In this dissertation, we study about the extension of results of psumming operators to Lipschitz p-summing maps and their respective relatives for 1 ≤ p < ∞ . Lipschitz p-summing and Lipschitz p-integral maps are the nonlinear version of (absolutely) p-summing and p-integral operators respectively. The p-summing operators were first introduced in the paper [13] by Pietsch in 1967 for 1 < p < ∞ and for p = 1 go back to Grothendieck which he introduced in his paper [9] in 1956. They were subsequently taken on with applications in 1968 by Lindenstrauss and Pelczynski as contained in [12] and these early developments of the subject are meticulously presented in [6] by Diestel et al. While the absolutely summing operators (and their relatives, the integral operators) constitute important ideals of operators used in the study of the geometric structure theory of Banach spaces and their applications to other areas such as Harmonic analysis, their confinement to linear theory has been found to be too limiting. The paper [8] by Farmer and Johnson is an attempt by the authors to extend known useful results to the non-linear theory and their first interface in this case has appealed to the uniform theory, and in particular to the theory of Lipschitz functions between Banach spaces. We find analogues for p-summing and p-integral operators for 1 ≤ p < ∞. This then divides the dissertation into two parts. In the first part, we consider results on Lipschitz p-summing maps. An application of Bourgain’s result as found in [2] proves that a map from a metric space X into ℓ2X 1 with |X| = n is Lipschitz 1-summing. We also apply the non-linear form of Grothendieck’s Theorem to prove that a map from the space of continuous real-valued functions on [0, 1] into a Hilbert space is Lipschitz p-summing for some 1 ≤ p < ∞. We also prove an analogue of the 2-Summing Extension Theorem in the non-linear setting as found in [6] by showing that every Lipschiz 2-summing map admits a Lipschiz 2-summing extension. When X is a separable Banach space which has a subspace isomorphic to ℓ1, we show that there is a Lipschitz p-summing map from X into R2 for 2 ≤ p < ∞ whose range contains a closed set with empty interior. Finally, we prove that if a finite metric space X of cardinality 2k is of supremal metric type 1, then every Lipschitz map from X into a Hilbert space is Lipschitz p-summing for some 1 ≤ p < ∞. In the second part, we look at results on Lipschitz p-integral maps. The main result is that the natural inclusion map from ℓ1 into ℓ2 is Lipschitz 1-summing but not Lipschitz 1-integral. / Dissertation (MSc)--University of Pretoria, 2013. / gm2014 / Mathematics and Applied Mathematics / unrestricted

Testing of summing electronics and VDC A/D Cards was performed to assure proper functioning and operation within defined parameters. In both the summing modules and the VDC A/D cards, testing for minimum threshold voltage for each channel and crosstalk between neighboring channels was performed. Additionally, the modules were installed in Hall A with input signals from shower detectors arranged to establish a trigger by summing signals together with the use of tested modules. Testing involved utilizing a pulser to mimic PMT signals, a discriminator, an attenuator, a scaler, a level translator, an oscilloscope, a high voltage power supply, and a special apparatus used to power and send signal to the A/D cards. After testing, modules were obtained that meet necessary criteria for use in the APEX experiment, and the A/D cards obtained were determined to have adequate specifications for their utilization, with specific results included in the appendix.

No description available.

Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-05-02T19:03:09Z No. of bitstreams: 1 Arquivototal.pdf: 737510 bytes, checksum: a205d9714f9ec661929aea54c8a55145 (MD5) / Made available in DSpace on 2018-05-02T19:03:09Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 737510 bytes, checksum: a205d9714f9ec661929aea54c8a55145 (MD5) Previous issue date: 2017-08-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The main goal of this work is to study a new sequence space introduced in 2014 by Karn and Sinha, namely the space of mid p-summable sequences. More speci cally, we will study a recent work by G. Botelho and J.R. Campos, which deepens the seminal study of this space and presents new classes of operators involving the new space and the classical sequence spaces of absolutely and weakly p-summable sequences, called absolutely mid p-summing and weakly mid p-summing operators. From this, we study a new factorization theorem, involving these new classes of operators, for the absolutely p-summing operators. / O principal objetivo desta dissertação é estudar um novo espaço de sequências introduzido por Karn e Sinha em 2014, a saber, o espaçoo das sequências mid p-somáveis. Mais especi camente, estudaremos um recente trabalho de G. Botelho e J. R. Campos que aprofunda o estudo seminal do espa co e apresenta novas classes de operadores envolvendo este novo espa co e os espa cos cl assicos de sequ^encias absolutamente e fracamente p-somáveis, denominados operadores absolutamente mid p-somantes e operadores fracamente mid p-somantes. A partir disto, estudamos um novo teorema de fatoração, envolvendo estas novas classes de operadores, para os operadores absolutamente p-somantes. mid p-somáveis; Operadores absolutamente e fracamente mid p-somantes.

We study analogues, in the Lipschitz and Operator Spaces categories, of several classical ideals of operators between Banach spaces. We introduce the concept of a Banach-space-valued molecule, which is used to develop a duality theory for several nonlinear ideals of operators including the ideal of Lipschitz p-summing operators and the ideal of factorization through a subset of a Hilbert space. We prove metric characterizations of p-convex operators, and also of those with Rademacher type and cotype. Lipschitz versions of p-convex and p-concave operators are also considered. We introduce the ideal of Lipschitz (q,p)-mixing operators, of which we prove several characterizations and give applications. Finally the ideal of completely (q,p)-mixing maps between operator spaces is studied, and several characterizations are given. They are used to prove an operator space version of Pietsch's composition theorem for p-summing operators.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-22T16:24:35Z No. of bitstreams: 1 arquivototal.pdf: 1096557 bytes, checksum: 096bafe0cd5d1cf118a6fa1546070e5d (MD5) / Made available in DSpace on 2017-08-22T16:24:35Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1096557 bytes, checksum: 096bafe0cd5d1cf118a6fa1546070e5d (MD5) Previous issue date: 2016-03-03 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study a recent general version of the Extrapolation Theorem, due to Botelho, Pellegrino, Santos and Seoane-Sep ulveda [6] that improves and uni es a number of known Extrapolation-type theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. / Neste trabalho, dissertamos sobre uma recente vers~ao geral do Teorema de Extrapola c~ao, devida a Botelho, Pellegrino, Santos e Seoane-Sep ulveda [6], que melhora e uni ca v arios teoremas do tipo Extrapola c~ao para certas classes de fun c~oes que generalizam o ideal dos operadores lineares absolutamente p-somantes.

Thesis (Ph.D. (Mathematics))--North-West University, Potchefstroom Campus, 2006.

Abstract does not display correctly / Thesis (Ph.D. (Mathematics))--North-West University, Potchefstroom Campus, 2006

Abstract does not display correctly / Thesis (Ph.D. (Mathematics))--North-West University, Potchefstroom Campus, 2006

Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-29T12:08:37Z No. of bitstreams: 1 arquivototal.pdf: 967006 bytes, checksum: bd1b76a7b376f5fda6d282d14e851d1a (MD5) / Made available in DSpace on 2016-03-29T12:08:37Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 967006 bytes, checksum: bd1b76a7b376f5fda6d282d14e851d1a (MD5) Previous issue date: 2014-03-12 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study two generalizations of the well-known concept of absolutely summing operators. The rst one consists of the multiple summing multilinear operators and it is focused on a result of coincidence that is equivalent to the Bohnenblust- Hille inequality. This inequality asserts that, for K = R or C and every positive integer m there exists positive scalars BK;m 1 such that N X i1;:::;im=1 U(ei1 ; : : : ; eim) 2m m+1!m+1 2m BK;m sup z1;:::;zm2DN jU(z1; :::; zm)j for every m-linear mapping U : KN KN ! K and every positive integer N, where (ei)N i=1 denotes the canonical basis of KN: In this line our main goal is the investigation of the best constants BK;m satisfying the above inequality. The second generalization involves the concept of absolutely summing multilinear operators at a given point; we present an abstract version of these operators involving many of their properties. We prove that, considering appropriate sequence spaces, we have other kind of operators as particular cases of our version. / No presente trabalho vamos trabalhar com duas generalizações dos bem conhecidos operadores absolutamente somantes. A primeira envolve os operadores multilineares múltiplo somantes e nos focaremos num resultado de coincidência que é equivalente à desigualdade multilinear de Bohnenblust-Hille. Esta a rma que, para = R ou C, e todo inteiro positivo m 1, existem escalares BK;m 1 tais que N X i1;:::;im=1 U(ei1 ; : : : ; eim) 2m m+1!m+1 2m BK;m sup z1;:::;zm2DN jU(z1; :::; zm)j para toda forma m-linear U : KN KN ! K e todo inteiro positivo N, onde )N i=1 é a base canônica de KN: Nessa linha, nosso objetivo será a investigação das melhores constantes BK;m que satisfazem essa desigualdade. A segunda generalização envolve o estudo dos operadores multilineares absolutamente somantes num ponto; apresentaremos uma versão abstrata destes operadores que engloba várias de suas propriedades. Veremos que, considerando os espaços de sequências adequados, teremos outros tipos de operadores como casos