Miracle-dz/UniFAR-FTUs huggingface dataset:
Atmospheric Wake of Madeira: First Aerial Observations and Numerical Simulations

AbstractThe island of Madeira is well known for giving rise to atmospheric wakes. Strong and unsteady atmospheric wakes, resembling a von Karman vortex street, are frequently observed in satellite images leeward of Madeira, especially during summer months, when conditions favoring the formation of atmospheric wakes occur frequently under the influence of the Azores high.Reported here is the analysis of the first airborne measurements of Madeira’s wake collected during the 2010 Island-induced Wake (I-WAKE) campaign. High-resolution in situ and remote sensing data were collected in the I-WAKE by a research aircraft. The measurements reveal distinctive wake signatures, including strong lateral wind shear zones and warm and dry eddies downwind of the island. A strong anticorrelation of the horizontal wind speed and sea surface temperature (SST) was found within the wake.High-resolution numerical simulations with the Weather Research and Forecasting (WRF) Model were used to study the dynamics of the wake gener.
Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity

Complete Elliptic Integrals and the Arithmetic-Geometric Mean Iteration. Theta Functions and the Arithmetic-Geometric Mean Iteration. Jacobi's Triple-Product and Some Number Theoretic Applications. Higher Order Transformations. Modular Equations and Algebraic Approximations to pi. The Complexity of Algebraic Functions. Algorithms for the Elementary Functions. General Means and Iterations. Some Additional Applications. Other Approaches to the Elementary Functions. Pi. Bibliography. Symbol List. Index.
Capillary oscillations on liquid jets

Capillary oscillations on modulated liquid jets have been investigated using laser illumination and electronic detection of the magnified jet shadow. The amplitudes of several wave harmonics of a growing spatial instability were measured as a function of distance from the orifice for a range of jet velocities and initial‐disturbance amplitudes. The experimentally determined growth rates at the fundamental frequency are compared with theories of capillary‐wave propagation. An empirically derived explanation of the suppression of satellite formation is given. Experimental evidence for infinite‐wavelength capillary oscillations is reported; a description of these oscillations in terms of the Rayleigh theory is presented.
Completeness of generalized transmission eigenstates

We prove the completeness of the generalized (interior) transmission eigenstates for the acoustic and Schrödinger equations. The method uses the ellipticity theory of Agranovich and Vishik. Research supported by the Mittag-Leffler Institute Research supported by the ERC 2010 Advanced Grant 267700
Boundedness up to blow-up of the difference between two solutions to a semilinear heat equation

We consider u1 and u2, two blow-up solutions of ∂t u = Δu + | u | p-1 u (x, t) N × [0, T ) where p > 1, (N - 2) p < N + 2 and either u(0) ≥ 0 or (3N - 4) p < 3N + 8. We assume that u1 and u2 blow-up at the same time T, at the same unique point a N and that they have the same (generic) profile. We then obtain a sharp estimate on | u1 - u2 | for all (x, t) N × [0, T ). In particular, we show that, up to a scaling, this difference is uniformly bounded and goes to zero as (x, t) → (a,T ), provided that N = 1 and p ≥ 3. As an application of our result, we show the stability of the considered profile in N dimensions.
Electron velocity distributions near the Earth's bow shock

A survey of two-dimensional electron velocity distributions, ƒ(V), measured near the earth's bow shock using Los Alamos/Garching plasma instrumentation aboard ISEE 2 is presented. This survey provides clues to the mechanisms of electron thermalization within the shock and the relaxation of both the upstream and downstream velocity distributions. First, near the foreshock boundary, fluxes of electrons having a power law shape at high energies backstream from the shock. Although most often they appear as a monotonically decreasing extension of solar wind distributions in the backward hemisphere along the magnetic field direction, , they occasionally appear as a resolved peak in energy. Within the interior of the foreshock, in addition to the hot, isotropic electrons at higher energies, field-aligned depressions in ƒ(V) are observed at the lowest energies (E ≲ 15 eV) and twin angular peaks centered on are observed at intermediate energies (15 eV ≲ E ≲ 45 eV). Such distributions are associated closely with 1-Hz whistler waves. Second, within the shock, cuts through ƒ(V) along ƒ(V∥), often show single maxima offset toward the magnetosheath by speeds comparable to, but larger than, the upstream thermal speed. When sequences of such distributions are observed in a single shock transition, offset speeds increase and peak heights of ƒ(V∥) decrease with increasing penetration toward the downstream (magnetosheath) side. Third, magnetosheath distributions generally have flat tops out to an energy, E0, with maxima substantially lower than that in the solar wind. Occasionally, cuts through ƒ(V) along show one and sometimes two small peaks at the edge of the flat tops making them appear concave upward. The magnetosheath distributions often have strong angular anisotropies which depend on energy. For energies less than E0, ƒ(V∥) > ƒ(V⊥) at constant E, whereas for E > E0, ƒ(V∥) < ƒ(V⊥). The electron distributions characteristic of these three regions are interpreted as arising from the effects of macroscopic (scale size comparable to or larger than the shock width) electric and magnetic fields and the subsequent effects of microscopic (scale size small in comparison with the shock width) fields. In particular, our results suggest that field-aligned instabilities are likely to be present in the earth's bow shock.
Monotonicity of the Sample Range of 3-D Data: Moments of Volumes of Random Tetrahedra

The sample range of uniform random points $X_1, \dots , X_n$ chosen in a given convex set is the convex hull ${\rm conv}[X_1, \dots, X_n]$. It is shown that in dimension three the expected volume of the sample range is not monotone with respect to set inclusion. This answers a question by Meckes in the negative. The given counterexample is the three-dimensional tetrahedron together with an infinitesimal variation of it. As side result we obtain an explicit formula for all even moments of the volume of a random simplex which is the convex hull of three uniform random points in the tetrahedron and the center of one facet.
Smooth and singular Kahler-Einstein metrics

Smooth Kähler–Einstein metrics have been studied for the past 80 years. More recently, singular Kähler–Einstein metrics have emerged as objects of intrinsic interest, both in differential and algebraic geometry, as well as a powerful tool in better understanding their smooth counterparts. This article is mostly a survey of some of these developments.
Distortion elements for surface homeomorphisms

Let S be a compact orientable surface and f be an element of the group Homeo_{0}(S) of homeomorphisms of S isotopic to the identity. Denote by F a lift of f to the universal cover of S. In this article, the following result is proved: if there exists a fundamental domain D of the universal cover of S such that the sequence (d_{n}log(d_{n})/n) converges to 0 where d_{n} is the diameter of F^{n}(D), then the homeomorphism f is a distortion element of the group Homeo_{0}(S).
High magnetic field study of the Gd-Co exchange interactions in GdCo12B6

Pulsed magnetic fields up to 68 Tesla have been used to determine the intersublattice coupling strength and its temperature dependence of GdCo12B6 compound. This compound exhibits ferrimagnetic behaviour below 163 ± 2 K. Two antiferromagnetically coupled sublattices cancel out at compensation temperature at about 48 K. They are carrying magnetization of typically 0.42 μB/Co atom and 7 μB/Gd. The intrinsic magnetic properties of the GdCo12B6 compound have been determined by combining low temperature magnetic measurements in both steady and pulsed magnetic field, as well as isofield studies in steady field. At 4.2 K, the magnetization curve of GdCo12B6 is found to reach the full saturation with sum of both sublattice magnetizations for an applied magnetic field of about 68 T. In addition a detailed study is presented in the whole ordered temperature range on the basis of magnetization curves recorded using pulsed magnetic field up to 60 T. This has enabled to investigate the intersublattice coupling strengt.
Curvature Properties of Quasi-Para-Sasakian Manifolds

The present paper is devoted to quasi-Para-Sasakian manifolds. Basic properties of such manifolds are obtained and general curvature identities are investigated. Next it is proved that if $M$ is quasi-Para-Sasakian manifold of constant curvature $K$. Then $K$ $\leq 0$ and $(i)~$if $K=0$, the manifold is paracosymplectic, $(ii)$ if $K<0$, the quasi-para-Sasakian structure of $M$ is obtained by a homothetic deformation of a para-Sasakian structure.
Local asymptotics for the area under the random walk excursion

Abstract We study the tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and light-tailed increments. We determine the asymptotics for local probabilities for the area and prove a local central limit theorem for the duration of the excursion conditioned on the large values of its area.
Fluid Flow in a System with Separate Laminar and Turbulent Zones

Attention is focused on physical situations in which separate zones of laminar and turbulent flow coexist within a given device. The specific motivating application for this study is a complex fluid-flow manifold used in the thermal management of electronic equipment. The adopted approach to the solution of this fluid-flow problem was to employ a turbulent-flow model for the entire solution space but to use several turbulence models as inputs. The goal of the study was to quantify the behavior of popular turbulence models in regions where the flow is laminar according to the accepted Reynolds number criteria. Three models were considered: 1) standard k-ϵ, 2) k-ω, and 3) SST. Evaluation of the models was based on the values of the ratio μ t /μ in nominally laminar regions, where μ t and μ are, respectively, the turbulent and molecular viscosities. Values of this ratio well below one in a nominally laminar region would indicate that a turbulence model reduces, in effect, to a laminar model. It was found that the standard k-ϵ model failed to provide values of μ t /μ << 1 for channel Reynolds numbers as low as 370. On the other hand, both the k-ω and SST models yielded values of μ t /μ << 1 for Re = 370. For these models, acceptably small values of the ratio were encountered for Reynolds numbers up to 370. At still higher Reynolds numbers, these turbulence models did not reduce to laminar models. Results for the relationship between the overall pressure drop and the system flowrate are also presented for use in practical applications.
Structure of martingale transports in finite dimensions

We study the structure of martingale transports in finite dimensions. We consider the family $\mathcal{M}(\mu,\nu) $ of martingale measures on $\mathbb{R}^N \times \mathbb{R}^N$ with given marginals $\mu,\nu$, and construct a family of relatively open convex sets $\{C_x:x\in \mathbb{R}^N \}$, which forms a partition of $\mathbb{R}^N$, and such that any martingale transport in $\mathcal{M}(\mu,\nu) $ sends mass from $x$ to within $\overline{C_x}$, $\mu(dx)$--a.e. Our results extend the analogous one-dimensional results of M. Beiglbock and N. Juillet (2016) and M. Beiglbock, M. Nutz, and N. Touzi (2015). We conjecture that the decomposition is canonical and minimal in the sense that it allows to characterise the martingale polar sets, i.e. the sets which have zero mass under all measures in $\mathcal{M}(\mu,\nu)$, and offers the martingale analogue of the characterisation of transport polar sets proved in M. Beiglbock, M. Goldstern, G. Maresch, and W. Schachermayer (2009).
Perverse Coherent Sheaves on Blow-ups at Codimension 2 Loci

Let $f \colon X \to Y$ be the blow-up of a smooth projective variety $Y$ along its codimension two smooth closed subvariety. In this paper, we show that the moduli space of stable sheaves on $X$ and $Y$ are connected by a sequence of flip-like diagrams. The result is a higher dimensional generalization of the result of Nakajima and Yoshioka, which is the case of $\dim Y=2$. As an application of our general result, we study the birational geometry of the Hilbert scheme of two points.
Unitaires multiplicatifs en dimension finie et leurs sous-objets

Dans cet article, nous etudions l'equivalent des sous-groupes pour les algebres de Kac de dimension finie. Nous montrons que les \og sous-groupes\fg\ en notre sens correspondent aux sous-algebres coideales des algebres de Hopf (\cf \eg [\ref\Mon]) et donc aux facteurs intermediaires des inclusions de profondeur 2
The elliptic evolution of non-self-adjoint degree-2 Hamiltonians

We study the relationship between the classical Hamilton flow and the quantum Schrodinger evolution where the Hamiltonian is a degree-2 complex-valued polynomial. When the flow obeys a strict positivity condition equivalent to compactness of the evolution operator, we find geometric expressions for the L^2 operator norm and a singular-value decomposition of the Schrodinger evolution, using the Hamilton flow. The flow also gives a geometric composition law for these operators, which correspond to a large class of integral operators with nondegenerate Gaussian kernels.
Sensitivity analysis for optimal control problems governed by nonlinear evolution inclusions

Abstract We consider a nonlinear optimal control problem governed by a nonlinear evolution inclusion and depending on a parameter λ. First we examine the dynamics of the problem and establish the nonemptiness of the solution set and produce continuous selections of the solution multifunction ξ ↦ S ⁢ ( ξ ) ${\xi\mapsto S(\xi\/)}$ (ξ being the initial condition). These results are proved in a very general framework and are of independent interest as results about evolution inclusions. Then we use them to study the sensitivity properties of the optimal control problem. We show that we have Hadamard well-posedness (continuity of the value function), and we establish the continuity properties of the optimal multifunction. Finally, we present an application on a nonlinear parabolic distributed parameter system.
New methods for bounding the number of points on curves over finite fields

We provide new upper bounds on N_q(g), the maximum number of rational points on a smooth absolutely irreducible genus-g curve over F_q, for many values of q and g. Among other results, we find that N_4(7) = 21 and N_8(5) = 29, and we show that a genus-12 curve over F_2 having 15 rational points must have characteristic polynomial of Frobenius equal to one of three explicitly given possibilities. We also provide sharp upper bounds for the lengths of the shortest vectors in Hermitian lattices of small rank and determinant over the maximal orders of small imaginary quadratic fields of class number 1. Some of our intermediate results can be interpreted in terms of Mordell-Weil lattices of constant elliptic curves over one-dimensional function fields over finite fields. Using the Birch and Swinnerton-Dyer conjecture for such elliptic curves, we deduce lower bounds on the orders of certain Shafarevich-Tate groups.
A classification of finite locally 2-transitive generalized quadrangles

Ostrom and Wagner (1959) proved that if the automorphism group $G$ of a finite projective plane $\pi$ acts $2$-transitively on the points of $\pi$, then $\pi$ is isomorphic to the Desarguesian projective plane and $G$ is isomorphic to $\mathrm{P\Gamma L}(3,q)$ (for some prime-power $q$). In the more general case of a finite rank $2$ irreducible spherical building, also known as a \emph{generalized polygon}, the theorem of Fong and Seitz (1973) gave a classification of the \emph{Moufang} examples. A conjecture of Kantor, made in print in 1991, says that there are only two non-classical examples of flag-transitive generalized quadrangles up to duality. Recently, the authors made progress toward this conjecture by classifying those finite generalized quadrangles which have an automorphism group $G$ acting transitively on antiflags. In this paper, we take this classification much further by weakening the hypothesis to $G$ being transitive on ordered pairs of collinear points and ordered pairs of concurrent lines.
On the entropy of Japanese continued fractions

We consider a one-parameter family of expanding interval maps $\{T_{\alpha}\}_{\alpha \in [0,1]}$ (Japanese continued fractions) which include the Gauss map ($\alpha=1$) and the nearest integer and by-excess continued fraction maps ($\alpha=\frac{1}{2},\,\alpha=0$). We prove that the Kolmogorov-Sinai entropy $h(\alpha)$ of these maps depends continuously on the parameter and that $h(\alpha) \to 0$ as $\alpha \to 0$. Numerical results suggest that this convergence is not monotone and that the entropy function has infinitely many phase transitions and a self-similar structure. Finally, we find the natural extension and the invariant densities of the maps $T_{\alpha}$ for $\alpha=\frac{1}{n}$.
On Fourier Orthogonal Projections in the Rotation Algebra

Projections are constructed in the rotation algebra that are orthogonal to their Fourier transform and which are fixed under the flip automorphism. Such projections are expected in a construction of an inductive limit structure for the irrational rotation algebra that is invariant under the Fourier transform (namely, as two circle algebras of the same dimension, which are swapped by the Fourier transform, plus a few points). The calculation is based on Rieffel's construction of the Schwartz space as an equivalence bimodule of rotation algebras as well as on the theory of theta functions.
Complex singularities and PDEs

In this paper we give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tracking method based on the analysis of the Fourier spectrum. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Pad\'e approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the study of the singularity formation of some nonlinear dispersive and dissipative one dimensional PDE of the 2D Prandtl equation, of the 2D KP equation, and to Navier-Stokes equation for high Reynolds number incompressible flows in the case of interaction with rigid boundaries.
On splitting rank of non-compact-type symmetric spaces and bounded cohomology

Let [Formula: see text] be a higher rank symmetric space of non-compact type where [Formula: see text]. We define the splitting rank of [Formula: see text], denoted by [Formula: see text], to be the maximal dimension of a totally geodesic submanifold [Formula: see text] which splits off an isometric [Formula: see text]-factor. We compute explicitly the splitting rank for each irreducible symmetric space. For an arbitrary (not necessarily irreducible) symmetric space, we show that the comparison map [Formula: see text] is surjective in degrees [Formula: see text], provided [Formula: see text] has no direct factors of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. This generalizes the result of [J.-F. Lafont and S. Wang, Barycentric straightening and bounded cohomology, to appear in J. Eur. Math. Soc. ] regarding Dupont’s problem.
On periods: from global to local

Complex periods are algebraic integrals over complex algebraic domains, also appearing as Feynman integrals and multiple zeta values. The Grothendieck-de Rham period isomorphisms for p-adic algebraic varieties defined via Monski-Washnitzer cohomology, is briefly reviewed. The relation to various p-adic analogues of periods are considered, and their relation to Buium-Manin arithmetic differential equations.
Deformations of certain reducible Galois representations III

Let [Formula: see text] be an odd prime and [Formula: see text] a power of [Formula: see text]. We examine the deformation theory of reducible and indecomposable Galois representations [Formula: see text] that are unramified outside a finite set of primes [Formula: see text] and whose image lies in a Borel subgroup. We show that under some additional hypotheses, such representations have geometric lifts to the Witt vectors [Formula: see text]. The main theorem of this paper is a higher-dimensional generalization of the result of [S. Hamblen and R. Ramakrishna, Deformations of certain reducible Galois II, Amer. J. Math. 130(4) (2008) 913–944] [5].
Oblique propagation of 30 s period fast magnetosonic foreshock waves: A Cluster case study

It is accepted that the 30 s period Ultra‐Low‐Frequency waves observed in the terrestrial foreshock are generated by backstreaming ions through the ion‐ion right hand instability. However, such waves are generally observed to propagate obliquely to the field, in direct contrast to theoretical predictions of parallel propagation. A case study, based on data from Cluster, examining the oblique propagation of ULF waves when the IMF cone angle is large is presented. Errors associated with the analysis are considered. It is found that although the waves propagate obliquely to the magnetic field, they are principally confined to the plane defined by the magnetic field and the x GSE direction. The observed systematic deviation by ∼20° of the wave k vector in this plane is explained in terms of non‐local wave refraction processes, requiring careful consideration of the relative motion between the backstreaming ions and the upstream waves.
Estimating surface water area changes using time-series Landsat data in the Qingjiang River Basin, China

Abstract. The Qingjiang River Basin, which is 423 km long in the Hubei province, China, is the first large tributary of the Yangtze River below the Three Gorges. The Qingjiang River Basin surface water area monitoring plays an important role in the water resource management strategy and regular monitoring management of the Yangtze River watershed. Hydropower cascade exploitation, which started in 1987, has formed three reservoirs including the Geheyan reservoir, the Gaobazhou reservoir, and the Shuibuya reservoir in the midstream and downstream of the Qingjiang River Basin. They have made a great impact on surface water area changes of the Qingjiang River Basin and need to be taken into account. We monitor the Qingjiang River Basin surface water area changes from 1973 to 2010. Ten scenes from the Multispectral Scanner System (MSS), seven scenes from the Thematic Mapper (TM), and two scenes from the Enhanced Thematic Mapper Plus ( ETM + ) remote sensing data of Landsat satellites, the normalized different water index (NDWI), the modified NDWI (MNDWI), and Otsu image segmentation method were employed to quantitatively estimate the Qingjiang River Basin surface water area in the 1970s, 1980s, 1990s, and 2000s, respectively. The results indicate that the surface water area of the Qingjiang River Basin shows a growing trend with the hydropower cascade development from the 1980s to the first decade of the 21st century. The study concluded the significance of human activities impact on surface water spatiotemporal distribution. Surface water accretion is significant in most parts of the Qingjiang River Basin and might be related to the constructed cascade hydropower dams.
Dimensions, Whitney covers, and tubular neighborhoods

Working in doubling metric spaces, we examine the connections between different dimensions, Whitney covers, and geometrical properties of tubular neighborhoods. In the Euclidean space, we relate these concepts to the behavior of the surface area of the boundaries of parallel sets. In particular, we give characterizations for the Minkowski and the spherical dimensions by means of the Whitney ball count.