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101.
We consider quadratic diophantine equations of the shape
for a polynomial Q(X1, ..., Xs) Z[X1, ..., Xs] of degree 2.Let H be an upper bound for the absolute values of the coefficientsof Q, and assume that the homogeneous quadratic part of Q isnon-singular. We prove, for all s 3, the existence of a polynomialbound s(H) with the following property: if equation (1) hasa solution x Zs at all, then it has one satisfying
For s = 3 and s = 4 no polynomial bounds s(H) were previouslyknown, and for s 5 we have been able to improve existing boundsquite significantly. 2000 Mathematics Subject Classification11D09, 11E20, 11H06, 11P55. 相似文献
102.
Structure of Degenerate Block Algebras 总被引:13,自引:0,他引:13
Given a non-trivial torsion-free abelian group (A,+,Q), a field F of characteristic 0, and a non-degenerate bi-additive skew-symmetric map
: A
A
F, we define a Lie algebra
=
(A,
) over F with basis {ex | x
A/{0}} and Lie product [ex,ey] =
(x,y)ex+y. We show that
is endowed uniquely with a non-degenerate symmetric invariant bilinear form and the derivation algebra Der
of
is a complete Lie algebra. We describe the double extension D(
, T) of
by T, where T is spanned by the locally finite derivations of
, and determine the second cohomology group H2(D(
, T),F) using anti-derivations related to the form on D(
, T). Finally, we compute the second Leibniz cohomology groups HL2(
, F) and HL2(D(
, T), F).2000 Mathematics Subject Classification: 17B05, 17B30This work was supported by the NNSF of China (19971044), the Doctoral Programme Foundation of Institution of Higher Education (97005511), and the Foundation of Jiangsu Educational Committee. 相似文献
103.
V. I. Arnold 《Functional Analysis and Its Applications》2003,37(3):177-190
We study the graph each of whose edges connects an element of a given ring with the square of itself. For a finite commutative group (e.g., for the multiplicative group of coprime residue classes modulo a positive integer), we describe this graph explicitly: each of its connected components is an oriented attracting cycle equipped with identical
-vertex rooted trees of special form whose roots reside on the cycle. We also compute the graphs of permutation groups on not too many elements and of the subgroups of even permutations; the connected components of these graphs are also uniformly equipped cycles. 相似文献
104.
This paper presents improved bounds for the norms of exceptional finite places of the group , where is an imaginary quadratic field of class number 2 or 3. As an application we show that .
105.
An O(n
2) Active Set Algorithm for Solving Two Related Box Constrained Parametric Quadratic Programs
Manuel A. Gómez 《Numerical Algorithms》2001,27(4):367-375
Recently, O(n
2) active set methods have been presented for minimizing the parametric quadratic functions (1/2)x
Dx–a
x+|
x–c| and (1/2)x
Dx–a
x+(/2)(
x–c)2, respectively, subject to lxb, for all nonnegative values of the parameter . Here, D is a positive diagonal n×n matrix, and a are arbitrary n-vectors, c is an arbitrary scalar; l and b are arbitrary n-vectors such that lb. In this paper, we show that each one of these algorithms may be used to simultaneously solve both parametric programs withno additional computational cost. 相似文献
106.
Schehrazad Selmane. 《Mathematics of Computation》2001,70(234):845-851
In this paper, we enumerate all number fields of degree of discriminant smaller than in absolute value containing a quintic field having one real place. For each one of the (resp. found fields of signature (resp. the field discriminant, the quintic field discriminant, a polynomial defining the relative quadratic extension, the corresponding relative discriminant, the corresponding polynomial over , and the Galois group of the Galois closure are given.
In a supplementary section, we give the first coincidence of discriminant of (resp. nonisomorphic fields of signature (resp. .
107.
Global Optimality Conditions in Maximizing a Convex Quadratic Function under Convex Quadratic Constraints 总被引:2,自引:0,他引:2
Jean-Baptiste Hiriart-Urruty 《Journal of Global Optimization》2001,21(4):443-453
For the problem of maximizing a convex quadratic function under convex quadratic constraints, we derive conditions characterizing a globally optimal solution. The method consists in exploiting the global optimality conditions, expressed in terms of -subdifferentials of convex functions and -normal directions, to convex sets. By specializing the problem of maximizing a convex function over a convex set, we find explicit conditions for optimality. 相似文献
108.
We compute the subdirectly irreducible factors of the free Hermitean (semi)lattice generated by a single element a subject to the relation aa
; we also compute the factors of its induced distributive presentation. 相似文献
109.
Numerical analysis of a quadratic matrix equation 总被引:8,自引:0,他引:8
The quadratic matrix equation AX2+ BX + C = 0in n x nmatricesarises in applications and is of intrinsic interest as oneof the simplest nonlinear matrix equations. We give a completecharacterization of solutions in terms of the generalized Schurdecomposition and describe and compare various numerical solutiontechniques. In particular, we give a thorough treatment offunctional iteration methods based on Bernoullis method.Other methods considered include Newtons method with exact line searches, symbolic solution and continued fractions.We show that functional iteration applied to the quadraticmatrix equation can provide an efficient way to solve the associated quadratic eigenvalue problem (2A + B + C)x = 0. 相似文献
110.
The method of quasilinearization is a procedure for obtaining approximate solutions of differential equations. In this paper, this technique is applied to a differential-algebraic problem. Under some natural assumptions, monotone sequences converge quadratically to a unique solution of our problem. 相似文献