Miracle-dz/UniFAR-FTUs huggingface dataset:
No Singular Modulus Is a Unit

A result of the 2nd-named author states that there are only finitely many complex multiplication (CM)-elliptic curves over $\mathbb{C}$ whose $j$-invariant is an algebraic unit. His proof depends on Duke’s equidistribution theorem and is hence noneffective. In this article, we give a completely effective proof of this result. To be precise, we show that every singular modulus that is an algebraic unit is associated with a CM-elliptic curve whose endomorphism ring has discriminant less than $10^{15}$. Through further refinements and computer-assisted arguments, we eventually rule out all remaining cases, showing that no singular modulus is an algebraic unit. This allows us to exhibit classes of subvarieties in ${\mathbb{C}}^n$ not containing any special points.
Asymmetric mass loading effect at Titan's ionosphere

Because of the fact that Titan does not possess an intrinsic magnetic field, the corotating plasma in the Saturnian magnetosphere can interact directly with the nitrogen-rich atmosphere of Titan. In this work we perform three-dimensional resistive MHD simulations of the interaction between Titan and the Saturnian magnetosphere. The magnetic field of Saturn is modeled as a dipole field located at the origin of a cylindrical coordinate system. Of particular interest is the mass loading effect in the vicinity of Titan. The pickup of atmospheric ions is strongly influenced by the ionization rate and scale lengths of the system. The fact that the ion gyroradius of the system is of the order of the radius of Titan has important consequences. Ions emerging from Titan's ionosphere at the hemisphere facing toward Saturn get lost back into the ionosphere, whereas ions at the opposite hemisphere may contribute to the satellite's mass loading by enhanced atmospheric sputtering. This results in an asymmetry of the mass loading patterns between the planet-facing hemisphere and the antiplanet hemisphere. For different mass loading ratios we investigate the effect of this asymmetry. By comparing our results with Voyager 1 measurements we conclude that a mass loading asymmetry could in principle provide an explanation of the observed deflection in the magnetic fields as well as the asymmetry of the plasma flow in the wake region.
A new look at the problem of gauge invariance in quantum field theory

Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in order to obtain a physically correct result. In this paper we will examine this problem and determine why a theory that is supposed to be gauge invariant produces non-gauge invariant results.
Dynamic anisotropy and localization in elastic lattice systems

This paper presents an analytical study and numerical simulations concerning the dynamic anisotropy of lattice systems in vector problems of elasticity. Connections are made with models of optics involving interaction of light with a small aperture and aberration effects. Special attention is given to standing waves possessing directional localization of different kinds. We analyze a special class of waveforms corresponding to saddle points on the dispersion surfaces. Furthermore, a modeling algorithm is developed to design a structured slab of finite thickness, which possesses focusing properties for waves within a certain frequency range.
Robust delay-dependent sliding mode control for uncertain time-delay systems

This paper is devoted to designing robust linear sliding surfaces for linear systems with time-delay in the presence of mismatched parametric uncertainty in the state model. A sufficient condition which is dependent on the size of the the delay is given for the existence of linear sliding surfaces in terms of LMIs. A reaching motion controller is also proposed for such systems by means of the reaching law.
A SELF-SIMILAR EXPANSION MODEL FOR USE IN SOLAR WIND TRANSIENT PROPAGATION STUDIES

Since the advent of wide-angle imaging of the inner heliosphere, a plethora of techniques have been developed to investigate the three-dimensional structure and kinematics of solar wind transients, such as coronal mass ejections, from their signatures in single- and multi-spacecraft imaging observations. These techniques, which range from the highly complex and computationally intensive to methods based on simple curve fitting, all have their inherent advantages and limitations. In the analysis of single-spacecraft imaging observations, much use has been made of the fixed ϕ fitting (FPF) and harmonic mean fitting (HMF) techniques, in which the solar wind transient is considered to be a radially propagating point source (fixed ϕ, FP, model) and a radially expanding circle anchored at Sun centre (harmonic mean, HM, model), respectively. Initially, we compare the radial speeds and propagation directions derived from application of the FPF and HMF techniques to a large set of STEREO/Heliospheric Imager (HI) observations. As the geometries on which these two techniques are founded constitute extreme descriptions of solar wind transients in terms of their extent along the line of sight, we describe a single-spacecraft fitting technique based on a more generalized model for which the FP and HM geometries form the limiting cases. In addition to providing estimates of a transient's speed and propagation direction, the self-similar expansion fitting (SSEF) technique provides, in theory, the capability to estimate the transient's angular extent in the plane orthogonal to the field of view. Using the HI observations, and also by performing a Monte Carlo simulation, we assess the potential of the SSEF technique.
Bounds for the regularity of edge ideal of vertex decomposable and shellable graphs

In this paper we give upper bounds for the regularity of edge ideal of some classes of graphs in terms of invariants of graph. We introduce two numbers $a'(G)$ and $n(G)$ depending on graph $G$ and show that for a vertex decomposable graph $G$, $\reg(R/I(G))\leq \min\{a'(G),n(G)\}$ and for a shellable graph $G$, $\reg(R/I(G))\leq n(G)$. Moreover it is shown that for a graph $G$, where $G^c$ is a $d$-tree, we have $\pd(R/I(G))=\max_{v\in V(G)} \{\deg_G(v)\}$.
Separate contributions to the pyroelectricity in poly(vinylidene fluoride) from the amorphous and crystalline phases, as well as from their interface

New selective poling schemes for polar semicrystalline polymers are described, and appropriate poling fields and temperatures are specified. In the following investigation of the pyroelectric response and the thermally stimulated depolarization (TSD), poly(vinylidene fluoride) is used as an example for a semicrystalline ferroelectric polymer. It is shown that the amorphous and the crystalline phase, as well as the interface between them contribute to the pyroelectric effect. From dynamic pyroelectrical measurements and TSD experiments, the permanent polarization of the dipoles in the crystalline phase, the frozen-in polarization of the dipoles in the amorphous phase, and the effect of the excess charges of the Maxwell– Wagner interface polarization can be identified. With the proposed selective poling schemes (poling temperatures below and/or above the glass transition temperature, as well as poling fields lower and/or higher than the coercive field), it is possible to clearly separate the respective cont.
Extension of Whitney jets of controlled growth

We revisit Whitney's extension theorem in the ultradifferentiable Roumieu setting. Based on the description of ultradifferentiable classes by weight matrices, we extend results on how growth constraints on Whitney jets on arbitrary compact subsets in Rn are preserved by their extensions to Rn . More precisely, for any admissible class C of ultradifferentiable functions on Rn we determine a class C′ such that all ultradifferentiable Whitney jets of class C′ on arbitrary compact subsets admit extensions in C . The class C′ can be explicitly computed from C .
Green’s formula and a Dirichlet-to-Neumann operator for fractional-order pseudodifferential operators

Abstract This article treats boundary value problems for the fractional Laplacian , a > 0, and more generally for classical pseudodifferential operators (ψdo’s) P of order 2a with even symbol, applied to functions on a smooth subset Ω of . There are several meaningful local boundary conditions, such as the Dirichlet and Neumann conditions , k = 0, 1, where . We show a new Green’s formula where B is a first-order ψdo on depending on the first two terms in the symbol of P. Moreover, we show in the elliptic case how the Poisson-like solution operator KD for the nonhomogeneous Dirichlet problem is constructed from P+ in the factorization obtained in earlier work. The Dirichlet-to-Neumann operator is derived from this as a first-order ψdo on , with an explicit formula for the symbol. This leads to a characterization of those operators P for which the Neumann problem is Fredholm solvable.
Thermodynamic theory of the lead zirconate-titanate solid solution system

Abstract Compositions within the lead zirconate-titanate (PZT) solid solution system have been extensively used in polycrystalline ceramic form in a wide range of piezoelectric transducer application. However, the growth of good quality PZT single crystals for compositions across the entire phase diagram has not been accomplished. Due to the lack of single crystal data, an understanding of the properties of ceramic PZT has been limited. If the single domain (intrinsic) properties of PZT could be determined, then the extrinsic contributions (e.g., domain wall and defect motions) to the ceramic properties could be separated from the intrinsic contributions. The purpose of this research has been to develop a thermodynamic phenomenological theory to model the phase transitions and single domain properties of the PZT system. A two-sublattice theory, where each sublattice has a separate polarization, was used to account for the ferroelectric and antiferroelectric phases. An additional order parameter was also i.
Implicit Event Argument Extraction With Argument-Argument Relational Knowledge

As a challenging sub-task of event argument extraction, implicit event argument extraction seeks to identify document-level arguments that play direct or implicit roles in a given event. Prior work mainly focuses on capturing direct relations between arguments and the event trigger; however, the lack of reasoning ability imposes limitations to the extraction of implicit arguments. In this work, we propose an Argument-argument Relation-enhanced Event Argument extraction (AREA) learning framework to tackle this issue through reasoning in event frame-level scope. The proposed method leverages related arguments of the expected one as clues, and utilizes such argument-argument dependencies to guide the reasoning process. To bridge the distribution gap between oracle knowledge used in the training phase and the imperfect related arguments in the test stage, we introduce a conventional knowledge distillation strategy to drive a final model that can work without extra inputs by mimicking the behaviour of a well-informed teacher model. In addition, considering that conventional knowledge distillation methods transfer knowledge individually, we integrate it with a novel relational knowledge distillation mechanism to explicitly capture the structural mutual argument-argument relation. Moreover, since the training process is not compatible with the real situation, a curriculum learning method is further introduced to make the training process smoother. Experimental results demonstrate that the learning framework obtains state-of-the-art performance on the RAMS and Wikievents datasets. Ablation study and further discussion also show it could handle long-range dependency and implicit argument problems effectively.
Stratification of algebraic quotients and character varieties.

In this paper, we study a weaker version of algebraic quotient for the action of an algebraic group on an algebraic variety that is well behaved under stratification. Focusing on the topological properties of these quotients, we obtain a series of results about their structure and uniqueness. As an application, we compute the $K$-theory image of the Hodge structure of $\mathrm{SL}_2(\mathbb{C})$-character varieties for free groups and surface groups, as well as their counterparts with punctures of Jordan type.
Isomorphism Invariants for Multivariable C*-Dynamics

To a given multivariable C*-dynamical system $(A, \al)$ consisting of *-automorphisms, we associate a family of operator algebras $\alg(A, \al)$, which includes as specific examples the tensor algebra and the semicrossed product. It is shown that if two such operator algebras $\alg(A, \al)$ and $\alg(B, \be)$ are isometrically isomorphic, then the induced dynamical systems $(\hat{A}, \hat{\al})$ and $(\hat{B}, \hat{\be})$ on the Fell spectra are piecewise conjugate, in the sense of Davidson and Katsoulis. In the course of proving the above theorem we obtain several results of independent interest. If $\alg(A, \al)$ and $\alg(B, \be)$ are isometrically isomorphic, then the associated correspondences $X_{(A, \al)}$ and $X_{(B, \be)}$ are unitarily equivalent. In particular, the tensor algebras are isometrically isomorphic if and only if the associated correspondences are unitarily equivalent. Furthermore, isomorphism of semicrossed products implies isomorphism of the associated tensor algebras. In the case of multivariable systems acting on C*-algebras with trivial center, unitary equivalence of the associated correspondences reduces to outer conjugacy of the systems. This provides a complete invariant for isometric isomorphisms between semicrossed products as well.
Defective sewing stitch semantic segmentation using DeeplabV3+ and EfficientNet

Defective stitch inspection is an essential part of garment manufacturing quality assurance. Traditional mechanical defect detection systems are effective, but they are usually customized with handcrafted features that must be operated by a human. Deep learning approaches have recently demonstrated exceptional performance in a wide range of computer vision applications. The requirement for precise detail evaluation, combined with the small size of the patterns, undoubtedly increases the difficulty of identification. Therefore, image segmentation (semantic segmentation) was employed for this task. It is identified as a vital research topic in the field of computer vision, being indispensable in a wide range of real-world applications. Semantic segmentation is a method of labeling each pixel in an image. This is in direct contrast to classification, which assigns a single label to the entire image. And multiple objects of the same class are defined as a single entity. DeepLabV3+ architecture, with encoder-decoder architecture, is the proposed technique. EfficientNet models (B0-B2) were applied as encoders for experimental processes. The encoder is utilized to encode feature maps from the input image. The encoder's significant information is used by the decoder for upsampling and reconstruction of output. Finally, the best model is DeeplabV3+ with EfficientNetB1 which can classify segmented defective sewing stitches with superior performance (MeanIoU: 94.14%).
Wiener index, Harary index and Hamiltonicity of graphs

In this paper, we prove tight sufficient conditions for traceability and Hamiltonicity of connected graphs with given minimum degree, in terms of Wiener index and Harary index. We also prove some result on Hamiltonicity of balanced bipartite graphs in the similar fashion. In two recent papers \cite{LDJ2016,LDJ2017}, Liu et al. corrected some previous work on traceability of connected graphs in terms of Wiener index and Harary index, respectively, such as \cite{HW2013,Y2013}. We generalize these results and give short and unified proofs. All results in this paper are best possible.
Mixed Convection Between Two Vertically Eccentric Rotating Spheres with Time-Dependent Angular Velocities

The mixed convection heat transfer and the transient motion of a viscous, incompressible fluid in an annulus between two vertically eccentric spheres maintained at different surface temperatures and rotating about a common axis with different angular velocities is considered numerically by solving the coupled, time-dependent, nonlinear, partial differential Navier–Stokes and energy equations in which the angular velocities can be arbitrary functions of time and a uniform gravitational field acts parallel to the axis of rotation. The density in the body force term of the momentum equation is modeled by the Boussinesq approximation and viscous dissipation is also considered. The application in most mixers in industry and their starting and stopping movements suggests exponential and sinusoidal angular velocities as practical. The resulting flow pattern, temperature distribution, and heat transfer characteristics for the case of these angular velocities, for example, are presented. It is observed that the ef.
INFLUENCING FACTORS OF BANK EMPLOYEES' MOTIVATION AND ITS IMPACT ON EMPLOYEES' PERFORMANCE

In this globalization era, banking institutions are facing competition in the marketplace. The demands of the customers are changing immensely day by day. Integration and globalization have become closer and closer to every firm in the competitive market. The main purpose of this study is to determine the motivational factors of bank employees that are related to employees' performance in the working place. The study was qualitative and was conducted using different sources to find out the motivational factors and their impact on employee performance. The researchers focus on the intrinsic and extrinsic motivation of the employees. For this study, data have been collected from previous studies and different sources like the ABDC database, Scopus database, Emerald database, ABS database, Springer database, and previous banking profiles. The study showed that employee empowerment, job security, emotional intelligence, attractive compensation package, and training and development have a positive and significant impact on creating motivation among the employees, which creates better performance in work. Based on the findings of this study, the organization should provide another attractive motivational factor and change HR policies and procedures to create employee motivation. Recommendations were also made for improvement in a certain area, creating motivation for better performance of bank employees in Bangladesh.
Construction of Green's functions from an exact S matrix

The bootstrap program for determining Green's functions from an exact $S$ matrix is carried out for the simplest soliton field theory of a scalar field with $S$-matrix operator $S={(\ensuremath{-}1)}^{\frac{N(N\ensuremath{-}1)}{2}}$, where $N$ is the total number operator. Despite the formal simplicity of the $S$ matrix, the Green's functions derived have a rich structure. The results can be checked since this field theory is none other than that of the order variable of the Ising model in the scaling limit above the critical temperature.
Outermost apparent horizons diffeomorphic to unit normal bundles

Given a submanifold $S \subset \mathbb R^n$ of codimension at least three, we construct an asymptotically Euclidean Riemannian metric on $\mathbb R^n$ with nonnegative scalar curvature for which the outermost apparent horizon is diffeomorphic to the unit normal bundle of $S$.
Temperature dependent resistance of magnetic tunnel junctions as a quality proof of the barrier

Tunnel junctions of Co(10 nm)/AlOx (nominally 2 nm)/Co(20 nm) have been prepared by molecular beam epitaxy applying a shadow mask technique in conjunction with an UV light-assisted oxidation process of the AlOx barrier. The quality of the AlOx barrier has been proven by x-ray photoelectron spectroscopy and temperature dependent tunneling magnetoresistance (TMR) measurements. Optimum-oxidized tunnel junctions show a TMR of 20% at 285 K and up to 36% at 100 K. At 285 K the TMR values as a function of oxidation time are not symmetric about the optimum time. For underoxidized junctions the TMR is reduced more strongly than for overoxidized junctions. The temperature dependence of the junction’s resistance is a clear and reliable indicator whether pinholes (or imperfections) contribute to the conduction across the barrier.
A construction of pseudo-Anosov braids with small normalized entropies

Let $b$ be a pseudo-Anosov braid whose permutation has a fixed point and let $M_b$ be the mapping torus by the pseudo-Anosov homeomorphism defined on the genus $0$ fiber $F_b$ associated with $b$. This paper describes a structure of the fibered cone $\mathcal{C}$ of $F$ for $M_b$. We prove that there is a $2$-dimensional subcone $\mathcal{C}_0$ contained in the fibered cone $ \mathcal{C}$ of $F_b$ such that the fiber $F_a$ for each primitive integral class $a \in \mathcal{C}_0$ has genus $0$. We also give a constructive description of the monodromy $ \phi_a: F_a \rightarrow F_a$ of the fibration on $M_b$ over the circle, and consequently provide a construction of many sequences of pseudo-Anosov braids with small normalized entropies. As an application we prove that the smallest entropy among skew-palindromic braids with $n$ strands is comparable to $1/n$, and the smallest entropy among elements of the odd/even spin mapping class groups of genus $g$ is comparable to $1/g$.
The Impact of Electronic Cigarettes (e-Cigs) Smoking Habit on Periodontal Status and Salivary pH among Some Passive e-Cigs Smokers Referred to the College of Dentistry Clinics, King Khalid University

Background: Electronic cigarette (e-cigs) smoking is substitutional to traditional cigarette smoking to reduce the dangerous combustion of products. Moreover, passive smoking is involuntarily tobacco smoking due to the exposure to cigarette or tobacco smoke among non-smokers and due to there being little knowledge about the impact of passive e-cigs smoking on periodontal status and salivary pH. Therefore, the present study aimed to evaluate the effect of e-cigs smoking habit on periodontal tissue and salivary pH among some passive e-cigs smokers referred to the college of dentistry clinics, King Khalid University. Material and Methods: Ninety male participants who were referred to the college of dentistry clinics at King Khalid University were included in the study. Age, gender, e-cigs smoking, and general health were recorded. The participants were divided into three equal groups (n = 30) as follows: Group I (Non-passive e-cigs smokers and non-smokers) as the control group, Group II (e-cigs users), and Group III (Passive e-cigs smokers). Salivary pH, plaque control record (PCR), gingival bleeding index (GBI), clinical attachment loss (CAL)
Distinguishing infinite graphs with bounded degrees

Call a colouring of a graph distinguishing if the only colour preserving automorphism is the identity. A conjecture of Tucker states that if every automorphism of a connected graph G $G$ moves infinitely many vertices, then there is a distinguishing 2‐colouring. We confirm this conjecture for graphs with maximum degree Δ≤5 ${\rm{\Delta }}\le 5$ . Furthermore, using similar techniques we show that if an infinite graph has maximum degree Δ≥3 ${\rm{\Delta }}\ge 3$ , then it admits a distinguishing colouring with Δ−1 ${\rm{\Delta }}-1$ colours. This bound is sharp.