Mathematic`s Blog

Metode matriks: mencari solusi partikulir   persamaan diferensial linear orde dua tak homogen dengan  koefisien konstanta Zulmahdi Dailami Jurusan Matematika, FMIPA-UT E-mail: zaul@ka.ut.ac.id   Abstrak Metode matriks adalah suatu rumus atau formula alternatif untuk mencari solusi partikulir persamaan diferensial (PD) linear orde dua tak homogen dengan koefisien konstanta , dengan ; . Metode ini diturunkan dari metode koefisien tak tentu dengan menggunakan konsep Matriks, lineari­tas, Identitas Euler, dan sifat-sifat solusi PD .

Bilangan prima adalah dasar dari matematika, termasuk salah satu misteri alam semesta. Tidak pernah terbayangkan oleh manusia sebelumnya, sampai ditemukan bahwa bilangan prima juga merupakan dasar dari kehidupan alam, yang dengan usaha keras ingin dijelaskan oleh ilmu ini dalam sains. Pandangan orang umumnya mengatakan bahwa matematika hanyalah penemuan manusia biasa. Sebaliknya, beberapa pemikir masa lalu - Pythagoras, Plato, Cusanus, Kepler, Leibnitz, Newton, Euler, Gauss, termasuk para revolusioner abad ke-20, Planck, Einstein dan Sommerffeld - yakin bahwa keberadaan angka dan bentuk geometris merupakan konsep alam semesta dan konsep yang bebas ( independent ). Galileo sendiri beranggapan bahwa matematika adalah bahasa Tuhan ketika menulis alam semesta.

Picture on Left is Dwarf galaxy forming one billion years after the Big Bang. The background image shows the large-scale cosmic context (the panel is approximately 100,000 light years across); the inset shows the central 2,000 light years of the dwarf galaxy where powerful feedback from newly born star clusters drives bulk motions in the gas. Stars are shown in yellow; colours from violet to blue to green to white correspond to gas of increasing density. (Credit: S. Mashchenko, J. Wadsley, and H. M. P. Couchman) ============================================= ScienceDaily (Nov. 30, 2007) — Researchers using supercomputer simulations have exposed a very violent and critical relationship between interstellar gas and dark matter when galaxies are born -- one that has been largely ignored by the current model of how the universe evolved. The findings, published in Science, solve a longstanding problem of the widely accepted model -- Cold Dark Matter cosmology -- which suggests there is muc...

Electron. J. Diff. Eqns., Vol. 2007(2007), No. 01, pp. 1-7. On oscillation and asymptotic behaviour of a neutral differential equation of first order with positive and negative coefficients Radhanath Rath, Prayag Prasad Mishra, Laxmi Narayan Padhy Abstract: In this paper sufficient conditions are obtained so that every solution of tends to zero or to as tends to , where are positive real numbers, , and , is non decreasing with for . The two primary assumptions in this paper are and . The results hold when is linear, super linear,or sublinear and also hold when . This paper generalizes and improves some of the recent results in [5,7,8,10]. Submitted November 2, 2006. Published January 2, 2007 Math Subject Classifications: 34C10, 34C15, 34K40. Key Words: Oscillatory solution; nonoscillatory solution; asymptotic behaviour. Show me the DVI (62K), PDF (216K), TEX and other files for this article. source from : ELECTRONIC...

Plug flow and the breakdown of Bagnold scaling in cohesive granular flows Robert Brewster,1 Gary S. Grest,2 James W. Landry,3 and Alex J. Levine1 1Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095-1596, USA 2Sandia National Laboratories, Albuquerque New Mexico 87185, USA 3BAE Systems Burlington, Massachusetts 01803, USA
Received 5 September 2005; published 21 December 2005 Cohesive granular media flowing down an inclined plane are studied by discrete element simulations. Previous work on cohesionless granular media demonstrated that within the steady flow regime where gravitational energy is balanced by dissipation arising from intergrain forces, the velocity profile in the flow direction scales with depth in a manner consistent with the predictions of Bagnold. Here we demonstrate that this Bagnold scaling does not hold for the analogous steady flows in cohesive granular media. We develop a generalization of the Bagnold constitutive relation to account for...

Beyond Probability GOD'S MESSAGE IN MATHEMATICS by ABDULLAH ARIK FOREWORD This discussion would be unprofitable if it did not lead us to appreciate the wisdom of our Creator, and the wondrous knowledge of the Author of the world, who in the beginning created the world out of nothing and set everything in number, measure and weight, and then in time and age of man formulated a science which reveals fresh wonders the more we study it . Hrovista of Gandersheim (980 AD) All of us, at one time or another, have been compelled to contemplate creation. Questions such as the purpose of our lives and the existence of God, have been pondered upon from time immemorial. There have always been those who choose to interpret the harmony and order of the cosmos as a fluke of nature, but a closer look gives clear evidence of a design, and thus a designer. The discoveries being made on all frontiers are making this picture clearer by the day. Most contemporary scientists are a...