Thesis advisor: Ilija Zeljkovic / Kagome lattice is a versatile platform that can host both strongly correlated electronic phenomena and topological Bloch electrons. Correlated electronic states in kagome metals show some resemblance to those in high-temperature superconductors, such as cuprates and iron-based superconductors, where rotational and/or translational symmetries of the electronic structure are spontaneously broken. Many of the kagome materials are now also known to break time-reversal symmetry, even if spin magnetism is entirely absent. In our studies, we use scanning tunneling microscopy/spectroscopy (STM/S) to discover novel emergent phenomena in several representative families of kagome metals.In the first part of the thesis, I focus on a family of kagome superconductors AV3Sb5 (A = Cs, Rb, K). Using STM/S, we visualize a surprising C6 to C2 rotation symmetry breaking in the charge density wave (CDW) state of AV3Sb5. Moreover, we discover distinct temperature scales associated with a two-fold symmetric 2a_0×2a_0 CDW (~70+ K), a unidirectional 4a0 stripe-charge order (~50-60 K), and unidirectional coherent states in AV3Sb5 (~30-35 K). In isostructural system CsTi3Bi5 Kagome crystal, we revealed rotational symmetry breaking, or electronic nematicity, without the underlying CDW state. Our experiments shed light on a rich phase diagram hosting a variety of symmetry-breaking electronic phases in kagome metals. In the second part of the thesis, we focus on the topological aspects of the electronic band structure of kagome metals. When electrons hop (nearly) freely in kagome lattices, spin-orbit coupling can open a topological Dirac gap at the K point and induce either quantum anomalous Hall or quantum spin Hall phases when the Fermi level is positioned in the gap. In strongly spin-orbit coupled kagome metals YMn6Sn6 and TbV6Sn6, we discovered enormous crystal momentum-dependent magnetic-field induced electronic band renormalization, which could be attributed to unusual orbital magnetization. Modern orbital magnetization theory describes that orbital magnetization comes from (spin) Berry Curvature associated with the Chern Dirac band. Using quasiparticle interference imaging, we map the Dirac band renormalization under external magnetic field and measure the values of orbital magnetic moments as a function of crystal momenta. Our experiments provide the first effort to resolve momentum-space orbital magnetic moments in a single crystal with atomic resolution. / Thesis (PhD) — Boston College, 2024. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Black mothers socialize their daughters to embody the strong Black woman (SBW) schema to help them navigate gendered racist oppression. While research indicates that ascribing to the SBW schema offers Black women psychosocial benefits (e.g., increased self-esteem), identifying with the SBW schema has been linked to several negative psychological outcomes (e.g., anxiety, depression, and stress). Considering the evidenced negative implications associated with identifying with the SBW schema on Black women's mental health, the current study had three aims: (1) investigate the socialization messages Black women received about strong Black womanhood, (2) explore the extent to which they identified with these messages, and (3) assess the implications of this socialization on Black women's functioning. To address these aims researchers conducted semi-structured interviews with 11 Black college women (Mage = 20.09; SD = 1.04). For this manuscript, we extracted data pertaining to aim one and analyzed this data using a consensual qualitative research (CQR) data approach. Findings revealed messages Black women were given about strong Black womanhood (i.e., know your worth, depend on yourself, overcome societal barriers, little to no messages about strong Black womanhood, and additional responses) and illuminated behaviors mothers modeled that exemplified strength (i.e., self-sufficient, preserving, caretaking, and additional responses). Findings derived from this study have the potential to inform clinical intervention with Black women and, more specifically, provide insight as to how clinicians may work with Black women to mitigate the impact of the SBW schema on their mental health.

This thesis examines the domination number of the semi-strong product of two graphs G and H where both G and H are simple and connected graphs. The product has an edge set that is the union of the edge set of the direct product of G and H together with the cardinality of V(H), copies of G. Unlike the other more common products (Cartesian, direct and strong), the semi-strong product is neither commutative nor associative. The semi-strong product is not supermultiplicative, so it does not satisfy a Vizing like conjecture. It is also not submultiplicative so it shares these two properties with the direct product. After giving the basic definitions related with graphs, domination in graphs and basic properties of the semi-strong product, this paper includes a general upper bound for the domination of the semi-strong product of any two graphs G and H as less than or equal to twice the domination numbers of each graph individually. Similar general results for the semi-strong product perfect-paired domination numbers of any two graphs G and H, as well as semi-strong products of some specific types of cycle graphs are also addressed.

In the 1970’s, L. Lovász proved that two graphs G and H are isomorphic if and only if for every graph X , the number of homomorphisms from X → G equals the number of homomorphisms from X → H . He used this result to deduce cancellation properties of the direct product of graphs. We develop a result analogous to Lovász’s theorem, but in the class of graphs without loops and with weak homomorphisms. We apply it prove a general cancellation property for the strong product of graphs.

Stochastic differential equations (SDE’s) are used to describe systems which are influenced by randomness. Here, randomness is modelled as some external source interacting with the system, thus ensuring that the stochastic differential equation provides a more realistic mathematical model of the system under investigation than deterministic differential equations. The behaviour of the physical system can often be described by probability and thus understanding the theory of SDE’s requires the familiarity of advanced probability theory and stochastic processes. SDE’s have found applications in chemistry, physical and engineering sciences, microelectronics and economics. But recently, there has been an increase in the use of SDE’s in other areas like social sciences, computational biology and finance. In modern financial practice, asset prices are modelled by means of stochastic processes. Thus, continuous-time stochastic calculus plays a central role in financial modelling. The theory and application of interest rate modelling is one of the most important areas of modern finance. For example, SDE’s are used to price bonds and to explain the term structure of interest rates. Commonly used models include the Cox-Ingersoll-Ross model; the Hull-White model; and Heath-Jarrow-Morton model. Since there has been an expansion in the range and volume of interest rate related products being traded in the international financial markets in the past decade, it has become important for investment banks, other financial institutions, government and corporate treasury offices to require ever more accurate, objective and scientific forms for the pricing, hedging and general risk management of the resulting positions. Similar to ordinary differential equations, many SDE’s that appear in practical applications cannot be solved explicitly and therefore require the use of numerical methods. For example, to price an American put option, one requires the numerical solution of a free-boundary partial differential equation. There are various approaches to solving SDE’s numerically. Monte Carlo methods could be used whereby the physical system is simulated directly using a sequence of random numbers. Another method involves the discretisation of both the time and space variables. However, the most efficient and widely applicable approach to solving SDE’s involves the discretisation of the time variable only and thus generating approximate values of the sample paths at the discretisation times. This paper highlights some of the various numerical methods that can be used to solve stochastic differential equations. These numerical methods are based on the simulation of sample paths of time discrete approximations. It also highlights how these methods can be derived from the Taylor expansion of the SDE, thus providing opportunities to derive more advanced numerical schemes. / Dissertation (MSc (Mathematics of Finance))--University of Pretoria, 2007. / Mathematics and Applied Mathematics / MSc / unrestricted

No description available.

Doctor of Philosophy / Department of Physics / Itzhak Ben-Itzhak / Present advances in laser technology allow the production of ultrashort (≲5 fs, approaching single cycle at 800 nm), intense tabletop laser pulses. At these high intensities laser-matter interactions cannot be described with perturbation theory since multiphoton processes are involved. This is in contrast to photodissociation by the absorption of a single photon, which is well described by perturbation theory. For example, at high intensities (≳5×10[superscript]13 W/cm[superscript]2) the fragmentation of molecular hydrogen ions has been observed via the absorption of three or more photons. In another example, an intriguing dissociation mechanism has been observed where molecular hydrogen ions seem to fragment by apparently absorbing no photons. This is actually a two photon process, photoabsorption followed by stimulated emission, resulting in low energy fragments. We are interested in exploring these kinds of multiphoton processes. Our research group has studied the dynamics and control of fragmentation induced by strong laser fields in a variety of molecular targets. The main goal is to provide a basic understanding of fragmentation mechanisms and possible control schemes of benchmark systems such as H[subscript]2[superscript]+. This knowledge is further extended to more complex systems like the benchmark H[subscript]3[superscript]+ polyatomic and other molecules. In this dissertation, we report research based on two types of experiments. In the first part, we describe laser-induced fragmentation of molecular ion-beam targets. In the latter part, we discuss the formation of highly-excited neutral fragments from hydrogen molecules using ultrashort laser pulses. In carrying out these experiments, we have also extended experimental techniques beyond their previous capabilities. We have performed a few experiments to advance our understanding of laser-induced fragmentation of molecular-ion beams. For instance, we explored vibrationally resolved spectra of O[subscript]2[superscript]+ dissociation using various wavelengths. We observed a vibrational suppression effect in the dissociation spectra due to the small magnitude of the dipole transition moment, which depends on the photon energy --- a phenomenon known as Cooper minima. By changing the laser wavelength, the Cooper minima shift, a fact that was used to identify the dissociation pathways. In another project, we studied the carrier-envelope phase (CEP) dependences of highly-excited fragments from hydrogen molecules. General CEP theory predicts a CEP dependence in the total dissociation yield due to the interference of dissociation pathways differing by an even net number of photons, and our measurements are consistent with this prediction. Moreover, we were able to extract the difference in the net number of photons involved in the interfering pathways by using a Fourier analysis. In terms of our experimental method, we have implemented a pump-probe style technique on a thin molecular ion-beam target and explored the feasibility of such experiments. The results presented in this work should lead to a better understanding of the dynamics and control in molecular fragmentation induced by intense laser fields.

The main object of this thesis is to obtain numerous applications of fractional derivative operator concerning analytic and ρ-valent (or multivalent) functions in the open unit disk by introducing new classes and deriving new properties. Our finding will provide interesting new results and indicate extensions of a number of known results. In this thesis we investigate a wide class of problems. First, by making use of certain fractional derivative operator, we define various new classes of ρ-valent functions with negative coefficients in the open unit disk such as classes of ρ-valent starlike functions involving results of (Owa, 1985a), classes of ρ-valent starlike and convex functions involving the Hadamard product (or convolution) and classes of κ-uniformly ρ-valent starlike and convex functions, in obtaining, coefficient estimates, distortion properties, extreme points, closure theorems, modified Hadmard products and inclusion properties. Also, we obtain radii of convexity, starlikeness and close-to-convexity for functions belonging to those classes. Moreover, we derive several new sufficient conditions for starlikeness and convexity of the fractional derivative operator by using certain results of (Owa, 1985a), convolution, Jack's lemma and Nunokakawa' Lemma. In addition, we obtain coefficient bounds for the functional |α_ρ+2-θα²_ρ+1| of functions belonging to certain classes of p-valent functions of complex order which generalized the concepts of starlike, Bazilevič and non-Bazilevič functions. We use the method of differential subordination and superordination for analytic functions in the open unit disk in order to derive various new subordination, superordination and sandwich results involving the fractional derivative operator. Finally, we obtain some new strong differential subordination, superordination, sandwich results for ρ-valent functions associated with the fractional derivative operator by investigating appropriate classes of admissible functions. First order linear strong differential subordination properties are studied. Further results including strong differential subordination and superordination based on the fact that the coefficients of the functions associated with the fractional derivative operator are not constants but complex-valued functions are also studied.

Le 1er transfert de brin, étape cruciale de la transcription inverse impliquant la protéine de nucléocapside du VIH-1 (NC), repose sur l’appariement de la séquence r de l’ADN « strong stop » (ADNss) avec la séquence 3’ R de l’ARN viral (3’UTR) qui forme les tiges-boucles TAR et polyA. La séquence r est supposé former les tiges-boucles cTAR et cpolyA. Le transfert repose donc probablement sur l’hybridation de molécules structurées. La structure secondaire de l’ADNss n’a jamais été déterminée. L’objectif a été d’identifier les interactions et structures gouvernant l’hybridation de l’ADNss avec l’ARN 3’UTR. Les outils de la biologie moléculaire et trois sondes de structure ciblant l’ADN ont été utilisés pour atteindre cet objectif. Nos résultats sont les suivants : 1) l’ADN cTAR nu se replie sous la forme de deux conformations différentes qui sont en équilibre ; 2) la NC peut déplacer l’équilibre vers l’une des conformations et se fixer préférentiellement sur la boucle interne du cTAR ; 3) la NC est exigée pour former un hétéroduplex constitué de l’intégralité de l’ADNss et du 3’ UTR ; 4) l’hybridation ADNss-3’UTR peut être initiée à partir de plusieurs sites dans 0,2 mM MgCl2 ; 5) l’ADNss forme deux conformations en équilibre dans 0,2 mM MgCl2 et principalement une seule dans 2 mM MgCl2 ; 6) dans l’ADNss, la NC se fixe préférentiellement au niveau de la région simple-brin qui relie les tiges-boucles cTAR et cpolyA. Cette fixation joue probablement un rôle important dans l’hybridation des tiges-boucles ARN et ADN complémentaires. Notre étude permet de mieux comprendre la transcription inverse et la recombinaison qui dépend du transfert de brin interne. / The 1st strand transfer, a crucial step of reverse transcription involving the HIV-1 nucleocapsid protein (NC), relies on base pairing of the r sequence of strong-stop DNA (ssDNA) with the 3’ R sequence of viral RNA (3’ UTR) which forms the TAR and polyA stem-loops. The r sequence can form the cTAR and cpolyA stem-loops. Therefore, the transfer relies probably on annealing of folded molecules. This process is not well known at the molecular and structural level. The tools of molecular biology and three DNA-targeted probes were used to get insights into the annealing process. Our results were the following: 1) in the absence of NC, the cTAR DNA folds into two distinct conformations in equilibrium; 2) NC slightly shifts the equilibrium toward one conformation and binds tightly the internal loop of the cTAR hairpin; 3) NC is required for the formation of heteroduplex of the full-length ssDNA and 3’ UTR; 4) the annealing of ssDNA to 3’ UTR can be initiated from different sites in the presence of 0.2 mM MgCl2; 5) the full-length ssDNA folds into two conformations in equilibrium in 0.2 mM MgCl2 but mainly into one conformation in 2 mM MgCl2 ; 6) NC preferentially binds to the single-stranded region between the cTAR and cpolyA hairpins in ssDNA. This binding site probably plays an important role in the annealing of complementary DNA and RNA hairpins. This study helps us to gain insights into the reverse transcription process and the associated genetic recombination.

A degradação ambiental proporcionada pelo consumo de produtos (JORGENSON, 2003) é fruto tanto da evolução de uma sociedade que se distancia da natureza (MORAN, 2011), quanto de suas reais necessidades (FRY, 2005). Da mesma forma, os interesses do mercado, de governos e de consumidores enrijecem a manutenção de uma sociedade hiperconsumista (FRY, 2005). Este fato é observado pela existência de políticas governamentais de consumo (corrente do consumo verde) que prezam pela rotulagem ambiental, depositam a responsabilidade da redução da degradação ambiental no consumidor (AKENJI, 2014), e que não consideram que o aumento da ecoeficiência, sem questionar quais são os limites ambientais impostos para a realização das atividades humanas, provocam um efeito de rebote que pode elevar ainda mais a degradação ambiental (HANLEY et al., 2009). Em contrapartida, a corrente do consumo sustentável afirma ser necessário repensar os níveis de consumo de modo a não ultrapassarmos os limites impostos pelo ambiente à realização das nossas atividades (AKENJI, 2014). Desta forma, a informação necessária para a corrente do consumo sustentável é aquela que indica em que medida as capacidades de suporte do ambiente foram superadas (ALCOTT, 2008). Dentre todos os instrumentos capazes de fornecer informação sobre os aspectos ambientais de produtos, a Avaliação do Ciclo de Vida (ACV) é o único instrumento desenhado para avaliar as consequências ambientais relacionadas ao ciclo de vida de um produto (CHEHEBE, 1997). Entretanto, as evidências encontradas na bibliografia indicam que os métodos utilizados pela ACV para mensurar as consequências ambientais do produto (métodos de AICV - Avaliação do Impacto do Ciclo de Vida) foram estruturados para calcular majoritariamente a ecoeficiência dos produtos, pois são poucos (ou não indicados pela bibliografia) os casos em que a capacidade de suporte do ambiente é avaliada por estes métodos (POTTING; HAUSCHILD, 2006). Diante deste quadro, esta dissertação se propôs a avaliar se os métodos de AICV existentes estão alinhados à sustentabilidade forte ou se estão alinhados à sustentabilidade fraca. Dois critérios de avaliação foram definidos com base nos princípios da sustentabilidade forte: (i) O resultado do indicador da Categoria de Impacto deve apresentar quanto da capacidade de suporte foi ultrapassada ou não para as emissões relacionadas ao ciclo de vida do produto - alinhado ao princípio (a) da sustentabilidade forte, de que as atividades humanas devem ser limitadas à capacidade de suporte do ambiente (COSTANZA; DALY, 1992) - e, (ii) Todas as Categorias de Impacto (CIs) do método de AICV devem atender ao requisito (i) - alinhado ao princípio (b) da sustentabilidade forte, de que não há substitutabilidade completa entre os diferentes elementos do capital natural (COSTANZA; DALY, 1992). Dos métodos de AICV avaliados (CML 2002, Eco-Indicator 99, Eco-Factors 2006, EDIP 2003, IMPACT2002+, MEErP 2011) verificou-se que nenhum método está alinhado aos princípios da sustentabilidade forte, pois os critérios (i) e (ii) não foram atendidos concomitantemente. Desta forma, concluiu-se que por não estarem alinhados aos princípios da sustentabilidade forte, os métodos de AICV avaliados não são capazes de atender à demanda do consumo sustentável por informações. Sua utilização demonstra que as políticas de consumo verde continuam a depositar a maior responsabilidade pela reversão da degradação ambiental nos consumidores, sem alterar a estrutura sistêmica criada pelos governos, pelo mercado e consumidores na qual o hiperconsumo prevalece. / The environmental degradation provided by the consumption of products (JORGENSON, 2003) is the result of the evolution of a society that distances itself away from nature (MORAN, 2011) and from its real needs (FRY, 2005). At the same time, the interests of the market, governments and consumers maintain the hyper-consumption society (FRY, 2005). This fact is noticed by the presence of government consumption policies that appreciate environmental labeling, lay the responsibility for the reduction of the environmental degradation on the consumer (green consumption current) (AKENJI, 2014), and do not consider that the increase in eco-efficiency, without questioning the environmental limits for human activities, causes a rebound effect that can further raise environmental degradation (HANLEY et al., 2009). In contrast, the sustainable consumption current claims to be necessary to rethink consumption levels in order not to overpass the limits imposed by the environment for our activities (AKENJI, 2014). Thus, the necessary information for the sustainable consumption current is the one that indicates to what extent the environmental carrying capacity is exceeded (ALCOTT, 2008). Among all the instruments able to provide information on the environmental aspects of products, the Life Cycle Assessment (LCA) is the only instrument designed to assess the environmental consequences related to the life cycle of a product (CHEHEBE, 1997). However, the evidence found in the literature indicates that the methods used by LCA to measure the environmental impact of products (LCIA methods - Life Cycle Impact Assessment) were structured to mainly calculate the eco-efficiency of products, once there are only a few cases (or no indicated by references) in which the environmental carrying capacity is assessed by these methods (POTTING; HAUSCHILD, 2006). Given this context, this work aimed to evaluate whether existing LCIA methods are aligned to the strong or weak sustainability currents. Two evaluation criteria were defined on the basis of strong sustainability: (i) The results of the Impact Category indicator should present how much of the carrying capacity has been exceeded or not by the emissions related to the product life cycle according to the principle (a) of the strong sustainability, which states that human activities should be limited by the environmental carrying capacity (COSTANZA; DALY, 1992) - and (ii) All Impact Categories of a LCIA method must meet the requirement (i) - according to the principle (b) of the strong sustainability, which states that there is no complete substitutability between the different elements of natural capital (COSTANZA; DALY, 1992). From the evaluation of the LCIA methods (CML 2002, Eco-Indicator 99 Eco-Factors 2006, EDIP 2003 IMPACT2002+ and MEErP 2011) it was found that any of these methods are aligned with the principles of the strong sustainability, once the methods do not comply with criteria (i) and (ii ) concurrently. Thus, it was concluded that once they are not aligned to the principles of strong sustainability, the evaluated LCIA methods are not able to meet the demand of sustainable consumption for information. Its use demonstrates that green consumption policies continue to place the greatest responsibility for the reversal of the environmental degradation on consumers, without changing the systemic structure created by governments, the market and consumers in which hyper-consumption prevails.