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Parametrization of ϵ-rational curves: error analysis [article]

Sonia L. Rueda, Juana Sendra
2010 arXiv   pre-print
The authors deeply thank Sonia Pérez-Díaz and J. Rafael Sendra for many useful discussions on the topics treated in this paper.  ...  Let L 1 and L 2 be the real asymptotes of C parallel to L 1 and L 2 respectively. We the value of η = max{H(L 1 , L 1 ), H(L 2 , L 2 ))} for all the non compact curves of F in the next table.  ...  The same process is repeated for y = j, to obtain the negative and positive integers τ 3 , τ 4 , respectively such that min{|ρ R 2 (a, j) − H(L 1 , L 1 )|, |ρ R 2 (a, j) − H(L 2 , L 2 )| / (a, j) ∈ Ω j  ... 
arXiv:1004.2148v1 fatcat:yojqlv6mwnecdjxrou42uixknq

Finite dimensional representations of invariant differential operators [article]

Ian M. Musson, Sonia L. Rueda
2003 arXiv   pre-print
χ and Lµ = Lν.  ...  Then O(Y ) G = span{Q α ∈ O(Y )|Lα = 0} ∼ = kΣ L the semigroup algebra on Σ L . If Γ, ∆ are as in the lemma and L ′ = ΓL∆, there is an isomorphism Σ L −→ Σ L ′ (17) given by x → ∆ −1 x.  ... 
arXiv:math/0305279v1 fatcat:rhy7nu56qfgmjctrsajyak5jxq

Approximate Parametrization of Plane Algebraic Curves by Linear Systems of Curves [article]

Sonia Perez-Diaz, Sonia L. Rueda, Juana Sendra, J. Rafael Sendra
2009 arXiv   pre-print
We say that an algebraic plane curve has proper degree if its defining polynomial has proper degree . The notion of ǫ-point is as follows. Definition 1.2.  ...  Let L be the algebraic closure of C(t), and C 1 , C 2 two plane projective curves over L with defining polynomials G 1 (x, y, z), G 2 (x, y, z) ∈ C[t][x, y, z], respectively.  ... 
arXiv:0901.0320v1 fatcat:xtissooypzfo5furlcd2yn6puy

On the computation of graded components of Laurent polynomial rings [article]

Sonia L. Rueda
2006 arXiv   pre-print
Consider the n × l matrix E =   0 0 0 D I l ′ 0   (8) with D as in section 2, the integer l ′ = l − t and I l ′ the l ′ × l ′ identity matrix.  ...  If p > s then permute the first r columns of L to obtain L c so that rank(subm(L c , 1 . . . n, l + 1 . . . r)) = p − s. 3. L := L c .  ... 
arXiv:math/0605567v1 fatcat:fjtc6xmulbf27kzmdvx6gk4kwq

A perturbed differential resultant based implicitization algorithm for linear DPPEs [article]

Sonia L. Rueda
2010 arXiv   pre-print
Then M φ (L h ) is an L h × L h matrix with elements in K[p] and there exists an L h × L h matrix M φ with elements in K such that M φ (L h ) = M(L h ) − p M φ .  ...  We have A D = L 1 (x 1 ) + L 2 (x 2 ) + L 3 (x 3 ) + L 4 (x 4 ) with L 1 = −864∂ 3 + 972∂ 2 − 972∂ 4 = −108∂ 2 (8∂ − 9 + 9∂ 2 ), L 2 = −216∂ 2 , L 3 = −972∂ 3 + 648∂ 2 = −324∂ 2 (3∂ − 2), L 4 = 540∂ 2  ...  For this purpose let S and M L−1 be the leading and principal matrices of P(X, U) respectively. Let P φ (X, U) be a perturbed system of P(X, U) of degree D φ ≥ 0.  ... 
arXiv:1003.4375v1 fatcat:a3cmwxduo5dgtcj27eg4h6q45m

Factorization of KdV Schrödinger operators using differential subresultants [article]

Juan J. Morales-Ruiz, Sonia L. Rueda, Maria-Angeles Zurro
2019 arXiv   pre-print
Rueda has been partially supported by the "Ministerio de Economía y Competitividad"under the project MTM2014-54141-P. M.A. Zurro is partially supported by Grupo UCM 910444.  ...  Computing the commutator with L s we obtain 0 = [A 2s+1 − µ 0 , L s ] = [QL s , L s ] − [λ 0 , L s ] = [Q, L s ]L s .  ...  Since P 2n+3 = O + P 2n−1 L where O = v n+1 ∂ − 1 2 ∂(v n+1 ), we have [L, P 2n+3 ] = [L, O] + [L, P 2n+1 ]L = [L, O] − 2∂(v n+1 )L, with [L, O] = −2∂(v n+1 )∂ 2 + (1/2)∂ 3 (v n+1 ) − v n+1 u ′ , 2∂(v  ... 
arXiv:1902.05443v1 fatcat:a7jdx3hksnftnlftkgowera73e

ACTIONS OF TORI AND FINITE FANS

SONIA L. RUEDA
2006 Algebras, Rings and Their Representations  
Let I l be the identity l × l matrix and E the n × l matrix with I l in the last l rows and zeroes in the first m rows. Then L E = 0. We define E := P E .  ...  With respect to B the vectors v l+1 , . . . , v n have coordinates v j = (− 1 d b j−l,1 , . . . , − 1 d b j−l,l ), j = l + 1, . . . , n. (19) Let m = r − l.  ... 
doi:10.1142/9789812774552_0019 fatcat:rhqumed7d5bntlo4ap56csxfrq

Linear sparse differential resultant formulas [article]

Sonia L. Rueda
2012 arXiv   pre-print
Given l ∈ T , if l ∈ T m , by (36), η l = η m • ρ(m, l) and {η l (t) | t ∈ T l } ⊆ {η m (t) | t ∈ T }, else there exist l 1 , . . . , l p ∈ {1, . . . , m − 1} such that l ∈ T lp , l k ∈ T l k−1 , k = 2  ...  , . . . , p and l 1 ∈ T m , by (36) {η l (t) | t ∈ T l } ⊆ {η lp (t) | t ∈ T \{l p }} = {η l p−1 (t) | t ∈ T \{l p−1 }} = · · · = {η l 1 (t) | t ∈ T \{l 1 }} ⊆ {η m (t) | t ∈ T }.  ... 
arXiv:1112.3921v3 fatcat:qfqhqzexprbtda6v6adkgrz5a4

Linear sparse differential resultant formulas

Sonia L. Rueda
2013 Linear Algebra and its Applications  
Given l ∈ T , if l ∈ T m , by (36), η l = η m • ρ(m, l) and {η l (t) | t ∈ T l } ⊆ {η m (t) | t ∈ T }, else there exist l 1 , . . . , l p ∈ {1, . . . , m − 1} such that l ∈ T lp , l k ∈ T l k−1 , k = 2  ...  by S(L) = {k ∈ N 0 | α k ̸ = 0}, and define ldeg(L) := min S(L), deg(L) := max S(L).  ... 
doi:10.1016/j.laa.2013.01.016 fatcat:t4jgs3a5l5gnvchdp6kekmy2tu

Approximate parametrization of plane algebraic curves by linear systems of curves

Sonia Pérez-Díaz, J. Rafael Sendra, Sonia L. Rueda, Juana Sendra
2010 Computer Aided Geometric Design  
Moreover, we introduce the polynomials X>i(t,s) = /(£i(t,s))€l(t)[s], P 2 (fl,l),s) = /(£ 2 ((i,l),s))eC(C)[s], where R(t) denotes the algebraic closure of R(t) and C(C) the field of rational functions  ...  z] such that L=UiGi(x,y,0) + U 2 G 2 (x,y,0)+zU 3 .  ... 
doi:10.1016/j.cagd.2009.12.002 fatcat:q6iwmfnanvfitpldhcpafd7ody

Rational Hausdorff Divisors: a New approach to the Approximate Parametrization of Curves [article]

Sonia L. Rueda, Juana Sendra, J. Rafael Sendra
2013 arXiv   pre-print
Λ), where L is a finite algebraic extension of K of degree k.  ...  [General Parametrization Theorem] There exists a rational proper parametrization of Curve(H(n, D)) with coefficients in L(Λ), where L is a finite algebraic extension of K of degree at most n.  ... 
arXiv:1308.4466v1 fatcat:6yi74zk66ja2zb5c7ejnjdfgv4

Commuting Ordinary Differential Operators and the Dixmier Test [article]

Emma Previato, Sonia L. Rueda, Maria-Angeles Zurro
2019 arXiv   pre-print
Dixmier, to give necessary conditions for an operator M to be in the centralizer of L. Whenever the centralizer equals the algebra generated by L and M, we call L, M a Burchall-Chaundy (BC) pair.  ...  Centralizers are maximal-commutative subalgebras, and we review the properties of a basis of the centralizer of an operator L in normal form, following the approach of K.R.  ...  C D (L) = {p 0 (L) + p 1 (L)B | p 0 , p 1 ∈ C[L]} = C[L, B].  ... 
arXiv:1902.01361v1 fatcat:de3m2tvd2nbk7miarnuaibml2e

An algorithm to parametrize approximately space curves

Sonia L. Rueda, Juana Sendra, J. Rafael Sendra
2013 Journal of symbolic computation  
We introduce the following polynomial A(t) = { c 1 (t) ∏ i=2 u i,1 (t)q i (t) + · · · + c (t) ∏ −1 i=1 u i, (t)q i (t) if > 1 c 1 (t) if = 1.  ...  Let = deg xn (G 1 ). Since = tdeg(G 1 ), Lemma 2.2.  ...  If = 1 the result is trivial. Let > 1 and let R(t), Q(t) be the remainder and quotient of the division of A(t) by q(t), respectively. Clearly deg(R) < deg(q).  ... 
doi:10.1016/j.jsc.2013.04.002 fatcat:5ahvnkfgdje5dhbhg3sfnj5zgi

Thermal Noise in Electro-Optic Devices at Cryogenic Temperatures [article]

Sonia Mobassem, Nicholas J. Lambert, Alfredo Rueda, Johannes M. Fink, Gerd Leuchs, Harald G. L. Schwefel
2020 arXiv   pre-print
The quantum bits (qubits) on which superconducting quantum computers are based have energy scales corresponding to photons with GHz frequencies. The energy of photons in the gigahertz domain is too low to allow transmission through the noisy room-temperature environment, where the signal would be lost in thermal noise. Optical photons, on the other hand, have much higher energies, and signals can be detected using highly efficient single-photon detectors. Transduction from microwave to optical
more » ... requencies is therefore a potential enabling technology for quantum devices. However, in such a device the optical pump can be a source of thermal noise and thus degrade the fidelity; the similarity of input microwave state to the output optical state. In order to investigate the magnitude of this effect we model the sub-Kelvin thermal behavior of an electro-optic transducer based on a lithium niobate whispering gallery mode resonator. We find that there is an optimum power level for a continuous pump, whilst pulsed operation of the pump increases the fidelity of the conversion.
arXiv:2008.08764v1 fatcat:7a5rz2vmjzehjpwyvvzdo3t7oa

Differential elimination by differential specialization of Sylvester style matrices

Sonia L. Rueda
2015 ACM Communications in Computer Algebra  
To start, through derivations, a system ps(P) of L polynomials in L − 1 algebraic variables is obtained, which is non sparse in the order of derivation.  ...  Furthermore Ll=1 τ l ∑ h=1 r l,h y σ l,h P l = y α Ll=1 τ l ∑ h=1 r l,h C l α−σ l,h = y α D. Since D ∈ Q[C], we have D = y −α Ll=1 τ l ∑ h=1 r l,h y σ l,h P l ∈ (ags(P)) ∩ Q[C].  ...  This proves g 1,1 Ll=1 τ l ∑ h=1 r l,h (y σ l,h P l − C l α−σ l,h y α ) = γ Ll=1 τ l ∑ h=1 g l,h (y σ l,h P l − C l α−σ l,h y α ) = 0, and g 1,1 ̸ = 0 in the domain Q[C][Y ± ] implies Ll=1 τ l  ... 
doi:10.1145/2768577.2768635 fatcat:skxdncfggzasdewztx74mhzlqm
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