Miracle-dz/UniFAR-FTUs huggingface dataset:
Adequate subgroups

Let l be a prime, and let Γ be a finite subgroup of GLn(Fl) = GL(V ). With these assumptions we say that Condition (C) holds if for every irreducible Γ-submodule W ⊂ ad V there exists an element g ∈ Γ with an eigenvalue α such that tr eg,αW 6= 0. Here, eg,α denotes the projection to the generalised α-eigenspace of g. This condition arises in the definition of adequacy in section 2. Let Γ denote the subset of Γ consisting of the elements that are semisimple (i.e. of order prime to l).
Construction of minimal skew products of amenable minimal dynamical systems

For an amenable minimal topologically free dynamical system $\alpha$ of a group on a compact metrizable space $Z$ and for a compact metrizable space $Y$ satisfying a mild condition, we construct a minimal skew product extension of $\alpha$ on $Z\times Y$. This generalizes a result of Glasner and Weiss. We also study the pure infiniteness of the crossed products of minimal dynamical systems arising from this result. In particular, we give a generalization of a result of R{\o}rdam and Sierakowski.
A review exploring coach knowledge, attitudes/beliefs and behaviours towards low energy availability in athletes

Coaches are important figures of influence with potential to create environments that influence athlete health and performance outcomes. Ideally, coaches provide supportive environments that lead to performance optimisation and long-term health. Coaches who employ language and behaviours that overemphasise body composition and/or provide misinformed nutrition advice may predispose athletes to low energy availability (LEA) and the associated health consequences. Having a clear understanding of current knowledge, attitudes and beliefs of coaches with regard to LEA is required to guide future coach education/support initiatives to optimise athlete health and performance. Thus, the aim of this investigation was to systematically review published literature regarding coach knowledge, attitudes/beliefs and behaviours of LEA. Data from 20 eligible studies was extracted into predetermined categories according to coach ‘knowledge‘; ‘attitudes/ beliefs’; and ‘behaviours’ regarding LEA/Relative Energy Deficiency in Sport/Female Athlete Triad and/or eating disorders and/or disordered eating. Any single study could provide outcomes to inform one or multiple of these categories. The majority of results were drawn from studies conducted prior to LEA being defined as a concern for athlete health, which limited our understanding of the contemporary knowledge, attitudes/eliefs and behaviours of coaches on this important issue. That said, indications of gaps in coach knowledge and the employment of inappropriate attitudes/beliefs and behaviours regarding issues associated with LEA were evident. An opportunity exists for key stakeholders to develop comprehensive coach education frameworks, which equip coaches with the adequate capability, opportunity and motivation to support athlete health and avoid the consequences of LEA.
On a local mass dimension one Fermi field of spin one-half and the theoretical crevice that allows it

Since the 1928 seminal work of Dirac, and its subsequent development by Weinberg, a view is held that there is a unique Fermi field of spin one-half. It is endowed with mass dimension three-half. Combined, these characteristics profoundly affect the phenomenology of the high energy physics, astrophysics, and cosmology. We here present a counter example by providing a local, mass dimension one, Fermi field of spin one-half. The theory, inter alia, thus allows dimensionless quartic self interaction for the new fermions, and its only other dimensionless coupling is quadratic in the new fermions and in the standard-model scalar field. For these reasons, the immediate application of the new theory resides in the dark-matter sector of physical reality. The lowest-mass associated new particle may leave its unique signature at the Large Hadron Collider. We discuss in detail the theoretical crevice that allows the existence of the new quantum field.
Morse functions to graphs and topological complexity for hyperbolic $3$-manifolds

Scharlemann and Thompson define the width of a 3-manifold M as a notion of complexity based on the topology of M. Their original definition had the property that the adjacency relation on handles gave a linear order on handles, but here we consider a more general definition due to Saito, Scharlemann and Schultens, in which the adjacency relation on handles may give an arbitrary graph. We show that for compact hyperbolic 3-manifolds, this is linearly related to a notion of metric complexity, based on the areas of level sets of Morse functions to graphs, which we call Gromov area.
Upper Tails for Edge Eigenvalues of Random Graphs

In this note we prove a precise large deviation principle for the largest and second largest eigenvalues of a sparse Erd\H{o}s-R\'enyi graph. Our arguments rely on various recent breakthroughs in the study of mean field approximations for large deviations of low complexity non-linear functions of independent Bernoulli variables and solutions of the associated entropic variational problems.
RANDOM MATRICES WITH SLOW CORRELATION DECAY

We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.
Factors affecting Firm Value of Miscellaneous Industry Companies on Indonesia Stock Exchange

The purpose of this research is to analyze the influence of leverage, dividend policy, effectiveness, efficiency and firm size to firm value with Ln stock price proxy, and compare it to prior research that correlates with this research. Data used in this research is the annual financial statements of miscellaneous industry companies, which is listed in Indonesia Stock Exchange 2012-2020 period. The sampling method used in this research is purposive sampling, which 5 companies met the criteria, and analyzed using panel data with fixed effect model. The result of this research indicates that leverage, dividend policy, efficiency and firm size don’t influence firm value, while efficiency has an influence on firm value.
Complex cellular structures

We introduce the notion of a \emph{complex cell}, a complexification of the cells/cylinders used in real tame geometry. Complex cells are equipped with a natural notion of holomorphic extension, and the hyperbolic geometry of a cell within its extension provides the class of complex cells with a rich geometric function theory absent in the real case. We use this to prove a complex analog of the cellular decomposition theorem of real tame geometry. In the algebraic case we show that the complexity of such decompositions depends polynomially on the degrees of the equations involved. Using this theory, we sharpen the Yomdin-Gromov algebraic lemma on $C^r$-smooth parametrizations of semialgebraic sets: we show that the number of $C^r$ charts can be taken to be polynomial in the smoothness order $r$ and in the complexity of the set. The algebraic lemma was initially invented in the work of Yomdin and Gromov to produce estimates for the topological entropy of $C^\infty$ maps. Combined with work of Burguet, Liao and Yang, our refined version establishes an optimal sharpening of these estimates for \emph{analytic} maps, in the form of tight bounds on the tail entropy and volume growth. This settles a conjecture of Yomdin who proved the same result in dimension two in 1991. A self-contained proof of these estimates using the refined algebraic lemma is given in an appendix by Yomdin. The algebraic lemma has more recently been used in the study of rational points on algebraic and transcendental varieties. We use the theory of complex cells in these two directions. In the algebraic context we prove a sharpening of a result of Heath-Brown on interpolating rational points in algebraic varieties. In the transcendental context we prove an interpolation result for (unrestricted) logarithmic images of subanalytic sets.
On product of difference sets for sets of positive density

In this paper we prove that given two sets $E_1,E_2 \subset \mathbb{Z}$ of positive density, there exists $k \geq 1$ which is bounded by a number depending only on the densities of $E_1$ and $E_2$ such that $k\mathbb{Z} \subset (E_1-E_1)\cdot(E_2-E_2)$. As a corollary of the main theorem we deduce that if $\alpha,\beta > 0$ then there exist $N_0$ and $d_0$ which depend only on $\alpha$ and $\beta$ such that for every $N \geq N_0$ and $E_1,E_2 \subset \mathbb{Z}_N$ with $|E_1| \geq \alpha N, |E_2| \geq \beta N$ there exists $d \leq d_0$ a divisor of $N$ satisfying $d \, \mathbb{Z}_N \subset (E_1-E_1)\cdot(E_2-E_2)$.
A Positive Feedback Between Crustal Thickness and Melt Extraction for the Origin of the Martian Dichotomy

A North/South difference in crustal thickness is likely at the origin of the Martian dichotomy in topography. Recent crustal thickness maps were obtained by inversion of topography and gravity data seismically anchored at the InSight station. On average, the Martian crust is 51–71 km thick with a southern crust thicker by 18–28 km than the northern one. The origin of this crustal dichotomy is still debated although the hypothesis of a large impact is at present very popular. Here, we propose a new mechanism for the formation of this dichotomy that involves a positive feedback between crustal growth and mantle melting. As the crust is enriched in heat‐producing elements, the lid of a one‐plate planet is hotter and thinner where the crust is thicker, inducing a larger amount of partial melt below the lid and hence a larger rate of melt extraction and crustal growth. We first demonstrate analytically that larger wavelength perturbations, that is, hemispherical perturbations, grow faster because smaller wavelengths are more attenuated by thermal diffusion. We then use a parameterized thermal evolution model with a well‐mixed mantle topped by two different lids characterized by their thermal structures and thicknesses to study the growth of the crust in the two hemispheres. Our results demonstrate that this positive feedback can generate a significant crustal dichotomy.
Noncommutative harmonic analysis on semigroups

In this paper we obtain some noncommutative multiplier theorems and maximal inequalities on semigroups. As applications, we obtain the corresponding individual ergodic theorems. Our main results extend some classical results of Stein and Cowling on one hand, and simplify the main arguments of Junge-Le Merdy-Xu's related work [15].
Model Topoi and Motivic Homotopy Theory

Given a small simplicial category $\C$ whose underlying ordinary category is equipped with a Grothendieck topology $\tau$, we construct a model structure on the category of simplicially enriched presheaves on $\C$ where the weak equivalences are the local weak equivalences of the underlying (non-enriched) simplicial presheaves. We show that this model category is a $t$-complete model topos and describe the Grothendieck topology $[\tau]$ on the homotopy category of $\C$ that corresponds to this model topos. After we first review a proof showing that the motivic homotopy theory is not a model topos, we specialize this construction to the category of smooth schemes of finite type, which is simplicially enriched using the standard algebraic cosimplicial object, and compare the result with the motivic homotopy theory. We also collect some partial positive results on the exactness properties of the motivic localization functor.
Solvability of the $F_4$ Integrable System

It is shown that the $F_4$ rational and trigonometric integrable systems are exactly-solvable for {\it arbitrary} values of the coupling constants. Their spectra are found explicitly while eigenfunctions by pure algebraic means. For both systems new variables are introduced in which the Hamiltonian has an algebraic form being also (block)-triangular. These variables are invariant with respect to the Weyl group of $F_4$ root system and can be obtained by averaging over an orbit of the Weyl group. Alternative way of finding these variables exploiting a property of duality of the $F_4$ model is presented. It is demonstrated that in these variables the Hamiltonian of each model can be expressed as a quadratic polynomial in the generators of some infinite-dimensional Lie algebra of differential operators in a finite-dimensional representation. Both Hamiltonians preserve the same flag of polynomials and each subspace of the flag coincides with the finite-dimensional representation space of this algebra. Quasi-exactly-solvable generalization of the rational $F_4$ model depending on two continuous and one discrete parameters is found.
How Do Good Corporate Governance and Financial Performance Affect the Value of State-Owned Enterprises?

This study examines the effect of good corporate governance and financial performance on the value of state-owned enterprises (SEOs). The population of this study was all companies listed on the Indonesia stock exchange, with a sample of 20 SEOs companies in 2015-2019. The independent variables in this study were Good Corporate Governance with the Independent Board of Commissaries and the Audit Committee and financial performance with the Return on Equity proxy. The dependent variable in this study was the value of SEOs with the price to book value proxy. Hypotheses were tested using SPSS 21.0 software, and data were analysed using multiple linear regression tests. This study found that the Independent Board of Commissaries had a negative and significant effect on the value of SEOs; Audit Committee had a positive and significant effect on the value of SEOs. On the other side, ROE has a negative and insignificant effect on the value of SEOs.
Heat shock protein and gene regulation in goats during heat stress

Heat shock proteins (HSPs), also known as molecular chaperons are prominent stress markers. Heat shock proteins consist of highly conserved protein expressed at the time of stress, and play an important role in adaptation to the environmental stress. Although, the expression pattern of HSP70 gene is species and breed specific, variations in adaptation and thermal tolerance is due to the nature of environment and adaptive capacity of a species. The present study was conducted to evaluate the adaptive capability of different goat (Capra hircus) breeds, i.e. Jamunapari, Barbari, Jakhrana and Sirohi under peak dry summer. The targeted gene HSP70 (HSPA6) was evaluated for this purpose using specific primers. The expression of HSP70 gene and protein was estimated by RT PCR and ELISA kits respectively. The expression of HSP70 gene was found lowest in sirohi breeds implying that this breed was more adapted followed by Jakhrana, Barbari and Jamunapari during peak summer season. Whereas, the level of HSP70 protein in blood was significantly higher in Jamunapari, followed by Barbari, Jakhrana and lowest in Sirohi. These results indicated that, during adverse climatic stress the quantum of expression (HSP70 gene and protein) was more in Jamunapari. It is concluded that Sirohi breed is better adapted to heat stress than Jamunapari, Jakhrana and Barbari and HSP70 may be a potential molecular biomarker in the future for selection of climate resilient animals.
A generalization of prefactored compact schemes for advection equations

A generalized prefactorization of compact schemes aimed at reducing the stencil and improving the computational efficiency is proposed here in the framework of transport equations. By the prefactorization introduced here, the computational load associated with inverting multi-diagonal matrices is avoided, while the order of accuracy is preserved. The prefactorization can be applied to any centered compact difference scheme with arbitrary order of accuracy (results for compact schemes of up to sixteenth order of accuracy are included in the study). One notable restriction is that the proposed schemes can be applied in a predictor-corrector type marching scheme framework. Two test cases, associated with linear and nonlinear advection equations, respectively, are included to show the preservation of the order of accuracy and the increase of the computational efficiency of the prefactored compact schemes.
Enumeration of Grothendieck's dessins and KP hierarchy

Branched covers of the complex projective line ramified over $0,1$ and $\infty$ (Grothendieck's {\em dessins d'enfant}) of fixed genus and degree are effectively enumerated. More precisely, branched covers of a given ramification profile over $\infty$ and given numbers of preimages of $0$ and $1$ are considered. The generating function for the numbers of such covers is shown to satisfy a PDE that determines it uniquely modulo a simple initial condition. Moreover, this generating function satisfies an infinite system of PDE's called the KP (Kadomtsev-Petviashvili) hierarchy. A specification of this generating function for certain values of parameters generates the numbers of {\em dessins} of given genus and degree, thus providing a fast algorithm for computing these numbers.
Nonlinear evolution of ordinary frontal waves induced by low‐level potential vorticity anomalies

Linear, semi-geostrophic (SG) theory reveals the instability of steady fronts with low-level potential vorticity anomalies. Joy and Thorpe (1990) have shown in this context the most unstable normal modes to have sub-synoptic wavelenghts. The present study uses a primitive equation (PE) model to construct, at these wavelenghts and along the same fronts, the PE normal modes and extends the evolution tot he nonliner regime. IT is shown that PE normal modes have a structure similar to the original SG modes at the same given wavenumber. In the nonlinear experiments, two different kinds of behaviour are found, depending on the initial wavelenght of the perturbation, the frontal baroclinicity and the width of the potential vorticity anomaly. The first kind, and main finding of this study, is characterized by the inability of a barotropically unstable mode (in the energy sense) to lead to large pressure falls in the vortex. Such a mode, with its wavelenght smaller than the Rossby radius, is successful in breaking the frontal flow but saturates within two days. The other occurs when the wavelengh is larger than the Rossby radius. Then, it is shown that the initially significant barotropic contribution to the growth vanishes and the wave enters a phase of classical baroclinic growth. It is only when this second phase occurs that the frontal change in structure is accompanied by significant deepening of the surface low. IT saturates in a way similar to larger-scale baroclinic waves, by increasing the upper-level jet and shear.
Biophotonics determination of 6-benzylaminopurine (6-BAP) plant growth regulator using OFRR biosensor

The identification of pesticide and 6-benzylaminopurine (6-BAP) plant growth regulator was carried out using a label-free opto-fluidic ring resonator (OFRR) biosensor. The OFRR sensing platform is a recent advancement in opto-fluidic technology that integrates photonic sensing technology with microfluidics. It features quick detection time, small sample volume, accurate quantitative and kinetic results. The most predominant advantage of the OFRR integrated with microfluidics is that we can potentially realize the multi-channel and portable biosensor that detects numerous analytes simultaneously. Antisera for immunoassay were raised in rabbits against the 6-BAP-BSA conjugate. Using the immunization protocol and unknown cytokinin reacting with same antibody, comparable sensitivity and specificity were obtained. 6-BAP antibody was routinely used for cytokinin analysis. A sensitive and simple OFRR method with a good linear relationship was developed for the determination of 6-BAP. The detection limit was also examined. The biosensor demonstrated excellent reproducibility when periodically exposed to 6-BAP.
Uniqueness and factorization method for inverse elastic scattering with a single incoming wave

The first part of this paper is concerned with the uniqueness to inverse time-harmonic elastic scattering from bounded rigid obstacles in two dimensions. It is proved that a connected polygonal obstacle can be uniquely identified by the far-field pattern corresponding to a single incident plane wave. Our approach is based on a new reflection principle for the first boundary value problem of the Navier equation. In the second part, we propose a revisited factorization method to recover a rigid elastic body with a single far-field pattern.
Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth

We investigate a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn–Hilliard type equation for the phase field variable, a reaction diffusion equation for the nutrient concentration and a Brinkman type equation for the velocity field. These PDEs are endowed with homogeneous Neumann boundary conditions for the phase field variable, the chemical potential and the nutrient as well as a “no-friction” boundary condition for the velocity. The control represents a medication by cytotoxic drugs and enters the phase field equation. The aim is to minimize a cost functional of standard tracking type that is designed to track the phase field variable during the time evolution and at some fixed final time. We show that our model satisfies the basics for calculus of variations and we present first-order and second-order conditions for local optimality. Moreover, we present a globality condition for critical controls and we show that the optimal control is unique on small time intervals.
Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by d-sets

In the framework of the Laplacian transport, described by a Robin boundary value problem in an exterior domain in $\mathbb{R}^n$, we generalize the definition of the Poincare-Steklov operator to $d$-set boundaries, $n-2< d<n$, and give its spectral properties to compare to the spectra of the interior domain and also of a truncated domain, considered as an approximation of the exterior case. The well-posedness of the Robin boundary value problems for the truncated and exterior domains is given in the general framework of $n$-sets. The results are obtained thanks to a generalization of the continuity and compactness properties of the trace and extension operators in Sobolev, Lebesgue and Besov spaces, in particular, by a generalization of the classical Rellich-Kondrachov Theorem of compact embeddings for $n$ and $d$-sets.