differential polynomials and their ideals
Differential Equations and Their Applications Part 1 doc
... finance and their relationship with FBSDEs Consider a security market that contains, say, one bond and one stock Suppose that their prices are subject to the following system of stochastic differential ... 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 ... 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,...
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Differential Equations and Their Applications Part 2 doc
... 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 ... X, Y taking values in IRn and ]Rm, respectively Then, by Proposition 3.1, we see that for any duration T > and any dimensions n, m, ~ and d for the processes X, Y, Z and the Brownian motion W(t),...
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Differential Equations and Their Applications Part 3 pptx
... 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 ... follows, we will not distinguish (2.12) and (2.14), and we will let (2.15) { d~(t) = A~(t)dt + Al~(t)dW(t), ~(0) = I t E [0, T], If we call (X,Y) the state and Z the control, (2.12) is called a ... ]R"~ and Z C 7-/, such that (3.5) g = (O, I)O(T) ( ~ ) y + lCZ, and define (X, Y) by (3.2) Then (X, Y, Z) E AA[0, T] is an adapted solution of (2.12) Hence, the study of operators O(T) and /(7...
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Differential Equations and Their Applications Part 4 ppsx
... 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
... 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
... 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, ... 8~(x)h < M h Dividing h and letting h + we derive lim~-~oo 8~(x) = Further, note that ~ - a ( x , ~ [ - b ( x , ) S x + h(x)8 - 1] T h e boundedness of 8, 8~, and 8xz~ exists and is continuous expansion...
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Differential Equations and Their Applications Part 7 docx
... (H),~ if and only if {A,B,~d,b,c} satisfies (H),~, where ~ and b are given by (1.4) Thus, we have the exact statements as Theorems 2.1, 2.2 and 2.3 for BSPDE (1.5) with a and b replaced by ~ and b ... the Gelfand triple V r H = H' ~ +V' We denote the inner product and the induced norm of H by (-, ")0 and [-10, respectively The duality paring between V and V' is denoted by ( , ) , and the ... 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
... 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
... [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
... 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
... 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 ... SDE (4.1) We assume the following (H6) b and a are independent of 7r and are time-homogeneous; g _> and belongs boundedly to C 2+~ for some a E (0, 1); and r is uniformly bounded Define x(t) =...
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Differential Equations and Their Applications Part 13 pot
... 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 ... approximation of the quasilinear PDE 245 by virtue of Theorem 2.2 and the definitions of h and At This proves (3) To show (2), let n and t be fixed, and assume that t E (t k, tk+l] Then, u (n) (t, x) = w...
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Differential Equations and Their Applications Part 14 docx
... 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, ... Stochastic 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 ... [1] Backward-forward stochastic differential equations and stochastic games, preprint Hamadene, S., and Lepeltier, J P., [1] Zero-sum stochastic differential games and backward equations, Sys Control...
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Báo cáo hóa học: " Some new nonlinear integral inequalities and their applications in the qualitative analysis of differential equations" potx
... this article as: Zheng and Feng: Some new nonlinear integral inequalities and their applications in the qualitative analysis of differential equations Journal of Inequalities and Applications 2011 ... Zheng and Feng Journal of Inequalities and Applications 2011, 2011:20 http://www.journalofinequalitiesandapplications.com/content/2011/1/20 Page 11 of 15 Then z(x0 , y) ≤ J−1 [v(x0 , y)], (41) and ... dsdt ∈ Dom(Y −1 ), Zheng and Feng Journal of Inequalities and Applications 2011, 2011:20 http://www.journalofinequalitiesandapplications.com/content/2011/1/20 Page 12 of 15 and β(y) u(x, y) ≤ φ −1...
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Báo cáo toán học: "The characteristic polynomial of a graph is reconstructible from the characteristic polynomials of its vertex-deleted subgraphs and their complements" doc
... 22x2 and PH (x) = PG (x) + The two graphs have identical degree sequence and PG2 (x) = PH2 (x), PG3 (x) = PH3 (x) Moreover, the characteristic polynomials of the pairs G7 , H7 , G11 , H12 and ... characteristic polynomials of a graph and its complement and main angles (see, for example, [3] p 99) References [1] D.M Cvetkovi´, M Doob and H Sachs, Spectra of Graphs - Theory and Applicac tions, Academic ... dG,j then |E(Gi )| < |E(Gj )| and by Lemma 2.1, there is an interval (0, εij ) such that WGi (x) < WGj (x) If, on the other hand dG,i < dG,j , then |E(Gi)| > |E(Gj )| and there is an interval (0,...
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Báo cáo y học: " Differential binding and co-binding pattern of FOXA1 and FOXA3 and their relation to H3K4me3 in HepG2 cells revealed by ChIP-seq" docx
... through ChIP and sequencing on the SOLiD platform Furthermore, we intended to examine their possible interactions with each other, with FOXA2, and their correlation with H3K4me3 and other TFs ... transient and rapid in the cells These interactions might also be very weak and therefore easily lost during the treatments and washes, and hence not detected by Co-IP Instances where FOXA1, FOXA2, and ... NP40 and 1% Na-deoxycholate, and once with TE-buffer Then the chromatin was eluted with 1% SDS and 0.1 M NaHCO3 before RNase-treatment and reversal of the cross-linking at 65°C for hours and Proteinase-K...
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attrators for parametric delay differential equations without uniqueness and their upper semicontinuous behavious
... C(X ), and K (X ) will denote the classes of all nonempty, nonempty and closed, and nonempty and compact subsets of X respectively B X (a, r ) will denote the open ball of X with center a and radius ... Theorem, and its proof is similar to those of [4, Prop.10] and [5, Prop.2] Proposition 10 Consider T > and a functional h : C T → Rn continuous, bounded (i.e maps bounded sets onto bounded sets), and ... non-autonomous and random dynamical systems, Dyn Contin Discrete Impuls Syst Ser A Math Anal 10 (4) (2003) 491–513 [4] T Caraballo, P Mar´ın-Rubio, J Valero, Autonomous and non-autonomous attractors for differential...
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Attackers and Their Attacks
... disinformation and propaganda – Deny service to legitimate computer users – Commit unauthorized intrusions into systems and networks that result in critical infrastructure outages and corruption ... malicious intent • Use their skills to expose security flaws Crackers • Person who violates system security with malicious intent • Have advanced knowledge of computers and networks and the skills to ... employees, and cyberterrorists • Password guessing is a basic attack that attempts to learn a user’s password by a variety of means • Cryptography uses an algorithm and keys to encrypt and decrypt...
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