In this paper the non density of AP, the set of almost periodic functions in the sense of Bohr, in the space S of almost periodic functions in the sense of Stepanov is proven.

Thesis (Ph. D.)--Carleton University, 2001. / Includes bibliographical references (p. 118-133). Also available in electronic format on the Internet.

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Using C. Fefferman's embedding of a charge space in a measure space allows us to apply standard interpolation theorems to the establishment of norm inequalities for Besicovitch almost periodic functions. This yields a significant improvement to the results of A. Avantaggiati, G. Bruno and R. Iannacci. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

Thesis--Copenhagen. / "Litteraturfortegnelse": p. [93]-94.

Thesis--Copenhagen. / "Litteraturfortegnelse": p. [93]-94.

Nonsymmetric Macdonald polynomials can be symmetrized in all their variables to obtain the (symmetric) Macdonald polynomials. We generalize this process, symmetrizing the nonsymmetric Macdonald polynomials in only the first k out of n variables. The resulting partially-symmetric Macdonald polynomials interpolate between the symmetric and nonsymmetric types. We begin developing theory for these partially-symmetric polynomials, and prove results including their stability, an integral form, and a Pieri-like formula for their multiplication with certain elementary symmetric functions. / Doctor of Philosophy / There are two well-understood types of polynomials known as the nonsymmetric Macdonald polynomials and symmetric Macdonald polynomials. We define a new form of Macdonald polynomials, which we call partially-symmetric, that are somewhere between the symmetric and nonsymmetric versions. We examine properties of these new partially-symmetric polynomials, including what happens when adding additional symmetric variables, how to multiply them by a constant to clear out denominators in their coefficients, and what happens when multiplying them by another symmetric polynomial.

We present a geometric construction of almost Poisson brackets for nonholonomic mechanical systems whose configuration space is a Lie group G. We study the so-called LL and LR systems where the kinetic energy defines a left invariant metric on G and the constraints are invariant with respect to left (respectively right) translation on G.For LL systems, the equations on the momentum phase space, T*G, can be left translated onto g*, the dual space of the Lie algebra g. We show that the reduced equations on g* can be cast in Poisson form with respect to an almost Poisson bracket that is obtained by projecting the standard Lie-Poisson bracket onto the constraint space.For LR systems, we use ideas of semidirect product reduction to transfer the equations on T*G into the dual Lie algebra, s*, of a semidirect product. This provides a natural Lie algebraic setting for the equations of motion commonly found in the literature. We show that these equations can also be cast in Poisson form with respect to an almost Poisson bracket that is obtained by projecting the Lie-Poisson structure on s* onto a constraint submanifold.In both cases the constraint functions are Casimirs of the bracket and are satisfied automatically. Our construction is a natural generalization of the classical ideas of Lie-Poisson and semidirect product reduction to the nonholonomic case. It also sets a convenient stage for the study of Hamiltonization of certain nonholonomic systems.Our examples include the Suslov and the Veselova problems of constrained motion of a rigid body, and the Chaplygin sleigh.In addition we study the almost Poisson reduction of the Chaplygin sphere. We show that the bracket given byBorisov and Mamaev is obtained by reducing a nonstandard almost Poisson bracket that is obtained by projecting a non-canonical bivector onto the constraint submanifold using the Lagrange-D'Alembert principle.The examples that we treat show that it is possible to cast the reduced equations of motion of certain nonholonomic systems in Hamiltonian form (in the Poisson formulation) either by multiplication by a conformal factor, by the use of nonstandard brackets or simply by reduction methods.

Denna studie utvärderar ekonomiska styrmedels effekt på konsumtionen av livsmedel samt ifall skatter och subventioner kan vara en metod som styr matkonsumtionen mot hälsosamma livsmedelsval. Sex livsmedelsgrupper analyseras i studien och dessa är sötsaker och glass, kött, grönsaker, mejerivaror, bröd och spannmålsprodukter samt frukt och bär. Fyra scenarier som representerar olika skatte- och/eller subventionsreformer simuleras för att analysera vilken effekt ekonomiska styrmedel kan ha på matkonsumtion och hälsa. Responsen som de ekonomiska styrmedlen har på matkonsumtionen beräknas med elasticiteter som tagits fram från parameterestimat i AIDS-modellen. Den data som ligger till grund för den ekonometriska modellen är aggregerad konsumtionsdata, konsumentprisindex och livsmedelsförsäljning. Resultatet från studien visar att det går att styra konsumtionen av livsmedel men att substitution mellan varor kan leda till att de hälsomål som reformen är menad att nå inte uppfylls.

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