共查询到20条相似文献,搜索用时 484 毫秒
1.
We describe the so-called method of virtual components for tight wavelet framelets to increase their approximation order and vanishing moments in the multivariate setting. Two examples of the virtual components for tight wavelet frames based on bivariate box splines on three or four direction mesh are given. As a byproduct, a new construction of tight wavelet frames based on box splines under the quincunx dilation matrix is presented. 相似文献
2.
Young-Jun Choi 《Journal of Geometric Analysis》2012,22(1):168-205
This paper pertains to the J-Hermitian geometry of model domains introduced by Lee (Mich. Math. J. 54(1), 179–206, 2006; J. Reine Angew. Math. 623, 123–160, 2008). We first construct a Hermitian invariant metric on the Lee model and show that the invariant metric actually coincides
with the Kobayashi-Royden metric, thus demonstrating an uncommon phenomenon that the Kobayashi-Royden metric is J-Hermitian in this case. Then we follow Cartan’s differential-form approach and find differential-geometric invariants, including
torsion invariants, of the Lee model equipped with this J-Hermitian Kobayashi-Royden metric, and present a theorem that characterizes the Lee model by those invariants, up to J-holomorphic isometric equivalence. We also present an all dimensional analysis of the asymptotic behavior of the Kobayashi
metric near the strongly pseudoconvex boundary points of domains in almost complex manifolds. 相似文献
3.
M. M. H. Pang 《Semigroup Forum》2009,78(2):238-252
We adapt a method originally developed by E.B. Davies for second order elliptic operators to obtain an upper heat kernel bound
for the Laplacian defined on a uniform grid on the plane. 相似文献
4.
In the paper we obtain an explicit formula for the intrinsic diameter of the surface of a rectangular parallelepiped in 3-dimensional
Euclidean space. As a consequence, we prove that an parallelepiped with relation
for its edge lengths has maximal surface area among all rectangular parallelepipeds with given intrinsic diameter. 相似文献
5.
Hassen Ben Mohamed 《The Ramanujan Journal》2010,21(2):145-171
In this work, we consider the Jacobi-Dunkl operator Λ
α,β
,
a 3 b 3 \frac-12\alpha\geq\beta\geq\frac{-1}{2}
,
a 1 \frac-12\alpha\neq\frac{-1}{2}
, on ℝ. The eigenfunction
Yla,b\Psi_{\lambda}^{\alpha,\beta}
of this operator permits to define the Jacobi-Dunkl transform. The main idea in this paper is to introduce and study the Jacobi-Dunkl
transform and the Jacobi-Dunkl convolution product on new spaces of distributions 相似文献
6.
The core is a set-valued solution concept for cooperative games. In situations where the characteristic function is not monotone
the classical definition may not be sufficient. Hence, we propose a subset of the core that is called subcoalition-perfect
core. It will be proven that the subcoalition-perfect core coincides with the set of non-negative core allocations. Furthermore,
an ellipsoid algorithm is provided which may be applied in many applications to compute an element in the subcoalition-perfect
core. In addition, we discuss an application where the characteristic function is not monotone and perform a computational
study. 相似文献
7.
Tiefeng Jiang 《Journal of Theoretical Probability》2010,23(4):1227-1243
Let Γ
n
=(γ
ij
)
n×n
be a random matrix with the Haar probability measure on the orthogonal group O(n), the unitary group U(n), or the symplectic group Sp(n). Given 1≤m<n, a probability inequality for a distance between (γ
ij
)
n×m
and some mn independent F-valued normal random variables is obtained, where F=ℝ, ℂ, or ℍ (the set of real quaternions). The result is universal for the three cases. In particular, the inequality for
Sp(n) is new. 相似文献
8.
Ali Jabbari 《Arkiv f?r Matematik》2012,50(2):291-304
The topological center of the spectrum of the Weyl algebra W, i.e. the norm closure of the algebra generated by the set of functions , is characterized in a recent paper by Jabbari and Namioka (Ellis group and the topological center of the flow generated by the map , to appear in Milan J. Math.). By the techniques essentially used in the cited paper, the topological center of the spectrum of the subalgebra W k , the norm closure of the algebra generated by the set of functions , will be characterized, for all k∈ℕ. Also an example of a non-minimal dynamical system, with the enveloping semigroup Σ, for which the set of all continuous elements of Σ is not equal to the topological center of Σ, is given. 相似文献
9.
In a randomized incremental construction of the minimization diagram of a collection of n hyperplanes in ℝ
d
, for d≥2, the hyperplanes are inserted one by one, in a random order, and the minimization diagram is updated after each insertion.
We show that if we retain all the versions of the diagram, without removing any old feature that is now replaced by new features,
the expected combinatorial complexity of the resulting overlay does not grow significantly. Specifically, this complexity
is O(n
⌊d/2⌋log n), for d odd, and O(n
⌊d/2⌋), for d even. The bound is asymptotically tight in the worst case for d even, and we show that this is also the case for d=3. Several implications of this bound, mainly its relation to approximate halfspace range counting, are also discussed. 相似文献
10.
With a plane curve singularity one associates a multi-index filtration on the ring of germs of functions of two variables
defined by the orders of a function on irreducible components of the curve. The Poincaré series of this filtration turns out
to coincide with the Alexander polynomial of the curve germ. For a finite set of divisorial valuations on the ring corresponding
to some components of the exceptional divisor of a modification of the plane, in a previous paper there was obtained a formula
for the Poincaré series of the corresponding multi-index filtration similar to the one associated with plane germs. Here we
show that the Poincaré series of a set of divisorial valuations on the ring of germs of functions of two variables defines
“the topology of the set of the divisors” in the sense that it defines the minimal resolution of this set up to combinatorial
equivalence. For the plane curve singularity case, we also give a somewhat simpler proof of the statement by Yamamoto which
shows that the Alexander polynomial is equivalent to the embedded topology. 相似文献
11.
Gregg Musiker 《Journal of Algebraic Combinatorics》2009,30(2):255-276
Let q be a power of a prime, and E be an elliptic curve defined over
. Such curves have a classical group structure, and one can form an infinite tower of groups by considering E over field extensions
for all k≥1. The critical group of a graph may be defined as the cokernel of L(G), the Laplacian matrix of G. In this paper, we compare elliptic curve groups with the critical groups of a certain family of graphs. This collection
of critical groups also decomposes into towers of subgroups, and we highlight additional comparisons by using the Frobenius
map of E over
.
This work was partially supported by the NSF, grant DMS-0500557 during the author’s graduate school at the University of California,
San Diego, and partially supported by an NSF Postdoctoral Fellowship. 相似文献
12.
We show that the cyclic lamplighter group C 2 ? C n embeds into Hilbert space with distortion $\mathrm{O}(\sqrt{\log n})We show that the cyclic lamplighter group C
2
≀
C
n
embeds into Hilbert space with distortion
O(?{logn})\mathrm{O}(\sqrt{\log n})
. This matches the lower bound proved by Lee et al. (Geom. Funct. Anal., 2009), answering a question posed in that paper. Thus, the Euclidean distortion of C
2
≀
C
n
is
\varTheta(?{logn})\varTheta(\sqrt{\log n})
. Our embedding is constructed explicitly in terms of the irreducible representations of the group. Since the optimal Euclidean
embedding of a finite group can always be chosen to be equivariant, as shown by Aharoni et al. (Isr. J. Math. 52(3):251–265,
1985) and by Gromov (see de Cornulier et. al. in Geom. Funct. Anal., 2009), such representation-theoretic considerations suggest a general tool for obtaining upper and lower bounds on Euclidean embeddings
of finite groups. 相似文献
13.
Heleno Cunha Francisco Dutenhefner Nikolay Gusevskii Rafael Santos Thebaldi 《Journal of Geometric Analysis》2012,22(2):295-319
We consider the space M\mathcal{M} of ordered m-tuples of distinct complex geodesics in complex hyperbolic 2-space,
H\mathbbC2{\rm\bf H}_{\mathbb{C}}^{2}, up to its holomorphic isometry group PU(2,1). One of the important problems in complex hyperbolic geometry is to construct
and describe the moduli space for M\mathcal{M}. This is motivated by the study of the deformation space of groups generated by reflections in complex geodesics. In the
present paper, we give the complete solution to this problem. 相似文献
14.
To compare continued fraction digits with the denominators of the corresponding approximants we introduce the arithmetic-geometric
scaling. We will completely determine its multifractal spectrum by means of a number-theoretical free-energy function and
show that the Hausdorff dimension of sets consisting of irrationals with the same scaling exponent coincides with the Legendre
transform of this free-energy function. Furthermore, we identify the asymptotic of the local behaviour of the spectrum at
the right boundary point and discuss a connection to the set of irrationals with continued-fraction digits exceeding a given
number which tends to infinity. 相似文献
15.
Manfred Reimer 《Constructive Approximation》2009,29(3):407-419
We investigate the restriction Δ
r,μ
of the Laplace operator Δ onto the space of r-variate homogeneous polynomials F of degree μ. In the uniform norm on the unit ball of ℝ
r
, and with the corresponding operator norm, ‖Δ
r,μ
F‖≤‖Δ
r,μ
‖⋅‖F‖ holds, where, for arbitrary F, the ‘constant’ ‖Δ
r,μ
‖ is the best possible. We describe ‖Δ
r,μ
‖ with the help of the family T
μ
(σ
x),
, of scaled Chebyshev polynomials of degree μ. On the interval [−1,+1], they alternate at least (μ−1)-times, as the Zolotarev polynomials do, but they differ from them by their symmetry. We call them Zolotarev polynomials
of the second kind, and calculate ‖Δ
r,μ
‖ with their help. We derive upper and lower bounds, as well as the asymptotics for μ→∞. For r≥5 and sufficiently large μ, we just get ‖Δ
r,μ
‖=(r−2)μ(μ−1). However, for 2≤r≤4 or lower values of μ, the result is more complicated. This gives the problem a particular flavor. Some Bessel functions and the φcot φ-expansion are involved.
相似文献
16.
In this paper, the bifurcation of nontrivial periodic solutions for an impulsively perturbed system of ordinary differential equations which models an integrated pest management strategy is studied by means of a fixed point approach. A biological control, consisting in the periodic release of infective pests, and a chemical control, consisting in pesticide spraying, are employed to maintain susceptible pests below an acceptable level. It is assumed that the biological and chemical control act with the same periodicity, but not in the same time. It is then shown that if the constant amount of infective pests released each time reaches a certain threshold value, then the trivial susceptible pest-eradication periodic solution loses its stability, which is transferred to a newly emerging nontrivial periodic solution. 相似文献
17.
J. C. Pardo 《Journal of Theoretical Probability》2009,22(2):514-542
We establish integral tests in connection with laws of the iterated logarithm at 0 and at +∞, for the upper envelope of positive
self-similar Markov processes. Our arguments are based on the Lamperti representation and on the study of the upper envelope
of the future infimum due to the author (see Pardo in Stoch. Stoch. Rep. 78:123–155, [2006]). These results extend laws of the iterated logarithm for Bessel processes due to Dvoretsky and Erdős (Proceedings of the
Second Berkeley Symposium, [1951]) and stable Lévy processes with no positive jumps conditioned to stay positive due to Bertoin (Stoch. Process. Appl. 55:91–100,
[1995]).
Research supported by a grant from CONACYT (Mexico). 相似文献
18.
Marco Schlichting 《Inventiones Mathematicae》2010,179(2):349-433
We prove localization and Zariski-Mayer-Vietoris for higher Gro-thendieck-Witt groups, alias hermitian K-groups, of schemes admitting an ample family of line-bundles. No assumption on the characteristic is needed, and our schemes
can be singular. Along the way, we prove Additivity, Fibration and Approximation theorems for the hermitian K-theory of exact categories with weak equivalences and duality. 相似文献
19.
Yves Lucet Heinz H. Bauschke Mike Trienis 《Computational Optimization and Applications》2009,43(1):95-118
A new computational framework for computer-aided convex analysis is proposed and investigated. Existing computational frameworks
are reviewed and their limitations pointed out. The class of piecewise linear-quadratic functions is introduced to improve
convergence and stability. A stable convex calculus is achieved using symbolic-numeric algorithms to compute all fundamental
transforms of convex analysis. Our main result states the existence of efficient (linear time) algorithms for the class of
piecewise linear-quadratic functions. We also recall that such class is closed under convex transforms. We illustrate the
results with numerical examples, and validate numerically the resulting computational framework. 相似文献
20.
The classical Garman-Kohlhagen model for the currency exchange assumes that the domestic and foreign currency risk-free interest
rates are constant and the exchange rate follows a log-normal diffusion process.
In this paper we consider the general case, when exchange rate evolves according to arbitrary one-dimensional diffusion process
with local volatility that is the function of time and the current exchange rate and where the domestic and foreign currency
risk-free interest rates may be arbitrary continuous functions of time. First non-trivial problem we encounter in time-dependent
case is the continuity in time argument of the value function of the American put option and the regularity properties of
the optimal exercise boundary. We establish these properties based on systematic use of the monotonicity in volatility for
the value functions of the American as well as European options with convex payoffs together with the Dynamic Programming
Principle and we obtain certain type of comparison result for the value functions and corresponding exercise boundaries for
the American puts with different strikes, maturities and volatilities.
Starting from the latter fact that the optimal exercise boundary curve is left continuous with right-hand limits we give a
mathematically rigorous and transparent derivation of the significant early exercise premium representation for the value
function of the American foreign exchange put option as the sum of the European put option value function and the early exercise
premium.
The proof essentially relies on the particular property of the stochastic integral with respect to arbitrary continuous semimartingale
over the predictable subsets of its zeros. We derive from the latter the nonlinear integral equation for the optimal exercise
boundary which can be studied by numerical methods. 相似文献