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781.
We give a new expression for the inner product of two kernel functions associated to a cusp form. Among other applications,
it yields an extension of a formula of Kohnen and Zagier, and another proof of Manin’s Periods Theorem. Cohen’s representation
of these kernels as series is also generalized. 相似文献
782.
We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on (associative) substructural logics over the full Lambek Calculus (see, for example, Ono (2003) [34], Galatos and Ono (2006) [18], Galatos et al. (2007) [17]). We present a Gentzen-style sequent system that lacks the structural rules of contraction, weakening, exchange and associativity, and can be considered a non-associative formulation of . Moreover, we introduce an equivalent Hilbert-style system and show that the logic associated with and is algebraizable, with the variety of residuated lattice-ordered groupoids with unit serving as its equivalent algebraic semantics.Overcoming technical complications arising from the lack of associativity, we introduce a generalized version of a logical matrix and apply the method of quasicompletions to obtain an algebra and a quasiembedding from the matrix to the algebra. By applying the general result to specific cases, we obtain important logical and algebraic properties, including the cut elimination of and various extensions, the strong separation of , and the finite generation of the variety of residuated lattice-ordered groupoids with unit. 相似文献
783.
Polyhedral relaxations have been incorporated in a variety of solvers for the global optimization of mixed-integer nonlinear programs. Currently, these relaxations constitute the dominant approach in global optimization practice. In this paper, we introduce a new relaxation paradigm for global optimization. The proposed framework combines polyhedral and convex nonlinear relaxations, along with fail-safe techniques, convexity identification at each node of the branch-and-bound tree, and learning strategies for automatically selecting and switching between polyhedral and nonlinear relaxations and among different local search algorithms in different parts of the search tree. We report computational experiments with the proposed methodology on widely-used test problem collections from the literature, including 369 problems from GlobalLib, 250 problems from MINLPLib, 980 problems from PrincetonLib, and 142 problems from IBMLib. Results show that incorporating the proposed techniques in the BARON software leads to significant reductions in execution time, and increases by 30% the number of problems that are solvable to global optimality within 500 s on a standard workstation. 相似文献
784.
Nikolaos Metaxas Andromachi Karagiannidou 《International Journal of Computers for Mathematical Learning》2010,15(1):63-71
Visualization of mathematical relationships enables students to formulate conjectures as well as to search for mathematical
arguments to support these conjectures. In this project students are asked to discover the sufficient and necessary condition
so that two circles form the circumscribed and inscribed circle of a triangle and investigate how this condition effects the
type of triangle in general and its perimeter in particular. Its open-ended form of the task is a departure from the usual
phrasing of textbook’s exercises “show that…”. 相似文献
785.
Evgenia H. Papageorgiou Nikolaos S. Papageorgiou 《Proceedings Mathematical Sciences》2004,114(3):269-298
In this paper we study second order non-linear periodic systems driven by the ordinary vectorp-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth
critical point theory. We prove existence and multiplicity results under general growth conditions on the potential function.
Then we establish the existence of non-trivial homoclinic (to zero) solutions. Our theorem appears to be the first such result
(even for smooth problems) for systems monitored by thep-Laplacian. In the last section of the paper we examine the scalar non-linear and semilinear problem. Our approach uses a
generalized Landesman-Lazer type condition which generalizes previous ones used in the literature. Also for the semilinear
case the problem is at resonance at any eigenvalue. 相似文献
786.
Nikolaos S Papageorgiou 《Proceedings Mathematical Sciences》1990,100(1):65-77
In this paper we examine infinite-dimensional control systems governed by semilinear evolution equations and having both state and control constraint. We introduce the relaxed system and show that the original trajectories are dense in an appropriate function space in the relaxed ones. We also determine the dependence of the solution set on the initial conditions. Then using those results we establish necessary and sufficient conditions for optimality for some optimization problems. Finally we prove some controllability results. 相似文献
787.
PhPCp 2 could be prepared by the reaction ofPhPCl2 withCpNa. The metallation ofPhPCp 2 withn-BuLi and the following reaction with TiCl4 led to the first P-bridged [1]titanocenophane. Structural assignments of this compound could be made on the base of its1H-NMR spectrum. 相似文献
788.
Gerogiannaki-Christopoulou M Kyriakidis NV Athanasopoulos PE 《Journal of AOAC International》2003,86(6):1232-1235
A study of the correlation between the refractive index (RI) method adopted by the European Community (EC) and a reference pycnometric method for the measurement of alcoholic strength was undertaken. A new RI method with greater accuracy was also developed. Alcoholic strength measured by both RI methods presented a relatively constant negative bias compared with results by the pycnometric method. Differences found between the RI methods and the pycnometric method were 0.6-0.9% (v/v) when RI was measured by the EC method and 0.4-0.5% (v/v) when the new RI method developed in our laboratory was used. Statistical analysis of the results showed that differences between the 2 RI methods and the reference pycnometric method were statistically significant at the 95% confidence level. Correction factors are proposed for the accurate use of measurements of alcoholic strength obtained for small volume samples. 相似文献
789.
790.
Danopoulos AA Tsoureas N Green JC Hursthouse MB 《Chemical communications (Cambridge, England)》2003,(6):756-757
The first authenticated example of migration of a methyl group from palladium(II) to a coordinated N-heterocyclic carbene is described. 相似文献