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961.
Arno Berger Leonid A. Bunimovich Theodore P. Hill 《Transactions of the American Mathematical Society》2005,357(1):197-219
Near a stable fixed point at 0 or , many real-valued dynamical systems follow Benford's law: under iteration of a map the proportion of values in with mantissa (base ) less than tends to for all in as , for all integer bases 1$">. In particular, the orbits under most power, exponential, and rational functions (or any successive combination thereof), follow Benford's law for almost all sufficiently large initial values. For linearly-dominated systems, convergence to Benford's distribution occurs for every , but for essentially nonlinear systems, exceptional sets may exist. Extensions to nonautonomous dynamical systems are given, and the results are applied to show that many differential equations such as , where is with F'(0)$">, also follow Benford's law. Besides generalizing many well-known results for sequences such as or the Fibonacci numbers, these findings supplement recent observations in physical experiments and numerical simulations of dynamical systems.
962.
963.
Leonid A. Kurdachenko Alexey V. Sadovnichenko Igor Ya. Subbotin 《Central European Journal of Mathematics》2009,7(2):176-185
Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dim
F
(BFG/B) is finite. A subspace B is called almost G-invariant, if dim
F
(B/Core
G
(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.
相似文献
964.
L. O. Chekhov 《Proceedings of the Steklov Institute of Mathematics》2009,266(1):228-250
We interpret the previously developed Teichmüller theory of surfaces with marked points on boundary components (bordered surfaces)
as the Teichmüller theory of Riemann surfaces with orbifold points of order 2. In the Poincaré uniformization pattern, we
describe necessary and sufficient conditions for the group generated by the Fuchsian group of the surface with added inversions
to be of the almost hyperbolic Fuchsian type. All the techniques elaborated for the bordered surfaces (quantization, classical
and quantum mapping-class group transformations, and Poisson and quantum algebra of geodesic functions) are equally applicable
to the surfaces with orbifold points. 相似文献
965.
Leonid Gurvits 《Discrete and Computational Geometry》2009,41(4):533-555
Let K=(K
1,…,K
n
) be an n-tuple of convex compact subsets in the Euclidean space R
n
, and let V(⋅) be the Euclidean volume in R
n
. The Minkowski polynomial V
K
is defined as V
K
(λ
1,…,λ
n
)=V(λ
1
K
1+⋅⋅⋅+λ
n
K
n
) and the mixed volume V(K
1,…,K
n
) as
Our main result is a poly-time algorithm which approximates V(K
1,…,K
n
) with multiplicative error e
n
and with better rates if the affine dimensions of most of the sets K
i
are small. Our approach is based on a particular approximation of log (V(K
1,…,K
n
)) by a solution of some convex minimization problem. We prove the mixed volume analogues of the Van der Waerden and Schrijver–Valiant
conjectures on the permanent. These results, interesting on their own, allow us to justify the abovementioned approximation
by a convex minimization, which is solved using the ellipsoid method and a randomized poly-time time algorithm for the approximation
of the volume of a convex set. 相似文献
966.
We consider the Schr?dinger operator Hγ = ( − Δ)l + γ V(x)· acting in the space
$$L_2 (\mathbb{R}^d ),$$ where 2l ≥ d, V (x) ≥ 0, V (x) is continuous and is not identically zero, and
$$\lim _{|{\mathbf{x}}| \to \infty } V({\mathbf{x}}) = 0.$$ We obtain an asymptotic expansion as
$$\gamma \uparrow 0$$of the bottom negative eigenvalue of Hγ, which is born at the moment γ = 0 from the lower bound λ = 0 of the spectrum σ(H0) of the unperturbed operator H0 = ( − Δ)l (a virtual eigenvalue). To this end we develop a supplement to the Birman-Schwinger theory on the process of the birth of
eigenvalues in the gap of the spectrum of the unperturbed operator H0. Furthermore, we extract a finite-rank portion Φ(λ) from the Birman- Schwinger operator
$$X_V (\lambda ) = V^{\frac{1} {2}} R_\lambda (H_0 )V^{\frac{1}{2}} ,$$ which yields the leading terms for the desired asymptotic
expansion. 相似文献
967.
We describe the prime and primitive spectra for quantized enveloping algebras at roots of 1 in characteristic zero in terms of the prime spectrum of the underlying enveloping algebra. Our methods come from the theory of Hopf algebra crossed products. For primitive ideals we obtain an analogue of Duflo's Theorem, which says that every primitive ideal is the annihilator of a simple highest weight module. This depends on an extension of Lusztig's tensor product theorem.
968.
Tandem transformations of tetrahydrobenzothieno[2,3-c]pyridines in the presence of activated alkynes
Leonid G. Voskressensky Svetlana A. Kovaleva Anna V. Listratova Valery S. Tolkunov Alexey V. Varlamov 《Tetrahedron》2010,66(48):9421-9430
The reactivity of some new tetrahydrothienopyridines towards activated alkynes was investigated. A novel cascade cleavage-spiroannulation process, leading to the formation of previously unreported derivatives of 1′H-spiro[1-benzothiophene-3,4′-pyridine] was discovered and studied. 相似文献
969.
The pulsed field ionization-zero kinetic energy photoelectron technique has been used to observe the low-lying energy levels of UO+. Rotationally resolved spectra were recorded for the ground state and the first nine electronically excited states. Extensive vibrational progressions were characterized. Omega+ assignments were unambiguously determined from the first rotational lines identified in each vibronic band. Term energies, vibrational frequencies, and anharmonicity constants for low-lying energy levels of UO+ are reported. In addition, accurate values for the ionization energies for UO [48,643.8(2) cm(-1)] and U [49,957.6(2) cm(-1)] were determined. The pattern of low-lying electronic states for UO+ indicates that they originate from the U3+(5f3)O2- configuration, where the uranium ion-centered interactions between the 5f electrons are significantly stronger than interactions with the intramolecular electric field. The latter lifts the degeneracy of U3+ ion-core states, but the atomic angular momentum quantum numbers remain reasonably well defined. 相似文献
970.
Physico‐mechanical properties of polymers in solid state, in particular conditions of their structural transformations, are substantially defined by existence and mobility of elementary nonlinear excitations. The localized oscillatory excitations (breathers), which have been revealed earlier in crystalline polyethylene alongside with topological solitons, turn out to be significant for thermodynamic studies as well as for investigation of energy transfer. We consider analytically the breathers in more complex crystalline polytetrafluoroethylene. It is shown that introduction of adequate variables allows to construct the continuum model describing spatially localized excitations with several internal degrees of freedom. Characteristic parameters of breathers and conditions of their mobility are defined.