Miracle-dz/UniFAR-FTUs huggingface dataset:
Lectures on knot homology

We provide various formulations of knot homology that are predicted by string dualities. In addition, we also explain the rich algebraic structure of knot homology which can be understood in terms of geometric representation theory in these formulations. These notes are based on lectures in the workshop "Physics and Mathematics of Link Homology" at Centre de Recherches Mathematiques, Universite de Montreal.
Existence results of positive solutions for nonlinear cooperative elliptic systems involving fractional Laplacian

In this article, we prove existence results of positive solutions for the following nonlinear elliptic problem with gradient terms: \begin{eqnarray*} \left\{\begin{array}{l@{\quad }l} (-\Delta)^\alpha u=f(x,u,v,\nabla u, \nabla v) &{\rm in}\,\,\Omega,\\ (-\Delta)^\alpha v=g(x,u,v,\nabla u, \nabla v) &{\rm in}\,\,\Omega,\\ u=v=0\,\,&{\rm in}\,\,\R^N\setminus\Omega, \end{array} \right. \end{eqnarray*} where $(-\Delta)^\alpha$ denotes the fractional Laplacian and $ \Omega $ is a smooth bounded domain in $ \R^N $. It shown that under some assumptions on $ f $ and $ g $, the problem has at least one positive solution $(u,v)$. Our proof is based on the classical scaling method of Gidas and Spruck and topological degree theory.
Market risk and expected minimum return of the chemical substance and product manufacturing sector: Period 2011 – 2020

Riesgo y rentabilidad son dos aspectos interdependientes en la actividad empresarial: se debe asumir un cierto nivel de riesgo para lograr una mayor rentabilidad. El modelo de valoración de activos de capital (CAPM) es uno de los modelos más utilizados en la práctica para determinar la rentabilidad exigida en una inversión en un activo financiero en función del riesgo asumido. Existen diversos modelos y herramientas estadísticas que buscan predecir el riesgo financiero. En el presente trabajo de investigación se determinó, a través de información contable, el riesgo de mercado y rendimiento mínimo esperado en el sector de fabricación de substancias y productos químicos (CIIU C20). La data fue obtenida de la Superintendencia, Valores y Seguros y correspondió al periodo 2011-2020, y se analizaron los resultados en periodos de 5 años, para de esta manera, conocer las variaciones que se presentan entre los distintos periodos. Para el análisis de este sector se consideraron 3.756 observaciones (376 empresas por año en promedio) en el periodo. Además, se consideraron como mercado un total de 513.895 observaciones. En el modelo CAPM se consideró como tasa libre de riesgo la tasa pasiva del Banco Central del Ecuador y como rendimiento de mercado un ROE ajustado del total de empresas del sector societario del Ecuador. El coeficiente Beta desapalancado y apalancado obtenido en los 5 periodos analizados es superior a 1, es decir, que se considera un sector riesgoso. El rendimiento mínimo esperado del sector se reduce de 12,15% en el periodo 2011-2015 a 4,98% en el periodo 2016-2020. Los resultados indican que el sector de fabricación de substancias y productos químicos tiene un mejor desempeño que el mercado en conjunto, ya que posee un rendimiento mayor al exigido. Si se considera el alto nivel de incertidumbre existente actualmente, determinar el riesgo de mercado es una herramienta
A Rigidity Result for Overdetermined Elliptic Problems in the Plane

Let f:[0,+∞)→ℝ be a (locally) Lipschitz function and Ω⊂ℝ2 a C1,α domain whose boundary is unbounded and connected. If there exists a positive bounded solution to the overdetermined elliptic problem [{ Δu+f(u)=0in Ω,u=0on Ω,∂u∂ν→=1on Ω, we prove that Ω is a half‐plane. In particular, we obtain a partial answer to a question raised by H. Berestycki, L. Caffarelli, and L. Nirenberg in 1997. © 2017 Wiley Periodicals, Inc.
SYMMETRY AND LINEAR STABILITY IN SERRIN'S OVERDETERMINED PROBLEM VIA THE STABILITY OF THE PARALLEL SURFACE PROBLEM

We consider the solution of the problem �u = f(u) and u > 0 in , u = 0 on , where is a bounded domain in R N with boundary of class C 2,� , 0 0, where re and ri are the radii of a spherical annulus containing , � is a surface parallel to at distance � and sufficiently close to , and ( u) � is the Lipschitz semi-norm of u on � ; secondly, if in addition uis constant on , show that (u) � = o(C�) as � ! 0 + . In this paper, we prove that this strategy is successful. As a by-product of this method, for C 2,� -regular domains, we also obtain a linear stability estimate for Serrin's symmetry result. Our result is optimal and greatly improves the similar logarithmic-type estimate of (ABR) and the Holder estimate of (CMV) that was restricted to convex domains.
On the self similarity of generalized Cantor sets

We consider the self-similar structure of the class of generalized Cantor sets $$\Gamma_{\mathcal{D}}=\Big\{\sum_{n=1}^\infty d_n\beta^{n}: d_n\in D_n, n\ge 1\Big\},$$ where $0<\beta<1$ and $D_n, n\ge 1,$ are nonempty and finite subsets of $\mathbb{Z}$. We give a necessary and sufficient condition for $\Gamma_{\mathcal{D}}$ to be a homogeneously generated self similar set. An application to the self-similarity of intersections of generalized Cantor sets will be given.
Arctic curves in path models from the tangent method

Recently, Colomo and Sportiello introduced a powerful method, known as the tangent method, for computing the arctic curve in statistical models which have a (non- or weakly-) intersecting lattice path formulation. We apply the tangent method to compute arctic curves in various models: the domino tiling of the Aztec diamond for which we recover the celebrated arctic circle; a model of Dyck paths equivalent to the rhombus tiling of a half-hexagon for which we find an arctic half-ellipse; another rhombus tiling model with an arctic parabola; the vertically symmetric alternating sign matrices, where we find the same arctic curve as for unconstrained alternating sign matrices. The latter case involves lattice paths that are non-intersecting but that are allowed to have osculating contact points, for which the tangent method was argued to still apply. For each problem we estimate the large size asymptotics of a certain one-point function using LU decomposition of the corresponding Gessel–Viennot matrices, and a reformulation of the result amenable to asymptotic analysis.
Archaeobotanical evidence of plant cultivation from the Sanbaopi site in south-western Taiwan during the Late Neolithic and Metal Age

Despite decades of lively debate about Taiwan’s role in the spread of early agriculture, crops and cultivation practices to the Indo-Pacific region, there is little archaeobotanical data from the island. Here we present the first directly dated and systematically analysed macrobotanical records from Taiwan obtained by flotation at the archaeological site Sanbaopi 5 (23°07′03′′N, 120°15′32′′E), representing the Dahu (1400 BCE–100 CE) and Niaosong (100–1400 CE) culture periods. The results suggest that Middle Dahu (900–100 BCE) communities in the study area practiced rainfed crop cultivation with mainly foxtail (Setaria italica) and broomcorn (Panicum miliaceum) millet and rice (Oryza sativa). Pulses (Vigna angularis, Glycine soja/max) were also part of the subsistence of local farmers and used as supplementary food and/or green manure. The archaeobotanical record together with archaeological site data for prehistoric China substantiates evidence that the Dahu culture originates in the Lower Yellow River region and migrated to Taiwan along the East China Sea coast. The emergence of the Dahu culture coincided with the spread of mixed millet-rice farming to the Korean Peninsula and Japan and was possibly related to enhanced economic and political expansion of the Shang and Western Zhou dynasties and the long-term weakening of summer monsoon precipitation. Pigeon pea (Cajanus cajan) and mung bean (V. radiata var. radiata) assemblages from the sixth century CE Niaosong period highlight the influx of goods, crops, knowledge and people from South and Southeast Asia via southern routes in the context of enhanced exchange across the South China Sea region.
A priori bounds for geodesic diameter. Part III. A Sobolev-Poincar\'e inequality and applications to a variety of geometric variational problems

Based on a novel type of Sobolev-Poincar\'e inequality (for generalised weakly differentiable functions on varifolds), we establish a finite upper bound of the geodesic diameter of generalised compact connected surfaces-with-boundary of arbitrary dimension in Euclidean space in terms of the mean curvatures of the surface and its boundary. Our varifold setting includes smooth immersions, surfaces with finite Willmore energy, two-convex hypersurfaces in level-set mean curvature flow, integral currents with prescribed mean curvature vector, area minimising integral chains with coefficients in a complete normed commutative group, varifold solutions to Plateau's problem furnished by min-max methods or by Brakke flow, and compact sets solving Plateau problems based on \v{C}ech homology. Due to the generally inevitable presence of singularities, path-connectedness was previously known neither for the class of varifolds (even in the absence of boundary) nor for the solutions to the Plateau problems considered.
The Effect of Religiosity and Job Placement on Work Loyalty through Work Motivation of Employees of Bank Aceh Syariah Tapak Tuan Aceh Selatan Branch

This study aims to analyze the effect of religiosity and job placement on work loyalty mediated by work motivation. This research was conducted at Bank Aceh Syariah Tapak Tuan Aceh Selatan Branch (BAS Asel Branch), with a population of 150 people. To determine the sample, the saturated sampling technique was used. Data were analyzed using AMOS-SEM statistical equipment. Data were collected by interviewing and distributing questionnaires. The results prove that Religiosity, Job Placement, Motivation, and Work loyalty of BAS Asel Branch have not gone well; significantly, religiosity and job placement affect work motivation and work loyalty, Work motivation affects work loyalty; and significantly Work motivation partially mediates the effect of religiosity and job placement on work loyalty at BAS Asel Branch. These results figure that the condition of implementing variables in the model in general is still not going well, and the model of improving BAS Asel Branch work loyalty is the functions of strengthening their religiosity, matching their job placements, and increasing their work motivation
Anticyclotomic p-adic l-functions and the exceptional zero phenomenon

Let A be a modular elliptic curve over a totally real field F, and let E/F be a totally imaginary quadratic extension. In the event of exceptional zero phenomenon, we prove a formula for the derivative of the multivariable anticyclotomic p-adic L-function attached to (A,E), in terms of the Hasse-Weil L-function and certain p-adic periods attached to the respective automorphic forms. Our methods are based on a new construction of the anticyclotomic p-adic L-function by means of the corresponding automorphic representation.
Conservation priorities for global marine biodiversity across multiple dimensions

Abstract Marine biodiversity plays important roles in ocean ecosystem services and has substantial economic value. Species diversity, genetic diversity and phylogenetic diversity, which reflect the number, evolutionary potential and evolutionary history of species in ecosystem functioning, are three important dimensions of biodiversity. Marine-protected areas have been demonstrated as an effective area-based tool for protecting marine biodiversity, but only 2.8% of the ocean has been fully protected. It is urgent to identify global conservation priority areas and percentage of the ocean across multiple dimensions of biodiversity based on Post-2020 Global Biodiversity Framework. Here, we investigate the spatial distribution of marine genetic and phylogenetic diversity using 80 075 mitochondrial DNA barcode sequences from 4316 species and a newly constructed phylogenetic tree of 8166 species. We identify that the Central Indo-Pacific Ocean, Central Pacific Ocean and Western Indian Ocean harbor high levels of biodiversity across three dimensions of biodiversity, which could be designated as conservation priority areas. We also find that strategically protecting ∼22% of the ocean would allow us to reach the target of conserving ∼95% of currently known taxonomic, genetic and phylogenetic diversity. Our study provides insights into the spatial distribution pattern of multiple marine diversities and the findings would help to design comprehensive conservation schemes for global marine biodiversity.
Children’s experiences of hospitalization over time: An evaluation of using poetry and creative writing by children to assess their experiences of hospitalization

This article explores children’s experiences of hospital admissions through their poetry and creative writing and assesses the validity of this medium compared to other methods of evaluation. Pediatric patient experiences of hospital and their effects on children have been studied in various ways and there have been stepwise changes throughout the past century, matching the overall changes of medical care from paternalistic to patient centered. 17 poems were analyzed from children aged 6-13 years old (median 10) for recurrent themes whilst admitted to a large tertiary hospital in the north of England. Children frequently wrote about attacks on their senses, missing friends and family as well as their interactions with hospital staff. Other aspects described by the children included invasive procedures, difficulty with sleep, and their opinions of hospital food. Not all things were described in a negative way, with positivity surrounding play areas, meeting new peers and the availability of play therapists. Ch ildren’s voices are often lost in the hospital setting and it is of vital importance that they are heard so that their care can be optimized and lessen any damaging effects that traumatic experiences have on them. The results of this article match those of previous investigations and show creative writing can be used as a patient experience analysis tool.
Real bounds and quasisymmetric rigidity of multicritical circle maps

Let $f, g:S^1\to S^1$ be two $C^3$ critical homeomorphisms of the circle with the same irrational rotation number and the same (finite) number of critical points, all of which are assumed to be non-flat, of power-law type. In this paper we prove that if $h:S^1\to S^1$ is a topological conjugacy between $f$ and $g$ and $h$ maps the critical points of $f$ to the critical points of $g$, then $h$ is quasisymmetric. When the power-law exponents at all critical points are integers, this result is a special case of a general theorem recently proved by T. ~Clark and S. ~van Strien \cite{CS}. However, unlike the proof given in \cite{CS}, which relies on heavy complex-analytic machinery, our proof uses purely real-variable methods, and is valid for non-integer critical exponents as well. We do not require $h$ to preserve the power-law exponents at corresponding critical points.
Iwasawa theory of overconvergent modular forms, I: Critical $p$-adic $L$-functions

We construct an Euler system of $p$-adic zeta elements over the eigencurve which interpolates Kato's zeta elements over all classical points. Applying a big regulator map gives rise to a purely algebraic construction of a two-variable $p$-adic $L$-function over the eigencurve. As a first application of these ideas, we prove the equality of the $p$-adic $L$-functions associated with a critical-slope refinement of a modular form by the works of Bella\"iche/Pollack-Stevens and Kato/Perrin-Riou.
Egocentric anchoring-and-adjustment underlies social inferences about known others varying in similarity and familiarity.

How do people infer the content of another person's mind? One documented strategy-at least when inferring the minds of strangers-entails anchoring on the content of one's own mind and serially adjusting away from this egocentric anchor. Yet, many social inferences concern known others in existing social relationships. In eight experiments with four sets of stimuli, we tested whether an egocentric anchoring-and-adjustment mechanism underlies social inferences about known targets, and whether it varies based on the target's similarity and familiarity to oneself. In Experiments 1-7, participants (Ntotal = 4,790) rated themselves and a known target on various characteristics (e.g., preferences, habits, traits), and response times for the target ratings were recorded. An integrative data analysis revealed that, consistent with egocentric anchoring-and-adjustment, the more discrepant the target ratings were from participants' self ratings, the longer participants took to provide target ratings. Importantly, this pattern of anchoring-and-adjustment was stronger for similar (vs. dissimilar) and familiar (vs. unfamiliar) targets, but it emerged in all experimental conditions. Experiment 8 (N = 549) suggested that these results were unlikely to be explained solely by a memory search process. We discuss implications for anchoring-and-adjustment as a mechanism underlying social inferences. (PsycInfo Database Record (c) 2022 APA, all rights reserved).
Automorphisms and homology of non-positively curved cube complexes

We define an integer-valued invariant of special cube complexes called the genus, and prove that having genus one characterizes special cube complexes with abelian fundamental group. Using the genus, we obtain a new proof that the fundamental group of a special cube complex is either free abelian or surjects onto a non-cyclic free group. We also investigate automorphisms of special cube complexes, and give a new geometric proof that the Torelli subgroup for a right-angled Artin group is torsion-free.
Sasaki–Einstein metrics and K–stability

We show that a polarized affine variety admits a Ricci flat K\"ahler cone metric, if and only if it is K-stable. This generalizes Chen-Donaldson-Sun's solution of the Yau-Tian-Donaldson conjecture to K\"ahler cones, or equivalently, Sasakian manifolds. As an application we show that the five-sphere admits infinitely many families of Sasaki-Einstein metrics.
Generalized Connes-Chern characters in KK-theory with an application to weak invariants of topological insulators

We use constructive bounded Kasparov K-theory to investigate the numerical invariants stemming from the internal Kasparov products $K_i(\mathcal A) \times KK^i(\mathcal A, \mathcal B) \rightarrow K_0(\mathcal B) \rightarrow \mathbb R$, $i=0,1$, where the last morphism is provided by a tracial state. For the class of properly defined finitely-summable Kasparov $(\mathcal A,\mathcal B)$-cycles, the invariants are given by the pairing of K-theory of $\mathcal B$ with an element of the periodic cyclic cohomology of $\mathcal B$, which we call the generalized Connes-Chern character. When $\mathcal A$ is a twisted crossed product of $\mathcal B$ by $\mathbb Z^k$, $\mathcal A = \mathcal B \rtimes_\xi^\theta \mathbb Z^k$, we derive a local formula for the character corresponding to the fundamental class of a properly defined Dirac cycle. Furthermore, when $\mathcal B = C(\Omega) \rtimes_{\xi'}^{\phi} \mathbb Z^j$, with $C(\Omega)$ the algebra of continuous functions over a disorder configuration space, we show that the numerical invariants are connected to the weak topological invariants of the complex classes of topological insulators, defined in the physics literature. The end products are generalized index theorems for these weak invariants, which enable us to predict the range of the invariants and to identify regimes of strong disorder in which the invariants remain stable. The latter will be reported in a subsequent publication.
Online Adaptive Current Vector Adjustment for Deep Flux-Weakening Control of IPMSM

This article presents a novel online adaptive and accurate deep flux-weakening (FW) control for interior permanent magnet synchronous machine (IPMSM) drives. Based on the fundamental equations of IPMSM, the proposed online current vector adjustment in conjunction with the adaptive torque angle control loop contributes to improving model-based existing literature in two aspects. First, current vector control is constructed on the proposed flexible current vector recognition algorithm, which can be applied for motoring and generating modes. The optimum reference current vector for the FW region is analytically obtained using electrical speed as a feedback signal instead of using voltage feedback. Second, the proposed adaptive gain for the torque angle control loop is obtained using the small-signal approach to overcome the nonlinear effects in deep FW and improve dynamic performance. The effect of adaptive gain is compared using a bode diagram and an experimental test. Also, the stability of the proposed control scheme under parameter variations is maintained and shown by numerical and experimental analyses. The running of the IPMSM with the proposed control provides a smooth transition between regions, including maximum torque per ampere, FW, and deep FW applicable for EVs application. The experimental results confirm the performance of the proposed control strategy.
The diversity of banana cultivars in East Kalimantan based on morphological characteristic

Banana is a plant with nutritious fruit and can help prevent stunting. Banana plants are widely cultivated in East Kalimantan, but the type characterization has not been identified. The purpose of this study was to determine the diversity of banana plants in East Kalimantan and to characterize banana plants based on morphology. This research is explorative in nature by identifying directly in the field the cultivated banana cultivars. Morphological characterization of stems, leaves and fruit was carried out based on the banana description contained in IPGRI-INIBAP/CIRAD. The research instrument is a banana morphology observation sheet which contains parameters: leaf habit, pseudostem color, predominant underlying color of the pseudostem, sap color, blotches at the petiole base, blotches color, petiole canal leaf III, color of leaf upper surface, color of midrib dorsal surface, color of leaf lower surface, color of midrib ventral surface, wax on leaves. The result shows that at East Kalimantan is found 12 types of banana cultivars were found, Talas bananas, Rutai bananas, Kepok bananas, Mas bananas, Morosebo bananas, Tanduk bananas, Susu bananas, Maulin bananas, Red bananas, Ambon bananas, Raja bananas, and Cavendish bananas.There are variations in the morphological characteristics of banana plants, leaves and fruit that can characterize each banana.
The Grothendieck--Teichm\"{u}ller group of~PSL(2,q)

Abstract In this paper, we show that the Grothendieck–Teichmüller group of PSL⁡(2,q){\operatorname{PSL}(2,q)}, or more precisely the group 𝒢⁢𝒯1⁢(PSL⁡(2,q)){\mathcal{G\kern-0.569055ptT}_{\kern-1.707165pt1}(\operatorname{PSL}(2,q))} as previously defined by the author, is the product of an elementary abelian 2-group and several copies of the dihedral group of order 8. Moreover, when q is even, we show that it is trivial. We explain how it follows that the moduli field of any “dessin d’enfant” whose monodromy group is PSL⁡(2,q){\operatorname{PSL}(2,q)} has derived length ≤3{\leq 3}. This paper can serve as an introduction to the general results on the Grothendieck–Teichmüller group of finite groups obtained by the author.
Integrals of logarithmic forms on semi-algebraic sets and a generalized Cauchy formula, Part I: convergence theorems

In this paper consisting of two parts, we study the integral of a logarithmic differential form on a compact semi-algebraic set in R^n or C^n. In Part I, we prove the convergence of the integral when the semi-algebraic set satisfies allowability (or admissibility), a condition on the dimension of the intersection of the set and the pole divisor of the differential form.