Miracle-dz/UniFAR-FTUs huggingface dataset:
On quaternionic tori and their moduli space

Quaternionic tori are defined as quotients of the skew field $\mathbb{H}$ of quaternions by rank-4 lattices. Using slice regular functions, these tori are endowed with natural structures of quaternionic manifolds (in fact quaternionic curves), and a fundamental region in a $12$-dimensional real subspace is then constructed to classify them up to biregular diffeomorphisms. The points of the moduli space correspond to suitable \emph{special} bases of rank-4 lattices, which are studied with respect to the action of the group $GL(4, \mathbb{Z})$, and up to biregular diffeomeorphisms. All tori with a non trivial group of biregular automorphisms - and all possible groups of their biregular automorphisms - are then identified, and recognized to correspond to five different subsets of boundary points of the moduli space.
Robust attitude controller design for miniature quadrotors

This paper addresses the robust attitude control problem of miniature quadrotors. A simplified linear dynamical model is obtained for each attitude angle, whereas nonlinear dynamics, interaxis coupling, parameter perturbations, and external disturbances are considered as uncertainties. For each channel, a linear time‐invariant and decoupled robust controller are proposed based on a linear reduced‐order observer and a robust compensator. The observer is applied to estimate the angular velocities, and the robust compensator is introduced for reducing the effects of uncertainties. It is proven that the estimation errors of angular velocities and angular tracking errors can converge to the given neighborhood of the origin in a finite time. Experimental results on the miniature quadrotor are presented to verify the effectiveness of the proposed control approach. Copyright © 2015 John Wiley & Sons, Ltd.
Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field

We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor Fμν; the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor Tμν, suffice to reduce the general Fμν to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingly similar to the Reissner-Nordstr{öm one. This points to a connection between the black hole geometry and the cosmological solution here found, which is the analog of the known correlation between the Schwarzschild and the Kantowski-Sachs metrics. The configuration space is drastically modified by the presence of the magnetic charge from a 3D flat to a 3D pp wave geometry. We map the emerging linear and quadratic classical integrals of motion, to quantum observables. Along with the Wheeler-DeWitt equation these observables provide unique, up to constants, wave functions. The employment of a Bohmian interpretation of these quantum states results in deterministic (semi-classical) geometries most of which are singularity free.
In-situ deposition of tungsten oxide hole-contact by Hot-Wire CVD and its application in dopant-free heterojunction solar cells

The tungsten oxide (WO x ) thin films have been deposited by a novel hot filament oxidation-sublimation process and applied in the dopant-free heterojunction solar cells as the hole selective contacts. The oxygen flow ratio plays a significant role during the deposition process. With increasing the oxygen flow ratio from 1.7% to 6.7%, the morphology of WO x films changes from small cauliflower-like particles to large cluster accumulation, and the ratio of W6+ increases from 76.1% to 91.4% with the ratio of W5+ decreasing from 23.9% to 8.6%. The work function of WO x can be tailored in a range of 5.5–6.1 eV by increasing the oxygen flow ratio. Its optical band gap maintains above 3.2 eV with the conductivity of about 10−5 S·cm−1. We have applied the WO x films in dopant-free silicon heterojunction solar cells as the hole selective contact layer by replacing the p-type amorphous silicon layer. By taking advantage of the highly transparent WO x layer, a high photon-current density of 39.6 mA·cm−2 was achieved with the oxygen flow ratio of 1.7%. It is interesting to find that the optimum cell conversion efficiencies of 14.9% were obtained with the oxygen flow ratio of 1.7% and the thickness of 10–20 nm for the deposition of WO x layer. This work proves the feasibility and good potential of Hot-Wire CVD prepared WO x hole selective contact for efficient dopant-free silicon heterojunction solar cells.
Spectra of fuzzy sets of $S^1$

In this article we explore some aspects of Fourier analysis on fuzzy sets. This work was part of a broader project jointly with Professor Vittorio Cafagna which spanned over a few years between 1998 and 2005. Professor Cafagna passed away unexpectedly in 2007. His intellectual breadth and inspiring passion for mathematics is still very well alive today.
A lifting functor for toric sheaves

For a variety X which admits a Cox ring we introduce a functor from the category of quasi-coherent sheaves on $X$ to the category of graded modules over the homogeneous coordinate ring of $X$. We show that this functor is right-adjoint to the sheafification functor and therefore left-exact. Moreover, we show that this functor preserves torsion-freeness and reflexivity. For the case of toric sheaves we give a combinatorial characterization of its right-derived functors in terms of certain right-derived limit functors.
The Role of Environmental, Social, and Governance Performance on Attracting Foreign Ownership: Evidence from Saudi Arabia

This research aims to examine whether corporate social responsibility (CSR) and corporate governance (CG) attract foreign investors as key indicators of a firm’s sustainability. By adopting both stakeholder theory and legitimacy theory, it is assumed that a firm could build trustworthiness and legitimacy with its stakeholders by enhancing its environmental, social, and governance (ESG) performance. Using a sample of 110 firms from the Saudi stock market from different industries, this study employs both OLS and System-GMM estimation to test the effect of both ESG performance and CG on foreign investment in Saudi Arabia. The findings indicate that ESG performance positively affects foreign investment. Additionally, it is found that the corporate governance score has a greater effect than social and environmental scores. These empirical findings suggest that companies in Saudi Arabia should adopt global schemes to improve ESG performance to maximize the share of foreign investment, thus boosting the country’s economy and increasing the level of competitive advantages and sustainability.
Covid-19 Redefining School Leadership Practice in Zimbabwe

In Zimbabwean schools, it is now government policy to keep the learners in schools safe and learning. The Ministry of Primary and Secondary Education (MoPSE) has come up with a covid-19 response strategy to limit exposure to the disease and reduce the probability of its transmission amongst learners, teachers, and staff and school communities, minimize disruptions to learning and proposing measures to build back better and safer school environments.MoPSE has introduced various measures to ensure learners‟ continued right to education, including alternative learning programmes using radio, digital and online facilities and distribution of supplementary reading materials. This change has witnessed the operating environment in schools shifting suggesting the need for a corresponding shift in school leadership practices. It is because of this information above that this research set out to assess the new leadership practices that school heads in Masvingo urban district have adopted to cope with Covid-19.
Constructing Associative 3-folds by Evolution Equations

This paper gives two methods for constructing associative 3-folds in R^7, based around the fundamental idea of evolution equations, and uses these methods to construct examples of these geometric objects. The paper is a generalisation of the work by Joyce in math.DG/0008021, math.DG/0008155, math.DG/0010036 and math.DG/0012060 on special Lagrangian 3-folds in C^3. The two methods described involve the use of an affine evolution equation with affine evolution data and the area of ruled submanifolds. We first give a derivation of an evolution equation for associative 3-folds from which we derive an affine evolution equation using affine evolution data. We then use this on an example of such data to construct a 14-dimensional family of associative 3-folds. One of the main result of the paper is then an explicit solution of the system of differential equations generated in a particular case to give a 12-dimensional family of associative 3-folds. We also find that there is a straightforward condition that ensures that the associative 3-folds constructed are closed and diffeomorphic to S^1xR^2, rather than R^3. In the final section we define ruled associative 3-folds and derive an evolution equation for them. This then allows us to characterise a family of ruled associative 3-folds using two real analytic maps that must satisfy two partial differential equations. We finish by giving a means of constructing ruled associative 3-folds M from r-oriented two-sided associative cones M_0 such that M is asymptotically conical to M_0 with order O(r^{-1}).
Implementation of Bilinear Hamiltonian Interactions between Linear Quantum Stochastic Systems via Feedback

A number of recent works employ bilinear Hamiltonian interactions between Linear Quantum Stochastic Systems (LQSSs). Contrary to naturally occurring Hamiltonian interactions between physical systems, such interactions must be engineered. In this work, we propose a simple model for the implementation of an arbitrary bilinear interaction between two given LQSSs via a feedback interconnection.
Linear-Quadratic-Gaussian Mixed Mean-Field Games with Heterogeneous Input Constraints

We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex subsets $\Gamma_{k}$ of $\mathbb{R}^{m}. $ The decentralized strategies for individual agents and consistency condition system are represented in an unified manner through a class of mean-field forward-backward stochastic differential equations involving projection operators on $\Gamma_{k}$. The well-posedness of consistency system is established in both the local and global cases by the contraction mapping and discounting method respectively. Related $\varepsilon-$Nash equilibrium property is also verified.
The Hopf conjecture for manifolds with low cohomogeneity or high symmetry rank

We prove that the Euler characteristic of an even-dimensional compact manifold with positive (nonnegative) sectional curvature is positive (nonnegative) provided that the manifold admits an isometric action of a compact Lie group G with principal isotropy group H and cohomogeneity k such that k - (rankG - rank H) l.
Contact Structures on G_2-Manifolds and Spin 7-Manifolds

We show that there exist infinitely many pairwise distinct non- closed G2-manifolds (some of which have holonomy full G2) such that they admit co-oriented contact structures and have co-oriented contact submani- folds which are also associative. Along the way, we prove that there exists a tubular neighborhood N of every orientable three-submanifold Y of an ori- entable seven-manifold with spin structure such that for every co-oriented contact structure on Y , N admits a co-oriented contact structure such that Y is a contact submanifold of N. Moreover, we construct infinitely many pairwise distinct non-closed seven-manifolds with spin structures which ad- mit co-oriented contact structures and retract onto co-oriented contact sub- manifolds of co-dimension four.
The gap phenomenon in the dimension study of finite type systems

Several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the symmetries of geometric structures and differential equations. A general result clarifying this effect in the case when the structure is associated to a vector distribution, is proposed.
Continuity of attractors for a nonlinear parabolic problem with terms concentrating in the boundary

We analyze the dynamics of the flow generated by a nonlinear parabolic problem when some reaction and potential terms are concentrated in a neighborhood of the boundary. We assume that this neighborhood shrinks to the boundary as a parameter \epsilon goes to zero. Also, we suppose that the "inner boundary" of this neighborhood presents a highly oscillatory behavior. Our main goal here is to show the continuity of the family of attractors with respect to \epsilon. Indeed, we prove upper semicontinuity under the usual properties of regularity and dissipativeness and, assuming hyperbolicity of the equilibria, we also show the lower semicontinuity of the attractors at \epsilon=0.
Dependence of the Rossby Number on Helium and Metal Abundances

Convective turnover times, tau, are calculated for solar-type stars of the zero-age main-sequence models of VandenBerg and Poll (1989) with helium abundances = 0.22, 0.27, and 0.32 and metal abundances = 0.0169, 0.024, and 0.03. Emphasis is given to the possible dependence of turnover times on the chemical composition of a star. It is found that deviations in log tau from a mean dependence on the (B-V) color are less than + or - 0.1. Thus, the predicted shape of the log tau vs. (B-V) relation is quite robust. 15 refs.
Labial movement dynamics for speech

Interpreting central nervous system control of speech movement depends in part on understanding the detailed parameters of that movement. For example, the motor control significance of the often‐reported reflex responses elicited during speech depends upon whether the external eliciting stimuli generate mechanoreceptor activity that is comparable to that generated naturally by speech movements [cf., Caligiuri and Abbs, Society for Neurosciences (1984)]. Similarly, kinematic analyses of articulatory movement confined to average velocity without considering instantaneous velocity and acceleration are likely to be misleading insofar as the critical neuromotor actions are likely to be misinterpreted. For these reasons the labial dynamics for speech were investigated in five young adults. The maximum peak acceleration and velocity obtained during normal speech production were 544.9 cm/s2 and 39.7 cm/s, respectively, with means of 260.7 cm/s2 and 25.5 cm/s. Further analyses of the effects of increasing speaking.
The ρ parameter at three loops and elliptic integrals

We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the $\rho$ parameter. In particular, we present the calculation of the master integrals for which the corresponding differential equations do not factorize to first order. The homogeneous solutions to these differential equations are obtained in terms of hypergeometric functions at rational argument. These hypergeometric functions can further be mapped to complete elliptic integrals, and the inhomogeneous solutions are expressed in terms of a new class of integrals of combined iterative non-iterative nature.
On chemical distances and shape theorems in percolation models with long-range correlations

In this paper we provide general conditions on a one parameter family of random infinite subsets of Z^d to contain a unique infinite connected component for which the chemical distances are comparable to the Euclidean distances, focusing primarily on models with long-range correlations. Our results are in the spirit of those by Antal and Pisztora proved for Bernoulli percolation. We also prove a shape theorem for balls in the chemical distance under such conditions. Our general statements give novel results about the structure of the infinite connected component of the vacant set of random interlacements and the level sets of the Gaussian free field. We also obtain alternative proofs to the main results in arXiv:1111.3979. Finally, as a corollary, we obtain new results about the (chemical) diameter of the largest connected component in the complement of the trace of the random walk on the torus.
Homotopy types and geometries below Spec Z

After the first heuristic ideas about `the field of one element' F_1 and `geometry in characteristics 1' (J.~Tits, C.~Deninger, M.~Kapranov, A.~Smirnov et al.), there were developed several general approaches to the construction of `geometries below Spec Z'. Homotopy theory and the `the brave new algebra' were taking more and more important places in these developments, systematically explored by B. ~Toen and M. ~Vaquie, among others. This article contains a brief survey and some new results on counting problems in this context, including various approaches to zeta--functions and generalised scissors congruences. The new version includes considerable extensions and revisions suggested by I. Zakharevich.
Path large deviations for interacting diffusions with local mean-field interactions in random environment

We consider a system of N spins in random environment with a random local meanfield type interaction. Each spin has a fixed spatial position on the torus T, an attached random environment and a spin value in R that evolves according to a space and environment dependent Langevin dynamic. The interaction between two spins depends on the spin values, the spatial distance and the random environment of both spins. We prove the path large deviation principle from the hydrodynamic (or local mean-field McKean-Vlasov) limit and derive different expressions of the rate function for the empirical process and for the empirical measure of the paths. To this end we generalize an approach of Dawson and Gärtner.
Classical r-matrices via semidualisation

We study the interplay between double cross sum decompositions of a given Lie algebra and classical r-matrices for its semidual. For a class of Lie algebras which can be obtained by a process of generalised complexification we derive an expression for classical r-matrices of the semidual Lie bialgebra in terms of the data which determines the decomposition of the original Lie algebra. Applied to the local isometry Lie algebras arising in three-dimensional gravity, decomposition, and semidualisation yields the main class of non-trivial r-matrices for the Euclidean and Poincare group in three dimensions. In addition, the construction links the r-matrices with the Bianchi classification of three-dimensional real Lie algebras.
The Propagation of a Pulse in the Atmosphere

In a recent paper (Pekeris 1937) it has been shown that under certain assumed temperature distributions above 35 km. the atmosphere is found to have a period of free oscillation of nearly 12 solar hours. In this mode of oscillation, which will be referred to as the second mode, the pressure variations above and below 30 km. are in opposite phase. There is also another mode of free oscillation (the first mode) of a period of about 10 1/2 hr. , in which there is no reversal of phase in the pressure variation. A free period of 12 solar hours is required by Kelvin’s “resonance” theory of the semidiurnal variation of the barometer and the reversal of phase as well as the large amplitudes at great heights of the pressure variation in the second mode are in accordance with the interpretation of diurnal variation of the earth’s magnetic field by the “dynamo” theory (Chapman 1934). There is additional evidence about the free modes of oscillation of the atmosphere from the propagation of long waves, since, according to a theorem of G. I. Taylor (1936) there corresponds to every free mode a definite speed of long waves. Now the atmospheric wave which was caused by the Krakatoa eruption in 1883 travelled with a speed corresponding to the first mode, and the question arises whether the apparent lack of a second wave in the Krakatoa disturbance is evidence against the existence of the second mode. Qualitatively, it can be argued that a volcanic eruption which takes place at the ground would excite a higher amplitude in the first mode because in it the energy distribution is more concentrated toward the ground than in the second mode. This would follow from the general dynamical principle that one cannot excite a free mode by applying a pulse at a nodal point, as is strikingly manifested by the fact (Stoneley 1931) that the deeper the focus of an earthquake the smaller are the amplitudes of the surface (free) waves.
Correlation Similarity Measure based Document Clustering with Directed Ridge Regression

Correlation Preserving Indexing (CPI) can discover the intrinsic structures implanted in high-dimensional document space. To predict the result of one variable based on another variable is not suitable for all the situations since two variable prediction problems takes places. In this paper, Directed Ridge Regression is introduced to predict two or more variables which are highly correlated in high dimensional document space. Directed Ridge Regression is a statistical technique to estimate the relationship among the variables based on the Eigen values to find the similarity between the documents. The directed ridge estimator alters the diagonal elements of the Eigen values. The objective of the Directed Ridge Regression is to achieve efficient document clustering in similarity measure. Experimental results shows that compared to Correlation Preserving Indexing, the Directed Ridge Regression achieves efficient document clustering.
Arcsine Law as the Classical Limit for interacting Fock spaces

In the present paper we discuss how to generalize ``Quantum-Classical Correspondence'' by means of the notion of interacting Fock spaces, which associates algebraic probability theory and the theory of orthogonal polynomials of probability measures. As an application we show that the Arcsine Law is ``Classical Limit'' for interacting Fock spaces corresponnding to certain kind of symmetric probability measures such as q-Gaussians. We also discuss the case of the exponential distribution as a simple example of asymmetric probability measures.
Multiresolution wavelet analysis of Bessel functions of scale $\nu +1$

We identify multiresolution subspaces giving rise via Hankel transforms to Bessel functions. They emerge as orthogonal systems derived from geometric Hilbert-space considerations, the same way the wavelet functions from a multiresolution scaling wavelet construction arise from a scale of Hilbert spaces. We study the theory of representations of the C*-algebra O_{\nu+1} arising from this multiresolution analysis.
Empirical Likelihood Ratio Confidence Regions

than are those based on Student's t statistic. An effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable. The method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain. Algorithms exist for finding the unique global minimum at a superlinear rate of convergence. A byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points. The multivariate empirical likelihood regions are justified for functions of several means, such as variances, correlations and regression parameters and for statistics with linear estimating equations. An algorithm is given for computing profile empirical likelihoods for these statistics.