painlev´e equations and their special solutions
Tài liệu Project (written version):“The problems of the “Citibus” (bus operating company) and their possible solutions. Drawing a contract.” doc
Ngày tải lên :
20/12/2013, 19:15
... who will monitor and assess the work of the drivers during, for example, a month Then the jury will sum it up and according to their decision some best drivers will be rewarded and, vice versa, ... effective and efficient strategy is to make a contract whick will determine the rights and obligations of both parties: the administration of the “Citibus”operating company and its drivers and which ... cleanness of their buses, maintenance of its technical conditions, being consistent with the bus schedule, being inetrested in making as many scheduled and unscheduled runs as possible and making...
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báo cáo hóa học:" Aflatoxin levels, plasma vitamins A and E concentrations, and their association with HIV and hepatitis B virus infections in Ghanaians: a cross-sectional study" pdf
Ngày tải lên :
20/06/2014, 08:20
... dried grains and nuts under hot, humid and unsanitary conditions Acute and chronic exposures to aflatoxins compromise immunity and enhance macro- and micro-nutrient malnutrition and neonatal ... HIV-positive and HIV-negative males and females 19 years of age and older was conducted in Kumasi (a major maize and peanut-producing and consuming area) in the Ashanti Region of Ghana All HIV-positive and ... aflatoxin in their diets and examined the association of vitamins A and E concentrations, HIV status, AF-ALB levels and hepatitis B virus (HBV) infection Methods Study location, design and target...
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Báo cáo sinh học: " Research Article Symmetric Three-Term Recurrence Equations and Their Symplectic Structure" potx
Ngày tải lên :
21/06/2014, 16:20
... differential equations or Hamiltonian systems and their corresponding Riccati differential equations Applications in Sturmian Theory In 1, Sections 5.3 and 5.6 , several Sturmian comparison and separation ... functionals FT and F, and FT and FJ Proposition 3.6 Quadratic functionals for T and S Assume that i either Sk , Tk satisfy the conditions in Notation 2.1 with Ak , Bk , Ck , Dk , and uk being ... transformations in Propositions 2.8 and 2.9 for the passage between equation J and system S and the transformations in Theorem 3.1 and Corollary 3.4 for the passage between equation T and system S In this...
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Báo cáo hóa học: "ON THE IDENTITY OF TWO q-DISCRETE PAINLEVÉ EQUATIONS AND THEIR GEOMETRICAL DERIVATION" docx
Ngày tải lên :
22/06/2014, 22:20
... Roberts, and C J Thompson, Integrable mappings and soliton equations II, Physica D Nonlinear Phenomena 34 (1989), no 1-2, 183–192 [10] A Ramani, Y Ohta, J Satsuma, and B Grammaticos, Self-duality and ... ax + 1/ pq + ax/ pq (3.3) yw = We now solve (3.2) and (3.3) for x and x and use (3.1b) in order to obtain an equation involving just y, w, and w: ⎞ ⎛ w y − 1/(pq) ⎝ y w − 1/(pq) ⎠ = ( y + r/ ... something to be assessed for each case at hand In this paper we will concentrate on two recently discovered discrete Painlev´ equations and show that they are one and the same e equation Moreover we...
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Differential Equations and Their Applications Part 1 doc
Ngày tải lên :
10/08/2014, 20:20
... Chapter we content ourselves with the linear FBSDEs The special structure of the linear equations enables us to treat the problem in a special way, and the solvability is studied thoroughly The study ... National Outstanding Youth Foundation of China, and Li Foundation at San Francisco, USA Finally, of course, both authors would like to take this opportunity to thank their families for their support, ... Both of them are required to be {:Tt}t_>0-adapted and square integrable For simplicity, we assume X, u and W are all one-dimensional, and a and b are constants We introduce the so-called cost...
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Differential Equations and Their Applications Part 2 doc
Ngày tải lên :
10/08/2014, 20:20
... existence and uniqueness of the adapted solutions to (4.1) [] We now prove the continuous dependence of the solutions on the final data ~ and the function h 4.4 Let h,-h e L2~(O,T;WI'~~ • ~m• and ~,~ ... suitable sizes, b, a, b and ~ are stochastic processes and g is a random variable We are looking for {gvt}t>0-adapted processes X(.), Y(-) and Z(-), valued in ]Rn, ]Rm and IR~, respectively, satisfying ... o n 3.2 Assume that b, a, h and ~ satisfy (2.6) Assume further that a and ~ are continuous in (t, x, y) uniformly in x, for each w E ~; and that g C C M C~(R~; R m) and is deterministic Suppose...
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Differential Equations and Their Applications Part 3 pptx
Ngày tải lên :
10/08/2014, 20:20
... for all g C H if and only if (3.17) and (3.19) hold In this case, the adapted solution to (2.12) is unique (for any given g E H) Proof Theorems 3.2 and 3.3 tell us that (3.17) and (3.19) are necessary ... deterministic matrix-valued function and p : [0, T] • ~ + ]Rm is an {Svt)t>_0-adapted process We are going to derive the equations for P(.) and p(-) First of all, from (4.1) and the terminal condition ... - PC1) -1 [(PAl + P B P ) X + P B l p + q], where P and (p, q) are (adapted) solutions of (4.10) and (4.12), respectively Denote Y = Y - Y and Z = Z - Z Then a direct computation shows that [...
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Differential Equations and Their Applications Part 4 ppsx
Ngày tải lên :
10/08/2014, 20:20
... L and T, and may change from line to line By (1.24) and (1.15), we obtain (1.25) E[Y~(T)I < EIg(X~(T)) I + ElY,(T) - g(X~(T)) I _< C(1 + Ixl) +E _< C(1 + Ixl) w Dynamic programming method and ... hold Then (i) ~ , ~ ( s , ~, y) and V ~,~(s, x, y) are continuous in (x, y) ~ " • ~ m , uniformly in s C [0, T] and 6, E >_ O; For fixed > and e > O, ~5,~ (s, x, y) and Va'~(s,x,y) are continuous ... similar to that of Proposition 3.1 and the proof of (ii) and (iii) are by now standard, which we omit here for simplicity of presentation (see Yong-Zhou [1] and Fleming-Soner [1], for details)...
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Differential Equations and Their Applications Part 5 pptx
Ngày tải lên :
10/08/2014, 20:20
... of the coefficients of the system (2.1) (i.e., b, h, a, and 3(z) - z) and their derivatives Therefore using assumptions (H1) and (H4), and noting that supt IZ(k)(t)l
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Differential Equations and Their Applications Part 6 ppt
Ngày tải lên :
10/08/2014, 20:20
... (3.7) has multiple solutions, we have the non-uniqueness of the nodal solutions (and hence the non-uniqueness of the adapted solutions) to (3.1); and the number of the nodal solutions will be ... which are C in x and C in t with H51der continuous v , ~ s and vt of exponent a and a12, respectively Moreover, we have (3.54) IwR(t,x)l < M, (t,x) e [0,~) • BR, and for any Xo C ~ " and T > O, (0 ... between (1.1) and (2.12) holds for adapted strong and weak solutions, respectively On the other hand, from (2.13) we see easily that the group {A, B, a, b, c} satisfies (H)m if and only if {A,...
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Differential Equations and Their Applications Part 7 docx
Ngày tải lên :
10/08/2014, 20:20
... BSPDE (1.5) with a and b replaced by ~ and b w Uniqueness of Adapted Solutions In this section, we are going to establish the uniqueness of adapted weak, strong and classical solutions to our BSPDEs ... the induced norm of H by (-, ")0 and [-10, respectively The duality paring between V and V' is denoted by ( , ) , and the norms of V and V' are denoted by 1]" I[ and I[" []*, respectively We know ... Gelfand triple H 1(~n) ~+ L 2(~n) ~_+H-1 (IRa) Here, H - I ( I R ~) is the dual space of H l ( ~ n ) , and the embeddings are dense and continuous We denote the duality paring between H (]Rn) and...
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Differential Equations and Their Applications Part 8 pps
Ngày tải lên :
10/08/2014, 20:20
... condition (2.2) and (H),~ (for some m _> 1) hold for (6.2) and (6.3) Then by Theorem 2.3, for any pairs (f, g) and (f, ~) satisfying (2.14), there exist unique adapted weak solutions (u, q) and (~, ~) ... (2.11) and working on (v,p) for the transformed equations [] Our main comparison result is the following T h e o r e m 6.2 Let (1.6), (2.2) and (H),~ hold for (6.2) and (6.3) Let (f,g) and (f,~) ... the case that and ~ are not necessarily smooth enough, we may make approximation [] P r o p o s i t i o n 6.5 Let A, B, -5, b and -~ be independent of x Let f and be convex in x and nonnegative...
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Differential Equations and Their Applications Part 9 pps
Ngày tải lên :
10/08/2014, 20:20
... [0, T]) for suitable choice of and Co Again, we let L be the common Lipschitz constant for b, a, h and g We will choose and Co so that (3.21) a(T) + 23 + c(T)L > 5, and h(t)]xI + c(t)iy] + c(t)]z] ... (5.30) and (5.32), we must have (5.29) Hence, we obtain (5.25) This shows that a strong bridge ~(t) has been constructed with K, and s being given by (5.19) and (5.28), respectively, and we may ... to see that under (3.17)-(3.18), (3.21) implies (1.8) and (3.22) implies (1.7) and (1.9)' (Note (1.8) implies (1.8)') We see that the left hand side of (3.22) can be controlled by the following:...
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Differential Equations and Their Applications Part 11 pdf
Ngày tải lên :
10/08/2014, 20:20
... nondecreasing and RCLL paths, such that C(0) = and C(T) < c~, a.s.-P; and E f J 17r(s)12ds < c~ Clearly, under suitable conditions, for a given strategy (Tr,C) and the initial values p > and x >_ ... assumption (A1), we see that a and fl are bounded, adapted processes Therefore, subtracting (2.9) from (2.8), using (2.10) and (2.11), and noting the facts that u(t, x) = qo(t, x) and u(r, X(r)) _< qo(r, ... of Harrison and Kreps [1], and we so 202 Chapter Applications of FBSDEs that satisfies both (3.2) and (3.3)? If so, can Y also be described by an SDE? In an earlier work Brennan and Schwartz...
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Differential Equations and Their Applications Part 12 pot
Ngày tải lên :
10/08/2014, 20:20
... in the variables ~, x and 7r, and thus so is bo Moreover, note that for any 1-2 ~ (t, ~, ~, ~)g"(~) = l~2(t,~,x ' ~)e~2g"(~ ~) is uniformly bounded and Lipschitz in ~, x and 7r by either (H5) ... that both al and f12 are adapted processes and are uniformly bounded in (t, w) Similarly, by conditions (H1) (H3) and (H5'), we see that the process O(.,P(.)) is uniformly bounded and that there ... we know that X and X must have the form x l ( t ) = 01(t, Pl(t)); X2(t) = 02(t, P2(t)), where 01 and 02 are the classical solutions to the PDE (4.11) with terminal conditions g I and g2, respectively...
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Differential Equations and Their Applications Part 13 pot
Ngày tải lên :
10/08/2014, 20:20
... inequality in (5.18) is reversed Since both (5.4) and (5.14) are linear and homogeneous, ( - ~ , - ~ ) and ( - u , ) are both solutions to (5.14) and (5.4) as well, with the terminal condition being ... satisfies xh~(x) - h(x) 7_ O, and that § and are true interest rate and volatility such that they are {~'t}t_>o-adapted random fields satisfying ~(t,x) > r(t,x), and ~(t,x) > ~(t,x), V(t,x) Then, ... {Vik}, and that of 0., b, b and their partial derivatives Consequently, (2.36) ! k 1(4)}1 < C~{l~k I+ I~:~ I} +63 ' (h + At), Vk, i Use of the maximum principle and the estimates (2.33), (2.35) and...
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Differential Equations and Their Applications Part 14 docx
Ngày tải lên :
10/08/2014, 20:20
... Buckdahn, R., and Pardoux, E., [1] Backward stochastic differential equations and integral-partial differential equations, Stochastics and Stochastics Reports, 60 (1997), 57-83 Bellman, R., and Wing, ... Nonlinear Elliptic and Parabolic Equations of the Second Order, Reidel, Dordrecht, Holland, 1987 Krylov, N N., and Rozovskii, B L., [1] Stochastic partial differential equations and diffusion processes, ... Differential Equations and Applications, Vol 1, Academic Press, 1975 Geoffard, P Y., [1] Discounting and optimizing, preprint Gilbarg, D., and Trudinger, N S., [1] Elliptic Partial Differential Equations...
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Nonlinear equations and their solution by iteration
Ngày tải lên :
16/02/2015, 19:32
... equation and some other elliptic partial differential equations, it is useful to write A = D + L + U, 210 Nonlinear Equations and Their Solution by Iteration where D is the diagonal part of A, L and ... the solution with respect to the right hand side From T (u1 ) = b1 and T (u2 ) = b2 , we obtain T (u1 ) − T (u2 ) = b1 − b2 206 Nonlinear Equations and Their Solution by Iteration Then (T (u1 ... Nonlinear Equations and Their Solution by Iteration and c0 = c, b M Then the initial value problem (5.2.18) has a unique continuously differentiable solution u(·) on [t0 − c0 , t0 + c0 ]; and the...
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M rahman integral equations and their applications 2007
Ngày tải lên :
28/07/2016, 23:37
... integral equations We shall outline these equations using basic definitions and properties of each type 1.4.1 Volterra integral equations The most standard form of Volterra linear integral equations ... CH001.tex 26/4/2007 13: 43 Page 6 Integral Equations and their Applications 1.4.2 Fredholm integral equations The most standard form of Fredholm linear integral equations is given by the form b φ(x)u(x) ... classes and two related types of integral equations In particular, the four types are given below: • • • • Volterra integral equations Fredholm integral equations Integro-differential equations...
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