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21.
Thomas I. Seidman 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):3911-3917
For sets given as finite intersections the basic normal cone is given as , but such a result is not, in general, available for infinite intersections. A comparable characterization of is obtained here for a class of such infinite intersections. 相似文献
23.
The ball number function is extended here to platonic bodies and corresponding generalized uniform distributions on platonic spheres are considered. A platonic disintegration formula of the Lebesgue measure is proved as well as a thin layers property. 相似文献
24.
25.
We study the orbits of G=GL(V) in the enhanced nilpotent cone , where is the variety of nilpotent endomorphisms of V. These orbits are parametrized by bipartitions of n=dimV, and we prove that the closure ordering corresponds to a natural partial order on bipartitions. Moreover, we prove that the local intersection cohomology of the orbit closures is given by certain bipartition analogues of Kostka polynomials, defined by Shoji. Finally, we make a connection with Kato's exotic nilpotent cone in type C, proving that the closure ordering is the same, and conjecturing that the intersection cohomology is the same but with degrees doubled. 相似文献
26.
Let be the complement of the intersection graph G of a family of translations of a compact convex figure in Rn. When n=2, we show that , where γ(G) is the size of the minimum dominating set of G. The bound on is sharp. For higher dimension we show that , for n?3. We also study the chromatic number of the complement of the intersection graph of homothetic copies of a fixed convex body in Rn. 相似文献
27.
We present a data structure for ray-shooting queries in a set of convex fat polyhedra of total complexity n in . The data structure uses O(n2+ε) storage and preprocessing time, and queries can be answered in O(log2n) time. A trade-off between storage and query time is also possible: for any m with n<m<n2, we can construct a structure that uses O(m1+ε) storage and preprocessing time such that queries take time.We also describe a data structure for simplex intersection queries in a set of n convex fat constant-complexity polyhedra in . For any m with n<m<n3, we can construct a structure that uses O(m1+ε) storage and preprocessing time such that all polyhedra intersecting a query simplex can be reported in O((n/m1/3)logn+k) time, where k is the number of answers. 相似文献
28.
Papu Kalita Biman Medhi Haobam Kisan Singh Himangshu Pratim Bhattacharyya Nikhil Gupt Dr. Manabendra Sarma 《Chemphyschem》2023,24(3):e202200727
The conical intersection (CI) governs the ultra-fast relaxation of excited states in a radiationless manner and are observed mainly in photochemical processes. In the current work, we investigated the effects of substituents on the reaction dynamics for the conversion of gauche-1,3-butadiene to bicyclobutane via photochemical electrocyclization. We incorporated both electron withdrawing (−F) and donating (−CH3) groups in the conjugated system. In our study, we optimized the minimum energy conical intersection (MECI) geometries using the multi-configurational state-averaged CASSCF approach, whereas, to study the ground state reaction pathways for the substituted derivatives, dispersion corrected, B3LYP-D3 functional was used. The non-adiabatic surface hopping molecular dynamics simulations were performed to observe the behaviour of electronic states involved throughout the photoconversion process. The results obtained from the multi-reference second-order perturbation correction of energy at the XMS-CASPT2 level of theory, topography analysis, and non-adiabatic dynamics suggest that the −CH3 substituted derivatives can undergo faster thermal conversion to the product in the ground state with a smaller activation energy barrier compared to −F substituted derivative. Our study also reveals that the GBUT to BIBUT conversion follows both conrotatory and disrotatory pathways, whereas, on substitution with −F or −CH3, the conversion proceeds via the conrotatory pathway. 相似文献
29.
Let p≥2, n
1≤⋅⋅⋅≤n
p
be positive integers and
be independent planar Brownian motions started uniformly on the boundary of the unit circle. We define a p-fold intersection exponent ς
p
(n
1,…,n
p
), as the exponential rate of decay of the probability that the packets
, i=1,…,p, have no joint intersection. The case p=2 is well-known and, following two decades of numerical and mathematical activity, Lawler et al. (Acta Math. 187:275–308,
2001) rigorously identified precise values for these exponents. The exponents have not been investigated so far for p>2. We present an extensive mathematical and numerical study, leading to an exact formula in the case n
1=1, n
2=2, and several interesting conjectures for other cases. 相似文献
30.
Chang-jian Zhao 《Geometriae Dedicata》2009,141(1):109-122
Duals of the basic projection and mixed projection inequalities are established for intersection and mixed intersection bodies.
相似文献