— numerical solution of wave problems governed by hyperbolic partial differential equations

... follow the derivations of the heat and wave equations The principal objective of the book is solving boundary value problems involving partial differential equations Separation of variables receives ... genuine problems with real data A new feature of this edition is a CD with auxiliary materials: animations of convergence of Fourier series; animations of solutions of the heat and wave equations ... left blank Ordinary Differential Equations CHAPTER 0.1 Homogeneous Linear Equations The subject of most of this book is partial differential equations: their physical meaning, problems in which...

Ngày tải lên: 17/02/2014, 14:20

... Discretization of the governing equations 30 Chapter The numerical study of wave propagations in 1-D poroelastic media by use of the LDQ method 39 3.1 General 39 3.2 Wave propagation problems in ... Derivation of the analytical solutions of 1-D problems 46 3.4 Remarks 50 Chapter Wave propagations in 2-D and 2-D holed poroelastic media by use of the LDQ method 61 4.1 General 61 4.2 Wave propagation ... seismic waves Careful analysis of the profiles of the seismic waves leads geography scientists to plot the density variations and compositions of the earth In medicine, by detecting the changes of...

Ngày tải lên: 26/09/2015, 09:39

... Bruti-Liberati Numerical Solution of Stochastic Differential Equations with Jumps in Finance Eckhard Platen Nicola Bruti-Liberati (1975–2007) School of Finance and Economics Department of Mathematical ... about the numerical solution of stochastic differential equations on the webpage of the first author under Numerical Methods”: http://www.business.uts.edu.au/ finance/staff/Eckhard /Numerical Methods.html ... any partial derivative ∂yi g(y) of order j ≤ 2(β + 1) Weak schemes provide approximations of the probability measure generated by the solution of a given SDE These schemes are appropriate for problems...

Ngày tải lên: 19/02/2014, 22:20

... Bruti-Liberati Numerical Solution of Stochastic Differential Equations with Jumps in Finance Eckhard Platen Nicola Bruti-Liberati (1975–2007) School of Finance and Economics Department of Mathematical ... about the numerical solution of stochastic differential equations on the webpage of the first author under Numerical Methods”: http://www.business.uts.edu.au/ finance/staff/Eckhard /Numerical Methods.html ... any partial derivative ∂yi g(y) of order j ≤ 2(β + 1) Weak schemes provide approximations of the probability measure generated by the solution of a given SDE These schemes are appropriate for problems...

Ngày tải lên: 28/06/2014, 17:20

... Delay -differential equations In this thesis we are concerned with the numerical solution of delay -differential equations (DDE's) Delay -differential equations may best be regarded as extensions of ... we consider the development of numerical software for the solution of such problems Our discussion opens with a brief introduction to the theory of delay -differential equations Attention is paid ... for the solution of systems of delay -differential equations A novel representation for the differential equation is used to acknowledge structural differences between delay- and ordinary differential...

Ngày tải lên: 11/10/2014, 04:02

... 8) — (Y IP)(i)(t ' — 6)) = ()(hP+1-i) b.o+ Regarding {F(t,Fi(t))1[in,in+,1) as the image of f {Y7-IA) under a map defined by this implies cj l Urn {— (j) (t 8,!17 ( i + 6))F(t — 8, y i(t — (5))) ... transitive closure of E Heuristically, by an extension of the above arguments, we may think of Ei as defining the set of points whose continuity bounds can affect the continuity bound, ci , of yi El ... sk and = n — then d(b, a) = k PROOF by contradiction: Suppose d(b,a) < k Then calling our original path, {sX_ , path one we construct a second path tit) r a = to, b = tk, (7) i= — of length k'...

Ngày tải lên: 11/10/2014, 04:03

... revised numerical model is first validated for the study of wave damping over porous seabeds The effects of wave nonlinearity, wavelength and seabed thickness on wave damping are studied by using ... short waves and long waves have smaller wave damping when compared to damping of waves in intermediate water depths The present numerical model is validated for both long wave and solitary wave ... 6.5.3.1 Wave reflection and transmission 166 6.5.3.2 Wave energy dissipation 169 6.5.4 Effects of depth of submergence 171 6.5.5 Effects of porosity 172 6.5.6 6.6 Analysis of solitary wave transformation...

Ngày tải lên: 12/09/2015, 21:16

... file 2: A complete list of 2567 differentially expressed genes in five tissues of O logistaminata Word file for the list of genes differentially expressed in five tissues of Oryza longistaminata ... high expression of genes near the top of the panel and moderate or low expression of genes below, while leaves (labeled 5) show low or moderate expression of genes near the top of the panel and ... http://www.biomedcentral.com/1471-2229/11/18 Page of 14 Table Four cis-elements abundant in genes specifically enriched in five tissues of O longistaminata identified by bioinformatic analyses of the promoter regions of the genes...

Ngày tải lên: 11/08/2014, 11:21

... B ◦ = x ∈ Rd (∀α ∈ B) α | x (3.5) is the polar of B Denote by µ(B) the (maximal) value of Problem (3.4) and by ν(B) the dimension of its set of solutions We put also (3.6) r(B) = 1/µ(B) One can ... intersection of Γ(P ) with a supporting hyperplane of Γ(P ) is called a face of Γ(P ) The dimension of a face ranges from to d − A vertex is a 0-dimensional face The set of vertices of Γ(P ) is ... Introduction The aim of the present paper is to study Kolmogorov n-widths of classes of multivariate periodic functions given by a differential operator In order to describe the exact setting of the problem...

Ngày tải lên: 14/10/2015, 15:17

Ngày tải lên: 12/06/2014, 16:17

... difference equations, differential equations, and differential equations with impulses The study of abstract measure differential equations was initiated by Sharma [1] in 1970s From then on, properties of ... for existence of solutions are less conservative An example is given to illustrate the effectiveness of our existence theorem of solutions Introduction Abstract measure differential equations are ... existence of solutions for perturbed abstract measure functional differential equations Based on the Arzel`–Ascoli theorem and the fixed point theorem, we give sufficient conditions for existence of a solutions...

Ngày tải lên: 18/06/2014, 22:20

... estimate of mild solution in space C (I,X) which can be proved by Gronwall lemma Step by step, the existence of PCl -mild solution of (3.1) can be derived Let xu denote the PCl -mild solution of system ... Existence of optimal controls In this section, we not only present the existence of PCl -mild solution of the controlled system (1.1) but also give the existence of optimal controls of systems governed ... the existence and uniqueness of PCl -mild solution for (1.1) are proved Next, we consider a Lagrange problem of system governed by (1.1) and prove the existence of optimal controls In order to...

Ngày tải lên: 22/06/2014, 19:20

... Boundary Value Problems investigate the existence of solutions to the problem by means of differential inequalities and Schaefer fixed point theorem Their results complement and extend those of [22, 23] ... ≤ T, (2.10) ≤ t ≤ s ≤ T Proof If u ∈ PC1 ([0,T]; Rn ) C ([0,T] \ {t1 }, Rn ) is a solution of (2.6), setting v(t) = u (t) − r2 u(t), (2.11) then by the first equation of (2.6), we have v (t) − ... boundary value problems of first-order differential equations, ” Journal of Mathematical Analysis and Applications, vol 325, no 1, pp 226–236, 2007 [23] J J Nieto, “Periodic boundary value problems for...

Ngày tải lên: 22/06/2014, 19:20

... − m), (2.41) then liminf w(t) = (2.42) t →b The proof of this lemma is given in [12] 2.3 Lemmas on the sequences of solutions of auxiliary problems Suppose a < t0k < t1k < b (k = 1,2, ), lim ... only trivial solutions Hence in view of Corollaries 1.4 and 1.6 the unique solvability of problems (1.34), (1.2) and (1.34), (1.3) follows in C n−1,m (]a,b[) Let n− us show that these problems in ... singularities and this solution satisfies the boundary conditions (1.2) (the boundary conditions (1.3)) if and only if c1 , ,cn−m−1 are solutions of the system of linear algebraic equations n−m−1 gk...

Ngày tải lên: 23/06/2014, 00:20

... should also satisfy 2.1 Solution of the PDEs There exist many methods for solving Equations (1) and (2) ranging from analytic solutions to sophisticated numerical methods The problems we address ... modelling of human limbs affected by oedema and venous ulcers In what follows, we discuss two examples of shape modelling of human limbs namely modelling of an arm shape and modelling of a leg ... function X as a mapping of a point in Ω to a point X(u, v) in the physical space The shape of the surface patch is usually determined by specifying a set of boundary data at the edge of (∂)Ω Typically...

Ngày tải lên: 13/08/2014, 23:20

... cylinders, (b) Three cylinders Wave Force 2a incident incident wave wave 2a D Y D X Wave force in x -direction acting on cylinder versus wave number ka incident wave Y X 2a D Wave force in x -direction ... versus wave number ka incident wave Y X D 2a Wave force in x -direction acting on the three cylinders in array versus wave number ka triangular Effect of Cylinder Spacing 2a incident wave Y D X Wave ... Effect of Incident Wave Angle  incident wave Y X 2a D Wave force in x -direction acting on the cylinder at various incident wave angle   0 ,30 ,450 ,60 for ka  1.0  incident wave Y X 2a D Wave...

Ngày tải lên: 26/07/2014, 07:20

... points obtained by dilution of a 140-lM stock solution are indicated by circles, while those obtained by further concentration of the stock solution are indicated by squares All of the data points ... concentration range of 30–150 lM (1.3–6.5 mgÆmL)1), 90 lL of arrestin solution was mixed with 10 lL of 10 mM peptide solution to yield a final peptide concentration of mM For higher concentrations of arrestin ... molecular mass of the scattering species The forward scattering values for various concentrations of wild-type arrestin were measured by extrapolation of Guinier curves [21] to an S value of qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1...

Ngày tải lên: 22/02/2014, 07:20

... In  Fig.  1,  the  wave gauge  G1  is  setup  for  the measurement of the incident waves; wave gauges  G6  and  G9  are  for  the  waves  in  the  shoaling area; and the wave gauges G16 and  ... solitary  wave comes to the island, the wave refraction  appears  due  to  the  variation  of water  depth.  Behind the island, the edge waves come from  two sides of the island due to waves bending  ... Fig. 5. Runup of water around the island due to the solitary wave (270 deg.: at foreside in the normal   direction of wave propagation; 90 deg.: at the leeside of the island; 0 deg.: at the right side of the island;  ...

Ngày tải lên: 14/03/2014, 15:20

... length of loop I is longer in short neurotoxins The NMR structure of NTX-1 is closest to that of the a-cobratoxin crystal The superposition of these two ˚ structures shows an RMSD value of 3.00 ... forms of the molecule [44] Furthermore poor experimental restraints and possibly bulkiness of the tip portion of loop II in long neurotoxins compared to short ones, as well as the finding of Bystrov ... double-stranded b-sheet is stabilized by three hydrogen bonds The largest loop of NTX-1 (loop II) consists of residues 21–44, which is cross-linked to loop I by a disulfide bond between Cys3 and...

Ngày tải lên: 23/03/2014, 13:20