titolo: Evaluation of harmonic sums with integrals
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11585/661496.12018-01-01T00:00:00ZElliptic integral solutions of spatial elastica of a thin straight rod bent under concentrated terminal forceshttp://hdl.handle.net/11585/80407Titolo: Elliptic integral solutions of spatial elastica of a thin straight rod bent under concentrated terminal forces
Abstract: In this article, we solve in closed form a system of nonlinear differential equations modelling the elastica in space of a thin, flexible, straight rod, loaded by a constant thrust at its free end. Common linearizations of strength of materials are of course not applicable any way, because we analyze great deformations, even if not so large to go off the linear elasticity range. By passing to cylindrical coordinates ρ, θ, z, we earn a more tractable differential system evaluating ρ as elliptic function of polar anomaly θ and also providing z through elliptic integrals of I and III kind. Deformed rod’s centerline is then completely described under both tensile or compressive load. Finally, the planar case comes out as a degeneracy, where the Bernoulli lemniscatic integral appears.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11585/804072006-01-01T00:00:00ZHigher order approximation of the period-energy function for single degree of freedom Hamiltonian systemshttp://hdl.handle.net/11585/5683Titolo: Higher order approximation of the period-energy function for single degree of freedom Hamiltonian systems
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/11585/56832004-01-01T00:00:00ZIdentities for Catalan’s Constant Arising from Integrals Depending on a Parameterhttp://hdl.handle.net/11585/793515Titolo: Identities for Catalan’s Constant Arising from Integrals Depending on a Parameter
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11585/7935152020-01-01T00:00:00ZEOQ under exogenous and periodic demandhttp://hdl.handle.net/11585/75770Titolo: EOQ under exogenous and periodic demand
Abstract: In this paper we give a sufficient condition for the existence of the economic batch to a Wilson-type inventory model loaded by a fully exogenous continuous demand function of time. After some cases solvable in closed form, the computational problem is introduced of inverting the reordering time versus the ordered quantity as necessary step to obtain the cost function to be minimized. Such a mixed (theoretical/numerical) approach is applied to a demand consisting of three different behaviors: growth, decrease and prolonged zero. Such a wave-form is assumed to iterate itself periodically and the relevant seasonal demand is expanded in a Fourier series of time. Performing the integration and reverting the reordering time, the cost function is computed and its minimizing EOQ detected. Finally an example shows that the above conditions guarantee the existence but not uniqueness to solution.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11585/757702009-01-01T00:00:00ZSpecial functions and rod nonlinear theoryhttp://hdl.handle.net/11585/793869.1Titolo: Special functions and rod nonlinear theory
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11585/793869.12020-01-01T00:00:00ZMathematical properties of EOQ models with special cost structurehttp://hdl.handle.net/11585/133755Titolo: Mathematical properties of EOQ models with special cost structure
Abstract: An existence-uniqueness theorem is proved about a minimum cost order for a class of inventory models whose holding costs grow according to a stock level power law. The outcomes of a previous work of two of the authors are then extended to different environments: i.e. when the holding costs change during time generalizing the Weiss model, or with invariable holding costs but adopting a backordering strategy. Application cases are provided assuming several functional behaviors of demand versus the stock level
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11585/1337552013-01-01T00:00:00ZThe meridian curve of a wetting drop: a boundary value problem and its elliptic integrals solutionhttp://hdl.handle.net/11585/389303Titolo: The meridian curve of a wetting drop: a boundary value problem and its elliptic integrals solution
Abstract: In this article we study the shape of free surfaces of a static fluid under gravity. We consider the meridian curve of a heavy liquid drop standing on a horizontal base: the main assumption concerns the liquid wetting capability, namely its contact angle well below pi/2. The nonlinear differential boundary problem is solved through the shooting method. Our treatment is self-consistent as holding all demonstrations of existence, uniqueness, and computability. We conclude providing the eigenvalues set to the radius and the meridian curve of the drop through elliptic integrals: such a new exact solution—see (3.9) and (3.10) —is enriching the literature on capillarity.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11585/3893032014-01-01T00:00:00ZExact solution to a first-fifth power nonlinear unforced oscillatorhttp://hdl.handle.net/11585/96121Titolo: Exact solution to a first-fifth power nonlinear unforced oscillator
Abstract: A one-dimensional, undamped, anharmonic oscillator whose restoring force is an odd polynomial function of displacement, is solved exactly through the elliptic functions and inverted, providing oscillation amplitude through time, and then revealing a new fully integrable nonlinear system. The closed form relationship linking the period $mathbb{T}$ to the initial motion amplitude textit{a} can then play as a benchmark to the approximate values of literature
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11585/961212010-01-01T00:00:00Z