共查询到20条相似文献,搜索用时 15 毫秒
1.
A. L. Fedorov 《Mathematical Notes》1972,11(3):173-177
An n-dimensional domain K is considered with boundary ?K = k0 tu K1 ∪ K2 such that the closure ¯K is the image of a cylinder B=Sx[0, 1] (S is a closed (n?1)-dimensional cell) under a one-one Lipschitz map. For the p-conductance of the domain K, defined by the equation $$c_p (K) = \mathop {\inf }\limits_{U(K)} \int K |\nabla f|^p dx (p > 1),$$ , where∪ (K) = f (x):f ∈ W p 1 (K)∩C (¯K),f = 1 on k1,f = 0 on K0, the isoperimetric inequality cp(K) ≤ V/rP is established. Here V is the n-dimensional volume of the domain K, r is the shortest distance between k0 and K1, measured in K. Equality is achieved on the right cylinder. 相似文献
2.
Kh. K. Ishkin 《Mathematical Notes》2008,84(3-4):515-528
We consider the Sturm-Liouville equation $ - y'' + qy = \lambda ^2 y $ in an annular domain K from ? and obtain necessary and sufficient conditions on the potential q under which all solutions of the equation ?y″(z) + q(z)y(z) = λ 2 y(z), z ∈ γ, where γ is a certain curve, are unique in the domain K for all values of the parameter λ ∈ ?. 相似文献
3.
In this note we exhibit bases of the polynomial identities satisfied by the Grassmann algebras over a field of positive characteristic. This allows us to answer the following question of Kemer: Does the infinite dimensional Grassmann algebra with 1, over an infinite fieldK of characteristic 3, satisfy all identities of the algebraM 2(K) of all 2×2 matrices overK? We give a negative answer to this question. Further, we show that certain finite dimensional Grassmann algebras do give a positive answer to Kemer's question. All this allows us to obtain some information about the identities satisfied by the algebraM 2(K) over an infinite fieldK of positive odd characteristic, and to conjecture bases of theidentities ofM 2(K). 相似文献
4.
Byungchul Cha 《Journal of Number Theory》2005,111(1):154-178
Let E be an elliptic curve over Q and ? be an odd prime. Also, let K be a number field and assume that E has a semi-stable reduction at ?. Under certain assumptions, we prove the vanishing of the Galois cohomology group H1(Gal(K(E[?i])/K),E[?i]) for all i?1. When K is an imaginary quadratic field with the usual Heegner assumption, this vanishing theorem enables us to extend a result of Kolyvagin, which finds a bound for the order of the ?-primary part of Shafarevich-Tate groups of E over K. This bound is consistent with the prediction of Birch and Swinnerton-Dyer conjecture. 相似文献
5.
C.-G. Schmidt 《Journal of Number Theory》1980,12(3):283-310
Let K be an absolute abelian number field. The conductor of the Hecke characters of K formed by Gaussian sums is investigated. In some cases we obtain formulas for this conductor while in others a bound is given. These enable us to obtain a general upper bound for the conductor in terms of the class field theoretic conductor of K. Our bound is an improvement on existing bounds in the literature. 相似文献
6.
Fixing a nontrivial automorphism of a number field K, we associate to ideals in K an invariant (with values in {0,±1}) which we call the spin and for which the associated L-function does not possess Euler products. We are nevertheless able, using the techniques of bilinear forms, to handle spin value distribution over primes, obtaining stronger results than the analogous ones which follow from the technology of L-functions in its current state. The initial application of our theorem is to the arithmetic statistics of Selmer groups of elliptic curves. 相似文献
7.
In this article we explore asymptotic properties of some statistics based on K-sample extensions of multivariate empirical copula processes. These statistics can be used to test the equality of copulas pertaining to K independent samples. 相似文献
8.
Let R be an integral domain with quotient field K and f(x) a polynomial of positive degree in K[x]. In this paper we develop a method for studying almost principal uppers to zero ideals. More precisely, we prove that uppers to zero divisorial ideals of the form I = f(x)K[x] ∩ R[x] are almost principal in the following two cases:
- J, the ideal generated by the leading coefficients of I, satisfies J ?1 = R.
- I ?1 as the R[x]-submodule of K(x) is of finite type.
- I ?1 ∩ K[x] = (I: K(x) I).
- If there exists p/q ∈ I ?1 ? K[x], then (q, f) ≠ 1 in K[x]. If in addition q is irreducible and I is almost principal, then I′ = q(x)K[x] ∩ R[x] is an almost principal upper to zero.
9.
Piotr Jędrzejewicz 《Central European Journal of Mathematics》2013,11(5):900-909
We obtain two equivalent conditions for m polynomials in n variables to form a p-basis of a ring of constants of some polynomial K-derivation, where K is a unique factorization domain of characteristic p > 0. One of these conditions involves Jacobians while the other some properties of factors. In the case m = n this extends the known theorem of Nousiainen, and we obtain a new formulation of the Jacobian conjecture in positive characteristic. 相似文献
10.
For a time-frequency lattice Λ = A Z d B Z d , it is known that an orthonormal super Gabor frame of length L exists with respect to this lattice if and only if |det( AB) | = 1 L . The proof of this result involves various techniques from multi-lattice tiling and operator algebra theory, and it is far from constructive. In this paper we present a very general scheme for constructing super Gabor frames for the rational lattice case. Our method is based on partitioning an arbitrary fundamental domain of the lattice in the frequency domain such that each subset in the partition tiles R d by the lattice in the time domain. This approach not only provides us a simple algorithm of constructing various kinds of orthonormal super Gabor frames with flexible length and multiplicity, but also allows us to construct super Gabor (non-Riesz) frames with high order smoothness and regularity. Several examples are also presented. 相似文献
11.
Michael J. Fisher 《Discrete Mathematics》2008,308(11):2240-2246
We determine the values of s and t for which there is a coloring of the edges of the complete bipartite graph Ks,t which admits only the identity automorphism. In particular, this allows us to determine the distinguishing number of the Cartesian product of complete graphs. 相似文献
12.
Tom Kempton 《Acta Mathematica Hungarica》2014,142(2):403-419
We construct a Lebesgue measure preserving natural extension of a skew product system related to the random β-transformation K β . This allows us to give a formula for the density of the absolutely continuous invariant probability measure of K β , answering a question of Dajani and de Vries, and also to evaluate some estimates on the typical branching rate of the set of β-expansions of a real number. 相似文献
13.
In this paper we prove an existence result for the nonlinear elliptic problem:-△u = Ku~5,u 0 in Ω,u = 0 on?Ω,where Ω is a smooth bounded domain of R~3 and K is a positive function in Ω.Our method relies on studying its corresponding subcritical approximation problem and then using a topological argument. 相似文献
14.
Jean-Luc Chabert 《Journal of Number Theory》2010,130(2):458-468
Let D be an integral domain with quotient field K. For any subset S of K, the D-polynomial closure of S is the largest subset T of K such that, for every polynomial f in K[X], if f maps S into D then f maps also T into D. When D is not local, the D-polynomial closure is not a topological closure. We prove here that, when D is any rank-one valuation domain, then there exists a topology on K such that the closed subsets for this topology are exactly the D-polynomially closed subsets of K. 相似文献
15.
Frank Gerth 《Journal of Number Theory》1983,17(2):191-203
Let K be a cyclic Galois extension of the rational numbers Q of degree ?, where ? is a prime number. Let h? denote the order of the Sylow ?-subgroup of the ideal class group of K. If h? = ?s(s ≥ 0), it is known that the number of (finite) primes that ramify in K/Q is at most s + 1 (or s + 2 if K is real quadratic). This paper shows that “most” of these fields K with h? = ?s have exactly s + 1 ramified primes (or s + 2 ramified primes if K is real quadratic). Furthermore the Sylow ?-subgroup of the ideal class group is elementary abelian when h? = ?s and there are s + 1 ramified primes (or s + 2 ramified primes if K is real quadratic). 相似文献
16.
Wolfgang Müller 《Monatshefte für Mathematik》1988,106(3):211-219
LetK be a cubic number field. Denote byA K (x) the number of ideals with ideal norm ≤x, and byQ K (x) the corresponding number of squarefree ideals. The following asymptotics are proved. For every ε>0 ε>0 $$\begin{gathered} {\text{ }}A_K (x) = c_1 x + O(x^{43/96 + \in } ), \hfill \\ Q_K (x) = c_2 x + O(x^{1/2} \exp {\text{ }}\{ - c(\log {\text{ }}x)^{3/5} (\log \log {\text{ }}x)^{ - 1/5} \} ). \hfill \\ \end{gathered}$$ Herec 1,c 2 andc are positive constants. Assuming the Riemann hypotheses for the Dedekind zeta function ζ K , the error term in the second result can be improved toO(x 53/116+ε). 相似文献
17.
M. A. Dubovitskaya 《Mathematical Notes》2007,81(5-6):753-756
The two-dimensional local field K = F q((u))((t)), char K = p, and its Brauer group Br(K) are considered. It is proved that, if L = K(x) is the field extension for which we have x p ? x = ut ?p =: h, then the condition that (y, f | h]K = 0 for any y ε K is equivalent to the condition f ε Im(Nm(L*)). 相似文献
18.
K is a cyclic quartic extension of Q iff , where d > 1, p and r are rational integers, d squarefree, for which p2 + q2 = r2d for some integer q. Following a paper of A. A. Albert we show that the absolute discriminant, , of the general cyclic quartic extension is given by for an explicitly computable rational integer W. We next find that the relative discriminant, , is given by , where is K′s uniquely determined quadratic subfield. We use this last result in conjunction with Corollary 3, page 359, of Narkiewicz's “Elementary and Analytic Theory of Algebraic Numbers” (PWN-Polish Scientific Publishers, 1974) to establish the following Theorem 1: If the (wide) class number ofis odd then every cyclic quartic extensionKofQcontainingFhas a relative integral basis overF. We give a second, more organic, proof of Theorem 1 which also allows us to prove the following converse result, namely Theorem 2: Suppose the quadratic fieldFis contained in some cyclic quartic extension ofQand suppose thatFhas even (wide) class number. There then is a cyclic quartic extensionKofQcontainingFsuch thatKhas no relative integral basis overF. 相似文献
19.
In this paper we consider the following nonlinear problem: \({{-\Delta u=Ku^{5}}}\), u > 0 in \({{\Omega}}\), u = 0 on \({{\partial \Omega}}\), where K > 0 in \({{\Omega}}\), K = 0 on \({{\partial \Omega}}\) and \({{\Omega}}\) is a bounded domain of \({{\mathbb{R}^{3}}}\). We prove a version of a Morse lemma at infinity for this problem, which allows us to describe the critical points at infinity of the associated variational functional. Using a topological argument, we prove an existence result. 相似文献
20.
Stéphane R. Louboutin 《Journal of Number Theory》2009,129(10):2289-2294
J. Cohen, J. Sonn, F. Sairaiji and K. Shimizu proved that there are only finitely many imaginary quadratic number fields K whose Ono invariants OnoK are equal to their class numbers hK. Assuming a Restricted Riemann Hypothesis, namely that the Dedekind zeta functions of imaginary quadratic number fields K have no Siegel zeros, we determine all these K's. There are 114 such K's. We also prove that we are missing at most one such K. M. Ishibashi proved that if OnoK is large enough compared with hK, then the ideal class groups of K is cyclic. We give a short proof and a precision of Ishibashi's result. We prove that there are only finitely many imaginary quadratic number fields K satisfying Ishibashi's sufficient condition. Assuming our Restricted Riemann Hypothesis, we prove that the absolute values dK of their discriminants are less than 2.3⋅109. We determine all these K's with dK?106. There are 76 such K's. We prove that there is at most one such K with dK?1.8⋅1011. 相似文献