Miracle-dz/UniFAR-FTUs huggingface dataset:
On a conjectured reverse Faber-Krahn inequality for a Steklov-type Laplacian eigenvalue

For a given bounded Lipschitz set $\Omega$, we consider a Steklov--type eigenvalue problem for the Laplacian operator whose solutions provide extremal functions for the compact embedding $H^1(\Omega)\hookrightarrow L^2(\partial \Omega)$. We prove that a conjectured reverse Faber--Krahn inequality holds true at least in the class of Lipschitz sets which are "close" to a ball in a Hausdorff metric sense. The result implies that among sets of prescribed measure, balls are local minimizers of the embedding constant.
Relationship of the Hennings and Chern-Simons Invariants For Higher Rank Quantum Groups

The Hennings invariant for the small quantum group associated to an arbitrary simple Lie algebra at a root of unity is shown to agree with Jones- Witten-Reshetikhin-Turaev invariant arising from Chern-Simons filed theory for the same Lie algebra and the same root of unity on all integer homol- ogy three-spheres, at roots of unity where both are defined. This partially generalizes the work of Chen, et al. ([CYZ12, CKS09]) which relates the Hennings and Chern-Simons invariants for SL(2) and SO(3) for arbitrary rational homology three-spheres.
Characteristic numbers of manifold bundles over surfaces with highly connected fibers

We study smooth bundles over surfaces with highly connected almost parallelizable fiber M of even dimension, providing necessary conditions for a manifold to be bordant to the total space of such a bundle and showing that, in most cases, these conditions are also sufficient. Using this, we determine the characteristic numbers realized by total spaces of bundles of this type, deduce divisibility constraints on their signatures and Â ‐genera, and compute the second integral cohomology of BDiff+(M) up to torsion in terms of generalized Miller–Morita–Mumford classes. We also prove analogous results for topological bundles over surfaces with fiber M and discuss the resulting obstructions to smoothing them.
Transnational Couples: The Intersections of Race, Ethnicity, Nativity, and Gender

ABSTRACT Over one in ten heterosexual married couples are interracial and close to 10% of marriages are transnational. Even with the increasing rates of intermarriage there continues to be opposition to such marriages and their families. This study aimed to explore the lived experiences of transnational couples, where both partners hail from different countries, as they navigate life in the U.S. Six heterosexual transnational couples across the country were interviewed separately and together using a phenomenological design, and within and across case analyses were conducted. Race, skin color, visibility, nativity, gender, and language interconnected to engender experiences that were different across every couple as they conceptualized how best to protect their families while navigating through varying social narratives, and familial and societal expectations about their relationship. The emergent themes organized into three intersecting processes -internal, intermediary, and external- as these couples navigated their different values, each other, and other systems in their lives. Implications for research and clinical practice follow.
The self-similar solutions to full compressible Navier–Stokes equations without heat conductivity

In this work, we establish a class of globally defined large solutions to the free boundary problem of compressible full Navier–Stokes equations with constant shear viscosity, vanishing bulk viscosity and heat conductivity. We establish such solutions with initial data perturbed around the self-similar solutions when [Formula: see text]. In the case when [Formula: see text], solutions with bounded entropy can be constructed. It should be pointed out that the solutions we obtain in this fashion do not in general keep being a small perturbation of the self-similar solution due to the second law of thermodynamics, i.e. the growth of entropy. If, in addition, in the case when [Formula: see text], we can construct a solution as a global-in-time small perturbation of the self-similar solution and the entropy is uniformly bounded in time. Our result extends the one of Hadžić and Jang [Expanding large global solutions of the equations of compressible fluid mechanics, J. Invent. Math. 214 (2018) 1205. ] from the isentropic inviscid case to the non-isentropic viscous case.
Exponential mixing of frame flows for convex cocompact hyperbolic manifolds

The aim of this paper is to establish exponential mixing of frame flows for convex cocompact hyperbolic manifolds of arbitrary dimension with respect to the Bowen–Margulis–Sullivan measure. Some immediate applications include an asymptotic formula for matrix coefficients with an exponential error term as well as the exponential equidistribution of holonomy of closed geodesics. The main technical result is a spectral bound on transfer operators twisted by holonomy, which we obtain by building on Dolgopyat's method.
Hilbert series of residual intersections

We give explicit formulas for the Hilbert series of residual intersections of a scheme in terms of the Hilbert series of its conormal modules. In a previous paper, we proved that such formulas should exist. We give applications to the number of equations defining projective varieties and to the dimension of secant varieties of surfaces and three-folds.
Ramification theory and perfectoid spaces

Abstract Let $K_1$ and $K_2$ be complete discrete valuation fields of residue characteristic $p>0$. Let $\pi _{K_1}$ and $\pi _{K_2}$ be their uniformizers. Let $L_1/K_1$ and $L_2/K_2$ be finite extensions with compatible isomorphisms of rings $\mathcal{O}_{K_1}/(\pi _{K_1}^m)\, {\simeq }\, \mathcal{O}_{K_2}/(\pi _{K_2}^m)$ and $\mathcal{O}_{L_1}/(\pi _{K_1}^m)\, {\simeq }\, \mathcal{O}_{L_2}/(\pi _{K_2}^m)$ for some positive integer $m$ which is no more than the absolute ramification indices of $K_1$ and $K_2$. Let $j\leq m$ be a positive rational number. In this paper, we prove that the ramification of $L_1/K_1$ is bounded by $j$ if and only if the ramification of $L_2/K_2$ is bounded by $j$. As an application, we prove that the categories of finite separable extensions of $K_1$ and $K_2$ whose ramifications are bounded by $j$ are equivalent to each other, which generalizes a theorem of Deligne to the case of imperfect residue fields. We also show the compatibility of Scholl’s theory of higher fields of norms with the ramification theory of Abbes–Saito, and the integrality of small Artin and Swan conductors of $p$-adic representations with finite local monodromy.
Exact L_2-Small Deviation Asymptotics for Some Brownian Functionals

We find exact small deviation asymptotics with respect to weighted Hilbert norm for some well-known Gaussian processes. Our approach does not require the knowledge of eigenfunctions of the covariance operator of a weighted process. Such a peculiarity of the method makes it possible to generalize many previous results in this area. We also obtain new relations connected to exact small deviation asymptotics for a Brownian excursion, a Brownian meander, and Bessel processes and bridges.
Associated primes of Local cohomology modules over Regular rings

Let $R$ be an excellent regular ring of dimension $d$ containing a field $K$ of characteristic zero. Let $I$ be an ideal in $R$. We show that $Ass \ H^{d-1}_I(R)$ is a finite set. As an application we show that if $I$ is an ideal of height $g$ with $height \ Q = g$ for all minimal primes of $I$ then for all but finitely many primes $P \supseteq I$ with $height \ P \geq g +2$, the topological space $Spec^\circ(R_P/IR_P)$ is connected.
Confinement and Mayer cluster expansions

In this paper, we study a class of grand-canonical partition functions with a kernel depending on a small parameter ϵ. This class is directly relevant to Nekrasov partition functions of 𝒩 = 2 SUSY gauge theories on the 4d Ω-background, for which ϵ is identified with one of the equivariant deformation parameter. In the Nekrasov–Shatashvili limit ϵ→0, we show that the free energy is given by an on-shell effective action. The equations of motion take the form of a TBA equation. The free energy is identified with the Yang–Yang functional of the corresponding system of Bethe roots. We further study the associated canonical model that takes the form of a generalized matrix model. Confinement of the eigenvalues by the short-range potential is observed. In the limit where this confining potential becomes weak, the collective field theory formulation is recovered. Finally, we discuss the connection with the alternative expression of instanton partition functions as sums over Young tableaux.
Preliminary Results of a Prospective Clinical and Radiological Study with Roentgen Stereophotogrammetric Analysis (RSA) after Implantation of a Posterior Dynamic Stabilization Device in the Lumbar Spine

Introduction: Posterior dynamic stabilization (PDS) can be based on interspinous distraction devices (IDD). The goals of these implants are maintaining or restoring intervertebral range of motion (ROM) in a controlled fashion and avoiding a complete restriction of mobility. Clinical and radiological data with the Wallis® spacer as one type of IDD have been rarely reported. The goal of this study was to present clinical and radiological data including roentgen stereophotogrammetric analysis (RSA) after a short- to mid-term follow-up period. Patients and Methods: 10 patients were included in this prospective monocentric study and had PDS of the lumbar spine with an IDD (Wallis® spacer). Before and soon after operation and 3, 6, and 12 months later clinical and radiological evaluations were performed. Pain and disability were analyzed by use of visual analog scale for back and leg pain, Oswestry Disability Index, Roland-Morris Disability Questionnaire and Short-Form-36 Health Survey. The ROM of the operated levels and the total lumbar spine was determined by use of lateral functional x-ray images with calculation of the differences of the segmental and total lumbar spine angles in flexion and extension. Furthermore, RSA was used to measure the segmental ROM. Results: After a follow-up of 12 months, the results of the pain intensity and the disability and health related quality of life scores showed statistical significant improvement. The segmental angles of the operated levels demonstrated statistical significant reduction in ROM during the different follow-up examinations. The discrepancy of the conventionally determined segmental angles and the data measured by RSA were low with a mean of 1.77°. The mean total lumbar spine angles did not change statistically significantly during the postoperative controls. Conclusions: According to the radiological results of this study, the used implant leads to a posterior dynamic stabilization. The clinical findings are promising, but they are to be interpreted with caution because of the small number of patients and the lack of a control group.
Nonzero positive solutions of a multi-parameter elliptic system with functional BCs

We prove, by topological methods, new results on the existence of nonzero positive weak solutions for a class of multi-parameter second order elliptic systems subject to functional boundary conditions. The setting is fairly general and covers the case of multi-point, integral and nonlinear boundary conditions. We also present a non-existence result. We provide some examples to illustrate the applicability of our theoretical results.
Predicting Deleterious Non-Synonymous Single Nucleotide Polymorphisms (nsSNPs) of HRAS Gene and In Silico Evaluation of Their Structural and Functional Consequences towards Diagnosis and Prognosis of Cancer

Simple Summary The HRAS gene has been reported to cause cancer, and identifying alleles that could potentially predispose one to cancer could lead to early diagnosis and better prognosis. Here for the first time, we conducted a machine-learning approach to identify high-risk predictive alleles of the HRAS gene. Our study reported alleles that may serve as potential targets for different proteomic studies, diagnoses, and therapeutic interventions focusing on cancer. Abstract The Harvey rat sarcoma (HRAS) proto-oncogene belongs to the RAS family and is one of the pathogenic genes that cause cancer. Deleterious nsSNPs might have adverse consequences at the protein level. This study aimed to investigate deleterious nsSNPs in the HRAS gene in predicting structural alterations associated with mutants that disrupt normal protein–protein interactions. Functional and structural analysis was employed in analyzing the HRAS nsSNPs. Putative post-translational modification sites and the changes in protein–protein interactions, which included a variety of signal cascades, were also investigated. Five different bioinformatics tools predicted 33 nsSNPs as “pathogenic” or “harmful”. Stability analysis predicted rs1554885139, rs770492627, rs1589792804, rs730880460, rs104894227, rs104894227, and rs121917759 as unstable. Protein–protein interaction analysis revealed that HRAS has a hub connecting three clusters consisting of 11 proteins, and changes in HRAS might cause signal cascades to dissociate. Furthermore, Kaplan–Meier bioinformatics analyses indicated that the HRAS gene deregulation affected the overall survival rate of patients with breast cancer, leading to prognostic significance. Thus, based on these analyses, our study suggests that the reported nsSNPs of HRAS may serve as potential targets for different proteomic studies, diagnoses, and therapeutic interventions focusing on cancer.
Refined ramification breaks in characteristic $p$

Let $K$ be a local field of characteristic $p$ and let $L/K$ be a totally ramified elementary abelian $p$-extension with a single ramification break $b$. Byott and Elder defined the refined ramification breaks of $L/K$, an extension of the usual ramification data. In this paper we give an alternative definition for the refined ramification breaks, and we use Artin-Schreier theory to compute both versions of the breaks in some special cases.
The Electromagnetic Christodoulou Memory Effect in Neutron Star Binary Mergers

Gravitational waves are predicted by the general theory of relativity. In [6] D. Christodoulou showed that gravitational waves have a nonlinear memory. We proved in [3] that the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In the present paper, we study this electromagnetic Christodoulou memory effect and compute it for binary neutron star mergers. These are typical sources of gravitational radiation. During these processes, not only mass and momenta are radiated away in form of gravitational waves, but also very strong magnetic fields are produced and radiated away. Thus the observed effect on test masses of a laser interferometer gravitational wave detector will be enlarged by the contribution of the electromagnetic field. Therefore, the present results are important for the planned experiments. Looking at the null asymptotics of spacetimes, which are solutions of the Einstein-Maxwell (EM) equations, we derived in [3] the electromagnetic Christodoulou memory effect. Moreover, our results allow to answer astro- physical questions, as the knowledge about the amount of energy radiated away in a neutron star binary merger enables us to gain information about the source of the gravitational waves.
Local structure of singular hyperkahler quotients

When a compact Lie group acts freely and in a Hamiltonian way on a symplectic manifold, the Marsden-Weinstein theorem says that the reduced space is a smooth symplectic manifold. If we drop the freeness assumption, the reduced space might be singular, but Sjamaar-Lerman (1991) showed that it can still be partitioned into smooth symplectic manifolds which "fit together nicely" in the sense that they form a stratification. In this paper, we prove a hyperkahler analogue of this statement, using the hyperkahler quotient construction. We also show that singular hyperkahler quotients are complex spaces which are locally biholomorphic to affine complex-symplectic GIT quotients with biholomorphisms that are compatible with natural holomorphic Poisson brackets on both sides.
Asymptotic behavior of the Verblunsky coefficients for the OPUC with a varying weight

We present an asymptotic analysis of the Verblunsky coefficients for the polynomials orthogonal on the unit circle with the varying weight e−nV(cos x), assuming that the potential V has four bounded derivatives on [−1, 1] and the equilibrium measure has a one interval support. We obtain the asymptotics as a solution of the system of “string” equations.
The scaling relation chi = 2 xi - 1 for directed polymers in a random environment

We prove the scaling relation chi = 2 xi - 1 between the transversal exponent xi and the fluctuation exponent chi for directed polymers in a random environment in d dimensions. The definition of these exponents is similar to that proposed by S. Chatterjee in first-passage percolation. The proof presented here also establishes the relation in the zero temperature version of the model, known as last-passage percolation.
Phenotypic Characterization and Fine Mapping of a Major-Effect Fruit Shape QTL FS5.2 in Cucumber, Cucumis sativus L., with Near-Isogenic Line-Derived Segregating Populations

Cucumber (Cucumis sativus L.) fruit size/shape (FS) is an important yield and quality trait that is quantitatively inherited. Many quantitative trait loci (QTLs) for fruit size/shape have been identified, but very few have been fine-mapped or cloned. In this study, through marker-assisted foreground and background selections, we developed near-isogenic lines (NILs) for a major-effect fruit size/shape QTL FS5.2 in cucumber. Morphological and microscopic characterization of NILs suggests that the allele of fs5.2 from the semi-wild Xishuangbanna (XIS) cucumber (C. s. var. xishuangbannesis) reduces fruit elongation but promotes radial growth resulting in shorter but wider fruit, which seems to be due to reduced cell length, but increased cellular layers. Consistent with this, the NIL carrying the homozygous XIS allele (fs5.2) had lower auxin/IAA contents in both the ovary and the developing fruit. Fine genetic mapping with NIL-derived segregating populations placed FS5.2 into a 95.5 kb region with 15 predicted genes, and a homolog of the Arabidopsis CRABS CLAW (CsCRC) appeared to be the most possible candidate for FS5.2. Transcriptome profiling of NIL fruits at anthesis identified differentially expressed genes enriched in the auxin biosynthesis and signaling pathways, as well as genes involved in cell cycle, division, and cell wall processes. We conclude that the major-effect QTL FS5.2 controls cucumber fruit size/shape through regulating auxin-mediated cell division and expansion for the lateral and longitudinal fruit growth, respectively. The gibberellic acid (GA) signaling pathway also plays a role in FS5.2-mediated fruit elongation.
Growth rate of binary matroids with no $P_9^*$-minor

We prove that the non-regular binary matroids with no $P_9^*$-minor have linear growth rate and the maximum size binary matroids with no $P_9^*$-minor are graphic. The main technique in the proof is the Strong Splitter Theorem using which we find the precise infinite families of 3-connected binary matroids with no $P_9^*$-minor.
Use of Compost in Onion Cultivation under No-Tillage System: Effect on Nutrient Uptake

ABSTRACT The nutrition of onion grown in a no-tillage system with compost requires research to provide alternatives to mineral fertilizers. Our objective was to evaluate the effect of compost rates on the nutrient content in the tissue of onion grown in a no-tillage system. We conducted a field experiment with the following treatments: 0, 10, 20, 30, and 60 Mg ha−1 of compost and mineral fertilization. We applied these treatments in 2018, 2019, and 2020 for onion cultivation. We used a 3 × 6 factorial scheme (year x treatment) and four replications. We evaluated the bulbs and whole plant nutrient contents of N, P, K, Ca, Mg, S, Fe, Mn, Zn, Cu, and B. In 2020, nutrient content in the bulb from 10 Mg ha−1 of compost was similar to the mineral fertilizer’s treatment. Therefore, compost can replace mineral fertilizers to supply nutrients to the onion. However, the continuous application of compost requires soil monitoring due to nutrient accumulation.
Local regularity results for value functions of tug-of-war with noise and running payoff

Abstract We prove local Lipschitz continuity and Harnack's inequality for value functions of the stochastic game tug-of-war with noise and running payoff. As a consequence, we obtain game-theoretic proofs for the same regularity properties for viscosity solutions of the inhomogeneous p-Laplace equation when p > 2.
Optimizing Spectral Waveband Selection for Spectral Radiation Detection of Hypersonic Vehicle

Space-based spectral radiation detection is one of the most effective approaches for detecting hypersonic vehicles. However, due to complex characteristics of the plasma sheath that is generated by aerodynamic thermal effect and envelopes hypersonic vehicle, space-based spectral radiation detection is still confronted with great challenges. Based on the mechanisms of spectral radiation and transmission, we establish a model to conduct optimal selection on spectral wavebands for detecting hypersonic vehicle. Through using the established model, we obtain the spectral radiation characteristics of plasma-sheath-enveloped vehicles (RAM-CII and HTV2) under different flight conditions (at 40–70-km altitude with 10–25-Mach velocity). The optimal spectral wavebands for space-based detection are analyzed and identified using the calculated spectral data, upon which the results reveal that significant differences exist in spectral radiation intensities of different flight status for those two vehicles. The overall radiation intensity of RAM-CII vehicle is higher than that of HTV2 vehicle, to which the optimized detection wavebands corresponding to velocity and altitude differ. Generally, at different altitudes, the optimal wavebands for both vehicles are 5.00–7.86, 2.59–3.44, and 1.81–2.10 <inline-formula> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula>. At different flight speeds, the optimal bands are 0.78–1.13 <inline-formula> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> and 99–130 nm, respectively. Combined with the optimized speed and height bands, the optimal detection bands of RAM-CII vehicle and HTV2 vehicle are 5.00–7.86 <inline-formula> <tex-math notation="LaTeX">$ \mu \text{m}$ </tex-math></inline-formula>, 2.59–3.44 <inline-formula> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula>, and 99–130 nm. The above findings can provide useful data for in-depth study of space-based spectral radiation detection.
Chaos in periodically forced reversible vector fields

We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of pulse form may be added to them to yield topological chaotic behaviour. Chaos here means that the resulting dynamics is semi-conjugate to a shift in a finite alphabet. The results rely on the classification of reversible vector fields and on the theory of topological horseshoes. This work is part of a project of studying periodic forcing of symmetric vector fields.
Evaluation of the ADM mass and center of mass via the Ricci tensor

We prove directly without using a density theorem that (i) the ADM mass defined in the usual way on an asymptotically flat manifold is equal to the mass defined intrinsically using Ricci tensor; (ii) the Hamiltonian formulation of center of mass and the center of mass defined intrinsically using Ricci tensor are the same.