Miracle-dz/UniFAR-FTUs huggingface dataset:
On the Euler--Maruyama scheme for degenerate stochastic differential equations with non-sticky boundary condition

The aim of this paper is to study weak and strong convergence of the Euler–Maruyama scheme for a solution of one-dimensional degenerate stochastic differential equation dXt = σ(Xt)dWt with non-sticky boundary condition. For proving this, we first prove that the Euler–Maruyama scheme also satisfies non-sticky boundary condition. As an example, we consider stochastic differential equation dXt = |Xt| αdWt, α ∈ (0, 1/2) with non-sticky boundary condition and we give some remarks on CEV models in mathematical finance. 2010 Mathematics Subject Classification: 65C30; 60H35; 91G60
Relationship between Low-Level Jet Properties and Turbulence Kinetic Energy in the Nocturnal Stable Boundary Layer

Abstract In the nighttime stable boundary layer (SBL), shear and turbulence are generated in the layer between the maximum of the low-level jet (LLJ) and the earth's surface. Here, it is investigated whether gross properties of the LLJ—its height and speed—could be used to diagnose turbulence intensities in this subjet layer. Data on the height and speed of the LLJ maximum were available at high vertical and temporal resolution using the high-resolution Doppler lidar (HRDL). These data were used to estimate a subjet layer shear, which was computed as the ratio of the speed to the height of the jet maximum, and a jet Richardson number RiJ, averaged at 15-min intervals for 10 nights when HRDL LLJ data were available for this study. The shear and RiJ values were compared with turbulence kinetic energy (TKE) values measured near the top of the 60-m tower at the Cooperative Atmosphere–Surface Exchange Study-1999 (CASES-99) main site. TKE values were small for RiJ greater than 0.4, but as RiJ decreased to less .
Conductive path formation in glasses of phase change memory

We present a model of data retention for phase change memory devices in which the active medium is a thin layer of chalcogenide glass. Data retention capability is compromised when a crystalline path is spontaneously formed in the glassy host, essentially shunting the device. We determine the probability and statistics of device failure for systems in which the crystalline volume fraction is below the critical volume fraction of percolation theory. In that regime, we show that rectilinear crystalline path formation is favored and we determine the criteria for when such paths dominate over the typical percolation cluster scenario. Our analytical approach, based on modeling the formation of such paths in terms of a half-space random walk, leads to closed form expressions that relate data retention characteristics to device parameters. The model is used to examine the effects of device geometry, temperature, and external fields. The temporal statistics of device reliability are also considered for several fa.
Compact asymptotically harmonic manifolds

A complete Riemannian manifold without conjugate points is called asymptotically harmonic if the mean curvature of its horospheres is a universal constant. Examples of asymptotically harmonic manifolds include flat spaces and rank one locally symmetric spaces of noncompact type. In this paper we show that this list exhausts the compact asymptotically harmonic manifolds under a variety of assumptions including nonpositive curvature or Gromov hyperbolic fundamental group. We then present a new characterization of symmetric spaces amongst the set of all visibility manifolds
An Astrometric Study of the Low-Mass Binary Star Ross 614

Long accepted as the quintessential low-mass star, the secondary of the nearby diminutive astrometric binary Ross 614 has attracted considerable astrophysical interest. Unfortunately, the orbital period of 16.6 yr exceeds the duration of the mission-limited studies of most space-borne or instrumental-proving observational programs. As with most such binaries, the only full-orbit studies are based on photographic materials. The last extended study of this system was based upon the plate collections of the McCormick and Sproul Observatories. The work reported here combines data from the Multichannel Astrometric Photometer, the Hipparcos Intermediate Astrometric Data, the previously unmeasured photographic plates of the Allegheny Observatory, published observations of the visual binary, and recently published radial velocities of the system. Together, these data span more than three orbits of the low-mass binary system. Limiting our analysis to the most recent observations of the binary, and five older observations that are in fair agreement with them, we find masses of 0.2228 ± 0.0055 and 0.1107 ± 0.0028 M⊙ for the primary and secondary, respectively, with the largest source of error being the visual separations of the system. We find a parallax of 244.07 ± 0.73 mas, a period of 16.595 ± 0.0077 yr, and an increased estimate of the semimajor axis of 1101.2 ± 8.2 mas. The latter led to a significant increase in the computed masses. All other aspects of the orbital elements and astrometry are in excellent agreement with those found in the independent study of the McCormick and Sproul plates. The importance of long-term astrometric coverage is pointed out by the fact that the orbital motion of the system only resulted in an acceleration during the compilation of the Hipparcos Catalogue. No orbital parameters or mass estimates can be discerned from these high-precision but short-term data.
A non-smooth extension of Frechet differentiability of the norm with applications to numerical ranges

The following result in the theory of numerical ranges in Banach algebras is well known (see [3, Theorem 12.2]). The numerical range of an element F in the bidual of a unital Banach algebra A is the closure of the set of values at F of the w*-continuous states of . As a consequence of the results in this paper the following
Stein's method of exchangeable pairs for the Beta distribution and generalizations

Abstract. We propose a version of Stein’s method of exchangeable pairs, which, given a suitable exchangeable pair (W,W ) of real-valued random variables, suggests the approximation of the law of W by a certain absolutely continuous distribution, which is characterized by a first order differential Stein operator, whose coefficients γ and η are motivated by two regression properties satisfied by the pair (W,W ). Furthermore, the general theory of Stein’s method for such an absolutely continuous distribution is developed and a general characterization result as well as general bounds on the solution to the Stein equation are given. This abstract approach is a certain extension of the theory developed in the papers [CS11] and [EL10], which only consider the framework of the density approach, i.e. η ≡ 1. As an illustration of our technique we prove a general plug-in result, which bounds a certain distance of the distribution of a given random variable W to a Beta distribution in terms of a given exchangeable pair (W,W ) and provide new bounds on the solution to the Stein equation for the Beta distribution, which in a way complement the existing bounds from [GR13]. The abstract plug-in result is then applied to derive bounds of order n for the distance between the distribution of the relative number of drawn red balls after n drawings in a Pólya urn model and the limiting Beta distribution.
Processes with Block-Associated Increments

This paper is motivated by relations between association and independence of random variables. It is well known that, for real random variables, independence implies association in the sense of Esary, Proschan and Walkup (1967), while, for random vectors, this simple relationship breaks. We modify the notion of association in such a way that any vector-valued process with independent increments also has associated increments in the new sense - association between blocks. The new notion is quite natural and admits nice characterization for some classes of processes. In particular, using the covariance interpolation formula due to Houdré, Pérez-Abreu and Surgailis (1998), we show that within the class of multidimensional Gaussian processes, block association of increments is equivalent to supermodularity (in time) of the covariance functions. We also define corresponding versions of weak association, positive association, and negative association. It turns out that the central limit theorem for weakly associated random vectors due to Burton, Dabrowski and Dehling (1986) remains valid, if the weak association is relaxed to the weak association between blocks.
The curvature of almost Robinson manifolds

An almost Robinson structure on an $n$-dimensional Lorentzian manifold $(\mcM,g)$, where $n=2m+\epsilon$, $\epsilon \in \{ 0 ,1 \}$, is a complex $m$-plane distribution $\mcN$ that is totally null with respect to the complexified metric, and intersects its complex conjugate in a real null line distribution $\mcK$, say. When $\mcN$ and its orthogonal complement $\mcN^\perp$ are in involution, the line distribution $\mcK$ is tangent to a congruence of null geodesics, and the quotient of $\mcM$ by this flow acquires the structure of a CR manifold. In four dimensions, such a congruence is shearfree. We give classifications of the tracefree Ricci tensor, the Cotton-York tensor and the Weyl tensor, invariant under i) the stabiliser of a null line, and ii) the stabiliser of an almost Robinson structure. For the Weyl tensor, these are generalisations of the Petrov classification to higher dimensions. Since an almost Robinson structure is equivalent to a projective pure spinor field of real index $1$, the present work can also be viewed as spinorial classifications of curvature tensors. We illustrate these algebraic classifications by a number of examples of higher-dimensional general relativity that admit integrable almost Robinson structures, emphasising the degeneracy type of the Weyl tensor in each case.
Large change in perpendicular magnetic anisotropy induced by an electric field in FePd ultrathin films

The magnetic properties of FePd ultrathin films and their variation under the influence of an electric field are investigated by magneto-optical Kerr effect (MOKE) measurements. L10-ordered FePd shows a spin reorientation transition when varying the thickness. The easy axis of magnetization is found to be normal to the plane at thicknesses above 9 monolayers (MLs) and in-plane below 9 ML. The coercive field, the perpendicular magnetic anisotropy and the MOKE signal at saturation vary with the applied electric field. The sensitivity of the interface magnetic anisotropy is estimated to be 602 fJ/V m.
Recursive algorithms, urn processes and chaining number of chain recurrent sets

This paper investigates the dynamical properties of a class of urn processes and recursive stochastic algorithms with constant gain which arise frequently in control, pattern recognition, learning theory, and elsewhere. It is shown that, under suitable conditions, invariant measures of the process tend to concentrate on the Birkhoff center of irreducible (i.e. chain transitive) attractors of some vector field $F: {\Bbb R}^d \rightarrow {\Bbb R}^d$ obtained by averaging. Applications are given to simple situations including the cases where $F$ is Axiom A or Morse–Smale, $F$ is gradient-like, $F$ is a planar vector field, $F$ has finitely many alpha and omega limit sets.
Topological classification of generic real meromorphic functions

In this article, to each generic real meromorphic function (i.e., having only simple branch points in the appropriate sense) we associate a certain combinatorial gadget which we call the park of a function. We show that the park determines the topological type of the generic real meromorphic function and that the set of all parks is in $1-1$-correspondence with the set of all connected components in the space of generic real meromorphic functions. For any of the above components, we introduce and calculate the corresponding Hurwitz number. Finally as a consequence of our results we determine the topological types of real meromorphic functions from monodromy of orbifold coverings.
On non-K\"ahler compact complex manifolds with balanced and astheno-K\"ahler metrics

In this note we present, for every $n \geq 4$, a non-K\"ahler compact complex manifold $X$ of complex dimension $n$ admitting a balanced metric and an astheno-K\"ahler metric which is in addition $k$-th Gauduchon for any $1\leq k\leq n-1$.
On the Stokes matrices of the $tt^*$-Toda equation

We derive a formula for the signature of the symmetrized Stokes matrix $\cal{S}+\cal{S}^\mathrm{T}$ for the $tt^*$-Toda equation. As a corollary, we verify a conjecture of Cecotti and Vafa regarding when $\cal{S}+\cal{S}^\mathrm{T}$ is positive definite, reminiscent of a formula of Beukers and Heckmann for the generalized hypergeometric equation. The condition that $\cal{S}+\cal{S}^\mathrm{T}$ is positive definite is prominent in the work of Cecotti and Vafa on the $tt^*$ equation; we show that the Stokes matrices $\cal{S}$ satisfying this condition are parameterized by the points of an open convex polytope.
On Equal Point Separation by Planar Cell Decompositions

In this paper, we investigate the problem of separating a set $X$ of points in $\mathbb{R}^{2}$ with an arrangement of $K$ lines such that each cell contains an asymptotically equal number of points (up to a constant ratio). We consider a property of curves called the stabbing number, defined to be the maximum countable number of intersections possible between the curve and a line in the plane. We show that large subsets of $X$ lying on Jordan curves of low stabbing number are an obstacle to equal separation. We further discuss Jordan curves of minimal stabbing number containing $X$. Our results generalize recent bounds on the Erdős-Szekeres Conjecture, showing that for fixed $d$ and sufficiently large $n$, if $|X| \ge 2^{c_dn/d + o(n)}$ with $c_d = 1 + O(\frac{1}{\sqrt{d}})$, then there exists a subset of $n$ points lying on a Jordan curve with stabbing number at most $d$.
Photoluminescence Decay Time Studies of Type II GaAs/AlAs Quantum Well Structures

We have investigated the temperatdre dependence of the photoluminescence (PL) decay kinetics of a series of GaAs/AlAs quantum well structures where the GaAs thickness was kept constant at 25Å and the AlAs was varied between 41Å and 19Å. In these structures the band alignment is type II and the dominant photoluminescence process at 4K is due to recombination of excitons involving electrons confined at the AlAs X point and holes in the GaAs. At 4K on the low energy side of the zero phonon type II transition the PL decay is a single exponential over at least two decades. The time constant of this decay is a strong function of the AlAs layer thickness. The variation of this decay time is in line with a change in oscillation strength of the type II process due to the change in the mixing between the Xz(AlAs) electron states and the Γ (GaAs) electron states. At higher temperatures (T>15K) the photoluminescence intensity and the decay time decrease very rapidly with increasing temperature. This is due to the increased influence of non-radiative proceses as the type II excitons become delocalised.
Mean-field limit for collective behavior models with sharp sensitivity regions

We rigorously show the mean-field limit for a large class of swarming individual based models with local sharp sensitivity regions. For instance, these models include nonlocal repulsive-attractive forces locally averaged over sharp vision cones and Cucker-Smale interactions with discontinuous communication weights. We construct global-in-time defined notion of solutions through a differential inclusion system corresponding to the particle descriptions. We estimate the error between the solutions to the differential inclusion system and weak solutions to the expected limiting kinetic equation by employing tools from optimal transport theory. Quantitative bounds on the expansion of the 1-Wasserstein distance along flows based on a weak-strong stability estimate are obtained. We also provide different examples of realistic sensitivity sets satisfying the assumptions of our main results.
On the return to equilibrium problem for axisymmetric floating structures in shallow water

In this paper we address the return to equilibrium problem for an axisymmetric floating structure in shallow water. First we show that the equation for the solid motion can be reduced to a delay differential equation involving an extension–trace operator whose role is to describe the influence of the fluid equations on the solid motion. It turns out that the compatibility conditions on the initial data for the return to equilibrium configuration are not satisfied, so we cannot use the result from Bocchi (2020 SIAM J. Math. Anal. 52 306–39) for the nonlinear problem. Hence, assuming small amplitude waves, we linearize the equations in the exterior domain and we keep the nonlinear equations in the interior domain. For such configurations, the extension–trace operator can be computed explicitly and the delay term in the differential equation can be put in convolution form. The solid motion is therefore governed by a nonlinear second order integro-differential equation, whose linearization is the well-known Cummins equation. We show global in time existence and uniqueness of the solution using the conservation of the total fluid-structure energy.
Simple Multicloud Models for the Diurnal Cycle of Tropical Precipitation. Part I: Formulation and the Case of the Tropical Oceans

AbstractThe variation of tropical precipitation due to the diurnal cycle of solar heating is examined here in the context of two simple models for tropical convection. The models utilize three cloud types—congestus, deep, and stratiform—that are believed to characterize organized tropical convection and are based on the two first baroclinic modes of vertical structure plus a boundary layer mode. The two models differ mainly in the way they treat the boundary layer dynamics. The first one is purely thermodynamical and is reduced to a single equation for the equivalent potential temperature θe connecting the boundary layer to the upper troposphere through downdrafts and to the surface through evaporation while the second uses full bulk boundary layer (FBBL) dynamics with a careful separation between sensible and latent heat fluxes and parameterization of nonprecipitating shallow cumulus. It turns out that in the case of the precipitation over the ocean where the Bowen ratio is small, both models yield a qua.
Zero-One Law for random uniform hypergraphs

In this work limit probabilities of first-order properties of the random $s$-uniform hypergraph in the binomial model $G^{s}(n,p)$ are studied. We give a complete discription of all positive $\alpha$ such that $G^{s}(n,n^{-\alpha})$ obeys Zero-One Law. Moreover, for any rational $\rho\geq 1/(s-1)$ we prove the existence of a strictly balanced $s$-uniform hypergraph with the density $\rho$.
A new version of Brakke's local regularity theorem

Consider an integral Brakke ow ( t), t2 [0;T ] inside some ball in Euclidean space. If 0 has small height, its measure does not deviate too much from that of a plane and if T is non-empty, than Brakke’s local regularity theorem yields that ( t) is actually smooth and graphical inside a smaller ball for times t2 (C;T C) for some constant C. Here we extend this result to times t2 (C;T ). The main idea is to prove that a Brakke ow that is initially locally graphical with small gradient will remain graphical for some time.
Diagonal-preserving graded isomorphisms of Steinberg algebras

We study Steinberg algebras constructed from ample Hausdorff groupoids over commutative integral domains with identity. We reconstruct (graded) groupoids from (graded) Steinberg algebras and use this to characterize when there is a diagonal-preserving (graded) isomorphism between two (graded) Steinberg algebras. We apply this characterization to groupoids of directed graphs in order to study diagonal-preserving (graded) isomorphisms of Leavitt path algebras and ∗-isomorphisms of graph [Formula: see text]-algebras.
Two-dimensional alloy of immiscible metals: Single and binary monolayer films of Pb and Sn on Rh(111)

The single and binary metal films of Pb and Sn on Rh(111) have been studied at room temperature by scanning tunneling microscopy (STM), low-energy electron diffraction, and Auger electron spectroscopy. Both Pb and Sn are mobile at low coverage and form commensurate overlayers of (4X4)-Pb and c(2×4)-Sn, respectively. From atomically resolved STM images, the atomic arrangements of (4X4)-Pb and c(2×4)-Sn have been identified to be hexagonal and rectangular structures, respectively. With increasing coverage, both commensurate phases change into incommensurate phases followed by island formation (Stranski-Krastanov growth). This shows that Rh(111) is static and inert enough to support two-dimensional (2D) phases of Pb and/or Sn without alloying at room temperature. The Pb-Sn bimetallic film on Rh(111) forms an ordered 2D alloy of PbSn 3 with an incommensurate structure close to (7×7), contrary to the immiscibility of Pb and Sn in the bulk. From atomically resolved STM images, the atomic arrangement of this (7×7)-(Pb,Sn) structure has been determined.
ON THE ASYMPTOTIC BEHAVIOR OF THE LINEARITY DEFECT

This work concerns the linearity defect of a module $M$ over a Noetherian local ring $R$ , introduced by Herzog and Iyengar in 2005, and denoted $\text{ld}_{R}M$ . Roughly speaking, $\text{ld}_{R}M$ is the homological degree beyond which the minimal free resolution of $M$ is linear. It is proved that for any ideal $I$ in a regular local ring $R$ and for any finitely generated $R$ -module $M$ , each of the sequences $(\text{ld}_{R}(I^{n}M))_{n}$ and $(\text{ld}_{R}(M/I^{n}M))_{n}$ is eventually constant. The first statement follows from a more general result about the eventual constancy of the sequence $(\text{ld}_{R}C_{n})_{n}$ where $C$ is a finitely generated graded module over a standard graded algebra over $R$ .
Foliations and the cohomology of moduli spaces of bounded global G-shtukas

We decompose Newton strata in the special fiber of moduli spaces of global G-shtukas into a product of Rapoport-Zink spaces and Igusa varieties. This decomposition holds as well for associated adic spaces, which allows for comparing the l-adic cohomology of these spaces together with its action by the reductive group G and the Galois-group of the underlying ground field. The occuring representations play an important role in the Langlands' program.
First mesospheric observations using an imaging Doppler interferometer adaptation of the dynasonde at Halley, Antarctica

The digital ionospheric sounder, or dynasonde, located at the British Antarctic Survey's research station at Halley, Antarctica, has recently been operated as an imaging Doppler interferometer (IDI). The implementation of this mode of operation does not require any changes to the system hardware but involves a specially written sounding configuration and newly designed data analysis software. Using four independent antennas and two receivers, the signals returned from mesospheric altitudes are range‐gated and processed using Doppler sorting and spatial interferometry. A three‐dimensional (3‐D) image of the scattering locations can then be built up for a region stretching to over 30 degrees from the zenith. The sky map locations and Doppler velocities of the individual scattering points are used to fit a 3‐D velocity vector representing the motion of the neutral wind in the mesosphere. In this paper the radar hardware, sounding configuration, and data processing are described, and the relative merits of the IDI technique as applied at Halley are discussed. The characteristics of the scattering points are outlined, and initial neutral wind measurements are presented.