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111.
Jean-Paul Doignon 《Journal of Geometry》1973,3(1):71-85
A subset of a (cristallographical) lattice n is called convex whenever it is the intersection of the lattice with a convex set of the affine space containing n. We give a characterization of the convex sets which is intrinsic to the lattice and do the same for other related notions, e.g. the boundary of a convex set of n. A statement analogous to Helly's theorem is also proved. 相似文献
112.
In 1966 H. Tverberg gave a far reaching generalization of the well-known classical theorem of J. Radon. In this paper a similar generalization of the classical Helly theorem is given and it is shown that among these two generalized theorems a relationship holds similar to a theorem proved by F.W. Levi in 1951. Also the generalized Helly theorem in the convex product and convex sum space are investigated. 相似文献
113.
Zhou J Wu J Hafdi N Behr JP Erbacher P Peng L 《Chemical communications (Cambridge, England)》2006,(22):2362-2364
Genuine, nondegraded PAMAM dendrimers self-assemble with siRNA into nanoscale particles that are efficient for siRNA delivery and induce potent endogenous gene silencing. 相似文献
114.
Schaffner AP Lena G Roussel S Wawrezinieck A Aubry A Briand JP Didierjean C Guichard G 《Chemical communications (Cambridge, England)》2006,(39):4069-4071
Enantiopure dipeptide-derived 1,3,5-triazepan-2,6-diones and form H-bonded 3(1) helical molecular tapes with P chirality in the solid state; in the case of , these columnar tapes self-assemble through aromatic-aromatic interactions to give hollow tubular structures. 相似文献
115.
Pastorin G Wu W Wieckowski S Briand JP Kostarelos K Prato M Bianco A 《Chemical communications (Cambridge, England)》2006,(11):1182-1184
Multi-walled carbon nanotubes have been covalently functionalized via 1,3-dipolar cycloaddition of azomethine ylides with orthogonally protected amino functions that can be selectively deprotected and subsequently modified with drugs and fluorescent probes. 相似文献
116.
Bethany Nicholson John D. Siirola Jean-Paul Watson Victor M. Zavala Lorenz T. Biegler 《Mathematical Programming Computation》2018,10(2):187-223
We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differential equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers. 相似文献
117.
Jean-Paul Cardinal 《Linear algebra and its applications》2010,432(1):161-172
In this paper, we explore a family of congruences over N∗ from which one builds a sequence of symmetric matrices related to the Mertens function. From the results of numerical experiments, we formulate a conjecture about the growth of the quadratic norm of these matrices, which implies the Riemann hypothesis. This suggests that matrix analysis methods may come to play a more important role in this classical and difficult problem. 相似文献
118.
Let a finite semiorder, or unit interval order, be given. When suitably defined, its numerical representations are the solutions of a system of linear inequalities. They thus form a convex polyhedron. We show that the facets of the representation polyhedron correspond to the noses and hollows of the semiorder. Our main result is to prove that the system defining the polyhedron is totally dual integral. As a consequence, the coordinates of the vertices and the components of the extreme rays of the polyhedron are all integral multiples of a common value. Total dual integrality is in turn derived from a particular property of the oriented cycles in the directed graph of noses and hollows of a strictly upper diagonal step tableau. Our approach delivers also a new proof for the existence of the minimal representation of a semiorder, a concept originally discovered by Pirlot (Theory Decis 28:109–141, 1990). Finding combinatorial interpretations of the vertices and extreme rays of the representation polyhedron is left for future work. 相似文献
119.
We suggest that the transition that occurs at large N_{c} in the eigenvalue distribution of a Wilson loop may have a turbulent origin. We arrived at this conclusion by studying the complex-valued inviscid Burgers-Hopf equation that corresponds to the Makeenko-Migdal loop equation, and we demonstrate the appearance of a shock in the spectral flow of the Wilson loop eigenvalues. This picture supplements that of the Durhuus-Olesen transition with a particular realization of disorder. The critical behavior at the formation of the shock allows us to infer exponents that have been measured recently in lattice simulations by Narayanan and Neuberger in d=2 and d=3. Our analysis leads us to speculate that the universal behavior observed in these lattice simulations might be a generic feature of confinement, also in d=4 Yang-Mills theory. 相似文献
120.
In this paper, we extend and complete the classification of the generic singularities of the 3D-contact sub-Riemmanian conjugate locus in a neighborhood of the origin. 相似文献