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71.
Applications of operator identities to the multiple q-binomial theorem and q-Gauss summation theorem
In this paper, we first give an interesting operator identity. Furthermore, using the q-exponential operator technique to the multiple q-binomial theorem and q-Gauss summation theorem, we obtain some transformation formulae and summation theorems of multiple basic hypergeometric series. 相似文献
72.
Chun-Gang Ji 《Discrete Mathematics》2008,308(23):5860-5863
Let a(k,n) be the k-th coefficient of the n-th cyclotomic polynomials. In 1987, J. Suzuki proved that . In this paper, we improve this result and prove that for any prime p and any integer l≥1, we have
{a(k,pln)∣n,k∈N}=Z. 相似文献
73.
Benjamin Shapiro 《Journal of magnetism and magnetic materials》2009,321(10):1594-1599
Magnetic drug delivery has the potential to target therapy to specific regions in the body, improving efficacy and reducing side effects for treatment of cancer, stroke, infection, and other diseases. Using stationary external magnets, which attract the magnetic drug carriers, this treatment is limited to shallow targets (<5 cm below skin depth using the strongest possible, still safe, practical magnetic fields). We consider dynamic magnetic actuation and present initial results that show it is possible to vary magnets one against the other to focus carriers between them on average. The many remaining tasks for deep targeting in-vivo are then briefly noted. 相似文献
74.
We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α ∈ (n-1,n) in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder's inequality, a suitable singular Gronwall's inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results. 相似文献
75.
This paper presents a theory of dynamics of closed relations on compact Hausdorff spaces. It contains an investigation of set valued maps and establishes generalizations for some topological aspects of dynamical systems theory, including recurrence, attractor–repeller structure and the Conley decomposition theorem. 相似文献
76.
ABSTRACTThis paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a sufficiently small Lipschitz constant, the existence and uniqueness of such BSDEs is obtained. As an adjoint process, a class of stochastic differential equations (SDEs) is introduced, whose coefficients also depend on the present, the past and the future of its solutions. The existence and uniqueness of such SDEs is proved for a sufficiently small time advance or a sufficiently small Lipschitz constant. A duality between such BSDEs and SDEs is established. 相似文献
77.
The purpose of this paper is to investigate the eight-dimensional non-associative unital division algebras {0}≠A over finite fields, admitting elementary abelian 2-group of automorphisms E≤Aut(A), of order 8, using tools from algebraic geometry. 相似文献
78.
We show that two simple semiclassical strategies, one based on the Wilson–Sommerfeld rule and the other on the uncertainty principle, yield the exact modified form of the virial theorem for confined systems. An alternative, easier quantum mechanical route to arrive at this result is also sketched. Pilot calculations on confined oscillators reveal decisive trends. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 相似文献
79.
The reaction force is a global property of a chemical reaction that arises when applying the Hellmann–Feynmann theorem to
the potential energy surface that links reactants, products and transition states. In the present work, the reaction force
is defined rigorously from the cartesian components coming out from all forces exerted over each atom of a molecular system
during the chemical reaction; it is demonstrated that the reaction force is a scalar property.
An erratum to this article can be found at 相似文献
80.
Gouranga C. Nayak 《Annals of Physics》2010,325(2):514-3898
Factorization theorem plays the central role at high energy colliders to study standard model and beyond standard model physics. The proof of factorization theorem is given by Collins, Soper and Sterman to all orders in perturbation theory by using diagrammatic approach. One might wonder if one can obtain the proof of factorization theorem through symmetry considerations at the lagrangian level. In this paper we provide such a proof. 相似文献