Neste trabalho, introduzimos a função zeta de Riemann \'ZETA\'(s), para s \'PERTENCE\' C \\ e apresentamos muito do que é conhecido como justificativa para a hipótese de Riemann. A importância de \'ZETA\' (s) para a teoria analítica dos números é enfatizada e fornecemos uma prova conhecida do Teorema dos Números Primos. No final, discutimos a importância de \'ZETA\'(s) para alguns modelos físicos de interesse e concluimos descrevendo como a hipótese de Riemann pode ser acessada estudando estes sistemas / In this work, we introduce the Riemann zeta function \'ZETA\'(s), s \'IT BELONGS\' C \\ and present much of what is known to support the Riemann hypothesis. The importance of \'ZETA\'(s) to the Analytic number theory is emphasized and a proof for the Prime Number Theorem is reviewed. In the end, we report on the importance of \'ZETA\'(s) to some relevant physical models and conclude by describing how the Riemann Hypothesis can be accessed by studying these systems

acase@tulane.edu / Modular-type transformation formulas are the identities that are invariant under the transformation α → 1/α, and they can be represented as F (α) = F (β) where α β = 1. We derive a new transformation formula of the form F (α, z, w) = F (β, z, iw) that is a one-variable generalization of the well-known Ramanujan-Guinand identity of the form F (α, z) = F (β, z) and a two-variable generalization of Koshliakov’s formula of the form F (α) = F (β) where α β = 1. The formula is generated by first finding an integral J that is comprised of an invariance function Z and evaluating the integral to give F (α, z, w) mentioned above. The modified Bessel function K z (x) appearing in Ramanujan-Guinand identity is generalized to a new function, denoted as K z,w (x), that yields a pair of functions reciprocal in the Koshliakov kernel, which in turn yields the invariance function Z and hence the integral J and the new formula. The special function K z,w (x), first defined as the inverse Mellin transform of a product of two gamma functions and two confluent hypergeometric functions, is shown to exhibit a rich theory as evidenced by a number of integral and series representations as well as a differential-difference equation. The second topic of the thesis is 2-adic valuations of integer sequences associated with quadratic polynomials of the form x 2 +a. The sequence {n 2 +a : n ∈ Z} contains numbers divisible by any power of 2 if and only if a is of the form 4 m (8l+7). Applying this result to the sequences derived from the sums of four or fewer squares when one or more of the squares are kept constant leads to interesting results, that also points to an inherent connection with the functions r k (n) that count the number of ways to represent n as sums of k integer squares. Another class of sequences studied is the shifted sequences of the polygonal numbers given by the quadratic formula, for which the most common examples are the triangular numbers and the squares. / 1 / Aashita Kesarwani

Electroosmotic flow is a convenient mechanism for transporting polar fluid in a microfluidic device. The flow is generated through the application of an external electric field that acts on the free charges that exists in a thin Debye layer at the channel walls. The charge on the wall is due to the chemistry of the solid-fluid interface, and it can vary along the channel, e.g. due to modification of the wall. This investigation focuses on the simulation of the electroosmotic flow (EOF) profile in a cylindrical microchannel with step change in zeta potential. The modified Navier-Stoke equation governing the velocity field and a non-linear two-dimensional Poisson-Boltzmann equation governing the electrical double-layer (EDL) field distribution are solved numerically using finite control-volume method. Continuities of flow rate and electric current are enforced resulting in a non-uniform electrical field and pressure gradient distribution along the channel. The resulting parabolic velocity distribution at the junction of the step change in zeta potential, which is more typical of a pressure-driven velocity flow profile, is obtained. / Singapore-MIT Alliance (SMA)

This thesis describes the synthesis and assembly of metal and semiconductor nanoparticles (NPs). The two research topics include i) hetero-assembly of metal and semiconductor NPs, ii) effect of ionic strength on homo-assembly of gold nanorods (GNRs). First, we present hetero-assembly of GNRs and semiconductor quantum dots (QDs) in a chain using biotin-streptavidin interaction. We synthesized alloyed CdTeSe QDs and modified them with mercaptoundecanoic acid to render them water-soluble and to attach streptavidin. We synthesized GNRs by a seed-mediated method and selectively modified the ends with biotin. Hetero-assembly of QDs and GNRs depended on the size, ligands, and ratio of QDs and GNRs. Second, we controlled the rate of homo-assembly of GNRs by varying the ionic strength of the DMF/water solution. The solubility of polystyrene on the ends of GNRs depended on the ionic strength of the solution, which correlated with the rate of assembly of GNRs into chains.

This thesis describes the synthesis and assembly of metal and semiconductor nanoparticles (NPs). The two research topics include i) hetero-assembly of metal and semiconductor NPs, ii) effect of ionic strength on homo-assembly of gold nanorods (GNRs). First, we present hetero-assembly of GNRs and semiconductor quantum dots (QDs) in a chain using biotin-streptavidin interaction. We synthesized alloyed CdTeSe QDs and modified them with mercaptoundecanoic acid to render them water-soluble and to attach streptavidin. We synthesized GNRs by a seed-mediated method and selectively modified the ends with biotin. Hetero-assembly of QDs and GNRs depended on the size, ligands, and ratio of QDs and GNRs. Second, we controlled the rate of homo-assembly of GNRs by varying the ionic strength of the DMF/water solution. The solubility of polystyrene on the ends of GNRs depended on the ionic strength of the solution, which correlated with the rate of assembly of GNRs into chains.

No description available.

Firing an underwater spark discharge generates an expanding plasma which causes a spherical shockwave to propagate through the surrounding water. The shockwave can have many effects, including resonance effects on bubbles, mechanical destructive effects on solid surfaces and living organisms, and sonochemical oxidative effects on particles and chemical species present in the water. This phenomenon has been shown to improve the efficiency of ink removal in a laboratory flotation deinking cell, while simultaneously decreasing fiber loss. These process improvements are attributed to the sonochemical oxidation of ink particle surfaces, caused by shockwave-induced cavitation. This finding is supported by zeta potential measurements. Sparking was found to reduce the zeta potential of ink particles by up to 20 mV. When sparking was performed during deinking, no effect was found on either ink removal or solids loss. However, when the pulp was pretreated with sparking before flotation, a significant improvement was seen in the brightness gain. Further, fiber loss was decreased by up to 25% in a single flotation stage. The economics of this process are attractive; payback is on the order of three months based on fiber savings alone. Also, at about 1.5 kJ per spark, the power requirements are minimal with respect to the benefit derived.

Thesis (Ph. D.)--Institute of Paper Chemistry, 1967. / Includes bibliographical references (p. 69-71).

published_or_final_version / Mathematics / Master / Master of Philosophy

published_or_final_version / Mathematics / Master / Master of Philosophy