weierstrass theorem and approximation
Girsanov’s theorem and the risk-neutral measure
... Williams’ “standard machine” f IP and IP Z The intuition behind the formula f IP A = is that we want to have A Z T dIP 8A F f IP ! = Z T; ! IP ! ; f f but since IP ! = and I ! = ... T is normal with mean zero and variance P mean T and variance T e T Under IP , B T is normal with Means change, variances don’t When we use the Girsanov Theorem to change the probability ... proved Lemmas 1.53 and 1.54, we have not proved Girsanov’s Theorem We will not prove it completely, but here is the beginning of the proof Lemma 1.55 Using the notation of Girsanov’s Theorem, we have...
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Tài liệu Báo cáo khoa học: "Extraction and Approximation of Numerical Attributes from the Web" pdf
... any pre-specified (e.g., (Riloff and Jones, 1999; Chklovski and Pantel, 2004)) and unspecified (e.g., (Banko et al., 2007; Rosenfeld and Feldman, 2007; Davidov and Rappoport, 2008b)) relation types ... acceptable values and an approximation range Crudeness of desired approximation depends both on potential applications and on object type Some objects show much greater variability in size (and hence ... value was used as an answer • NOCB: No boundary and no comparison data were collected and processed (Pcompare and Pbounds were empty) We only collected and processed a set of values for the similar...
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Báo cáo hóa học: " Research Article Real-Time Guitar Preamp Simulation Using Modified Blockwise Method and Approximations Jaromir Macak and Jiri Schimmel" docx
... Vin (21) and the fractional part is obtained from p = Vin − i (22) The system of (12) has three inputs (input voltage and two input voltages on capacitors), and therefore M = and N = and three ... system (N = 2) Generally, it requires 2(N −1) − linear interpolations and 2(N −1) spline approximations All approximations and interpolations work with indexes into a vector of spline coefficients ... 16 cg + c p , where i1 , i2 , and i3 are numbers of iterations of the first, second, and third block, respectively Simulation Using Modified Blockwise Method and Approximation A system of differential...
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báo cáo hóa học:" Research Article Browder’s Fixed Point Theorem and Some Interesting Results in Intuitionistic Fuzzy Normed Spaces" doc
... 26, 27 As a consequence of Theorem 4.1 30 and Browder’s theorems 26, 27 in crisp normed linear space we have Browder’s theorems in intuitionistic fuzzy normed space Theorem 2.1 Let K be a nonempty ... Science and Its Applications, vol 3, no 2, pp 96–109, 2010 13 R Saadati, S Sedghi, and N Shobe, “Modified intuitionistic fuzzy metric spaces and some fixed point theorems,” Chaos, Solitons and Fractals, ... Chitra and P V Subrahmanyam, “Fuzzy sets and fixed points,” Journal of Mathematical Analysis and Applications, vol 124, no 2, pp 584–590, 1987 27 V Gregori and S Romaguera, “Fixed point theorems...
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Báo cáo hóa học: "Research Article Common Fixed Point and Approximation Results for Noncommuting Maps on Locally Convex Spaces" docx
... f − T y and hence F T ∩ F f ∩ F g / ∅ Theorem 2.7 extends and improves 14, Theorem 2.2 , 7, Theorems 2.2-2.3, and Corollaries 2.4–2.7 , 13, Theorem , and the main results of Tarafdar and Taylor ... singleton The following result generalizes 19, Theorem 2.3 , 24, Theorem 2.11 , and 21, Theorem 2.2 and improves 14, Theorem 2.2 and 13, Theorem Theorem 3.4 Let M be a nonempty τ-bounded subset ... Li 23 , Hussain 24 , Hussain and Berinde 25 , Hussain and Jungck , Hussain and Khan , Hussain and Rhoades , Jungck and Sessa 13 , Khan and Akbar 19, 20 , Pathak and Hussain 21 , Sahab et al 12...
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Báo cáo hóa học: " Research Article Remarks on Separation of Convex Sets, Fixed-Point Theorem, and Applications in Theory of Linear Operators" pot
... respect to X Theorem 2.7 Let X be a space as in Theorem 2.6, and let K0 and K1 be disjoint bounded open convex sets relative to subspaces X0 and X1 of X, respectively, that is, K0 ⊂ X0 and Kamal ... that the sets K0 and K1 are open relative to the subspaces X0 and X1 of X, respectively, and we will consider case For the proof in this case, we will use the theorem of Kakutani and Tukey [23] ... well-known result (Theorem 2.2) From here the statement of the theorem follows For the proof of case 3, one may use the proof of Theorem 2.6 and cases 1, Thus we obtain the validity of Theorem 2.7 Note...
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Báo cáo hóa học: "GEOMETRIC AND APPROXIMATION PROPERTIES OF SOME SINGULAR INTEGRALS IN THE UNIT DISK" doc
... 2 Geometric and approximation properties ∗ Here Pξ ( f ) is said to be of Picard type, Qξ ( f ), Qξ ( f ), and Rξ ( f ) are said to be of Poisson∗ Cauchy type, and Wξ ( f ) and Wξ ( f ) are ... · Qξ ( f ) and (1/c1 (ξ)) · Rξ ( f ) are similar, which proves the theorem Remarks 3.3 (1) Theorem 3.2(iii) says that if f ∈ S3,b1 (ξ) , then Qξ ( f ) is starlike and univalent on D and if f ∈ ... proof of Theorem 2.1(i), page 252]) Remark 2.2 Theorem 2.1(ii) and (iii) remain valid for f only continuous on D In what follows, we present some geometric properties of Pξ ( f )(z) Theorem 2.3...
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Báo cáo hóa học: " THE LEFSCHETZ-HOPF THEOREM AND AXIOMS FOR THE LEFSCHETZ NUMBER" pot
... prove the Lefschetz-Hopf theorem in a quite natural manner by showing that the fixed-point index satisfies the axioms of Theorem 1.1 That is, we prove the following theorem Theorem 1.3 (normalization ... Lefschetz-Hopf theorem Thus, the homotopy and additivity properties of the fixed-point index imply that the normalization property follows from the Lefschetz-Hopf theorem Lefschetz numbers and exact ... where X,P,Q ∈ Ꮿ and (X;P,Q) is a proper triad [6, page 34] If f : X → X is a map such that f (P) ⊆ P and f (Q) ⊆ Q, then, for fP , fQ , and fP∩Q being the restrictions of f to P, Q, and P ∩ Q, respectively,...
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Báo cáo hóa học: " NEW VERSIONS OF THE FAN-BROWDER FIXED POINT THEOREM AND EXISTENCE OF ECONOMIC EQUILIBRIA" pot
... point theorem and economic equilibria we show that a number of Urai’s results [12] (e.g., Theorem for the case (K∗ ), Theorem for the case (NK∗ ), Theorem for the case (K∗ ), Theorem 19, and their ... point theorem, other (approximate) fixed point theorems, and so on In fact, from Theorem 2.2, we can easily deduce the following Fan-Browder fixed point theorem Corollary 2.3 (Browder [1, Theorem ... proof Note that Theorem 2.2 is actually equivalent to Theorem 2.1 Proof of Theorem 2.1 using Theorem 2.2 Suppose that there exists M ∈ D such that z∈M F(z) = ∅ under the hypothesis of Theorem 2.1...
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METHODS FOR DETERMINATION AND APPROXIMATION OF THE DOMAIN OF ATTRACTION IN THE CASE OF AUTONOMOUS pdf
... < ≤ A , then there exist p ≥ and r p > such that B(r p ) ⊂ Ω and f p (x) < x for any p ∈ { p, p + 1, ,2 p − 1} and x ∈ B(r p ) \ {0} Proof We have that ρ(A) < if and only if lim p→∞ A p = (see ... − 1} and x ∈ B(R) \ {0} 8 Domains of attraction—dynamical systems If for any r > 0, we have that B(r) ⊂ Ω and f p (x) < x for any p ∈ { p, p + 1, , p − 1} and x ∈ B(r) \ {0}, then R = +∞ and ... B(R) Remark 3.9 If R = +∞ (i.e., Ω = Rn and f p (x) < x , for any p ∈ { p, p + 1, ,2 p − 1} and x ∈ R \ {0}), then N p = Rn for any p ≥ and Da (0) = Rn Theorem 3.10 For any x ∈ Da (0) there exists...
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Báo cáo toán học: "Mountain Pass Theorem and Nonuniformly Elliptic Equations" doc
... ≥ α and β is a critical value of I Our main results are the following theorems, which generalize the Z2 version of Mountain Pass Theorem and Saddle Point Theorem in [9, p 24, Theorem 4.6 and ... cited Theorem A.4, and arguing as in the proofs of the cited Theorems 8.1 and 9.12, we get the desired result 2.5 Proof of Theorem 1.4 Arguing as in the proof of Theorem 1.3 above, we have Theorem ... generalizations of Mountain Pass Theorem and Saddle Point Theorem The main tool for proving these theorems is Theorem 2.2, which is a generalized deformation theorem Hence, Theorem 2.2 is most important...
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Báo cáo toán học: "The q-Binomial Theorem and two Symmetric q-Identities" doc
... q-binomial theorem and Theorems 1.2 and 1.3 Our combinatorial proof of the q-binomial theorem is based on Theorem 2.1, and is essentially the same as that of Alladi [2] or Pak [8] Proof of Theorem ... on the right-hand side is equal to q |µ| aodd(µ) µ∈P1 (µ)≤n The proof then follows from the involution σ in the proof of Theorem 2.1 Proof of Theorem 1.2 Replacing q and z by q and −zq, respectively, ... due to Andrews, Jim´nez-Urroz, and Ono [4] Here we describe Chapman’s proof e Proof of Theorem 2.1 We shall construct an involution σ on P1 such that σ preserves |λ| while interchanging (λ) and...
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Báo cáo toán học: "Minimum Common String Partition Problem: Hardness and Approximations" pptx
... theorem Theorem 3.1 An α -approximation algorithm for MIN 2-SAT yields α-approximations for both 2-MCSP and 2-SMCSP Corollary 3.2 There exist polynomial 1.1037 -approximation algorithms for 2-MCSP and ... from A and the other one from B, such that = bj and ai+1 = bj+1 Two matches (ai ai+1 , bj bj+1 ) and (ak ak+1 , bl bl+1 ), i ≤ k, are in conflict if either i = k and j = l, or i + = k and j + ... result of this section is the following theorem Theorem 2.1 2-MCSP and 2-SMCSP are APX-hard problems We start by proving a weaker result Theorem 2.2 2-MCSP and 2-SMCSP are NP-hard problems Proof:...
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Báo cáo toán học: "Kocay’s lemma, Whitney’s theorem, and some polynomial invariant reconstruction problems" docx
... the graphs F1 and F2 has a component isomorphic to G When F2 = 2G, then Equation (10) follows from Lemma 2.9 and Corollary 2.10 When F1 = G + X and F2 = G + Y , and v(X) < v(G) and v(Y ) < v(G), ... covered by ΛI = G, and then construct N (Λj ), and assign it a multiplicity equal to the edge label on ΛI − Λj Remark It is is possible that for distinct j and k, the matrices N(Λj ) and N(Λk ) are ... two graphs Λi and Λj in Λ(G + H) σ(Λj ) Λj We have to consider only the case in which at least one of Λi and Λj has a component isomorphic to G or H, and v(Λj ) ≤ v(Λi ) Λj = G + X and Λi = G +...
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Báo cáo toán học: "Flexible Color Lists in Alon and Tarsi’s Theorem, and Time Scheduling with Unreliable Participants" pot
... Alon and Tarsi’s Theorem We use our strengthening to provide paintability versions of Alon and Tarsi’s bound of the list chromatic number of bipartite and planar bipartite graphs (Theorem 3.3 and ... Paint cannot move any more, and Mrs Correct’s strategy succeeds Applications of Alon and Tarsi’s Theorem There are several “classical” applications of Alon and Tarsi’s Theorem The proofs in these ... slots at each edge of K5 , and H¨ggkvist and a Janssen’s Theorem guarantees that appropriate appointments can be made Now, our strengthening of H¨ggkvist and Janssen’s Theorem tells us that even...
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Báo cáo toán học: "Hybrid Proofs of the q-Binomial Theorem and other identities" ppsx
... aq) Analytic proofs were given by Watson [32] and Andrews [1], and a combinatorial proof has been given in [9] by Berndt, Kim and Yee Theorem If |q| < and a = −q −2n for any integer n > 0, then ... 1986 [5] G E Andrews, A Knopfmacher and J Knopfmacher, Engel expansions and the Rogers-Ramanujan identities, J Number Theory 80 (2000), no 2, 273–290 [6] G E Andrews, A Knopfmacher and P Paule, ... Math 25 (2000), no 1, 2–11 [7] G E Andrews and A Berkovich, The WP-Bailey tree and its implications, J London Math Soc (2) 66 (2002), no 3, 529–549 [8] G E Andrews and B C Berndt, Ramanujan’s Lost...
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