Miracle-dz/UniFAR-FTUs huggingface dataset:
On Gaps Between Primitive Roots in the Hamming Metric

We consider a modification of the classical number theoretic question about the gaps between consecutive primitive roots modulo a prime p, which by the well-known result of Burgess are known to be at most p 1/4+o(1) . Here we measure the distance in the Hamming metric and show that if p is a sufficiently larger-bit prime, then for any integer n ∈ [1,p] one can obtain a primitive root modulo p by changing at most 0.11002786. r binary digits of n. This is stronger than what can be deduced from the Burgess result. Experimentally, the number of necessary bit changes is very small. We also show that each Hilbert cube contained in the complement of the primitive roots modulo p has dimension at most O(p 1/5+ǫ ),
Yetter-Drinfeld modules for Hom-bialgebras

The aim of this paper is to define and study Yetter-Drinfeld modules over Hom-bialgebras, a generalized version of bialgebras obtained by modifying the algebra and coalgebra structures by a homomorphism. Yetter-Drinfeld modules over a Hom-bialgebra with bijective structure map provide solutions of the Hom-Yang-Baxter equation. The category $_H^H{\mathcal YD}$ of Yetter-Drinfeld modules with bijective structure maps over a Hom-bialgebra H with bijective structure map can be organized, in two different ways, as a quasi-braided pre-tensor category. If H is quasitriangular (respectively coquasitriangular) the first (respectively second) quasi-braided pre-tensor category $_H^H{\mathcal YD}$ contains, as a quasi-braided pre-tensor subcategory, the category of modules (respectively comodules) with bijective structure maps over H.
Machine Learning for Real Estate Time Series Prediction

Several researchers have demonstrated that real estate investments have improved the risk-adjusted performance of mixed-asset portfolios belonging to institutional investors. In order for these portfolio strategies to be more effective, one could use price predictions (instead of historical data) to optimize weights. The goal of this paper is to investigate the predictive performance on price time series of REITs (real estate investment trusts), stocks and bonds, of five different machine learning (ML) algorithms. These algorithms are: linear regression; support vector regression; gradient boosting; long short-term memory neural networks; and k-nearest neighbour. We run experiments on 90 datasets and compare the ML results to those of an ARIMA model, which is a popular econometric benchmark used in financial time series predictions. Our results show that machine learning algorithms statistically outperform ARIMA. In addition, we find that all machine learning algorithms are able to produce very low root mean square errors, with linear regression and long short-term memory obtaining the lowest error values.
COMPARATIVE EVALUATION OF PHYTOCHEMICALS, ANTIOXIDANT AND ANTIBACTERIAL EFFICIENCY OF CASSIA OCCIDENTALIS AND PITHECELLOBIUM DULCE LEAVES EXTRACT

: In the present study, two indigenous plant species of C.occidentalis and P. dulce are selected and comparative analysis of phytochemicals, antioxidant and anti-bacterial activity of leaves extracts was carried out with different solvents of aqueous, petroleum ether, chloroform and ethanol. The extractive values of these extracts ranged from 3.9-17.5 %w/w and showed the existence of alkaloids, flavonoids, sterols, anthraquione, cardiac glycosides, tannins and terpenoids of both the plant species. The total phenolic content of both the plant species were in range of 10- 92 µg/mg and the highest was recorded 92.45 ±1.26 µg/mg in ethanolic extract of C.occidentalis and the least value10.81 ± 0.31 µg/mg was observed in the petroleum extract of the P.dulce . The TFC are in the range of 9-148 µg/mg in both plants. The highest value of 148.99 ± 6. 01µg/mg was observed in ethanolic extract of C.occidentalis and 79.49± 1. 59µg/mg was recorded in petroleum ether of P.dulce respectively. The ethanolic and chloroform extracts showed strong antioxidant and reducing power potentials. Ethanolic and chloroform extracts given the best results in anti-bacterial screening and the MIC were in the range of 200-800µg/ml confirming the pharmacognostic feature.
The local density approximation in density functional theory

We give the first mathematically rigorous justification of the Local Density Approximation in Density Functional Theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the Uniform Electron Gas energy of this density. The error involves gradient terms and justifies the use of the Local Density Approximation in the situation where the density is very flat on sufficiently large regions in space.
Distance sets of two subsets of vector spaces over finite fields

We investigate the size of the distance set determined by two subsets of finite dimensional vector spaces over finite fields. A lower bound of the size is given explicitly in terms of cardinalities of the two subsets. As a result, we improve upon the results by Rainer Dietmann. In the case that one of the subsets is a product set, we obtain further improvement on the estimate.
Interpretations of anomalous LHC events with electrons and jets

The CMS Collaboration has recently reported some excess events in final states with electrons and jets, in searches for leptoquarks and $W'$ bosons. Although these excesses may be due to some yet-to-be-understood background mismodeling, it is useful to seek realistic interpretations involving new particles that could generate such events. We show that resonant pair production of vector-like leptons that decay to an electron and two jets leads to kinematic distributions consistent with the CMS data.
Combined effect of phase change material and fluid flow on solar thermal energy storage

The combined effect of phase change material (PCM) and fluid flow on the thermal efficiency of solar thermal storage was experimentally investigated in this study in order to determine the appropriate operating conditions. Moreover, a sensitivity analysis was employed to evaluate the greatest effect on thermal efficiency. In the experiments, the effect of PCM weight was tested with three values of 4, 6, and 8 kg. The effect of fluid flow rate was also examined with three values of 2.4, 4.8, and 7.2 L/min. From the experiment, PCM and fluid flow had a significant effect on thermal efficiency. In the case of optimal conditions, the PCM of 6 kg and flow rate of 4.8 L/min provided the water and air heating efficiencies of 65% and 45%, respectively. From the sensitivity analysis, PCM showed the greatest effect on thermal efficiency, leading to a priority factor for solar thermal storage design.
Mean Hα+[N II]+[S II] EW inferred for star-forming galaxies at z ~ 5.1-5.4 using high-quality Spitzer/IRAC photometry

Recent Spitzer/InfraRed Array Camera (IRAC) photometric observations have revealed that rest-frame optical emission lines contribute significantly to the broad-band fluxes of high-redshift galaxies. Specifically, in the narrow redshift range z ∼ 5.1–5.4 the [3.6]–[4.5] colour is expected to be very red, due to contamination of the 4.5 μm band by the dominant Hα line, while the 3.6 μm filter is free of nebular emission lines. We take advantage of new reductions of deep Spitzer/IRAC imaging over the Great Observatories Origins Deep Survey-North+South fields (Labbe et al. 2015) to obtain a clean measurement of the mean Hα equivalent width (EW) from the [3.6]–[4.5] colour in the redshift range z = 5.1–5.4. The selected sources either have measured spectroscopic redshifts (13 sources) or lie very confidently in the redshift range z = 5.1–5.4 based on the photometric redshift likelihood intervals (11 sources). Our z_(phot) = 5.1–5.4 sample and z_(spec) = 5.10–5.40 spectroscopic sample have a mean [3.6]–[4.5] colour of 0.31 ± 0.05 and 0.35 ± 0.07 mag, implying a rest-frame EW (Hα+[N II]+[S II]) of 665 ± 53 and 707 ± 74 A, respectively, for sources in these samples. These values are consistent albeit slightly higher than derived by Stark et al. at z ∼ 4, suggesting an evolution to higher values of the Hα+[N ii]+[S II] EW at z > 2. Using the 3.6 μm band, which is free of emission line contamination, we perform robust spectral energy distribution fitting and find a median specific star formation rate of sSFR = 17^(+2)_(−5) Gyr−1, 7^(+1)_(−2)× higher than at z ∼ 2. We find no strong correlation (<2σ) between the Hα+[N II]+[S II] EW and the stellar mass of sources. Before the advent of JWST, improvements in these results will come through an expansion of current spectroscopic samples and deeper Spitzer/IRAC measurements.
DETERMINANTS OF PROACTIVE CAREER BEHAVIOUR AMONG FEMALE WORKERS: PROACTIVE PERSONALITY AS A MODERATOR

: Nowadays, the increasing trend of female labour force participation in Malaysia signifies a positive impact on Malaysia gross domestic product (GDP) which helps to boost the economy. Many companies begin to realise the significance of women in the organization as they will help to improve the quality of engagement and mutual understanding between organizations and the community. Nevertheless, the proactive career behaviour of women becomes more vital to be understood for encouraging and retaining women in the workplace. Female employees slowly become an important contributor to today's economy and yet, there is scare of researches on this related topic. In this, the researchers are motivated to study the determinants of proactive career behaviour among female employee. This study is based on 150 female employees who work in the private sectors in Peninsular Malaysia. The motivating factors include future work self, career adaptability, perceived career barriers, dispositional hope and proactive personality. The moderator role of proactive personality was also assessed in the model. Descriptive and inferential statistics are used to determine the relationship between those variables. In this research, the result has shown that future work self and proactive personality are significant influence the proactive career behaviour of female employees. Contrary to our expectation, there is insufficient evidence to support moderating effects in the study. This study contributes some implication to management to act to foster the proactive behaviour of female employees. Common method variance and generalisation issue due to small sample size are some of the limitations. Thus, some recommendation for future research were laid out in the study.
Discrete Analogues in Harmonic Analysis: Directional Maximal Functions in $\mathbb{Z}^2$

Let $V = \{ v_1,\dots,v_N\}$ be a collection of $N$ vectors that live near a discrete sphere. We consider discrete directional maximal functions on $\mathbb{Z}^2$ where the set of directions lies in $V$, given by \[ \sup_{v \in V, k \geq C \log N} \left| \sum_{n \in \mathbb{Z}} f(x-v\cdot n ) \cdot \phi_k(n) \right|, \ f:\mathbb{Z}^2 \to \mathbb{C}, \] where and $\phi_k(t) := 2^{-k} \phi(2^{-k} t)$ for some bump function $\phi$. Interestingly, the study of these operators leads one to consider an "arithmetic version" of a Kakeya-type problem in the plane, which we approach using a combination of geometric and number-theoretic methods. Motivated by the Furstenberg problem from geometric measure theory, we also consider a discrete directional maximal operator along polynomial orbits, \[ \sup_{v \in V} \left| \sum_{n \in \mathbb{Z}} f(x-v\cdot P(n) ) \cdot \phi_k(n) \right|, \ P \in \mathbb{Z}[-] \] for $k \geq C_d \log N$ sufficiently large.
Quasiconformal mappings on the Heisenberg group: An overview

We present a brief overview of the Kor\'anyi-Reimann theory of quasiconformal mappings on the Heisenberg group stressing on the analogies as well as on the differences between the Heisenberg group case and the classical two-dimensional case. We examine the extensions of the theory to more general spaces and we state some known results and open problems.
Reversed-Phase High-Performance Liquid Chromatography Quantification, Gas Chromatography-Mass Spectrometry Study and In Vitro Antioxidant Potential of Clerodendrum serratum Linn. Roots

The present study was aimed to identify and to quantify the phytoconstituents by gas chromatography-mass spectrometry, reversed phase-high performance liquid chromatography techniques and further to evaluate their in vitro antioxidant potential. In this study, the roots of Clerodendrum serratum Linn. was subjected to soxhlet extraction using n-hexane, chloroform, ethyl acetate and ethanol solvents and the obtained extracts were analyzed by gas chromatography-mass spectrometry technique. The caffeic acid and beta-sitosterol were quantified from the extracts using reversed phase high performance liquid chromatography technique. Total phenolic and flavonoid content were determined using established methods viz . Folin-Ciocalteu and aluminium chloride colorimetric assay. Antioxidant potential was assessed using in vitro methods such as 2, 2-diphenyl-1-picrylhydrazyl scavenging activity; ferric reducing ability of plasma assay and total antioxidant activity. The gas chromatography-mass spectrometry analysis revealed the presence of 48 compounds, out of which 41 compounds were identified and among them caffeic acid and beta-sitosterol were quantified using reversed phase high performance liquid chromatography technique. The abundance of phenolic and flavonoid content was found in ethyl acetate and residual aqueous fractions. The half maximal inhibitory concentration values of 2, 2-diphenyl-1-picrylhydrazyl assay was found to be 1.24, 3.36, 10.61 μg/ml for the residual aqueous fraction, ethyl acetate and chloroform fractions respectively and the total antioxidant activity was found to be 960±0.25, 766±0.14 and 816.6±0.28 μg/mg for the chloroform, ethyl acetate and residual aqueous fractions respectively showing strong antioxidant activity. The ferric reducing ability of plasma assay showed strongest reducing power for residual aqueous fraction and ethyl acetate fractions. The results showed that the residual aqueous fraction and ethyl acetate fractions had strong antioxidant potential. It may be concluded from the results that the Clerodendrum serratum Linn. roots possesses significant antioxidant potential may be due to presence of potent phenolic and flavonoid compounds and these finding supports the traditional use of plant to treat the oxidative stress and related disorders.
An alternative approach for general covariant Hořava-Lifshitz gravity and matter coupling

Recently, in [3] Hořava and Melby–Thompson proposed a nonrelativistic gravity theory with extended gauge symmetry that is free of the spin-0 graviton. We propose a minimal substitution recipe to implement this extended gauge symmetry which reproduces the results obtained by them. Our prescription has the advantage of being manifestly gauge invariant and immediately generalizable to other fields, like matter. We briefly discuss the coupling of gravity with scalar and vector fields found by our method. We show also that the extended gauge invariance in gravity does not force the value of λ to be λ = 1 as claimed in [3]. However, the spin-0 graviton is eliminated even for general λ.
Hamiltonian systems and semiclassical dynamics for interacting spins in QED

In this article, we consider fixed spin-1/2 particles interacting through the quantized electromagnetic field in a constant magnetic field. We give approximate evolutions of coherent states. This uses spins-photon classical Hamiltonian mechanics. These approximations enable to derive that the approximate average fields and spins follow Maxwell-Bloch equations with a current density coming from spins. In addition, we obain a law concerning the evolution of the approximate average number of photons. Next, we provide stationary points of the spins-photon Hamiltonian when the spin particles belong to an orthogonal plane to the constant magnetic field. This allows for the construction of quasimodes with spins colinear to the constant magnetic field. Finally, a quasimode with an arbitrary high accuracy is built up and its first order radiative correction is computed.
Integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions

We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is integrable and separable, extending the results of the odd dimensional case discussed in arXiv:1703.00713. We find the general solution of the Hamilton-Jacobi equations for these systems and present explicit expressions for the Liouville integrals, discuss Killing tensors and the associated constants of motion. We analyze special cases of the background near-horizon geometry were the system possesses more constants of motion and is hence superintegrable. Finally, we consider near-horizon extremal vanishing horizon case which happens for Myers-Perry black holes in odd dimensions and show that geodesic equations on this geometry are also separable and work out its integrals of motion.
Current fluctuations and large deviations for periodic TASEP on the relaxation scale

The one-dimensional totally asymmetric simple exclusion process (TASEP) with N particles on a periodic lattice of L sites is an interacting particle system with hopping rates breaking detailed balance. The total time-integrated current of particles Q between time 0 and time T is studied for this model in the thermodynamic limit L,N→∞ ? > with finite density of particles ρ¯=N/L ? >. The current Q takes at leading order a deterministic value which follows from the hydrodynamic evolution of the macroscopic density profile by the inviscid Burgers’ equation. Using asymptotics of Bethe ansatz formulas for eigenvalues and eigenvectors, an exact expression for the probability distribution of the fluctuations of Q is derived on the relaxation time scale T∼L3/2 ? > for an evolution conditioned on simple initial and final states. For flat initial and final states, a large deviation function expressed simply in terms of the Airy function is obtained at small rescaled time T/L3/2.
Spectral characterizations of two families of nearly complete bipartite graphs

It is not hard to find many complete bipartite graphs which are not determined by their spectra. We show that the graph obtained by deleting an edge from a complete bipartite graph is determined by its spectrum. We provide some graphs, each of which is obtained from a complete bipartite graph by adding a vertex and an edge incident on the new vertex and an original vertex, which are not determined by their spectra.
Luzin's condition (N) and modulus of continuity

Abstract In this paper, we establish Luzin's condition (N) for mappings in certain Sobolev–Orlicz spaces with certain moduli of continuity. Further, given a mapping in these Sobolev–Orlicz spaces, we give bounds on the size of the exceptional set where Luzin's condition (N) may fail. If a mapping violates Luzin's condition (N), we show that there is a Cantor set of measure zero that is mapped to a set of positive measure.
Intrinsic square functions with arbitrary aperture

We consider intrinsic square functions defined using (log-)Dini continuous test functions on spaces of homogeneous type. We prove weighted estimates with optimal (at least in the Euclidean case) dependence on the aperture of the cone used to define the square function and linear dependence on the (log-)Dini modulus of continuity.
ESTIMATION OF TURBULENT DIFFUSIVITY WITH DIRECT NUMERICAL SIMULATION OF STELLAR CONVECTION

We investigate the value of horizontal turbulent diffusivity η by numerical calculation of thermal convection. In this study, we introduce a new method whereby the turbulent diffusivity is estimated by monitoring the time development of the passive scalar, which is initially distributed in a given Gaussian function with a spatial scale d0. Our conclusions are as follows: (1) assuming the relation η = Lcvrms/3, where vrms is the root-mean-square (rms) velocity, the characteristic length Lc is restricted by the shortest one among the pressure (density) scale height and the region depth. (2) The value of turbulent diffusivity becomes greater with the larger initial distribution scale d0. (3) The approximation of turbulent diffusion holds better when the ratio of the initial distribution scale d0 to the characteristic length Lc is larger.
Matrix models for multilevel Heckman-Opdam and multivariate Bessel measures

We study multilevel matrix ensembles at general beta by identifying them with a class of processes defined via the branching rules for multivariate Bessel and Heckman-Opdam hypergeometric functions. For beta = 1, 2, we express the joint multilevel density of the eigenvalues of a generalized beta-Wishart matrix as a multivariate Bessel ensemble, generalizing a result of Dieker-Warren. In the null case, we prove the conjecture of Borodin-Gorin that the joint multilevel density of the beta-Jacobi ensemble is given by a principally specialized Heckman-Opdam measure.
The development and utilization of bauxite resources in the Guizhou Province and relevant challenges

long-term or development has a series environmental problems, the and destruction of land resources and heavy metal pollution in soil and water bodies. based on the existing research results in China and abroad, this paper analyzes the current situation, distribution characteristics, and development and utilization of bauxite resources in Guizhou to explain the corresponding environmental impacts. The results show that because of the many types and high concentrations of associated elements in bauxite and the high alkalinity, heavy metal components, and radioactive elements in red mud, the development and utilization of bauxite resources are associated with higher environmental risk. And more impact of bauxite mining on regional biodiversity, soil, air, surface water, and groundwater need to be evaluated. This paper also proposes coping strategies or countermeasures of environmental governance and control to achieve the green, sustainable and high-quality development of bauxite-related industries for meeting future environmental requirements.
Bounds for Serre’s open image theorem for elliptic curves over number fields

For an elliptic curve E/K without potential complex multiplication we bound the index of the image of Gal K/Kin GL2(b), the representation being given by the action on the Tate modules of E at the various primes. The bound is explicit and only depends on (K : Q) and on the stable Faltings height of E. We also prove a result relating the structure of closed subgroups of GL2(Zl) to certain Lie algebras naturally attached to them.
Depressive symptoms in dentistry students – prevalence, risk factors and resilience factors

of Inventory-II to assess depressive Five-Factor to assess the personality trait neuroticism, a self-description study questionnaire study-related 8 resilience Results: 41,8 % of the students showed mild (18,3 %), moderate (17,0 %), or severe (6,5 %) depressive symptoms. 5 potential risk factors, 4 potential stress factors and 5 potential resilience factors were identified, which also revealed a cumulative effect: The more risk and stress factors the students indicated, the more depressive symptoms they showed. The opposite was true for the resilience factors. strain on dental students but also regarding their role in the health care system. Students should be informed and sensitized regarding this issue. Specific education on depression is useful to destigmatize the issue and raise awareness of the condition. University programs can also contribute to an early recognition and prevention of depressive symptoms to protect the mental health of potential future dentists.