Miracle-dz/UniFAR-FTUs huggingface dataset:
On the Hamilton–Waterloo Problem with Odd Orders

Given nonnegative integers v,m,n,α,β , the Hamilton–Waterloo problem asks for a factorization of the complete graph Kv into α Cm ‐factors and β Cn ‐factors. Without loss of generality, we may assume that n≥m . Clearly, v odd, n,m≥3 , m∣v , n∣v and α+β=(v−1)/2 are necessary conditions. To date results have only been found for specific values of m and n. In this paper, we show that for any integers n≥m , these necessary conditions are sufficient when v is a multiple of mn and v>mn , except possibly when β=1 or 3. For the case where v=mn we show sufficiency when β>(n+5)/2 with some possible exceptions. We also show that when n≥m≥3 are odd integers, the lexicographic product of Cm with the empty graph of order n has a factorization into α Cm ‐factors and β Cn ‐factors for every 0≤α≤n , β=n−α , with some possible exceptions.
Some strongly bounded classes of Banach spaces

We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable reflexive Banach space containing isomorphic copies of every separable uniformly convex Banach spaces.
A Cautionary Note on the Method of Least Median Squares

Abstract This article describes and illustrates a local instability that may arise when using the method of least median squares (LMS) to fit models to data. This idea is contrary to the generally held belief that the method is highly resistant to perturbations in the data. In fact, slight changes in centrally located data can cause the LMS estimate to change by a large amount. The LMS method uses a criterion function that is calculated on half samples. If there are two or more half-samples with roughly the same value of the criterion function, then by slight changes in some of the data the LMS solution can be made to jump from one half sample to the other. An example of a data set from a standard text that exhibits this feature is presented. This suggests that some caution should be exercised when using this method. It does not automatically guarantee complete robustness to misspecifications in the data.
Weighted Ostrowski Type inequality Involving Integral Means

The ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The aim of this paper is to establish a new inequality using weight function which generalizes the inequalities of Dragomir, Wang and Cerone . The current article obtains bounds for the deviation of a function from a combination of integral means over the end intervals covering the entire interval. A variety of earlier results are recaptured as particular instances of the current development. Applications for cumulative distribution function are also discussed.
On the role of wall-pressure fluctuations in deterministic motions in the turbulent boundary layer

The wall-pressure fluctuations beneath a turbulent boundary layer have been conditionally sampled on a basis of the high-frequency activity of the pressure fluctuations themselves, the high-frequency activity of the streamwise velocity fluctuations in the vicinity of the wall, and the excursions in velocity in the vicinity of the wall. This has led to the identification of a characteristic wall-pressure fluctuation pattern which is associated with the burst–sweep cycle of events in the wall region. The pattern has the form of an overpressure over a streamwise extent of about 1·5−2·0δ*, with a region of underpressure and a pressure minimum to either side of it, the distance between pressure minima being about 3·0−3·5δ*. This pattern is convected at a velocity 0·67 times the freestream velocity. Its phase relationship with velocity fluctuations close to the wall and the wall shear-stress fluctuations during the burst–sweep cycle have been established. It appears to be produced by the inclined shear layer which forms the upstream surface of the large organized structures in the layer, and calculated pressure patterns support this conclusion. The phase relationships indicate that fluid involved in the bursting process is subjected to a favourable streamwise pressure gradient by the characteristic wall-pressure pattern at the time that the lift-up of low-speed streaks in the wall region begins. In addition, order-of-magnitude estimates suggest that the adverse pressure gradients associated with the characteristic pressure pattern, even if their phasing with streak lift-up were appropriate, would be insufficient to initiate the lift-up. It is therefore concluded that the streamwise pressure gradients associated with the pressure patterns do not play an active role in the dynamics of the wall flow and are not the direct cause of the bursting process.
Heat invariants of the perturbed polyharmonic Steklov problem

For a given bounded domain $\Omega$ with smooth boundary in a smooth Riemannian manifold $(\mathcal{M},g)$, we establish a procedure to get all the coefficients of the asymptotic expansion of the trace of the heat kernel associated with the perturbed polyharmonic Dirichlet-to-Neumann operator $\Lambda_m$ ($m\ge 1$) as $t\to 0^+$. We also explicitly calculate the first four coefficients of this asymptotic expansion. These coefficients (i.e., heat invariants) provide precise information for the area and curvatures of the boundary $\partial \Omega$ in terms of the spectrum of the perturbed polyharmonic Steklov problem. In particular, when $m=1$ and $q\equiv 0$ our work recovers the previous corresponding results in \cite{PS} and \cite{Liu3}.
The interior of dynamical vacuum black holes I: The $C^0$-stability of the Kerr Cauchy horizon

We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations defined on a hypersurface already within the black hole interior, representing the expected geometry just inside the event horizon. We prove that for all such data, the maximal Cauchy evolution can be extended across a non-trivial piece of Cauchy horizon as a Lorentzian manifold with continuous metric. In subsequent work, we will retrieve our assumptions on data assuming only that the black hole event horizon geometry suitably asymptotes to a rotating Kerr solution. In particular, if the exterior region of the Kerr family is proven to be dynamically stable---as is widely expected---then it will follow that the $C^0$-inextendibility formulation of Penrose's celebrated strong cosmic censorship conjecture is in fact false. The proof suggests, however, that the $C^0$-metric Cauchy horizons thus arising are generically singular in an essential way, representing so-called "weak null singularities", and thus that a revised version of strong cosmic censorship holds.
On $(\alpha_n)$-regular sets

We define $(\alpha_n)$ -regular sets in uniformly perfect metric spaces. This definition is quasisymmetrically invariant and the construction resembles generalized dyadic cubes in metric spaces. For these sets we then determine the necessary and sufficient conditions to be fat (or thin). In addition we discuss restrictions of doubling measures to these sets, and in particular give a sufficient condition to retain at least some of the restricted measures doubling on the set. Our main result generalizes and extends analogous results that were previously known to hold in the real-line.
Ascending chains of ideals in the polynomial ring

Assume that $K$ is a field and $I_{1}\subsetneq . \subsetneq I_{t}$ is an ascending chain (of length $t$) of ideals in the polynomial ring $K[x_{1},,. ,x_{m}]$, for some $m\geq 1$. Suppose that $I_{j}$ is generated by polynomials of degrees less or equal to some natural number $f(j)\geq 1$, for any $j=1,. ,t$. In the paper we construct, in an elementary way, a natural number $\mathcal{B}(m,f)$ (depending on $m$ and the function $f$) such that $t\leq\mathcal{B}(m,f)$. We also discuss some possible applications of this result.
Linear stability analysis and numerical simulation of miscible two-layer channel flow

The stability of miscible two-fluid flow in a horizontal channel is examined. The flow dynamics are governed by the continuity and Navier–Stokes equations coupled to a convective-diffusion equation for the concentration of the more viscous fluid through a concentration-dependent viscosity. Our analysis of the flow in the linear regime delineates the presence of convective and absolute instabilities and identifies the vertical gradients of viscosity perturbations as the main destabilizing influence in agreement with previous work. Our transient numerical simulations demonstrate the development of complex dynamics in the nonlinear regime, characterized by roll-up phenomena and intense convective mixing; these become pronounced with increasing flow rate and viscosity ratio, as well as weak diffusion.
Effect of the loop capacitance on resonant modes in superconducting two-junction interferometers

Self‐resonant current steps in superconducting interferometers are investigated. The case of interferometers with non‐negligible loop capacitance is considered. A theoretical analysis based on an equivalent electrical circuit is performed to get the resonance frequencies in the current‐controlled case. Careful measurements on a slightly asymmetrical (C1≠C2) interferometer are reported. The magnetic field dependence of the maximum amplitude of the resonant steps and their voltage position have been studied. A good agreement between theory and experiments is obtained.
General criteria for the study of quasi-stationarity

For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of attraction by an integrability condition, prove the existence of a right eigenvector for the semigroup of the process and the existence and exponential ergodicity of the Q-process. These results are applied to one-dimensional and multi-dimensional diffusion processes, to pure jump continuous time processes, to reducible processes with several communication classes, to perturbed dynamical systems and discrete time processes evolving in discrete state spaces.
C*-algebras of self-similar graphs over arbitrary graphs

The first-named author was partially supported by CNPq. The third named author was partially supported by PAI III grant FQM-298 of the Junta de Andalucia, and by the DGI-MINECO and European Regional Development Fund, jointly, through grants MTM2014-53644-P and MTM2017-83487-P. The third named author was partially supported by a Carleton University internal research grant.
Weak backward error analysis for overdamped Langevin processes

We consider numerical approximations of overdamped Langevin stochastic differential equations by implicit methods. We show a weak backward error analysis result in the sense that the generator associated with the numerical solution coincides with the solution of a modified Kolmogorov equation up to high order terms with respect to the stepsize. This implies that every measure of the numerical scheme is close to a modified invariant measure obtained by asymptotic expansion. Moreover, we prove that, up to negligible terms, the dynamic associated with the implicit scheme considered is exponentially mixing.
Regularity and approximation of strong solutions to rate-independent systems

Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this work we prove the existence of Holder-regular strong solutions for a class of rate-independent systems. We also establish additional higher regularity results that guarantee the uniqueness of strong solutions. The proof proceeds via a time-discrete Rothe approximation and careful elliptic regularity estimates depending in a quantitative way on the (local) convexity of the potential featuring in the model. In the second part of the paper we show that our strong solutions may be approximated by a fully discrete numerical scheme based on a spatial finite element discretization, whose rate of convergence is consistent with the regularity of strong solutions whose existence and uniqueness are established.
Extension of potentialities of millisecond pulsed Nd:YAG lasers in the welding technology

The dependences of the dynamic parameters of the growth of a vapour-gas channel and the depth of the melting zone on the shape of laser pulses and the spatial beam parameters are studied. Based on this study, the requirements are formulated to the characteristics of radiation providing a many-fold increase in the melting depth with respect to the depth that was previously considered as limiting. A new laser setup for deep high-quality welding was built. The role of the buffer volume of a melt in the suppression of ejection of molten metal from the laser-heated region upon deflection of the melt surface is substantiated. An increase in the rate of growth of a vapour-gas channel during an increase in its length (the self-concentration of a heat source) was experimentally observed. At the depths corresponding to the preferential vertical orientation of fluid flows, a large-scale vortex motion of the melt was observed. The dependence of the penetration depth of the melting front on the aperture angle ? was experimentally found to have an extremum. The maximum penetration depth was obtained for ? = 0.075 ? 0.80 rad. Recommendations for designing pulsed laser technological systems for high-quality welding of metals are formulated.
Value distribution of the sequences of the derivatives of iterated polynomials

We establish the equidistribution of the sequence of the averaged pullbacks of a Dirac measure at any value in $\mathbb{C}\setminus\{0\}$ under the derivatives of the iterations of a polynomials $f\in\mathbb{C}[z]$ of degree more than one towards the $f$-equilibrium (or canonical) measure $\mu_f$ on $\mathbb{P}^1$. We also show that for every $C^2$ test function on $\mathbb{P}^1$, the convergence is exponentially fast up to a polar subset of exceptional values in $\mathbb{C}$. A parameter space analog of the latter quantitative result for the monic and centered unicritical polynomials family is also established.
Dust in the Universe

The possible existence of intergalactic dust with properties similar to interstellar dust is examined in some detail. If such dust does exist, it could result in a correction to the observed deceleration parameter. (As little as 2 x 10/sup -4/ mag Mpc/sup -1/ absorption would cause a measurement error of (.delta.q/sub 0/)/sub Dust/ approx.1. ) The relation of the dust to possible intergalactic gas is examined, including survival times in a hot gas. The possible origins of intergalactic dust are also discussed. It is shown that uniform filling of the unverse with dust is exceedingly unlikely whereas dust halos around galaxies and clusters of galaxies may be quite. The dust optical depth across a cluster halo is estimated to be . pi.approx. =0.1.
X-ray photoemission spectroscopy study of fluorinated single-walled carbon nanotubes

We have investigated the change of atomic and electronic structures of fluorinated single-walled carbon nanotubes (SWCNTs) using x-ray photoemission spectroscopy (XPS), electrical resistivity measurements, and transmission electron microscopy (TEM). The fluorine content increases with increasing reaction temperature up to 300 °C. XPS indicated that the fluorinated SWCNT reveals an ionic-bonding character at low concentration and covalent-bonding character at high concentration. The resistivity increases with reaction temperatures, resulting from the band gap enlargement at high fluorine concentration. It is also observed from TEM that the fluorination at reaction temperature above 250 °C leads to the disintegration of the CNT structures and formation of various phases such as multiwall-like and turbostratic morphologies.
On Schoen surfaces

We give a new construction of the irregular, generalized Lagrangian, surfaces of general type with p_g=5, \chi=2, K^2=8, recently discovered by Chad Schoen. Our approach proves that, if S is a general Schoen surface, its canonical map is a finite morphism of degree 2 onto a canonical surface with invariants p_g=5, \chi=6, K^2=8, a complete intersection of a quadric and a quartic hypersurface in P^4, with 40 even nodes.
Geometric derivation of the Schrödinger equation from classical mechanics in curved Weyl spaces

A theory physically equivalent to traditional nonrelativistic quantum mechanics is presented, in which both dynamical and probabilistic concepts enter in a classical way. Particle trajectories are deterministically governed by classical mechanics, only the initial position being at random. Quantum effects are supposed to arise from a modification of the geometry of space, due to the presence of matter. However, unlike gravitational forces, which are related to the metric of space-time, quantum-mechanical forces are proved to be related to the transplantation law of vectors. The resulting geometry of space, in the nonrelativistic limit, is found to be Weyl's geometry. Both particle motion and geometry of space are obtained from a unique averaged least-action principle.
Geometric engineering of (framed) BPS states

BPS quivers for $\mathcal{N} = 2 \: SU(N)$ gauge theories are derived via geometric engineering from derived categories of toric Calabi-Yau threefolds. While the outcome is in agreement of previous low energy constructions, the geometric approach leads to several new results. An absence of walls conjecture is formulated for all values of $N$, relating the field theory BPS spectrum to large radius D-brane bound states. Supporting evidence is presented as explicit computations of BPS degeneracies in some examples. These computations also prove the existence of BPS states of arbitrarily high spin and infinitely many marginal stability walls at weak coupling. Moreover, framed quiver models for framed BPS states are naturally derived from this formalism, as well as a mathematical formulation of framed and unframed BPS degeneracies in terms of motivic and cohomological Donaldson-Thomas invariants. We verify the conjectured absence of BPS states with 'exotic' $SU(2)_R$ quantum numbers using motivic DT invariants. This application is based in particular on a complete recursive algorithm which determines the unframed BPS spectrum at any point on the Coulomb branch in terms of noncommutative Donaldson-Thomas invariants for framed quiver representations.
Descent and the Koszul Duality for Locally Constant Factorisation Algebras

Generalizing Jacob Lurie's idea on the relation between the Verdier duality and the iterated loop space theory, we study the Koszul duality for locally constant factorization algebras. We formulate an analogue of Lurie's "nonabelian Poincare duality" theorem (which is closely related to earlier results of Graeme Segal, of Dusa McDuff, and of Paolo Salvatore) in a symmetric monoidal stable infinity category carefully, using John Francis' notion of excision. Its proof is done by first studying the Koszul duality for E_n-algebras in detail. As a consequence, we obtain a Verdier type equivalence for factorization algebras by a Koszul duality construction. At a foundational level, we study descent properties of Lurie's topological chiral homology. We prove that this homology theory satisfies descent for a factorizing cover, as defined by Kevin Costello and Owen Gwilliam. We also obtain a generalization of Lurie's approach to this homology theory, which leads to a product formula for the infinity category of factorization algebras, and its twisted generalization.
Remarks about bubbles

We make some remarks about bubbling on, not necessarily proper, champs de Deligne-Mumford, i.e. compactification of the space of mappings from a given (wholly scheme like) curve, so, in particular, on quasi-projective projective varieties. Under hypothesis on both the interior and the boundary such as Remark \ref{rmk:interior} below, this implies an optimal logarithmic variant of Mori's Bend-and-Break. The main technical remark is \ref{thm:logMM}, while our final remark, the cone theorem, \ref{rmk:cone}, is a variant.
A Free Boundary Problem for a Predator-prey Model with Double Free Boundaries

In this paper we investigate a free boundary problem for a predator-prey model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the free boundaries represent expanding fronts of the predator species and are described by Stefan-like condition. We prove a spreading-vanishing dichotomy for this model, namely the predator species either successfully spreads to infinity as $t\to \infty$ at both fronts and survives in the new environment, or it fails to establish and dies out in the long run while the prey species stabilizes at a positive equilibrium state. The long time behavior of solution and criteria for spreading and vanishing are also obtained.
Twisted K-theory

Twisted complex K-theory can be defined for a space X equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C ∗ -algebras. Up to equivalence, the twisting corresponds to an element of H 3 (X; Z). We give a systematic account of the definition and basic properties of the twisted theory, emphasizing some points where it behaves differently from ordinary K-theory. (We omit, however, its relations to classical coho- mology, which we shall treat in a sequel.) We develop an equivariant version of the theory for the action of a compact Lie group, proving that then the twistings are classified by the equivariant cohomology group H 3 G (X; Z). We also consider some basic examples of twisted K-theory classes, related to those appearing in the recent work of Freed-Hopkins-Teleman.
DISTINGUISHED MODELS OF INTERMEDIATE JACOBIANS

We show that the image of the Abel–Jacobi map admits functorially a model over the field of definition, with the property that the Abel–Jacobi map is equivariant with respect to this model. The cohomology of this abelian variety over the base field is isomorphic as a Galois representation to the deepest part of the coniveau filtration of the cohomology of the projective variety. Moreover, we show that this model over the base field is dominated by the Albanese variety of a product of components of the Hilbert scheme of the projective variety, and thus we answer a question of Mazur. We also recover a result of Deligne on complete intersections of Hodge level 1.
Canonical Forms of $2 \times 2 \times 2$ and $2 \times 2 \times 2 \times 2$ Symmetric Tensors over Prime Fields

We consider symmetric tensors of format $2 \times 2 \times 2$ and $2 \times 2 \times 2 \times 2$ over prime fields. Using computer algebra we compute the canonical forms of these tensors. For $2 \times 2 \times 2$ symmetric tensors, we consider the prime fields $\mathbb{F}_p$ for $p = 2, 3, 5, 7, 11, 13, 17$. For $2 \times 2 \times 2 \times 2$ symmetric tensors, we consider the prime fields $\mathbb{F}_p$ for $p = 2, 3, 5, 7$. For each canonical form, we determine the size of its orbit and the symmetric rank of the symmetric tensors in its orbit.
On the Hardy–Sobolev equation

In this paper we study the problem where Ω = ℝ N or Ω = B 1, N ⩾ 3, p > 1 and . Using a suitable map we transform problem (1) into another one without the singularity 1/|x|2. Then we obtain some bifurcation results from the radial solutions corresponding to some explicit values of λ.