Miracle-dz/UniFAR-FTUs huggingface dataset:
Mixed product Poisson structures associated to Poisson Lie groups and Lie bialgebras

We introduce and study some mixed product Poisson structures on product manifolds associated to Poisson Lie groups and Lie bialgebras. For quasitriangular Lie bialgebras, our construction is equivalent to that of fusion products of quasi-Poisson G-manifolds introduced by Alekseev, Kosmann- Schwarzbach, and Meinrenken. Our primary examples include four series of holomorphic Poisson structures on products of flag varieties and related spaces of complex semi-simple Lie groups.
Comparison of CEA and IgG serum levels in oral lichenoid lesions before and after treatment with topical corticosteroids

Background. Lichen planus is considered a potentially malignant condition with an unknown etiology. This study aimed to determine the carcinoembryonic antigen (CEA) and IgG serum levels in different oral lichenoid lesions before and after treatment with local corticosteroids. Methods. Two groups of 23 individuals, including oral ulcerative lichenoid lesions patients and healthy ones, were evaluated. Toluidine blue staining and biopsy examinations were carried out while visual analog scale (VAS) was used to evaluate symptoms. By applying corticosteroids, CEA and IgG serum levels were determined before and three weeks after intervention and at the end of the study (9 weeks) with ELISA and turbidimetry methods, respectively. Results. Before the intervention, there was no significant difference in CEA serum levels between the control and case groups (P=0.19). Moreover, the CEA serum levels indicated no significant difference before and after treatment in the case group (P=0.30). While IgG serum level was significantly higher before the intervention (P=0.01), it decreased significantly in the case group after treatment (P=0.02). In addition, pain intensity reduced significantly in the case group (P=0.05). According to statistics, 8.2% out of 21.7% of patients with positive staining results exhibited dysplasia signs. Conclusion. However, neither CEA nor IgG serum levels were different in patients diagnosed with or without dysplasia and positive or negative staining results (P>0.05). IgG serum levels and pain severity effectively decreased in the oral ulcerative lichenoid lesions patients treated with local corticosteroids. Therefore, this treatment can be considered an effective and low-complication treatment modality for lichenoid lesions.
Nearly-Regular Hypergraphs and Saturation of Berge Stars

Given a graph $G$, we say a $k$-uniform hypergraph $H$ on the same vertex set contains a Berge-$G$ if there exists an injection $\phi:E(G)\to E(H)$ such that $e\subseteq\phi(e)$ for each edge $e\in E(G)$. A hypergraph $H$ is Berge-$G$-saturated if $H$ does not contain a Berge-$G$, but adding any edge to $H$ creates a Berge-$G$. The saturation number for Berge-$G$, denoted $\mathrm{sat}_k(n,\text{Berge-}G)$ is the least number of edges in a $k$-uniform hypergraph that is Berge-$G$-saturated. We determine exactly the value of the saturation numbers for Berge stars. As a tool for our main result, we also prove the existence of nearly-regular $k$-uniform hypergraphs, or $k$-uniform hypergraphs in which every vertex has degree $r$ or $r-1$ for some $r\in \mathbb{Z}$, and less than $k$ vertices have degree $r-1$.
ZEROS OF VARYING LAGUERRE–KRALL ORTHOGONAL

In this paper we introduce a sequence of varying orthogonal polynomials related to a Laguerre weight where this absolutely continuous measure is perturbed by a sequence of nonnegative masses located at the origin. The main objective is to obtain asymptotic relations between the zeros of these polynomials and the zeros of the Bessel functions of the ﬁrst kind (or linear combinations of them). This is done through Mehler–Heine type formulas. With these relations we can easily compute asymptotically the zeros of these polynomials. We show some numerical experiments.
BOREL DENSITY FOR APPROXIMATE LATTICES

We extend classical density theorems of Borel and Dani–Shalom on lattices in semisimple, respectively solvable algebraic groups over local fields to approximate lattices. Our proofs are based on the observation that Zariski closures of approximate subgroups are close to algebraic subgroups. Our main tools are stationary joinings between the hull dynamical systems of discrete approximate subgroups and their Zariski closures.
Volume of the set of locally diagonalizable bipartite states

The purpose of this article is to investigate the geometry of the set of locally diagonalizable bipartite quantum states. We have the following new results: the Hilbert–Schmidt volume of all locally diagonalizable states, and a necessary and sufficient condition for local diagonalizability in the qubit-qubit case. Besides, we partition the set of all locally diagonalizable states as local unitary orbits (or coadjoint orbits) of diagonal forms. It is well-known that the Riemannian volume of a coadjoint orbit for a regular point in a specified Weyl chamber can be calculated by Harish–Chandra’s volume formula. By modifying Harish–Chandra’s volume formula, we give, for the first time, a specific formula for the Riemannian volume of a local unitary orbit of a regular point in a specified Weyl chamber. Several open questions are presented as well.
On M-functions associated with modular forms

Let $f$ be a primitive cusp form of weight $k$ and level $N,$ let $\chi$ be a Dirichlet character of conductor coprime with $N,$ and let $\mathfrak{L}(f\otimes \chi, s)$ denote either $\log L(f\otimes \chi, s)$ or $(L'/L)(f\otimes \chi, s). $ In this article we study the distribution of the values of $\mathfrak{L}$ when either $\chi$ or $f$ vary. First, for a quasi-character $\psi\colon \mathbb{C} \to \mathbb{C}^\times$ we find the limit for the average $\mathrm{Avg}_\chi \psi(L(f\otimes\chi, s)),$ when $f$ is fixed and $\chi$ varies through the set of characters with prime conductor that tends to infinity. Second, we prove an equidistribution result for the values of $\mathfrak{L}(f\otimes \chi,s)$ by establishing analytic properties of the above limit function. Third, we study the limit of the harmonic average $\mathrm{Avg}^h_f \psi(L(f, s)),$ when $f$ runs through the set of primitive cusp forms of given weight $k$ and level $N\to \infty. $ Most of the results are obtained conditionally on the Generalized Riemann Hypothesis for $L(f\otimes\chi, s). $
Mean field model for collective motion bistability

We consider the Czir\'ok model for collective motion of locusts along a one-dimensional torus. In the model, each agent's velocity locally interacts with other agents' velocities in the system, and there is also exogenous randomness to each agent's velocity. The interaction tends to create the alignment of collective motion. By analyzing the associated nonlinear Fokker-Planck equation, we obtain the condition for the existence of stationary order states and the conditions for their linear stability. These conditions depend on the noise level, which should be strong enough, and on the interaction between the agent's velocities, which should be neither too small, nor too strong. We carry out the fluctuation analysis of the interacting system and describe the large deviation principle to calculate the transition probability from one order state to the other. Numerical simulations confirm our analytical findings.
A practical procedure for vehicle sound package design using statistical energy analysis

Vehicle sound package has a substantial role in attenuation of vehicle noise for the purpose of improving interior comfort and reducing environmental noise pollution. In this paper, two approaches of absorptive design and multi-layer design are investigated to improve the performance of a sound package in automotive applications. For this purpose, the sound package of the engine compartment including hoodliner and dash insulator is studied. Furthermore, this paper proposes an experimentally validated prediction model through Statistical Energy Analysis (SEA) to evaluate the sound insulation of a vehicle body sound package. For this purpose, the research includes characterization techniques of sound package materials to determine intrinsic parameters of different layers required to develop a reliable SEA model. The inverse method and time-temperature superposition principle (TTSP) are utilized to characterize porous materials and heavy layer properties, respectively. The comparison of results that are experimentally obtained by acoustic cabin shows a fairly well agreement with the proposed SEA modeling procedure for the desired frequency range. By observing the results of the simulation for the hoodliner and dash insulator, it was revealed that the absorptive design combines the benefits of high sound absorption capability, wide absorption frequency band, and lightweight. Indeed, with an appropriate combination of layers, the multi-layer design can simultaneously provide a mixture of absorptive design attributes and sound insulation capabilities. The transmission loss obtained from the proposed design of the dash insulator revealed an increase by 42% without any reduction in the amount of sound absorption. Also, the sound absorption of the proposed hoodliner is enhanced more than twice in reference to the base design.
On Deformations of Hyperbolic Varities

In this paper we study flat deformations of real subschemes of $\mathbb{P}^n$, hyperbolic with respect to a fixed linear subspace, i.e. admitting a finite surjective and real fibered linear projection. We show that the subset of the corresponding Hilbert scheme consisting of such subschemes is closed and connected in the classical topology. Every smooth variety in this set lies in the interior of this set. Furthermore, we provide sufficient conditions for a hyperbolic subscheme to admit a flat deformation to a smooth hyperbolic subscheme. This leads to new examples of smooth hyperbolic varieties.
Role of ER Stress in Xenobiotic-Induced Liver Diseases and Hepatotoxicity

The liver is a highly metabolic organ and plays a crucial role in the transportation, storage, and/or detoxication of xenobiotics. Liver damage induced by xenobiotics (e.g., heavy metal, endocrine disrupting chemicals, Chinese herbal medicine, or nanoparticles) has become a pivotal reason for liver diseases, leading to great clinical challenge and much attention for the past decades. Given that endoplasmic reticulum (ER) is the prominent organelle involved in hepatic metabolism, ER dysfunction, namely, ER stress, is clearly observed in various liver diseases. In response to ER stress, a conserved adaptive signaling pathway known as unfolded protein response (UPR) is activated to restore ER homeostasis. However, the prolonged ER stress with UPR eventually leads to the death of hepatocytes, which is a pathogenic event in many hepatic diseases. Therefore, analyzing the perturbation in the activation or inhibition of ER stress and the UPR signaling pathway is likely an effective marker for investigating the molecular mechanisms behind the toxic effects of xenobiotics on the liver. We review the role of ER stress in hepatic diseases and xenobiotic-induced hepatotoxicity, which not only provides a theoretical basis for further understanding the pathogenesis of liver diseases and the mechanisms of hepatotoxicity induced by xenobiotics but also presents a potential target for the prevention and treatment of xenobiotic-related liver diseases.
Equidistribution of saddle connections on translation surfaces

Fix a translation surface $X$, and consider the measures on $X$ coming from averaging the uniform measures on all the saddle connections of length at most $R$. Then as $R\to\infty$, the weak limit of these measures exists and is equal to the Lebesgue measure on $X$. We also show that any weak limit of a subsequence of the counting measures on $S^1$ given by the angles of all saddle connections of length at most $R_n$, as $R_n\to\infty$, is in the Lebesgue measure class. The proof of the first result uses the second result, together with the result of Kerckhoff-Masur-Smillie that the directional flow on a surface is uniquely ergodic in almost every direction.
Reissner-Nordstrom Solution from Weyl Transverse Gravity

We study classical solutions in the Weyl-transverse (WTDiff) gravity coupled to an electro-magnetic field in four space-time dimensions. The WTDiff gravity is invariant under both the local Weyl (conformal) transformation and the volume preserving diffeormorphisms (transverse diffeomorphisms) and is known to be equivalent to general relativity at least at the classical level (perhaps even in the quantum regime). In particular, we find that only in four space-time dimensions, the charged Reissner-Nordstrom black hole metric is a classical solution when it is expressed in the Cartesian coordinate system.
Balanced representations, the asymptotic Plancherel formula, and Lusztig's conjectures for $\tilde{C}_2$

We prove Lusztig's conjectures ${\bf P1}$-${\bf P15}$ for the affine Weyl group of type $\tilde{C}_2$ for all choices of positive weight function. Our approach to computing Lusztig's $\mathbf{a}$-function is based on the notion of a `balanced system of cell representations'. Once this system is established roughly half of the conjectures ${\bf P1}$-${\bf P15}$ follow. Next we establish an `asymptotic Plancherel Theorem' for type $\tilde{C}_2$, from which the remaining conjectures follow. Combined with existing results in the literature this completes the proof of Lusztig's conjectures for all rank $1$ and $2$ affine Weyl groups for all choices of parameters.
Directly Observing the Galaxies Likely Responsible for Reionization

We report a new analysis of the Hubble Frontier Fields clusters Abell 2744 and MACS 0416 using wavelet decomposition to remove the cluster light, enabling the detection of highly magnified (>50×) galaxies a factor of 10× fainter in luminosity than previous studies. We find 167 galaxies at , and with this sample we are able to characterize the UV luminosity function to at , −14 at , and −15 at . We find a steep faint-end slope ( ), and with our improved statistics at the faint end we reduce the fractional uncertainty on α to at and 4% at . We also investigate the systematic uncertainty due to the lens modeling by using every available lens model individually and comparing the results; this systematic fractional uncertainty on α is at all redshifts. We now directly observe galaxies in the luminosity regime where some simulations predict a change in the faint-end slope of the luminosity function, yet our results provide statistically very strong evidence against any turnover in the luminosity range probed, more consistent with simulations in which stars form in lower-mass halos. Thus, we find strong support for the extension of the steep luminosity function to at , consistent with the number of faint galaxies needed to reionize the universe under standard assumptions.
Variable enstrophy flux and energy spectrum in two-dimensional turbulence with Ekman friction

Experiments and numerical simulations reveal that in the forward cascade regime, the energy spectrum of two-dimensional turbulence with Ekman friction deviates from Kraichnan's prediction of k−3 power spectrum. In this letter we explain this observation using an analytic model based on variable enstrophy flux arising due to Ekman friction. We derive an expression for the enstrophy flux which exhibits a logarithmic dependence in the inertial range for the Ekman-friction–dominated flows. The energy spectrum obtained using this enstrophy flux shows a power law scaling for large Reynolds number and small Ekman friction, but has an exponential behaviour for large Ekman friction and relatively small Reynolds number.
Harmonic analysis, Ergodic theory and Counting for thin groups

For a geometrically finite group Gamma of G=SO(n,1), we survey recent developments on counting and equidistribution problems for orbits of Gamma in a homogeneous space H\G where H is trivial, symmetric or horospherical. Main applications are found in an affine sieve on orbits of thin groups as well as in sphere counting problems for sphere packings invariant under a geometrically finite group. In our sphere counting problems, spheres can be ordered with respect to a general conformal metric.
The self-calibrating Hubble diagram

As an increasing number of well measured type Ia supernovae (SNe Ia) become available, the statistical uncertainty on w has been reduced to the same size as the systematic uncertainty. The statistical error will decrease further in the near future, and hence the improvement of systematic uncertainties needs to be addressed, if further progress is to be made. We study how uncertainties in the primary reference spectrum ? which are a main contribution to the systematic uncertainty budget ? affect the measurement of the Dark Energy equation of state parameter w from SNe Ia. The increasing number of SN observations can be used to reduce the uncertainties by including perturbations of the reference spectrum as nuisance parameters in a cosmology fit, thus self-calibrating the Hubble diagram. We employ this method to real SNe data for the first time and find the perturbations of the reference spectrum consistent with zero at the 1%-level. For future surveys we estimate that ~3500 SNe will be required for our method to outperform the standard method of deriving the cosmological parameters.
THE ULTRAVIOLET BRIGHTEST TYPE Ia SUPERNOVA 2011de

We present and discuss the ultraviolet (UV)/optical photometric light curves and absolute magnitudes of the Type Ia supernova (SN Ia) 2011de from the Swift Ultraviolet/Optical Telescope. We find it to be the UV brightest SN Ia yet observed—more than a factor of 10 brighter than normal SNe Ia in the mid-ultraviolet. We find that the UV/optical brightness and broad light curve evolution can be modeled with additional flux from the shock of the ejecta hitting a relatively large red giant companion separated by 6 × 1013 cm. However, the post-maximum behavior of other UV-bright SNe Ia can also be modeled in a similar manner, including objects with UV spectroscopy or pre-maximum photometry which is inconsistent with this model. This suggests that similar UV luminosities can be intrinsic or caused by other forms of shock interaction. The high velocities reported for SN 2011de make it distinct from the UV-bright “super-Chandrasekhar” SNe Ia and the NUV–blue group of normal SNe Ia. SN 2011de is an extreme example of the UV variations in SNe Ia.
Asymptotically cylindrical Calabi-Yau manifolds

Let M be a complete Ricci-flat Kahler manifold with one end and assume that this end converges at an exponential rate to [0,oo) x X for some compact connected Ricci-flat manifold X. We begin by proving general structure theorems for M; in particular we show that there is no loss of generality in assuming that M is simply-connected and irreducible with Hol(M) = SU(n), where n is the complex dimension of M. If n > 2 we then show that there exists a projective orbifold barM and a divisor barD in |-K_barM| with torsion normal bundle such that M is biholomorphic to barM \ barD, thereby settling a long-standing question of Yau in the asymptotically cylindrical setting. We give examples where barM is not smooth: the existence of such examples appears not to have been noticed previously. Conversely, for any such pair (barM, barD) we give a short and self-contained proof of the existence and uniqueness of exponentially asymptotically cylindrical Calabi-Yau metrics on barM \ barD.
Effects of screened Coulomb impurities on autoionizing two-electron resonances in spherical quantum dots

There are several reasons why exotic and artificial atoms attract the interest of different scientific communities.In exotic atoms, matter and antimatter can coexist for surprisingly long times. Thus, they present a unique natural laboratory for high precision antimatter studies. In artificial atoms, electrons can be confined in an externally controlled way. This aspect is crucial, as it opens new possibilities for high precision measurements and also makes artificial atoms promising potential candidates for qubits, i.e. the essential bricks for quantum computation.The first part of the thesis presents theoretical studies of resonant states in antiprotonic atoms and spherical two-electron quantum dots, where well established techniques, frequently used for conventional atomic systems, can be applied after moderate modifications. In the framework of Markovian master equations, it is then demonstrated that systems containing resonant states can be approached as open systems in which the resonance width determines the environmental coupling. The second part of the thesis focuses on possible quantum computational aspects of two kinds of artificial atoms, quantum dots and Penning traps. Environmentally induced decoherence, the main obstacle for a practical realization of a quantum computer based on these devices, is studied within a simple phenomenological model. As a result, the dependence of the decoherence timescales on the temperature of the heat bath and environmental scattering rates is obtained.
A SHORT PROOF OF A THEOREM OF MORTON BROWN ON CHAINS OF CELLS

Suppose that a topological space X is the union of an increasing sequence of open subsets each of which is homeomorphic to the Euclidean space R n . Then X itself is homeomorphic to R n . This is an old theorem of Morton Brown. We observe that this theorem is an immediate con- sequence of other two theorems of Morton Brown concerning near homeomorphisms and cellular sets.
The Galactic Branches as a Possible Evidence for Transient Spiral Arms

With the use of a background Milky-Way-like potential model, we performed stellar orbital and magnetohydrodynamic (MHD) simulations. As a first experiment, we studied the gaseous response to a bisymmetric spiral arm potential: the widely employed cosine potential model and a self-gravitating tridimensional density distribution based model called PERLAS. Important differences are noticeable in these simulations, while the simplified cosine potential produces two spiral arms for all cases, the more realistic density based model produces a response of four spiral arms on the gaseous disk, except for weak arms -i.e. close to the linear regime- where a two-armed structure is formed. In order to compare the stellar and gas response to the spiral arms, we have also included a detailed periodic orbit study and explored different structural parameters within observational uncertainties. The four armed response has been explained as the result of ultra harmonic resonances, or as shocks with the massive bisymmetric spiral structure, among other. From the results of this work, and comparing the stellar and gaseous responses, we tracked down an alternative explanation to the formation of branches, based only on the orbital response to a self-gravitating spiral arms model. The presence of features such as branches, might be an indication of transiency of the arms.