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81.
Maspoch D Domingo N Ruiz-Molina D Wurst K Hernández JM Vaughan G Rovira C Lloret F Tejada J Veciana J 《Chemical communications (Cambridge, England)》2005,(40):5035-5037
A metal-organic open-framework with an unprecedented (6,3)-helical topology, large channels and mixed ferro- and antiferromagnetic interactions has been synthesized using a three-connecting tricarboxylic polychlorotriphenylmethyl radical and Co(ii) ions. 相似文献
82.
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84.
In this paper, we study the polynomial integrability of natural Hamiltonian systems with two degrees of freedom having a homogeneous potential of degree k given either by a polynomial, or by an inverse of a polynomial. For k=−2,−1,…,3,4, their polynomial integrability has been characterized. Here, we have two main results. First, we characterize the polynomial integrability of those Hamiltonian systems with homogeneous potential of degree −3. Second, we extend a relation between the nontrivial eigenvalues of the Hessian of the potential calculated at a Darboux point to a family of Hamiltonian systems with potentials given by an inverse of a homogeneous polynomial. This relation was known for such Hamiltonian systems with homogeneous polynomial potentials. Finally, we present three open problems related with the polynomial integrability of Hamiltonian systems with a rational potential. 相似文献
85.
In this paper we classify the centers localized at the origin of coordinates, and their isochronicity for the polynomial differential systems in R2 of degree d that in complex notation z=x+iy can be written as where j is either 0 or 1. If j=0 then d?5 is an odd integer and n is an even integer satisfying 2?n?(d+1)/2. If j=1 then d?3 is an integer and n is an integer with converse parity with d and satisfying 0<n?[(d+1)/3] where [⋅] denotes the integer part function. Furthermore λ∈R and A,B,C,D∈C. Note that if d=3 and j=0, we are obtaining the generalization of the polynomial differential systems with cubic homogeneous nonlinearities studied in K.E. Malkin (1964) [17], N.I. Vulpe and K.S. Sibirskii (1988) [25], J. Llibre and C. Valls (2009) [15], and if d=2, j=1 and C=0, we are also obtaining as a particular case the quadratic polynomial differential systems studied in N.N. Bautin (1952) [2], H. Zoladek (1994) [26]. So the class of polynomial differential systems here studied is very general having arbitrary degree and containing the two more relevant subclasses in the history of the center problem for polynomial differential equations. 相似文献
86.
In this work we study the narrow relation between reversibility and the center problem and also between reversibility and the integrability problem. It is well known that an analytic system having either a non-degenerate or nilpotent center at the origin is analytically reversible or orbitally analytically reversible, respectively. In this paper we prove the existence of a smooth map that transforms an analytic system having a degenerate center at the origin with either an analytic first integral or a C∞ inverse integrating factor into a reversible linear system (after rescaling the time). Moreover, if the degenerate center has an analytic or a C∞ reversing symmetry, then the transformed system by the map also has a reversing symmetry. From the knowledge of a first integral near the center we give a procedure to detect reversing symmetries. 相似文献
87.
Jaume Llibre 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(4):1261-1271
We study the limit cycles of generalized Kukles polynomial differential systems using averaging theory of first and second order. 相似文献
88.
Cavallini M Gomez-Segura J Albonetti C Ruiz-Molina D Veciana J Biscarini F 《The journal of physical chemistry. B》2006,110(24):11607-11610
We report a new patterning process which takes place as a result of demixing of a binary polymer/solute mixture. An efficient, sustainable approach for ordering nanosized rings of so-called single molecule magnets (SMMs) is thus provided. It exploits the self-organization process in which SMM patterned film evolves to a spatially correlated pattern of nanosized rings. At long time, the anisotropic patterning of the film drives the ring to coalesce, into parallel lines of nanometric width. 相似文献
89.
90.
This paper consists of two parts. In the first part we study the relationship between conic centers (all orbits near a singular point of center type are conics) and isochronous centers of polynomial systems. In the second part we study the number of limit cycles that bifurcate from the periodic orbits of cubic reversible isochronous centers having all their orbits formed by conics, when we perturb such systems inside the class of all polynomial systems of degree n. 相似文献