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1.
Wolfgang Hein 《manuscripta mathematica》1985,52(1-3):97-130
Pair algebras which have a non degenerate (left- and right-) invariant bilinear form and for which the inner derivation algebra is completely reducible are characterised by pairs (C,), where C is a n×n matrix satisfying certain conditions and is a sequence of n integers equal to 0 or 1. They occur as pair algebras of type (S(C,)–1,S(C,)1), xuy=[[x,u],y], where (S(C,)r)r is the gradation induced by . in the Kac-Moody algebraS(C). If C is an affin Cartan matrix (as in the case of Lie triple systems), there exists a finite dimensional simple Lie algebrag and a Aut (g), ord =m< such that the pair algebra is isomorphic to the pair algebra (g
–1,g
1), xuy=[[x,u],y] (product ing), whereg
i. is the eigenspace of of eigenvalue i, a primitive m-th root of unity. 相似文献
2.
Jesüs M. Ruiz 《manuscripta mathematica》1984,46(1-3):193-214
Let XoR
n be an irreducible analytic germ and the order space of its field of meromorphicfunetion germs. A formal half-branch in Xo is a kind of C-map germ c[0,)Xo; an ordering is centered at c if it contains the functions which are positive on c. We obtain a partition 1,...,d, d=dim Xo, of the set * of central (i.e.: centered at some half-branch) orderings, according to the dimension of half-branches. Then we show that all e, e= 1,.,d, as well as the set \* of noncentral orderings, are dense in . Finally, we solve the 17th Hubert Problem for analytic germs. 相似文献
3.
Philippe Bonnet 《Transformation Groups》2002,7(1):3-14
In this paper we establish two results concerning algebraic (,+)-actions on
n
. First, let be an algebraic (,+)-action on 3. By a result of Miyanishi, its ring of invariants is isomorphic to [t
1,t
2]. Iff
1,f
2 generate this ring, the quotient map of is the mapF:32,x(f
1(x), f2(x)). By using some topological arguments we prove thatF is always surjective. Secon, we are interested in dominant polynomial mapsF:
n
n-1
whose connected components of their generic fibers are contractible. For such maps, we prove the existence of an algebraic (,+)-action on
n
for whichF is invariant. Moreover we give some conditions so thatF*([t
1,...,t
n-1
]) is the ring of invariants of .Dedicated to all my friends and my family 相似文献
4.
For a solution u of –u=u(1–|u|2) on the whole plane, |u|<1 holds everywhere unless u=ei for some ; the derivatives of order k have moduli a constant M
kdepending only on k. For a solution u on an open set 2, the moduli of u and its derivatives have upper bounds depending only on the distance to 2\ therefore the set of solutions on a given is compact in C() for the topology of uniform convergence on compact subsets of . For a solution u such that |u|<1, 1–|u| satisfies an estimation similar to the classical Harnack inequality for positive harmonic functions.Finally, if is bounded and |u| has a lim supm at each boundary point, the |u|m in if m1, but if m<1 then |u| admits only a majorant S
m
with values in ]m, 1[ and sufficient conditions are given for lim S
m
=0 or S
m
=O(m) as m0. 相似文献
5.
Weak L
2
-solutions u of the Schrödinger equation, –u + q(x) u – u = f(x) in L
2
, are represented by a Fourier series using spherical harmonics in order to prove the following strong maximum and anti-maximum principles in
(N 2): Let 1 denote the positive eigenfunction associated with the principal eigenvalue 1 of the Schrödinger operator
. Assume that the potential q(x) is radially symmetric and grows fast enough near infinity, and f is a `sufficiently smooth' perturbation of a radially symmetric function, f 0 and 0 f / C const a.e. in
. Then u is 1-positive for - < < 1 (i.e., u c 1 with c const > 0) and 1-negative for 1 < < 1 + (i.e., u –c1 with c const > 0), where > 0 is a number depending on f. The constant c > 0 depends on both and f. 相似文献
6.
V. I. Vichirko 《Journal of Mathematical Sciences》1986,34(4):1751-1753
An algorithm is described for the approximate calculation of a collection of sums of the form k=
j–1
n
cj/(j+k), 1kn, where 0<j. The working time of the algorithm is 0(n(t+ log n)(t+log n)) if k calculated to within 2–t; here the function (l) denotes the time of multiplication of twoZ-bit numbers.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 137, pp. 3–6, 1984.In conclusion, the author expresses thanks to A. O. Slisenko and Yu. A. Kuznetsov, who drew the attention of the author to the problem considered. 相似文献
7.
Arturo A. L. Sangalli 《manuscripta mathematica》1972,6(2):177-205
In this paper we propose an axiomatization of the notion of system of terms of a theory by means of which we obtain a representation of equational classes (or varieties) of algebras. We define analgebraic
transformational
system (S.T.A.) as a quadruple (T,v,S,+) satisfying the axioms, where T is a set containing the variables v(n), n, and having operators S(): TT, . In addition there are operations Q+ on T commuting with the operators. A notion of morphism between S.T.A. 's is defined to obtain the category which is shown to be equivalent to the dual of the category of equational classes. In the last section we establish the equivalence between and Lawvere's category of algebraic theories in which every definable constant is present.
Extrait de la Thèse de doctorat de l'auteur, Université de Montréal, 1971. 相似文献
Extrait de la Thèse de doctorat de l'auteur, Université de Montréal, 1971. 相似文献
8.
Summary For solving the nonlinear systemG(x, t)=0,G|
n
× 1
n
, which is assumed to have a smooth curve of solutions a continuation method with self-choosing stepsize is proposed. It is based on a PC-principle using an Euler-Cauchy-predictor and Newton's iteration as corrector. Under the assumption thatG is sufficiently smooth and the total derivative (1
G(x, t)2
G(x, t)) has full rankn along the method is proven to terminate with a solution (x
N
, 1) of the system fort=1. It works succesfully, too, if the Jacobians 1
G(x, t) become singular at some points of , e.g., if has turning points. The method is especially able to give a point-wise approximation of the curve implicitly defined as solution of the system mentioned above. 相似文献
9.
Using a capacity approach, we prove in this article that it is always possible to define a realization of the Laplacian on L
2() with generalized Robin boundary conditions where is an arbitrary open subset of R
n
and is a Borel measure on the boundary of . This operator generates a sub-Markovian C
0-semigroup on L
2(). If d=d where is a strictly positive bounded Borel measurable function defined on the boundary and the (n–1)-dimensional Hausdorff measure on , we show that the semigroup generated by the Laplacian with Robin boundary conditions has always Gaussian estimates with modified exponents. We also obtain that the spectrum of the Laplacian with Robin boundary conditions in L
p
() is independent of p[1,). Our approach constitutes an alternative way to Daners who considers the (n–1)-dimensional Hausdorff measure on the boundary. In particular, it allows us to construct a conterexample disproving Daners' closability conjecture. 相似文献
10.
Thewidth (chain number) of a partial order P, < is the smallest cardinal such that ¦A¦< 1 + whenever A is an antichain (chain) in P. We prove that, if a partial order (P, <) has width and cf()=, then P contains antichains An (n<) such that ¦A
0¦<¦A1¦ <...<={¦An¦: n < < } and either A01 A2< ... or A0>A1 >A2> ... A similar structure result is obtained for partial orders with chain number if cf()=. As an application we solve a problem of van Douwen, Monk and Rubin [1] by showing that if a Boolean algebra has width , thencf() .This work has been partially supported by NATO grant No. 339/84.Presented by Bjarni Jonsson. 相似文献
11.
We consider the method for constrained convex optimization in a Hilbert space, consisting of a step in the direction opposite to an
k
-subgradient of the objective at a current iterate, followed by an orthogonal projection onto the feasible set. The normalized stepsizes
k
are exogenously given, satisfying
k=0
k = ,
k=0
k
2
< , and
k is chosen so that
k k for some > 0. We prove that the sequence generated in this way is weakly convergent to a minimizer if the problem has solutions, and is unbounded otherwise. Among the features of our convergence analysis, we mention that it covers the nonsmooth case, in the sense that we make no assumption of differentiability off, and much less of Lipschitz continuity of its gradient. Also, we prove weak convergence of the whole sequence, rather than just boundedness of the sequence and optimality of its weak accumulation points, thus improving over all previously known convergence results. We present also convergence rate results. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Research of this author was partially supported by CNPq grant nos. 301280/86 and 300734/95-6. 相似文献
12.
A. T. Semenov 《Mathematical Notes》1974,15(4):362-366
Let 1, 2, ... be a sequence of independent identically distributed random variables with zero means. We consider the functional
n
=
k=o
n
(S
k
) where S1=0, Sk=
i=1
k
i (k1) and(x)=1 for x0,(x) = 0 for x<0. It is readily seen that n is the time spent by the random walk Sn, n0, on the positive semi-axis after n steps. For the simplest walk the asymptotics of the distribution P (n = k) for n and k, as well as for k = O(n) and k/n<1, was studied in [1]. In this paper we obtain the asymptotic expansions in powers of n–1 of the probabilities P(hn = nx) and P(nx1 n nx2) for 0<1, x = k/n 2<1, 0<1x122<1.Translated from Matematicheskie Zametki, Vol. 15, No. 4, pp. 613–620, April, 1974.The author wishes to thank B. A. Rogozin for valuable discussions in the course of his work. 相似文献
13.
S. R. Treil' 《Journal of Mathematical Sciences》1989,44(6):868-869
It is proved that for every sequence of points n from the unit circle, n1, and for an arbitrary sequence of positive numbers An, An, there exists a continuous real function u, such that for the Toeplitz operator T (acting in the Hardy space H2) with the symbol =e
iu
we have the estimates (T–nI)–1>An, n.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, AN SSSR, Vol. 157, pp. 175–177, 1987. 相似文献
14.
Walter Benz 《Journal of Geometry》1977,10(1-2):45-56
Denote (xi,yi=cti), i=1,2, by Xi and (x2–x1)2–(y2–y1)2 by F(X1,X2). Then our result is the following: Given a fixed real number 0 and given a bijection of M=IR2 such that F(X1,X2) = iff F(X
in1
su
,
in2
su
) =p for all X1, X2 M. Then must be a Lorentz transformation (time reversal and inhomogeneity included). 相似文献
15.
Martin Schottenloher 《manuscripta mathematica》1977,21(4):315-327
Given a function: + on a domain spread over an infinite dimensional complex Banach space E with a Schauder basis such that -log is plurisubharmonic and d (d denotes the boundary distance on ) one can find a holomorphic function f: with
f, where
f is the radius of convergence of f. If, in addition, is locally Lipschitz continuous with constant 1, f can be chosen so that (3M)–1
f, where M is the basis constant of E. In the particular case of E=
1 there are holomorphic functions f on with=
f. 相似文献
16.
G. V. Radzievskii 《Ukrainian Mathematical Journal》1990,42(2):173-182
One investigates the minimality of derivative chains, constructed from the root vectors of polynomial pencils of operators, acting in a Hilbert space. One investigates in detail the quadratic pencil of operators. In particular, for L()=L0+L1+2L2 with bounded operators L00, L20 and Re L10, one shows the minimality in the space173-02 of the system {xk, kekxk}, where xk are eigenvectors of L(), corresponding to the characteristic numbers kin the deleted neighborhoods of which one has the representation L–1()=(–k)–1RK+WK() with one-dimensional operators Rk and operator-valued functions WK(), k=1, 2, ..., analytic for =k.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 195–205, February, 1990. 相似文献
17.
V. G. Sushko 《Mathematical Notes》1970,8(3):646-652
The proximity is investigated of the solution of Cauchy's problem for the equation u
t
+((u))x= u
xx
((u) > 0) to the solution of Cauchy's problem for the equation ut+ ((u))x= 0, when the solution of the latter problem has a finite number of lines of discontinuity in the strip 0 t T. It is proved that, everywhere outside a fixed neighborhood of the lines of discontinuity, we have |u–u| C, where the constant C is independent of. Similar inequalities are derived for the first derivatives of u–u.Translated from Matematicheskie Zametki, Vol. 8, No. 3, pp. 309–320, September, 1970.In conclusion we express our gratitude to L. A. Chudov for his valuable advice concerning this work. 相似文献
18.
Dr. Richard Weiss 《Monatshefte für Mathematik》1977,83(1):65-75
An undirected graph of valencyd and girth is called a (d, )-cage if its automorphism group acts transitively on the set of alls-paths in ands(+1)/2. We discuss an elementary construction of two known families of cages which allows us to prove easily some facts about their automorphism groups. We give, for example, a new proof of the fact that the automorphism group ofSp
4(2
n
) contains elements which are not induced by Sp
4(2
n
). 相似文献
19.
The difference sequence spaces (), c(), and c
0() were studied by Kzmaz. The main purpose of the present paper is to introduce the space bv
p consisting of all sequences whose differences are in the space
p
, and to fill up the gap in the existing literature. Moreover, it is proved that the space bv
p is the BK-space including the space
p
. We also show that the spaces bv
p and
p
are linearly isomorphic for 1 p . Furthermore, the basis and the -, -, and -duals of the space bv
p are determined and some inclusion relations are given. The last section of the paper is devoted to theorems on the characterization of the matrix classes (bv
p : ), (bv :
p
), and (bv
p : 1), and the characterizations of some other matrix classes are obtained by means of a suitable relation. 相似文献
20.
Consider the stochastic partial differential equationdu
(t,x) = (t)u
(t, x)dt + dW
Q(t,x), 0 t T
where = 2/x
2, and is a class of positive valued functions. We obtain an estimator for the linear multiplier (t) and establish the consistency, rate of convergence and asymptotic normality of this estimator as 0. 相似文献