Miracle-dz/UniFAR-FTUs huggingface dataset:
Geometric structures and Lie algebroids

In this thesis we study geometric structures from Poisson and generalized complex geometry with mild singular behavior using Lie algebroids. The process of lifting such structures to their Lie algebroid version makes them less singular, as their singular behavior is incorporated in the anchor of the Lie algebroid. We develop a framework for this using the concept of a divisor, which encodes the singularities, and show when structures exhibiting such singularities can be lifted to a Lie algebroid built out of the divisor. Once one has successfully lifted the structure, it becomes possible to study it using more powerful techniques. In the case of Poisson structures one can turn to employing symplectic techniques. These lead for example to normal form results for the underlying Poisson structures around their singular loci. In this thesis we further adapt the methods of Gompf and Thurston for constructing symplectic structures out of fibration-like maps to their Lie algebroid counterparts. More precisely, we introduce the notion of a Lie algebroid Lefschetz fibration and show when these give rise to A-symplectic structures for a given Lie algebroid A. We then use this general result to show how log-symplectic structures arise out of achiral Lefschetz fibrations. Moreover, we introduce the concept of a boundary Lefschetz fibration and show when they allow their total space to be equipped with a stable generalized complex structure. Other results in this thesis include homotopical obstructions to the existence of A-symplectic structures using characteristic classes, and splitting results for A-Lie algebroids (i.e., Lie algebroids whose anchor factors through that of a fixed Lie algebroid A), around specific transversal submanifolds.
Topological Triviality of Families of Singular Surfaces

We study the topological triviality of families of singular surfaces in ${\mathbb C}^3$ parametrized by $\mathcal A$-finitely determined map germs. We prove that the constancy of the Milnor number of the double point locus characterizes the topological triviality of the family.
Randers Ricci soliton homogeneous nilmanifolds

Let $F$ be a left invariant Randers metric on a simply connected nilpotent Lie group $N$, induced by a left invariant Riemannian metric ${\hat{\textbf{\textit{a}}}}$ and a Killing vector field $X$ of the Riemannian manifold $(N,{\hat{\textbf{\textit{a}}}})$. Then, $(N,F)$ is a Ricci soliton if and only if $(N,F)$ is a semialgebraic Ricci soliton.
THE PRISM MULTI-OBJECT SURVEY (PRIMUS). I. SURVEY OVERVIEW AND CHARACTERISTICS

We present the PRIsm MUlti-object Survey (PRIMUS), a spectroscopic faint galaxy redshift survey to z ∼ 1. PRIMUS uses a low-dispersion prism and slitmasks to observe ∼2500 objects at once in a 0.18 deg2 field of view, using the Inamori Magellan Areal Camera and Spectrograph camera on the Magellan I Baade 6.5 m telescope at Las Campanas Observatory. PRIMUS covers a total of 9.1 deg2 of sky to a depth of iAB ∼ 23.5 in seven different deep, multi-wavelength fields that have coverage from the Galaxy Evolution Explorer, Spitzer, and either XMM or Chandra, as well as multiple-band optical and near-IR coverage. PRIMUS includes ∼130,000 robust redshifts of unique objects with a redshift precision of σz/(1 + z) ∼ 0.005. The redshift distribution peaks at z ∼ 0.6 and extends to z = 1.2 for galaxies and z = 5 for broad-line active galactic nuclei. The motivation, observational techniques, fields, target selection, slitmask design, and observations are presented here, with a brief summary of the redshift precision; a forthcoming paper presents the data reduction, redshift fitting, redshift confidence, and survey completeness. PRIMUS is the largest faint galaxy survey undertaken to date. The high targeting fraction (∼80%) and large survey size will allow for precise measures of galaxy properties and large-scale structure to z ∼ 1.
Innovations, energy consumption and carbon dioxide emissions in the global world countries: An empirical investigation

Technological innovations are the important sources of economic growth of a country and it is inter associated with other factors such as energy consumption, economic growth and carbon dioxide emission. A change in these factors affect the capability of technological innovation and thus the effect of these factors on innovations need to be explored. This study investigates the effect of carbon dioxide, energy consumption and economic growth on innovations proxies by different innovations indicators. The sample data is collected from 1980 to 2019 of the world 181 countries and OLS, fixed effect, two step Generalized method of moments and panel quantile regression models were employed for data analysis. The results reveal that carbon dioxide and economic growth increase technological innovations while the inflow of FDI decrease innovations output. Energy consumption also negatively affects innovation indicators except for research and development. In the case of quantile regression, energy consumption is positive while carbon dioxide and foreign direct investment are negative across different quantiles for research and development. Energy consumption and foreign direct investment reduce technological innovations proxy by patent application residents while carbon dioxide and economic growth increase it. The findings of this study have considerable policy suggestions for the global countries.
Symplectic approach to quantum constraints

A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions to the constrained dynamics of systems of multiple spin particles. When the motion is constrained to a certain product space containing all of the energy eigenstates, the dynamics thus obtained are quasi-unitary in the sense that the equations of motion take a form identical to that of unitary motion, but with different boundary conditions. When the constrained subspace is a product space of disentangled states, the associated motion is more intricate. Nevertheless, the equations of motion satisfied by the dynamical variables are obtained in closed form.
Extended and Reshetikhin twists for sl(3)

The properties of the set of extended Jordanian twists for algebra sl(3) are studied. Starting from the simplest algebraic construction - the peripheric Hopf algebra - we explicitly construct the complete family of extended twisted algebras {(sl(3))} corresponding to the set of four-dimensional Frobenius subalgebras {L()} in sl(3). It is proved that the extended twisted algebras with different values of the parameter are connected by a special kind of Reshetikhin twist. We study the relations between the family {(sl(3))} and the one-dimensional set {(sl(3))} produced by the standard Reshetikhin twist from the Drinfeld-Jimbo quantization (sl(3)). These sets of deformations are in one-to-one correspondence: each element of {(sl(3))} can be obtained by a limiting procedure from the unique point in the set {(sl(3))}.
Linear perturbation constraints on multi-coupled dark energy

The Multi-coupled Dark Energy (McDE) scenario has been recently proposed as a specific example of a cosmological model characterized by a non-standard physics of the dark sector of the universe that nevertheless gives an expansion history which does not significantly differ from the one of the standard ΛCDM model. Thanks to a dynamical screening mechanism, in fact, the interaction between the Dark Energy field and the Dark Matter sector is effectively suppressed at the background level during matter domination. As a consequence, background observables cannot discriminate a McDE cosmology from ΛCDM for a wide range of model parameters. On the other hand, linear perturbations are expected to provide tighter bounds due to the existence of attractive and repulsive fifth-forces associated with the dark interactions. In this work, we present the first constraints on the McDE scenario obtained by comparing the predicted evolution of linear density perturbations with a large compilation of recent data sets for the growth rate fσ8, including 6dFGS, LRG, BOSS, WiggleZ and VIPERS. Confirming qualitative expectations, growth rate data provide much tighter bounds on the model parameters as compared to the extremely loose bounds that can be obtained when only the background expansion history is considered. In particular, the 95% confidence level on the coupling strength |β| is reduced from |β| ⩽ 83 (background constraints only) to |β| ⩽ 0.88 (background and linear perturbation constraints). We also investigate how these constraints further improve when using data from future wide-field surveys such as supernova data from LSST and growth rate data from Euclid-type missions. In this case the 95% confidence level on the coupling further reduce to |β| ⩽ 0.85. Such constraints are in any case still consistent with a scalar fifth-force of gravitational strength, and we foresee that tighter bounds might be possibly obtained from the investigation of nonlinear structure formation in McDE cosmologies.
EVIDENCE FOR TWO DISTINCT STELLAR INITIAL MASS FUNCTIONS

We present velocity dispersion measurements of 20 Local Group stellar clusters (7 < log(age [yr]) <10.2) from integrated light spectra and examine the evolution of the stellar mass-to-light ratio, ϒ*. We find that the clusters deviate from the evolutionary tracks corresponding to simple stellar populations drawn from standard stellar initial mass functions (IMFs). The nature of this failure, in which ϒ* is at first underestimated and then overestimated with age, invalidates potential simple solutions involving a rescaling of either the measured masses or modeled luminosities. A range of possible shortcomings in the straightforward interpretation of the data, including subtleties arising from cluster dynamical evolution on the present-day stellar mass functions and from stellar binarity on the measured velocity dispersions, do not materially affect this conclusion given the current understanding of those effects. Independent of further conjectures regarding the origin of this problem, this result highlights a basic failing of our understanding of the integrated stellar populations of these systems. We propose the existence of two distinct IMFs, one primarily, but not exclusively, valid for older, metal-poor clusters and the other for primarily, but not exclusively, younger, metal-rich clusters. The young (log(age [yr]) < 9.5) clusters are well described by a bottom-heavy IMF, such as a Salpeter IMF, while the older clusters are better described by a top-heavy IMF, such as a light-weighted Kroupa IMF, although neither of these specific forms is a unique solution. The sample is small, with the findings currently depending on the results for four key clusters, but doubling the sample is within reach.
COLLEGE ADMINISTRATIVE SUPPORT IN INTEGRATION OF ADAPTIVE TECHNOLOGY FOR VISUALLY IMPAIRED STUDENT TEACHERS IN PRIMARY TEACHER TRAINING COLLEGES: THE KENYAN EXPERIENCE

Administrative support is key in inclusive education and more so in the integration of adaptive technology for visually impaired (VI) student teachers. Integration of adaptive technology improves the quality of education, removes learning barriers and ensures that the visually impaired student teachers graduate as skilled, confident and competent primary school teachers. This study assessed the college administration’s support in the integration of adaptive technology for visually impaired student teachers. The study was guided by the diffusion of innovation theory by Rogers which gives a basis for the adoption of innovations in institutions and other settings. The study adopted a descriptive survey research design. The study population included administrators and tutors in three primary teachers training colleges which admit student teachers with visual impairment in Kenya. The purposive sampling technique was used to select three deans of the curriculum while simple random sampling was used to select nine heads of departments and 93 tutors making a sample of 105 respondents. Data collection instruments were questionnaires and interview schedules. Descriptive statistics like frequencies and percentages were used to analyze the quantitative data. A qualitative procedure was applied to information from interviews where respondents’ answers were presented in words and interpretations made. The findings of this study revealed that the college administration’s support for the integration of adaptive technology was low. The recommendation made was that the college administration of public primary TTCs should fully support the integration of adaptive technology for VI student teachers in the primary TTCs by availing resources and training tutors on the integration of adaptive technology. Article visualizations:
Extremal primes for elliptic curves without complex multiplication

Fix an elliptic curve E over Q. An extremal prime for E is a prime p of good reduction such that the number of rational points on E modulo p is maximal or minimal in relation to the Hasse bound. Assuming that all the symmetric power L-functions associated to E are automorphic and satisfy the Generalized Riemann Hypothesis, we give the first non-trivial upper bounds for the number of such primes when E is a curve without complex multiplication. In order to obtain this bound, we use explicit equidistribution for the Sato-Tate measure as in the work of Rouse and Thorner (arXiv:1305.5283) and refine certain intermediate estimates taking advantage of the fact that extremal primes have a very small Sato-Tate measure.
DETERMINANTS OF MULTINATIONAL COMPANIES' CHOICE OF MARKET-ENTRY MODE FOR OPERATING IN ETHIOPIA: AN EMPIRICAL STUDY

Multinational corporations must make a difficult decision because their entry strategy is influenced by a number of factors. The purpose of this research is to look into the factors that influence the entry strategies chosen by multinational corporations doing business in Ethiopia. To collect data at a specific time, this study used cross-sectional surveys and an explanatory research methodology. Data from multinational corporations were collected for this study using deliberate sampling methods. In the end, only 120 (or 80%) of the 154 surveys distributed were returned. However, only 112 surveys were used for the statistical analysis, yielding a response rate of 72 percent. To investigate the factors influencing the choice of entry mode, a multinomial legit model was used. The study discovered that, at a 5% level of significance, the size of the firm and the size of the market had a positive and substantial influence on the decision to choose export and intermediate entry over the hierarchical entrance. However, at a 10% significance level, factors such as global experience, market infrastructure, cultural distance, flexibility, and degree of control are favourably and significantly impacting the decision to choose the export and intermediate modes of entrance over the hierarchical modes. The recommendations based on the study's findings consider how the study may affect different stakeholders, such as the Ethiopian government, regional businesses, international firms, and other researchers. Article visualizations:
European Journal of Open Education and E-learning Studies

This study aimed at enhancing pre-service teachers’ understanding and attitudes toward naming and reactions of organic compounds using the jigsaw approach. It was a descriptive study that used a quantitative approach in collecting the data for analysis. The research design was a quasi-experimental one, which adapted the non-randomised control group pre-test/post-test intact class design. A sample of 144 pre-service teachers, comprising 72 in the experimental group and 72 in the control group were engaged in the study. Intact classes were used for the study; thus, the sample selection was nonrandomised. ‘Organic Chemistry Concept Understanding Test’ (OCCUT) in the form of a pre-test and a post-test as well as an ‘Organic Chemistry Attitude Scale’ (OCAS) were the instruments used for the study. The reliability indices of the pre-test and the post-test were 0.721 and 0.724 respectively, whereas, Cronbach’s alpha reliability coefficient of the ‘OCAS’ was 0.899. This study found that in terms of the pre-service teachers’ prior knowledge on naming and reactions of organic compounds, the experimental group and the control group both had more misunderstanding and partial understanding than a sound understanding of the concepts. The findings further revealed that the majority of the pre-service teachers in the experimental group had a sound understanding of the naming and reactions of organic compounds after they were taught through the jigsaw approach. Nevertheless, quite a large number of the pre-service teachers in the control group continue to show a misunderstanding of the concepts after they were taught through the traditional lecture-method. Again, the study found that the jigsaw approach enhanced the pre-service teachers’ attitudes toward the organic chemistry concepts than the traditional lecture-method.
Jordanian twists on deformed carrier subspaces

The nontrivial subspaces with primitive coproducts are found in the deformed universal enveloping algebras. They can form carrier subspaces for additional Jordanian twists. The latter can be used to construct sequences of twists for algebras whose root systems contain long series of roots. The corresponding twist for the so(5) algebra is given explicitly.
Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier-Stokes Equations

In this paper we analyze a finite element method applied to a continuous downscaling data assimilation algorithm for the numerical approximation of the two and three dimensional Navier-Stokes equations corresponding to given measurements on a coarse spatial mesh. We obtain uniform-in-time estimates for the error between a finite element approximation and the reference solution corresponding to the coarse spatial mesh measurements.
Topological modular forms with level structure: Decompositions and duality

Topological modular forms with level structure were introduced in full generality by Hill and Lawson. We will show that these decompose additively in many cases into a few simple pieces and give an application to equivariant $TMF$. Furthermore, we show which $Tmf_1(n)$ are self-Anderson dual up to a shift, both with and without their natural $C_2$-action.
DISTRIBUTION OF SATELLITE GALAXIES IN HIGH-REDSHIFT GROUPS

We use galaxy groups at redshifts between 0.4 and 1.0 selected from the Great Observatories Origins Deep Survey to study the color-morphological properties of satellite galaxies and investigate possible alignment between the distribution of the satellites and the orientation of their central galaxy. We confirm the bimodal color and morphological-type distribution for satellite galaxies at this redshift range: the red and blue classes correspond to the early and late morphological types, respectively, and the early-type satellites are on average brighter than the late-type ones. Furthermore, there is a morphological conformity between the central and satellite galaxies: the fraction of early-type satellites in groups with an early-type central is higher than those with a late-type central galaxy. This effect is stronger at smaller separations from the central galaxy. We find a marginally significant signal of alignment between the major axis of the early-type central galaxy and its satellite system, while for the late-type centrals no significant alignment signal is found. We discuss the alignment signal in the context of shape evolution of groups.
UNIVERSITY STUDENTS’ KNOWLEDGE AND MISCONCEPTIONS ABOUT CELL STRUCTURE AND FUNCTIONS

This study aims to assess the level of understanding of biology students and to identify their misconceptions about cell concepts. Participants of the study (n=160) were students enrolled in biology undergraduate level. Data analysis showed that the students had cell-related misconceptions. The misconceptions were found in four basic competencies of the cell concepts. The most common misconceptions (55.68%) among students are those related to the relationship between the structure and function of the nucleus and endoplasmic reticulum. We denote that most of the students have assimilated the concepts related to the chemical constituents of the cell. There are several potential factors that cause the occurrence of misconceptions among the participants in this study, including low retention of knowledge obtained in previous school levels, lack of learning resources, incomprehensible terms, and low interest of biology students in cell concepts. Article visualizations:
LHC Bounds on UV-Complete Models of Dark Matter

We analyze the sensitivity of searches for dark matter in the jets and missing energy channel in the case where the particle mediating interactions between hadronic matter and DM is collider accessible. We consider all tree level UV completions of interactions between fermion DM and quarks which contribute to direct detection, and derive bounds which apply to elastic or inelastic scattering dark matter explanations of direct detection signals. We find that studies based on effective operators give robust bounds when the mediator is heavy enough to resonantly produce the final state in question.
Existence of bound and ground states for fractional coupled systems in $\mathbb{R}^{N}$

In this work we consider the following class of nonlocal linearly coupled systems involving Schr\"{o}dinger equations with fractional laplacian $$ \left\{ \begin{array}{lr} (-\Delta)^{s_{1}} u+V_{1}(x)u=f_{1}(u)+\lambda(x)v, & x\in\mathbb{R}^{N}, (-\Delta)^{s_{2}} v+V_{2}(x)v=f_{2}(v)+\lambda(x)u, & x\in\mathbb{R}^{N}, \end{array} \right. $$ where $(-\Delta)^{s}$ denotes de fractional Laplacian, $s_{1},s_{2}\in(0,1)$ and $N\geq2$. The coupling function $\lambda:\mathbb{R}^{N} \rightarrow \mathbb{R}$ is related with the potentials by $|\lambda(x)|\leq \delta\sqrt{V_{1}(x)V_{2}(x)}$, for some $\delta\in(0,1)$. We deal with periodic and asymptotically periodic bounded potentials. On the nonlinear terms $f_{1}$ and $f_{2}$, we assume "superlinear" at infinity and at the origin. We use a variational approach to obtain the existence of bound and ground states without assuming the well known Ambrosetti-Rabinowitz condition at infinity. Moreover, we give a description of the ground states when the coupling function goes to zero.