Solutions Of Certain Nonlinear Problems Research Articles

Fast accurate multi-key weight measurement

We consider an industrial problem brought to the Mathematics in Industry New Zealand study group in 2016, where items pass briefly over load cells resulting in a noisy oscillatory signal, from which the mass of the item is to be computed. We compare results obtained using a single load cell for one piece of fruit, with results from passing over two load cells in tandem or in succession with fruit on multiple keys. We develop mathematical models to assist with the computation of total load mass, considering both deterministic and statistical approaches. The fitting of simple harmonic motion plus a step function exhibits the possibility of rapid estimates of load mass. We find that using multiple keys to measure the weight of a fruit provides more accurate results than using the single-key method. References minz-2004, Case Study Compac. http://www.minz.org.nz/assets/downloads/Case-Study-Compac.pdf Kesilmis, Z., and Baran, T. (2016). A Geometric Approach to Beam Type Load Cell Response for Fast Weighing. doi:10.1007/s12647-016-0168-2 K. Levenberg, A method for the solution of certain non-linear problems in least squares. Quarterly of applied mathematics , 2(1944), pp. 164–168. http://www.jstor.org/stable/43633451 D. W. Marquardt, An algorithm for least-squares estimation of nonlinear parameters. Journal of the society for Industrial and Applied Mathematics , 11(1963), pp. 431–441. doi:10.1137/0111030

Convergence analysis of common solution of certain nonlinear problems

Convergence analysis of common solution of certain nonlinear problems

Asymptotic solution of certain nonlinear problems of time-optimal response: PMM vol. 42, n≗ 1, 1978, pp. 76–86

Asymptotic solution of certain nonlinear problems of time-optimal response: PMM vol. 42, n≗ 1, 1978, pp. 76–86

On the asymptotic behavior of solutions of certain nonlinear problems of hydrodynamics: PMM vol. 35, n≗6, pp. 978–985, 1971

Periodic solutions of heat conduction equations with boundary conditions of the relay kind are found for a finite interval, and the behavior of such solutions at unlimited time increase is analyzed. Periodic solutions of heat conduction equations with nonlinear boundary conditions were considered in [1–4, 10], while in [5, 6] periodic solutions of nonhomogeneous heat conduction equations with their right-hand sides nonlinear with respect to the unknown functions are presented, and the asymptotic behavior of related initial problems is analyzed. Solutions of this kind define self-oscillating processes occurring in various branches of hydrodynamics (theory of filtration and diffusion [3–6]).

An Algorithm for Least-Squares Estimation of Nonlinear Parameters

An Algorithm for Least-Squares Estimation of Nonlinear Parameters

Solution of the basic problem of exterior ballistics

An approximate method of analytic solution of certain nonlinear problems is presented. The applicability of the method is demonstrated with the example of the solution of the problem concerning the motion of a heavy particle of variable mass, projected at an angle to the horizon. Another example contains the analytic solution of the basic problem of exterior ballistics of a projectile in the most general formulation.

The Matric Solution of Certain Nonlinear Problems in Structural Analysis

The matric formulation of the Maxwell-Mohr equations of continuity is applied to the solution of certain nonlinear problems in the analysis of indeterminate structures. These problems are characterized by the dependence of the flexibility matrix upon the internal loads. Nonlinearities resulting from plasticity and from certain types of buckling have this characteristic. General nonlinear load and deflection equations are given, and an iterative form for their solution b}^ the Newton-Raphson method is derived. The analysis is applied to an indeterminate swept-wing structure in which the members are subject to plastic behavior. Convergence is shown to be rapid even when plasticity is fully developed. The high-speed digital computer is utilized in the numerical solution.

A method for the solution of certain non-linear problems in least squares

A method for the solution of certain non-linear problems in least squares