Miracle-dz/UniFAR-FTUs huggingface dataset:
Alternative Angle-Based Approach to the KS-Map. An Interpretation Through Symmetry and Reduction

The $\mathcal{KS}$ map is revisited in terms of an $S^1$-action in $T^*\mathbb{H}_0$ with the bilinear function as the associated momentum map. Indeed, the $\mathcal{KS}$ transformation maps the $S^1$-fibers related to the mentioned action to single points. By means of this perspective a second twin-bilinear function is obtained with an analogous $S^1$-action. We also show that the connection between the 4-D isotropic harmonic oscillator and the spatial Kepler systems can be done in a straightforward way after regularization and through the extension to 4 degrees of freedom of the Euler angles, when the bilinear relation is imposed. This connection incorporates both bilinear functions among the variables. We will show that an alternative regularization separates the oscillator expressed in Projective Euler variables. This setting takes advantage of the two bilinear functions and another integral of the system including them among a new set of variables that allows to connect the 4-D isotropic harmonic oscillator and the planar Kepler system. In addition, our approach makes transparent that only when we refer to rectilinear solutions, both bilinear relations defining the $\mathcal{KS}$ transformations are needed.
Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube

We study a two-parameter generalization of the Catalan numbers: $C_{d,p}(n)$ is the number of ways to subdivide the $d$-dimensional hypercube into $n$ rectangular blocks using orthogonal partitions of fixed arity $p$. Bremner \& Dotsenko introduced $C_{d,p}(n)$ in their work on Boardman--Vogt tensor products of operads; they used homological algebra to prove a recursive formula and a functional equation. We express $C_{d,p}(n)$ as simple finite sums, and determine their growth rate and asymptotic behaviour. We give an elementary proof of the functional equation, using a bijection between hypercube decompositions and a family of full $p$-ary trees. Our results generalize the well-known correspondence between Catalan numbers and full binary trees.
Cosmic Gamma-Ray Bursts from Black Hole Tidal Disruption of Stars?

Prior to its ultimate tidal disruption, any star plunging sufficiently deeply within the Roche radius of a giant black hole in a galactic nucleus will briefly undergo compression into highly flattened pancake configuration in the plane of its orbit. If it is assumed (as a provisional hypothesis) that a substantial part of the thermal energy briefly made available by this process is dissipated as electromagnetic radiation, one finds that the most energetic cases would give rise to cosmic gamma-ray bursts whose total energy and duration are remarkably consistent with what is actually observed
A 4D gravity theory and G2-holonomy manifolds

Bryant and Salamon gave a construction of metrics of G2 holonomy on the total space of the bundle of anti-self-dual (ASD) 2-forms over a 4-dimensional self-dual Einstein manifold. We generalise it by considering the total space of an SO(3) bundle (with fibers R^3) over a 4-dimensional base, with a connection on this bundle. We make essentially the same ansatz for the calibrating 3-form, but use the curvature 2-forms instead of the ASD ones. We show that the resulting 3-form defines a metric of G2 holonomy if the connection satisfies a certain second-order PDE. This is exactly the same PDE that arises as the field equation of a certain 4-dimensional gravity theory formulated as a diffeomorphism-invariant theory of SO(3) connections. Thus, every solution of this 4-dimensional gravity theory can be lifted to a G2-holonomy metric. Unlike all previously known constructions, the theory that we lift to 7 dimensions is not topological. Thus, our construction should give rise to many new metrics of G2 holonomy. We describe several examples that are of cohomogeneity one on the base.
White light-emitting, biocompatible, water-soluble metallic magnesium nanoclusters for bioimaging applications

Ultra-small (1.6 nm), water-soluble, white light-emitting (WLE), highly stable (∼8 months) BSA templated metallic (Mg0) nanoclusters (fluorescent magnesium nanoclusters = FMNCs) is developed using the green and facile route. Synthesis was facilitated by the reduction of magnesium salt, where template bovine serum albumin is utilized as a reducing agent and ascorbic acid act as a capping agent to impart stability in water, thereby obtaining stabilized Mg0 nanoclusters In solution, stabilized Mg0 nanoclusters produce white light (450–620 nm with FWHM ∼120 nm) upon 366 nm light excitation. This white light emission was found to have a CIE coordinate of 0.30, 0.33 [pure white light CIE (0.33, 0.33)]. Taking advantage of WLE and ultrasmall size, FMNCs were used for in vitro fluorescence imaging of HaCaT cell lines, yielding blue (τ = 2.94 ns, with a relative of QY = 1.2 % w.r.t QS), green (τ = 3.07 ns; relative quantum yield of 4.6% w.r.t R6G) and red (τ = 0.3 ns) images. Further, incubation of FMNCs with HEK293 (Human embryonic kidney cell) and cancerous MDA-MB-231 (Breast cancer cell line) human cell lines yielded 100 % cell viability. Current work is envisioned to contribute significantly in the area of science, engineering, and nanomedicine.
Local and global structure of connections on nonarchimedean curves

Consider a vector bundle with connection on a $p$-adic analytic curve in the sense of Berkovich. We collect some improvements and refinements of recent results on the structure of such connections, and on the convergence of local horizontal sections. This builds on work from the author’s 2010 book and on subsequent improvements by Baldassarri and by Poineau and Pulita. One key result exclusive to this paper is that the convergence polygon of a connection is locally constant around every type 4 point.
More than a visitor? Rethinking metaphors for family care in long-term care homes

Recent public and policy interventions aim to recognise formally the contributions of family care-givers to long-term residential care in Canada, with some arguing family carers are more than visitors and should be recognised as essential care-givers. These developments call for reconsidering how family care roles are understood and operationalised. Drawing on ethnographic research conducted in three care homes in Ontario, Canada, we present an in-depth feminist rhetorical analysis of the narrated lives and work practices of 12 unpaid family carers. Specifically, we explore how unpaid family carers themselves draw on broader discursive ‘ruling metaphors’ to interpret their roles and activities (e.g. as essential care-givers, visitors, team members), and how these metaphors invoke, organise and/or give rise to particular practices, responsibilities and relations. We contrast the stories of a family member who positioned herself as an essential care-giver and expressed a more onerous sense of individual responsibility with the stories of people who enjoyed the pleasures of visiting, who contributed as team members in ways that went beyond caring for their own relatives' care needs, and who embraced the possibilities that came with volunteering and with being able to influence change. Our analysis situates and contextualises participants' stories of their involvement and unpaid work in relation to their everyday material conditions and circumstances. We elaborate how different ways of understanding caring roles shape the nature of carers' unpaid work, as well as their options to share responsibility or set limits on that work. We also raise questions about the organisational conditions needed to help enact care as a shared collective responsibility.
Rigorous numerics for nonlinear operators with tridiagonal dominant linear part

We present a method designed for computing solutions of infinite dimensional non linear operators $f(x) = 0$ with a tridiagonal dominant linear part. We recast the operator equation into an equivalent Newton-like equation $x = T(x) = x - Af(x)$, where $A$ is an approximate inverse of the derivative $Df(\overline x)$ at an approximate solution $\overline x$. We present rigorous computer-assisted calculations showing that $T$ is a contraction near $\overline x$, thus yielding the existence of a solution. Since $Df(\overline x)$ does not have an asymptotically diagonal dominant structure, the computation of $A$ is not straightforward. This paper provides ideas for computing $A$, and proposes a new rigorous method for proving existence of solutions of nonlinear operators with tridiagonal dominant linear part.
Relationship between Reticulorumen Parameters Measured in Real Time and Methane Emission and Heat Stress Risk in Dairy Cows

Simple Summary We have found only a few publications in the literature on the link between rumen pH and CH4. Based on this, we hypothesized that reticulorumen pH and temperature, where the latter is registered on an online system, affect greenhouse gas CH4 emissions. As a result, to the best of our knowledge, this is the first study that has assessed the relationship of CH4 emissions with reticulorumen pH and temperature. According to the aim of this study, we found that cows with a higher pH (6.22–6.42) produce 46.18% more methane emissions than cows with a lower pH. Moreover, cows with a higher risk of heat stress had a higher risk of subclinical acidosis. The novel aspect of the study is that, by using real-time reticulorumen pH, a temperature-registration system, and a laser methane detector, we could establish a relationship between reticulorumen parameters measured in real time and methane emissions and heat-stress risk in dairy cows. For this reason, more studies should be conducted to evaluate this process. Abstract The objective of this study was to investigate a connection between CH4 emissions and reticulorumen pH and temperature. During the experiment, we registered the following parameters: reticulorumen pH (pH), reticulorumen temperature (RR temp.), reticulorumen temperature without drinking cycles, ambient temperature, ambient relative humidity, cow activity, heat index, temperature–humidity index (THI), and methane emissions (CH4). The experimental animals were divided into two groups based on the reticulorumen pH: 1. pH < 6.22 and 2. pH 6.22–6.42. We found that cows assigned to the second pH class had higher (46.18%) average values for methane emissions (p < 0.01). For the other indicators, higher average values were detected in cows of the first pH class, RR temperature (2.80%), relative humidity (20.96%), temperature–humidity index (2.47%) (p < 0.01), and temperature (3.93%) (p < 0.05), which were higher compared to cows of the second pH class. Reticulorumen pH was highly negatively correlated with THI and temperature (r = −0.667 to 0.717, p < 0.001) and somewhat negatively with heat index, relative humidity, and RR temperature (r = −0.536, p < 0.001; r = −0.471 to 0.456, p < 0.01). Cows with a higher risk of heat stress had a higher risk of lower reticulorumen pH.
Mode Poset Probability Polytopes

A mode of a probability distribution is an elementary event that has more probability mass than each of its direct neighbors, with respect to some vicinity structure on the set of elementary events. The mode inequalities cut out a polytope from the simplex of probability distributions. Related to this is the concept of strong modes. A strong mode of a probability distribution is an elementary event that has more probability mass than all its direct neighbors together. The set of probability distributions with a given set of strong modes is again a polytope. We study the vertices, the facets, and the volume of such polytopes depending on the sets of (strong) modes and the vicinity structures.
Hermite-Birkhoff Interpolation on Arbitrarily Distributed Data in Banach Spaces

A class of cardinal basis functions is proposed in order to achieve a generalization to Banach spaces of Hermite-Birkhoff interpolation on arbitrarily distributed data. First, a constructive characterization of the class of cardinal basis functions is given. Then, the interpolation problem is solved by using a suitable combination of such functions and Taylor-Fréchet expansions. The performance of the obtained interpolants is improved by applying a localizing scheme, and the corresponding approximation error is estimated. A noteworthy case in Hilbert spaces and a numerical test comparing the Hermite-Birkhoff and Lagrange interpolants complete the presentation.
Measurement of the spin structure of the neutron using polarised deep inelastic scattering

The measurement of the spin structure function gy of the proton and its integral l? ; by the EMC experiment a t CERN in 1988 indicated that only 12% f 17% of the proton spin is carried by quarks. This unexpected result the so called 'spin crisis' lead to a series of new experimental proposals. One of these, the HERMES experiment, uses the polarised positron beam of the HERA accelerator together with a polarised internal gas target of hydrogen, deuterium or 3He for the study of the spin structure of the nucleon. The scattered positrons and other products of the reaction are detected in a forward spectrometer with large acceptance. This thesis focuses on three topics, after a review of the relevant theory and an overview of the HERMES experiment: The HERMES transition radiation detector (TRD), which is used to distinguish high energy positrons from hadrons, the HERMES particle identification (PID) system and the measurement of the'spin structure function g;" of the neutron. The HERMES TRD is the main Canadian contribution to the apparatus of the experiment. The HERMES PID system allows the identification of positrons from deep inelastic scattering with an efficiency of 99% and a hadron contamination of less than 0.5%. The first physics result from the 1995 HERMES data is the measurement of the spin structure function g:(x) of the neutron. The value of the resulting integral r; = J,' g;(x) dx confirms previous measurements a t SLAC and violates the EllisJaffe sum rule by about one sigma. The contribution of the quarks to the spin of the neutron can be calculated in the framework of the quark parton model to be 3 7 f 16%, indicating that less than half of the spin of the neutron is carried by quarks. SCHULER Ich wunschte recht gelehrt zu werden, Und mochte gern, was auf der Erden, Und in dem Himmel ist, erfassen, Die Wissenschaft und die Natur. MEPHISTOPHELES Da seid Ihr auf der rechten Spur; Doch mufit Ihr Euch nicht zerstreuen lassen. SCHULER Ich bin dabei mit See1 und Leib; Doch freilich wiirde mir behagen Ein wenig Freiheit und Zeitvertreib An schonen Sommerfeiertagen.
On Integrable modules for the twisted full toroidal Lie algebra

The paper is to classify irreducible integrable modules for the twisted full toroidal Lie algebra with some technical conditions. The twisted full toroidal Lie algebra are extensions of multiloop algebra twisted by sevaral finite order automorphisms. The result genaralizes a result by Fu Jiayuan and Cuipo Jiang, where they consider only one automorphism.
Intersection theory and the Alesker product

Alesker has introduced the space $\mathcal V^\infty(M)$ of {\it smooth valuations} on a smooth manifold $M$, and shown that it admits a natural commutative multiplication. Although Alesker's original construction is highly technical, from a moral perspective this product is simply an artifact of the operation of intersection of two sets. Subsequently Alesker and Bernig gave an expression for the product in terms of differential forms. We show how the Alesker-Bernig formula arises naturally from the intersection interpretation, and apply this insight to give a new formula for the product of a general valuation with a valuation that is expressed in terms of intersections with a sufficiently rich family of smooth polyhedra.
System Transformation-Based Event-Triggered Fuzzy Control for State Constrained Nonlinear Systems With Unknown Control Directions

This article focuses on the event-triggered (ET) fuzzy tracking control for uncertain state constrained strict-feedback systems with unknown control directions. A novel nonlinear transformed function is developed to transform the constrained system states into the counterpart without any constraints. An ingenious adaptation law is developed to co-design the control law and the ET rule, thereby effectively compensating the sampling error caused by the ET rule under unknown control directions. Based on the presented adaptation law and the Nussbaum gain technique, a novel ET fuzzy tracking control strategy is proposed, which can handle the situations with and without state constraints in a unified way without readjusting the control scheme. Subsequently, the nonlinear transformed function is extended to the time-varying state constraints, and the corresponding ET fuzzy control scheme is also modified to guarantee the closed-loop boundedness. The proposed two control strategies guarantee the satisfactory tracking performance, avoid the violation of the prescribed state constraints, and decrease the communication load effectively. Finally, the usefulness of the developed methods is verified through two simulation examples.
Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes

CONTENTS: Preliminary remarks; Brownian motion, poisson process, alpha-stable Levy motion; Computer simulation of alpha-stable random variables; Stochastic integration; Spectral representations of stationary processes; Computer approximations of continuous time processes; Examples of alpha-stable stochastic modelling; Convergence of approximate methods; Chaotic behaviour of stationary processes; Hierarchy of chaos for stable and ID stationary processes. Appendix - A guide to simulation.
On the Hodge conjecture for products of certain surfaces

In this paper we prove the Hodge conjecture for products of the form $S_1 \times . S_n$, where $S_i$ are smooth projective surfaces such that $p_g(S_i)=1, q(S_i)=2$. We also prove the Hodge conjecture for arbitrary self-products of a K3 surface $X$ such that $End_{hodge}(T(X))$ is a CM number field.
Class numbers and $p$-ranks in ${\mathbb Z}_p^d$-towers

To extend Iwasawa's classical theorem from ${\mathbb Z}_p$-towers to ${\mathbb Z}_p^d$-towers, Greenberg conjectured that the exponent of $p$ in the $n$-th class number in a ${\mathbb Z}_p^d$-tower of a global field $K$ ramified at finitely many primes is given by a polynomial in $p^n$ and $n$ of total degree at most $d$ for sufficiently large $n$. This conjecture remains open for $d\geq 2$. In this paper, we prove that this conjecture is true in the function field case. Further, we propose a series of general conjectures on $p$-adic stability of zeta functions in a $p$-adic Lie tower of function fields.
PLANAR PSEUDO-ALMOST LIMIT CYCLES AND APPLICATIONS TO SOLITARY WAVES

Bourama ToniVirginia State University,Department of Mathematics & Computer Science, Petersburg VA 23806.btoni@vsu.eduABSTRACTWe investigate the existence of pseudo-almost limit cycles, a new class of non-periodicityat the interface of the theories of limit cycles and pseudo-almost periodicity. We de-termine the conditions of existence for several systems including some pseudo-almostperiodic perturbations of the harmonic oscillator and the renowned Li´enard systems.We apply to derive the existence of pseudo-almost periodic solitary waves by perturbingﬁrst then transforming some hyperbolic and parabolic partial diﬀerential equations toLi´enard-type equations. Included also are open questions on the co-existence of limitcycles and strictly pseudo-almost periodic limit cycles partitioning the phase space, andthe existence of isochronous pseudo-almost limit cycles.RESUMENInvestigamos laexistenciadeciclos seudo-casi l´imites, unanuevaclasedeno-periodicidaden la interfaz de las teor´ias de ciclos l´imites y seudo-casi periodicidad. Determinamoscondiciones de existencia de muchos sistemas, incluyendo algunas perturbaciones seudo-casi perio´dicas del oscilador armo´nico y los sistemas de Li´enard. Aplicamos las condi-ciones para derivar la existencia de ondas solitarias seudo-cuasi perio´dicas, primero per-turbando y luego transformando algunas ecuaciones diferenciales parciales hiperb´olicasy parab´olicas a ecuaciones del tipo Li´enard. Tambi´en se incluyen preguntas abiertas so-bre la co-existencia de ciclos l´imite y estrictamente pseudo-casi perio´dicos ciclos l´imitede partici´on del espacio de fases, y la existencia de is´ocrono pseudo-casi ciclos l´imite . Keywords and Phrases: Limit cycles. Almost and pseudo-almost periodic orbits. Periodicwaves. Isochronous systems and Isochrons. Li´enard systems. Hyperbolic and parabolic equations.2010 AMS Mathematics Subject Classiﬁcation: 34C05, 34C07, 34C27, 34K14
Completions of mu-algebras

A $\mu$-algebra is a model of a first order theory that is an extension of the theory of bounded lattices, that comes with pairs of terms $(f,\mu_{x}.f)$ where $\mu_{x}. f$ is axiomatized as the least prefixed point of $f$, whose axioms are equations or equational implications. Standard $\mu$-algebras are complete meaning that their lattice reduct is a complete lattice. We prove that any non trivial quasivariety of $\mu$-algebras contains a $\mu$-algebra that has no embedding into a complete $\mu$-algebra. We focus then on modal $\mu$-algebras, i.e. algebraic models of the propositional modal $\mu$-calculus. We prove that free modal $\mu$-algebras satisfy a condition -- reminiscent of Whitman's condition for free lattices -- which allows us to prove that (i) modal operators are adjoints on free modal $\mu$-algebras, (ii) least prefixed points of $\Sigma_{1}$-operations satisfy the constructive relation $\mu_{x}. f = \bigvee_{n \geq 0} f^{n}(\bot)$. These properties imply the following statement: {\em the MacNeille-Dedekind completion of a free modal $\mu$-algebra is a complete modal $\mu$-algebra and moreover the canonical embedding preserves all the operations in the class $Comp(\Sigma_{1},\Pi_{1})$ of the fixed point alternation hierarchy. }
Large Deviations in Renewal Theory and Renewal Models of Statistical Mechanics

We present and establish large deviations principles for general multivariate renewal-reward processes associated with a classical discrete-time renewal process. A renewal-reward process describes a cumulative reward over time, supposing that a broad-sense multivariate reward is obtained at each occurrence of the event that is renewed under the renewal process. We consider both the standard model and a constrained model that is constructed conditioning on the event that one of the renewals occurs at a predetermined time. With a different interpretation of the time coordinate, the constrained renewal model includes several important models of statistical mechanics, such as the model of polymer pinning, the Poland-Scheraga model of DNA denaturation, the Wako-Sait\^o-Mu\~noz-Eaton model of protein folding, and the Tokar-Dreyss\'e model of strained epitaxy. We attack the problem of large deviations in constrained renewal models by an argument based on convexity and super-additivity. Then, we transfer results to standard renewal processes by resorting to conditioning. In the context of constrained renewal models, we also propose an explicit application of the general theory to deterministic rewards that grow no faster than the time elapsed between two successive occurrences of the renewed event. This type of rewards codifies the extensive variables of statistical mechanics.
Blowing up and down compacta with geometrically finite convergence actions of a group

We consider two compacta with minimal non-elementary convergence actions of a countable group. When there exists an equivariant continuous map from one to the other, we call the first a blow-up of the second and the second a blow-down of the first. When both actions are geometrically finite, it is shown that one is a blow-up of the other if and only if each parabolic subgroup with respect to the first is parabolic with respect to the second. As an application, for each compactum with a geometrically finite convergence action, we construct its blow-downs with convergence actions which are not geometrically finite.