共查询到20条相似文献,搜索用时 31 毫秒
1.
In Finsler geometry, minimal surfaces with respect to the Busemann-Hausdorff measure and the Holmes-Thompson measure are called
BH-minimal and HT-minimal surfaces, respectively. In this paper, we give the explicit expressions of BH-minimal and HT-minimal
rotational hypersurfaces generated by plane curves rotating around the axis in the direction of
[(b)\tilde]\sharp{\tilde{\beta}^{\sharp}} in Minkowski (α, β)-space
(\mathbbVn+1,[(Fb)\tilde]){(\mathbb{V}^{n+1},\tilde{F_b})} , where
\mathbbVn+1{\mathbb{V}^{n+1}} is an (n+1)-dimensional real vector space, [(Fb)\tilde]=[(a)\tilde]f([(b)\tilde]/[(a)\tilde]), [(a)\tilde]{\tilde{F_b}=\tilde{\alpha}\phi(\tilde{\beta}/\tilde{\alpha}), \tilde{\alpha}} is the Euclidean metric, [(b)\tilde]{\tilde{\beta}} is a one form of constant length
b:=||[(b)\tilde]||[(a)\tilde], [(b)\tilde]\sharp{b:=\|\tilde{\beta}\|_{\tilde{\alpha}}, \tilde{\beta}^{\sharp}} is the dual vector of [(b)\tilde]{\tilde{\beta}} with respect to [(a)\tilde]{\tilde{\alpha}} . As an application, we first give the explicit expressions of the forward complete BH-minimal rotational surfaces generated
around the axis in the direction of
[(b)\tilde]\sharp{\tilde{\beta}^{\sharp}} in Minkowski Randers 3-space
(\mathbbV3,[(a)\tilde]+[(b)\tilde]){(\mathbb{V}^{3},\tilde{\alpha}+\tilde{\beta})} . 相似文献
2.
D. Wolke 《Archiv der Mathematik》2000,74(4):276-281
On the assumption of the truth of the Riemann hypothesis for the Riemann zeta function we construct a class of modified von-Mangoldt functions with slightly better mean value properties than the well known function L\Lambda . For every e ? (0,1/2)\varepsilon \in (0,1/2) there is a [(L)\tilde] : \Bbb N ? \Bbb C\tilde {\Lambda} : \Bbb N \to \Bbb C such that¶ i) [(L)\tilde] (n) = L (n) (1 + O(n-1/4 logn))\tilde {\Lambda} (n) = \Lambda (n) (1 + O(n^{-1/4\,} \log n)) and¶ii) ?n \leqq x [(L)\tilde] (n) (1- [(n)/(x)]) = [(x)/2] + O(x1/4+e) (x \geqq 2).\sum \limits_{n \leqq x} \tilde {\Lambda} (n) \left(1- {{n}\over{x}}\right) = {{x}\over{2}} + O(x^{1/4+\varepsilon }) (x \geqq 2).¶Unfortunately, this does not lead to an improved error term estimation for the unweighted sum ?n \leqq x [(L)\tilde] (n)\sum \limits_{n \leqq x} \tilde {\Lambda} (n), which would be of importance for the distance between consecutive primes. 相似文献
3.
We define a generalized Li coefficient for the L-functions attached to the Rankin–Selberg convolution of two cuspidal unitary automorphic representations π and π
′ of
GLm(\mathbbAF)GL_{m}(\mathbb{A}_{F})
and
GLm¢(\mathbbAF)GL_{m^{\prime }}(\mathbb{A}_{F})
. Using the explicit formula, we obtain an arithmetic representation of the n th Li coefficient
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
attached to
L(s,pf×[(p)\tilde]f¢)L(s,\pi _{f}\times \widetilde{\pi}_{f}^{\prime })
. Then, we deduce a full asymptotic expansion of the archimedean contribution to
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
and investigate the contribution of the finite (non-archimedean) term. Under the generalized Riemann hypothesis (GRH) on non-trivial
zeros of
L(s,pf×[(p)\tilde]f¢)L(s,\pi _{f}\times \widetilde{\pi}_{f}^{\prime })
, the nth Li coefficient
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
is evaluated in a different way and it is shown that GRH implies the bound towards a generalized Ramanujan conjecture for
the archimedean Langlands parameters μ
π
(v,j) of π. Namely, we prove that under GRH for
L(s,pf×[(p)\tilde]f)L(s,\pi _{f}\times \widetilde{\pi}_{f})
one has
|Remp(v,j)| £ \frac14|\mathop {\mathrm {Re}}\mu_{\pi}(v,j)|\leq \frac{1}{4}
for all archimedean places v at which π is unramified and all j=1,…,m. 相似文献
4.
Christopher Hammond 《Mathematische Zeitschrift》2010,266(2):285-288
Let Ω be a domain in ${\mathbb{C}^{2}}Let Ω be a domain in
\mathbbC2{\mathbb{C}^{2}}, and let
p: [(W)\tilde]? \mathbbC2{\pi: \tilde{\Omega}\rightarrow \mathbb{C}^{2}} be its envelope of holomorphy. Also let W¢=p([(W)\tilde]){\Omega'=\pi(\tilde{\Omega})} with
i: W\hookrightarrow W¢{i: \Omega \hookrightarrow \Omega'} the inclusion. We prove the following: if the induced map on fundamental groups i*:p1(W) ? p1(W¢){i_{*}:\pi_{1}(\Omega) \rightarrow \pi_{1}(\Omega')} is a surjection, and if π is a covering map, then Ω has a schlicht envelope of holomorphy. We then relate this to earlier
work of Fornaess and Zame. 相似文献
5.
We prove that the generalized Temperley–Lieb algebras associated with simple graphs Γ have linear growth if and only if the
graph Γ coincides with one of the extended Dynkin graphs [(A)\tilde]n {\tilde A_n} , [(D)\tilde]n {\tilde D_n} , [(E)\tilde]6 {\tilde E_6} , or [(E)\tilde]7 {\tilde E_7} . An algebra TLG, t T{L_{\Gamma, \tau }} has exponential growth if and only if the graph Γ coincides with none of the graphs An {A_n} , Dn {D_n} , En {E_n} , [(A)\tilde]n {\tilde A_n} , [(D)\tilde]n {\tilde D_n} , [(E)\tilde]6 {\tilde E_6} , and [(E)\tilde]7 {\tilde E_7} . 相似文献
6.
Viorel Catană 《Integral Equations and Operator Theory》2010,66(1):41-52
We give a formula for the one-parameter strongly continuous semigroups ${e^{-tL^{\lambda}}}We give a formula for the one-parameter strongly continuous semigroups e-tLl{e^{-tL^{\lambda}}} and e-t [(A)\tilde]{e^{-t \tilde{A}}}, t > 0 generated by the generalized Hermite operator Ll, l ? R\{0}{L^{\lambda}, \lambda \in {\bf R}\backslash \{0\}} respectively by the generalized Landau operator ?. These formula are derived by means of pseudo-differential operators of the Weyl type, i.e. Weyl transforms, Fourier-Wigner
transforms and Wigner transforms of some orthonormal basis for L
2(R
2n
) which consist of the eigenfunctions of the generalized Hermite operator and of the generalized Landau operator. Applications
to an L
2 estimate for the solutions of initial value problems for the heat equations governed by L
λ respectively ?, in terms of L
p
norm, 1 ≤ p ≤ ∞ of the initial data are given. 相似文献
7.
Martin Reiris 《Annales Henri Poincare》2010,10(8):1559-1604
Let (g, K)(k) be a CMC (vacuum) Einstein flow over a compact three-manifold Σ with non-positive Yamabe invariant (Y(Σ)). As noted by Fischer and Moncrief, the reduced volume ${\mathcal{V}(k)=\left(\frac{-k}{3}\right)^{3}{\rm Vol}_{g(k)}(\Sigma)}Let (g, K)(k) be a CMC (vacuum) Einstein flow over a compact three-manifold Σ with non-positive Yamabe invariant (Y(Σ)). As noted by Fischer and Moncrief, the reduced volume
V(k)=(\frac-k3)3Volg(k)(S){\mathcal{V}(k)=\left(\frac{-k}{3}\right)^{3}{\rm Vol}_{g(k)}(\Sigma)} is monotonically decreasing in the expanding direction and bounded below by
Vinf=(\frac-16Y(S))\frac32{\mathcal{V}_{\rm \inf}=\left(\frac{-1}{6}Y(\Sigma)\right)^{\frac{3}{2}}}. Inspired by this fact we define the ground state of the manifold Σ as “the limit” of any sequence of CMC states {(g
i
, K
i
)} satisfying: (i) k
i
= −3, (ii) Viˉ Vinf{\mathcal{V}_{i}\downarrow \mathcal{V}_{\rm inf}}, (iii) Q
0((g
i
, K
i
)) ≤ Λ, where Q
0 is the Bel–Robinson energy and Λ is any arbitrary positive constant. We prove that (as a geometric state) the ground state
is equivalent to the Thurston geometrization of Σ. Ground states classify naturally into three types. We provide examples
for each class, including a new ground state (the Double Cusp) that we analyze in detail. Finally, consider a long time and
cosmologically normalized flow
([(g)\tilde],[(K)\tilde])(s)=((\frac-k3)2g,(\frac-k3)K){(\tilde{g},\tilde{K})(\sigma)=\left(\left(\frac{-k}{3}\right)^{2}g,\left(\frac{-k}{3}\right)K\right)}, where s = -ln(-k) ? [a,¥){\sigma=-\ln (-k)\in [a,\infty)}. We prove that if [(E1)\tilde]=E1(([(g)\tilde],[(K)\tilde])) £ L{\tilde{\mathcal{E}_{1}}=\mathcal{E}_{1}((\tilde{g},\tilde{K}))\leq \Lambda} (where E1=Q0+Q1{\mathcal{E}_{1}=Q_{0}+Q_{1}}, is the sum of the zero and first order Bel–Robinson energies) the flow ([(g)\tilde],[(K)\tilde])(s){(\tilde{g},\tilde{K})(\sigma)} persistently geometrizes the three-manifold Σ and the geometrization is the ground state if Vˉ Vinf{\mathcal{V}\downarrow \mathcal{V}_{\rm inf}}. 相似文献
8.
Dani Szpruch 《The Ramanujan Journal》2011,26(1):45-53
Let
\mathbbF\mathbb{F} be a p-adic field, let χ be a character of
\mathbbF*\mathbb{F}^{*}, let ψ be a character of
\mathbbF\mathbb{F} and let gy-1\gamma_{\psi}^{-1} be the normalized Weil factor associated with a character of second degree. We prove here that one can define a meromorphic
function [(g)\tilde](c,s,y)\widetilde{\gamma}(\chi ,s,\psi) via a similar functional equation to the one used for the definition of the Tate γ-factor replacing the role of the Fourier transform with an integration against y·gy-1\psi\cdot\gamma_{\psi}^{-1}. It turns out that γ and [(g)\tilde]\widetilde{\gamma} have similar integral representations. Furthermore, [(g)\tilde]\widetilde{\gamma} has a relation to Shahidi‘s metaplectic local coefficient which is similar to the relation γ has with (the non-metalpectic) Shahidi‘s local coefficient. Up to an exponential factor, [(g)\tilde](c,s,y)\widetilde{\gamma}(\chi,s,\psi) is equal to the ratio
\fracg(c2,2s,y)g(c,s+\frac12,y)\frac{\gamma(\chi^{2},2s,\psi)}{\gamma(\chi,s+\frac{1}{2},\psi)}. 相似文献
9.
Jakob Jonsson 《Annals of Combinatorics》2010,14(4):487-505
Let 1 ≤ m ≤ n. We prove various results about the chessboard complex M
m,n
, which is the simplicial complex of matchings in the complete bipartite graph K
m,n
. First, we demonstrate that there is nonvanishing 3-torsion in
[(H)\tilde]d(\sf Mm,n; \mathbb Z){{\tilde{H}_d({\sf M}_{m,n}; {\mathbb Z})}} whenever
\fracm+n-43 £ d £ m-4{{\frac{m+n-4}{3}\leq d \leq m-4}} and whenever 6 ≤ m < n and d = m − 3. Combining this result with theorems due to Friedman and Hanlon and to Shareshian and Wachs, we characterize all triples
(m, n, d ) satisfying
[(H)\tilde]d (\sf Mm,n; \mathbb Z) 1 0{{\tilde{H}_d \left({\sf M}_{m,n}; {\mathbb Z}\right) \neq 0}}. Second, for each k ≥ 0, we show that there is a polynomial f
k
(a, b) of degree 3k such that the dimension of
[(H)\tilde]k+a+2b-2 (\sf Mk+a+3b-1,k+2a+3b-1; \mathbb Z3){{\tilde{H}_{k+a+2b-2}}\,\left({{\sf M}_{k+a+3b-1,k+2a+3b-1}}; \mathbb Z_{3}\right)}, viewed as a vector space over
\mathbbZ3{\mathbb{Z}_3}, is at most f
k
(a, b) for all a ≥ 0 and b ≥ k + 2. Third, we give a computer-free proof that
[(H)\tilde]2 (\sf M5,5; \mathbb Z) @ \mathbb Z3{{\tilde{H}_2 ({\sf M}_{5,5}; \mathbb {Z})\cong \mathbb Z_{3}}}. Several proofs are based on a new long exact sequence relating the homology of a certain subcomplex of M
m,n
to the homology of M
m-2,n-1 and M
m-2,n-3. 相似文献
10.
Let V be a finite dimensional p-adic vector space and let τ be an operator in GL(V). A probability measure μ on V is called τ-decomposable or
m ? [(L)\tilde]0(t)\mu\in {\tilde L}_0(\tau)
if μ = τ(μ)* ρ for some probability measure ρ on V. Moreover, when τ is contracting, if ρ is infinitely divisible, so is μ, and if ρ is embeddable, so is μ. These two subclasses
of
[(L)\tilde]0(t){\tilde L}_0(\tau)
are denoted by L
0(τ) and L
0
#(τ) respectively. When μ is infinitely divisible τ-decomposable for a contracting τ and has no idempotent factors, then it
is τ-semi-selfdecomposable or operator semi-selfdecomposable. In this paper, sequences of decreasing subclasses of the above
mentioned three classes,
[(L)\tilde]m(t) é Lm(t) é L#m(t), 1 £ m £ ¥{\tilde L}_m(\tau)\supset L_m(\tau) \supset L^\#_m(\tau), 1\le m\le \infty
, are introduced and several properties and characterizations are studied. The results obtained here are p-adic vector space versions of those given for probability measures on Euclidean spaces. 相似文献
11.
Hassan Issa 《Integral Equations and Operator Theory》2011,70(4):569-582
Let
W ì \mathbb Cd{\Omega \subset{\mathbb C}^{d}} be an irreducible bounded symmetric domain of type (r, a, b) in its Harish–Chandra realization. We study Toeplitz operators Tng{T^{\nu}_{g}} with symbol g acting on the standard weighted Bergman space Hn2{H_\nu^2} over Ω with weight ν. Under some conditions on the weights ν and ν
0 we show that there exists C(ν, ν
0) > 0, such that the Berezin transform [(g)\tilde]n0{\tilde{g}_{\nu_{0}}} of g with respect to H2n0{H^2_{\nu_0}} satisfies:
\labele0||[(g)\tilde]n0||¥ £ C(n,n0)||Tng||,\label{e0}\|\tilde{g}_{\nu_0}\|_\infty \leq C(\nu,\nu_0)\|T^\nu_g\|, 相似文献
12.
For β > 0 and an integer r ≥ 2, denote by [(H)\tilde]¥,br\tilde H_{\infty ,\beta }^r those 2π-periodic, real-valued functions f on ℝ, which are analytic in S
β
:= {z ∈ ℂ: |Im z| < β} and satisfy the restriction |f
(r)(z)|≤1, z ∈ S
β
. The optimal quadrature formulae about information composed of the values of a function and its kth (k = 1, ..., r − 1) derivatives on free knots for the classes [(H)\tilde]¥,br\tilde H_{\infty ,\beta }^r are obtained, and the error estimates of the optimal quadrature formulae are exactly determined. 相似文献
13.
Pierre Angl��s 《Advances in Applied Clifford Algebras》2011,21(2):233-246
This self-contained short note deals with the study of the properties of some real projective compact quadrics associated
with a a standard pseudo-hermitian space H
p,q
, namely [(Q(p, q))\tilde], [(Q2p+1,1)\tilde], [(Q1,2q+1)\tilde], [(Hp,q)\tilde]. [(Q(p, q))\tilde]{\widetilde{Q(p, q)}, \widetilde{Q_{2p+1,1}}, \widetilde{Q_{1,2q+1}}, \widetilde{H_{p,q}}. \, \widetilde{Q(p, q)}} is the (2n – 2) real projective quadric diffeomorphic to (S
2p–1 × S
2q–1)/Z
2. inside the real projective space P(E
1), where E
1 is the real 2n-dimensional space subordinate to H
p,q
. The properties of [(Q(p, q))\tilde]{\widetilde{Q(p, q)}} are investigated. [(Hp,q)\tilde]{\widetilde{H_p,q}} is the real (2n – 3)-dimensional compact manifold-(projective quadric)- associated with H
p,q
, inside the complex projective space P(H
p,q
), diffeomorphic to (S
2p–1 × S
2q–1)/S
1. The properties of [(Hp,q)\tilde]{\widetilde{H_{p,q}}} are studied. [(Q2p+1,1)\tilde]{\widetilde{Q_{2p+1,1}}} is a 2p-dimensional standard real projective quadric, and [(Q1,2q+1)\tilde]{\widetilde{Q_{1,2q+1}}} is another standard 2q-dimensional projective quadric. [(Q2p+1,1)\tilde] è[(Q1,2q+1)\tilde]{\widetilde{Q_{2p+1,1}} \cup \widetilde{Q_{1,2q+1}}}, union of two compact quadrics plays a part in the understanding of the "special pseudo-unitary conformal compactification"
of H
p,q
. It is shown how a distribution y → D
y
, where y ? H\{0},H{y \in H\backslash\{0\},H} being the isotropic cone of H
p,q
allows to [(Hp+1,q+1)\tilde]{\widetilde{H_{p+1,q+1}}} to be considered as a "special pseudo-unitary conformal compactified" of H
p,q
× R. The following results precise the presentation given in [1,c]. 相似文献
14.
This paper is a contribution to the study of a quasi-order on the set Ω of Boolean functions, the simple minor quasi-order. We look at the join-irreducible members of the resulting poset [(W)\tilde]\tilde{\Omega}. Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial
property of hypergraphs. We observe that among Steiner systems, those which yield join-irreducible members of [(W)\tilde]\tilde{\Omega} are the − 2-monomorphic Steiner systems. We also describe the graphs which correspond to join-irreducible members of [(W)\tilde]\tilde{\Omega}. 相似文献
15.
To every nilpotent commutative algebra N{\mathcal{N}} of finite dimension over an arbitrary base field of characteristic zero a smooth algebraic subvariety S ì N{S\subset\mathcal{N}} can be associated in a canonical way whose degree is the nil-index and whose codimension is the dimension of the annihilator A{\mathcal{A}} of N{\mathcal{N}}. In case N{\mathcal{N}} admits a grading, the surface S is affinely homogeneous. More can be said if A{\mathcal{A}} has dimension 1, that is, if N{\mathcal{N}} is the maximal ideal of a Gorenstein algebra. In this case two such algebras N{\mathcal{N}}, [(N)\tilde]{\tilde{\mathcal{N}}} are isomorphic if and only if the associated hypersurfaces S, [(S)\tilde]{\tilde S} are affinely equivalent. If one of S, [(S)\tilde]{\tilde S} even is affinely homogeneous, ‘affinely equivalent’ can be replaced by ‘linearly equivalent’. In case the nil-index of N{\mathcal{N}} does not exceed 4 the hypersurface S is always affinely homogeneous. Contrary to the expectation, in case nil-index 5 there exists an example (in dimension 23) where S is not affinely homogeneous. 相似文献
16.
The bigraded Frobenius characteristic of the Garsia-Haiman module M
μ
is known [7, 10] to be given by the modified Macdonald polynomial [(H)\tilde]m[X; q, t]{\tilde{H}_{\mu}[X; q, t]}. It follows from this that, for
m\vdash n{\mu \vdash n} the symmetric polynomial ?p1 [(H)\tilde]m[X; q, t]{{\partial_{p1}} \tilde{H}_{\mu}[X; q, t]} is the bigraded Frobenius characteristic of the restriction of M
μ
from S
n
to S
n-1. The theory of Macdonald polynomials gives explicit formulas for the coefficients c
μ
v
occurring in the expansion ?p1 [(H)\tilde]m[X; q, t] = ?v ? mcmv [(H)\tilde]v[X; q, t]{{\partial_{p1}} \tilde{H}_{\mu}[X; q, t] = \sum_{v \to \mu}c_{\mu v} \tilde{H}_{v}[X; q, t]}. In particular, it follows from this formula that the bigraded Hilbert series F
μ (q, t) of M
μ
may be calculated from the recursion Fm (q, t) = ?v ? mcmv Fv (q, t){F_\mu (q, t) = \sum_{v \to \mu}c_{\mu v} F_v (q, t)}. One of the frustrating problems of the theory of Macdonald polynomials has been to derive from this recursion that Fm(q, t) ? N[q, t]{F\mu (q, t) \in \mathbf{N}[q, t]}. This difficulty arises from the fact that the c
μ
v
have rather intricate expressions as rational functions in q, t. We give here a new recursion, from which a new combinatorial formula for F
μ
(q, t) can be derived when μ is a two-column partition. The proof suggests a method for deriving an analogous formula in the general case. The method
was successfully carried out for the hook case by Yoo in [15]. 相似文献
17.
Given two maps
h : X ×K ? \mathbbR{h : X \times K \rightarrow \mathbb{R}} and g : X → K such that, for all x ? X, h(x, g(x)) = 0{x \in X, h(x, g(x)) = 0} , we consider the equilibrium problem of finding [(x)\tilde] ? X{\tilde{x} \in X} such that h([(x)\tilde], g(x)) 3 0{h(\tilde{x}, g(x)) \geq 0} for every x ? X{x \in X} . This question is related to a coincidence problem. 相似文献
18.
Mianmian Zhang 《Algebras and Representation Theory》2012,15(2):203-210
Let Q be a finite quiver of type A
n
, n ≥ 1, D
n
, n ≥ 4, E
6, E
7 and E
8, σ ∈ Aut(Q), k be an algebraic closed field whose characteristic does not divide the order of σ. In this article, we prove that the dual quiver [(GQ)\tilde]\widetilde{\Gamma_{Q}} of the Auslander–Reiten quiver Γ
Q
of kQ, the Auslander–Reiten quiver of kQ#kás?kQ\#k\langle\sigma\rangle, and the Auslander–Reiten quiver G[(Q)\tilde]\Gamma_{\widetilde{Q}} of k[(Q)\tilde]k\widetilde{Q}, where [(Q)\tilde]\widetilde{Q} is the dual quiver of Q, are isomorphic. 相似文献
19.
L. Sanguiao Sande 《Geometriae Dedicata》2011,151(1):305-321
20.
B.-Y. Chen 《Archiv der Mathematik》2000,74(2):154-160
Let M n be a Riemannian n-manifold. Denote by S(p) and [`(Ric)](p)\overline {Ric}(p) the Ricci tensor and the maximum Ricci curvature on M n at a point p ? Mnp\in M^n, respectively. First we show that every isotropic submanifold of a complex space form [(M)\tilde]m(4 c)\widetilde M^m(4\,c) satisfies S £ ((n-1)c+ [(n2)/4] H2)gS\leq ((n-1)c+ {n^2 \over 4} H^2)g, where H2 and g are the squared mean curvature function and the metric tensor on M n, respectively. The equality case of the above inequality holds identically if and only if either M n is totally geodesic submanifold or n = 2 and M n is a totally umbilical submanifold. Then we prove that if a Lagrangian submanifold of a complex space form [(M)\tilde]m(4 c)\widetilde M^m(4\,c) satisfies [`(Ric)] = (n-1)c+ [(n2)/4] H2\overline {Ric}= (n-1)c+ {n^2 \over 4} H^2 identically, then it is a minimal submanifold. Finally, we describe the geometry of Lagrangian submanifolds which satisfy the equality under the condition that the dimension of the kernel of second fundamental form is constant. 相似文献
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