COMBINED NEWTON’S THIRD-ORDER CONVERGENCE METHOD FOR MINIMIZE ONE VARIABLE FUNCTIONS

Contex. The article deals with the actual problem of numerical optimization of slowly computed unimodal functions of one variable. The analysis of existing methods of minimization of the first and second orders of convergence, which showed that these methods can be used to quickly solve these problems for functions, the values of which can be obtained without difficulty. For slowly computed functions, these methods give slow algorithms; therefore, the problem of developing fast methods for minimizing such functions is urgent. Objective. Development of a combined third-order Newtonian method of convergence to minimize predominantly slowly computed unimodal functions, as well as the development of a database, including smooth, monotonic and partially constant functions, to test the method and compare its effectiveness with other known methods. Method. A technique and an algorithm for solving the problem of fast minimization of a unimodal function of one variable by a combined numerical Newtonian method of the third order of convergence presented. The method is capable of recognizing strictly unimodal, monotonic and constant functions, as well as functions with partial or complete sections of a flat minimum. Results. The results of comparison of the proposed method with other methods, including the fast Brent method, presented. 6954 problems were solved using the combined Newtonian method, while the method turned out to be faster than other methods in 95.5% of problems, Brent’s method worked faster in only 4.5% of problems. In general, the analysis of the calculation results showed that the combined method worked 1.64 times faster than the Brent method. Conclusions. A combined third-order Newtonian method of convergence proposed for minimizing predominantly slowly computed unimodal functions of one variable. A database of problems developed, including smooth, monotone and partially constant functions, to test the method and compare its effectiveness with other known methods. It is shown that the proposed method, in comparison with other methods, including the fast Brent method, has a higher performance.

Duhem’s Analysis of Newtonian Method and the Logical Priority of Physics over Metaphysics

This article offers a discussion of Duhemian analysis of Newton's method in the Principia considering both the traditional response to this analysis (Popper et alii) and the more recent ones (Harper et alii). It is argued that in General Scholium to the Principia, Newton is not advocating what Duhem suggests in his best-known criticism, but he is proposing something very close to the establishment of a logical priority of physics over metaphysics, a familiar thesis defended by the French physicist himself.

Effects of Separation Strategy on Deployment of Multitethered Chain-Type Satellite System

This paper investigates the effects of separation strategy and parameters related to deployment on the dynamic behavior of multitethered chain-type satellite system. The system, including several satellites connected by tethers which are considered as massless and straight, is modeled as an extension of a two-body dumbbell tethered system. The dynamic equations of system in absence of perturbations and external disturbances are derived using Newtonian Method. To observe the effect of deployment rate on the motion of system, a parametric analysis of the deployment of a three-body tethered system with different deployment rates is carried out. Moreover, a four-body tethered system is used to investigate the effect of separation strategies on the dynamic behavior of system during the deployment phase. The numerical results suggest that the system with simultaneous separation costs less time to complete the deployment. If the ratio of deployment rates is in consistence with that of their desired lengths, the tethers deployed simultaneously would have a synchronous motion. It is also observed that the system employing separation bolt has a better performance than the system separated by spring mechanism since the larger separation velocity which is not along local vertical may cause a rotation.

Study of the Phan-Thien–Tanner Equation of Viscoelastic Blood Non- Newtonian Flow in a Pipe-Shaped Artery under an Emotion-Induced Pressure Gradient

In this paper, a three-dimensional, unsteady state non-Newtonian fluid flow in a pipe-shaped artery of viscoelastic blood is considered in the presence of emotion-induced pressure gradient. The results have been expressed in terms of radial profiles of both axial velocity and viscosity and were presented numerically by using the shooting technique coupled with the Newtonian method and the Boubaker polynomials expansion scheme. The effects of some parameters on the dynamics are analyzed.

STUDI KEKUATAN TARIK DAN KEKERASAN LOGAM BAJA P.25 dan S.25 DENGAN METODE NEWTON

STUDI KEKUATAN TARIK DAN KEKERASAN LOGAM BAJAP.25 dan S.25 DENGAN METODE NEWTON Jan Ady1) 1) Departemen Fisika Fakultas Sains dan Teknologi Universitas Airlangga Surabaya [email protected] ABSTRAK Telah dilakukan studi tentang sifat mekanik logam baja jenis polos P.25 dan ulir S.25 dengan metode Newton. Uji kekuatan tarik dilakukan dengan mengukur tegangan-regangan menggunakan Autograph sedangkan uji kekerasan dilakukan dengan pengukuran Hardness Vickers Tester. Nilai modulus elastisitas baja S. 25 adalah 54,80 Kg/mm2 dan 31,78 Kg/mm2 untuk baja P.25. Rata-rata nilai kekerasan adalah 227,2 kgf/mm2 untuk baja S.25 dan 195,6 kgf/mm2 untuk baja P.25. Hasil ini menunjukkan bahwa logam baja S.25 memiliki kekuatan tarik dan kekerasan yang relatif lebih baik dari pada logam baja P.25, sesuai demgan pengukuran dan perhitungan menggunakan metode Newton. Kata Kunci: Baja P.25 and S.25, kekerasan, kuat tarik, metode Newton STUDY ON THE TENSILE STRENGTH AND HARDNESS OF STEEL TYPE P.25 AND S.25 USING NEWTONIAN METHOD ABSTRACT The mechanical properties of steel P.25 (smooth type) and S.25 (screwed type) was studied using Newtonian method. The tensile strength was evaluated by measuring the stress-strain using autograph, whereas the hardness was measured by Hardness Vickers Tester. The modulus elasticity was 54,80 Kg/mm2 for steel S.25 and 31,78 Kg/mm2 for steel P.25. The average hardness was 227,2 kgf/mm2 for steel S.25 and 195,6 kgf/mm2 for steelP.25. These results indicated that the tensile strength and hardness of steel S.25 were relatively better than steel P.25, based on the measurement and calculation using Newtonian method. Keywords : Steel P.25 and S.25, Newtonian, Hardness, Tensile strength, Newtonian method