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81.
Antal Járai 《Aequationes Mathematicae》2003,65(3):236-266
Summary. We prove that - under certain conditions - measurable solutions $f$ of the functional equation $f(x)=h(x,y,f(g_{1}(x,y)),\ldots,f(g_{n}(x,y))),\quad(x,y)\in D \subset \mathbb{R}^{s} \times \mathbb{R}^{l}$ are continuous, even if $1\le l\le s$. As a tool we introduce new classes of functions which - roughly speaking - interpolate between continuous and Lebesgue measurable functions. Connection between these classes are also investigated. 相似文献
82.
Igor V. Dolgachev 《Milan Journal of Mathematics》2004,72(1):163-187
We review the classical definition of the dual homogeneous form of arbitrary even degree which generalizes the well-known notion of the dual quadratic form. Following the ideas of S. Mukai we apply this construction to the study of the varieties parametrizing representations of a homogeneous polynomial as a sum of powers of linear forms.Research supported in part by NSF Grant DMS 0245203.Lecture held in the Seminario Matematico e Fisico on October 15, 2003Received: April, 2004 相似文献
83.
David F. Anderson 《Journal of Pure and Applied Algebra》2003,180(3):221-241
For a commutative ring R with set of zero-divisors Z(R), the zero-divisor graph of R is Γ(R)=Z(R)−{0}, with distinct vertices x and y adjacent if and only if xy=0. In this paper, we show that Γ(T(R)) and Γ(R) are isomorphic as graphs, where T(R) is the total quotient ring of R, and that Γ(R) is uniquely complemented if and only if either T(R) is von Neumann regular or Γ(R) is a star graph. We also investigate which cardinal numbers can arise as orders of equivalence classes (related to annihilator conditions) in a von Neumann regular ring. 相似文献
84.
Harm Derksen 《Advances in Mathematics》2004,185(2):207-214
Suppose that G is a linearly reductive group. Good degree bounds for generators of invariant rings were given in (Proc. Amer. Math. Soc. 129 (4) (2001) 955). Here we study minimal free resolutions of invariant rings. For finite linearly reductive groups G it was recently shown in (Adv. Math. 156 (1) (2000) 23, Electron Res. Announc. Amer. Math. Soc. 7 (2001) 5, Adv. Math. 172 (2002) 151) that rings of invariants are generated in degree at most the group order |G|. In characteristic 0 this degree bound is a classical result by Emmy Noether (see Math. Ann. 77 (1916) 89). Given an invariant ring of a finite linearly reductive group G, we prove that the ideal of relations of a minimal set of generators is generated in degree at most ?2|G|. 相似文献
85.
We solve a bitangential interpolation problem for contractive multipliers
on the Arveson space with an arbitrary interpolating set in the closed
unit ball . The solvability criterion is established in terms of positive
kernels. The set of all solutions is parametrized by a Redheffer transform.
Submitted: February 2, 2002. 相似文献
86.
87.
88.
Eugenio Hernández Xihua Wang Guido Weiss 《Journal of Fourier Analysis and Applications》1997,3(1):23-41
The main purpose of this paper is to give a procedure to “mollify” the low-pass filters of a large number ofMinimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA. Hence, we are able
to approximate (in the L
2
-norm) MSF wavelets by wavelets with any desired degree of smoothness on the Fourier transform side. Although the MSF wavelets
we consider are bandlimited, this may not be true for their smooth approximations. This phenomena is related to the invariant
cycles under the transformation x ↦2x (mod2π). We also give a characterization of all low-pass filters for MSF wavelets. Throughout the paper new and interesting examples
of wavelets are described. 相似文献
89.
Takanari Yasui Takeshi Ohtsuka Tetsu Suzuki Shigeki Okajima Kazuya Nakayama Mitsuru Tomioka Katsuhiro Kamimura Takeo Namekata Hiroaki Minamide Hiromasa Ito 《International Journal of Infrared and Millimeter Waves》2006,27(2):199-210
A new, wide-band, high-speed and high-sensitivity THz detector has been developed. The prototype detector consists of a parabolic
cylindrical mirror, a long wire antenna and a Schottky barrier diode. Direct detection measurements have shown a stable sensitivity
of 150 ± 50 V/W for 1–2 THz without any adjustments. The long wire antenna was fixed at the focus of parabolic cylindrical
mirror then it has been realized less operation steps, easy coupling to the external THz signals and a dramatic enhancement
in the practicality of this system. The optically polished mirror and frosted surface one showed comparable sensitivities,
thus easy polishing and less cost mirror fabrication can be applied for this system. The radiation pattern showed a maximum
radiation angle of approximately 23° with its dominant main lobe, which was attributed to the wire antenna character and confirmed
good agreements with classical antenna theory. 相似文献
90.
Rupert L. Frank Ari Laptev Elliott H. Lieb Robert Seiringer 《Letters in Mathematical Physics》2006,77(3):309-316
Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential. 相似文献