Miracle-dz/UniFAR-FTUs huggingface dataset:
Sistem Pendidikan Dayah Tradisional di Aceh

Dayah is the earliest educational institution in the archipelago. In the context of Aceh, dayah is not only a center for Islamic education, but also as a very important center for da'wah and social empowerment. In modern life, even though the dayah has not lost its role and function as a forum or study of science, even though many modern educational institutions have sprung up. Dayah as a center of traditional education in Aceh still survives without having to abandon its unique characteristics. The uniqueness of dayah education to date is its consistent education system. The focus of the study is the yellow book text in bare Arabic (without shakal). The education system commonly used in recitation and studying standard books in the dayah is the teacher reading the book, translating, then explaining the intent and purpose, while the students listen and pay attention to the reading with full concentration. For mubtadi students, the teacher usually reads slowly and translates word for word literally, so that they are easy to respond to and understand. In addition, the education system developed is Muzakarah or Munablood, Majlis Ta`lim and Muhadharah. In general, there are similarities in all dayahs regarding the main subjects taught, such as knowledge of Islamic law (Fiqh Science), grammar (Nahwu and Neuroscience), Tawhid and interpretation. Dayah has four significant uses as a center of religious learning, a bulwark against forces against colonial penetration, an agent of development and as a school for the community.
On the probabilistic well-posedness of the nonlinear Schrödinger equations with non-algebraic nonlinearities

We consider the Cauchy problem for the nonlinear Schrodinger equations (NLS) with non-algebraic nonlinearities on the Euclidean space. In particular, we study the energy-critical NLS on \begin{document}$ \mathbb{R}^d $\end{document} , \begin{document}$ d = 5,6 $\end{document} , and energy-critical NLS without gauge invariance and prove that they are almost surely locally well-posed with respect to randomized initial data below the energy space. We also study the long time behavior of solutions to these equations: (ⅰ) we prove almost sure global well-posedness of the (standard) energy-critical NLS on \begin{document}$ \mathbb{R}^d $\end{document} , \begin{document}$ d = 5, 6 $\end{document} , in the defocusing case, and (ⅱ) we present a probabilistic construction of finite time blowup solutions to the energy-critical NLS without gauge invariance below the energy space.
What produces the extended LINER-type emission in the NUGA galaxy NGC 5850?

(Abridged) The role of low ionization nuclear emission region (LINER) galaxies within the picture of active galactic nuclei (AGN) has been controversial. It is still not clear whether they host an AGN in a low accretion mode, or whether they are not active at all but dominated by alternative ionization mechanisms, namely shocks, winds/outflows, or photoionization by a post asymptotic giant branch (p-AGB) stellar population. The detection of extended LINER-like emission was often taken as evidence of ionization by stellar components but this has not been undisputed. We performed optical integral field spectroscopic observations on the central approx. 4 kpc of NGC 5850 using VIMOS at the VLT, which provides spatially-resolved spectra for the gas emission and the stellar continuum. We derive and analyse emission line and kinematic maps. We find the central few kpc of NGC 5850 to be dominated by extended LINER-like emission. The emission-line ratios that are sensitive to the ionization parameter increase with radial distance to the nucleus. Therefore, the extended LINER-like emission in NGC 5850 is dominated by ionization from distributed ionization sources, probably by stars on the p-AGB. The LINER-like region is surrounded by emission that is classed as 'composite', likely due to a mixture of a LINER-like ionization pattern and photoionization by low-level star formation. Two star-forming regions are present in the 21"x19" field of view. One of them is located approximately in the ring surrounding the kinematically decoupled core. The second one is close to the nucleus and is the origin of a region of decreased emission line ratios oriented radially outwards. We find the interstellar gas to have areas of steep velocity gradients and a complex kinematic morphology, probably caused by the lopsided (m=1) distribution of the gas. The inflow of gas toward the center appears possible.
Generation of semigroups for the thermoelastic plate equation with free boundary conditions

We consider the linear thermoelastic plate equations with free boundary conditions in uniform \begin{document}$ C^4 $\end{document} -domains, which includes the half-space, bounded and exterior domains. We show that the corresponding operator generates an analytic semigroup in \begin{document}$ L^p $\end{document} -spaces for all \begin{document}$ p\in(1, \infty) $\end{document} and has maximal \begin{document}$ L^q $\end{document} - \begin{document}$ L^p $\end{document} -regularity on finite time intervals. On bounded \begin{document}$ C^4 $\end{document} -domains, we obtain exponential stability.
Hidden Symmetries, Special Geometry and Quaternionic Manifolds

The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same special geometry that is known from nonlinear sigma models in N=2 supergravity theories. We discuss the symmetry structure of special real, complex and quaternionic spaces. Maps between these spaces are implemented via dimensional reduction. We analyze the emergence of extra and hidden symmetries. This analysis is then applied to homogeneous special spaces and the implications for the classification of homogeneous quaternionic spaces are discussed.
REDUCTIONS OF POINTS ON ALGEBRAIC GROUPS, II

Abstract Let A be the product of an abelian variety and a torus over a number field K, and let $$m \ge 2$$ be a square-free integer. If $\alpha \in A(K)$ is a point of infinite order, we consider the set of primes $\mathfrak p$ of K such that the reduction $(\alpha \bmod \mathfrak p)$ is well defined and has order coprime to m. This set admits a natural density, which we are able to express as a finite sum of products of $\ell$ -adic integrals, where $\ell$ varies in the set of prime divisors of m. We deduce that the density is a rational number, whose denominator is bounded (up to powers of m) in a very strong sense. This extends the results of the paper Reductions of points on algebraic groups by Davide Lombardo and the second author, where the case m prime is established.
Simple trapped-ion architecture for high-fidelity Toffoli gates

We discuss a simple architecture for a quantum toffoli gate implemented using three trapped ions. The gate, which, in principle, can be implemented with a single laser-induced operation, is effective under rather general conditions and is strikingly robust (within any experimentally realistic range of values) against dephasing, heating, and random fluctuations of the Hamiltonian parameters. We provide a full characterization of the unitary and noise-affected gate using three-qubit quantum process tomography.
Extensions and duality

For a fixed finite group $Q$ and semi-simple finite dimensional algebra $S$, we examine an equivalence between strongly $Q$-graded algebras (extensions) with identity component $S$ and $S^1$-gerbes on action groupoids of $Q$ on the set of isomorphism classes of simple objects of the category of $S$-modules. This clarifies the nature of the map considered in arXiv:1312.7316. Motivated by this and arXiv:0909.3140(2) we suggest and study a notion of extensions suitable to the case when $S$ is replaced by a Hopf algebra, in the sense that there is a bijection between extensions with "fiber" $H$ and $H^*$. In particular we focus on the case of $H$ equal to the group algebra of a finite group. When $K$ is abelian, the answer is particularly symmetric as duality of Hopf algebras does not take us outside of the category of groups.
The congruence 𝒴∗ on quasi completely regular semirings

A semiring [Formula: see text] is said to be a quasi-orthodox semiring if for any [Formula: see text], there exists some positive integer [Formula: see text] such that [Formula: see text]. In this paper, we investigate the congruence generated by [Formula: see text] on quasi completely regular semirings with and without the special conditions like being quasi-orthodox. We further establish that the interval which [Formula: see text] belongs to is [Formula: see text].
Bounds for discrete moments of Weyl sums and applications

We prove two bounds for discrete moments of Weyl sums. The first one can be obtained using a standard approach. The second one involves an observation how this method can be improved, which leads to a sharper bound in certain ranges. The proofs both build on the recently proved Vinogradov's Mean Value Theorem. We present two selected applications: First, we prove a new $k$-th derivative test for the number of integer points close to a curve by an exponential sum approach. This yields a stronger bound than existing results obtained via geometric methods, but it is only applicable for specific functions. As second application we prove a new improvement of the polynomial large sieve inequality for one-variable polynomials of degree $k\geq 2$.
Fault Diagnosis of Analog Electronic Circuits with Tolerances in Mind Design for testability with analysis of influence of components tolerance

This paper presents analysis of components toler- ance influence on fault diagnosis efficiency of analog electronic circuits. There has been proposed method of finding optimal fre- quency of input periodic excitation with simultaneous maximiza- tion of components tolerances in order to keep assumed level of diagnosis efficiency. There has been also proposed departure from classical "location after detection" schema. Combination of detec- tion and location in a single step can remarkably shorten diagno- sis time. The optimization process involves genetic algorithm.
Combining Extensions of the Hales-Jewett Theorem with Ramsey Theory in Other Structures

The Hales-Jewett Theorem states that given any finite nonempty set ${\mathbb A}$ and any finite coloring of the free semigroup $S$ over the alphabet ${\mathbb A}$ there is a variable word over ${\mathbb A}$ all of whose instances are the same color. This theorem has some extensions involving several distinct variables occurring in the variable word. We show that, when combined with a sufficiently well behaved homomorphism, the relevant variable word simultaneously satisfies a Ramsey-Theoretic conclusion in the other structure. As an example we show that if $\tau$ is the homomorphism from the set of variable words into the natural numbers which associates to each variable word $w$ the number of occurrences of the variable in $w$, then given any finite coloring of $S$ and any infinite sequence of natural numbers, there is a variable word $w$ whose instances are monochromatic and $\tau(w)$ is a sum of distinct members of the given sequence.Our methods rely on the algebraic structure of the Stone-Čech compactification of $S$ and the other semigroups that we consider. We show for example that if $\tau$ is as in the paragraph above, there is a compact subsemigroup $P$ of $\beta{\mathbb N}$ which contains all of the idempotents of $\beta{\mathbb N}$ such that, given any $p\in P$, any $A\in p$, and any finite coloring of $S$, there is a variable word $w$ whose instances are monochromatic and $\tau(w)\in A$. We end with a new short algebraic proof of an infinitary extension of the Graham-Rothschild Parameter Sets Theorem.
The conjugacy problem in GL (n,Z)

We present a new algorithm that, given two matrices in GL (n,Q) , decides if they are conjugate in GL (n,Z) and, if so, determines a conjugating matrix. We also give an algorithm to construct a generating set for the centraliser in GL (n,Z) of a matrix in GL (n,Q) . We do this by reducing these problems, respectively, to the isomorphism and automorphism group problems for certain modules over rings of the form OK[y]/(yl) , where OK is the maximal order of an algebraic number field and l∈N , and then provide algorithms to solve the latter. The algorithms are practical and our implementations are publicly available in Magma.
Asymptotic representation theory and the spectrum of a random geometric graph on a compact Lie group

Let $G$ be a compact Lie group, $N\geq 1$ and $L>0$. The random geometric graph on $G$ is the random graph $\Gamma(N,L)$ whose vertices are $N$ random points $g_1,\ldots,g_N$ chosen under the Haar measure of $G$, and whose edges are the pairs $\{g_i,g_j\}$ with $d(g_i,g_j)\leq L$, $d$ being the distance associated to the standard Riemannian structure on $G$. In this paper, we describe the asymptotic behavior of the spectrum of the adjacency matrix of $\Gamma(N,L)$, when $N$ goes to infinity. If $L$ is fixed and $N \to + \infty$ (Gaussian regime), then the largest eigenvalues of $\Gamma(N,L)$ converge after an appropriate renormalisation towards certain explicit linear combinations of values of Bessel functions. If $L = O(N^{-\frac{1}{\dim G}})$ and $N \to +\infty$ (Poissonian regime), then the random geometric graph $\Gamma(N,L)$ converges in the local Benjamini-Schramm sense, which implies the weak convergence in probability of the spectral measure of $\Gamma(N,L)$. In this situation, we explain how to compute the first moments of the limiting spectral measure by using the asymptotic representation theory of the group $G$. The computation of the higher moments relies on a conjecture on certain functionals of the irreducible representations of $G$, which we state at the end of the paper.
Approximating fractional derivative of the Gaussian function and Dawson's integral

A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial or discrete Fourier basis, we take an alternative approach which is based on expressing the Riemann-Liouville definition of the fractional integral for the semi-infinite axis in terms of a moment problem. As a result, fractional derivatives of the Gaussian function and Dawson's integral are expressed as a weighted sum of complex scaled Gaussian and Dawson's integral. Error bounds for the approximation are provided. Another distinct feature of the proposed method compared to the previous approaches, it can be extended to approximate partial derivative with respect to the order of the fractional derivative which may be used in PDE constraint optimization problems.
Women on Board and Firm Performance amidst Covid-19 Outbreak

The study examines the relationship between women on board and firm performance in Malaysian Capital Market amidst Covid-19 outbreak. The study also aims to investigate the effect of different types of industries namely Environmentally Sensitive Industry (ESI) and Customer Proximity Industry (CPI) on firm performance. The study employs OLS regression on top 100 companies listed under Bursa Malaysia for the year 2020. The findings reveal that gender diversity has a favorable and significant effect on the firm’s performance measured by Profit Margin (PM), Return on Asset (ROA) & Return on Equity (ROE) and ESI significantly affect firm performance. Meaning that the market places a high value on the involvement of women on boards of directors since it boosts the board's independence and profitability and the different types of industry play significant roles in firm performance. The findings of this study suggest the policymakers to enact suitable legislation requiring a diverse representation of genders on the board of directors.
THE VERY LARGE ARRAY 1.4 GHz SURVEY OF THE EXTENDED CHANDRA DEEP FIELD SOUTH: SECOND DATA RELEASE

Deep radio observations at 1.4 GHz for the Extended Chandra Deep Field South were performed in 2007 June through September and presented in a first data release. The survey was made using six separate pointings of the Very Large Array with over 40 hr of observation per pointing. In the current paper, we improve on the data reduction to produce a second data release (DR2) mosaic image. This DR2 image covers an area of about a third of a square degree, reaches a best rms sensitivity of 6 μJy, and has a typical sensitivity of 7.4 μJy per 2. ″8 by 1. ″6 beam. We also present a more comprehensive catalog, including sources down to peak flux densities of five or more times the local rms noise along with information on source sizes and relevant pointing data. We discuss in some detail the consideration of whether sources are resolved under the complication of a radio image created as a mosaic of separate pointings each suffering some degree of bandwidth smearing, and the accurate evaluation of the flux densities of such sources. Finally, the radio morphologies and optical/near-IR counterpart identifications are used to identify 17 likely multiple-component sources and arrive at a catalog of 883 radio sources, which is roughly double the number of sources contained in the first data release.
Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem

We investigate a singularly perturbed, non-convex variational problem arising in material science with a combination of geometrical and numerical methods. Our starting point is a work by Stefan Muller, where it is proven that the solutions of the variational problem are periodic and exhibit a complicated multi-scale structure. In order to get more insight into the rich solution structure, we transform the corresponding Euler-Lagrange equation into a Hamiltonian system of first order ODEs and then use geometric singular perturbation theory to study its periodic solutions. Based on the geometric analysis we construct an initial periodic orbit to start numerical continuation of periodic orbits with respect to the key parameters. This allows us to observe the influence of the parameters on the behavior of the orbits and to study their interplay in the minimization process. Our results confirm previous analytical results such as the asymptotics of the period of minimizers predicted by Muller. Furthermore, we find several new structures in the entire space of admissible periodic orbits.
Problems on invariants of knots and 3-manifolds

This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance. This list was made by editing open problems given in problem sessions in the workshop and seminars on `Invariants of Knots and 3-Manifolds' held at Kyoto in 2001.
From asymmetric to symmetric consumption opportunities: Extractions from common resources by privileged and underprivileged group members

In social dilemmas, asymmetric opportunities among actors can aggravate the conflict between individual and collective interests. We examine if and under what conditions redistributing extraction opportunities symmetrically fosters sustainable resource consumption. Participants in two studies (total n=640) completed a common resource game, first under asymmetric distribution of extraction opportunities (i.e., two advantaged group members could extract more than two disadvantaged group members) and then under symmetric distribution (i.e., all group members could extract the same amount). Advantaged (vs. disadvantaged) individuals took more from the resource in the asymmetric game and voted more often for the maintenance of the asymmetric system. Consumption was overall not more sustainable under symmetric (vs. asymmetric) distribution. We did not find evidence that these effects depend on the legitimacy of status positions. Of note, the symmetric game elicited higher satisfaction and fairness ratings in both status groups. The findings demonstrate how unequal access to resources fosters unequal consumption despite broad support for symmetry as the fairer system.
Constraint dynamics and gravitons in three dimensions

The complete non-linear three-dimensional Einstein gravity with gravitational Chern-Simons term and cosmological constant are studied in dreibein formulation. The constraints and their algebras are computed in an explicit form. From counting the number of first and second class constraints, the number of dynamical degrees of freedom, which equals to the number of propagating graviton modes, is found to be 1, regardless of the value of cosmological constant. I note also that the usual equivalence with Chern-Simons gauge theory does not work for general circumstances.
Transform Methods for Heavy-Traﬃc Analysis

The drift method was recently developed to study queueing systems in steady-state. It was successfully used to obtain bounds on the moments of the scaled queue lengths, that are asymptotically tight in heavy-traﬃc, in a wide variety of systems including generalized switches [11], input-queued switches [42, 41], bandwidth sharing networks [62], etc. In this paper we develop the use of transform techniques for heavy-traﬃc analysis, with a special focus on the use of moment generating functions. This approach simpliﬁes the proofs of the drift method, and provides a new perspective on the drift method. We present a general framework and then use the MGF method to obtain the stationary distribution of queue lengths in heavy-traﬃc in queueing systems that satisfy the Complete Resource Pooling condition. In particular, we study load balancing systems and generalized switches under general settings.
MASS TRANSFER IN BINARY STARS USING SMOOTHED PARTICLE HYDRODYNAMICS. II. ECCENTRIC BINARIES

Despite numerous efforts to better understand binary star evolution, some aspects of it remain poorly constrained. In particular, the evolution of eccentric binaries has remained elusive mainly because the Roche lobe formalism derived for circular binaries does not apply. Here we report the results of our smoothed particle hydrodynamic simulations of mass transfer in eccentric binaries using an alternate method in which we model only the outermost layers of the stars with appropriate boundary conditions. Using this technique, along with properly relaxed model stars, we characterize the mass transfer episodes of binaries with various orbital parameters. In particular, we show that these episodes can be described by Gaussians with an FWHM of ∼0.12Porb and that the peak rates occur after periastron, at an orbital phase of ∼0.58, independently of the eccentricity and mass of the stars. The accreted material is observed to form a rather sparse envelope around either or both stars. Although the fate of this envelope is not modeled in our simulations, we show that a constant fraction (∼5%) of the material transferred is ejected from the systems. We discuss this result in terms of the non-conservative mass transfer scenario. We suggest that our results could be incorporated in analytical and binary population synthesis studies to help better understand the evolution of eccentric binaries and the formation of exotic stellar populations.