Dissertations / Theses on the topic 'Derivators'

Denna studie har som syfte att utifrån ett didaktiskt perspektiv undersöka hur derivata introduceras i gymnasiets Matematik 3-kurser. I en granskning av väsentlig litteratur har tidigare forskning och olika teorier inom området granskats. Ett antal intervjuer av gymnasielärare med varierade erfarenhet i ämnet matematik har genomförts. Som komplement till dessa intervjuer har en litteraturstudie av fyra Ma3b-kursböcker utförts. Det centrala innehållet i skolverkets kursplaner är det samma för båda Ma3b och Ma3c kurserna.Resultatet av analysen visar att de lärare som deltagit i studien undervisar begreppet derivata på ett liknande sätt. Det finns inte heller några avgörande skillnader i kurslitteraturen. Sammanfattningsvis visar analysen att det finns en röd tråd i hur detta avsnitt undervisas. En väg som både kursmaterial och lärare följer utan alltför stora avvikelser. Det som avviker från äldre studier är att inslagen av stöd i undervisningen av digitala hjälpmedel har ökat.

The main claim of this paper is that the minimalist framework and optimality theory adopt more or less the same architecture of grammar: both assume that a generator defines a set S of potentially well-formed expressions that can be generated on the basis of a given input, and that there is an evaluator that selects the expressions from S that are actually grammatical in a given language L. The paper therefore proposes a model of grammar in which the strengths of the two frameworks are combined: more specifically, it is argued that the computational system of human language CHL from MP creates a set S of potentially well-formed expressions, and that these are subsequently evaluated in an optimality theoretic fashion.

Thesis: Ph. D. in Linguistics, Massachusetts Institute of Technology, Department of Linguistics and Philosophy, September, 2020
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 349-370).
In this dissertation, I identify and analyze several new generalizations about how phrasal displacement and discontinuity are constrained in natural language. These patterns reveal, I argue, that many limitations of syntactic derivations are attributable to the way in which syntactic operations are cyclically interleaved with the component of the grammar that establishes word order. This finding has consequences for many phenomena, and for the architecture of grammar in general. Chapter 1 introduces the theory of cyclic linearization that serves as the foundation for this work, and several principles about the locality of movement that importantly interact with it. Chapter 2 shows that these concepts predict the crosslinguistic distribution of stranding in intermediate positions. Chapter 3 extends these considerations to an analysis of possessor extraction in colloquial English, a phenomenon subject to numerous intricate but systematic limitations. Chapter 4 provides further evidence for the theory advanced here from constraints on subextraction in Russian. Chapter 5 argues that certain facts about parasitic gaps in sentences with overlapping moved phrases reveal further evidence that linearization constrains syntactic derivations, with consequences for the nature of movement more generally. Chapter 6 argues that linear order constrains extraposition, and proposes an account of this phenomenon that addresses a number of puzzles about its distribution. Chapter 7 diverges from the theme of linearization to explore parasitic gaps in relative clauses, which connect to several results from chapter 5. Chapter 8 summarizes the findings of this dissertation, and discusses several more general implications of the framework advanced here.
by Colin Pierce Bryon Davis.
Ph. D. in Linguistics
Ph.D.inLinguistics Massachusetts Institute of Technology, Department of Linguistics and Philosophy

In this thesis, we introduce the theory of locally nilpotent derivations and use it to compute certain ring invariants. We prove some results about quasi-extensions of derivations and use them to show that certain rings are non-rigid. Our main result states that if k is a field of characteristic zero, C is an affine k-domain and B = C[T,Y] / < T^nY - f(T) >, where n >= 2 and f(T) \in C[T] is such that delta^2(f(0)) != 0 for all nonzero locally nilpotent derivations delta of C, then ML(B) != k. This shows in particular that the ring B is not a polynomial ring over k.

Un corps local non commutatif f admettant un sous-corps k de representants de son corps residuel est un corps gauche de series de laurent en une variable x, a coefficients dans k. Le produit y est defini a l'aide d'une haute derivation s de k (au sens de p. M. Cohn) et l'on note f = k((x,s)). Cette these est consacree a la description des hautes derivations d'un corps k de caracteristique nulle, et a la recherche de conditions pour que deux hautes derivations s et s' de k soient equivalentes; c'est-a-dire definissent sur k le meme corps local k((x,s)) = k((x',s')). On introduit et on etudie deux grands types de hautes derivations: la construction des hautes derivations interieures conduit a la determination du centre des corps k((x,s)); celle des hautes derivations monogenes, dont chaque terme est un polynome differentiel de k, resoud en la generalisant une conjecture formulee en 1984 par h. H. Brungs et g. Torner. On donne alors une classification des hautes derivations de k, complete dans le cas ou k est commutatif, et partielle sinon

The Japanese causative verb exhibits the effects of blocking, whereby a causative verb (V-sase) is blocked from taking on lexical meaning if there is a competing lexical causative verb (Miyagawa (1980, 1984)). Given that the causative verb is most reasonably viewed as being formed in syntax, the blocking effect leads to the conclusion that the lexical causatives also are formed in syntax, contrary to the traditional view. A similar blocking effect is observed with English causatives formed with make, and this, together with what we can observe in Japanese, suggest that blocking is best viewed as one that arises in the process of deriving the causative verb (e.g., Embick and Marantz (2008)), and not as a result of a filter on the output of the generative component (e.g., Kiparsky (2005)).

Let 𝑋 be a compact subset of the complex plane and denote by 𝑅𝑝(𝑋) the closure of rational functions with poles off 𝑋 in the 𝐿𝑝(𝑋) norm. We show that if a point 𝑥0 admits a bounded point derivation on 𝑅𝑝(𝑋) for 𝑝 > 2, then there is an approximate derivative at 𝑥0. We also prove a similar result for higher order bounded point derivations. This extends a result of Wang, which was proven for 𝑅(𝑋), the uniform closure of rational functions with poles off 𝑋. In addition, we show that if a point 𝑥0 admits a bounded point derivation on 𝑅(𝑋) and if 𝑋 contains an interior cone, then the bounded point derivation can be represented by the difference quotient if the limit is taken over a non-tangential ray to 𝑥0. We also extend this result to the case of higher order bounded point derivations. These results were first shown by O'Farrell; however, we prove them constructively by explicitly using the Cauchy integral formula.

Given a UFD R containing Q , we study R-elementary derivations of B = R[Y1,..., Ym], i.e., R-derivations satisfying D( Yi) ∈ R for all i; in the particular case of m = 3, we will show that if R is a polynomial ring in n variables over a field k (of characteristic zero), and a1, a3, a3 ∈ R are three monomials, then the kernel of the derivation i=13ai6 /6Yi of B is generated over R by at most three linear elements in the Yi's. This gives a partial answer to a question of A. van den Essen ([27]) about the existence of elementary derivations in dimension six whose kernels are not finitely generated. A set of generators is given for the kernel of R-elementary fixed point free derivations of B. Also, some interesting examples of elementary derivations in dimensions six and seven are provided as well as a criterion for a derivation of R[2] (i.e., a polynomial ring in two variables over R) to be R-elementary. Given a field k of characteristic zero, it is well-known that the kernel of any linear derivation of k[X 1,..., Xn] (that is, a k-derivation which maps each Xi to a linear form in X1,..., Xn) is a finitely generated k-algebra (see [28]). All known proofs of this result are non-constructive in the sense that we do not know a generating set for the kernel. Nowicki conjectured in [25] that the kernel of the derivation d = i=1nXi6 /6Yi of k[X1,..., Xn, Y1,..., Yn] is generated over k by the elements uij = XiYj - XjYi for 1 ≤ i ≤ j ≤ n. Using the theory of Groebner bases, we prove this conjecture in the more general case of the derivation D = i=1nXti i6/6Yi where each ti is a nonnegative integer. Note that in the case of the derivation D, the finite generation of the kernel is no longer evident. Note also that the generators of ker D are linear in the Yi's over k[X1,..., Xn]; we will show that this is not always the case for elementary derivations by giving an example of an elementary derivation in dimension seven whose kernel is finitely generated but cannot be generated by linear forms.

Виконано під керівництвом Миленкової Р.В.
У дослідженні розглядаються похідні від іноземних мов до української юридичного мови. Запозичення служать важливим фактором у розвитку мови. Слова іноземного походження постійно проникають в систему національної мови, і це явище привертає увагу вчених.
В исследовании рассматриваются производные от иностранных языков юридического языка. Заимствования служат важным фактором в развитии языка. Слова иностранного происхождения постоянно проникают в систему национального языка, и это явление привлекает внимание ученых.
The study deals with foreign language derivatives in legal language. Derivations serve as an important factor in language development. Words of foreign origin constantly penetrate the national language system, and this phenomenon attracts the attention of scholars.

Les glicines a,a-disubstituïdes poden actuar com a inhibidors d'enzims o modificar la conformació dels pèptids en els quals són incorporades. A la primera part d'aquesta tesi hem descrit una nova metodologia per preparar a,a-dialquilglicines basada en la utilització de D-ribonolactona (assequible comercialment) com auxiliar quiral. La primera etapa és la preparació de l'acetoacetat de la 2,3-O-isopropiliden-g-D-ribonolactona. Aquest s'alquila en condicions bàsiques amb iodur de metil o de butil. Els acetoacetats dialquilats s'han preparat mitjançant una etapa de dialquilació diastereoselectiva utilitzant NaH com a base i diversos agents alquilants (bromur de benzil, de 4-bromobenzil, de 2-metilnaftil). A continuació es realitza una etapa de transesterificació i una posterior transposició de Schmidt i s'obtenen els amidoèsters. Finalment una hidròlisi àcida permet obtenir els clorhidrats dels aminoàcids en forma enantiopura. La configuració absoluta va ser assignada preparant les 3-metil-2-pirazolin-5-ones 4,4-disubstituïdes enantiomèricament pures.
A la segona part d'aquesta tesi s'han preparat diversos precursors enantiomèricament purs de l'esfinganina que és el precursor biològic de l'esfingosina. Aquests s'han preparat partint dels 3-oxoestearats de diversos auxiliars quirals (sultama d'Oppolzer, oxazolidinona d'Evans, D-ribonolactona). La primera etapa consisteix en una addició de Michael catalitzada pel salicilaldehiat de níquel (II) i els acceptors de Michael són diversos azodicarboxilats (azodicarboxilat de dietil, de dibenzil, de di-tert-butil i de bis-tricloroetil). La segona etapa és una reducció amb BH3.SMe2 utilitzant TiCl4 com agent quelatant. S'obtenen els alcohols de configuració syn amb bones relacions diastereomèriques i rendiments correctes. A més a més s'han preparat pirazoles enantiomèricament purs que presenten un auxiliar quiral i una cadena de 15 carbonis.
a,a-disubstituted glycines present remarkable properties as enzyme inhibitors and as conformational modifiers of peptides. In the first part of this thesis we describe a new simple methodology to prepare enantiopure a,a-dialkylglycines based on the use of commercially available D-ribonolactone as a chiral auxiliary. The first step is tre preparation of 2,3-O-isopropylidene-g-D-ribonolactone acetoacetate. This product is alkylated in basic conditions with methyl iodide or butyl iodide. Dilakylated products are prepared through diastereoselective alkylation using NaH as a base and some alkyl halides (benzyl bromide, 4-bromobenzyl bromide, 2-methylnaftyl bromide). Then a transesterification step followed by a Schmidt rearrangement affords the acetamides. Finally an acid hydrolisis affords the hydrochlorides in good yields. Absolute configuration was assigned through preparation of enantiopure 4,4-disubstituted 3-methyl-2-pyrazolin-5-ones.
In the second part of this thesis some enantiopure precursors of sphinganine (the biosynthetic precursor of sphingosine) have been prepared. Firstly 3-oxoestearates of some chiral auxiliaries (Evans oxazolidinone, Oppolzer's sultame and D-ribonolactone acetonide) have been synthesized. The first step is a Michael addition catalyzed by nickel salicilaldehide where the Michael acceptors are some azodicarboxilates (dibenzyl, diethyl, di-tert-butyl and bis-trichloroethyl). The next step is a stereoselective reduction using BH3-SMe2 in the presence of TiCl4 (chelator Lewis acid). Alcohols with a syn configuration are obtained with good diastereomeric ratios and correct yields. Moreover enantiomerically pure pyrazoles that present a chiral auxiliary and a long chain (15 carbons)

Один з чинників низького рівня управління фінансовими ризиками в банківські сфері – відсутність розвиненого та стабільного ринку похідних фінансових інструментів. Відчувається як недолік методології застосування похідного інструментарію, так і дефіцит кваліфікованих кадрів, здатних його ефективно використовувати.

This thesis is based on recent work by Paige which gave a formalism for presenting and analyzing the class of algorithms which manipulate an appropriate Krylov subspace in solving large sparse systems of linear equations. This formalism--a way of dividing a method of solution into a Krylov process and an associated subproblem--is described and then applied to several of the more popular algorithms in use today including the methods of Conjugate Gradients and BiConjugate Gradients. The aim is to clarify these algorithms to make them easier to understand, analyze and use. Several of the methods presented in this thesis were developed in exactly this way--notably the Symmetric LQ method and the Generalized Minimum Residual method--and required little or no effort to characterize using the formalism. It was successfully applied to Conjugate Gradients and BiConjugate Gradients, already recognized as being closely related to the symmetric and unsymmetric Lanczos processes respectively. The newer algorithms such as Conjugate Gradients Squared and BiConjugate Gradients Stabilized, with less obvious relation to a specific Krylov process, provided more difficulty in their clarification.

In the first half of the thesis a necessary and sufficient condition is given for a separable C*-algebra to be *-isomorphic to a maximal full algebra of cross-sections over a base-space such that the fibre algebras are primitive throughout a dense subset. The condition is that the relation of inseparability for pairs of points in the primitive ideal space should be an open equivalence relation. In the second half of the thesis a characterisation is given of those C*- algebras A for which each self-adjoint inner derivation D(α, A) satisfies ∥D(α, A)∥ = 2 inf {∥α-z∥ : z ∈Z(A), the centre of A}. This time the characterisation is that A should be quasicentral and the relation of inseparability for pairs of points in the primitive ideal space should be an equivalence relation. Those C*-algebras for which every inner derivation satisfies the equation are characterised in a similar way.

Includes abstract.
Includes bibliographical references (p.122-132) and index.
A few decades ago, Kaplansky raised the question whether unital linear invertibility preserving maps between unital algebras are Jordan homomorphisms. This question is still unanswered, and the progress that has been made has mainly been in the context of Banach algebras, including C*-algebras and von Neumann algebras. Let M be a von Neumann algebra with a faithful semifinite normal trace τ , and M~ the algebra of τ-measurable operators (measurable for short) affiliated with M. The algebra M~ can be endowed with a topology Уcm, called the topology of convergence in measure, such that M~ becomes a complete metrizable topological *-algebra in which M is dense. One of the aims of this thesis is to find answers to Kaplansky’s question in the context of algebras of measurable operators.

In vitro toxicology studies are hindered by the use of specific cellular systems which solely examine one cell type. Precision-cut tissue slices mimic specific organ toxicity as normal cellular heterogeneity and organ architecture are retained. Experiments were performed using tissue slices from transgenic mice with enzyme reporter proteins for rapid analysis. CYP 1A1/β-galactosidase transgenic mouse liver and kidney slices challenged with 20 μM BNF for 24 hr remain viable and display organ-specific induction of β-galactosidase (~30-fold in liver and 3-fold in kidney). AP-1/luciferase transgenic mouse tissue slices incubated with 9 μM TPA also remained viable while exhibiting a tissue- and time-dependent induction of luciferase. In kidney slices, luciferase induction was approximately 1.5-fold at 2 hr, which increased to 2.5-fold at 4 hr. Liver slices displayed a rapid increase in luciferase at 2 hr (approximately 3-fold) which was abolished at 4 hr. To quicken experimental design via decreased sample preparation, a custom transgenic mouse was created based upon a fluorescent reporter protein. Subsequent studies with slices from this strain and another fluorescent-based transgenic strain did not display reporter induction. For optimization of the smaller tissues of mice and to create an easily deployable method of rapid detection, a tissue chip based system was created for generating large numbers of samples from a single organ and coupled with fluorescent indicators to maximize detection sensitivity for specific cellular processes. Fluorescence of 5-carboxyfluorescein increased at high concentrations of iodoacetamide (IAM), a quick-acting toxicant, indicating disruption of cellular membranes. The mitochondrial probe, TMRE, exhibited an increase in fluorescence with increasing IAM concentrations. Monobromobimane, a sulfhydryl probe, displayed a decrease in fluorescent intensity at higher IAM challenge; a finding confirmed with Ellman’s reagent. A probe used for calcium measurement, FURA-2, demonstrated an increase in fluorescence with increasing IAM concentrations. Importantly, the number of samples per organ/mouse was increased at least 3-fold and a significant time reduction per analysis was realized. These results suggest that both transgenic-based tissue slice studies and studies with fluorescent probes in naïve tissue chips are two methods of higher-throughput analyses to evaluate toxicant perturbations with in vitro studies.

We generalize the results of Leger and Luks and other researchers about generalized derivations to the cases of ternary Lie algebras and n-BiHom Lie algebras. We investigate the derivations algebras of ternary Lie algebras induced from Lie algebras, we explore the subalgebra of quasi-derivations and give their properties. Moreover, we give a classification of the derivations algebras for low dimensional ternary Lie algebras. For the class of n-BiHom Lie algebras, we study the algebras of generalized derivations and prove that the algebra of quasi-derivations can be embedded in the derivation algebra of a larger n-BiHom Lie algebra.

L’objectif de cette étude est de développer de nouveaux matériaux à base de chitosane, de ses dérivés et de fibres de cellulose, sous la forme de nanofibres ou de feuille de papier. Des échantillons de chitosane purifié ont été utilisées afin de préparer les films nanocomposites transparents à base de chitosane (CH) comme matrice (deux chitosanes avec différentes masses molaires et leurs dérivés solubles dans l'eau) et de cellulose nanofibrillaire (NFC) ou de cellulose bactérienne (BC). Les films obtenus sont très transparents; ils affichent de meilleures propriétés mécaniques que ceux à base de chitosane seul. Une autre démarche a consisté à revêtir des feuilles de papier à base d’E. Globulus avec le chitosane ou deux dérivés de chitosane, l'un fluorescent et l'autre soluble dans l'eau. Tout d'abord, un dérivé du chitosane fluorescent a été déposé couche par couche sur des feuilles de papier et sa distribution,a été évaluée. Les résultats montrent que, que la répartition en surface est très homogène et que la pénétration du chitosane dans les pores du papier cesse après un dépôt de trois couches, au-delà une augmentation de l'ensemble de ses épaisseurs et aptitude filmogène. Ensuite, l'effet du chitosane et de son dérivé soluble dans l'eau sur les propriétés finales des papiers a été étudié. En général, chitosane et le chitosane soluble dans l'eau ont un impact positif sur les propriétés finales des papiers couchés. Finalement, la chitine et le chitosane ont été convertis en polyols visqueux à travers une réaction d'oxypropylation simple , dans le but de valoriser les fractions les moins nobles ou les sous-produits de ces précieuses ressources renouvelables
The purpose of this study was to develop new materials based on chitosan and its derivatives and cellulose, in the form of nanofibres or paper sheet. . Chitosan samples were then used to prepare transparent nanocomposite films based on different chitosan (CH) matrices (two chitosans with different DPs and corresponding water-soluble derivatives) and nanofibrillated cellulose (NFC) and bacterial cellulose (BC). The films obtained were shown to be highly transparent, displayed better mechanical properties than the corresponding unfilled chitosan films and showed increased thermal stability. Another approach involved the coating of E. Globulus based paper sheets with chitosan and two different chitosan derivatives, a fluorescent and a water-soluble derivative, on a pilot-size press machine. First, a fluorescent chitosan derivative was deposited layer-by-layer onto conventional paper sheets and its distribution was assessed. The results showed that the surface distribution was highly homogeneous and the penetration of chitosan within the paper pores ceased after a three-layer deposit, beyond coating only produced an increase in its overall thickness and film-forming aptitude. Then, the effect of chitosan and chitosan quaternization on the final properties of chitosan-coated papers was investigated. In general, both chitosan and water-soluble chitosan coatings had a positive impact on the final properties of the coated papers. Finally, chitin and chitosan were converted into viscous polyols through a simple oxypropylation reaction, with the aim of valorizing the less noble fractions or by-products of these valuable renewable resources

Les dérivations localement nilpotentes sur les anneaux des polynômes sont des objets de grande importance dans beaucoup de domaines de mathématiques. Durant la dernière décennie, elles ont connu un véritable progrès et sont devenues un élément essentiel pour la compréhension de la géométrie algébrique affine et d’algèbre commutative. Cette importance est due au fait que certains problèmes classiques dans ces domaines, telles que la conjecture jacobienne, le problème d’élimination, le problème de plongement et le problème de linéarisation, ont été reformulés dans la théorie des dérivations localement nilpotentes. Cette thèse porte sur l’étude algorithmique des problèmes liés aux dérivations localement nilpotentes et leurs applications aux auto-morphismes polynomiaux de l’espace affine. Elle a pour objectif de présenter, d’une part, quelques problèmes dans lesquels les dérivations localement nilpotentes jouent un rôle crucial, à savoir le problème des coordonnées et le problème de paramétrisation polynomial des courbes algébriques dans l’espace affine. Et d’autre part, de donner quelques algorithmes qui peuvent contribuer à la compréhension des dérivations localement nilpotente en dimension trois, à savoir les algorithmes du rang et de triangulabilité des dérivations localement nilpotentes
Derivations, especially locally nilpotent ones, over polynomial rings are objects of great importance in many fields of pure and applied mathematics. Nowadays, locally nilpotent derivations have made remarkable progress and became an important topic in understanding affine algebraic geometry and commutative algebra. This is due to the fact that some classic problems in these areas, such as the Jacobian conjecture, the Linearization problem and the Cancellation problem, can be reformulated in terms of locally nilpotent derivations. This thesis is about the algorithmic study of problems linked to locally nilpotent derivations and their applications to the study of polynomial automorphisms of the affine space. Its aim is to present, on one hand, some problems in which locally nilpotent derivations play a crucial role, namely, the coordinate problem and the parametrization problem. On the other hand, give some algorithms concerning locally nilpotent derivations, which may contribute in understanding locally nilpotent derivations in three dimensional case, namely, rang and triangulability algorithms of locally nilpotent derivations

Quasi-hom-Lie algebras (qhl-algebras) were introduced by Larsson and Silvestrov (2004) as a generalisation of hom-Lie algebras, which are a deformation of Lie algebras. Lie algebras are defined by an operation called bracket, [·,·], and a three-term Jacobi identity. By the theorem from Hartwig, Larsson, and Silvestrov (2003), this bracket and the three-term Jacobi identity are deformed into a new bracket operation, <·,·>, and a six-term Jacobi identity, making it a quasi-hom-Lie algebra. Throughout this thesis we deform the Lie algebra sl2(F), where F is a field of characteristic 0. We examine the quasi-deformed relations and six-term Jacobi identities of the following polynomial algebras: F[t], F[t]/(t2), F[t]/(t3), F[t]/(t4), F[t]/(t5), F[t]/(tn), where n is a positive integer ≥2, and F[t]/((t-t0)3). Larsson and Silvestrov (2005) and Larsson, Sigurdsson, and Silvestrov (2008) have already examined some of these cases, which we repeat for the reader's convenience. We further investigate the following σ-twisted derivations, and how they act in the different cases of mentioned polynomial algebras: the ordinary differential operator, the shifted difference operator, the Jackson q-derivation operator, the continuous q-difference operator, the Eulerian operator, the divided difference operator, and the nilpotent imaginary derivative operator. We also introduce a new, general, σ-twisted derivation operator, which is σ(t) as a polynomial of degree k.

O principal objetivo desta dissertação é estudar um contraexemplo para o Décimo Quarto Problema de Hilbert no caso de dimensão n = 5, que foi apresentado por Arno van den Essen ([6]) em 2006 e que é baseado em um contraexemplo de D. Daigle e G. Freudenburg ([4]). Para isso, serão estudados os conceitos fundamentais da teoria de derivações e os princípios básicos das derivações localmente nilpotentes, bem como seus respectivos corolários. Dentre esses princípios encontra-se o Princípio 13, que garante que, se B é uma k- álgebra polinomial, digamos B = k[x1; ..., xn], (onde k é um corpo de característica zero) e D é uma derivação localmente nilpotente sobre B, então seu núcleo A = ker D satisfaz A = B &cap: Frac(A). Assim encontramos o contraexemplo esperado, ao mostrar que A não é finitamente gerado sobre k. Além disso, no apêndice deste trabalho, é dada uma prova para o caso de dimensão 1 do Décimo Quarto Problema de Hilbert.
The main objective of this thesis is to study a counterexample to the Hilberts Fourteenth Problem in dimension n = 5, which was presented by Arno van den Essen ([6]) in 2006 and that is based on a counterexample of D. Daigle and G. Freudenburg ([4]). For these purpose, we study the fundamental concepts of the theory of derivations and the basic principles of locally nilpotent derivations and their corollaries. Among these principles, Principle 13 ensures that if B is a k-algebra polynomial, say B = k[x1; ..., xn], (where k is a field of characteristic zero) and D is a locally nilpotent derivation on B, then its kernel A = ker D satisfies A = B ∩ Frac(A). Once we have proved that A is not finitely generated over k, we find the expected counterexample. In addition, in the appendix of this work is given a proof for the Hilberts Fourteenth Problemin dimension n = 1.

The skin is an amazing elastic and relatively impermeable barrier that provides protective, perceptive and communication functions to the body. The stratum corneum is widely accepted as the barrier of the skin - limiting the transport of molecules into and across the skin. It is evident that the transdermal permeation of drugs depend on a number of factors of which the physicochemical properties play the most prevalent role. The potential of using intact skin as the site of administration for dermatological preparations to elicit pharmacological action in the skin tissue has been well recognised. Transdermal drug delivery offers several advantages over oral and parenteral dosing. They include avoiding hepatic first pass metabolism, maintaining constant blood levels for longer periods of time, improving bioavailabiliv, decreasing the administered dose, adverse effects and gastrointestinal side effects, easy discontinuation in case of toxic effects and improved patient compliance. Optimal transport through the skin requires a drug to possess lipophilic as well as hydrophilic properties. Research has indicated that the ideal log P value for optimal transdermal permeation is between 1 and 2. Acetylsalicylic acid (aspirin) possesses anti-inflammatory, analgesic and antipyretic activity, and as an anti-inflammatory analgesic agent it is used in the treatment of musculoskeletal disorders, such as rheumatoid arthritis. Its use is limited to the relief of pain and inflammation, as it does not halt the progression of the pathological injury caused to the tissue. Acetylsalicylic acid is also used in the treatment of fever, prevention of thromboembolic disorders, reducing the incidence of colon cancer and it delays the onset of Alzheimer's disease. The most common adverse effect of acetylsalicylic acid occurring with therapeutic doses is gastro-intestinal disturbances. The primary aim of this study was to determine the transderrnal penetration of acetylsalicylic acid and some of its derivatives and to establish a correlation, if any, with selected physicochemical properties. The ten derivatives of acetylsalicylic acid were prepared by esterification of acetylsalicyloyl chloride with ten different alcohols. The structures of the products were confirmed by mass spectroscopy (MS), nuclear magnetic resonance spectroscopy (NMR), infrared spectroscopy (IR) and differential scanning calorimetry (DSC) for methyl acetylsalicylate. Experimental aqueous solubility and partition coefficients were determined for acetylsalicylic acid and its different derivatives at a pH of 4,5. In vitro penetration was measured through excised female human abdominal skin in diffusion cells. The prediction software Interactive Analysis (IA) was used to predict aqueous solubility, while prediction software IA, &,Win and ACD Labs were used to predict the log P values for each derivative. None of the predicted values correlated with the experimental values. The experimental aqueous solubilily, partition coefficient and transdermal flux values were determined for acetylsalicylic acid and its derivatives. The experimental aqueous solubilily of acetylsalicylic acid (6,56 mg/ml) was higher than that of the synthesised acetylsalicylate derivatives (ranging from 1,76 x lo3 to 3,32 mg/ml), and the partition coefficient of acetylsalicylic acid (-0,85) was lower than that of its derivatives (ranging from -0,25 to 1,954. There was thus a direct correlation between the aqueous solubility data and the partition coefficients. The experimental transdermal flux of acetylsalicylic acid (4733 pg/cm2/h) was much higher than that of its derivatives (ranging from 0,03 to 28,32 pg/cm2/h). With the ethyl derivative (28,32 pg/cm2/h) and the methyl derivative (10,06 pg/cm2/h) being the only derivatives with appreciable flux. Pentyl acetylsalicylate (0,03 pg/cm2/h) had the lowest flux. The higher flux values of acetylsalicylic acid and its methyl and ethyl derivatives might be due to the fact that it is more hydrophilic and had better aqueous solubilily, thus permeating through the proteins of the skin. Pentyl acetylsalicylate had a log P value of 1,95, but had the lowest flux (0,03 pg/cm2/h), just proving once again that to cross the stratum corneum a drug should posses both hydrophilic and lipophilic properties. Tert-butyl acetylsalicylate had a flux (7,30 &cm2/h) lower than that of methyl and ethyl acetylsalicylate, but a higher flux than the other synthesised derivatives which could be due to its log P value being slightly greater than 1 and having an average aqueous solubility. The low transdermal permeation may also be attributed to the fact that at the pH (45) chosen for transdermal studies, acetylsalicylate was only 9,09 % unionised. A higher degree of unionised species results in higher flux values. This study has confirmed that transdermal flux is dependent on several factors including optimum solubility, partitioning, diffusion and the degree of ionisation in the stratum corneum in addition to a suitable partition coefficient and high aqueous solubilily. The solution to the increased transdermal delivery of lipophilc drugs does not simply lie in producing a derivative with a higher aqueous solubilily and more ideal partition coefficient. Other means of increasing the transdermal permeation of lipophilic acetylsalicylic acid derivatives will have to be investigated in further studies.
Thesis (M.Sc. (Pharm.))--North-West University, Potchefstroom Campus, 2004.

Es presenten diferents reaccions de síntesi química, en les quals participa el glicerol com a reactiu, moltes d'elles amb rendiments elevats i bons percentatges de conversió. Un aspecte rellevant d'aquestes reaccions és l'obtenció de compostos o precursors sintètics de substàncies d'alt valor afegit.
Així, a partir de la síntesi d'esters de dicloropropil, usant glicerol i clorotrimetilsilà com a font de clor o amb clorur d'alumini usant un líquid iònic, s'han sintetitzat esters d'al·lil, alguns d'ells amb efecte ovicida en insectes. Un dels esters de dicloropropil sintetitzat a partir d'un àcid versàtic ha estat la referència per a la preparació d'esters dessimetritzats usant iodur, hidroxils o imidazoles com a nucleòfils.
Amb la finalitat de fer les reaccions més sostenibles, s'han usat reactius provinents de subproductes industrials, tant del sector d'olis i greixos, com de la indústria del biodiesel.
S'han emprat noves tècniques en síntesi orgànica, com els líquids iònics i les microones. L'ús de microreactors en una de les reaccions ha demostrat ser efectiu per a disminuir el temps de reacció, la qual cosa hauria de facilitar el seu escalat
Se presentan diferentes reacciones de síntesis química en las cuales participa el glicerol como reactivo. La mayoría de ellas presentan altos rendimientos y buenos porcentajes de conversión. Un aspecto relevante de estas reacciones es la obtención mediante síntesis química de compuestos o precursores sintéticos de sustancias de alto valor añadido.
Así, a partir de la síntesis de ésteres de dicloropropilo, usando glicerol y clorotrimetilsilano como fuente de cloro, o con cloruro de aluminio usando un líquido iónico, se han sintetizado ésteres de alilo, algunos de ellos con efecto ovicida. Una de los ésteres de dicloropropilo obtenido a partir de un ácido versático se ha usado como referencia para la preparación de ésteres desimetrizados usando ioduro, hidroxilo o imidazole como nucleófilos.
Con la finalidad de aumentar la sostenibilidad, se han usado reactivos procedentes de subproductos industriales, tanto del sector de aceites y grasas, como de la industria del biodiesel.
Las nuevas tecnologías, como los líquidos iónicos y las microondas, también han sido aplicadas en algunas de las reacciones estudiadas. Por otra parte, el uso de microreactores ha permitido mejorar el tiempo de reacción de uno de los procesos estudiados, hecho que debería facilitar su escalado.
Different synthetic reactions are shown, where glycerol is used as a starting material. High yields and conversions are reported in many of the described reactions. One relevant aspect is that compounds or synthetic precursors with high added value can be obtained.
Thus, starting from dichloropropyl esters, allyl esters can be obtained, some of them with ovicidal effects. These esters can be synthesised using glycerol and either chlorotrimetylsilane or aluminium chloride as chlorine source. In the later case an ionic liquid is needed. A versatic dichloropropyl ester has been the reference to prepare desymmetrized esters using iodine, hydroxy ion or imidazole derivatives as nucleophilic groups.
With the aim to develop sustainable reactions, industrial byproducts from the vegetable oil and fat industries, and from the biodiesel industries have been used as reagents.
New technologies, such as ionic liquids and microwaves have also been applied. A continuous process using a microreactor has been developed, which could allow the corresponding reaction to be scaled.

El polímers termoestables són materials de gran interès i amb una amplia versatilitat en el món industrial degut a les seves excel·lents propietats. El treball que es presenta, s'emmarca en aquest camp i es dirigeix cap a l'obtenció de nous materials epoxídics, que puguin ésser utilitzats com a recobriments de components electrònics. Els objectius que es van plantejar van ser: obtenir materials que 1) durant el procés de curat, experimentessin una baixa contracció, 2) permetessin una degradació tèrmica de forma controlada un cop ha finalitzat la vida útil dels components i 3) milloressin les propietats mecàniques respecte als materials epoxídics convencionals.

La contracció de la xarxa polimèrica durant el procés de curat produeix tensions mecàniques internes i conseqüentment pot conduir a l'aparició d'esquerdes. Els espiroortoesters (SOEs) són monòmers considerats expansibles, que experimenten expansió durant el procés de polimerització. La síntesi dels SOEs es pot portar a terme per reacció d'epòxids amb lactones en presència d'un catalitzador àcid de Lewis. L'expansió en volum d'aquests monòmers es deguda a que en la polimerització per obertura d'anell es produeix un canvi de distancies covalents en la forma cíclica a distancies de Van der Waals en la forma oberta. La copolimerització de reïnes epoxi amb lactones en presència d'un àcid de Lewis porta a la formació "in situ" d'espiroortoesters. Un cop formats, polimeritzen i donen lloc a unitats de poli(èter-ester) a la xarxa tridimensional. Al polimeritzar generen expansió en l'última etapa del curat, precisament quan el material no té mobilitat, evitant així l'aparició de tensions internes.

D'altra banda, l'estructura típica d'un termoestable implica que aquests materials, una vegada aplicats sobre un component electrònic, no poden ser eliminats ni mitjançant dissolvents ni per escalfament. La introducció de grups ester a la xarxa, especialment si son terciaris, permet disminuir la temperatura de degradació tèrmica en comparació a la dels materials epoxídics convencionals. Sotmesos els materials a un procés tèrmic, la xarxa termoestable sofreix una degradació parcial. Aquesta és suficient perquè es puguin eliminar per dissolució o mitjançant fricció mecànica. Així, el material electrònic pot ésser reparat o reciclat.

Finalment, la introducció de restes alifàtiques a la xarxa termoestable redueix la densitat d'entrecreuament i amb ella la fragilitat dels materials, fent-los més flexibles.

S'ha utilitzat una reïna comercial, el diglicidil èter del bisfenol A (DGEBA). Com a lactones el 2,2-dimetil-4,6-dioxo-1,3-dioxà o àcid de Meldrum (MA) i tres dels seus derivats amb la posició 5 disubstituïda. L'estructura d'aquests compostos permet introduir grups ester terciaris i cadenes alifàtiques a la xarxa epoxídica.

S'ha sintetitzat una nova reïna epoxi: la 5,5-bis(2,3-epoxipropil)-2,2-dimetil-4,6-dioxo-1,3-dioxà (DGMA), on es conjuga en un mateix compost l'anell de bislactona i els grups glicidílics. Aquesta reïna s'ha homopolimeritzat i copolimeritzat amb la reïna epoxi de diglicidil èter de bisfenol A.

Com a àcids de Lewis s'han estudiat els triflats de terres rares. Aquests permeten dur a terme el curat en condicions atmosfèriques. Els materials obtinguts amb els triflats de terres rares s'han comparat amb els obtinguts amb trifluorur de bor complexat, que és un iniciador catiònic convencional.

A més, s'han obtingut materials a partir dels mateixos monòmers utilitzant un iniciador aniònic. En aquest cas, el mecanisme de curat no implica la generació de grups espiroortoester, però igualment porta a xarxes amb estructura de poli(èter-ester).

Les etapes seguides en el present treball són:

1. Síntesi i caracterització estructural dels derivats de l'àcid de Meldrum.
2. Estudi del mecanisme de les reaccions de copolimerització catiònica i aniònica de la reïna epoxi amb l'àcid de Meldrum i derivats emprant els triflats de lantànid i el BF3·MEA i la DMAP, mitjançant calorimetria i FTIR/ATR.
3. S'ha estudiat la cinètica dels processos de curat per calorimetria.
4. Caracterització estructural dels diferents materials obtinguts.
5. Avaluació de les propietats tèrmiques i mecàniques dels materials i del grau de contracció que experimenten en curar.
6. Estudi dels processos de degradació dels materials termoestables obtinguts, així com les condicions que es produeix.

De l'estudi realitzat s'ha pogut concloure que s'ha assolit una reducció global de l'encongiment al curar, s'han obtingut materials que inicien la degradació a temperatures inferiors a les de les reïnes epoxi convencionals i que van resultar ser més flexibles.

ENGLISH
Thermosetting polymers are interesting materials widely versatilities in the electronics industry because of their good characteristics. The present work is included in this field and it is focused in obtaining new epoxydic thermosets that may be useful as coatings for electronic devices. The objectives posed in this work were to obtain materials that: 1) undergo low shrinkage during curing process, 2) allow to be thermally degraded in a controlled way once their service life is over and 3) improve the mechanical properties with respect to the conventional epoxy materials.
The shrinkage of the polymeric network during curing process produces internal mechanical stress and consequently it can lead to the appearance of microvoids and microcracks. Spiroorthoesters (SOEs) are considered to be expandable monomers, which experience expansion during polymerization process. SOEs can be synthesized by reaction of epoxides with lactones in the presence of a Lewis acid as catalyst. The expansion in volume of these monomers is due to the ring-opening polymerization process. It produces a change in atomic distances from the cyclic form (covalent distance) to the open one (Van der Waals distance). The copolymerization of epoxy resins with lactones in the presence of a Lewis acid leads to "in situ" formation of spiroorthoesters. Once it is formed, it polymerizes yielding poly(ether-ester) unities into the three-dimensional network. On polymerizing expansion is produced, just when the material has no mobility and therefore avoiding internal stress.
The typical structure of a thermoset implies that once it is applied over an electronic device neither solvents nor heat can remove it. The introduction of ester groups into the network, especially if are tertiary, allows diminishing the temperature of thermal degradation in comparison to that of conventional epoxy materials. When these new materials are subjected to a thermal process, the thermoset network undergoes a partial degradation. This is enough to remove it by dissolution or mechanical friction. Therefore, the electronic device can be repaired or recycled.

Finally, the introduction of aliphatic moieties into the thermoset network reduces the cross-linking density and the fragility of materials, giving more flexibility to the material.

In the present work, a commercial epoxy resin, diglycidyl ether of bisphenol A (DGEBA) was used. As lactones 2,2-dimethyl-4,6-dioxo-1,3-dioxane or Meldrum acid (MA) and three of its derivatives with the five position disubstituted. The structure of these compounds allows incorporating tertiary ester groups and aliphatic chains into the epoxydic network.

A new epoxy resin was synthesized: 5,5-bis(diglycidyl)-2,2-dimethyl-4,6-dioxo-1,3-dioxane (DGMA), which present both a bislactone ring and glicydilyc groups. This resin was homopolymerized and copolymerized with the epoxy resin of diglycidyl ether of bisphenol A.

As Lewis acids triflates of rare earths were studied. These allow curing in atmospheric conditions. The materials obtained with triflates of rare earths were compared to the materials obtained with boron trifluoride complex, which is a conventional cationic initiator.


Furthermore, materials from the same monomers were obtained by using an anionic initiator. In this case, the curing mechanism does not imply the generation of spiroorthoester groups, but equally it leads to networks with a poly (ether-ester) structure.

The followed steps in the present work are:

1. Synthesis and structural characterization of Meldrum acid derivatives.
2. Study of the mechanism of cationic and anionic copolymerization reactions of the epoxy resin with Meldrum acid and its derivatives using lanthanide triflats, BF3·MEA and DMAP, by differential scanning calorimetry and FTIR-ATR.
3. The kinetics of the curing process was studied by differential scanning calorimetry.
4. Structural characterization of the materials obtained.
5. Evaluation of the thermal and mechanical properties of materials and the degree of shrinkage experimented in the curing.
6. Study of the degradation process of thermosetting materials obtained and the conditions in which it is produced.

From the study carried out it can be concluded that a global reduction in the shrinkage on curing was achieved. Also, materials that start the degradation at lower temperatures than conventional epoxy resins were obtained. These materials come to be more flexible

Se han estudiado las reacciones intramoleculares de Pauson-Khand de los eteres 3-alcoxialil propargílicos y 3-alcoxipropargil alílicos derivados del 2-neopentiloxi-3-bornanol y del 3-neopentiloxi-iso-borneol. Las diastereoselectividades observadas en las reacciones de estos sistemas llegó hasta 14/1 (aproximación del inductor unido al alquino). Se ha abordado, también, el estudio de la inducción asimétrica en las reacciones intermoleculares de Pauson-Khand y en este contexto se diseñó y preparó un nuevo tipo de auxiliar quiral quelante. Las reacciones del complejo de dicobaltohexacarbonilo del 10-metiltio-iso-borniloxietino con olefinas tensionadas transcurre con elevada selectividad. En el caso del norbornadieno se llegó al 91% D.E.. En ambas aproximaciones, la intra y la intermolecular, se recuperaron los auxiliares quirales con excelentes rendimientos, y se determinaron las configuraciones absolutas de los respectivos aductos de Pauson-Khand.

碩士
國立清華大學
數學系
90
1. On certain subrings of prime rings with derivations Let R be a noncommutative prime ring with nonzero derivation d. U is a noncentral Lie ideal of R and U^{d} is not contained in Z. If d is outer, then the subring of R generated by {[d(x),x] ;x belong to U} contains a nonzero ideal of R except charR=2 and R satisfies S_{4}. 2. Jordan generalized derivations on semiprime rings Let R be a 2-torson free semiprime ring, then every Jordan generalized derivation on R is a generalized derivation.