Miracle-dz/UniFAR-FTUs huggingface dataset:
Biset Functors as Module Mackey Functors and its Relation to Derivators

In this article, we will show that the category of biset functors can be regarded as a reflective monoidal subcategory of the category of Mackey functors on the 2-category of finite groupoids. This reflective subcategory is equivalent to the category of modules over the Burnside functor. As a consequence of the reflectivity, we can associate a biset functor to any derivator on the 2-category of finite categories.
There are infinitely many elliptic Carmichael numbers

In 1987, Dan Gordon defined an elliptic curve analogue to Carmichael numbers known as elliptic Carmichael numbers. In this paper, we prove that there are infinitely many elliptic Carmichael numbers. In doing so, we resolve in the affirmative the question of whether there exist infinitely many Lucas–Carmichael numbers (that is, squarefree, composite integers n such that for every prime p that divides n , p+1|n+1 ) .
STRONGLY INTERACTING BLOW UP BUBBLES FOR THE MASS CRITICAL NLS

We consider the mass critical two dimensional nonlinear Schrodinger equation (NLS) i∂tu + ∆u + |u| 2 u = 0, t ∈ R, x ∈ R 2. Let Q denote the positive ground state solitary wave satisfying ∆Q − Q + Q 3 = 0. We construct a new class of multi–solitary wave solutions: given any integer K ≥ 2, there exists a global (for t > 0) solution u(t) of (NLS) that decomposes asymptotically into a sum of solitary waves centered at the vertices of a K–sided regular polygon and concentrating at a logarithmic rate as t → +∞ so that the solution blows up in infinite time with the rate ∇u(t) L 2 ∼ | log t| as t → +∞. This special behavior is due to strong interactions between the waves, in contrast with previous works on multi–solitary waves of (NLS) where interactions do not affect the blow up rate. Using the pseudo–conformal symmetry of the (NLS) flow, this yields the first example of solution v(t) of (NLS) blowing up in finite time with a rate strictly above the pseudo–conformal one, namely, ∇v(t) L 2 ∼ log |t| t as t ↑ 0. Such solution concentrates K bubbles at a point x0 ∈ R 2 , i.e. |v(t)| 2 ⇀ KQ 2 L 2 δx 0 as t ↑ 0.
KNOT THEORY IN HANDLEBODIES

We consider oriented knots and links in a handlebody of genus g through appropriate braid representatives in S3, which are elements of the braid groups Bg,n. We prove a geometric version of the Markov theorem for braid equivalence in the handlebody, which is based on the L-moves. Using this we then prove two algebraic versions of the Markov theorem. The first one uses the L-moves. The second one uses the Markov moves and conjugation in the groups Bg,n. We show that not all conjugations correspond to isotopies.
Arithmetic Spectral Transitions for the Maryland Model

We give a precise description of spectra of the Maryland model (hλ,α,θu)n=un+1+un−1+λtanπ(θ+nα)un for all values of parameters. We introduce an arithmetically defined index δ(α,θ) and show that for α∉ℚ , σsc(hλ,α,θ)={e:γλ(e)
Univalence and quasiconformal extension of an integral operator

In this paper we give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker's method. Further, new univalence criteria and the significant relationships with other results are given. A number of known univalence conditions would follow upon specializing the parameters involved in our main results.
Original technique for third-harmonic-generation measurements in liquids

An original technique, with a special design of liquid cell, is proposed for third‐harmonic generation in liquids. The technique is based on a principle of harmonic generation in an infinite medium by focused laser beam applied for liquid cell windows and uses a thin wedge‐shaped liquid compartment. The measurements can be performed in air, and a high precision in cubic susceptibility and refractive index dispersion determination can be obtained. The technique also allows measurements to be made on liquids absorbing at harmonic and fundamental frequencies and in function of external parameters like temperature, pressure, and electric or magnetic fields. Some results for organic solvents are presented and compared with those obtained by other methods.
A point-free approach to L-Surjunctivity and Stable Finiteness

The category of quasi frames (or qframes) is introduced and studied. In the context of qframes we can jointly study problems related to the L-Surjunctivity and Stable Finiteness Conjectures. As a consequence of our main results, we can generalize some of the known results on these conjectures. In particular, let R be a ring, let G be a soc group,
Quantizations of conical symplectic resolutions II: category $\mathcal {O}$ and symplectic duality

We define and study category $\mathcal O$ for a symplectic resolution, generalizing the classical BGG category $\mathcal O$, which is associated with the Springer resolution. This includes the development of intrinsic properties parallelling the BGG case, such as a highest weight structure and analogues of twisting and shuffling functors, along with an extensive discussion of individual examples. We observe that category $\mathcal O$ is often Koszul, and its Koszul dual is often equivalent to category $\mathcal O$ for a different symplectic resolution. This leads us to define the notion of a symplectic duality between symplectic resolutions, which is a collection of isomorphisms between representation theoretic and geometric structures, including a Koszul duality between the two categories.
Mazur-type manifolds with $L$-space boundaries

In this note, we prove that if the boundary of a Mazur-type $4$-manifold is an irreducible Heegaard Floer homology $L$-space, then the manifold must be the $4$-ball, and the boundary must be the $3$-sphere. We use this to give a new proof of Gabai's Property R.
Implementation of Point-Implicit Diffusion Operator in a Moving-Particle Method (MPPM)

A point-implicit strategy to circumvent the time-step constraint for diffusion process in a moving-particle method (MPPM) is proposed in this article. Since the Eulerian mesh has been established to deal with all pressure-related operators, it is also employed in constructing an accurate and effective local mesh (LM) formulation to represent the diffusion operator on the Lagranian particles. Explicit evaluation of the diffusion process will become inefficient due to the limited time step with a refined particle distribution. On the other hand, a fully implicit method requires an iterative procedure which will inevitably increase the computational burden. In the proposed point-implicit strategy, only the solution value at the objective particle is handled implicitly, and those at neighboring ones are treated explicitly. The time-step constraint on the diffusion process can then be taken out. All these efforts will result in an effective solution procedure for incompressible flow simulations.
Convexity of the Renormalized volume of hyperbolic 3-manifolds

The Hessian of the renormalized volume of geometrically finite hyperbolic $3$-manifolds without rank-$1$ cusps, computed at the hyperbolic metric $g_{\rm geod}$ with totally geodesic boundary of the convex core, is shown to be a strictly positive bilinear form on the tangent space to Teichm\"uller space. The metric $g_{\rm geod}$ is known from results of Bonahon and Storm to be an absolute minimum for the volume of the convex core. We deduce the strict convexity of the functional volume of the convex core at its minimum point.
Small Area Inference for Binary Variables in the National Health Interview Survey

Abstract The National Health Interview Survey is designed to produce precise estimates of finite population parameters for the entire United States but not for small geographical areas or subpopulations. Our investigation concerns estimates of proportions such as the probability of at least one visit to a doctor within the past 12 months. To include all sources of variation in the model, we carry out a Bayesian hierarchical analysis for the desired finite population quantities. First, for each cluster (county) a separate logistic regression relates the individual's probability of a doctor visit to his or her characteristics. Second, a multivariate linear regression links cluster regression parameters to covariates measured at the cluster level. We describe the numerical methods needed to obtain the desired posterior moments. Then we compare estimates produced using the exact numerical method with approximations. Finally, we compare the hierarchical Bayes estimates to empirical Bayes estimates and to stand.
On discrete values of bilinear forms

Let be a nondegenerate skew-symmetric bilinear form in the real plane. We prove that for finite a point set , the set of nonzero values of on , if nonempty, has cardinality . In the special case when , where is a set of at least two reals, we establish the following sum-product type estimates, corresponding to the symmetric and skew-symmetric form : These estimates improve their basic prototypes and , which readily follow from the Szemerédi-Trotter theorem. Bibliography: 28 titles.
Sequential estimation of quantal response curves: A new method of estimation

This paper studies methods given by Wetherill (1963) for estimating general percentage points of a quantal response curve. A new method of estimation is proposed which is both simple to compute and highly efficient. The use of this with the Up and Down Transformed Response Rule (UDTR) is investigated, by exact calculation of probability distributions and by empirical sampling trials. The use of the UDTR to estimate the slope of a response curve is outlined.
Transport equation with integral terms

We prove some theorems on the existence, uniqueness, stability and compactness properties of solutions to inhomogeneous transport equations with Sobolev coefficients, where the inhomogeneous term depends upon the solution through an integral operator. Contrary to the usual DiPerna-Lions approach, the essential step is to formulate the problem in the Lagrangian setting. Some motivations to study the above problem arise from the description of polymeric flows, where such kind of equations are coupled with other Navier-Stokes type equations. Using the results for the transport equation we will provide, in a separate paper, a sequential stability theorem for the full problem of the flow of concentrated polymers.
Semi-group structure of all endomorphisms of a projective variety admitting a polarized endomorphism

Let $X$ be a projective variety admitting a polarized (or more generally, int-amplified) endomorphism. We show: there are only finitely many contractible extremal rays; and when $X$ is $\mathbb{Q}$-factorial normal, every minimal model program is equivariant relative to the monoid $SEnd(X)$ of all surjective endomorphisms, up to finite index. Further, when $X$ is rationally connected and smooth, we show: there is a finite-index submonoid $G$ of $SEnd(X)$ such that $G$ acts via pullback as diagonal (and hence commutative) matrices on the Neron-Severi group; the full automorphisms group $Aut(X)$ has finitely many connected components; and every amplified endomorphism is int-amplified.
Penetration of free convection into a lateral cavity

The paper presents a theoretical and experimental study of natural convection in a horizontal cavity which communicates laterally with a large reservoir. The cavity walls and the reservoir are at different temperatures. It is shown theoretically that the flow consists of a horizontal counterflow which penetrates the cavity over a distinct length. The penetration length is shown to be proportional to the cavity height and to the square root of the Rayleigh number based on cavity height and cavity-reservoir temperature difference. The validity of the theory is demonstrated on the basis of a flow visualization experiment. It is shown also that the Nusselt number for cavity-reservoir heat exchange is proportional to the square root of the Rayleigh number, and is relatively insensitive to the Prandtl number in the Pr range 0·7 to ∞. The energy-engineering applications of the lateral penetration flow are discussed.
Three-dimensional spatial resolution of the nonlinear photoemission from biofunctionalized porous silicon microcavity

Infiltration of biomacromolecules into porous silicon photonic architectures results in biofunctionalized structures with unique properties. Characterization of their optical response and performance optimization in biomacromolecular detection and biophotonic application require a combination of optical and structural studies. Nonlinear optical microscopy is applied to study porous silicon microcavities with and without infiltrated glucose oxidase. The infiltrated protein acts as an internal two-photon-excited fluorescence emitter and second harmonic generator, enabling the in-depth visualization of the porous structure. Enhanced second harmonic generation and fluorescence emission by the porous silicon structure is experimentally associated with the defect layer.
Smooth entrywise positivity preservers, a Horn-Loewner master theorem, and Schur polynomial identities

A (special case of a) fundamental result of Horn and Loewner [Trans. Amer. Math. Soc. 1969] says that given an integer $n \geq 1$, if the entrywise application of a smooth function $f : (0,\infty) \to \mathbb{R}$ preserves the set of $n \times n$ positive semidefinite matrices with positive entries, then the first $n$ derivatives of $f$ are non-negative on $(0,\infty)$. Despite much interest and activity in the literature on entrywise positivity preservers, this has remained the only known necessary condition in fixed dimension for general preservers. On the other hand, in recent work with Belton-Guillot-Putinar [Adv. Math. 2016] and with Tao (2017), we used local, 'real analytic versions' of this condition at the origin, and using this discovered unexpected connections between entrywise polynomials preserving positivity and Schur polynomials. In this paper, we unify the two stories by (i) strengthening the Horn-Loewner result to prove the positivity of the first $n$ nonzero Taylor coefficients at each point; (ii) simultaneously unifying and extending the state-of-the-art variants of the Horn-Loewner theorem in the literature; and (iii) showing via a new determinantal identity that Schur polynomials naturally arise from considering arbitrary smooth entrywise maps (this extends known results involving polynomial preservers). We also explain using the work with Tao (2017) why our main result is sharp.
The dimensionless dissipation rate and the Kolmogorov (1941) hypothesis of local stationarity in freely decaying isotropic turbulence

An expression for the dimensionless dissipation rate was derived from the Karman-Howarth equation by asymptotic expansion of the second- and third- order structure functions in powers of the inverse Reynolds number. The implications of the time-derivative term for the assumption of local stationarity (or local equilibrium) which underpins the derivation of the Kolmogorov `4/5' law for the third-order structure function were studied. It was concluded that neglect of the time-derivative cannot be justified by reason of restriction to certain scales (the inertial range) nor to large Reynolds numbers. In principle, therefore, the hypothesis cannot be correct, although it may be a good approximation. It follows, at least in principle, that the quantitative aspects of the hypothesis of local stationarity could be tested by a comparison of the asymptotic dimensionless dissipation rate for free decay with that for the stationary case. But in practice this is complicated by the absence of an agreed evolution time for making the measurements during the decay. However, we can assess the quantitative error involved in using the hypothesis by comparing the exact asymptotic value of the dimensionless dissipation in free decay calculated on the assumption of local stationarity to the experimentally determined value (e.g. by means of direct numerical simulation), as this relationship holds for all measuring times. Should the assumption of local stationarity lead to significant error, then the `4/5' law needs to be corrected. Despite this, scale invariance in wavenumber space appears to hold in the formal limit of infinite Reynolds numbers, which implies that the `-5/3' energy spectrum does not require correction in this limit.
New characterization of two-state normal distribution

In this paper we give a purely noncommutative criterion for the characterization of two-state normal distribution. We prove that families of two-state normal distribution can be described by relations which is similar to the conditional expectation in free probability, but has no classical analogue. We also show a generalization of Bozejko, Leinert and Speichers formula from Ref. 10 (relating moments and noncommutative cumulants).
The Yang-Mills heat flow and the caloric gauge

This is the first part of the four-paper sequence, which establishes the Threshold Conjecture and the Soliton Bubbling vs.~Scattering Dichotomy for the energy critical hyperbolic Yang--Mills equation in the (4 + 1)-dimensional Minkowski space-time. The primary subject of this paper, however, is another PDE, namely the energy critical Yang--Mills heat flow on the 4-dimensional Euclidean space. Our first goal is to establish sharp criteria for global existence and asymptotic convergence to a flat connection for this system in $\dot{H}^{1}$, including the Dichotomy Theorem (i.e., either the above properties hold or a harmonic Yang--Mills connection bubbles off) and the Threshold Theorem (i.e., if the initial energy is less than twice that of the ground state, then the above properties hold). Our second goal is to use the Yang--Mills heat flow in order to define the caloric gauge, which will play a major role in the analysis of the hyperbolic Yang--Mills equation in the subsequent papers.
Parameters of the fine density structure in the stratosphere obtained from spacecraft observations of stellar scintillations

[1] Measurements of stellar scintillations caused by the atmosphere, conducted on board the space station Mir, are analyzed here. From scintillation spectra we obtained the parameters of spatial spectra of atmospheric density fluctuations (the altitudes 20–70 km) with vertical scales from hundreds of meters to tens of centimeters. The observed characteristic scales of atmospheric inhomogeneities are interpreted with a nonlinear model of internal wave spectrum and a theory of locally homogeneous and isotropic turbulence.
Nonradial normalized solutions for nonlinear scalar field equations

We study the following nonlinear scalar field equation Here , m > 0 is a given constant and arises as a Lagrange multiplier. In a mass subcritical case but under general assumptions on the nonlinearity f , we show the existence of one nonradial solution for any , and obtain multiple (sometimes infinitely many) nonradial solutions when N = 4 or . In particular, all these solutions are sign-changing.
Discrete probabilistic and algebraic dynamics: a stochastic commutative Gelfand-Naimark Theorem

We introduce a category of stochastic maps (certain Markov kernels) on compact Hausdorff spaces, construct a stochastic analogue of the Gelfand spectrum functor, and prove a stochastic version of the commutative Gelfand-Naimark Theorem. This relates concepts from algebra and operator theory to concepts from topology and probability theory. For completeness, we review stochastic matrices, their relationship to positive maps on commutative $C^*$-algebras, and the Gelfand-Naimark Theorem. No knowledge of probability theory nor $C^*$-algebras is assumed and several examples are drawn from physics.
Local cocycle 3-Hom-Lie Bialgebras and 3-Lie Classical Hom-Yang-Baxter Equation

In this paper, we introduce 3-Hom-Lie bialgebras whose compatibility conditions between the multiplication and comultiplication are given by local cocycle conditions. We study a twisted 3-ary version of the Yang-Baxter Equation, called the 3-Lie classical HomYang-Baxter Equation (3-Lie CHYBE), which is a general form of 3-Lie classical YangBaxter Equation studied in [2] and prove that the bialgebras induced by the solutions of 3-Lie CHYBE induce the coboundary local cocycle 3-Hom-Lie bialgebras.
Discreteness of silting objects and t ‐structures in triangulated categories

We introduce the notion of ST‐pairs of triangulated subcategories, a prototypical example of which is the pair of the bound homotopy category and the bound derived category of a finite‐dimensional algebra. For an ST‐pair (C,D) , we construct an injective order‐preserving map from silting objects in C to bounded t ‐structures on D and show that the map is bijective if and only if C is silting‐discrete if and only if D is t ‐discrete. Based on the work of Qiu and Woolf, the above result is applied to show that if C is silting‐discrete then the stability space of D is contractible. This is used to obtain the contractibility of the stability spaces of some Calabi–Yau triangulated categories associated to Dynkin quivers.
A Benamou–Brenier formulation of martingale optimal transport

We introduce a Benamou-Brenier formulation for the continuous-time martingale optimal transport problem as a weak length relaxation of its discrete-time counterpart. By the correspondence between classical martingale problems and Fokker-Planck equations, we obtain an equivalent PDE formulation for which basic properties such as existence, duality and geodesic equations can be analytically studied, yielding corresponding results for the stochastic formulation. In the one dimensional case, sufficient conditions for finiteness of the cost are also given and a link between geodesics and porous medium equations is partially investigated.
Quantum cluster variables via Serre polynomials

Abstract For skew-symmetric acyclic quantum cluster algebras, we express the quantum F-polynomials and the quantum cluster monomials in terms of Serre polynomials of quiver Grassmannians of rigid modules. As byproducts, we obtain the existence of counting polynomials for these varieties and the positivity conjecture with respect to acyclic seeds. These results complete previous work by Caldero and Reineke and confirm a recent conjecture by Rupel.
Operational extreme points and Cuntz's canonical endomorphism

Based on the fact that the Cuntz algebra $O_n$ is generated by the operators consisting of a finite operatorional partition, we study the notion of operational extreme points (which we introduce here) by using several completely positive maps on $O_n$. As a typical example, we show that the Cuntz's canonical endomorphism $Phi_n$ is an operational extreme point in the set of completely positive maps on $O_n$ and that it induces a completely positive map which is extreme but not operational extreme, etc.