Giovanni Mingari Scarpello

Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric Functions

The stress induced in a loaded beam will not exceed some threshold, but also its maximum deflection, as for all the elastic systems, will be controlled. Nevertheless, the linear beam theory fails to describe the large deflections; highly flexible linear elements, namely, rods, typically found in aerospace or oil applications, may experience large displacements—but small strains, for not leaving the field of linear elasticity—so that geometric nonlinearities become significant. In this article, we provide analytical solutions to large deflections problem of a straight, cantilevered rod under different coplanar loadings. Our researches are led by means of the elliptic integrals, but the main achievement concerns the Lauricella 𝐹𝐷(3) hypergeometric functions use for solving elasticity problems. Each of our analytic solutions has been individually validated by comparison with other tools, so that it can be used in turn as a benchmark, that is, for testing other methods based on the finite elements approximation.

Existence of EOQ and its Evaluation: Some Cases of Stock Blow Down Dynamics Depending on its Level

The EOQ mathematical models usually deal with the problem of a wholesaler who has to manage a goods restocking policy, settling his best amount of goods to be procured. Best means capable of minimizing all the costs concerning the trade of the stored goods. The relevant seminal contributions are due to Harris, and Wilson, who analyzed an easy scenario with a certain demand uniform all over the time so that its instantaneous change rate is fixed, with stocking charges not dependent on time. In such a field, our own contribution consists of establishing sufficient conditions on the well posedness to the minimum cost problem and relationships providing either closed form solutions or, alternatively, quadrature formulae—without ex ante approximations. All this allows a numerical solution to the transcendental (or algebraical of high degree) equation solving to the most economical batch. In short, such our paper is concerning the special family of EOQ mathematical models with different deterministic time-dependent demands.

Migration in a Solow Growth Model

In this work we deal with the Solow-Swan economic growth model, when the labor force is ruled by the Malthusian law added by a constant migration rate I. Considering a Cobb-Douglas production function, we prove some stability issues and find a closed-form solution for the emigration case, involving Gauss’ Hypergeometric functions. In addition, we prove that, depending on the value of the emigration rate, the economy could collapse, stabilize at a constant level, or grow more slowly than the Solow-Swan model. Immigration also can be analyzed by the model if the Malthusian manpower is declining.

The Goodwin cycle improved with generalized wages: phase portrait, periodic behaviour

Abstract The Goodwin cycling of developed economies has been by us modelled in a more general way by representing the Phillips curve f (v) beyond linearity through a growing and convex function of the employment share v . Then, by means of the Lambert functions, we express in exact and explicit form the phase portrait (u, v) of the differential system in the share u(t) of production absorbed by wages, and v(t) itself. Under easy assumptions it is proved that the (u, v) system: is such that all its not-constant solutions shall be periodic. After such a periodicity has been assessed, based on our previous work, an asymptotic (low-energy) expression of the period/energy function is computed, establishing a sufficient condition for its monotonicity.

A nonlinear boundary problem by the inventory’s optimization of a productive system with not wholly quadratic costs

Abstract In this paper a costs functional is assumed asymmetrical for the production and the inventory charges: As a state variable, the deviation u(t) = Iid(t)− Ire(t) between the inventories has been chosen. Obviously the manufacturer wishes to keep the cost-functional C(u) as a minimum. The relevant Euler-Lagrange time-equation ü(t) =α2u(t) + 2u(t)3, is faced with the initial condition u(0) = u0 ≠ 0 ; and with the final condition u(T) = 0 meaning that after a time T > 0 the deviation u(t) is re-absorbed at all. In the article the above nonlinear boundary value problem is solved through a much more tractable nonlinear (Cauchy) initial value problem, plus a “shooting”. The integration is carried out by means of the Jacobi elliptic functions, which do here their appearance in a micro-economic context for the first time. After having so detected the “optimal” deviation time law u(t) , a new production plan is then designed for driving the deviation till to its extinction within T .

Motions about a fixed point by hypergeometric functions: new non-complex analytical solutions and integration of the herpolhode

The present study highlights the dynamics of a body moving about a fixed point and provides analytical closed form solutions. Firstly, for the symmetrical heavy body, that is the Lagrange–Poisson case, we compute the second (precession,

Closed-Form Solutions to an Economic Growth Logistic Model with Migration

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The Solow Model Improved Through the Logistic Manpower Growth Law.

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