Dissertations / Theses on the topic 'Monoid ring'

Motivated by results of linear algebra over fields, rings and tropical semirings, we present a systematic way to understand the behaviour of matrices with entries in an arbitrary semiring. We focus on three closely related problems concerning the row and column spaces of matrices. This allows us to isolate and extract common properties that hold for different reasons over different semirings, yet also lets us identify which features of linear algebra are specific to particular types of semiring. For instance, the row and column spaces of a matrix over a field are isomorphic to each others' duals, as well as to each other, but over a tropical semiring only the first of these properties holds in general (this in itself is a surprising fact). Instead of being isomorphic, the row space and column space of a tropical matrix are anti-isomorphic in a certain order-theoretic and algebraic sense. The first problem is to describe the kernels of the row and column spaces of a given matrix. These equivalence relations generalise the orthogonal complement of a set of vectors, and the nature of their equivalence classes is entirely dependent upon the kind of semiring in question. The second, Hahn-Banach type, problem is to decide which linear functionals on row and column spaces of matrices have a linear extension. If they all do, the underlying semiring is called exact, and in this case the row and column spaces of any matrix are isomorphic to each others' duals. The final problem is to explain the connection between the row space and column space of each matrix. Our notion of a conjugation on a semiring accounts for the different possibilities in a unified manner, as it guarantees the existence of bijections between row and column spaces and lets us focus on the peculiarities of those bijections. Our main original contribution is the systematic approach described above, but along the way we establish several new results about exactness of semirings. We give sufficient conditions for a subsemiring of an exact semiring to inherit exactness, and we apply these conditions to show that exactness transfers to finite group semirings. We also show that every Boolean ring is exact. This result is interesting because it allows us to construct a ring which is exact (also known as FP-injective) but not self-injective. Finally, we consider exactness for residuated lattices, showing that every involutive residuated lattice is exact. We end by showing that the residuated lattice of subsets of a finite monoid is exact if and only if the monoid is a group.

This paper determines whether monoid rings with the two-generator property have the strong two-generator property. Dedekind domains have both the two-generator and strong two-generator properties. How common is this? Two cases are considered here: the zero-dimensional case and the one-dimensional case for monoid rings. Each case is looked at to determine if monoid rings that are not PIRs but are two-generated have the strong two-generator property. Full results are given in the zero-dimensional case, however only partial results have been found for the one-dimensional case.

Dependent type theories are a kind of mathematical foundations investigated both for the formalisation of mathematics and for reasoning about programs. They are implemented as the kernel of many proof assistants and programming languages with proofs (Coq, Agda, Idris, Dedukti, Matita, etc). Dependent types allow to encode elegantly and constructively the universal and existential quantifications of higher-order logics and are therefore adapted for writing logical propositions and proofs. However, their usage is not limited to the area of pure logic. Indeed, some recent work has shown that they can also be powerful for driving the construction of programs. Using more precise types not only helps to gain confidence about the program built, but it can also help its construction, giving rise to a new style of programming called Type-Driven Development. However, one difficulty with reasoning and programming with dependent types is that proof obligations arise naturally once programs become even moderately sized. For example, implementing an adder for binary numbers indexed over their natural number equivalents naturally leads to proof obligations for equalities of expressions over natural numbers. The need for these equality proofs comes, in intensional type theories (like CIC and ML) from the fact that in a non-empty context, the propositional equality allows us to prove as equal (with the induction principles) terms that are not judgementally equal, which implies that the typechecker can't always obtain equality proofs by reduction. As far as possible, we would like to solve such proof obligations automatically, and we absolutely need it if we want dependent types to be use more broadly, and perhaps one day to become the standard in functional programming. In this thesis, we show one way to automate these proofs by reflection in the dependently typed programming language Idris. However, the method that we follow is independent from the language being used, and this work could be reproduced in any dependently-typed language. We present an original type-safe reflection mechanism, where reflected terms are indexed by the original Idris expression that they represent, and show how it allows us to easily construct and manipulate proofs. We build a hierarchy of correct-by-construction tactics for proving equivalences in semi-groups, monoids, commutative monoids, groups, commutative groups, semi-rings and rings. We also show how each tactic reuses those from simpler structures, thus avoiding duplication of code and proofs. Finally, and as a conclusion, we discuss the trust we can have in such machine-checked proofs.

We begin our study of amalgamations by examining some ideas which are well-known for the category of R-modules. In particular we look at such notions as direct limits, pushouts, pullbacks, tensor products and flatness in the category of S-sets. Chapter II introduces the important concept of free extensions and uses this to describe the amalgamated free product. In Chapter III we define the extension property and the notion of purity. We show that many of the important notions in semigroup amalgams are intimately connected to these. In Section 2 we deduce that 'the extension property implies amalgamation' and more surprisingly that a semigroup U is an amalgamation base if and only if it has the extension property in every containing semigroup. Chapter IV revisits the idea of flatness and after some technical results we prove a result, similar to one for rings, on flat amalgams. In Chapter V we show that the results of Hall and Howie on perfect amalgams can be proved using the same techniques as those used in Chapters III and IV. We conclude the thesis with a look at the case of rings. We show that almost all of the results for semi group amalgams examined in the previous chapters, also hold for ring amalgams.

Posterior capsule opacification (PCO) is a major component of secondary cataract, a complication of current cataract surgery practice. This iatrogenic condition occurs in virtually all pediatric cases and to a lesser extent in adults. PCO correlates with the development in the latter half of the 20th Century of extracapsular cataract extraction (ECCE). In these surgeries, the lens capsule is left intact. During ECCE surgery a circular capsulotomy opening is created in the anterior lens capsule, and the cataractous, proteinaceous lens is removed, often via ultrasonic lens liquefaction i.e. phacoemulsification. The posterior, equatorial and remaining anterior portions of the sac-like capsule are left intact, permitting the insertion of an artificial lens into the emptied capsule. However, cells from the monolayer of epithelium on the inner surface of the capsule often begin to proliferate and migrate onto the normally cell-free inner surface of the posterior capsule, and may obscure the central axis of vision. Subsequently, a second surgery is necessary to create a small capsulotomy in the centre of the posterior capsule, usually employing an Nd:YAG laser. However, up to 5% of patients who have capsulotomies may then develop further serious, vision-threatening complications such as macular edema and retinal detachments. This thesis reports the photodynamic therapy (PDT) conditions required to prevent lens epithelial (LE) cell de novo proliferation and migration onto posterior lens capsules in a euthanized rabbit surgical model in order to predict parameters required to prevent PCO in humans. Experiments with primary in vitro cultures of human LE cells have shown rapid delivery of the photosensitizer benzoporphyrin derivative monoacid ring A (BPD-MA) and efficient killing with low light doses of 690 nm red light. Additional studies have shown the efficacy of various viscous agents in protecting the comeal endothelium. During model phacoemulsification ECCE surgeries, the use of hyaluronate viscoelastic carriers addressed the need for containment necessary for localized delivery of photosensitizer in the emptied capsule. Long-term monitoring of PDT-treated rabbit lens capsules in vitro has demonstrated a phototoxic effect including complete cell kill in this surgical model employing the prophylactic use of PDT.

Title: The realization problem for von Neumann regular rings Author: Samuel Mokriš Department: Department of Algebra Supervisor of the master thesis: Mgr. Pavel Růžička, Ph.D., Department of Algebra Abstract: With every unital ring R, one can associate the abelian monoid V (R) of isomor- phism classes of finitely generated projective right R-modules. Said monoid is a conical monoid with order-unit. Moreover, for von Neumann regular rings, it satisfies the Riesz refinement property. In the thesis, we deal with the question, under what conditions an abelian conical re- finement monoid with order-unit can be realized as V (R) for some unital von Neumann regular ring or algebra, with emphasis on countable monoids. Two generalizations of the construction of V (R) to the context of nonunital rings are presented and their interrelation is analyzed. To that end, necessary properties of rings with local units and modules over such rings are devel- oped. Further, the construction of Leavitt path algebras over quivers is presented, as well as the construction of a monoid associated with a quiver that is isomorphic to V (R) of the Leavitt path algebra over the same quiver. These methods are then used to realize directed unions of finitely generated free abelian monoids as V (R) of algebras over any given field. A method...

The aim of this thesis is to introduce the reader to the theory of affine monoids and, thereby, to present some results. We therefore start with some auxiliary sections, containing general introductions to convex geometry, affine monoids and their algebras, Hilbert functions and Hilbert series. One central part of the thesis then is the description of an algorithm for computing the integral closure of an affine monoid. The algorithm has been implemented, in the computer program `normaliz´; it outputs the Hilbert basis and the Hilbert function of the integral closure (if the monoid is positive). Possible applications include: finding the lattice points in a lattice polytope, computing the integral closure of a monomial ideal and solving Diophantine systems of linear inequalities. The other main part takes up the notion of multigraded Hilbert function: we investigate the effect of the growth of the Hilbert function along arithmetic progressions (within the grading set) on global growth. This study is motivated by the case of a finitely generated module over a homogeneous ring: there, the Hilbert function grows with a degree which is well determined by the degree of the Hilbert polynomial (and the Krull dimension).

Using the Winn tumour inhibition assay, lymphocytes from the lymph nodes but not the spleens of DBA/2 mice that had been cured of their Ml rhabdomyosarcoma with benzoporphyrin derivative monoacid ring A (BPD)-sensitized photodynamic therapy (PDT) were able to inhibit the growth of the Ml tumour in naive animals. Characterization of the lymph node cells through immuno-magnetic bead depletion showed that the tumour inhibitory activity was independent of B-cells and CD8+ cells. The CD4+-enriched lymph node cells were assessed for their T helper phenotype using intracellular cytokine staining and a polarization to T helper 1 or 2 was not observed during tumour growth or following PDT. However, intracellular cytokine staining did reveal that the activation state of the CD4+-enriched cells decreased during tumour growth and was partially restored following PDT. Ml tumour cells expressed high levels of stress proteins both in vitro and in vivo following treatment with BPD-sensitized PDT and the stress proteins were prepared from Ml cells for the analysis of in vitro proliferative responses of immune lymph node cells. Unseparated lymph node cells from PDT-treated animals responded in vitro to nitrocellulose preparations of 4 high molecular weight stress proteins and following optimization of the in vitro proliferation assay, a high degree of proliferation towards grp80 was detected. In contrast, CD4+- enriched cells from the lymph nodes of treated animals proliferated towards the Ml stress proteins in a manner that did not differ significantly from control lymph node cells. Following incubation of CD4+-enriched lymphocytes with nitrocellulose preparations of pure stress proteins prepared from two-dimensional gels, tumour inhibitory activity was maintained specifically in the presence of the hsp90 preparation that was at least as effective as freshly isolated CD4+ cells from PDT treated animals. For the first time, cell-mediated tumour immunity has been identified and characterized in the lymph nodes of animals treated with PDT. The antigenic target of the CD4+ cell tumour activity remains ambiguous as the response to stress proteins in vitro was not specific to PDT-treated animals; however, the presence of one of the stress proteins, hsp90, was able to maintain a high level of tumour inhibitory activity in vitro and may represent a signal of tissue damage that regulates cell-mediated tumour immunity. [Scientific formulae used in this abstract could not be reproduced.]

We initiate the study of a new class of semigroup C*-algebras arising from number-theoretic considerations; namely, we generalize the construction of Cuntz, Deninger, and Laca by considering the left regular C*-algebras of ax+b-semigroups from actions of congruence monoids on rings of algebraic integers in number fields. Our motivation for considering actions of congruence monoids comes from class field theory and work on Bost–Connes type systems. We give two presentations and a groupoid model for these algebras, and establish a faithfulness criterion for their representations. We then explicitly compute the primitive ideal space, give a semigroup crossed product description of the boundary quotient, and prove that the construction is functorial in the appropriate sense. These C*-algebras carry canonical time evolutions, so that our construction also produces a new class of C*-dynamical systems. We classify the KMS (equilibrium) states for this canonical time evolution, and show that there are several phase transitions whose complexity depends on properties of a generalized ideal class group. We compute the type of all high temperature KMS states, and consider several related C*-dynamical systems.
Graduate

The effect of photodynamic therapy (PDT) using the photosensitizer, benzoporphyrin derivative monoacid ring A (BPD) verteporfin which absorbs strongly at 690 nm, on murine skin allograft rejection was tested using a unique approach. Skin sections (C57BL/6)were exposed in vitro to varying doses of BPD (0.125 - 1.0 μg/mL) and 10 J/cm² light at a wavelength of 690 nm prior to implantation onto recipients (BALB/c). We found that pretreatment of skin to be grafted with PDT can significantly prolong the survival of allografts from 9.3 (n = 42) ± 2.2 days (control group) to 16.9 (n = 20) ± 1.7 days (treated group). Higher doses of BPD did not result in longer survival of the skin allografts. Rather, the most beneficial effects of the treatment were observed at lower doses of BPD (0.25 - 0.5 /μg/mL) as opposed to 1.0 /μg/mL and light (10 J/cm², 690 + 10 nm wavelength). Our strategy was, therefore, termed low-dose PDT to reflect the fact that we used low doses of BPD and visible light, doses where, even at the highest level, the histological features of pre-treated donor skins revealed no obvious tissue damage. In order to identify mechanisms by which pretreatment of donor skin could effect anti-allograft immune responses, we investigated the effect of low-dose PDT on the antigen presenting cells of the epidermis, the Langerhans cells (LC). Using flow cytometry, we found that the levels of expression of the major histocompatibility complex (class I and II) and the costimulatory (B7-1 and B7-2) molecules on LC isolated from treated skin was substantially reduced (60 - 90 % reduction) in comparison to the control preparations. On the contrary, the levels of the leukocyte common antigen (CD45), the adhesion molecule (ICAM-1), the endocytic receptor (DEC-205), the ectophosphatase intensities on L C , as well as LC viabilities, were unchanged. Furthermore, the ability of LC to stimulate the proliferation of naive or pre-sensitized alloreactive T cells was impaired. Finally, the histology and immunohistology of graft tissues from graft recipients revealed that this treatment kept the levels of inflammatory cellular infiltration into the graft low compared to the control grafts. Our findings suggest that the immunomodulatory effects of low-dose PDT of tissue grafts associated with extended engraftment may depend on a selective effect upon epidermal cells, especially LC and may not require cell depletion in order to permit the acceptance of skin allograft. Since the engagement of T cell receptors (TCR) in the absence of costimulation results in suboptimal activation of T cells and ultimately anergy, it appears that the immunomodulatory effects of low-dose PDT depends, in part, upon decreased expression of MHC and costimulatory molecules.

Tese de Doutoramento em Química, na especialidade de Catálise e Sustentabilidade, apresentada ao Departamento de Química da Faculdade de Ciências e Tecnologia da Universidade de Coimbra
The main goal of the work described in this dissertation was the preparation of homogeneous and heterogeneous metal catalysts (immobilized onto magnetic nanoparticles) of tetrapyrrolic macrocycles (metalloporphyrins), with a view to develop sustainable processes for the synthesis and functionalization of small organic molecules, including terpenes, with potential antiproliferative activity. This written thesis is divided into five chapters. Chapter 1 presents an historical perspective for the application of Catalysis within the Green Chemistry context, as well as a literature review (last five years) of all the topics focused in the experimental work. From this bibliographical review, we highlight the synthesis of cyclic carbonates via sequential epoxidation/CO2 cycloaddition, using metalloporphyrins as bio-inspired catalysts for activation of CO2, and O2 and H2O2 as oxidants for epoxidation reactions. Finally, a literature revision is also described for the one-pot preparation of terpene-aldehydes, from renewable substrates, via CO/H2 activation (hydroformylation). Chapter 2 refers to the synthesis and characterization of metalloporphyrin-based catalysts. Regarding the synthesis of symmetrical and non-symmetrical porphyrins, three synthetic approaches were used, namely nitrobenzene, nitrobenzene/NaY and a more sustainable strategy, involving water/microwave irradiation. Therefore, a family of symmetric porphyrins with different functionalities (F, CF3, Cl) and non-symmetrical porphyrins with appropriate functional groups (NH2, NO2) were synthesized. Then, the discussion of their subsequent covalent immobilization onto functionalized magnetic nanoparticles and their full characterization (UV-Vis, FT-IR, TG-DSC, TEM, ICP) are presented. In Chapter 3, we describe the use of heterobimetallic dual-catalytic systems for the implementation of sustainable sequential olefin transformations into high added-value cyclic carbonates, via epoxidation followed by CO2 cycloaddition reaction. The optimization studies regarding central metal and catalyst structure for each catalytic system - epoxidation and CO2 cycloaddition - is discussed. The catalytic systems (MnOAc-TDCPP 15Mn/isobutyraldehyde) and MnOAc-TDCPP 15Mn/NH4OAc gave rise to the most active and selective catalytic systems for the epoxidation of olefins, using O2 and H2O2 as oxidants, respectively. The catalytic system (CrCl-TPPpCF3 12 Cr/PPNCl) was found to be the most active and selective system for the synthesis of cyclic carbonates. Finally, the direct synthesis of cyclic carbonates from olefins, using homogeneous and/or heterogeneous sequential methodologies are described. The heterogeneous catalysts (MNP@SiO2-NH-17Mn and MNP@SiO2-NH-19Cr) are the ones that gave rise to the best sequential styrene to cyclic carbonate transformation. A remarkable result was achieved when these immobilized catalysts were reused, in several consecutive cycles, without significant loss of activity and selectivity. Concerning our interest in the development of sustainable methods for preparation of compounds with potential anti-proliferative activity against osteosarcoma, in Chapter 4 terpenes were chosen as renewable raw materials to implement selected chemical transformations, namely epoxidation, hydroformylation and epoxide ring-opening reactions. Thus, (–)-isopulegol was used as a model terpene and its epoxide derivative was synthesized, with good yield, using MNP@SiO2-NH-17Mn as an immobilized catalyst and O2 as the oxidant. The (–)-isopulegol benzyl ether aldehyde derivatives were synthesized through an hydroformylation reaction using Rh(acac)(CO)2/phosphite as a catalyst. Finally, an (–)-isopulegol amino alcohol was prepared via epoxide ring opening, using butylamine as a nucleophile and CrCl-TPPpCF3 (12Cr) as a catalyst. Moreover, the antiproliferative and cytotoxic activities of each diastereomer of (–)-isopulegol epoxide were evaluated against the human osteosarcoma cell line (MG-63). The measured IC50 values were significantly lower than those reported in the literature for similar compounds (diastereomer 33: MTT = 249.8 μM, SRB = 114.8 μM; diastereomer 34: MTT = 158.2 μM, SRB = 104.0 μM). Chapter 5 comprises the detailed description of all the experimental techniques and instrumentation, as well as of the synthesis/characterization of the new catalysts and catalytic reaction products.
O trabalho desenvolvido nesta dissertação orientou-se no sentido de preparar catalisadores metálicos homogéneos e heterogéneos (imobilizados em nanopartículas magnéticas) do tipo macrociclos tetrapirrólicos (porfirinas) para desenvolver processos sustentáveis de síntese e funcionalização de pequenas moléculas orgânicas, incluindo terpenos, com potencial atividade antiproliferativa. A presente dissertação encontra-se dividida em cinco capítulos. No Capítulo 1 apresenta-se uma discussão histórica e de aplicação da Catálise no contexto da Química Verde e uma revisão da literatura (últimos cinco anos) que engloba todos os tópicos desenvolvidos no trabalho. Desta revisão bibliográfica destacou-se a utilização de metaloporfirinas como catalisadores bioinspirados em reações de epoxidação utilizando O2 e H2O2 como oxidantes, e de metaloporfirinas como catalisadores para a ativação de CO2 em reações sequenciais de epoxidação/cicloadição de CO2 para a síntese de carbonatos cíclicos. Por fim descreveu-se a utilização de terpenos como substratos renováveis na reação de ativação de CO/H2 (hidroformilação) para a síntese de aldeídos. No Capítulo 2 descreve-se a síntese e caracterização de catalisadores metálicos baseados em porfirinas. Para a síntese das porfirinas simétricas e não-simétricas utilizaram-se três estratégicas sintéticas, nomeadamente a do nitrobenzeno, do nitrobenzeno/NaY e uma estratégica sustentável envolvendo água/micro-ondas. Desta forma, sintetizou-se uma família de porfirinas simétricas com diferentes funcionalidades (F, CF3, Cl) e uma série de porfirinas não-simétricas com grupos funcionais apropriados (NH2, NO2) para a sua posterior imobilização covalente em nanopartículas magnéticas funcionalizadas. Além disso, apresentam-se ainda os estudos de otimização para a obtenção de nanopartículas magnéticas funcionalizadas com complexos metálicos de porfirinas e a sua completa caraterização (UV-Vis, FT-IR, TG-DSC, TEM, ICP). No Capítulo 3 descreve-se a utilização de sistemas catalíticos duais heterobimetálicos para transformações sustentáveis e sequenciais de olefinas em epóxidos, seguidas de cicloadição com CO2 para a preparação de carbonatos cíclicos de elevado valor acrescentado. Neste capítulo, discutem-se ainda os estudos de otimização de cada sistema catalítico, tipo de metal/estrutura do catalisador (epoxidação e cicloadição de CO2) relativamente ao tipo de metal/estrutura do catalisador e condições reacionais utilizadas. Após otimização, os sistemas catalíticos (MnOAc-TDCPP 15Mn/isobutiraldeído) e (MnOAc-TDCPP 15Mn/NH4OAc) apresentaram-se como os mais ativos e seletivos para a epoxidação de olefinas, utilizando O2 e H2O2 como oxidantes, respetivamente. Relativamente à reação de cicloadição de CO2 em epóxidos, o catalisador (CrCl-TPPpCF3 12Cr/PPNCl) apresentou-se como o mais ativo e seletivo para a síntese de carbonatos cíclicos. Por fim, desenvolveram-se metodologias sequenciais homogéneas e heterogéneas para a síntese de carbonatos cíclicos a partir de olefinas, onde o sistema catalítico heterogéneo (MNP@SiO2-NH-17Mn e MNP@SiO2-NH-19Cr) foi capaz de promover sequencialmente a transformação do estireno em carbonato cíclico. Um resultado notório resulta do facto deste catalisador poder ser reutilizado em vários ciclos consecutivos sem perda significativa de atividade e seletividade. Atendendo ao nosso interesse no desenvolvimento de métodos sustentáveis para a preparação de compostos com potencial atividade anti-proliferativa contra o osteossarcoma, no Capítulo 4 foram selecionados terpenos como matérias primas renováveis para efetuar transformações químicas específicas, nomeadamente epoxidação, hidroformilação e reação de abertura de epóxido. Neste estudo, o (–)-isopulegol foi utilizado como terpeno modelo e o seu epóxido foi sintetizado com um bom rendimento, utilizando MNP@SiO2-NH-17Mn como catalisador e O2 como oxidante. O aldeído derivado do éter benzílico do (–)-isopulegol foi sintetizado através da reação de hidroformilação, utilizando um Rh(acac)(CO)2/fosfito como catalisador. Por fim, um aminoálcool derivado do (–)-isopulegol foi preparado utilizando CrCl-TPPpCF3 (12Cr) como catalisador e butilamina como nucleófilo. Neste capítulo salienta-se ainda a avaliação do(s) epóxido(s) derivados dos dois diastereoisômeros do (–)-isopulegol quanto à sua capacidade antiproliferativa e citotóxica face à linha celular humana de osteossarcoma (MG-63). Os resultados descritos nesta dissertação apresentam valores de IC50 significativamente mais baixos do que os reportados na literatura para compostos análogos (diastereoisômero 33: MTT = 249.8 μM, SRB = 114.8 μM; diastereoisômero 34: MTT = 158.2 μM, SRB = 104.0 μM). O Capítulo 5 contém a descrição detalhada das técnicas experimentais e da instrumentação, bem como todos os processos de síntese/caracterização dos novos catalisadores e produtos resultantes das reações catalíticas desenvolvidos no decorrer deste trabalho.
Bolsa de doutoramento do Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq – Brasil) 232620/2014-8 GDE