共查询到20条相似文献,搜索用时 31 毫秒
1.
Rossella Agliardi 《Annali dell'Universita di Ferrara》1993,39(1):93-109
A well-known example by Ivrii concerning the operatorP=D
t
2
−t2lD
x
2
+atkDx (a≠0), shows that there exists a delicate relation amongl, k and the Gevrey index of well-posedness of the Cauchy problem. In this paper we give a generalization to a class of pseudo-differential
operators includingP.
Sunto Un famoso esempio di Ivrii riguardante l'operatoreP=D t 2 −t2lD x 2 +atkDx (a≠0), mostra che c'è una relazione sottile tral, k e l'indice di Gevrey di buona positura del problema di Cauchy. In questo articolo viene data una generalizzazione ad una classe di operatori pseudodifferenziali che comprendeP.相似文献
2.
E. J. Cheon 《Designs, Codes and Cryptography》2009,51(1):9-20
In this paper, we determine the smallest lengths of linear codes with some minimum distances. We construct a [g
q
(k, d) + 1, k, d]
q
code for sq
k-1 − sq
k-2 − q
s
− q
2 + 1 ≤ d ≤ sq
k-1 − sq
k-2 − q
s
with 3 ≤ s ≤ k − 2 and q ≥ s + 1. Then we get n
q
(k, d) = g
q
(k, d) + 1 for (k − 2)q
k-1 − (k − 1)q
k-2 − q
2 + 1 ≤ d ≤ (k − 2)q
k-1 − (k − 1)q
k-2, k ≥ 6, q ≥ 2k − 3; and sq
k-1 − sq
k-2 − q
s
− q + 1 ≤ d ≤ sq
k-1 − sq
k-2 − q
s
, s ≥ 2, k ≥ 2s + 1 and q ≥ 2s − 1.
This work was partially supported by the Com2MaC-SRC/ERC program of MOST/KOSEF (grant # R11-1999-054) and was partially supported by the Korea Research Foundation Grant funded by the Korean Government(MOEHRD)(KRF-2005-214-C00175). 相似文献
3.
Olga Lavila-Vidal 《manuscripta mathematica》1998,95(1):47-58
We consider the blowing up of ℙ
k
/n−1
along a closed subscheme defined by a homogeneous idealI ∪A=k[X
1, …,X
n
] generated by forms of degree ≤d, and its projective embeddings by the linear systems corresponding to (I
e
)
c
, forc≥de+1. The homogeneous coordinate rings of these embeddings arek[(I
e
)
c
]. One wants to study the Cohen-Macaulay property of these rings. We will prove that if the Rees algebraR
A
(I) is Cohen-Macaulay, thenk[(I
e
)
c
] are Cohen-Macaulay forc>>e>0, thus proving a conjecture stated by A. Conca, J. Herzog, N.V. Trung and G. Valla.
Supported by a F.P.I. grant of Ministerio de Educación y Ciencia (Spain)
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. 相似文献
4.
Asymptotic Upper Bounds for Ramsey Functions 总被引:5,自引:0,他引:5
We show that for any graph G with N vertices and average degree d, if the average degree of any neighborhood induced subgraph is at most a, then the independence number of G is at least Nf
a
+1(d), where f
a
+1(d)=∫0
1(((1−t)1/(
a
+1))/(a+1+(d−a−1)t))dt. Based on this result, we prove that for any fixed k and l, there holds r(K
k
+
l
,K
n
)≤ (l+o(1))n
k
/(logn)
k
−1. In particular, r(K
k
, K
n
)≤(1+o(1))n
k
−1/(log n)
k
−2.
Received: May 11, 1998 Final version received: March 24, 1999 相似文献
5.
Gerhard Frey 《Israel Journal of Mathematics》1994,85(1-3):79-83
Thed-th symmetric productC
(d) of a curveC defined over a fieldK is closely related to the set of points ofC of degree ≤d. IfK is a number field, then a conjecture of Lang [Hi] proved by Faltings [Fa2] implies ifC
(d)
(K) is an infinite set, then there is aK-rational covering ofC → ℙ
|K
1
of degree ≤2d. As an application one gets that for fixed fieldK and fixedd there are only finitely many primes ι such that the set of all elliptic curves defined over some extensionsL ofK with [L∶K]≤d and withL-rational isogeny of degree ι is infinite. 相似文献
6.
Hanno Lefmann 《Discrete and Computational Geometry》2008,40(3):401-413
We consider a variant of Heilbronn’s triangle problem by investigating for a fixed dimension d≥2 and for integers k≥2 with k≤d distributions of n points in the d-dimensional unit cube [0,1]
d
, such that the minimum volume of the simplices, which are determined by (k+1) of these n points is as large as possible. Denoting by Δ
k,d
(n), the supremum of this minimum volume over all distributions of n points in [0,1]
d
, we show that c
k,d
⋅(log n)1/(d−k+1)/n
k/(d−k+1)≤Δ
k,d
(n)≤c
k,d
′/n
k/d
for fixed 2≤k≤d, and, moreover, for odd integers k≥1, we show the upper bound Δ
k,d
(n)≤c
k,d
″/n
k/d+(k−1)/(2d(d−1)), where c
k,d
,c
k,d
′,c
k,d
″>0 are constants.
A preliminary version of this paper appeared in COCOON ’05. 相似文献
7.
P. J. Maher 《Rendiconti del Circolo Matematico di Palermo》2007,56(3):459-463
Sea é un elemento di unaC
*-algebra tale chepa=a per qualche proiezionep, alloraa é una unitá inversa generalizzata, chiamata inversa di Moore-Penrose, e si denotata cona
+. Per leC
*-algebras, si ottiene altrest un risultato sulla minimizzazione di ∥axb−c∥.
相似文献
8.
S. Staněk 《Ukrainian Mathematical Journal》2008,60(2):277-298
We present existence principles for the nonlocal boundary-value problem (φ(u(p−1)))′=g(t,u,...,u(p−1), αk(u)=0, 1≤k≤p−1, where p ≥ 2, π: ℝ → ℝ is an increasing and odd homeomorphism, g is a Carathéodory function that is either regular or has singularities in its space variables, and α
k: C
p−1[0, T] → ℝ is a continuous functional. An application of the existence principles to singular Sturm-Liouville problems (−1)n(φ(u(2n−)))′=f(t,u,...,u(2n−1)), u(2k)(0)=0, αku(2k)(T)+bku(2k=1)(T)=0, 0≤k≤n−1, is given.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 240–259, February, 2008. 相似文献
9.
Elena Rubei 《Annali dell'Universita di Ferrara》2004,50(1):151-165
This paper deals with syzygies of the ideals of the Veronese embeddings. By Green’s Theorem we know thatO
P
n
(d) satisfies Green-Lazarsfeld’s PropertyN
p ∀d≥p, ∀n. By Ottaviani-Paoletti’s theorem ifn≥2, d≥3 and 3d−2≤p thenO
P
n
(d) does not satisfy PropertyN
p. The casesn≥3, d≥3, d<p<3d−2 are still open (exceptn=d=3). Here we deal with one of these cases, namely we prove thatO
P
n
(3) satisfies PropertyN
4 ∀n. Besides we prove thatO
P
n
(d) satisfiesN
p ∀n≥p iffO
P
n
(d) satisfiesN
p.
Sunto L’argomento di questo articolo sono le sizigie degli ideali delle varietà di Veronese. Per il teorema di Green sappiamo cheO P n (d) soddisfa la proprietàN p di Green-Lazarsfeld ∀d≥p, ∀n. Per il teorema di Ottaviani-Paoletti sen≥2, d≥3 and 3d−2≤p alloraO P n (d) non soddisfa la ProprietàN p. I casin≥3, d≥3, d<p<3d−2 sono ancora aperti (eccetton=d=3). Qui consideriamo uno di tali casi, precisamente proviamo cheO P n (3) soddisfa la ProprietàN 4 ∀n. Inoltre proviamo cheO P n (d) soddisfaN p ∀n≥p se e solo seO P p (d) satisfiesN p.相似文献
10.
LetC be the normalization of an integral plane curve of degreed with δ ordinary nodes or cusps as its singularities. If δ=0, then Namba proved that there is no linear seriesg
d
−2/1
and that everyg
d
−1/1
is cut out by a pencil of lines passing through a point onC. The main purpose of this paper is to generalize his result to the case δ>0. A typical one is as follows: Ifd≥2(k+1), and δ<kd−(k+1)2+3 for somek>0, thenC has no linear seriesg
d
−3/1
. We also show that ifd≥2k+3 and δ<kd−(k+1)2+2, then each linear seriesg
d
−2/1
onC is cut out by a pencil of lines. We have similar results forg
d
−1/1
andg
2d
−9/1
. Furthermore, we also show that all of our theorems are sharp. 相似文献
11.
We describe the moduli spaceM
1 (c
2) of 't Hooft bundles onP
3, that is instanton bundles having sections at the first twist. We prove that such a moduli space is a rational variety whose
singular locus is the moduli space of special 't Hooft bundles studied in [HN]. It turns out thatM
1 (c
2) possesses a canonical desingularization provided by the projectivized of a vector bundle on the Hilbert schemeH of the space curves which correspond to 't Hooft bundles in the Serre construction. Moreover, we show that the connected
components of such curves are lines or multiple lines, which are scheme-theoretically a product. On such multiple lines every
vector bundle splits, and we are able to determine their normal bundle. This allows to reprove the smoothness ofH, already known from [C], and the smoothness ofM
1, shown in [C] and [NT].
Sunto Si descrive lo spazio dei moduliM 1 (c 2) dei fibrati vettoriali di 't Hooft suP 3, cioè dei fibrati istantoni che ammettono una sezione lineare. Si dimostra che tale spazio è una varietà razionale il cui luogo singolare è costituito dai fibrati di 't Hooft speciali studiati in [HN]. Si trova, inoltre, una desingolarizzazione diM 1 (c 2) data da un aperto di un fibrato proiettivo sullo schema di Hilbert delle curve che sono luoghi degli zeri di sezioni lineari di fibrati di 't Hooft. Le componenti connesse di tali curve sono rette o rette multiple isomorfe a un prodotto. Questo risultato è conseguenza del fatto che ogni retta multiplaZ di genere aritmeticop a (Z)≤1—deg (Z) fibrata in punti multipli curvilinei è schematicamente isomorfa al multiplo di una sezione di una opportuna superficie rigata razionale.相似文献
12.
Riassunto Si considera il problema dell’esistenza e della molteplicità delle autofunzioni e dei relativi autovalori non lineari di −Δ−g su un aperto limitato di R
n
rispetto a due ostacoli assegnati. Si studiano le soluzioni che tengono conto dei valori degli ostacoli anche su insiemi
di misura di Lebesgue nulla ma di capacità positiva.
Summary We consider the existence and the multiplicity of the eigenfunctions and of the related non linear eigenvalues for the operator −Δ−g on a bounded open subset of R n with respect to two given obstacles. We study the solutions which takes into account the values of the obstacle functions even on sets of null Lebesgue measure but of positive capacity.相似文献
13.
Given a setS ofn points inR
d
, a subsetX of sized is called ak-simplex if the hyperplane aff(X) has exactlyk points on one side. We studyE
d
(k,n), the expected number of k-simplices whenS is a random sample ofn points from a probability distributionP onR
d
. WhenP is spherically symmetric we prove thatE
d
(k, n)≤cn
d−1 WhenP is uniform on a convex bodyK⊂R
2 we prove thatE
2
(k, n) is asymptotically linear in the rangecn≤k≤n/2 and whenk is constant it is asymptotically the expected number of vertices on the convex hull ofS. Finally, we construct a distributionP onR
2 for whichE
2((n−2)/2,n) iscn logn.
The authors express gratitude to the NSF DIMACS Center at Rutgers and Princeton. The research of I. Bárány was supported in
part by Hungarian National Science Foundation Grants 1907 and 1909, and W. Steiger's research was supported in part by NSF
Grants CCR-8902522 and CCR-9111491. 相似文献
14.
Markus Brodmann 《manuscripta mathematica》1992,76(1):181-192
Let M be a generalized Cohen-Macaulay module over a noetherian local ring (R,m). Fix a standard system x1, …, xd∈m with respect to M and let
. We construct a coherent Cohen-Macaulay sheafK over the projective space ℙ
R/I
d-1
whose cohomological Hilbert functions depend only on the lengths of the local cohomology modules H
m
i
(M), (i=0, …, d−1). 相似文献
15.
For a (smooth irreducible) curveC of genus g and Clifford indexc>2 with a linear seriesg
d
r
computing c (so
) it is well known thatc + 2 ≤d ≤2 (c + 2), and if
then 2c + 1 ≤g ≤ 2c + 4 unlessd = 2c + 4 in which caseg = 2c + 5.
Let c ≥ 0 andg be integers. If 2c + 1 ≤g ≤2c + 4 we prove that for any integerd <g such thatd ≡c mod 2 andc + 2 ≤d < 2(c + 2) there exists a curve of genus g and Clifford index c with a gd
r computing c. Ford ≥c + 6 (i.e.r ≥ 3) we construct this curve on a surface of degree 2r-2 in ℙr, and ford ≥c + 8 (i.e.r ≥ 4) we show that such a curve cannot be found on a surface in ℙr of smaller degree. In fact, if gd
r computes the Clifford index c of C such thatc + 8 ≤d ≤ 2c + 3 then the birational morphism defined by this series cannot map C onto a (maybe, singular) curve contained in a surface
of degree at most 2r-3 in ℙr. 相似文献
16.
For a finite p-group G and a positive integer k let I
k
(G) denote the intersection of all subgroups of G of order p
k
. This paper classifies the finite p-groups G with Ik(G) @ Cpk-1{{I}_k(G)\cong C_{p^{k-1}}} for primes p > 2. We also show that for any k, α ≥ 0 with 2(α + 1) ≤ k ≤ n−α the groups G of order p
n
with Ik(G) @ Cpk-a{{I}_k(G)\cong C_{p^{k-\alpha}}} are exactly the groups of exponent p
n-α
. 相似文献
17.
Guido Cortesani 《Annali dell'Universita di Ferrara》1997,43(1):27-49
Let Ω be an open and bounded subset ofR
n
with locally Lipschitz boundary. We prove that the functionsv∈SBV(Ω,R
m
) whose jump setS
vis essentially closed and polyhedral and which are of classW
k, ∞ (S
v,R
m) for every integerk are strongly dense inGSBV
p(Ω,R
m
), in the sense that every functionu inGSBV
p(Ω,R
m
) is approximated inL
p(Ω,R
m
) by a sequence of functions {v
k{j∈N with the described regularity such that the approximate gradients ∇v
jconverge inL
p(Ω,R
nm
) to the approximate gradient ∇u and the (n−1)-dimensional measure of the jump setsS
v
j converges to the (n−1)-dimensional measure ofS
u. The structure ofS
v can be further improved in casep≤2.
Sunto Sia Ω un aperto limitato diR n con frontiera localmente Lipschitziana. In questo lavoro si dimostra che le funzioniv∈SBV(Ω,R m ) con insieme di saltoS v essenzialmente chiuso e poliedrale che sono di classeW k, ∞ (S v,R m ) per ogni interok sono fortemente dense inGSBV p(Ω,R m ), nel senso che ogni funzioneu∈GSBV p(Ω,R m ) è approssimata inL p(Ω,R m ) da una successione di funzioni {v j}j∈N con la regolaritá descritta tali che i gradienti approssimati ∇v jconvergono inL p(Ω,R nm ) al gradiente approssimato ∇u e la misura (n−1)-dimensionale degli insiemi di saltoS v jconverge alla misura (n−1)-dimensionale diS u. La struttura diS vpuó essere migliorata nel caso in cuip≤2.相似文献
18.
Guido Zappa 《Annali di Matematica Pura ed Applicata》1962,57(1):211-219
Sunto. Hughes ha avanzato la seguente congettura: se G è un gruppo, p un numero primo, e Hp il sottogruppo generato dagli elementi di G che non hanno periodo p, si presenta uno dei tre casi seguenti: Hp=1; Hp=G; [G: Hp]=p. Vari autori hanno provato l'esattezza di tale congettura per larghe classi di gruppi. In questa Nota si dimostra che
tale congettura è esatta per i p-gruppi finiti in cui ogni sottogruppo generato da tre elementi, due dei quali di periodo
p, abbia classe ≤p; essa è quindi esatta in particolare per i p-gruppi di classe ≤p.
A Enrico Bompiani in occasione del suo Giubileo scientifico. 相似文献
Summary Hughes advanced the following conjecture: “let G be a group, p a prime and Hp the subgroup generated by elements of G having order p; then Hp=1 or Hp=G or [G: Hp]=p„. Several authors have proved this conjecture for various classes of groups. The Author proves Hughes conjecture for finite p-groups such that every subgroup {x 1 , x 2, y} generated by two elements x 1 , x 2 having order p, and by a thirth element y, has class ≤p; in particular, the conjecture is proved for finite p-groups having class ≤p.
A Enrico Bompiani in occasione del suo Giubileo scientifico. 相似文献
19.
Michael Cowling 《Milan Journal of Mathematics》1976,46(1):35-41
Si dà una nuova dimostrazione di un, teorema di Kunze e Stein, che dice che, se 1≤p<2,L
p(SL(2, R))*L
2(SL(2, R)) è contenuto inL
2(SL(2, R)). Questa nuova dimostrazione può essere generalizzata per provare lo stesso teorema per ogni gruppo di Lie connesso,
semisemplice, col centro finito. 相似文献
20.
We classify smooth subvarieties of codimension twoX⊂P
n
, 4≤n≤5, which are arithmetically Cohen-Macaulay and of non general type. By the way we exhibit some classes of non extendable
subvarieties. Then we give new proofs of the classification of scrolls inP
4; finally we consider smooth surfaces of non general type inP
4 arising from rank three vector bundles.
Sunto Classifichiamo le sottovarietà lisce di codimensione dueX⊂P n , 4≤n≤5, aritmeticamente Cohen-Macaulay e non di tipo generale. Nel contempo descriviamo alcune classi di sottovarietà non estendibili. Diamo poi due nuove dimostrazioni della classificazione degli scrolls inP 4; infine consideriamo superfici lisce inP 4, non di tipo generale, associate a fibrati di rango tre.相似文献