Miracle-dz/UniFAR-FTUs huggingface dataset:
Theory and computation of spheroidal wavefunctions

In this paper we report on a package, written in the Mathematica computer algebra system, which has been developed to compute the spheroidal wavefunctions of Meixner and Schafke (1954 Mathieusche Funktionen und Spharoidfunktionen) and is available online (physics.uwa.edu.au/~falloon/spheroidal/spheroidal.html). This package represents a substantial contribution to the existing software, since it computes the spheroidal wavefunctions to arbitrary precision for general complex parameters μ, ν, γ and argument z; existing software can only handle integer μ, ν and does not give arbitrary precision. The package also incorporates various special cases and computes analytic power series and asymptotic expansions in the parameter γ. The spheroidal wavefunctions of Flammer (1957 Spheroidal Wave functions) are included as a special case of Meixner's more general functions. This paper presents a concise review of the general theory of spheroidal wavefunctions and a description of the formulae and algorithms used in their computation, and gives high precision numerical examples.
Twisted calculus

ABSTRACT A twisted ring is a ring endowed with a family of endomorphisms satisfying certain relations. One may then consider the notions of twisted module and twisted differential module. We study them and show that, under some general hypothesis, the categories of twisted modules and integrable twisted differential modules are equivalent. As particular cases, one recovers classical results from the theory of finite difference equations or q-difference equations.
The rigidity theorems for Lagrangian self shrinkers

By the integral method we prove that any space-like entire graphic self-shrinking solution to Lagrangian mean curvature flow in $\R^{2n}_{n}$ with the indefinite metric $\sum_i dx_idy_i$ is flat. This result improves the previous ones in \cite{HW} and \cite{CCY} by removing the additional assumption in their results. In a similar manner, we reprove its Euclidean counterpart which is established in \cite{CCY}.
Free Group Algebras in Division Rings with Valuation II

Abstract We apply the filtered and graded methods developed in earlier works to find (noncommutative) free group algebras in division rings. If $L$ is a Lie algebra, we denote by $U(L)$ its universal enveloping algebra. P. M. Cohn constructed a division ring $\mathfrak{D}_{L}$ that contains $U(L)$. We denote by $\mathfrak{D}(L)$ the division subring of $\mathfrak{D}_{L}$ generated by $U(L)$. Let $k$ be a field of characteristic zero, and let $L$ be a nonabelian Lie $k$-algebra. If either $L$ is residually nilpotent or $U(L)$ is an Ore domain, we show that $\mathfrak{D}(L)$ contains (noncommutative) free group algebras. In those same cases, if $L$ is equipped with an involution, we are able to prove that the free group algebra in $\mathfrak{D}(L)$ can be chosen generated by symmetric elements in most cases. Let $G$ be a nonabelian residually torsion-free nilpotent group, and let $k(G)$ be the division subring of the Malcev–Neumann series ring generated by the group algebra $k[G]$. If $G$ is equipped with an involution, we show that $k(G)$ contains a (noncommutative) free group algebra generated by symmetric elements.
SEXTICS WITH SINGULAR POINTS IN SPECIAL POSITION

In this paper we show a Zariski pair of sextics which is not a degeneration of the original example given by Zariski. This is the first example of this kind known. The two curves of the pair have a trivial Alexander polynomial. The difference in the topology of their complements can only be detected via finer invariants or techniques. In our case the generic braid monodromies, the fundamental groups, the characteristic varieties and the existence of dihedral coverings of ℙ2 ramified along them can be used to distinguish the two sextics. Our intention is not only to use different methods and give a general description of them but also to bring together different perspectives of the same problem.
The Arithmetic of Calabi-Yau Manifolds and Mirror Symmetry

We study mirror symmetric pairs of Calabi--Yau manifolds over finite fields. In particular we compute the number of rational points of the manifolds as a function of the complex structure parameters. The data of the number of rational points of a Calabi--Yau $X/\mathbb{F}_q$ can be encoded in a generating function known as the congruent zeta function. The Weil Conjectures (proved in the 1970s) show that for smooth varieties, these functions take a very interesting form in terms of the Betti numbers of the variety. This has interesting implications for mirror symmetry, as mirror symmetry exchanges the odd and even Betti numbers. Here the zeta functions for a one-parameter family of K3 surfaces, $\mathbb{P}_3[4]$, and a two-parameter family of octics in weighted projective space, $\mathbb{P}_4{}^{(1, 1, 2, 2, 2)} [8]$, are computed. The form of the zeta function at points in the moduli space of complex structures where the manifold is singular (where the Weil conjectures apart from rationality are not applicable), is investigated. The zeta function appears to be sensitive to monomial and non-monomial deformations of complex structure (or equivalently on the mirror side, toric and non-toric divisors). Various conjectures about the form of the zeta function for mirror symmetric pairs are made in light of the results of this calculation. Connections with $L$-functions associated to both elliptic and Siegel modular forms are suggested.
Factors Affecting the Predictability of Hurricane Humberto (2007)

Abstract This study uses ensemble Kalman filter analyses and short-range ensemble forecasts to study factors affecting the predictability of Hurricane Humberto, which made landfall along the Texas coast in 2007. Humberto is known for both its rapid intensification and extreme forecast uncertainty, which makes it an ideal case in which to examine the origins of tropical cyclone strength forecast error. Statistical correlation is used to determine why some ensemble members strengthen the incipient low into a hurricane and others do not. During the analysis period, it is found that variations in midlevel moisture, low-level convective instability, and strength of a front to the north of the cyclone likely lead to differences in net precipitation, which ultimately leads to storm strength spread. Stronger storms are favored when the atmosphere is more moist and unstable and when the front is weaker, possibly because some storms in the ensemble begin entraining cooler and drier postfrontal air during this perio.
On convergence and compactness of space homeomorphisms

Various theorems on convergence of general space homeomorphisms are proved and, on this basis, theorems on convergence and compactness for classes of the so-called ring $Q$--homeomorphisms are obtained. In particular, it was established by us that a family of all ring $Q$--homeomorphisms $f$ in ${\Bbb R}^n$ fixing two points is compact provided that the function $Q$ is of finite mean oscillation. These results will have wide applications to Sobolev's mappings.
Smooth concordance of links topologically concordant to the Hopf link

It was shown by Jim Davis that a 2‐component link with Alexander polynomial one is topologically concordant to the Hopf link. In this paper, we show that there is a 2‐component link with Alexander polynomial one that has unknotted components and is not smoothly concordant to the Hopf link, answering a question of Jim Davis. We construct infinitely many concordance classes of such links, and show that they have the stronger property of not being smoothly concordant to the Hopf link with knots tied in the components.
Two measures of the shape of the dark halo of the Milky Way

In order to test the reliability of determinations of the shapes of dark-matter haloes of the galaxies, we have made such measurements for the Milky Way by two independent methods. First, we have combined the measurements of the overall mass distribution of the Milky Way derived from its rotation curve and the measurements of the amount of dark matter in the solar neighbourhood obtained from stellar kinematics to determine the flattening of the dark halo. Secondly, we have used the established technique based on the variation in thickness of the Milky Way’s H i layer with radius: by assuming that the H i gas is in hydrostatic equilibrium in the gravitational potential of a galaxy, one can use the observed flaring of the gas layer to determine the shape of the dark halo. These techniques are found to produce a consistent estimate for the flattening of the dark-matter halo, with a shortest-to-longest axis ratio of q∼0.8, but only if one adopts somewhat non-standard values for the distance to the Galactic centre, R0, and the local Galactic rotation speed, Θ0. For consistency, one requires values of R0≲7.6 kpc and Θ0≲190 km s−1. The results depend on the Galactic constants because the adopted values affect both distance measurements within the Milky Way and the shape of the rotation curve, which, in turn, alter the inferred halo shape. Although differing significantly from the current IAU-sanctioned values, these upper limits are consistent with all existing observational constraints. If future measurements confirm these lower values for the Galactic constants, then the validity of the gas-layer-flaring method will be confirmed. Further, dark-matter candidates such as cold molecular gas and massive decaying neutrinos, which predict very flat dark haloes with q≲0.2, will be ruled out. Conversely, if the Galactic constants were found to be close to the more conventional values, then there would have to be some systematic error in the methods for measuring dark halo shapes, so the existing modelling techniques would have to be viewed with some scepticism.
Some remarks on a paper by samimi on nonuniqueness criteria for ordinary differential equations

In [4] M. SAMIMI gives nonuniqueness theorems for initial value problems x′= f(t,x), x(0) =x0. where f is not defined at t = 0. But the result for the scalar case only holds with the additional assumption that one solution exists. The applicability of the revised theorem is shown. The result for the n-dimensional case is generalized.
The complexity of conjugacy, orbit equivalence, and von Neumann equivalence of actions of nonamenable groups

Building on work of Popa, Ioana, and Epstein--Tornquist, we show that, for every nonamenable countable discrete group Γ, the relations of conjugacy, orbit equivalence, and von Neumann equivalence of free ergodic (or weak mixing) measure preserving actions of Γ on the standard atomless probability space are not Borel, thus answering questions of Kechris. This is an optimal and definitive result, which establishes a neat dichotomy with the amenable case, since any two free ergodic actions of an amenable group on the standard atomless probability space are orbit equivalent by classical results of Dye and Ornstein--Weiss. The statement about conjugacy solves the nonamenable case of Halmos' conjugacy problem in Ergodic Theory, originally posed by Halmos in 1956 for ergodic transformations. In order to obtain these results, we study ergodic (or weak mixing) class-bijective extensions of a given ergodic countable probability measure preserving equivalence relation R. When R is nonamenable, we show that the relations of isomorphism and von Neumann equivalence of extensions of R are not Borel. When R is amenable, all the extensions of R are again amenable, and hence isomorphic by classical results of Dye and Connes--Feldman--Weiss. This approach allows us to extend the results about group actions mentioned above to the case of nonamenable locally compact unimodular groups, via the study of their cross-section equivalence relations.
Sign-indefinite second-order differential operators on finite metric graphs

The question of self-adjoint realizations of sign-indefinite second-order differential operators is discussed in terms of a model problem. Operators of the type $-\frac{d}{dx} {\rm sgn} (x) \frac{d}{dx}$ are generalized to finite, not necessarily compact, metric graphs. All self-adjoint realizations are parametrized using methods from extension theory. The spectral and scattering theories of the self-adjoint realizations are studied in detail.
Holomorphic Lorentzian simplicity constraints

We develop a Hamiltonian representation of the sl(2,C) algebra on a phase space consisting of N copies of twistors, or bi-spinors. We identify a complete set of global invariants, and show that they generate a closed algebra including gl(N,C) as a subalgebra. Then, we define the linear and quadratic simplicity constraints which reduce the spinor variables to (framed) 3d space-like polyhedra embedded in Minkowski spacetime. Finally, we introduce a new version of the simplicity constraints which (i) are holomorphic and (ii) Poisson-commute with each other, and show their equivalence to the linear and quadratic constraints.
Evaluation and regularization of generalized Eisenstein series and application to 2D cylindrical harmonic sums

In the study of periodic media, conditionally convergent series are frequently encountered and their regularization is crucial for applications. We derive an identity that regularizes two-dimensional generalized Eisenstein series for all Bravais lattices, yielding physically meaningful values. We also obtain explicit forms for the generalized series in terms of conventional Eisenstein series, enabling their closed-form evaluation for important high symmetry lattices. Results are then used to obtain representations for the related cylindrical harmonic sums, which are also given for all Bravais lattices. Finally, we treat displaced lattices of high symmetry, expressing them in terms of origin-centered lattices via geometric multi-set identities. These identities apply to all classes of two-dimensional sums, allowing sums to be evaluated over each constituent of a unit cell that possesses multiple inclusions.
Basis problem for analytic multiple gaps

A k-gap is a finite k-sequence of pairwise disjoint monotone families of infinite subsets of N mixed in such a way that we cannot find a partition of N such that each family is trival on one piece of the partition. We prove that, relative to the comparison given by restriction to infinite subsets of N, for every positive integer k there is a finite basis for the class of all analytic k-gaps . We also build the fine structure theory of analytic k-gaps and give some applications. The content of Chapter 1 of this manuscript have been published as: A. Aviles, S. Todorcevic, Finite basis for analytic multiple gaps, Publ. Math. IHES. 121 (2015), 57-79. The content of Chapter 2 (except some technical results from 2.5 and 2.6) and Section 3.1, largely revised and improved, has ben published as: A. Aviles, S. Todorcevic, Types in the n-adic tree and minimal analytic gaps, Adv. Math. 292 (2016), 558-600. The content of Sections 3.4, 4.1 and 4.3 have been published as: A. Aviles, S. Todorcevic, Isolating subgaps of a multiple gap, Monatsh. Math. 186 (2018), 373--392. The rest of contents may appear elsewhere.
Uniform Asymptotic Expansions of Laguerre Polynomials

Two asymptotic expansions are obtained for the Laguerre polynomial $L_n^{(\alpha )} (x)$ for large n and fixed $\alpha > - 1$. These expansions are uniformly valid in two overlapping intervals covering the entire x-axis. The leading terms of both agree with the two asymptotic formulas given by Erdelyi who used the theory of differential equations. Our approach is based on two integral representations for the Laguerre polynomials. The phase function of one of these integrals has two coalescing saddle points, and to this one the cubic transformation introduced by Chester, Friedman, and Ursell is applied. The phase function of the other integral also has two coalescing saddle points, but in addition it has a simple pole. Moreover, the saddle points coalesce onto this pole. In this case a rational transformation is used, which mimics the singular behavior of the phase function. In both cases explicit expressions are given for the remainders associated with the asymptotic expansions.
Magnetic Pinching of Hyperbolic Flux Tubes. II. Dynamic Numerical Model

In this paper we present the results of a series of numerical experiments that extend and supplement the recent analytical investigations by Titov et al. of the formation of strong current layers in coronal magnetic fields containing hyperbolic flux tubes (HFTs). The term "hyperbolic" refers to the special geometrical properties of the magnetic field, whereas the topology of the field is simple; i.e., there are no magnetic null points and separatrix lines or surfaces associated with them inside the coronal volume. However, the field lines passing through a hyperbolic flux tube show a large variation in the mapping between their photospheric endpoints. On the basis of analytical estimates, it has been suggested by Titov et al. that HFTs are preferred locations for the formation of strong current layers in coronal magnetic fields with trivial topologies, provided the driving motions on the photospheric boundary are of a special type. Such motions must have shearing components that are applied across narrow HFT feet as if trying to twist it. This system of motions is then capable of causing a pinching deformation of the HFT by a sustained stagnation point flow inside the HFT. The numerical experiments presented in this paper clearly confirm this suggestion. HFTs are generic features of geometrically complex but topologically trivial magnetic fields, and therefore our results are very important for understanding magnetic reconnection in such fields, since reconnection is occurring preferentially at locations with strong current densities.
Airglow response to vertically standing gravity waves

There is currently much interest in fluctuations of airglow emissions caused by atmospheric gravity waves. The fluctuations of brightness tend to be found in phase (or occasionally in antiphase) with the fluctuations of measured temperature, whereas current theory tends to anticipate substantial phase differences. We suggest here that the discrepancy results from failure of the common theoretical assumption that the relevant gravity waves are dominated by a single upgoing component: that, instead, there is an accompanying downgoing component of comparable magnitude, produced by reflection. In the case of total reflection, simple, steady state chemistry and vertical viewing, the phase difference is necessarily zero (or 180°).
Maximal torus theory for compact quantum groups

Associated to any compact quantum group $G\subset U_N^+$ is a canonical family of group dual subgroups $\widehat{\Gamma}_Q\subset G$, parametrized by unitaries $Q\in U_N$, playing the role of "maximal tori" for $G$. We present here a series of conjectures, relating the various algebraic and analytic properties of $G$ to those of the family $\{\widehat{\Gamma}_Q|Q\in U_N\}$.
Some aspects on solving transportation problem

In this paper, we consider a class of transportation problems which arises in sample surveys and other areas of statistics. The associated cost matrices to these transportation problems are of special structure. We observe that the optimality of North West corner solution holds for the problem where cost component is replaced by a convex function. We revisit assignment problem and present a weighted version of K? nig-Egerv? ry theorem. Finally, we propose weighted Hungarian method to solve the transportation problem.
Exact dynamic member stiffnesses for a beam on an elastic foundation

This paper gives exact Bernoulli–Euler dynamic flexural member equations for a uniform beam on an elastic foundation. These enable exact results to be obtained when the beam is included in free or sinusoidally forced vibration calculations for a plane or space frame, at any frequency. In addition, information is presented to ensure that no natural frequencies are missed in a free vibration analysis.
TWISTING ALL THE WAY: FROM ALGEBRAS TO MORPHISMS AND CONNECTIONS

Given a Hopf algebra H and an algebra A that is an H-module algebra we consider the category of left H-modules and A-bimodules ${^H}_A{\mathscr M}_A$, where morphisms are just right A-linear maps (not necessarily H-equivariant). Given a twist ${\mathcal F}$ of H we then quantize (deform) H to $H^{\mathcal F}$, A to A⋆ and correspondingly the category ${^H}_A{\mathscr M}_A$ to ${^H}^{\mathcal F}_{A_\star}{\mathscr M}_{A_\star}$. If we consider a quasitriangular Hopf algebra H, a quasi-commutative algebra A and quasi-commutative A-bimodules, we can further construct and study tensor products over A of modules and of morphisms, and their twist quantization. This study leads to the definition of arbitrary (i.e., not necessarily H-equivariant) connections on quasi-commutative A-bimodules, to extend these connections to tensor product modules and to quantize them to A⋆-bimodule connections. Their curvatures and those on tensor product modules are also determined.
Inductively defined sets of reals

1. Introduction. The concept of inductive definability has become of great interest to recursion theorists in recent years. Recursion over natural numbers, ordinals, and higher type objects may itself be defined by an inductive operator—see for example [7] and [9]. Many results have been obtained characterizing the closures of inductive operators over the natural numbers, and relating lengths of inductive definitions to various interesting ordinals ; see [3] for a brief summary. The purpose of this note is to present results on the closure ordinals and sets of inductive operators over the continuum. Details will appear later in [2], [4], and [5].
Local connectedness and the wallman compactification

Abstract For a regular frame L with a locally connected Wallman basis we obtain several criteria for its corresponding Wallman compactification to be perfect and locally connected. We then give an application of this result by proving that the Freudenthal compactification of a connected rim-compact frame is locally connected if and only if the frame is locally connected.
Qualitative properties of solutions for nonlinear Schrödinger equations with nonlinear boundary conditions on the half-line

In this paper, we study the interaction between a nonlinear focusing Robin type boundary source, a nonlinear defocusing interior source, and a weak damping term for nonlinear Schrodinger equations posed on the infinite half-line. We construct solutions with negative initial energy satisfying a certain set of conditions which blow-up in finite time in the H1-sense. We obtain a sufficient condition relating the powers of nonlinearities present in the model which allows construction of blow-up solutions. In addition to the blow-up property, we also discuss the stabilization property and the critical exponent for this model.
Reconsideration of the Pre-1970 Model for the Timing of Oil Expulsion from Source Rocks

The current model for oil expulsion occurring at 120-150°C by anhydrous pyrolysis is not consistent with either analyses of the total organic carbon (TOC) content of subsurface source rocks or the chemical attributes of shallow oils. New data from North Sea Upper Jurassic source-rock samples show no decline in TOC between 120 and 150°C, which is a key prediction by the current model for oil expulsion. Instead, it is proposed here that oil expulsion occurs mainly at around 30°C at depths <1 km, similar to models advocated prior to 1970. Expulsion is suggested to be facilitated by CO 2 gas generated from decomposing organic matter. Migration out of the source rock and into nearby high-permeable pathways occurs in the direction towards decreasing overburden via horizontal fractures that originate from swelling of load-bearing organic laminae. The thermally immature (heavy) oil is then converted to light oil within reservoirs by hydrogenation at 60-70°C. Hydrogen gas is common in subsurface fluids and is released by coalification of organic matter in mudstones in amounts sufficient to hydrogenate the reservoired heavy oil volumes. In this model, most heavy oil accumulations are interpreted as immature rather than the products