mathematical methods in science

... MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING MATHEMATICS AND MIND 5 1.3 MATHEMATICS AND MIND Almost, everywhere mathematics is a very useful and powerful language in expressing ... an integral part of the learning process. In a vast area like mathematical methods in science and engineering, there is always room for new approaches, new applications, and new topics. In ... naturally comes from the inner efficiency of our brain. Research on subjects like brain stimulators, hard wiring of our brain, and mind reading machines are all aiming at a faster and much...

Ngày tải lên: 22/03/2014, 13:20

Ngày tải lên: 27/06/2014, 05:20

Ngày tải lên: 27/06/2014, 18:20

Ngày tải lên: 05/03/2014, 23:20

... potential scattering problem in quantum mechanics. In some cases, the resulting equations are nonlinear integro-differential equations. A good example is the Schwinger–Dyson equation in quantum field ... nonlinear integro-differential equation, and is exact and closed. It provides the starting point of Feynman–Dyson type perturbation theory in configuration space and in momentum space. In some singular ... to be nonlinear integral equations. Depending on the form of the functionals, the resulting integral equations are said to be of the first kind, of the second kind, or of the third kind. If the...

Ngày tải lên: 17/03/2014, 14:28

... then |dist(x, Y ) − dist(z, Y )| ≤ dist(x, z). (0.13) In particular, x → dist(x, Y ) is continuous. Proof. Taking the in mum in the triangle inequality d(x, y) ≤ d(x, z) + d(z, y) shows dist(x, ... Banach space of continuous functions Now let us have a first look at Banach spaces by investigating set of contin- uous functions C(I) on a compact interval I = [a, b] ⊂ R. Since we want to handle ... Cauchy-Schwarz inequality we know that  ϕ : ψ → ϕ, ψ is a bounded linear functional (with norm ϕ). In turns out that in a Hilbert space every bounded linear functional can be written in this way. Theorem...

Ngày tải lên: 17/03/2014, 14:41

Ngày tải lên: 05/06/2014, 12:03

... the mathematical and materials sciences have much to gain from each other. Modern mathematical methods can aid in solving significant problems in materials science, while problems in materials science ... focus on enabling incremental advances in cross-disciplinary research that involves mathematical sciences applied to materials science. Some of the main obstacles to cross- disciplinary efforts, ... different subdisciplines of materials science (and subdisciplines of the mathematical sciences); continual efforts are needed to eliminate jargon as a barrier to interdisciplinary research. Some...

Ngày tải lên: 16/03/2014, 09:20

... said to be in involution, if dω θ k (v, w) = 0 for any ω ∈ CΛ 1 (J k (π)). (2) A subspace W ⊂ C k θ k is said to be involutive, if any two vectors v, w ∈ W are in involution. (3) An involutive ... Diffiety Institute, Moscow, Russia 1 Lectures given in August 1998 at the International Summer School in Levoˇca, Slovakia. This work was supported in part by RFBR gr ant 97- 01-00462 and INTAS ... contain i. But, as it follows from Proposition 3.6 on the preceding page, vector fields V j σ for |σ| ≤ k do not lie in C k . Thus, the Cartan distribution on J k (π) is not integrable. Introduce...

Ngày tải lên: 17/03/2014, 14:29

Ngày tải lên: 11/06/2014, 16:42

Ngày tải lên: 29/06/2014, 13:20

... advantage of identifying different clas- ses of antibodies in comparison to other agglutination methods. Different results may be obtained depend- ing on the nature of anti-globulin. This situation ... and blocking antibodies that form against brucella, the titers that it has determined were higher in number than STA and Coombs methods has higher sensitivity and specificity (4). In a study ... hand, appear in three weeks and reach a peak in six to eight weeks. Coombs test is needed to investigate blocking antibodies. Dilutions need to be performed in very high ratios in order to...

Ngày tải lên: 25/10/2012, 10:56

Ngày tải lên: 01/11/2013, 14:38

Ngày tải lên: 27/12/2013, 16:21

Ngày tải lên: 27/12/2013, 16:23

Ngày tải lên: 27/12/2013, 16:24

Ngày tải lên: 27/12/2013, 16:25

... Char Count= 0 10 Finite Difference Methods in Financial Engineering 1.4 INITIAL VALUE PROBLEMS In the previous section we examined a differential equation on a bounded interval. In this case we ... Char Count= 0 8 Finite Difference Methods in Financial Engineering 1.2 TWO-POINT BOUNDARY VALUE PROBLEM Let us examine a general second-order ordinary differential equation given in the form u  = ... Char Count= 0 16 Finite Difference Methods in Financial Engineering Γ η Ω Figure 2.3 Two-dimensional bounded region r Harmonic functions (Du Plessis, 1970; Rudin, 1970) r Mapping functions between...

Ngày tải lên: 23/01/2014, 06:20