共查询到20条相似文献,搜索用时 28 毫秒
1.
R. Fehlberg Jr. 《代数通讯》2013,41(6):2501-2512
Makar–Limanov's conjecture states that, if a division ring D is finitely generated and infinite dimensional over its center k, then D contains a free k-subalgebra of rank 2. In this work, we will investigate the existence of such structures in D, the division ring of fractions of the skew polynomial ring L[t; σ], where t is a variable and σ is a k-automorphism of L. For instance, we prove Makar-Limanov's conjecture when either L is the function field of an abelian variety or the function field of the n-dimensional projective space. 相似文献
2.
Jairo Z. Goncalves 《代数通讯》2017,45(12):5193-5201
Let k(t) be the field of rational functions over the field k, let σ be a k-automorphism of K = k(t), let D = K(X;σ) be the ring of fractions of the skew polynomial ring K[X;σ], and let D? be the multiplicative group of D. We show that if N is a noncentral normal subgroup of D?, then N contains a free subgroup. We also prove that when k is algebraically closed and σ has infinite order, there exists a specialization from D to a quaternion algebra. This allows us to explicitly present free subgroups in D?. 相似文献
3.
A code D over Z
2
n
is called a quasi-perfect Lee distance-(2t + 1) code if d
L(V,W) ≥ 2t + 1 for every two code words V,W in D, and every word in Z
2
n
is at distance ≤ t + 1 from at least one code word, where D
L(V,W) is the Lee distance of V and W. In this paper we present a fast decoding algorithm for quasi-perfect Lee codes. The basic idea of the algorithm comes from
a geometric representation of D in the 2-dimensional plane. It turns out that to decode a word it suffices to calculate its distance to at most four code
words. 相似文献
4.
W. G. Nowak 《Archiv der Mathematik》2002,78(3):241-248
For a convex planar domain D \cal {D} , with smooth boundary of finite nonzero curvature, we consider the number of lattice points in the linearly dilated domain t D t \cal {D} . In particular the lattice point discrepancy PD(t) P_{\cal {D}}(t) (number of lattice points minus area), is investigated in mean-square over short intervals. We establish an asymptotic formula for¶¶ òT - LT + L(PD(t))2dt \int\limits_{T - \Lambda}^{T + \Lambda}(P_{\cal {D}}(t))^2\textrm{d}t ,¶¶ for any L = L(T) \Lambda = \Lambda(T) growing faster than logT. 相似文献
5.
Shang Quan Bu 《数学学报(英文版)》2010,26(7):1223-1232
We study the well-posedness of the equations with fractional derivative D^αu(t) = Au(t) + f(t),0≤ t ≤ 2π, where A is a closed operator in a Banach space X, α 〉 0 and D^α is the fractional derivative in the sense of Weyl. Using known results on LP-multipliers, we give necessary and/or sufficient conditions for the LP-well-posedness of this problem. The conditions we give involve the resolvent of A and the Rademacher boundedness. Corresponding results on the well-posedness of this problem in periodic Besov spaces, periodic Triebel-Lizorkin spaces and periodic Hardy spaces are also obtained. 相似文献
6.
Paul R Wenston 《Journal of Differential Equations》1978,28(3):369-380
It is shown that an operator L with the canonical form L = Dt2p + 1 + a(t, Dx) is locally solvable if and only if a(t, Dx) satisfies a Nirenberg-Treves-type condition. 相似文献
7.
Pete L. Clark 《Israel Journal of Mathematics》2009,171(1):349-365
Let C be an algebraic curve defined over a number field K, of positive genus and without K-rational points. We conjecture that there exists some extension field L over which C has points everywhere locally but not globally. We show that our conjecture holds for all but finitely many Shimura curves
of the form X
0
D
(N)/ℚ or X
1
D
(N)/ℚ, where D > 1 and N are coprime squarefree positive integers. The proof uses a variation on a theorem of Frey, a gonality bound of Abramovich,
and an analysis of local points of small degree. 相似文献
8.
The Vlasov equation is a kinetic model describing the evolution of a plasma which is a globally neutral gas of charged particles.
It is self-consistently coupled with Poisson’s equation, which rules the evolution of the electric field. In this paper, we
introduce a new class of forward semi-Lagrangian schemes for the Vlasov–Poisson system based on a Cauchy Kovalevsky (CK) procedure
for the numerical solution of the characteristic curves. Exact conservation properties of the first moments of the distribution
function for the schemes are derived and a convergence study is performed that applies as well for the CK scheme as for a
more classical Verlet scheme. A L
1 convergence of the schemes will be proved. Error estimates [in
O(Dt2+h2 + \frach2Dt){O\left(\Delta{t}^2+h^2 + \frac{h^2}{\Delta{t}}\right)} for Verlet] are obtained, where Δt and h = max(Δx, Δv) are the discretization parameters. 相似文献
9.
Manuel Blickle Karl Schwede Shunsuke Takagi Wenliang Zhang 《Mathematische Annalen》2010,347(4):917-949
We prove that the F-jumping numbers of the test ideal
t(X; D, \mathfrakat){\tau(X; \Delta, \mathfrak{a}^t)} are discrete and rational under the assumptions that X is a normal and F-finite scheme over a field of positive characteristic p, K
X
+ Δ is
\mathbb Q{\mathbb {Q}}-Cartier of index not divisible p, and either X is essentially of finite type over a field or the sheaf of ideals
\mathfraka{\mathfrak{a}} is locally principal. This is the largest generality for which discreteness and rationality are known for the jumping numbers
of multiplier ideals in characteristic zero. 相似文献
10.
Summary. We study the 2D Ising model in a rectangular box Λ
L
of linear size O(L). We determine the exact asymptotic behaviour of the large deviations of the magnetization ∑
t∈ΛL
σ(t) when L→∞ for values of the parameters of the model corresponding to the phase coexistence region, where the order parameter m
* is strictly positive. We study in particular boundary effects due to an arbitrary real-valued boundary magnetic field. Using
the self-duality of the model a large part of the analysis consists in deriving properties of the covariance function <σ(0)σ(t)>, as |t|→∞, at dual values of the parameters of the model. To do this analysis we establish new results about the high-temperature
representation of the model. These results are valid for dimensions D≥2 and up to the critical temperature. They give a complete non-perturbative exposition of the high-temperature representation.
We then study the Gibbs measure conditioned by {|∑
t∈ΛL
σ(t) −m|Λ
L
||≤|Λ
L
|L
−
c
}, with 0<c<1/4 and −m
*<m<m
*. We construct the continuum limit of the model and describe the limit by the solutions of a variational problem of isoperimetric
type.
Received: 17 October 1996 / In revised form: 7 March 1997 相似文献
11.
María J. Cáceres José A. Cañizo Stéphane Mischler 《Journal de Mathématiques Pures et Appliquées》2011,96(4):334-362
We study the asymptotic behavior of linear evolution equations of the type t∂g=Dg+Lg−λg, where L is the fragmentation operator, D is a differential operator, and λ is the largest eigenvalue of the operator Dg+Lg. In the case Dg=−x∂g, this equation is a rescaling of the growth-fragmentation equation, a model for cellular growth; in the case Dg=−x∂(xg), it is known that λ=1 and the equation is the self-similar fragmentation equation, closely related to the self-similar behavior of solutions of the fragmentation equation t∂f=Lf.By means of entropy–entropy dissipation inequalities, we give general conditions for g to converge exponentially fast to the steady state G of the linear evolution equation, suitably normalized. In other words, the linear operator has a spectral gap in the natural L2 space associated to the steady state. We extend this spectral gap to larger spaces using a recent technique based on a decomposition of the operator in a dissipative part and a regularizing part. 相似文献
12.
Thefunction lattice L
P is the lattice of all isotone maps from a posetP into a latticeL.D. Duffus, B. Jónsson, and I. Rival proved in 1978 that for afinite poset P, the congruence lattice ofL
P is a direct power of the congruence lattice ofL; the exponent is |P|.This result fails for infiniteP. However, utilizing a generalization of theL
P construction, theL[D] construction (the extension ofL byD, whereD is a bounded distributive lattice), the second author proved in 1979 that ConL[D] is isomorphic to (ConL) [ConD] for afinite lattice L.In this paper we prove that the isomorphism ConL[D](ConL)[ConD] holds for a latticeL and a bounded distributive latticeD iff either ConL orD is finite.The research of the first author was supported by the NSERC of Canada.The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903. 相似文献
13.
E. L. Bashkirov 《Archiv der Mathematik》2002,79(5):321-327
We study the subgroups of
GLn(D) (n \geqq 3) GL_{n}(D) (n \geqq 3) over a skew field of quaternions D that comprise the subgroup of the unitary group Un(A, F) U_{n}(A, \Phi) over a subsfield
A \subseteqq D A \subseteqq D generated by all transvections in Un(A, F) U_{n}(A, \Phi) . 相似文献
14.
Shangbin Cui 《Journal of Fourier Analysis and Applications》2006,12(6):605-627
In this article we first establish some pointwise estimates for a class of multidimensional oscillatory integrals, and then
use such estimates to establish Lp – Lq estimates for a class of dispersive equations of the form Dtu − P(Dx)u = 0, where Dt = −i∂t, Dx = −i∇x, and P(Dx) is a partial differential operator whose symbol P(ξ) (ξ ∈ Rn) is an inhomogeneous real nondegenerate elliptic polynomial. These estimates not only improve, but also extend some known
results in the related topics. Tools used to obtain such results are the Van der Corput lemma, integration by parts, Young’s
inequality and the interpolation theory. 相似文献
15.
G. V. Radzievskii 《Ukrainian Mathematical Journal》2003,55(7):1218-1222
For the equation L
0
x(t) + L
1
x
(1)(t) + ... + L
n
x
(n)(t) = 0, where L
k, k = 0, 1, ... , n, are operators acting in a Banach space, we formulate conditions under which a solution x(t) that satisfies some nonlocal homogeneous boundary conditions is equal to zero. 相似文献
16.
Let K be a skew field with total subring V and G be a right ordered group with cone P, so that the crossed product algebra K*G has a skew field D of fractions. We consider total subrings R of D with R ∩ K = V, describe the overrings in D, as well as subrings of R. For particular extensions R of V we determine the prime ideals of R in terms of prime ideals of V and prime ideals of overcones of P in G. 相似文献
17.
Angelo Favini Gisèle Ruiz Goldstein Jerome A. Goldstein Enrico Obrecht Silvia Romanelli 《Mathematische Nachrichten》2010,283(4):504-521
We prove a very general form of the Angle Concavity Theorem, which says that if (T (t)) defines a one parameter semigroup acting over various Lp spaces (over a fixed measure space), which is analytic in a sector of opening angle θp, then the maximal choice for θp is a concave function of 1 – 1/p. This and related results are applied to give improved estimates on the optimal Lp angle of ellipticity for a parabolic equation of the form ?u /?t = Au, where A is a uniformly elliptic second order partial differential operator with Wentzell or dynamic boundary conditions. Similar results are obtained for the higher order equation ?u /?t = (–1)m +lAmu, for all positive integers m. 相似文献
18.
Shang Quan Bu 《数学学报(英文版)》2012,28(1):37-44
We study the well-posedness of the equations with fractional derivative Dαu(t)=Au(t)+f(t)(0 ≤t≤2π),where A is a closed operator in a Banach space X,0α1 and Dα is the fractional derivative in the sense of Weyl.Although this problem is not always well-posed in Lp(0,2π;X) or periodic continuous function spaces Cper([0,2π];X),we show by using the method of sum that it is well-posed in some subspaces of L p(0,2π;X) or C per([0,2π];X). 相似文献
19.
Eric S. Brussel 《Israel Journal of Mathematics》1996,96(1):141-183
LetF be a discretely Henselian field of rank one, with residue fieldk a number field, and letD/F be anF-division algebra. We conduct an exhaustive study of the decomposability of an arbitraryD. Specifically, we prove the following:D has a semiramified (SR)F-division subalgebra if and only ifD has a totally ramified (TR) subfield. However, there may be TR subfields not contained in any SR subalgebra. IfD has prime-power index, thenD is decomposable if and only ifD properly contains a SR division subalgebra. Equivalently,D has a decomposable Sylow factor if and only if ii(D
⊗n
)≠1/n
i(D) for somen dividing the period ofD, that is, if and only if the index fails to mimic the behavior of the period ofD. There exists indecomposableD with prime-power periodp
2 and indexp
3. Every proper division subalgebra ofD is indecomposable. Conversely, every indecomposableF-division algebra ofp-power index embeds properly in someD ofp-power index if and only ifk does not have a certain strengthened form of class field theory’s Special Case. Semiramified division algebras and division
algebras of odd index always properly embed. Finally, these results apply to an extent overk(t), and we prove that there exist indecomposablek(t)-division algebras of periodp
2 and indexp
3, solving an open problem of Saltman.
Dedicated to the memory of Amitsur
Research supported in part by NSF Grant DMS-9100148. 相似文献
20.
Abstract The Iwasava decomposition is proved for the Steinberg groups of types 2
A
2l−1, 2
D
l
, 2
E
6, 3
D
4 over the field of fractions of a principal ideal ring. By using this decomposition, it is described that subgroups exist
between the Steinberg groups over the rings D and K under some restrictions on the ring D.
This work was partially supported by RFFI (Grant No. 08-01-00824) 相似文献