Miracle-dz/UniFAR-FTUs huggingface dataset:
The space of rational maps on P^1

The set of morphisms $\f:\PP^1\to\PP^1$ of degree $d$ is parametrized by an affine open subset $\Rat_d$ of $\PP^{2d+1}$. We consider the action of~$\SL_2$ on $\Rat_d$ induced by the {\it conjugation action\/} of $\SL_2$ on rational maps; that is, $f\in\SL_2$ acts on~$\f$ via $\f^f=f^{-1}\circ\f\circ f$. The quotient space $\M_d=\Rat_d/\SL_2$ arises very naturally in the study of discrete dynamical systems on~$\PP^1$. We prove that~$\M_d$ exists as an affine integral scheme over~$\ZZ$, that $\M_2$ is isomorphic to~$\AA^2_\ZZ$, and that the natural completion of~$\M_2$ obtained using geometric invariant theory is isomorphic to~$\PP^2_\ZZ$. These results, which generalize results of Milnor over~$\CC$, should be useful for studying the arithmetic properties of dynamical systems.
Stability and convergence of the Sasaki–Ricci flow

We introduce a holomorphic sheaf E on a Sasaki manifold and study two new notions of stability for E along the Sasaki-Ricci flow related to the `jumping up' of the number of global holomorphic sections of E at infinity. First, we show that if the Mabuchi K-energy is bounded below, the transverse Riemann tensor is bounded in C^{0} along the flow, and the C -infinity closure of the Sasaki structure under the diffeomorphism group does not contain a Sasaki structure with strictly more global holomorphic sections of E, then the Sasaki-Ricci flow converges exponentially fast to a Sasaki-Einstein metric. Secondly, we show that if the Futaki invariant vanishes, and the lowest positive eigenvalue of the d-bar Laplacian on global sections of E is bounded away from zero uniformly along the flow, then the Sasaki-Ricci flow converges exponentially fast to a Sasaki-Einstein metric.
How the merger of two white dwarfs depends on their mass ratio: orbital stability and detonations at contact

Despite their unique astrophysical relevance, the outcome of white dwarf binary mergers has so far only been studied for a very restricted number of systems. Here we present the results of a survey with more than 200 simulations systematically scanning the white dwarf binary parameter space. We consider white dwarf masses ranging from 0.2 to 1.2 M⊙ and account for their different chemical compositions. We find excellent agreement with the orbital evolution predicted by mass transfer stability analysis. Much of our effort in this paper is dedicated to determining which binary systems are prone to a thermonuclear explosion just prior to merger or at surface contact. We find that a large fraction of He-accreting binary systems explode: all dynamically unstable systems with accretor masses below 1.1 M⊙ and donor masses above ∼0.4 M⊙ are found to trigger a helium detonation at surface contact. A substantial fraction of these systems could explode at earlier times via detonations induced by instabilities in the accretion stream, as we have demonstrated in our previous work. We do not find definitive evidence for an explosion prior to merger or at surface contact in any of the studied double carbon–oxygen systems. Although we cannot exclude their occurrence if some helium is present, the available parameter space for a successful detonation in a white dwarf binary of pure carbon–oxygen composition is small. We demonstrate that a wide variety of dynamically unstable systems are viable Type Ia candidates. The next decade thus holds enormous promise for the study of these events, in particular with the advent of wide-field synoptic surveys allowing a detailed characterization of their explosive properties.
RADIAL TRANSPORT OF LARGE-SCALE MAGNETIC FIELDS IN ACCRETION DISKS. I. STEADY SOLUTIONS AND AN UPPER LIMIT ON THE VERTICAL FIELD STRENGTH

Large-scale magnetic fields are key ingredients of magnetically driven disk accretion. We study how large-scale poloidal fields evolve in accretion disks, with the primary aim of quantifying the viability of magnetic accretion mechanisms in protoplanetary disks. We employ a kinematic mean-field model for poloidal field transport and focus on steady states where inward advection of a field balances with outward diffusion due to effective resistivities. We analytically derive the steady-state radial distribution of poloidal fields in highly conducting accretion disks. The analytic solution reveals an upper limit on the strength of large-scale vertical fields attainable in steady states. Any excess poloidal field will diffuse away within a finite time, and we demonstrate this with time-dependent numerical calculations of the mean-field equations. We apply this upper limit to large-scale vertical fields threading protoplanetary disks. We find that the maximum attainable strength is about 0.1 G at 1 AU, and about 1 mG at 10 AU from the central star. When combined with recent magnetic accretion models, the maximum field strength translates into the maximum steady-state accretion rate of ∼10−7 M☉ yr−1, in agreement with observations. We also find that the maximum field strength is ∼1 kG at the surface of the central star provided that the disk extends down to the stellar surface. This implies that any excess stellar poloidal field of strength ≳ kG can be transported to the surrounding disk. This might in part resolve the magnetic flux problem in star formation.
ON THE VOLUME OF A LINE BUNDLE

Using the Calabi–Yau technique to solve Monge-Ampere equations, we translate a result of T. Fujita on approximate Zariski decompositions into an analytic setting and combine this to the holomorphic Morse inequalities in order to express the volume of a line bundle as the maximum of the mean curvatures of all the singular Hermitian metrics on it, with a way to pick an element at which the maximum is reached and satisfying a singular Monge–Ampere equation. This enables us to introduce the volume of any (1,1)-class on a compact Kahler manifold, and Fujita's theorem is then extended to this context.
Inflating with large effective fields

We re-examine large scalar fields within effective field theory, in particular focussing on the issues raised by their use in inflationary models (as suggested by BICEP2 to obtain primordial tensor modes). We argue that when the large-field and low-energy regimes coincide the scalar dynamics is most effectively described in terms of an asymptotic large-field expansion whose form can be dictated by approximate symmetries, which also help control the size of quantum corrections. We discuss several possible symmetries that can achieve this, including pseudo-Goldstone inflatons characterized by a coset G/H (based on abelian and non-abelian, compact and non-compact symmetries), as well as symmetries that are intrinsically higher dimensional. Besides the usual trigonometric potentials of Natural Inflation we also find in this way simple large-field power laws (like V ∝ ϕ2) and exponential potentials, V(ϕ) = ∑kVxe−kϕ/M. Both of these can describe the data well and give slow-roll inflation for large fields without the need for a precise balancing of terms in the potential. The exponential potentials achieve large r through the limit |η| ≪ ϵ and so predict r ≃ (8/3)(1-ns); consequently ns ≃ 0.96 gives r ≃ 0.11 but not much larger (and so could be ruled out as measurements on r and ns improve). We examine the naturalness issues for these models and give simple examples where symmetries protect these forms, using both pseudo-Goldstone inflatons (with non-abelian non-compact shift symmetries following familiar techniques from chiral perturbation theory) and extra-dimensional models.
PROPERLY TWISTED GROUPS AND THEIR ALGEBRAS

A proper twist on a group G is a function � : G × G 7→ {−1,1} with the property that, if p,q ∈ G then �(p,q)�(q,q 1) = �(pq,q 1) and �(p 1,p)�(p,q) = �(p 1,pq). The span V of a set of unit vectors B = {ip |p ∈ G} over a ring K with product xy = P p,q �(p,q)xpyqipq is a twisted group algebra. If the twistis proper, then the conjugate defined by x� = P p �(p,p 1)xi p 1 and inner product hx,yi = P p xpy �, satisfy the adjoint properties hxy,zi= hy,xzi and hx,yzi = hxz � ,yi for all x,y,z ∈ V. Proper twists on Z N over the reals produce the complex numbers, quaternions, octonions and all higher order Cayley-Dickson and Clifford algebras.
BARYON CONTENT OF MASSIVE GALAXY CLUSTERS AT z = 0–0.6

We study the relationship between two major baryonic components in galaxy clusters, namely the stars in galaxies and the ionized gas in the intracluster medium (ICM), using 94 clusters that span the redshift range 0–0.6. Accurately measured total and ICM masses from Chandra observations and stellar masses derived from the Wide-field Infrared Survey Explorer and the Two Micron All Sky Survey allow us to trace the evolution of cluster baryon content in a self-consistent fashion. We find that, within r500, the evolution of the ICM-mass–total-mass relation is consistent with the expectation of the self-similar model, while there is no evidence for redshift evolution in the stellar-mass–total-mass relation. This suggests that the stellar mass and ICM mass in the inner parts of clusters evolve differently.
Thermal QCD transition with two flavors of twisted mass fermions

We investigate the thermal QCD transition with two flavors of maximally twisted mass fermions for a set of pion masses, 300 MeV \textless $m_\pi$ \textless 500 MeV, and lattice spacings $a$ \textless 0.09 fm. We determine the pseudo-critical temperatures and discuss their extrapolation to the chiral limit using scaling forms for different universality classes, as well as the scaling form for the magnetic equation of state. For all pion masses considered we find resonable consistency with O(4) scaling plus leading corrections. However, a true distinction between the O(4) scenario and a first order scenario in the chiral limit requires lighter pions than are currently in use in simulations of Wilson fermions.
The Herschel view of the nebula around the luminous blue variable star AG Carinae

Far-infrared Herschel PACS imaging and spectroscopic observations of the nebula around the luminous blue variable (LBV) star AG Car have been obtained along with optical imaging in the Hα+[N ii] filter. In the infrared light, the nebula appears as a clumpy ring shell that extends up to 1.2 pc with an inner radius of 0.4 pc. It coincides with the Hα nebula, but extends further out. Dust modeling of the nebula was performed and indicates the presence of large grains. The dust mass is estimated to be ∼0.2 M� . T he infrared spectrum of the nebula consists of forbidden emission lines over a dust continuum. Apart from ionized gas, these lines also indicate the existence of neutral gas in a photodissociation region that surrounds the ionized region. The abundance ratios point towards enrichment by processed material. The total mass of the nebula ejected from the central star amounts to ∼15 M� , assuming a dust-to-gas ratio typical of LBVs. The abundances and the mass-loss rate were used to constrain the evolutionary path of the central star and the epoch at which the nebula was ejected, with the help of available evolutionary models. This suggests an ejection during a
A Bochner principle and its applications to Fujiki class 𝒞 manifolds with vanishing first Chern class

We prove a Bochner-type vanishing theorem for compact complex manifolds [Formula: see text] in Fujiki class [Formula: see text], with vanishing first Chern class, that admit a cohomology class [Formula: see text] which is numerically effective (nef) and has positive self-intersection (meaning [Formula: see text], where [Formula: see text]). Using it, we prove that all holomorphic geometric structures of affine type on such a manifold [Formula: see text] are locally homogeneous on a non-empty Zariski open subset. Consequently, if the geometric structure is rigid in the sense of Gromov, then the fundamental group of [Formula: see text] must be infinite. In the particular case where the geometric structure is a holomorphic Riemannian metric, we show that the manifold [Formula: see text] admits a finite unramified cover by a complex torus with the property that the pulled back holomorphic Riemannian metric on the torus is translation invariant.
Multi-Model Cantor Sets

In this paper we define a new class of metric spaces, called multi-model Cantor sets. We compute the Hausdorff dimension and show that the Hausdorff measure of a multi-model Cantor set is finite and non-zero. We then show that a bilipschitz map from one multi-model Cantor set to another has constant Radon-Nikodym derivative on some clopen. We use this to obtain an invariant up to bilipschitz homeomorphism.
A METHOD TO SEARCH FOR BULK MOTIONS IN THE ICM WITH CHANDRA CCD SPECTRA: APPLICATION TO THE BULLET CLUSTER

We propose a strategy to search for bulk motions in the intracluster medium (ICM) of merging clusters based on Chandra CCD data. Our goal is to derive robust measurements of the average redshift of projected ICM regions obtained from the centroid of the Kα line emission. We thoroughly explore the effect of the unknown temperature structure along the line of sight to accurately evaluate the systematic uncertainties on the ICM redshift. We apply our method to the “Bullet cluster” (1E 0657-56). We directly identify 23 independent regions on the basis of the surface brightness contours, and measure the redshift of the ICM averaged along the line of sight in each. We find that the redshift distribution across these regions is marginally inconsistent with the null hypothesis of a constant redshift or no bulk motion in the ICM, at a confidence level of about 2σ. We tentatively identify the regions most likely affected by bulk motions and find a maximum velocity gradient of about (46 ± 13) km s−1 kpc−1 along the line of sight on a scale of ∼260 kpc along the path of the “bullet. ” We interpret this as the possible signature of a significant mass of ICM pushed away along a direction perpendicular to the merging. This preliminary result is promising for a systematic search for bulk motions in bright, moderate-redshift clusters based on spatially resolved spectral analysis of Chandra CCD data.
Structure of H-(co)module Lie algebras

Let $L$ be a finite dimensional Lie algebra over a field of characteristic $0$. Then by the original Levi theorem, $L = B \oplus R$ where $R$ is the solvable radical and $B$ is some maximal semisimple subalgebra. We prove that if $L$ is an $H$-(co)module algebra for a finite dimensional (co)semisimple Hopf algebra $H$, then $R$ is $H$-(co)invariant and $B$ can be chosen to be $H$-(co)invariant too. Moreover, the nilpotent radical $N$ of $L$ is $H$-(co)invariant and there exists an $H$-sub(co)module $S\subseteq R$ such that $R=S\oplus N$ and $[B,S]=0$. In addition, the $H$-(co)invariant analog of the Weyl theorem is proved. In fact, under certain conditions, these results hold for an $H$-comodule Lie algebra $L$, even if $H$ is infinite dimensional. In particular, if $L$ is a Lie algebra graded by an arbitrary group $G$, then $B$ can be chosen to be graded, and if $L$ is a Lie algebra with a rational action of a reductive affine algebraic group $G$ by automorphisms, then $B$ can be chosen to be $G$-invariant. Also we prove that every finite dimensional semisimple $H$-(co)module Lie algebra over a field of characteristic $0$ is a direct sum of its minimal $H$-(co)invariant ideals.
Apolarity for determinants and permanents of generic matrices

We show that the apolar ideals to the determinant and permanent of a generic matrix, the Pfaffian of a generic skew symmetric matrix and the Hafnian of a generic symmetric matrix are each generated in degree two. In each case we specify the generators and a Gr\"{o}bner basis of the apolar ideal. As a consequence, using a result of K. Ranestad and F. O. Schreyer we give lower bounds to the cactus rank and rank of each of these invariants. We compare these bounds with those obtained by J. Landsberg and Z. Teitler.
A note on elliptic type boundary value problems with maximal monotone relations

In this note we discuss an abstract framework for standard boundary value problems in divergence form with maximal monotone relations as “coefficients”. A reformulation of the respective problems is constructed such that they turn out to be unitarily equivalent to inverting a maximal monotone relation in a Hilbert space. The method is based on the idea of “tailor‐made” distributions as provided by the construction of extrapolation spaces, see e.g. [Picard, McGhee: Partial Differential Equations: A unified Hilbert Space Approach (De Gruyter, 2011)]. The abstract framework is illustrated by various examples.
A Study to Refix the Critical Limit of Copper in the Major Rice Growing Soils of Tamil Nadu, India

Aims: To refix the critical limit of Cu in the soils of the major rice-growing tracts of Tamil Nadu. Study Design: Completely Randomized Design and Randomized Block Design. Place and Duration of Study: Department of Soil Science and Agricultural Chemistry, Tamil Nadu Agricultural University between 2015 to 2018. Methodology: The pot culture study was conducted in the laboratory followed by the field trials in the selected farmers'plot itself. The soil and plant samples are analyzed for soil copper and the data were statistically analyzed by following the standard procedures. Results: The Cu deficient soils showed a significant response to the application of graded levels of Cu. For obtaining higher rice production in severely Cu-deficient soils (L1 to L9: 0.33 to 0.95 mg kg-1), the Cu fertilizers may be applied @ 1.50 kg ha-1 i.e. 6.0 kg CuSO4 ha-1 (+ NPK) while in moderately Cu deficient soils (L10 to L13: 1.28 mg kg-1), the Cu level @ 1.00 kg ha-1 i.e. 4.0 kg CuSO4 ha-1 (+ NPK) increased significantly the grain and straw yields and in soils having high initial Cu status (L14, L15: 1.91, 2.12 mg kg-1), the Cu level @ 0.50 kg ha-1 i.e. 2.0 kg CuSO4 ha-1 (+ NPK) showed a significant increase in grain and straw yields. Conclusion: The present investigation was carried out with the objective of re-fixing the critical limit in wetland soils and accordingly the critical limit for DTPA - Cu in wetland soils and rice crops at the panicle initiation stage was re-fixed as 0.93 and 4.82 mg kg-1, respectively. Based on this, it is possible that a graded dose of micronutrient fertilizers (Cu) may be prescribed to rice crops for the major rice-growing soils.
Content Analysis of Agricultural Information Dissemination by the Indigenous Language and National Print Media in Nigeria: Implications for Effective Communication

The study conducted content analysis of indigenous and national newspapers (NP) published between 2014 and 2015 with respect to agricultural information disseminated to stakeholders in agriculture. Both purposive and stratified sampling technique was used to select Akede and Alaroye as the indigenous and the Nation and Punch as NPs because of their popularity and coverage in Nigeria. A total of 384 newspapers were used for this study. Results showed that the newspapers featured less of agricultural related information despite the fact that the available agricultural information was carried in form of hard news (5.7% and 81.7%), features (7.3% and 91.7%), photography (4.7% and 50.0%), opinion issues (2.1% and 64.1%), and advertisement (1.6% and 56.2%) for indigenous language and national newspapers respectively. Also, information such as employment in agriculture-related (4.7% and 52.6%), health issues related to agriculture (6.2% and 53.1%), crop production (5.7% and 52.1%), animal husbandry (4.7% and 51.6%)for indigenous language and national newspapers respectively among others were the commonly featured news. Only 6.8% and 80.2% of the indigenous and National newspapers allotted column inches ranging from 0.00-7.0 to agriculture. About 6,8% and 60.4% and 4.7% and 58.9% of indigenous language and national NPs targeted the general audience and Male farmer for disseminating agricultural information. Significant difference existed in the agriculture information featured between the indigenous and national newspapers with an F-test value of 44.882 at p= 0.01; indicating that national newspapers featured agricultural news more than the indigenous ones. It was recorded that limited space was allocated to the few available information on agriculture in the sampled newspapers. It was concluded that agricultural news were not adequately disseminated in the dailies especially the local dailies that farmers mostly have access to. It was recommended that agriculture-related information should be published on the platforms where the target audience can access for effective communication
On the prime divisors of elements of a $D(-1)$ quadruple

We show that if {1, b, c, d} is a D(-1) diophantine quadruple with b<c<d and c=1+s^2, then the cases s=p^k, s=2p^k, c=p and c=2p^k do not occur, where p is an odd prime and k is a positive integer. For the integer d=1+x^2, we show that it is not prime and that x is divisible by at least two distinct odd primes. Furthermore, we present several infinite families of integers b such that the D(-1) pair {1, b} cannot be extended to a D(-1) quadruple. For instance, we show that if r=5p where p is an odd prime, then the D(-1) pair {1, r^2+1} cannot be extended to a D(-1) quadruple.
Classifying Resolving Subcategories

We use the theory of Auslander Buchweitz approximations to classify certain resolving subcategories containing a semidualizing or a dualizing module. In particular, we show that if the ring has a dualizing module, then the resolving subcategories containing maximal Cohen-Macaulay modules are in bijection with grade consistent functions and thus are the precisely the dominant resolving subcategories.
Chemotaxis can prevent thresholds on population density

We define and (for $q>n$) prove uniqueness and an extensibility property of $W^{1,q}$-solutions to $u_t =-\nabla\cdot(u\nabla v)+\kappa u-\mu u^2$ $ 0 =\Delta v-v+u$ $\partial_\nu v|_{\partial\Omega} = \partial_\nu u|_{\partial\Omega}=0,$ $ u(0,\cdot)=u_0 $ in balls in $\mathbb{R}^n$, which we then use to obtain a criterion guaranteeing some kind of structure formation in a corresponding chemotaxis system - thereby extending recent results of Winkler to the higher dimensional (radially symmetric) case. Keywords: chemotaxis, logistic source, blow-up, hyperbolic-elliptic system
Topological entropy of minimal geodesics and volume growth on surfaces

Let (M,g) be a compact Riemannian manifold of hyperbolic type, i.e M is a manifold admitting another metric of strictly negative curvature. In this paper we study the geodesic flow restricted to the set of geodesics which are minimal on the universal covering. In particular for surfaces we show that the topological entropy of the minimal geodesics coincides with the volume entropy of (M, g) generalizing work of Freire and Mane.
Recurrence and non-uniformity of bracket polynomials

A bracket polynomial on the integers is a function formed using the operations of addition, multiplication and taking fractional parts. For a fairly large class of bracket polynomials we show that if p is a bracket polynomial of degree k-1 on [N] then the function f defined by f(n) = e(p(n)) has Gowers U^k[N]-norm bounded away from zero, uniformly in N. We establish this result by first reducing it to a certain recurrence property of sets of bracket polynomials. Specifically, for a fairly large class of bracket polynomials we show that if p_1, . , p_r are bracket polynomials then their values, modulo 1, are all close to zero on at least some constant proportion of the points 1, . , N. The proofs rely on two deep results from the literature. The first is work of V. Bergelson and A. Leibman showing that an arbitrary bracket polynomial can be expressed in terms of a polynomial sequence on a nilmanifold. The second is a theorem of B. Green and T. Tao describing the quantitative distribution properties of such polynomial sequences. We give elementary alternative proofs of the first result, without reference to nilmanifolds, in certain "low-complexity" special cases.