共查询到20条相似文献,搜索用时 703 毫秒
1.
Heang Tuy 《Journal of Mathematical Analysis and Applications》1981,80(2):598-616
We define the Radon transform
and the back projection
* (adjoint of
) on the space of C∞ rapidly decreasing functions
and on the space of distributions of compact support
′. We show that
*
is a convolution operator. The result is true in the case of full views as well as in the case of a limited range of views. An application to the medical image reconstruction is given. 相似文献
2.
Ana M. Vargas 《Rendiconti del Circolo Matematico di Palermo》1995,44(2):273-282
LetM
e
0
be the maximal operator over segments of length 1 with directions belonging to a Cantor set. It has been conjectured that
this operator is bounded onL
2. We consider a sequence of operators over finite sets of directions converging toM
e
0
. We improve the previous estimate for the (L
2,L
2)-norm of these particular operators. We also prove thatM
e
0
is bounded from some subsets ofL
2 toL
2. These subsets are composed of positive functions whose Fourier transforms have a very weak decay or are supported in a vertical
strip.
Partially supported by Spanish DGICYT grant no. PB90-0187. 相似文献
3.
M. E. Muminov 《Theoretical and Mathematical Physics》2007,153(3):1671-1676
We consider a two-particle Hamiltonian on the d-dimensional lattice ℤd. We find a sufficient condition for the positivity of a family of operators h(k) appearing after the “separation of the center
of mass” of a system of two particles depending on the values of the total quasimomentum k ∈ Td (where Td is a d-dimensional torus). We use the obtained result to show that the operator h(k) has positive eigenvalues for nonzero
k ∈ Td.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 381–387, December, 2007. 相似文献
4.
We employ a piecewise-constant, discontinuous Galerkin method for the time discretization of a sub-diffusion equation. Denoting
the maximum time step by k, we prove an a priori error bound of order k under realistic assumptions on the regularity of the solution. We also show that a spatial discretization using continuous,
piecewise-linear finite elements leads to an additional error term of order h
2 max (1,logk
− 1). Some simple numerical examples illustrate this convergence behaviour in practice.
We thank the University of New South Wales for financial support provided by a Faculty Research Grant. 相似文献
5.
We sharpen and prove a conjecture suggested by Chen and Xie, which states that in Galerkineigenfunction discretization for -Δu = u3 , when the finite-dimensional subspace is taken as the eigensubspace corresponding to an N-fold eigenvalue of -Δ, the discretized problem has at least 3N-1 distinct nonzero solutions. We also present a related result on the multiplicities of eigenvalues of -Δ. 相似文献
6.
Chiara Bottero 《Mediterranean Journal of Mathematics》2010,7(1):51-61
We study the quantum dynamics of a resonator driven by a superconducting single-electron transistor. We prove the existence
of the Minimal Quantum Dynamical Semigroup T (min){\mathcal {T}^{\,({\rm min})}} solving the evolution equation for the density matrix, then we prove that T (min){\mathcal {T}^{\,({\rm min})}} is Markov. Moreover we prove the existence and uniqueness of a faithful normal stationary state and show that the dynamics
converges towards this stationary state when time goes to infinity. 相似文献
7.
Maculan N. Santiago C.P. Macambira E.M. Jardim M.H.C. 《Journal of Optimization Theory and Applications》2003,117(3):553-574
We consider the problem of projecting a vector on the intersection of a hyperplane and a box in Rn. This paper extends a previous result of Maculan, Minoux, and Plateau (Ref. 1) concerning the projection of a vector on the intersection of a hyperplane and Rn
+. We present an O(n) time algorithm based on the linear-time median-finding algorithm. This algorithm determines the median of the components of the vector to be projected. Computational results are also presented in order to evaluate the algorithm and its time complexity. We consider two sets of instances which are randomly generated for any given n. The algorithm was successful in solving all the instances in a reasonable time. 相似文献
8.
The article investigates unbounded solutions of the equation u
t
= div (u
σgrad u) + u
β in a plane. We numerically analyze the stability of two-dimensional self-similar solutions (structures) that increase with
blowup. We confirm structural stability of the simple structure with a single maximum and metastability of complex structures.
We prove structural stability of the radially symmetrical structure with a zero region at the center and investigate its attraction
region. We study the effect of various perturbations of the initial function on the evolution of self-similar solutions. We
further investigate how arbitrary compact-support initial distributions attain the self-similar mode, including distributions
whose support is different from a disk. We show that the self-similar mode described by a simple radially symmetrical structure
is achieved only in the central region, while the entire localization region does not have enough time to transform into a
disk during blowup. We show for the first time that simple structures may merge into a complex structure, which evolves for
a long time according to self-similar law. 相似文献
9.
Mikhail Belkin Hariharan Narayanan Partha Niyogi 《Random Structures and Algorithms》2013,43(4):407-428
We draw on the observation that the amount of heat diffusing outside of a heated body in a short period of time is proportional to its surface area, to design a simple algorithm for approximating the surface area of a convex body given by a membership oracle. Our method has a complexity of O*(n4), where n is the dimension, compared to O*(n8) for the previous best algorithm. We show that our complexity cannot be improved given the current state‐of‐the‐art in volume estimation. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 43, 407–428, 2013 相似文献
10.
We present two conjectures concerning the diameter of a direct power of a finite group. The first conjecture states that the diameter of Gn with respect to each generating set is at most n(|G|?rank(G)); and the second one states that there exists a generating set 𝒜, of minimum size, for Gn such that the diameter of Gn with respect to 𝒜 is at most n(|G|?rank(G)). We will establish evidence for each of the above mentioned conjectures. 相似文献
11.
O. V. Gladkivs’ka 《Ukrainian Mathematical Journal》1997,49(5):812-815
We construct a complete orthonormal system of generalized functions in a Hilbert space W ?1. We obtain an estimate of the error of approximation in W ?1, which is expressed in terms of the integral modulus of continuity of a function from L 2. 相似文献
12.
H. Maehara 《Discrete and Computational Geometry》1995,13(1):585-592
We present a special similarity ofR
4n
which maps lattice points into lattice points. Applying this similarity, we prove that if a (4n−1)-polytope is similar to a lattice polytope (a polytope whose vertices are all lattice points) inR
4n
, then it is similar to a lattice polytope inR
4n−1, generalizing a result of Schoenberg [4]. We also prove that ann-polytope is similar to a lattice polytope in someR
N
if and only if it is similar to a lattice polytope inR
2n+1, and if and only if sin2(<ABC) is rational for any three verticesA, B, C of the polytope. 相似文献
13.
We derive an exact formula for the average rank of a product fg of transformations of an n-element set in terms of the ranks
of f and g. We show that if no restrictions are placed on the ranks of f and g, this average rank asymptotically equals n(1−exp
(e−1−1)).
We show that there exist two transformations which generate a semigroup of nn−(n−1)n+(n−1) (−1)n+1+n elements. 相似文献
14.
Optimally Cutting a Surface into a Disk 总被引:1,自引:0,他引:1
We consider the problem of cutting a subset of the edges of a polyhedral manifold
surface, possibly with boundary, to obtain a single topological disk, minimizing
either the total number of cut edges or their total length. We show that this
problem is NP-hard in general, even for manifolds without boundary and for punctured
spheres. We also describe an algorithm with running time n
O(g+k), where n is
the combinatorial complexity, g is the genus, and k is the number of boundary
components of the input surface. Finally, we describe a greedy algorithm that
outputs a O(log2
g)-approximation of the minimum cut graph in O(g
2
n log n)
time. 相似文献
15.
Shun Shimomura 《Journal of Mathematical Analysis and Applications》2005,304(2):644-651
We treat a Riccati differential equation w′+w2+p(z)=0, where p(z) is a nonconstant doubly periodic meromorphic function. Under certain assumptions, every solution is meromorphic in the whole complex plane. We show that the growth order of it is equal to 2, and examine the frequency of α-points and poles. Furthermore, the number of doubly periodic solutions is discussed. 相似文献
16.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(8):653-658
We extend our results on weak diffeomorphism classes and decompositions of Sobolev functions to a more general framework. We introduce a family of decompositions of Sobolev functions W01,p rich enough that we conjecture it allows decomposition of all Sobolev functions, not just the “craterless” ones considered in [7]. The associated weak diffeomorphism classes of a W01,p Sobolev function are weakly closed when p ≥ n. 相似文献
17.
P. J. Grabner J. M. Thuswaldner 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1996,66(1):281-287
We consider Dirichlet series of the type Σ(logk)n(k)(logk)?-s. We prove the existence of an analytic continuation to the cut plane and give exact information about the singularity. We use this to generalize results, which occur in Ramanujan’s second notebook. 相似文献
18.
We consider a connection ?X{\nabla^X} on a complex line bundle over a Riemann surface with boundary M
0, with connection 1-form X. We show that the Cauchy data space of the connection Laplacian (also called magnetic Laplacian) L : = ?X*?X + q{L := \nabla^X{^*\nabla^X} + q} , with q a complex-valued potential, uniquely determines the connection up to gauge isomorphism, and the potential q. 相似文献
19.
《Quaestiones Mathematicae》2013,36(4):473-481
We define strong and weak affinities of a number a for a sequence (xk ) denoted by L (a,(xk )) and U (a, (xk )) respectively. We show U (a,(xk )) > 0 if and only if the number a is a statistical limit point of the sequence (xk ). We consider the distribution of sequences with positive weak and strong measures of affinity within the space l ∞ of bounded sequences. The main result is that the set of bounded sequences with U (a,(xk )) > 0, that is, the set of sequences with statistical limit points, is a dense subset in l ∞ of the first category. We also show the set of sequences with positive strong affinities is a nowhere dense subset of l ∞. 相似文献
20.
Dirk Siersma 《Commentarii Mathematici Helvetici》1990,65(1):181-197
Let {f=0} be a hypersurface inC
n+1 with a 1-dimensional singular set Σ. We consider the series of hypersurfaces {f+ɛx
N=0} wherex is a generic linear form.
We derive a formula, which relates the characteristic polynomials of the monodromies off andf+ɛx
N. Other ingredients in this formula are the horizontal and the vertical monodromies of the transversal (isolated) singularities
on each branch of the singular set. We use polar curves and the carrousel method in the proof.
The formula is a generalization of the Iomdin formula for the Milnor numbers: μ(f+ɛx
N
)=μ
n
(f)−μ
n
−1(f)+Ne
0(Σ) 相似文献