The topic of this dissertation was the preparation of a high-quality sulphate binder based on secondary raw materials. For this purpose, the work was primarily focused on the laboratory preparation of beta gypsum from the selected industrial gypsum, the design of the technological process of production and its verification by pilot tests. In the next step, the thesis dealt with the modification of beta gypsum by a selected set of liquefiers. In addition to commercial dehumidifiers, the possible beta casting of beta gypsum was tested by increasing the zeta potential of the gypsum suspension. At the end, a complete complex of construction products was developed based on laboratory and semi-prepared beta plasters, consisting of gypsum plasters, mastics, gypsum premix and small plaster casts.

[pt] Nas últimas décadas a demanda por elementos terras raras (ETRs) cresceu consideravelmente devido a sua importância estratégica. Os ETRs são amplamente utilizados em diferentes setores, tais como, medicina, engenharia química, eletrônica e fabricação de computadores. Entre os ETRs, está o Neodímio, que é um dos metais mais valiosos utilizados em ligas, componentes eletrônicos e filtros ópticos. A necessidade da alta pureza dessas espécies requer a separação seletiva, e entre os métodos disponíveis, a adsorção ganhou maior atenção devido à sua simplicidade, alta eficiência e baixo custo. Neste trabalho foi avaliado o argilomineral palygorskita como potencial sorvente para remoção de Nd (III) de soluções aquosas através de ensaios em batelada. Para este propósito, a amostra proveniente da região de Guadalupe (Piauí) foi beneficiada e estudada a composição química e mineralógica com o intuito de utilizar no processo adsortivo a amostra com maior grau de pureza. A composição química apresenta teores de óxidos, sendo os principais, SiO2, Al2O3 e MgO corroborando a presença de palygorskita na amostra. Os estudos de potencial zeta apontam que o argilomineral apresenta carga superficial negativa em toda faixa de pH, além disso, a elevada área superficial de 118 metros quadrados por grama justificam a aplicação como adsorvedor de cátions. Diferentes tipos de isotermas de adsorção e modelos cinéticos foram utilizados para descrever o comportamento do Nd (III) na adsorção e os resultados experimentais que melhor se ajustaram são referentes ao modelo de Langmuir, e a capacidade máxima de captação foi de 15,39 mg/L avaliada em pH 5. A cinética de adsorção para o Nd (III) foi modelada pela equação de pseudo segunda ordem. A adsorção foi encontrada e sugere-se que o processo é endotérmico e espontâneo (delta H igual 17,12 KJ/mol; delta G igual -26,3 KJ/mol) em relação aos parâmetros termodinâmicos obtidos. Os resultados gerais sugerem que este adsorvente demonstrou ser um potencial sorvente para separação de Nd(III) a partir de soluções aquosas. / [en] In recent decades, the rare-earth elements (REEs) demand has considerably grown because of its strategic importance. REEs are widely used in different high-tech sectors such as nuclear power, metallurgy, medicine, chemical engineering, electronics and computer manufacturing. Among REEs, is Neodymium, which is one of the most valuable metals used in alloys, electronic components and optical filters. The need for the high purity of these species requires selective separation, between the available methods, adsorption has earned greater attention due to its simplicity, high efficiency and low cost. The removal of metal ions is a complex task due to the high cost of treatment methods. Contributed to the intensification of research for low-cost adsorbent materials, reusable alternatives were added to the adsorption process. In this work was evaluated the clay mineral palygorskite as a sorbent potential for Nd (III) removal from aqueous solutions by batch trials. For this purpose, the sample from Guadalupe (Piauí) was benefited and the composition of the chemical and mineralogical was studied in order to use the sample with the highest purity in the adsorptive process. The samples were found to be essentially composed of palygorskite, kaolinite, quartz and diaspore. The chemical composition presents oxide contents, the main ones being SiO2, Al2O3 and MgO, corroborating the presence of palygorskite in the sample. Zeta Potential studies point out that the clay mineral has a negative surface charge in the whole pH range, in addition, the high surface area of 118.43 square meter per gram justifies the cation adsorber application. Different types of adsorption isotherms and kinetics models were used to describe the behavior of Nd (III) in adsorption and the best experimental results set refer to the Langmuir model and pseudo second order model, respectively, with the maximum uptake capacity was 15.39 mg/L evaluated at pH 5. Adsorption was found as an endothermic and spontaneous process ( delta H equal 17.12 KJ/mol; delta G equal -26.3 KJ/mol) in relation to thermodynamic parameters obtained. Overall results suggest that this adsorbent has been shown to be a potential sorbent for enrichment and separation of Nd (III) from aqueous solutions.

Thesis: M.S., Massachusetts Institute of Technology, Department of Mechanical Engineering, 1976 / Includes bibliographical references. / by Geary Y. Yee. / M.S. / M.S. Massachusetts Institute of Technology, Department of Mechanical Engineering

This thesis presents results in two apparently disparate mathematical fields which can both be examined -- and even united -- by means of pure analysis. Fractional calculus is the study of differentiation and integration to non-integer orders. Dating back to Leibniz, this idea was considered by many great mathematical figures, and in recent decades it has been used to model many real-world systems and processes, but a full development of the mathematical theory remains incomplete. Many techniques for partial differential equations (PDEs) can be extended to fractional PDEs too. Three chapters below cover my results in this area: establishing the elliptic regularity theorem, Malgrange-Ehrenpreis theorem, and unified transform method for fractional PDEs. Each one is analogous to a known result for classical PDEs, but the proof in the general fractional scenario requires new ideas and modifications. Fractional derivatives and integrals are not uniquely defined: there are many different formulae, each of which has its own advantages and disadvantages. The most commonly used is the classical Riemann-Liouville model, but others may be preferred in different situations, and now new fractional models are being proposed and developed each year. This creates many opportunities for new research, since each time a model is proposed, its mathematical fundamentals need to be examined and developed. Two chapters below investigate some of these new models. My results on the Atangana-Baleanu model proposed in 2016 have already had a noticeable impact on research in this area. Furthermore, this model and the results concerning it can be extended to more general fractional models which also have certain desirable properties of their own. Fractional calculus and zeta functions have rarely been united in research, but one chapter below covers a new formula expressing the Lerch zeta function as a fractional derivative of an elementary function. This result could have many ramifications in both fields, which are yet to be explored fully. Zeta functions are very important in analytic number theory: the Riemann zeta function relates to the distribution of the primes, and this field contains some of the most persistent open problems in mathematics. Since 2012, novel asymptotic techniques have been applied to derive new results on the growth of the Riemann zeta function. One chapter below modifies some of these techniques to prove asymptotics to all orders for the Hurwitz zeta function. Many new ideas are required, but the end result is more elegant than the original one for Riemann zeta, because some of the new methodologies enable different parts of the argument to be presented in a more unified way. Several related problems involve asymptotics arbitrarily near a stationary point. Ideally it should be possible to find uniform asymptotics which provide a smooth transition between the integration by parts and stationary phase methods. One chapter below solves this problem for a particular integral which arises in the analysis of zeta functions.

In this thesis we provide a body of knowledge that concerns Riemann zeta-function and its generalizations in a cohesive manner. In particular, we have studied and mentioned some recent results regarding Hurwitz and Lerch functions, as well as Dirichlet's L-function. We have also investigated some fundamental concepts related to these functions and their universality properties. In addition, we also discuss different formulations and approaches to the proof of the Prime Number Theorem and the Riemann Hypothesis. These two topics constitute the main theme of this thesis. For the Prime Number Theorem, we provide a thorough discussion that compares and contrasts Norbert Wiener's proof with that of Newman's short proof. We have also related them to Hadamard's and de la Vallee Poussin's original proofs written in 1896. As far as the Riemann Hypothesis is concerned, we discuss some recent results related to equivalent formulations of the Riemann Hypothesis as well as the Generalized Riemann Hypothesis.

The spectral zeta function, introduced by Minakshisundaram and Pleijel in [36] and denoted by ζg(s), encodes important spectral information for the Laplacian on Riemannian manifolds. For instance, the important notions of the determinant of the Laplacian and Casimir energy are defined via the spectral zeta function. On homogeneous manifolds, it is known that the spectral zeta function is critical with respect to conformal metric perturbations, (see e.g Richardson ([47]) and Okikiolu ([41])). In this thesis, we compute a second variation formula of ζg(s) on closed homogeneous Riemannian manifolds under conformal metric perturbations. It is well known that the quadratic form corresponding to this second variation is given by a certain pseudodifferential operator that depends meromorphically on s. The symbol of this operator was analysed by Okikiolu in ([42]). We analyse it in more detail on homogeneous spaces, in particular on the spheres Sn. The case n = 3 is treated in great detail. In order to describe the second variation we introduce a certain distributional integral kernel, analyse its meromorphic properties and the pole structure. The Casimir energy defined as the finite part of ζg(-½) on the n-sphere and other points of ζg(s) are used to illustrate our results. The techniques employed are heat kernel asymptotics on Riemannian manifolds, the associated meromorphic continuation of the zeta function, harmonic analysis on spheres, and asymptotic analysis.

This thesis explores various connections between multiple zeta values and modular forms of low level. In the first part, we consider double zeta values of odd weight. We generalize a result of Gangl, Kaneko and Zagier on period polynomial relations among double zeta values of even weights to this setting. This answers a question asked by Zagier. We also prove a conjecture of Zagier on the inverse of a certain matrix in this setting. In the second part, we study multiple zeta values of higher depth. In particular, we give a criterion and a conjectural criterion for "fake" relations in depth 4. In the last part, we consider multiple zeta values of levels 2 and 3. We describe one connection with the Hecke operators T₂ and T₃, and another connection with newforms of level 2 and 3. We also give a conjectural generalization of the Eichler-Shimura-Manin correspondence to the spaces of newforms of levels 2 and 3.

This thesis concerns representation growth of finitely generated torsion-free nilpotent groups. This involves counting equivalence classes of irreducible representations and embedding this counting into a zeta function. We call this the representation zeta function. We use a new, constructive method to calculate the representation zeta functions of two families of groups, namely the Heisenberg group over rings of quadratic integers and the maximal class groups. The advantage of this method is that it is able to be used to calculate the p-local representation zeta function for all primes p. The other commonly used method, known as the Kirillov orbit method, is unable to be applied to these exceptional cases. Specifically, we calculate some exceptional p-local representation zeta functions of the maximal class groups for some well behaved exceptional primes. Also, we describe the Kirillov orbit method and use it to calculate various examples of p-local representation zeta functions for almost all primes p.

As a major public health problem affecting more that 76.5 million Americans, chronic pain is one main reason why people seek medical attention. It is a pathological nervous system disorder that persists for months or years. Sensitization of nociceptive neurons in the dorsal horn of the spinal cord is crucial in the development of allodynia and hyperalgesia. The work presented in this thesis will focus on spinal protein kinase M zeta (PKMζ)-mediated plasticity and GABAergic disinhibition as spinal amplification mechanisms that orchestrate persistent changes in the dorsal horn of the spinal cord. As a result of central sensitization following peripheral nerve injruy, GABAergic disinhibition occurs due to an alteration in Cl- homeostasis via reduced KCC2 expression and function. Intrathecal administration of acetazolamide (ACT), a carbonic anhydrase inhibitor, attenuated neuropathic allodynia and spinal co-adminitation of ACT and midazolam (MZL), an allosteric modulator of the benzodiazepine class of GABAA receptors, synergistically inhibited neuropathic allodynia. Further studies concerning the impact of altered Cl-homeostasis via reduced KCC2-mediated Cl-extrusion capacity on the analgesic efficacy and potency of GABAA receptor agonist and allosteric modulators revealed that there is a differential regulation of the agonists and allosteric modulators at the GABAA receptor complex when Cl-homeostasis is altered. Another spinal amplification mechanism leading to central sensitization is PKMζ-mediated spinal LTP. In model of persistent nociceptive sensitization, allodynia induced by IL-6 injection or plantar incision was abolished by both the inhibition of protein translation machinery and PKMζ inhibitor, ZIP. However, only PKMζ inhibition prevented the enhanced pain hypersensitivity precipitated by a subsequent stimulus after the initial hypersensitivity had resolved, asserting that spinal PKMζ underlies the maintenance mechanisms of persistent nociceptive sensitization. Also, these results confirmed that the initiation mechanisms of persistent sensitization parallel LTP initiation mechanisms and the maintenance mechanisms of persistent sensitization parallel LTP maintenance mechanisms. Taken together, these results indicate that these amplification mechanisms drive a chronic persistent state in these models such that inhibition of these spinal amplication mechanisms will serve as an effective approach in the quenching chronic pain hypersensitivity in chronic pain models.

In this thesis we extend a method of Hall $[30, 34]$ which he used to show the existence of large gaps between consecutive zeros, on the critical line, of the Riemann zeta-function $zeta(s)$. Our modification involves introducing an "amplifier" and enables us to show the existence of gaps between consecutive zeros, on the critical line at height $T,$ of $zeta(s)$ of length at least $2.766 x (2pi/log{T})$. To handle some integral-calculations, we use the article $[44]$ by Hughes and Young. Also, we show that Hall's strategy can be applied not only to $zeta(s),$ but also to Dirichlet $L$-functions $L(s,chi),$ where $chi$ is a primitive Dirichlet character. This also enables us to use stronger integral-results, the article $[14]$ by Conrey, Iwaniec and Soundararajan is used. An unconditional result here about large gaps between consecutive zeros, on the critical line, of some Dirichlet $L$-functions $L(s,chi),$ with $chi$ being an even primitive Dirichlet character, is found. However, we will need to use the Generalised Riemann Hypothesis to make sense of the average gap-length between such zeros. Then the gaps, whose existence we show, have a length of at least $3.54$ times the average.