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Triposes, exact completions, and Hilbert's ε-operator

note on relations relative to a factorization system. In A. Carboni, M.C. Pedicchio, and G. Rosolini, editors, Category Theory '90, volume 1488 of Lecture Notes in Math., pages 249-261. Springer-Verlag, Como, 1992. [Law69a] F. W. Lawvere. Adjointness in foundations. Dialectica, 23:281{296, 1969. [Law69b] F.W. Lawvere. Diagonal arguments and cartesian closed categories. In Category Theory, Homology Theory and their Applications, II (Battelle Institute Conference, Seattle, Wash., 1968, Vol. Two), pages 134-145. Springer, 1969

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Introduction. A Personal Tribute to Peter Freyd and Bill Lawvere

Lecture Notes in Mathematics 61, Springer-Verlag (1968), 41-61. [24] F. W. Lawvere, Ordinal Sums and Equational Doctrines, Lecture Notes in Mathematics 80, Springer-Verlag (1969), 141-155. [25] F. W. Lawvere, Diagonal Arguments and Cartesian Closed Categories, Springer Lecture Notes in Mathematics 92, Springer-Verlag (1969), 134-145. [26] F. W. Lawvere, Quantiffers and Sheaves, Actes du Congrffes International des Mathffematiciens Nice 1970, 229-334. [27] F. W. Lawvere, Metric Spaces, Generalized Logic, and

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An efficient computational method based on the hat functions for solving fractional optimal control problems

, Commun Nonlinear Sci Numer Simulat, vol. 25 (2015), pp. 27-40. [16] Z. D. Jelicic and N. Petrovacki, Optimality conditions and a solution scheme for fractional optimal control problems, Struct Multidisc Optim, vol. 38 (2009), pp. 571-581. [17] A. Lotfi and S. A. Yousefi, Epsilon-ritz method for solving a class of fractional constrained optimization problems, J. Optim Theory Appl, vol. 163 (2014), pp. 884-899. [18] F. Jarad, T. Abdeljawad and D. Baleanu, Fractional variational optimal control problems with delayed arguments, m Nonlinear Dyn, vol. 62 (2010), pp. 609

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Combinatorial proofs of some Stirling number formulas


In this note, we provide bijective proofs of some recent identities involving Stirling numbers of the second kind, as previously requested. Our arguments also yield generalizations in terms of a well known q-Stirling number.

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