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This thesis consists of revised versions of five published papers on the development of neoclassical distribution theory, in the English-speaking world together with an introduction and conclusion, which draw together the themes of the papers. The thesis covers the origins of neo-classical distribution theory in the English-speaking world in the work of Jevons and Marshall, through to the second generation of Wicksteed, Clark and Pigou, and finally on to the 1930s and the new perspectives of Hicks and Robinson. Drawing on archival sources and primary and secondary texts, these essays review the major statements on distribution theory made by key figures in the Jevonian and Marshallian marginalist traditions. The essays shed new light on the origins of neoclassical distribution theory and provide insights into the methodology of nascent neoclassical distribution theory. A drive towards a universal, all-embracing marginal productivity theory of the distribution of income characterises the work of Clark and Wicksteed, but not so Marshall. A formalist mode of analysis, which was to become the hallmark of neoclassical economics in the second half of the twentieth century, is also evident in key works of the period. However, the role of empirical evidence in theory generation and appraisal remains an undeveloped component of late nineteenth and early twentieth century neoclassical theory—Marshall again provides an exception to the general rule. There is a common adherence, among the key figures examined, to the joint proposition that competitive market wage outcomes are ‘fair’, but that low incomes (fair or not) are unjust when they fail to meet minimum needs standards. State remedial action (tax and expenditure policies) is required to remove such injustices. Robinson’s theory of exploitation provided an important extension to the neoclassical normative framework. She highlighted the extent to which labour may be exploited due to imperfections in both product and labour markets.

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Haymen猜測:對任意的超越半純函數 f(z)，f'(z)f(z)^n 取所有值無窮多次，其中至多只有一個例外值。這個著名的猜測，大部分的情形已被證明是正確的。另外，Hayman 證明 f'(z)-af(z)^n 取所有有限值無窮多次 ，其中 a 為一複數且 n≧5 的正整數。在本篇論文裡，我們將探討以小函數為係數的半純函數微分多項式之值分佈問題。並將Hayman的結果推廣至 f^{k}(z)f(z)^n 與 f^{k}(z)-af(z)^n 的情形。同時，我們也證明一些 A類半純函數與其導數的值分佈結果。 / A famous conjecture of Hayman says that if f(z) is a transcendental meromorphic function, then f'(z)f(z)^n assumes all finite values except possibly zero infinitely often. The conjecture was solved in most cases. Another result of Hayman says that f'(z)-af(z)^n, where n≧5 and a is a complex number, assumes all finite values infinitely often. In this thesis, we will study the value distribution of some differential polynomial in a meromorphic function with small functions as coefficents. In fact, we will generalize Hayman's results to the cases f^(k)(z)f(z)^n and f^(k)(z)-af(z)^n. Also, the value distribution of meromorphic functions of class A with their derivatives are obtained.

Submitted by Flaviani Cristina da Silva Cruz (flavianicruz@gmail.com) on 2018-05-28T16:39:36Z No. of bitstreams: 1 dissertacao finallllll.pdf: 1641212 bytes, checksum: a98d0d98cacf7206b9dca507069233a8 (MD5) / Rejected by Ana Paula Santulo Custódio de Medeiros null (asantulo@rc.unesp.br), reason: - Folha de aprovação: falta o ano na data da defesa: 07 de maio .... - Ficha catalográfica incorreta: a ficha catalográfica só pode ser elaborada por um bibliotecário e não é a que você recebeu pela biblioteca em 21/05/2018: NOTA: De acordo com a Resolução CFB nº 184/2017 de 29/09/2017 – na Ficha catalográfica deve constar o nome do Bibliotecário/CRB, e ser elaborada de acordo com as normas vigentes segundo à AACR2. OBSERVAÇÃO: Caso se faça necessário acrescentar ou modificar alguma informação na Ficha catalográfica do seu trabalho, informá-la no campo recomendado do Sistema 3S ou responder este e-mail. É proibido perante a lei (Art. 297 – Código Penal) qualquer alteração documental, sem autorização do Bibliotecário responsável. DA FALSIDADE DOCUMENTAL: (I) FALSIDADE DE DOCUMENTO PUBLICO ART. 297: Falsificar, no todo ou em parte, documento publico, ou alterar documento publico verdadeiro: Pena – reclusão, de dois a seis anos, e multa. DOCUMENTO PUBLICO: é aquele elaborado por funcionário publico, de acordo com as formalidades, e desempenho de suas funções. Art. 232, CPP - Consideram-se documentos quaisquer escritos, instrumentos ou papéis, públicos ou particulares. on 2018-05-28T19:00:26Z (GMT) / Submitted by Flaviani Cristina da Silva Cruz (flavianicruz@gmail.com) on 2018-05-29T13:52:43Z No. of bitstreams: 1 dissertacao-final-final.pdf: 1600591 bytes, checksum: d5829fa27d80336f1e24b663680531f8 (MD5) / Approved for entry into archive by Adriana Aparecida Puerta null (dripuerta@rc.unesp.br) on 2018-05-29T14:23:36Z (GMT) No. of bitstreams: 1 cruz_fcs_me_rcla.pdf: 1625066 bytes, checksum: c010643fc4461e0b244b4ddd4414af66 (MD5) / Made available in DSpace on 2018-05-29T14:23:36Z (GMT). No. of bitstreams: 1 cruz_fcs_me_rcla.pdf: 1625066 bytes, checksum: c010643fc4461e0b244b4ddd4414af66 (MD5) Previous issue date: 2018-05-07 / Esta dissertação objetiva-se ao estudo analítico de técnicas de interpolação integral – fundamentadas na teoria de distribuição, também conhecida como teoria de funções generalizadas – e suas aplicações a reconstrução de imagens formadas por partículas (noise image) e à forma anisotrópica das equações da hidrodinâmica com partículas suavizadas, no inglês smoothed particle hydrodynamics, bem conhecida como SPH. A aplicação a processamento de imagens é um caso particular da técnica de interpolação utilizada em SPH. A imagem original é fragmentada na forma de partículas (em duas dimensões), aleatoriamente colhidas dos píxeis da imagem original, cuja densidade de probabilidade é proporcional à escala de cinza de cada píxel vizinho. Então é feita uma reconstrução da imagem através de interpolação anisotrópica, evidenciando que detalhes estruturais do contexto original são mais bem recuperados do que a correspondente técnica isotrópica. Apesar de não realizarmos diretamente simulações de mecânica dos fluidos neste trabalho, o que é proposto aqui é uma revisão das equações fundamentais da técnica de simulação SPH para o caso anisotrópico. As interpolações apresentadas neste trabalho foram feitas a partir de um núcleo normalizado de suavização, definido na forma de uma função regulada por partes, conhecida como cubic-B-spline, que é de classe analítica C2. / This mastered dissertation aims at the analytical study of integral interpolation techniques – based on the theory of distribution, also known as generalized function theory – and its applications the reconstruction of images formed by particles (noise image) and the anisotropic form of the fundamental equations of smoothed particle hydrodynamics, well known as SPH. The application to image processing is a particular case of the interpolation technique used in SPH. The original image is fragmented in the form of particles (in two dimensions), randomly drawn from the píxels of the original image, whose density is proportional to the gray scale of each neighboring píxel. Then a reconstruction of the image is made through anisotropic interpolation, evidencing that structural details of the original context are better recovered than the corresponding isotropic technique. Although we do not directly perform fluid mechanics simulations in this work, what is proposed here is a review of the fundamental equations of the SPH simulation technique for the anisotropic case. The interpolations presented in this work were made from a normalized smoothing kernel, defined as cubic-B-spline, which is of analytic class C2.

<p>In this thesis we introduce and study a notion of effectivity (or computability) for test functions and for distributions. This is done using the theory of effective (Scott-Ershov) domains and effective domain representations.</p><p>To be able to construct effective domain representations of the spaces of test functions considered in distribution theory we need to develop the theory of admissible domain representations over countable pseudobases. This is done in the first paper of the thesis. To construct an effective domain representation of the space of distributions, we introduce and develop a notion of partial continuous function on domains. This is done in the second paper of the thesis. In the third paper we apply the results from the first two papers to develop an effective theory of distributions using effective domains. We prove that the vector space operations on each space, as well as the standard embeddings into the space of distributions effectivise. We also prove that the Fourier transform (as well as its inverse) on the space of tempered distributions is effective. Finally, we show how to use convolution to compute primitives on the space of distributions. In the last paper we investigate the effective properties of a structure theorem for the space of distributions with compact support. We show that each of the four characterisations of the class of compactly supported distributions in the structure theorem gives rise to an effective domain representation of the space. We then use effective reductions (and Turing-reductions) to study the reducibility properties of these four representations. We prove that three of the four representations are effectively equivalent, and furthermore, that all four representations are Turing-equivalent. Finally, we consider a similar structure theorem for the space of distributions supported at 0.</p>

Thesis (Ph. D.)--University of Joensuu, 2006. / Includes bibliographical references (p. 25-27).

In this thesis we introduce and study a notion of effectivity (or computability) for test functions and for distributions. This is done using the theory of effective (Scott-Ershov) domains and effective domain representations. To be able to construct effective domain representations of the spaces of test functions considered in distribution theory we need to develop the theory of admissible domain representations over countable pseudobases. This is done in the first paper of the thesis. To construct an effective domain representation of the space of distributions, we introduce and develop a notion of partial continuous function on domains. This is done in the second paper of the thesis. In the third paper we apply the results from the first two papers to develop an effective theory of distributions using effective domains. We prove that the vector space operations on each space, as well as the standard embeddings into the space of distributions effectivise. We also prove that the Fourier transform (as well as its inverse) on the space of tempered distributions is effective. Finally, we show how to use convolution to compute primitives on the space of distributions. In the last paper we investigate the effective properties of a structure theorem for the space of distributions with compact support. We show that each of the four characterisations of the class of compactly supported distributions in the structure theorem gives rise to an effective domain representation of the space. We then use effective reductions (and Turing-reductions) to study the reducibility properties of these four representations. We prove that three of the four representations are effectively equivalent, and furthermore, that all four representations are Turing-equivalent. Finally, we consider a similar structure theorem for the space of distributions supported at 0.

在這篇論文裡，我們利用值分佈的理論來探討半純函數的共值與唯一性的問題，本文包含了以下的結果：將Jank與Terglane有關三個A類中的半純函數唯一性的結果推廣到任意q個半純函數的情形；證明了C. C. Yang的一個猜測；建構了一類半純函數恰有兩個虧值，而且算出它們的虧格；將 Nevanlinna 五個值的定理推廣至兩個半純函數部分共值的情形；探討純函數 與其導數的共值問題；最後，證明了兩個半純函數共四個值且重數皆不同的定 理。 / In this thesis, we study the sharing value problems and the uniqueness problems of meromorphic functions in the theory of value distribution. In fact, this thesis contains the following results: We generalize a unicity condition of three meromorphic functions given by Jank and Terglane in class A to the case of arbitrary q meromorphic functoins. An elementary proof of a conjecture of C. C. Yang is provided. We construct a class of meromorphic functions with exact two deficient values and their deficiencies are explicitly computed. We generalize the Nevanlinna's five-value theorem to the cases that two meromorphic functions partially share either five or more values, or five or more small functions. In each case, we formulate a way to measure how far these two meromorphic functions are from sharing either values or small functions, and use this measurement to prove a uniqueness theorem. Also, we prove some uniqueness theorems on entire functions that share a pair of values (a,-a) with their derivatives, which are reformulations of some important results about uniqueness of entire functions that share values with their derivatives. Finally, we prove that if two distinct non-constant meromorphic functions $f$ and $g$ share four distinct values a_1, a_2, a_3, a_4 DM such that each a_i-point is either a (p,q)-fold or (q,p)-fold point of f and g, then (p,q) is either (1,2) or (1,3) and f, g are in some particular forms.