Miracle-dz/UniFAR-FTUs huggingface dataset:
Evolution of the solar ionizing flux

A young magnetically active Sun, with enhanced ionizing radiations and an elevated solar wind, might have contributed to erosion of the primordial atmosphere of Mars (which is particularly vulnerable to dissociative recombination and sputtering by solar wind pickup ions). Spacecraft and ground-based observations of solar-type dwarfs in young galactic clusters have yielded a unified view of the early evolution and subsequent systematic decline of magnetic activity with age. Rotational braking by the coronal wind ultimately quenches the spin-catalyzed dynamo at the heart of stellar magnetism. Decay of the 10 6 -10 7 K corona is much faster than the 10 4 K chromosphere, but XUV emissions of both can be predicted reliably, and photoionization of key planetary atmospheric constituents can be modeled. The early Martian atmosphere (age 1 Gyr) probably was subjected to photoionization rates ∼5 times contemporary peak values (sunspot maximum), possibly more if the ages of galactic clusters have been underestimated.
On the locus of non-rigid hypersurfaces

We show that the Zariski closure of the set of hypersurfaces of degree $M$ in ${\mathbb P}^{M}$, where $M\geq 5$, which are either not factorial or not birationally superrigid, is of codimension at least $\binom{M-3}{2}+1$ in the parameter space.
Seasonal oscillations in length‐of‐day

Variations of annual and semiannual oscillations in rotation parameters have been investigated on the basis of length-f-ay(LOD) as well as atmospheric-ngular-omemtum (AAM) series. These oscillations were determined using band-ass filters. In order to show the character of variations of seaasonal oscillations, amplitudes, phases and periods were computed by a least-quares adjustment with the method of modified harmonic analysis at quarterly intervals. In addition, the seasonal imbalances in LOD and AAM budgets were determined and analysed in a similar way. These discrepancies were corrected for tidally excited effects. The non-tmospheric oscillations without the annual tide effect Sa and the semiannual tide effect Ssa have variable amplitudes between 0.02 and 0.10 msec.
Bayesian prediction of the total time on test using doubly censored rayleigh data

In a Bayesian setting, and on the basis of a doubly censored random sample of failure times drawn from a Rayleigh distribution, Fernandez (2000, Statist. Probab. Lett. , 48 , 393-399) considered the problem of predicting an independent future sample from the same distribution. In this article, we extend his work to include the estimation of the predictive distribution of the total time on test up to a certain failure in a future sample, as well as that of the remaining testing time time until all the items in the original sample have failed. Two examples are used to illustrate the prediction procedure.
Microscopic modeling of phonon dynamics and charge response in NdCuO

A description of phonon dynamics and charge response of the $n$-doped high-temperature superconductor (HTSC) NdCuO is presented based upon a microscopic modeling of the electronic density response. This is accomplished starting from the insulating state via the underdoped strange metallic to the more conventional metallic state by consecutive orbital selective incompressibility-compressibility transitions in terms of strict sum rules for the charge response. The approach proposed in this work for the $n$-doped HTSC's modifies the modeling recently applied to the $p$-doped compounds and expresses an electron-hole asymmetry introduced by doping. A qualitative physical picture consistent with our modeling of the electronic state in the cuprates is given in which a sufficiently broad set of orbital degrees of freedom, i.e. Cu3d/$4s$ and O$2p$ is essential. Within the framework of linear response theory we calculate full phonon dispersion curves in the different phases. In particular, the strongly doping dependent anomalous high-frequency oxygen bond-stretching modes (OBSM) found experimentally in the $p$-doped HTSC's and also recently for $n$-doped Nd$_{1.85}$Ce$_{0.15}$CuO$_{4}$ are investigated and compared with experimental results from inelastic neutron scattering and inelastic x-ray scattering, respectively. We calculate an anticrossing scenario for the OBSM in $n$-doped NdCuO which is absent in the case of $p$-doped LaCuO and relate it to the different crystal structure. Phonon-induced electronic charge redistributions of the anomalous OBSM due to nonlocal electron-phonon interaction effects of charge-fluctuation type giving reason to dynamic stripes are also studied.
Landau's theorems for certain biharmonic mappings

Let $f(z)=h(z)+\overline{g(z)}$ be a harmonic mapping of the unit disk $U$. In this paper, the sharp coefficient estimates for bounded planar harmonic mappings are established, the sharp coefficient estimates for normalized planar harmonic mappings with $|h(z)|+|g(z)|\leq M$ are also provided. As their applications, Landau's theorems for certain biharmonic mappings are provided, which improve and refine the related results of earlier authors.
On space-like constant slope surfaces and Bertrand curves in Minkowski 3-space

In the present paper, we define the notions of Lorentzian Sabban frames and de Sitter evolutes of the unit speed space-like curves on de Sitter 2-space $\mathbb{S}^{2}_{1}$. In addition, we investigate the invariants and geometric properties of these curves. Afterwards, we show that space-like Bertrand curves and time-like Bertrand curves can be constructed from unit speed space-like curves on de Sitter 2-space $\mathbb{S}^{2}_{1}$ and hyperbolic space $\mathbb{H}^{2}$, respectively. We obtain the relations between Bertrand curves and helices. Also we show that pseudo-spherical Darboux images of Bertrand curves are equal to pseudo-spherical evolutes in Minkowski 3-space $\mathbb{R}^{3}_{1}$. Moreover we investigate the relations between Bertrand curves and space-like constant slope surfaces in $\mathbb{R}^{3}_{1}$. Finally, we give some examples to illustrate our main results.
Quantitative Small Subgraph Conditioning

We revisit the method of small subgraph conditioning, used to establish that random regular graphs are Hamiltonian a.a. s. We refine this method using new technical machinery for random $d$-regular graphs on $n$ vertices that hold not just asymptotically, but for any values of $d$ and $n$. This lets us estimate how quickly the probability of containing a Hamiltonian cycle converges to 1, and it produces quantitative contiguity results between different models of random regular graphs. These results hold with $d$ held fixed or growing to infinity with $n$. As additional applications, we establish the distributional convergence of the number of Hamiltonian cycles when $d$ grows slowly to infinity, and we prove that the number of Hamiltonian cycles can be approximately computed from the graph's eigenvalues for almost all regular graphs.
From Monge to Higgs: a survey of distance computations in noncommutative geometry

This is a review of explicit computations of Connes distance in noncommutative geometry, covering finite dimensional spectral triples, almost-commutative geometries, and spectral triples on the algebra of compact operators. Several applications to physics are covered, like the metric interpretation of the Higgs field, and the comparison of Connes distance with the minimal length that emerges in various models of quantum spacetime. Links with other areas of mathematics are studied, in particular the horizontal distance in sub-Riemannian geometry. The interpretation of Connes distance as a noncommutative version of the Monge-Kantorovich metric in optimal transport is also discussed.
Nonwandering sets of interval skew products

In this paper we consider a class of skew products over transitive subshifts of finite type with interval fibres. For a natural class of 1-parameter families we prove that for all but countably many parameter values the nonwandering set (in particular, the union of all attractors and repellers) has zero measure. As a consequence, the same holds for a residual subset of the space of skew products.
Internal control for non-local Schr\"odinger and wave equations involving the fractional Laplace operator

We analyse the interior controllability problem for a non-local Schr\"odinger equation involving the fractional Laplace operator $(-\Delta)^s$, $s\in(0,1)$, on a bounded $C^{1,1}$ domain $\Omega\subset\mathbb{R}^n$. The controllability from a neighbourhood of the boundary of the domain is obtained for exponents $s$ in the interval $[1/2,1)$, while for $s\lt 1/2$ the equation is shown to be not controllable. As a consequence of that, we obtain the controllability for a non-local wave equation involving the higher order fractional Laplace operator $(-\Delta)^{2s}=(-\Delta)^s(-\Delta)^s$, $s\in[1/2,1)$. The results follow from a new Pohozaev-type identity for the fractional Laplacian recently proved by X. Ros-Oton and J. Serra and from an explicit computation of the spectrum of the operator in the one dimensional case.
Wavefront distortion measurements in the human breast

Published wavefront distortion (phase aberration) measurements for the human breast ranged from mild phase aberrations (8 ns r.m.s) to severe phase aberrations (67 ns r.m.s.). These measurements are required to specify arrays and assess the potentials of adaptive imaging. They require high inter-element uniformity so that receive signal variations between elements can be attributed to wave propagation effects. Array elements must be small to minimize the integration of the arriving wavefront across the face of the element. The authors have developed an apparatus to make concurrent pulse-echo and pitch-catch measurements in a clinical setting. The breast is stabilized between opposing transducers with light compression. After fixing the position of the transducers, pulse-echo and pitch-catch snapshots are captured sequentially with tissue and reference phantom targets. Data was collected from the left breast in twelve volunteers. Phase errors were significantly smaller for pulse-echo measurements (mean 25 ns r.m.s.) than for pitch-catch measurements (mean 55 ns r.m.s.).
An Accurate Parameterization of the Radiative Properties of Water Clouds Suitable for Use in Climate Models

Abstract A new parameterization of the radiative properties of water clouds is presented. Cloud optical properties for both solar and terrestrial spectra and for cloud equivalent radii in the range 2.5–60 µm are calculated from Mie theory. It is found that cloud optical properties depend mainly on equivalent radius throughout the solar and terrestrial spectrum and are insensitive to the details of the droplet size distribution, such as shape, skewness, width, and modality (single or bimodal). This suggests that in cloud models, aimed at predicting the evolution of cloud microphysics with climate change, it is sufficient to determine the third and the second moments of the size distribution (the ratio of which determines the equivalent radius). It also implies that measurements of the cloud liquid water content and the extinction coefficient are sufficient to determine cloud optical properties experimentally (i.e., measuring the complete droplet size distribution is not required). Based on the detailed cal.
Minimal $W$-Superalgebras and the Modular Representations of Basic Lie Superalgebras

Let $\mathfrak{g}=\mathfrak{g}_{\bar 0}+\mathfrak{g}_{\bar 1}$ be a basic Lie superalgebra over $\mathbb{C}$, and $e$ a minimal nilpotent element in $\mathfrak{g}_{\bar 0}$. Set $W_\chi'$ to be the refined $W$-superalgebra associated with the pair $(\mathfrak{g},e)$, which is called a minimal $W$-superalgebra. In this paper we present a set of explicit generators of minimal $W$-superalgebras and the commutators between them. In virtue of this, we show that over an algebraically closed field $\mathds{k}$ of characteristic $p\gg0$, the lower bounds of dimensions in the modular representations of basic Lie superalgebras with minimal nilpotent $p$-characters are attainable. Such lower bounds are indicated in \cite{WZ} as the super Kac-Weisfeiler property.
Artificial Neural Network Aided Loss Maps for Inductors and Transformers

The non-linear property of magnetics poses challenges for their loss modelling in power electronics due to lacking full physical models. As a practical approach for their loss estimation, the manufacturers can pre-measure the losses in standalone rigs and distribute the "loss maps" as interpolated look-up tables/curves for the end users. However, with more factors discovered that impact the losses, e.g., DC bias and load conditions, the dimensions of the loss maps cannot be solved by conventional surface/curve fitting methods. This paper addresses this problem by applying the Artificial Neural Network (ANN). For both inductors and transformers, Neural Network-aided loss maps (NNALMs) are designed and evaluated with comparisons against conventional loss maps to reveal the limitations of the latter caused by physically intercoupled input variables. The NNALMs not only show superior accuracy throughout the whole datasets, but also enable the loss maps to expand the dimensions to account for more factors (e.g., load conditions in transformers) and generate multiple outputs (e.g., both the winding loss and core loss). The ANN-aided loss maps can be distributed as digitized datasheets of standardized magnetics, enabling rapid, accurate and user-friendly loss estimations for power electronics engineers.
Local clustering coefficient of spatial preferential attachment model

In this paper, we study the clustering properties of the Spatial Preferential Attachment (SPA) model introduced by Aiello et al. in 2009. This model naturally combines geometry and preferential attachment using the notion of spheres of influence. It was previously shown in several research papers that graphs generated by the SPA model are similar to real-world networks in many aspects. For example, the vertex degree distribution was shown to follow a power law. In the current paper, we study the behavior of C(d), which is the average local clustering coefficient for the vertices of degree d. This characteristic was not previously analyzed in the SPA model. However, it was empirically shown that in real-world networks C(d) usually decreases as d^{-a} for some a>0 and it was often observed that a=1. We prove that in the SPA model C(d) degreases as 1/d.
Exponential inequalities for martingales with applications

The paper is devoted to establishing some general exponential inequalities for supermartingales. The inequalities improve or generalize many exponential inequalities of Bennett, Freedman, de la Pena, Pinelis and van de Geer. Moreover, our concentration inequalities also improve some known inequalities for sums of independent random variables. Applications associated with linear regressions, autoregressive processes and branching processes are provided. In particular, an interesting application of de la Pena’s inequality to self-normalized deviations is also provided.
Ensemble transform Kalman–Bucy filters

Two recent works have adapted the Kalman–Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo‐time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo‐time. Neither requires matrix inversions except for the frequently diagonal observation error covariance.
Exact p -divisibility of exponential sums via the covering method

In general, the methods to estimate the p -divisibility of exponential sums or the number of solutions of systems of polynomial equations over ﬁnite ﬁelds are non-elementary. In this paper we present the covering method, an elementary combinatorial method that can be used to compute the exact p -divisibility of exponential sums over a prime ﬁeld. The results here allow us to compute the exact p -divisibility of exponential sums of new families of polynomials, to unify and improve previously known results, and to construct families of systems of polynomial equations over ﬁnite ﬁelds that are solvable.
APR Tilting Modules and Graded Quivers with Potential

We study the quiver with relations of the endomorphism algebra of an APR tilting module. We give an explicit description of the quiver with relations by graded quivers with potential (QPs) and mutations. The result also implies that mutations of QPs with algebraic cuts induce tilting mutations between the associated truncated Jacobian algebras. Consequently, mutations of QPs provide a rich source of derived equivalence classes of algebras. As an application, we give a sufficient condition of QPs such that Derksen-Weyman-Zelevinsky's question has a positive answer.
Thoroughly Distributed Colorings

We consider (not necessarily proper) colorings of the vertices of a graph where every color is thoroughly distributed, that is, appears in every open neighborhood. Equivalently, every color is a total dominating set. We define $\td(G)$ as the maximum number of colors in such a coloring and $\FTD(G)$ as the fractional version thereof. In particular, we show that every claw-free graph with minimum degree at least~$2$ has~$\FTD(G)\ge 3/2$ and this is best possible. For planar graphs, we show that every triangular disc has $\FTD(G) \ge 3/2$ and this is best possible, and that every planar graph has $\td(G) \le 4$ and this is best possible, while we conjecture that every planar triangulation has $\td(G)\ge 2$. Further, although there are arbitrarily large examples of connected, cubic graphs with $\td(G)=1$, we show that for a connected cubic graph $\FTD(G) \ge 2-o(1)$, and conjecture that it is always at least~$2$. We also consider the related concepts in hypergraphs.
Unstable entropies and dimension theory of partially hyperbolic systems

In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carathéodory–Pesin dimension characteristic, motivated by the work of Bowen and Pesin etc. We then establish some basic results in dimension theory for Bowen unstable topological entropy, including an entropy distribution principle and a variational principle in general setting. As applications of this new concept, we study unstable topological entropy of saturated sets and extend some results in Bowen (1973 Trans. Am. Math. Soc. 184 125–36); Pfister and Sullivan (2007 Ergod. Theor. Dynam. Syst. 27 929–56). Our results give new insights to the multifractal analysis for partially hyperbolic systems.
Clinical Observation of Low-Temperature Plasma Knife Tonsil Adenoidectomy for Pediatric Snoring and Analysis of Influencing Factors

Objective To investigate the clinical efficacy of low-temperature plasma knife tonsil adenoidectomy for pediatric snoring and to analyze the factors influencing the efficacy. Methods 90 children with snoring who were scheduled for surgical treatment in our hospital from June 2020 to December 2021 were selected as the research objects. According to the random number table method, they were divided into control group (group C) and observation group (group O), with 45 cases in each group. The children in group C were treated with power cutting system to remove adenoids combined with conventional peeling of bilateral tonsils, while the children in group O were treated with low-temperature plasma adenoidectomy combined with bilateral tonsillectomy, and both the groups received psychological care, preoperative preparation, health guidance, postoperative posture care and close monitoring of vital signs during the perioperative period. The clinical efficacy, perioperative related indexes (including operation time, intraoperative bleeding, postoperative pain time, and hospital stay) were compared between the two groups. The apnea-hypopnea index (AHI), oxygen decrement index (ODI), longest apnea time (LAT), and lowest oxygen saturation (LSaO2) were measured before operation and 1 week after operation to evaluate the ventilatory function of the two groups. According to the curative effect, 90 children with snoring were divided into cure + significant effective group and valid + invalid group. The general data and preoperative biochemical indexes of the two groups were collected, and logistic regression model was used to analyze the related influencing factors of the curative effect. Results The total effective rate of group O (100.00%, 45 cases) was significantly higher than that of group C (91.11%, 41 cases) (P < 0.05); the operative time, intraoperative bleeding, postoperative pain time, and hospitalization time of group O were shorter/less than those of group C; the AHI, ODI, and LAT of group O at 1 week after surgery were shorter/less than those of the control group; and LSaO2 was higher than that of group C. The differences were statistically significant (P < 0.05). Univariate analysis showed that there were significant differences in age, BMI, course of disease, preoperative AHI, preoperative LsaO2, and surgical method between cure + significant effective group and valid + invalid group (P < 0.05). Multivariate analysis showed that high BMI, high preoperative AHI, and power cutting system for adenoids combined with routine peeling of the bilateral tonsils were independent risk factors for postoperative outcome in children with obstructive sleep apnea syndrome (OSAS) (P < 0.05).
The phase space of boxy–peanut and X-shaped bulges in galaxies – I. Properties of non-periodic orbits

The investigation of the phase-space properties of structures encountered in a dynamical system is essential for understanding their formation and enhancement. In the present paper we explore the phase space in energy intervals where we have orbits that act as building blocks for boxy-peanut (b/p) and "{\sf X}-shaped" structures in rotating potentials of galactic type. We underline the significance of the rotational tori around the 3D families x1v1 and x1v1$^{\prime}$ that have been bifurcated from the planar x1 family. These tori play a multiple role: (i) They belong to quasi-periodic orbits that reinforce the local density. (ii) They act as obstacles for the diffusion of chaotic orbits and (iii) they attract a large number of chaotic orbits that become sticky to them. There are also bifurcations of unstable families (x1v2, x1v2$^{\prime}$). Their unstable asymptotic curves wind around the x1v1 and x1v1$^{\prime}$ tori generating orbits with hybrid morphologies between that of x1v1 and x1v2. In addition, a new family of multiplicity 2, called x1mul2, is found to be important for the peanut construction. Our work shows also that there are peanut-supporting orbits before the vertical ILR. Non-periodic orbits associated with the x1 family secure this contribution as well as the support of b/p structures at several other energy intervals. Non-linear phenomena associated with complex instability of single and double multiplicity families of periodic orbits show that these structures are not interrupted in regions where such orbits prevail. Depending on the main mechanism behind their formation, boxy bulges exhibit different morphological features. Finally our analysis indicates that "X" features shaped by orbits in the neighbourhood of x1v1 and x1v1$^{\prime}$ periodic orbits are pronounced only in side-on or nearly end-on views of the bar.