Miracle-dz/UniFAR-FTUs huggingface dataset:
Influence of hot anisotropic ions on properties of nonlinear Alfven waves

The influence on properties of nonlinear Alfven waves produced by the introduction of a small quantity of hot anisotropic ions into the cold background plasma is studied. Nonlinear equations are obtained which describe the evolution of Alfven waves propagating along magnetic field lines. The addition of a small amount of hot anisotropic ions to the cold plasma results in a qualitative modification of the evolution equations in comparison with those obtained for a cold two-species plasma. A characteristic feature of the system is that a nonlinear stage of evolution is accompanied by the appearance of an electric field directed along the external magnetic field. Some specific solutions of these nonlinear equations are given. The stability of finite-amplitude monochromatic waves during the small-amplitude phase and in the presence of amplitude modulations is investigated.
Size and Structure of Large $(s, t)$-Union Intersecting Families

A family $F$ of $k$-sets on an $n$-set $X$ is said to be an $(s,t)$-union intersecting family if for any $A_1,\ldots,A_{s+t}$ in this family, we have $\left(\cup_{i=1}^s A_i\right)\cap\left(\cup_{i=1}^t A_{i+s}\right)\neq \varnothing. $ The celebrated Erdős-Ko-Rado theorem determines the size and structure of the largest intersecting (or $(1,1)$-union intersecting) family. Also, the Hilton-Milner theorem determines the size and structure of the second largest $(1,1)$-union intersecting family of $k$-sets. In this paper, for $t\geq s\geq 1$ and sufficiently large $n$, we find out the size and structure of some large and maximal $(s,t)$-union intersecting families. Our results are nontrivial extensions of some recent generalizations of the Erdős-Ko-Rado theorem such as the Han and Kohayakawa theorem~[Proc. Amer. Math. Soc. 145 (2017), pp. 73--87] which finds the structure of the third largest intersecting family, the Kostochka and Mubayi theorem~[Proc. Amer. Math. Soc. 145 (2017), pp. 2311--2321], and the more recent Kupavskii's theorem [arXiv:1810.009202018, (2018)] whose both results determine the size and structure of the $i$th largest intersecting family of $k$-sets for $i\leq k+1$. In particular, when $s=1$, we confirm a conjecture of Alishahi and Taherkhani [J. Combin. Theory Ser. A 159 (2018), pp. 269--282]. As another consequence, our result provides some stability results related to the famous Erdős matching conjecture.
A central limit like theorem for Fourier sums

We consider the probability distributions of values in the complex plane attained by Fourier sums of the form \sum_{j=1}^n a_j exp(-2\pi i j nu) /sqrt{n} when the frequency nu is drawn uniformly at random from an interval of length 1. If the coefficients a_j are i.i. d. drawn with finite third moment, the distance of these distributions to an isotropic two-dimensional Gaussian on C converges in probability to zero for any pseudometric on the set of distributions for which the distance between empirical distributions and the underlying distribution converges to zero in probability.
$\left( n , k , k - 1 \right)$-Steiner Systems in Random Hypergraphs

Let $H$ be a random $k$-uniform $n$-vertex hypergraph where every $k$-tuple belongs to $H$ independently with probability $p$. We show that for some $\varepsilon_k > 0$, if $p \geq n^{-\varepsilon_k}$, then asymptotically almost surely $H$ contains an $\left( n , k , k - 1 \right)$-Steiner System. Our main tool is Keevash's method of Randomized Algebraic Constructions.
Reconnaissance of Suspected Old Novae

Several of the "blank fields" in the novae atlas by Duerbeck were imaged at the WIYN 3.5 m telescope during technical engineering and commissioning activities in 1994–1995. Several old novae have been recovered utilizing CCD photometry. Multiobject spectroscopy with the Hydra/MOS instrumentation at WIYN was also used on random stars in the fields to search for a cataclysmic variable. The old novae candidates identified include SV Ari, V465 Cyg, SS LMi, V2104 Oph, GR Ori, V529 Ori, UW Per, and UW Tri.
Parameter identification and Synchronization of different chaotic systems

In order to study the synchronization and parameter identification of different chaotic systems with uncertain parameters, a parameter identifier and a full synchronic controller are designed based on Ulyanovsk stability theory. Take LU system as target system and Rossler system as response system to verify its effectiveness. The simulation results show that LU system and Rossler system can achieve complete synchronization by the parameter identifier and synchronization controller, and the parameters of LU chaos system can all get recognition.
RIGIDITY AND MODULARITY OF VERTEX TENSOR CATEGORIES

Let V be a simple vertex operator algebra satisfying the following conditions: (i) V(n) = 0 for n < 0, V(0) = ℂ1 and V′ is isomorphic to V as a V-module. (ii) Every ℕ-gradable weak V-module is completely reducible. (iii) V is C2-cofinite. (In the presence of Condition (i), Conditions (ii) and (iii) are equivalent to a single condition, namely, that every weak V-module is completely reducible. ) Using the results obtained by the author in the formulation and proof of the general version of the Verlinde conjecture and in the proof of the Verlinde formula, we prove that the braided tensor category structure on the category of V-modules is rigid, balanced and nondegenerate. In particular, the category of V-modules has a natural structure of modular tensor category. We also prove that the tensor-categorical dimension of an irreducible V-module is the reciprocal of a suitable matrix element of the fusing isomorphism under a suitable basis.
Distinguishing Graphs of Maximum Valence 3

The distinguishing number $D(G)$ of a graph $G$ is the smallest number of colors that is needed to color the vertices such that the only color-preserving automorphism fixes all vertices. We give a complete classification for all connected graphs $G$ of maximum valence $\Delta(G) = 3$ and distinguishing number $D(G) = 3$. As one of the consequences we show that all infinite connected graphs with $\Delta(G) = 3$ are $2$-distinguishable.
An Illustrated Guide of the Modern Approches of Hamilton-Jacobi Equations and Control Problems with Discontinuities

This manuscrit is a project of book on Hamilton-Jacobi Equations and Control Problems with discontinuities. For the time being, it is composed of 4 parts: -- Part I is a toolbox with key results which are used in all the other parts. -- Part II describes several approaches which were introduced recently to treat problems involving co-dimension 1 discontinuities or networks. -- Part III concerns stratified problems in $R^N$, i.e. problems with discontinuities of any co-dimensions. -- Part IV addresses the case of stratified problems in bounded or unbounded domains with state-constraints, allowing very surprising applications as well as singular boundary conditions. This second version is still imperfect and we will welcome any (fair) comment on it. In this second version, besides of improving few points in the first one, we have added applications to KPP (Kolmogorov-Petrovsky-Piskunov) type problems and started to develop the use of stratified solutions to treat problems with boundary conditions (Dirichlet, Neumann and mixed boundary conditions), where both the boundary may be non-smooth and the data may present discontinuities. Of course, for all these questions, we only provide examples of what can be done since developing a whole theory would be too long, out of the scope of this book and probably a little bit beyond what we are able to do up to now. In these two directions, we address, in particular, a new question which is interesting when considering applications: under which conditions can one prove that Ishii's viscosity solutions are stratified solutions? The interest of this question is clear: when these conditions hold, one can take advantages of both the nice stability properties of classical viscosity solutions and the general comparison result for stratified solutions. A priori the third version (next release planned in june 2020) will probably be the last one: besides of improving the second version, we plan to address Large Deviations and homogenization problems. This will be the occasion to test the results we have presented so far and to improve them.
$L^1$-Poincar\'e inequalities for differential forms on Euclidean spaces and Heisenberg groups

In this paper, we prove interior Poincar{e} and Sobolev inequalities in Euclidean spaces and in Heisenberg groups, in the limiting case where the exterior (resp. Rumin) differential of a differential form is measured in L 1 norm. Unlike for L p , p > 1, the estimates are doomed to fail in top degree. The singular integral estimates are replaced with inequalities which go back to Bourgain-Brezis in Euclidean spaces, and to Chanillo-van Schaftingen in Heisenberg groups.
More on the preservation of large cardinals under class forcing

We introduce first the large-cardinal notion of $\Sigma_n$-super\-com\-pact\-ness as a higher-level analog of the well-known Magidor's characterization of supercompact cardinals, and show that a cardinal is $C^{(n)}$-extendible if and only if it is $\Sigma_{n+1}$-supercompact. We then develop a general framework for the preservation of $\Sigma_n$-supercompact cardinals under class forcing iterations and prove a general preservation result. As an application we obtain new proofs of the consistency of the GCH with $C^{(n)}$-extendible cardinals (Tsaprounis) and the consistency of $\rm{VP}$ with the GCH (Brooke-Taylor). Further, $C^{(n)}$-extendible cardinals are preserved by forcing with standard Easton-support iterations for any possible $\Pi_1$-definable behaviour of the power-set function on regular cardinals. We show that one can force proper class-many disagreements between the universe and HOD with respect to the calculation of successors of regular cardinals, while preserving $C^{(n)}$-extendible cardinals. We also show that, assuming the GCH, the class forcing iteration of Cummings-Foreman-Magidor for forcing $\diamondsuit_{\kappa^+}^+$ at every $\kappa$ preserves $C^{(n)}$-extendible cardinals, hence it also preserves $\rm{VP}$. We finally address the question of the preservation of $C^{(n)}$-extendible cardinals under general, not necessarily definable, class forcing iterations $\mathbb{P}$ and show that under minor requirements on $\mathbb{P}$, every $\mathbb{P}$-$C^{(n)}$-extendible cardinal remains $C^{(n)}$-extendible in any $\mathbb{P}$-generic extension. In particular, when $\mathbb{P}$ is the standard class forcing that yields $\rm{V}=\rm{HOD}$.
Wave mechanics of breakdown

Kinematic wave theory is used to determine under what conditions breakdown of a steady or unsteady laminar flow into high frequency oscillations should occur. The analysis of a small-scale secondary wave riding on a large-scale inhomogeneity, such as that produced by a finite amplitude primary instability wave, reveals that the breakdown mechanism has three basic ingredients: (i) a self-excited secondary wave with a group velocity near the propagation velocity (phase velocity) of the primary wave, (ii) space-time focusing of the secondary wave train on the primary wave crest and (iii) a nonlinear filtering mechanism leading to rectification of the secondary wave. The theory is applied to a laminar shear flow. Good quantitative agreement with the experiments on boundary-layer transition by Klebanoff, Tidstrom & Sargent (1962) is found for the critical condition leading to breakdown. Also, the theory is able to explain all the main qualitative breakdown features observed by Klebanoff et al. and others, such as the rapid localized onset, and the formation of a hairpin vortex lifting up from the surface downstream of the primary wave crest.
Inducibility of topological trees

Abstract Trees without vertices of degree 2 are sometimes named topological trees. In this work, we bring forward the study of the inducibility of (rooted) topological trees with a given number of leaves. The inducibility of a topological tree S is the limit superior of the proportion of all subsets of leaves of T that induce a copy of S as the size of T grows to infinity. In particular, this relaxes the degree-restriction for the existing notion of the inducibility in d-ary trees. We discuss some of the properties of this generalised concept and investigate its connection with the degree-restricted inducibility. In addition, we prove that stars and binary caterpillars are the only topological trees that have an inducibility of 1. We also find an explicit lower bound on the limit inferior of the proportion of all subsets of leaves of T that induce either a star or a binary caterpillar as the size of T tends to infinity.
Observation of OH Meinel (7,4) P( N″=13) transitions in the night airglow

Improved spectral measurements of the OH Meinel {Delta}v = 3 night airglow emissions have revealed unexpectedly intense transitions from high rotational levels. The example selected for this communicaton involves the previously unreported P(N{double prime} = 13) transitions in the OH M (7,4) band. Under the extant conditions, the column emission rates associated with these new features exceeded by factors {approximately}10{sup 4} those expected on the basis of the assumption of rotational-kinetic equilibrium for the v{prime} = 7 rotational manifold. The authors present the key observations and discuss some of the implications.
Optoelectronic characterization of a fiber-coupled NbN superconducting nanowire single photon detector

This paper reports our experimental setups to characterize the superconducting nanowire single photon detector (SNSPD) that is packaged in-house. Our packaging method ensures not only a satisfied optical coupling efficiency but also a wide band electrical connection. The packaging approach has been proved to meet the needs of cryogenic operations. The basic optoelectronic characterization results including quantum efficiency and dark count rate indicate a good agreement with the expected values.
log gf values for astrophysically important transitions Fe II

Aims. In a recent measurement, Melendez & Barbuy (2009, A&A, 497, 611) report accurate log g f values for 142 important astrophysical lines with wavelengths in the range 4000 A to 8000 A. Their results include both solar and laboratory measurements. In this paper, we describe a theoretical study of these lines. Methods. The CIV3 structure codes, combined with our “fine-tuning” extrapolation process, are used to undertake a large-scale CI calculation involving the lowest 262 fine-structure levels belonging to the 3d64s, 3d7, 3d54s2, 3d64p, and 3d54s4p configurations. Results. We find that many of the 142 transitions are very weak intercombination lines. Other transitions are weak because the dominant configurations in the two levels differ by two orbitals. Conclusions. The comparison between our log g f values and the experimental values generally shows good agreement for most of these transitions, with our theoretical values agreeing slightly more closely with the solar than with the laboratory measurements. A detailed analysis of the small number of transitions for which the agreement between theory and experiment is not as good shows that such disagreements largely arise from severe cancellation due to CI mixing.
On the tropical discs counting on elliptic K3 surfaces with general singular fibres

<p>Using Lagrangian Floer theory, we study the tropical geometry of K3 surfaces with more general singular fibres other than simple nodal curves. In particular, we give the local models for the types <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="upper I Subscript n"> <mml:semantics> <mml:msub> <mml:mi>I</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">I_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="upper I upper I"> <mml:semantics> <mml:mrow> <mml:mi>I</mml:mi> <mml:mi>I</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">II</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="upper I upper I upper I"> <mml:semantics> <mml:mrow> <mml:mi>I</mml:mi> <mml:mi>I</mml:mi> <mml:mi>I</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">III</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="upper I upper V"> <mml:semantics> <mml:mrow> <mml:mi>I</mml:mi> <mml:mi>V</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">IV</mml:annotation> </mml:semantics> </mml:math> </inline-formula> singular fibres in the Kodaira classification. This generalizes the correspondence theorem in “Correspondence theorem between holomorphic discs and tropical discs on K3 surfaces”, arXiv:1703.00411 between open Gromov-Witten invariants/tropical discs counting to these cases. </p>
Moyal-Weyl deformations of $\mathrm{DGA}$ and $\mathrm{DGCA}$

We consider a natural variant of the Moyal-Weyl product and show that it yields a functorial deformation of differential graded algebras and coalgebras. Introduction In the last decades deformation theories appeared in many branches of mathematics and physics. The original idea of deformation seems quite hard to trace back, but some of the original literature surely are [5], [1], [2], [11] and finally the impressive proof of deformation quantization [9]. In quantization procedures it is common to denote the formal deformation parameter by ~ in honour of Max Planck. Of course in physics ~ ≈ 6.58211928. ×10−16eV ·s is not really a variable, neither a constant that we are able to determine exactly in experiments, therefore we expect quantizations to be rigid with respect to fluctuations of ~. Notice that the dimension of ~ is [mass][length]2/[time] and inverse to the dimension of the ordinary Poisson bracket on the phase space T (R) we will soon describe in formula 2. In the deformation quantization of a Poisson manifold (M,Π) the definition of a ⋆ product is central: A ⋆ product is a C[[~]]-bilinear associative operation ⋆ : C∞(M)[[~]]× C∞(M)[[~]] → C∞(M)[[~]] of the shape f ⋆ g = ∑∞ n=0 ~ Bn(f, g) with bi-differential operators Bn and with the properties 1 ⋆ f = f = f ⋆ 1, B0(f, g) = fg and B1(f, g) − B1(g, f) = i{f, g} where {·, ·} is the Poisson bracket. Two star products on (M,Π) are equivalent if there exists a formal series S = id + ∑∞ l=1 ~ Sl of C[[~]]-linear operators Sl : C ∞(M)[[~]] → C∞(M)[[~]] with Sl(1) = 0 for l ≥ 1 and f ⋆ g = S(Sf ⋆ Sg) ∀ f, g ∈ C(M)[[~]] (1) For the ordinary Poisson bracket on the phase space T (R) given by
Strong-field dissociative ionization of a linear triatomic molecule: Relationship between Coulomb-explosion energies and bond angle

Correlation images of the symmetric six-electron Coulomb-explosion channel of CO{sub 2} were used to isolate specific geometries (linear and bent) for angular-resolved analysis of the Coulomb-explosion energy in the framework of both the critical radius R{sub c} and dynamic screening models. We show that it is possible to connect the R{sub c} and screening pictures through a single parameter, a charge defect {sigma}, which depends on the charge state and the ratio between R{sub c} and the equilibrium bond length. Our data show that R{sub c} and hence {sigma} are slow varying functions of bond angle between 145 deg. and 180 deg. with R{sub c}{approx}4 a.u. and {sigma}{approx}0.5 for the symmetric six-electron channel of CO{sub 2}. In the R{sub c} picture, the experimental value for R{sub c} is consistent with a theoretical value associated with CO{sub 2}{sup 3+}, which is considerably smaller than that associated with CO{sub 2}{sup +}({approx}6 a.u.)
Definable equivalence relations and zeta functions of groups (with an appendix by Raf Cluckers)

The authors wish to thank Thomas Rohwer, Deirdre Haskell, Dugald Macpherson and Elisabeth Bouscaren for their comments on earlier drafts of this work, Martin Hils for suggesting that the proof could be adapted to finite extensions and Zo´e Chatzidakis for pointing out an error in how constants were handled in earlier versions. The second author is grateful to Jamshid Derakhshan, Marcus du Sautoy, Andrei Jaikin-Zapirain, Angus Macintyre, Dugald Macpherson, Mark Ryten, Christopher Voll and Michele Zordan for helpful conversations. We are grateful to Alex Lubotzky for suggesting studying representation growth; several of the ideas in Section 8 are due to him. The first author was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement no. 291111/ MODAG, the second author was supported by a Golda Meir Postdoctoral Fellowship at the Hebrew University of Jerusalem and the third author was partly supported by ANR MODIG (ANR-09-BLAN-0047) Model Theory and Interactions with Geometry. The author of the appendix would like to thank M. du Sautoy, C. Voll, and Kien Huu Nguyen for interesting discussions on this and related subjects. He was partially supported by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) with ERC Grant Agreement nr. 615722 MOTMELSUM and he thanks the Labex CEMPI (ANR-11-LABX-0007-01). We are grateful to the referee for their careful reading of the paper and for their many comments, corrections and suggestions for improving the exposition. In memory of Fritz Grunewald.
THE MODAL LOGIC OF SET-THEORETIC POTENTIALISM AND THE POTENTIALIST MAXIMALITY PRINCIPLES

Abstract We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and Löwe [14], including the use of buttons, switches, dials and ratchets. Among the potentialist conceptions we consider are: rank potentialism (true in all larger $V_\beta $ ), Grothendieck–Zermelo potentialism (true in all larger $V_\kappa $ for inaccessible cardinals $\kappa $ ), transitive-set potentialism (true in all larger transitive sets), forcing potentialism (true in all forcing extensions), countable-transitive-model potentialism (true in all larger countable transitive models of ZFC), countable-model potentialism (true in all larger countable models of ZFC), and others. In each case, we identify lower bounds for the modal validities, which are generally either S4.2 or S4.3, and an upper bound of S5, proving in each case that these bounds are optimal. The validity of S5 in a world is a potentialist maximality principle, an interesting set-theoretic principle of its own. The results can be viewed as providing an analysis of the modal commitments of the various set-theoretic multiverse conceptions corresponding to each potentialist account.
Vector-valued Reproducing Kernel Banach Spaces with Group Lasso Norms

Aiming at a mathematical foundation for kernel methods in coefficient regularization for multi-task learning, we investigate theory of vector-valued reproducing kernel Banach spaces (RKBS) with L_{p,1}-norms, which contains the sparse learning scheme $p=1$ and the group lasso p=2. We construct RKBSs that are equipped with such group lasso norms and admit the linear representer theorem for regularized learning schemes. The corresponding kernels that are admissible for the construction are discussed.
Les douze surfaces de Darboux et la trialité

The purpose of this article is to give a geometric interpretation to the so-called "twelve surfaces of Darboux", or "Darboux wreath", which appear by applying repeatedly certain simple transformations to a given infinitesimal isometric deformation of a surface in euclidean three space. This interpretation is a differential-geometric version of triality, concerning totally isotropic surfaces immersed in the real 6-dimensional projective quadric defined by a quadratic form of neutral signature (4,4).