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151.
Franciszek Hugon Szafraniec 《Reports on Mathematical Physics》2004,53(3):393-400
The classical Hamiltonian ) of the very classical quantum harmonic oscillator, which is regarded as a germ of the most of what comes about in quantum mechanics, can be sublimed to an abstract operator in a separable Hilbert space. Having this done one may ask for a condition which would allow it to be identified among operators of a suitable class. This class is that corresponding to three diagonal matrices and the property which makes the action successful is a kind of diagonal invariance (up to change of basis) within the class in question. 相似文献
152.
We present a framework aimed to reveal directed interactions of activated brain areas using time-resolved fMRI and vector autoregressive (VAR) modeling in the context of Granger causality. After describing the underlying mathematical concepts, we present simulations helping to characterize the conditions under which VAR modeling and Granger causality can reveal directed interactions from fluctuations in BOLD-like signal time courses. We apply the proposed approach to a dynamic sensorimotor mapping paradigm. In an event-related fMRI experiment, subjects performed a visuomotor mapping task for which the mapping of two stimuli (“faces” vs “houses”) to two responses (“left” or “right”) alternated periodically between the two possible mappings. Besides expected activity in sensory and motor areas, a fronto-parietal network was found to be active during presentation of a cue indicating a change in the stimulus-response (S-R) mapping. The observed network includes the superior parietal lobule and premotor areas. These areas might be involved in setting up and maintaining stimulus-response associations. The Granger causality analysis revealed a directed influence exerted by the left lateral prefrontal cortex and premotor areas on the left posterior parietal cortex. 相似文献
153.
The highly excited vibrational states of asymmetric linear tetratomic molecules are studied in the framework of Lie algebra.
By using symmetric groupU
1(4)U
2(4)⊗U
3(4), we construct the Hamiltonian that includes not only Casimir operators but also Majorana operators M12, M13 and M23, which are useful for getting potential energy surface and force constants in Lie algebra method. By Lie algebra treatment,
we obtain the eigenvalues of the Hamiltonian, and make the concrete calculation for molecule C2HF. 相似文献
154.
We consider a fifth-order partial differential equation (PDE) that is a generalization of the integrable Camassa–Holm equation. This fifth-order PDE has exact solutions in terms of an arbitrary number of superposed pulsons with a geodesic Hamiltonian dynamics that is known to be integrable in the two-body case N==2. Numerical simulations show that the pulsons are stable, dominate the initial value problem, and scatter elastically. These characteristics are reminiscent of solitons in integrable systems. But after demonstrating the nonexistence of a suitable Lagrangian or bi-Hamiltonian structure and obtaining negative results from Painlevé analysis and the Wahlquist–Estabrook method, we assert that this fifth-order PDE is not integrable. 相似文献
155.
In terms of hyperelliptic functions, we integrate a two-particle Hamiltonian with quartic potential and additional linear and nonpolynomial terms in the Liouville integrable cases 1:6:1 and 1:6:8. 相似文献
156.
We study the pure point spectrum of the energy operator H(P
) of a many-particle charged quantum system in a homogeneous magnetic field based on the results in our previous work under fixation of the sum P
of the pseudomomentum components of the system. We prove that the discrete spectrum H(P
) of a short-range system is infinite under some conditions (which, for example, hold for a system of two oppositely charged particles) even in the case of a finitely supported potential. For a long-range system of the type of a (+)-ion of an atom (including the ion), the discrete spectrum is infinite. 相似文献
157.
We address the problem of finding the worst possible traffic a
user of a telecommunications network can send.
We take worst to mean having the highest effective
bandwidth, a concept that arises in the Large Deviation theory of
queueing networks.
The traffic is assumed to be stationary and to satisfy leaky bucket
constraints, which represent the a priori knowledge the network
operator has concerning the traffic.
Firstly, we show that this optimization problem may be reduced to an
optimization over periodic traffic sources.
Then, using convexity methods, we show that the realizations of a
worst case source must have the following properties:
at each instant the transmission rate must be either zero,
the peak rate, or the leaky bucket rate; it may only be the latter when
the leaky bucket is empty or full;
each burst of activity must either start with the leaky
bucket empty or end with it full. 相似文献
158.
Zhi-quanHu FengTian 《应用数学学报(英文版)》2003,19(1):97-106
A graph G is κ-ordered Hamiltonian 2≤κ≤n,if for every ordered sequence S of κ distinct vertices of G,there exists a Hamiltonian cycle that encounters S in the given order,In this article,we prove that if G is a graph on n vertices with degree sum of nonadjacent vertices at least n 3κ-9/2,then G is κ-ordered Hamiltonian for κ=3,4,…,[n/19].We also show that the degree sum bound can be reduced to n 2[κ/2]-2 if κ(G)≥3κ-1/2 or δ(G)≥5κ-4.Several known results are generalized. 相似文献
159.
In this article we study Hamilton cycles in sparse pseudo‐random graphs. We prove that if the second largest absolute value λ of an eigenvalue of a d‐regular graph G on n vertices satisfies and n is large enough, then G is Hamiltonian. We also show how our main result can be used to prove that for every c >0 and large enough n a Cayley graph X (G,S), formed by choosing a set S of c log5 n random generators in a group G of order n, is almost surely Hamiltonian. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 17–33, 2003 相似文献
160.
In this article a simple form of expressing and studying the order conditions to be satisfied by starting algorithms for Runge–Kutta methods, which use information from the two previous steps is presented. In particular, starting algorithms of highest order for Runge–Kutta–Gauss methods up to seven stages are derived. Some numerical experiments with Hamiltonian systems to compare the behaviour of the new starting algorithms with other existing ones are presented. 相似文献