double pendulum in the plane

... nonvanishing Taking the logarithm and applying (1.5), (1.6) lead to u1 (z, k) = exp ikz + Ok |z| ´ CALDERON’S INVERSE CONDUCTIVITY PROBLEM IN THE PLANE 295 On the other hand, dropping temporarily the ... Liouville’s theorem and the principle of the argument Indeed, part b) implies that F is a homeomorphism With the condition F (z) = λz+ε(z)z the winding number of F around the origin is one It ... solutions serve as the key elements for the proof of Theorem ´ CALDERON’S INVERSE CONDUCTIVITY PROBLEM IN THE PLANE 271 The Beltrami equation and the Hilbert transform In a general domain Ω we identify...

Ngày tải lên: 16/02/2014, 05:20

... the fixed point lays on the line 10x 2y This is also the case in the general setting It follows from 4.22 that whenever σnk −1 then the point xn−k , yn−k is on the line containing the fixed point ... stable In √ the other case, it is clear that the fixed points 0, ± α2 are not attracting, since every solution starting on the line x is 2-periodic Remark 4.8 It is interesting to notice that, in the ... not in the α2 , then a there are two equilibrium points 0, ±β1 , b the equilibrium point 0, β1 attracts every complete solution not starting on a point of the line x 0, c the solutions starting...

Ngày tải lên: 21/06/2014, 05:20

... + αs Then the interval u v is in A and must intersect the interval uv in P Our second tool is an old result of Minkowski [16] Lemma (Minkowski [16]) Let K be a convex set in the plane Then (x+K)∩(y+K) ... handling these sets, the notion of Minkowski norm is quite useful Let K be a compact convex set on the plane, centrally symmetric about the origin For every point x on the plane, we define the Minkowski ... that the bound on the maximum degree in Theorem is sharp Example Let K be the unit circle whose center is the origin in the plane Let K2 be the circle of radius whose center is the origin For...

Ngày tải lên: 07/08/2014, 08:20

... condition for moving up in the Bruhat order requires adding (or subtracting, depending on conventions) positive combinations of positive roots The interesting question is one of identifying when this ... then the Bruhat ordering of W θ is tight Indeed, if θ is minuscule, then the same is true for every point in the W -orbit of θ, and thus every reflection acts on W θ by adding (or subtracting) ... displayed in Figure 3, with the covering edges generated by the i-th simple reflection labeled i The non-minimal vertices corresponding to Φ i -dominant points are those that are the upper endpoint...

Ngày tải lên: 07/08/2014, 08:22

... containing a round 4-tuple Such a 4-tuple must have points in U and points in T Since in T there are only pairs, there is a pair, {a, b} say, that is part of a round 4-tuple in ≥ 969/6, so in ... simple matter The reason is that, whereas two circles in the plane are the same if they have points in common, two spheres in 3-space sharing (or even more) points need not be the same Let a ... 6) having 766 points and in a set with R(13, 7) having 330 points These results are poor compared with the cardinalities one gets by Theorem 9: 79, 196 and 104, respectively Moreover in the third...

Ngày tải lên: 07/08/2014, 13:21

... developing countries in drafting and negotiating bilateral tax treaties, with a view to maintaining the desired balance What isobtaining more tax revenue from foreign investment and special about the ... the Why countries need Double Tax Treaties? investment and in the residence country of the investor), by allocating taxing rights over this income between the two countries Double Taxation Convention ... taxpayers against double taxation of the same income; - promote the flow of international trade and investment; - provide a framework of legal and fiscal certainty to investors; - prevent discrimination...

Ngày tải lên: 05/09/2013, 14:19

... constraints on the interior structure by determining the moments of inertia of the principal axes If a liquid layer, such as an outer core, decouples the inner core from the crust, then the moment ... coefficients of the planetary gravity field, C20 and C22 In Cassini State 1, the spin vector remains coplanar with the orbit normal and the normal to the plane of the Solar System about which the orbit ... showing the mission timeline, with extensive use of the gravitational assist technique developed for Mariner 10 during the five year cruise, and the first orbiting of Mercury during the nominal...

Ngày tải lên: 06/03/2014, 19:20

... NS1 in the replication initiation process allowing efficient and specific nicking of the 3' minimal origin and leaving NS1 covalently attached to the 5' end of the DNA at the nick site [16,17] The ... (figure 1) In anticipation of the difficulties expected in manipulating the left end hairpin and to increase the chances of obtaining the desired construct two copies of the left end termini were ... the CT doublet is positioned at the 5'end and the CTC triplet is positioned inboard at the 3'end in both hairpins In the hairpin arrangement an NS1 nick site is not present at the 5' end of the...

Ngày tải lên: 19/06/2014, 08:20

... contradiction that the constant factor in the reverse of 3.1 is not the best possible Thus the theorem is proved By the same way of Theorem 3.3, we still have the following theorem Theorem 3.4 By the assumptions ... where the constant factor π is the best possible Zeng and Xie 11 also give a new inequality in the whole plane By applying the method of 10, 11 and using the way of real and complex analysis, the ... constant factor in 3.1 is not the best possible Thus the theorem is proved Journal of Inequalities and Applications In view of Note and Theorem 3.1, we still have the following theorem Theorem 3.2...

Ngày tải lên: 21/06/2014, 05:20

... variations Equation 1.1 has been strengthened by Yang and others including double series inequalities 4–21 In 2008, Xie and Zeng gave a new Hilbert-type Inequality as follows If a > 0, b > 0, ... to build a new Hilbert-type inequality with homogeneous kernel of degree 0, by estimating the weight function The equivalent inequality is considered In the following, we always suppose that: ... by introducing some lemmas ∞ Lemma 2.1 If k1 : u−1 r ln 2u cos α u2 / 2u cos β u2 du, k2 : 2u cos β u2 / − 2u cos α u2 du, then k1 4π sin r β − α /2 sin r α r sin rπ k2 4π sin r β − α /2 sin...

Ngày tải lên: 21/06/2014, 07:20

... used to show the main theorem in Section The nonlinear diffusion waves In this section, we first construct the optimal nonlinear diffusion waves of (1.2) in the quarter plane To begin with, we define ... continuity arguments In order to obtain the asymptotic behavior and optimal decay rate, noting that E = ϕ1 − ϕ2 satisfies the damping “Klein-Gordon” equation (see [14, 15]), we first obtain the ... for the corresponding initial-boundary value problem is firstly shown Next, the asymptotic behavior of the solutions towards the nonlinear diffusion waves, which are solutions of the corresponding...

Ngày tải lên: 21/06/2014, 20:20

... box • In the Grid Spacing area verify the X direction spacing is • In the Grid Spacing area type the Y direction edit box • Click the OK button Click the “X” in the top right-hand corner of the ... When the analysis is complete check the messages in the Analysis window (there should be no warnings or errors) and then click the OK button to close the Analysis window 41 Click the Joint Reaction ... size in the Minimum Graphic Font Size edit box (usually about points is sufficient), click the OK button and then click the Refresh Window button on the main toolbar 25 Select joint 106 (coordinates...

Ngày tải lên: 06/07/2014, 09:20

... 2-coloring on H2,4 , then this only extends to a 2-coloring of the larger graph, whereas from the 4-coloring we obtain all other values in the spectrum It remains to prove the necessity of the condition ... an embedding of H2,4 in the plane, where a D-edge is indicated by a double- line between its two end-points A 2-coloring is given by the partition {1, 2, 3} ∪ {4, 5, 6} and a 4-coloring by {1} ... consider the mixed hypergraph obtained from H2,4 by including the vertices {7, , t + 2} and placing them in region ∗ Also include the C-edges {367, 368, , 36(t + 2)} If we have a 2-coloring...

Ngày tải lên: 07/08/2014, 06:22

... be the link diagram corresponding to C n (H) with the tangle T corresponding to the signed plane graph H Let Q(H) = Q[H]|A=t−1/4 and β(H) = β[H]|A=t−1/4 Then points satisfying the following ... results in [13] It is worth noting that there are two closely related results in [14] and [15] In the second part, we consider the Tutte polynomial of ‘ring of tangles’ links which include the well ... where the sum is over all subsets of the edge set E of G, FG−Y (1 − w) denotes the flow polynomial in q = − w of G − Y , the graph obtained from G by deleting the edges in Y , and a∈Y a denotes the...

Ngày tải lên: 08/08/2014, 12:22

... it were, then coloring the generations according to their parity would yield a valid two-coloring of a graph containing odd cycles, a contradiction The edges that join two vertices in the same ... vertices in its generation These edges link the vertices of each generation into a cycle, with all the cycles surrounding the origin, and the cycles of earlier generations nested within those ... terms of the solutions of these recurrences; he does not derive the generating functions Some of recurrences have inhomogeneous terms; as result they give little insight into either the rate...

Ngày tải lên: 08/08/2014, 14:23

... support However, when comparing their results, the number of maternal orphans incurred in South Africa with ART intervention was similar to our findings, indicating that their methodology paralleled ... in a 0.37% decrease in population-attributable fertility for each percentage point of HIV prevalence within a country [31] In order to incorporate this reduction in TFR in HIVinfected women into ... limitations relate to the detailed methodology for calculating AIDS orphans in the presence and absence of ART For instance, there is little quantitative information regarding the effect of ART on...

Ngày tải lên: 10/08/2014, 05:22

... remaining in aripiprazole (p = 97) Olanzapine-treated patients had significantly more weight gain and triglyceride elevations in both studies Data regarding time maintaining response for the ... conceived of the study and participated in the design of the study VS, HAS, and LL acquired the data; LL performed the data analysis VS, HAS, LL, TB, and RC participated in the interpretation of the data ... studies, all from within the Eli Lilly and Company Clinical Trial Database, met inclusion criteria, including trial each comparing olanzapine to risperidone [13], quetiapine [14], and aripiprazole...

Ngày tải lên: 11/08/2014, 16:23

... convincing for the SSRIs Furthermore, medication was superior to placebo in reducing the severity of the three symptom clusters of PTSD, as well as alleviating the symptoms of depression, and in ... limbic nuclei may become kindled or sensitized, resulting in increased susceptibility to physiologic arousal [15,16] The implication of the limbic kindling-like phenomenon in the pathophysiology of ... nightmares in 79% and decreased symptoms of intrusions in 94% in those patients with these symptoms There is only one double- blind, placebo- controlled study of topiramate as a monotherapy in PTSD...

Ngày tải lên: 11/08/2014, 17:20