Miracle-dz/UniFAR-FTUs huggingface dataset:
A priori error analysis of the $hp$-mortar FEM for parabolic problems

In this article we derive a priori error estimates for the $hp$-version of the mortar finite element method for parabolic initial-boundary value problems. Both semidiscrete and fully discrete methods are analysed in $L^2$- and $H^1$-norms. The superconvergence results for the solution of the semidiscrete problem are studied in an eqivalent negative norm, with an extra regularity assumption. Numerical experiments are conducted to validate the theoretical findings.
Formation of authigenic grey monazite: a marker of palaeo- thermal anomaly in very-low grade metamorphic rocks?

The reassessment of the rare earth element (REE) potential of France led us to investigate REE behaviour in black-shales belonging to the Middle Ordovician Angers-Traveusot formation from central Britany (France), with an emphasis on the formation of nodular grey monazite during the diagenetic and low-grade metamorphic evolution. Temperatures conditions and mass transfer underwent in the black shales were first characterized using rock geochemistry, rock-eval pyrolysis and by gradual changes of clay mineral crystallinity. Then, monazite texture, composition and U–Pb in-situ dating were determined and correlated with the diagenetic/anchimetamorphic conditions. In the Ordovician black shales, nodular monazite appears at the transition between the upper diagenesis and the anchizone metamorphic facies, at conditions between 140 and 250°C, in response to processes controlled by different proxies of competing influences such as the organic matter maturation, Fe oxide/hydroxide and clay transformation with fluid releasing. Monazite occurs mainly as elongated nodules, up to 2 mm in diameter that are mostly characterised by their grey colour due to abundance in host-rock mineral inclusions. Monazite nodules compositions are systematically low in Th and U contents but are zoned with Nd and middle REE rich cores surrounded by light REE-rich rims, with no evidence of inherited domains. More rarely, small grains of LREE-rich monazite are observed in late stage fractures. Monazite nodules were dated at ca. 405-400 Ma, which is proposed to record high heat flux responsible of the anchimetamorphic conditions recorded at the base of Angers-Traveusot formation. Late monazite-Ce were dated at ca. 385 and 350 Ma at the onset of the Variscan deformation. Preprint – Not peer-reviewed
hardy-littlewood inequalities and fourier multipliers on $SU(2)$

In this paper we prove a noncommutative version of Hardy-Littlewood inequalities relating a function and its Fourier coefficients on the group $SU(2)$. As a consequence, we use it to obtain lower bounds for the $L^p-L^q$ norms of Fourier multipliers on the group $SU(2)$, for $1 < p \leq 2 \leq q < 1$. In addition, we give upper bounds of a similar form, analogous to the known results on the torus, but now in the noncommutative setting of $SU(2)$.
Topological radicals, IV. Frattini theory for Banach Lie algebras

The paper develops the theory of topological radicals of Banach Lie algebras and studies the structure of Banach Lie algebras with sufficiently many Lie subalgebras of finite codimensions -- the intersection of all these subalgebras is zero. It is shown that the intersections of certain families of Lie subalgebras (closed Lie subalgebras of finite codimension, closed Lie ideals of finite codimension, closed maximal Lie subalgebras of finite codimension, closed maximal Lie ideals of finite codimension) correspond to different preradicals, and that these preradicals generate the same radical, the Frattini radical. The main attention is given to structural properties of Frattini-semisimple Banach Lie algebras and, in particular, to a new infinite-dimensional phenomenon associated with the strong Frattini preradical introduced in this paper. A constructive description of Frattini-free Banach Lie algebras is obtained.
Star-forming galaxies at z∼ 2 and the formation of the metal-rich globular cluster population

We examine whether the super star-forming (super-SF) clumps (R∼ 1–3 kpc; M∼ 108– 109.5 M⊙) now known to be a key component of star-forming galaxies at z∼ 2 could be the formation sites of the locally observed old globular cluster (GC) population. We find that the stellar populations of these super-SF clumps are excellent matches to those of local metal-rich GCs. Moreover, this GC population is known to be associated with the bulges/thick discs of galaxies, and we show that its spatial distribution and kinematics are consistent with the current understanding of the assembly of bulges and thick discs from super-SF clumps at high redshift. Finally, with the assumption that star formation in these clumps proceeds as a scaled-up version of local star formation in molecular clouds, this formation scenario reproduces the observed numbers and mass spectra of metal-rich GCs. The resulting link between the turbulent and clumpy discs observed in high-redshift galaxies and a local GC population provides a plausible co-evolutionary scenario for several of the major components of a galaxy: the bulge, the thick disc and one of the GC populations.
On the Cauchy problem for scalar conservation laws in the class of Besicovitch almost periodic functions: Global well-posedness and decay property

We study the Cauchy problem for a multidimensional scalar conservation law with merely continuous flux vector in the class of Besicovitch almost periodic functions. The existence and uniqueness of entropy solutions are established. We also uncover the necessary and sufficient condition for the decay of almost periodic entropy solutions as the time variable t → +∞. Our results are then interpreted in the framework of conservation laws on the Bohr compact.
Query on Negative Temperature, Internal Interactions and Decrease of Entropy

After negative temperature is restated, we find that it will derive necessarily decrease of entropy. Negative temperature is based on the Kelvin scale and the condition dU>0 and dS 0. But, negative temperature is contradiction with usual meaning of temperature and with some basic concepts of physics and mathematics. It is a question in nonequilibrium thermodynamics. We proposed a possibility of decrease of entropy due to fluctuation magnified and internal interactions in some isolated systems. From this we discuss some possible examples and theories.
CONSTRAINTS ON NEUTRINO MASSES FROM THE LENSING DISPERSION OF TYPE Ia SUPERNOVAE

We investigate how accurately the total mass of neutrinos is constrained from the magnitude dispersion of SNe Ia due to the effects of gravitational lensing. For this purpose, we use the propagation equation of light bundles in a realistic inhomogeneous universe and propose a sample selection for supernovae to avoid difficulties associated with small-scale effects such as strong lensing or shear effects. With a fitting formula for the nonlinear matter power spectrum taking account of the effects of massive neutrinos, we find that in our model it is possible to obtain the upper limit for future optical imaging surveys with the Wide-Field InfraRed Survey Telescope and Large Synoptic Survey Telescope. Furthermore, we discuss how far we need to observe SNe Ia and to what extent we have to reduce the magnitude error except for lensing in order to realize the current tightest limit .
Expression and relationship with immunity of LRFN4 in lung adenocarcinoma: Based on bioinformatics analysis

Leucine rich repeat and fibronectin type III domain containing 4(LRFN4) has been reported to be upregulated in multiple tumors and related to prognosis and survival of patients. However, the function of LRFN4 in LUAD is still unclear. Herein, bioinformatic approach was used for the first time to elucidate the relationship between LRFN4 and LUAD. In LUAD tissues, we discovered that LRFN4 mRNA expression was considerably higher. Higher LRFN4 expression was associated with poorer prognosis and higher clinical stage of LUAD patients. Paraffin pathology sections (12 samples including LUAD tissues and paired normal tissues from the Second Affiliated Hospital of Chongqing Medical University) were used to verify the expression of LRFN4 at the protein level by immunohistochemical staining. On the other hand, we identified that LRFN4 expression was related to multiple immune cells that constitute tumor immune microenvironment. Pathway enrichment analysis also suggested the enrichment of several tumor- and immune-related pathways, such as: Hippo pathway, NOD-like pathway, TNF pathway and P53 pathway. Finally, we constructed an 8-gene prognostic risk signature based on 35 LRFN4-related immunomodulators using the Cox regression model, and obtained reasonably good accuracy through Receiver Operating Characteristic curve (ROC curve) validation. The risk signature was further identified as an independent risk factor - was linked with worse survival of LUAD patients. Furthermore, a prognostic risk profile based on LRFN4-related immunomodulators was constructed. Meanwhile, other clinical features were integrated together as prognostic markers to construct a nomogram to predict the long-term survival probability of LUAD patients, and fairly high credibility was obtained by validation of calibration curves.
Altered structural connectome of children with auditory processing disorder: a diffusion MRI study

Auditory processing disorder (APD) is a listening impairment that some school-aged children may experience as difficulty understanding speech in background noise despite having normal peripheral hearing. Recent resting-state functional magnetic resonance imaging (MRI) has revealed an alteration in regional, but not global, functional brain topology in children with APD. However, little is known about the brain structural organization in APD. We used diffusion MRI data to investigate the structural white matter connectome of 58 children from 8 to 14 years old diagnosed with APD (n=29) and children without hearing complaints (healthy controls, HC; n=29). We investigated the rich-club organization and structural connection differences between APD and HC groups using the network science approach. The APD group showed neither edge-based connectivity differences nor any differences in rich-club organization and connectivity strength (i.e., rich, feeder, local connections) compared to HCs. However, at the regional network level, we observed increased average path length (APL) and betweenness centrality in the right inferior parietal lobule and inferior precentral gyrus, respectively, in children with APD. HCs demonstrated a positive association between APL in the left orbital gyrus and the listening-in-spatialized-noise-sentences task, a measure of auditory processing ability. This correlation was not observed in the APD group. In line with previous functional connectome findings, the current results provide evidence for altered structural networks at a regional level in children with APD, and an association with listening performance, suggesting the involvement of multimodal deficits and a role for structure-function alteration in listening difficulties of children with APD.
Magnetic fields of opposite polarity in sunspot penumbrae

Context. A significant part of the penumbral magnetic field returns below the surface in the very deep photosphere. For lines in the visible, a large portion of this return field can only be detected indirectly by studying its imprints on strongly asymmetric and three-lobed Stokes V profiles. Infrared lines probe a narrow layer in the very deep photosphere, providing the possibility of directly measuring the orientation of magnetic fields close to the solar surface. Aims. We study the topology of the penumbral magnetic field in the lower photosphere, focusing on regions where it returns below the surface. Methods. We analyzed 71 spectropolarimetric datasets from Hinode and from the GREGOR infrared spectrograph. We inferred the quality and polarimetric accuracy of the infrared data after applying several reduction steps. Techniques of spectral inversion and forward synthesis were used to test the detection algorithm. We compared the morphology and the fractional penumbral area covered by reversed-polarity and three-lobed Stokes V profiles for sunspots at disk center. We determined the amount of reversed-polarity and three-lobed Stokes V profiles in visible and infrared data of sunspots at various heliocentric angles. From the results, we computed center-to-limb variation curves, which were interpreted in the context of existing penumbral models. Results. Observations in visible and near-infrared spectral lines yield a significant difference in the penumbral area covered by magnetic fields of opposite polarity. In the infrared, the number of reversed-polarity Stokes V profiles is smaller by a factor of two than in the visible. For three-lobed Stokes V profiles the numbers differ by up to an order of magnitude.
Second variation of domain functionals and applications to problems with Robin boundary conditions

In this paper the rst and second domain variation for functionals related to elliptic boundary and eigenvalue problems with Robin boundary conditions is computed. Minimality and maximality properties of the ball among nearly circular domains of given volume are derived. The discussion leads to the investigation of the eigenvalues of a Steklov eigenvalue problem. As a byproduct a general characterization of the optimal shapes is obtained.
On Rogers–Shephard Type Inequalities for General Measures

In this paper we prove a series of Rogers–Shephard type inequalities for convex bodies when dealing with measures on the Euclidean space with either radially decreasing densities or quasi-concave densities attaining their maximum at the origin. Functional versions of classical Rogers–Shephard inequalities are also derived as consequences of our approach.
Incidence of strong Mg ii absorbers towards different types of quasars

We report the first comparative study of strong MgII absorbers seen towards radio-loud quasars of core-dominated (CDQs) and lobe-dominated (LDQs) types and normal QSOs. The MgII associated absorption systems having a velocity offset v 0.2. The computed redshift distribution for strong MgII absorbers towards CDQs now shows excellent agreement with that known for QSOs, as indeed is expected for purely intervening absorption systems. Thus, it appears that for CDQs the associated strong MgII absorbers can be seen at much larger velocities relative to the nucleus than the commonly adopted upper limit of 5000km/s.
Spectral analysis of subordinate Brownian motions on the half-line

We study one-dimensional Levy processes with Levy-Khintchine exponent psi(xi^2), where psi is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators, whose Levy measure has completely monotone density; or, equivalently, symmetric Levy processes whose Levy measure has completely monotone density on the positive half-line. Examples include symmetric stable processes and relativistic processes. The main result is a formula for the generalized eigenfunctions of transition operators of the process killed after exiting the half-line. A generalized eigenfunction expansion of the transition operators is derived. As an application, a formula for the distribution of the first passage time (or the supremum functional) is obtained.
FORMATION OF SILICON OXIDE GRAINS AT LOW TEMPERATURE

The formation of grains in the interstellar medium, i.e., at low temperature, has been proposed as a possibility to solve the lifetime problem of cosmic dust. This process lacks a firm experimental basis, which is the goal of this study. We have investigated the condensation of SiO molecules at low temperature using neon matrix and helium droplet isolation techniques. The energies of SiO polymerization reactions have been determined experimentally with a calorimetric method and theoretically with calculations based on the density functional theory. The combined experimental and theoretical values have revealed the formation of cyclic (SiO)k (k = 2–3) clusters inside helium droplets at T = 0.37 K. Therefore, the oligomerization of SiO molecules is found to be barrierless and is expected to be fast in the low-temperature environment of the interstellar medium on the surface of dust grains. The incorporation of numerous SiO molecules in helium droplets leads to the formation of nanoscale amorphous SiO grains. Similarly, the annealing and evaporation of SiO-doped Ne matrices lead to the formation of solid amorphous SiO on the substrate. The structure and composition of the grains were determined by infrared absorption spectroscopy, transmission electron microscopy, and energy-dispersive X-ray spectroscopy. Our results support the hypothesis that interstellar silicates can be formed in the low-temperature regions of the interstellar medium by accretion through barrierless reactions.
Tubes of finite Chen-type

In this paper, we consider surfaces in the 3-dimensional Euclidean space E which are of finite III-type, that is, they are of finite type, in the sense of B. -Y. Chen, corresponding to the third fundamental form. We present an important family of surfaces, namely, tubes in E. We show that tubes are of infinite III-type.
‘Quantum hairs’ and entropy of the quantum isolated horizon from Chern–Simons theory

We articulate the fact that the loop quantum gravity (LQG) description of the quantum macrostates of black hole horizons, modeled as quantum isolated horizons (QIHs), is completely characterized in terms of two independent integer-valued ‘quantum hairs’, viz, the coupling constant ( k ) ? > of the quantum SU ( 2 ) ? > Chern–Simons (CS) theory describing QIH dynamics, and the number of punctures ( N ) ? > produced by the bulk spin network edges piercing the isolated horizon (which act as pointlike sources for the CS fields). We demonstrate that the microcanonical entropy of macroscopic (both parameters assuming very large values) QIHs can be obtained directly from the microstates of this CS theory using standard statistical mechanical methods, without having to additionally postulate the horizon as an ideal gas of punctures, or incorporate any additional classical or semiclassical input from general relativity vis-a-vis the functional dependence of the isolated horizon mass on its area, or indeed, without having to restrict to any special class of spins. Requiring the validity of the Bekenstein–Hawking area law relates these two parameters (as an equilibrium ‘equation of state’), and consequently allows the Barbero–Immirzi parameter to take any real and positive value depending on the value of k / N ? > . The logarithmic correction to the area law obtained a decade ago by R Kaul and one of us (PM), ensues straightforwardly, with precisely the coefficient − 3 / 2 ? > , making it a signature of the LQG approach to black hole entropy.
Limits on gravitational Einstein equivalence principle violation from monitoring atomic clock frequencies during a year

Sun's gravitation potential at earth varies during a year due to varying Earth-Sun distance. Comparing the results of very accurate measurements of atomic clock transitions performed at different time in the year allows us to study the dependence of the atomic frequencies on the gravitational potential. We examine the measurement data for the ratio of the frequencies in Hg$^+$ and Al$^+$ clock transitions and absolute frequency measurements (with respect to caesium frequency standard) for Dy, Sr, H, hyperfine transitions in Rb and H, and obtain significantly improved limits on the values of the gravity related parameter of the Einstein Equivalence Principle violating term in the Standard Model Extension Hamiltonian $c_{00} = (3.0 \pm 5.7) \times 10^{-7}$ and the parameter for the gravity-related variation of the fine structure constant $\kappa_{\alpha} = (-5.3 \pm 10) \times 10^{-8}$.
Electron acceleration in three-dimensional magnetic reconnection with a guide field

Kinetic simulations of 3D collisionless magnetic reconnection with a guide field show a dramatic enhancement of energetic electron production when compared with 2D systems. In the 2D systems, electrons are trapped in magnetic islands that limit their energy gain, whereas in the 3D systems the filamentation of the current layer leads to a stochastic magnetic field that enables the electrons to access volume-filling acceleration regions. The dominant accelerator of the most energetic electrons is a Fermi-like mechanism associated with reflection of charged particles from contracting field lines.
Rational cobordisms and integral homology

We consider the question of when a rational homology $3$-sphere is rational homology cobordant to a connected sum of lens spaces. We prove that every rational homology cobordism class in the subgroup generated by lens spaces is represented by a unique connected sum of lens spaces whose first homology group injects in the first homology group of any other element in the same class. As a first consequence, we show that several natural maps to the rational homology cobordism group have infinite-rank cokernels. Further consequences include a divisibility condition between the determinants of a connected sum of $2$-bridge knots and any other knot in the same concordance class. Lastly, we use knot Floer homology combined with our main result to obstruct Dehn surgeries on knots from being rationally cobordant to lens spaces.
A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions

We establish a representation of the joint moments of the characteristic polynomial of a CUE random matrix and its derivative in terms of a solution of the -Painlevé V equation. The derivation involves the analysis of a formula for the joint moments in terms of a determinant of generalised Laguerre polynomials using the Riemann–Hilbert method. We use this connection with the -Painlevé V equation to derive explicit formulae for the joint moments and to show that in the large-matrix limit the joint moments are related to a solution of the -Painlevé III equation. Using the conformal block expansion of the -functions associated with the -Painlevé V and the -Painlevé III equations leads to general conjectures for the joint moments.
Effective model-completeness for p-adic analytic structures

In this paper, we combine classical techniques of model theory of p-adic subanalytic sets with results of tropical analytic geometry to obtain a result of effective model-completeness. We consider languages L_F=( +,.,0,1, P_n, f; for all n natural number and f in F) where F is a family of restricted analytic functions. Definable sets in this language are a collection of p-adic subanalytic sets. The main result of the paper gives conditions on F so that the structure with underlying set Zp (the ring of p-adic integers) in this language is effectively model-complete. An interesting example of language satisfying our hypotheses is the case where F={exp(px)}. This example gives a structure of exponential ring to Zp which is a natural $p$-adic equivalent to the (restricted) real exponential field.