Miracle-dz/UniFAR-FTUs huggingface dataset:
New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials

In recent years, many exceptional orthogonal polynomials (EOP) were introduced and used to construct new families of 1D exactly solvable quantum potentials, some of which are shape invariant. In this paper, we construct from Hermite and Laguerre EOP and their related quantum systems new 2D superintegrable Hamiltonians with higher-order integrals of motion and the polynomial algebras generated by their integrals of motion. We obtain the finite-dimensional unitary representations of the polynomial algebras and the corresponding energy spectrum. We also point out a new type of degeneracies of the energy levels of these systems that is associated with holes in sequences of EOP.
The s-multiplicity function of 2x2-determinantal rings

This article generalizes joint work of the first author and I. Swanson to the $s$-multiplicity recently introduced by the second author. For $k$ a field and $X = [ x_{i,j}]$ a $m \times n$-matrix of variables, we utilize Gr\"obner bases to give a closed form the length $\lambda( k[X] / (I_2(X) + \mathfrak{m}^{ \lceil sq \rceil} + \mathfrak{m}^{[q]} ))$ where $s \in \mathbf{Z}[p^{-1}]$, $q$ is a sufficiently large power of $p$, and $\mathfrak{m}$ is the homogeneous maximal ideal of $k[X]$. This shows this length is always eventually a {\it polynomial} function of $q$ for all $s$.
Analogs of certain quasi-analiticity results on Riemannian symmetric spaces of noncompact type.

An $L^2$ version of the celebrated Denjoy-Carleman theorem regarding quasi-analytic functions was proved by Chernoff \cite{CR} on $\mathbb R^d$ using iterates of the Laplacian. In $1934$ Ingham \cite{I} used the classical Denjoy-Carleman theorem to relate the decay of Fourier transform and quasi-analyticity of integrable functions on $\mathbb R$. In this paper we extend both these theorems to Riemannian symmetric spaces of noncompact type and show that the theorem of Ingham follows from that of Chernoff.
THE 37 MONTH MAXI/GSC SOURCE CATALOG OF THE HIGH GALACTIC-LATITUDE SKY

We present a catalog of high Galactic-latitude (|b| > 10°) X-ray sources detected in the first 37 months of data of the Monitor of All-sky X-ray Image/Gas Slit Camera (MAXI/GSC). To achieve the best sensitivity, we develop a background model of the GSC that well reproduces the data based on the detailed on-board calibration. Source detection is performed through image fits with a Poisson likelihood algorithm. The catalog contains 500 objects detected with significances of sD, 4–10 keV ⩾ 7 in the 4–10 keV band. The limiting sensitivity is ≈7.5 × 10−12 erg cm−2 s−1 (≈0.6 mCrab) in the 4–10 keV band for 50% of the survey area, which is the highest ever achieved in an all-sky survey mission covering this energy band. We summarize the statistical properties of the catalog and results from cross matching with the Swift/BAT 70 month catalog, the meta-catalog of X-ray detected clusters of galaxies, and the MAXI/GSC 7 month catalog. Our catalog lists the source name (2MAXI), position and its error, detection significances and fluxes in the 4–10 keV and 3–4 keV bands, the hardness ratio, and the basic information of the likely counterpart available for 296 sources.
Inequalities for series in q-shifted factorials and q-gamma functions

The paper studies logarithmic convexity and concavity of power series with coefficients involving q-gamma functions or q-shifted factorials with respect to a parameter contained in their arguments. The principal motivating examples of such series are basic hypergeometric functions. We consider four types of series. For each type we establish conditions sufficient for the power series coefficients of the generalized Turánian formed by these series to have constant sign. Finally, we furnish seven examples of basic hypergeometric functions satisfying our general theorems. This investigation extends our previous results on power series with coefficient involving the ordinary gamma functions and the shifted factorials.
A locally conservative and energy‐stable finite‐element method for the Navier‐Stokes problem on time‐dependent domains

We present a finite‐element method for the incompressible Navier‐Stokes problem that is locally conservative, energy‐stable, and pressure‐robust on time‐dependent domains. To achieve this, the space‐time formulation of the Navier‐Stokes problem is considered. The space‐time domain is partitioned into space‐time slabs, which in turn are partitioned into space‐time simplices. A combined discontinuous Galerkin method across space‐time slabs and space‐time hybridized discontinuous Galerkin method within a space‐time slab results in an approximate velocity field that is H(div)‐conforming and exactly divergence‐free, even on time‐dependent domains. Numerical examples demonstrate the convergence properties and performance of the method.
Moderate deviations principle for empirical covariance from a unit root

In the present paper, we consider the linear autoregressive model in $\rr$, $$ X_{k,n}=\theta_n X_{k,n-1}+\xi_k, k=0,1,. ,n, n\ge 1$$ where $\theta_n\in [0,1)$ is unknown, $(\xi_k)_{k\in\zz}$ is a sequence of centered i.i. d. r.v. valued in $\rr$ representing the noise. When $\theta_n\to 1$, the moderate deviations principle for empirical covariance is discussed and as statistical applications we provide the moderate deviation estimates of the least square and the Yule-Walker estimators of the parameter $\theta_n$.
One-parameter and multiparameter function classes are intersections of finitely many dyadic classes. ∗

We prove that the class of Muckenhoupt Ap weights coincides with the intersection of finitely many suitable translates of dyadic Ap, in both the one-parameter and multi- parameter cases, and that the analogous results hold for the reverse Holder class RHp, for doubling measures, and for the space VMO of functions of vanishing mean oscilla- tion. We extend to the multiparameter (product) space BMO of functions of bounded mean oscillation the corresponding one-parameter BMO result due to T. Mei, by means of the Carleson-measure characterization of multiparameter BMO. Our results hold in both the compact and non-compact cases. In addition, we survey several definitions of VMO and prove their equivalences, in the continuous, dyadic, one-parameter and mul- tiparameter cases. We show that the weighted Hardy space H 1 (! ) is the sum of finitely many suitable translates of dyadic weighted H 1 (! ), and that the weighted maximal function is pointwise comparable to the sum of finitely many dyadic weighted maximal functions for suitable translates of the dyadic grid and for each doubling weight !
Honeycomb-Lattice Minnaert Bubbles

The ability to manipulate the propagation of waves on subwavelength scales is important for many different physical applications. In this paper, we consider a honeycomb lattice of subwavelength resonators and prove, for the first time, the existence of a Dirac dispersion cone at subwavelength scales. As shown in [H. Ammari et al., A high-frequency homogenization approach near the Dirac points in bubbly honeycomb crystals, arXiv:1812.06178], near the Dirac points, honeycomb crystals of subwavelength resonators has a great potential to be used as near-zero materials. Here, we perform the analysis for the example of bubbly crystals, which is a classic example of subwavelength resonance, where the resonant frequency of a single bubble is known as the Minnaert resonant frequency. Our first result is an asymptotic formula for the quasi-periodic Minnaert resonant frequencies. We then prove the linear dispersion relation of a Dirac cone. Our findings in this paper are numerically illustrated in the case of circular bubbles, where the multipole expansion method provides an efficient technique for computing the band structure.
Spontaneous concentrations of solids through two-way drag forces between gas and sedimenting particles

The behaviour of sedimenting particles depends on the dust-to-gas ratio of the fluid. Linear stability analysis shows that solids settling in the Epstein drag regime would remain homogeneously distributed in non-rotating incompressible fluids, even when dust-to-gas ratios reach unity. However, the non-linear evolution has not been probed before. Here, we present numerical calculations indicating that in a particle-dense mixture solids spontaneously mix out of the fluid and form swarms overdense in particles by at least a factor 10. The instability is caused by mass-loaded regions locally breaking the equilibrium background stratification. The driving mechanism depends on non-linear perturbations of the background flow and shares some similarity to the streaming instability in accretion discs. The resulting particle-rich swarms may stimulate particle growth by coagulation. In the context of protoplanetary discs, the instability could be relevant for aiding small particles to settle to the midplane in the outer disc. Inside the gas envelopes of protoplanets, enhanced settling may lead to a reduced dust opacity, which facilitates the contraction of the envelope. We show that the relevant physical set up can be recreated in a laboratory setting. This will allow our numerical calculations to be investigated experimentally in the future.
Learned Variational Video Color Propagation Supplementary material – ECCV 2022

Inference Time. The run-time of our method depends on the number of used color proposals. Fig. 14 shows that already 3 proposals yield almost maximal PSNR scores (ours fast). Our unoptimzed PyTorch code takes approximately 1.75 seconds per frame (DAVIS, 854x480) on a NVIDIA Titan RTX. Approximately 1.2 seconds are spent in color proposal generation (fast = 3x local + 3x global proposals + 12 RAFT iterations) and roughly 0.55 seconds are spent in our unrolled refinement optimization (12 iterations) with our learned regularizer. Thus, our model takes roughly 4.3 s/MPixel, which is slightly faster than the 5.4 s/MPixel reported by DVCP [11]. With an additional CUDA sampling operator (not in main paper but on github), the inference can be improved from 1.75 to approximately 1 seconds with similar qualitative results. Since the feature matching and motion estimation can be precomputed once for a whole sequence, the 0.55 seconds become the relevant part if our model is used by a human operator in an interactive way. Page 5 provides another example of how user input can be easily integrated into our model after training.
Howe Correspondence of Unipotent Characters for a Finite Symplectic/Even-orthogonal Dual Pair

In this paper we give a complete description of the Howe correspondence of unipotent characters for a finite dual pair of a symplectic group and an even orthogonal group in terms of the Lusztig parametrization under a mild restriction of the characteristic of the base field. That is, the conjecture by Aubert-Michel-Rouquier is proved.
THE EMPIRE SURVEY: SYSTEMATIC VARIATIONS IN THE DENSE GAS FRACTION AND STAR FORMATION EFFICIENCY FROM FULL-DISK MAPPING OF M51

We present the first results from the EMPIRE survey, an IRAM large program that is mapping tracers of high-density molecular gas across the disks of nine nearby star-forming galaxies. Here, we present new maps of the 3 mm transitions of HCN, HCO+, and HNC across the whole disk of our pilot target, M51. As expected, dense gas correlates with tracers of recent star formation, filling the “luminosity gap” between Galactic cores and whole galaxies. In detail, we show that both the fraction of gas that is dense, f dense traced by HCN/CO, and the rate at which dense gas forms stars, SFE dense traced by IR/HCN, depend on environment in the galaxy. The sense of the dependence is that high-surface-density, high molecular gas fraction regions of the galaxy show high dense gas fractions and low dense gas star formation efficiencies. This agrees with recent results for individual pointings by Usero et al. but using unbiased whole-galaxy maps. It also agrees qualitatively with the behavior observed contrasting our own Solar Neighborhood with the central regions of the Milky Way. The sense of the trends can be explained if the dense gas fraction tracks interstellar pressure but star formation occurs only in regions of high density contrast.
Scalar Curvature and Intrinsic Flat Convergence

Herein we present open problems and survey examples and theorems concerning sequences of Riemannian manifolds with uniform lower bounds on scalar curvature and their limit spaces. Examples of Gromov and of Ilmanen which naturally ought to have certain limit spaces do not converge with respect to smooth or Gromov-Hausdorff convergence. Thus we focus here on the notion of Intrinsic Flat convergence, developed jointly with Wenger. This notion has been applied successfully to study sequences that arise in General Relativity. Gromov has suggested it should be applied in other settings as well. We first review intrinsic flat convergence, its properties, and its compactness theorems, before presenting the applications and the open problems.
Filamentary Accretion Flows in the Infrared Dark Cloud G14.225–0.506 Revealed by ALMA

Filaments are ubiquitous structures in molecular clouds and play an important role in the mass assembly of stars. We present results of dynamical stability analyses for filaments in the infrared dark cloud G14.225−0.506, where a delayed onset of massive star formation was reported in the two hubs at the convergence of multiple filaments of parsec length. Full-synthesis imaging is performed with the Atacama Large Millimeter/submillimeter Array to map the emission in two hub-filament systems with a spatial resolution of ∼0.034 pc. Kinematics are derived from a sophisticated spectral fitting algorithm that accounts for line blending, large optical depth, and multiple velocity components. We identify five velocity coherent filaments and derive their velocity gradients with principal component analysis. The mass accretion rates along the filaments are up to and are significant enough to affect the hub dynamics within one freefall time (∼105 yr). The filaments are in equilibrium with virial parameter αvir ∼ 1.2. We compare αvir measured in the filaments, filaments, 870 μm dense clumps, and 3 mm dense cores. The decreasing trend in αvir with decreasing spatial scales persists, suggesting an increasingly important role of gravity at small scales. Meanwhile, αvir also decreases with decreasing nonthermal motions. In combination with the absence of high-mass protostars and massive cores, our results are consistent with the global hierarchical collapse scenario.
Degenerations of toric varieties over valuation rings

We develop a theory of multistage degenerations of toric varieties over finite rank valuation rings, extending the Mumford–Gubler theory in rank 1. Such degenerations are constructed from fan‐like structures over totally ordered abelian groups of finite rank. Our main theorem describes the geometry of successive special fibers in the degeneration in terms of the polyhedral geometry of a system of recession complexes associated to the fan.
Lagging behind the Joneses: Relative Deprivation and Household Consumption in Rural China

Based on the Chinese Family Panel Studies (CFPS) 2010–2018, this article investigates how relative deprivation influences household consumption in rural China. High-dimensional fixed-effects (HDFE), the instrumental variable (IV), and causal mediation analysis (CMA) are leveraged to estimate the causal effect and mechanisms. Results show that relative deprivation reduces survival-oriented consumption of food, development-oriented consumption of transportation, telecommunication, and education, as well as enjoyment-oriented of durable goods, and increases survival-oriented consumption of residence and development-oriented consumption of healthcare and medical services. Mechanism analysis indicates that relative deprivation decreases household consumption through the anticipated effect and increases it through a cognitive trap effect. On the whole, the anticipated effect prevails over the cognitive trap effect.
Lyman α line and continuum radiative transfer in a clumpy interstellar medium

This thesis focuses on the intrinsically strongest spectral signature of star-forming galaxies: the Lyman alpha recombination line of the hydrogen atom (hereafter Lya). Located at the wavelength of 1215.67 A in the restframe far-ultraviolet spectra of star-forming galaxies, the Lya line proves to be a vital tracer and a powerful emission-line window to discover and to study the remote young star-forming galaxies of the early the Universe.Although intrinsically very strong, the Lya line is also a resonant line. As a consequence, the transport of Lya photons inside the interstellar medium (ISM) of star-forming galaxies is very complex and depends on many ISM quantities (HI mass, dust content, HI gas kinematics and ISM clumpiness). All this process has serious effects on the emergent features of the Lya line (strength, equivalent width and line profile) that need to be understood for ensuring a proper interpretation of all very promising Lya-oriented studies in astrophysics and cosmology. This is precisely the aim of this thesis to go deeper into our understanding of the complex radiative transport experienced by the Lya line in star-forming galaxies.In this work, we carry out both numerical and observational studies of Lya transport inside the ISM of galaxies.In Paper I and II, we perform detailed numerical studies that examine the effects of a clumpy ISM on the strength and the shape of the Lya line. Although poorly studied until now, the effects of a clumpy ISM on Lya have been routinely invoked to explain the origin of anomalously strong Lya line observed from high-redshift galaxies. Some analytical studies suggest indeed an higher transmission of Lya photons over UV continuum ones from clumpy ISMs, resulting in an enhanced Lya equivalent width EW(Lya). Our results show that although clumpiness facilitates the escape of Lya, it is highly unlikely that any real ISM should result in any enhancement of EW(Lya). Other possible causes are discussed in our papers, leading to the conclusion that the observed high EW(Lya) are more likely produced by cooling radiation or anisotropic escape of Lya radiation.Both Paper III and IV are related to the LARS project. This is an ambitious observational program in which 14 nearby star-forming galaxies have been observed with the Hubble Space Telescope (HST) with the aim to investigate how Lya is transported out of galaxies and what effects each ISM quantity produces on the Lya line. While Paper III examines the Lya properties and morphology of individual galaxies, Paper IV presents a detailed study of the surprising Lya emission line of Mrk1486 (the fifth galaxy of the sample).
Bridges of Lévy processes conditioned to stay positive

We consider Kallenberg’s hypothesis on the characteristic function of a Levy process and show that it allows the construction of weakly continuous bridges of the Levy process conditioned to stay positive. We therefore provide a notion of normalized excursions Levy processes above their cumulative minimum. Our main contribution is the construction of a continuous version of the transition density of the Levy process conditioned to stay positive by using the weakly continuous bridges of the Levy process itself. For this, we rely on a method due to Hunt which had only been shown to provide upper semi-continuous versions. Using the bridges of the conditioned Levy process, the Durrett–Iglehart theorem stating that the Brownian bridge from 0 to 0 conditioned to remain above −e converges weakly to the Brownian excursion as e → 0, is extended to Levy processes. We also extend the Denisov decomposition of Brownian motion to Levy processes and their bridges, as well as Vervaat’s classical result stating the equivalence in law of the Vervaat transform of a Brownian bridge and the normalized Brownian excursion.
The effect of an intermediate dose of Heparin solution in the Prevention of Central Venous Catheter occlusion on ICU admitted patients: A randomized Controlled Trial

Background and aim: Central venous catheters (CVC) are widely used in critical care units. Due to the high prevalence of central venous catheter dysfunction, the cost, and the complications of their replacement, finding the right way to prevent catheter occlusion becomes important. The current study aimed to evaluate the effect of an intermediate dose of heparin solution in the prevention of central venous catheter occlusion in ICU-admitted patients. Method: This randomized controlled trial was performed in the Adult Intensive Care Unit (AICU) of Imam Reza Hospital from 2019 to 2020. In each patient (153 patients), the lines were divided into two categories: active or inactive. Inactive lines in the intervention group (76 patients) were washed every 8 hours with 10 ml of saline solution and then filled with 1.5 ml of heparin solution (at a concentration of 100 units per ml). In the control group (77 patients) only washing with 10 ml of saline solution was performed. The active lines in the intervention group were first washed with 10 ml of saline solution after each use and filled with 1.5 ml of heparin solution if not used immediately. In the control group, only saline washing was performed. Each line was examined once daily during the morning shift to determine whether it was open or closed. Result: In the studied lines in 153 patients admitted to the intensive care unit who were divided into two groups of intervention (heparin) and control (saline), no significant difference was observed in the occlusion of the catheter lines (p>0.05). Conclusion: After 14 days of examination of central venous catheters in patients, the effectiveness of an intermediate dose of heparin in preventing catheter obstruction was not more than the saline solution. rinsing 10 ml of saline Active lines in intervention group saline each case no ml heparin In the control group, only saline was Each line was once daily during the morning shift determine or each
Gradient estimates for oblique derivative problems via the maximum principle

We prove gradient estimates for solutions of the oblique derivative problem for a large class of elliptic and parabolic quasilinear PDEs. In particular, we expand on previous work of the author using a maximum principle argument. In addition, we prove estimates for the parabolic problem of evolution via mean curvature with nonzero Neumann data, which seem to be new.
RESONANT CLUMPING AND SUBSTRUCTURE IN GALACTIC DISKS

We describe a method to extract resonant orbits from N-body simulations, exploiting the fact that they close in frames rotating with a constant pattern speed. Our method is applied to the N-body simulation of the Milky Way by Shen et al. This simulation hosts a massive bar, which drives strong resonances and persistent angular momentum exchange. Resonant orbits are found throughout the disk, both close to the bar and out to the very edges of the disk. Using Fourier spectrograms, we demonstrate that the bar is driving kinematic substructure even in the very outer parts of the disk. We identify two major orbit families in the outskirts of the disk, one of which makes significant contributions to the kinematic landscape, namely, the m:l = 3:−2 family, resonating with the bar. A mechanism is described that produces bimodal distributions of Galactocentric radial velocities at selected azimuths in the outer disk. It occurs as a result of the temporal coherence of particles on the 3:−2 resonant orbits, which causes them to arrive simultaneously at pericenter or apocenter. This resonant clumping, due to the in-phase motion of the particles through their epicycle, leads to both inward and outward moving groups that belong to the same orbital family and consequently produce bimodal radial velocity distributions. This is a possible explanation of the bimodal velocity distributions observed toward the Galactic anticenter by Liu et al. Another consequence is that transient overdensities appear and dissipate (in a symmetric fashion), resulting in a periodic pulsing of the disk’s surface density.