Miracle-dz/UniFAR-FTUs huggingface dataset:
Hardy-Hodge Decomposition of Vector Fields in $Rn$

We prove that a $IR n+1$-valued vector field on $IR n$ is the sum of the traces of two harmonic gradients, one in each component of $IR n+1 \ IR n$ , and of a $IR n$-valued divergence free vector field. We apply this to the description of vanishing potentials in divergence form. The results are stated in terms of Clifford Hardy spaces, the structure of which is important for our study.
Results of the IRAM M33 Large Program

Abstract A very sensitive survey of the CO(2−1) emission of the entire disk of the Local Group galaxy M 33 is virtually complete. Hundreds of clouds down to a mass of 10000M⊙ are detected and we show that the cloud mass function (assuming a constant ratio between CO emission and H2 mass) steepens away from the center of M 33. Through comparison with dust emission and cloud Virial masses, we estimate a N(H2)/ICO factor roughly twice Galactic.
To be or not to be valid in testing the significance of the slope in simple quantitative linear models with autocorrelated errors

In this article, the validity of procedures for testing the significance of the slope in quantitative linear models with one explanatory variable and first-order autoregressive [AR(1)] errors is analyzed in a Monte Carlo study conducted in the time domain. Two cases are considered for the regressor: fixed and trended versus random and AR(1). In addition to the classical t -test using the Ordinary Least Squares (OLS) estimator of the slope and its standard error, we consider seven t -tests with n-2\,\hbox{df} built on the Generalized Least Squares (GLS) estimator or an estimated GLS estimator, three variants of the classical t -test with different variances of the OLS estimator, two asymptotic tests built on the Maximum Likelihood (ML) estimator, the F -test for fixed effects based on the Restricted Maximum Likelihood (REML) estimator in the mixed-model approach, two t -tests with n - 2 df based on first differences (FD) and first-difference ratios (FDR), and four modified t -tests using various corrections of the number of degrees of freedom. The FDR t -test, the REML F -test and the modified t -test using Dutilleul's effective sample size are the most valid among the testing procedures that do not assume the complete knowledge of the covariance matrix of the errors. However, modified t -tests are not applicable and the FDR t -test suffers from a lack of power when the regressor is fixed and trended ( i.e. , FDR is the same as FD in this case when observations are equally spaced), whereas the REML algorithm fails to converge at small sample sizes. The classical t -test is valid when the regressor is fixed and trended and autocorrelation among errors is predominantly negative, and when the regressor is random and AR(1), like the errors, and autocorrelation is moderately negative or positive. We discuss the results graphically, in terms of the circularity condition defined in repeated measures ANOVA and of the effective sample size used in correlation analysis with autocorrelated sample data. An example with environmental data is presented.
Predictability Characteristics of Landfalling Cyclones along the North American West Coast

AbstractThe predictability of North Pacific cyclones can vary widely, from highly accurate prediction of storm intensity and location to forecast position errors of hundreds of kilometers and central pressure errors of tens of hectopascals. In this study, a Weather Research and Forecasting Model (WRF) ensemble Kalman filter is used to investigate predictability of landfalling cyclones on the west coast of North America over two winter seasons (2008/09 and 2009/10). Predictability is defined as the ensemble spread of cyclone central pressure at the final forecast time (24 h) where large spread means low predictability. Both ensemble spread and ensemble initial-condition sensitivity are examined for a wide variety of cyclones that occurred during the two seasons. Storms that are deepening and track from the southwest exhibit the largest ensemble initial-condition sensitivity and highest ensemble spread compared to decaying storms and storms that track from other directions. Storms that end south of 40°N, ty.
On the existence of stationary solutions for higher-order p-Kirchhoff problems

In this paper, we establish the existence of two nontrivial weak solutions of possibly degenerate nonlinear eigenvalue problems involving the p-polyharmonic Kirchhoff operator in bounded domains. The p-polyharmonic operators were recently introduced in [F. Colasuonno and P. Pucci, Multiplicity of solutions for p(x)-polyharmonic elliptic Kirchhoff equations, Nonlinear Anal.74 (2011) 5962–5974] for all orders L and independently, in the same volume of the journal, in [V. F. Lubyshev, Multiple solutions of an even-order nonlinear problem with convex-concave nonlinearity, Nonlinear Anal.74 (2011) 1345–1354] only for L even. In Sec. 3, the results are then extended to non-degeneratep(x)-polyharmonic Kirchhoff operators. The main tool of the paper is a three critical points theorem given in [F. Colasuonno, P. Pucci and Cs. Varga, Multiple solutions for an eigenvalue problem involving p-Laplacian type operators, Nonlinear Anal.75 (2012) 4496–4512]. Several useful properties of the underlying functional solution space , endowed with the natural norm arising from the variational structure of the problem, are also proved both in the homogeneous case p ≡ Const. and in the non-homogeneous case p = p(x). In the latter some sufficient conditions on the variable exponent p are given to prove the positivity of the infimum λ1 of the Rayleigh quotient for the p(x)-polyharmonic operator .
A Facile Route to Prepare Tetragonal BaTiO3 Nanoparticle Through Composition Control

In the present work, tetragonal BaTiO3 particles down to 20 nm have been synthesized by low temperature aqueous co-precipitation method through composition control. Field emission scanning electron microscopy (FE-SEM) images indicated that the precipitates contained fine (about 20–30 nm) faceted particles. The Raman spectra revealed that tetragonal phase appeared with the increase in Ba/Ti ratio in the precursor solution. The appearance of tetragonal phase in BaTiO3 nanoparticle was related with the lattice defect revealed by lattice parameter and lattice strain calculated by XRD results. The lattice defect can be modified through composition control.
Insensitizing Controls for the 1-D Wave Equation

We study the insensitizing controllability property of the one-dimensional wave equation observed in some open set in two cases: when the control acts in an interior region and when it acts on the boundary. In both cases, when the control time is sufficiently large the e-insensitizing controllability holds. Moreover, for the boundary controlled equation the (exact) insensitizing controllability also holds.
Ab initio calculation of electron-phonon scattering time in germanium

The intervalley scattering time in n-type germanium from thevalley to the L, � ,a ndX valleys, has been computed ab initio with a method based on the density functional perturbation theory. We demonstrate that the pressure dependence of the lifetime of the exciton limited by the electron-phonon interaction is well described. Moreover, we discuss relaxation times measured by various pump-probe experiments at low and ambient temperatures. The contributions of the various phonons to the scattering are computed. Relaxation times due to the electron-phonon coupling are provided for each intervalley transition, as well as their behavior under pressure.
Simulation of Gamma-Ray Bursts from Cooling Relativistic Electrons

The spectra and time structures in gamma-ray bursts (GRBs) are calculated based on the synchrotron radiation of the particles accelerated impulsively at shock fronts and subsequently cooled by the radiation losses in the optically thin shocked shell for an internal shock scenario. The effects of shock wave propagation on the resulted spectra and time structures are investigated. It is found that the spectral and temporal features of pulses predicted by our physical scenario are in agreement with those of recently determined individual GRB pulses.
Haptic-Based and $SE(3)$-Aware Object Insertion Using Compliant Hands

Object insertion is primarily studied using rigid robotic hands. However, these may have difficulties overcoming spatial uncertainties originating from an uncertain initial grasp. Compliant hands, on the other hand, can cope with <inline-formula><tex-math notation="LaTeX">$SE(3)$</tex-math></inline-formula> uncertainties and adapt to the environment upon contact. Nevertheless, contact forces may contribute additional uncertainties and lead to failure if not controlled properly. In this letter, we take inspiration from human insertion and study how <italic>haptic glances</italic> with compliant hands during contact can provide valuable information regarding object state. Using a force/torque sensor, we show that a haptic glance based on excitation of finger perturbations can provide accurate contact localization and indication of a successful insertion. With such insight, we propose an online learning scheme for general precision control of contact-rich object insertion. A deep residual Reinforcement Learning (RL) policy leverages the contact dynamics of the compliant hand to cope with <inline-formula><tex-math notation="LaTeX">$SE(3)$</tex-math></inline-formula> uncertainties. Several experiments of precision insertion tasks with various objects and grasp uncertainties exhibit high success rate and validate the effectiveness of the approach.
Existence, uniqueness and optimal regularity results for very weak solutions to nonlinear elliptic systems

We establish existence, uniqueness and optimal regularity results for very weak solutions to certain nonlinear elliptic boundary value problems. We introduce structural asymptotic assumptions of Uhlenbeck type on the nonlinearity, which are sufficient and in many cases also necessary for building such a theory. We provide a unified approach that leads qualitatively to the same theory as that one available for linear elliptic problems with continuous coeffcients, e.g. the Poisson equation. The result is based on several novel tools that are of independent interest: local and global estimates for (non)linear elliptic systems in weighted Lebesgue spaces with Muckenhoupt weights, a generalization of the celebrated div{curl lemma for identification of a weak limit in border line spaces and the introduction of a Lipschitz approximation that is stable in weighted Sobolev spaces.
Arthroscopic Management of Rotator Cuff and Other Shoulder Pathology in Diabetics

: Background: Musculoskeletal disease is one of the most common complications in patients with diabetes, and yet it receives relatively little attention. The severity and the risks of musculoskeletal complications might not be well recognized as cardiovascular complications; however, the associated ailments certainly inflict both physical and psychological harm on people with diabetes. Among the various musculoskeletal diseases, shoulder pain is one of the most common complaints. In general, it is characterized by pain and limited range of motion of one or both shoulders. Shoulder pain not only causes decreased quality of life, but also leads to disability in daily activities, and might interfere directly or indirectly with control of metabolic processes. Two of the most common shoulder disorders are frozen shoulder, also known as adhesive capsulitis‘ and rotator cuff disease. Aim and Objective: To evaluate shoulder arthroscopic surgery in management of rotator cuff and other shoulder pathology in diabetics. Methods: This was a prospective descriptive study which included 20 diabetic patients having rotator cuff and other shoulder pathology treated by shoulder arthroscopic surgery to evaluate its efficacy in management. Preoperative and ‎ postoperative ‎ evaluations were ‎ performed based on ‎ history, physical ‎ examination, and a ‎ modified University of ‎ California at Los ‎ Angeles (UCLA) score ‎ system. Results: At the end of the follow up period, on the modified UCLA shoulder rating scale, 17 of the 20 patients (85%) in this study achieved a satisfactory result and 3 (15%) were not. total UCLA score significantly improved from 15.3 ± 3.47 preoperatively to 30.6 ± 4.24 at the end of follow up (p<0.001). eight patients (40%) had excellent results, nine patients (45%) had good results, three patients (15%) had fair results and none of the cases were poor.
Resurfacing defects from mycobacterial skin and soft tissue infections using thoracodorsal artery perforator free flaps

Purpose: Skin and soft tissue infections (SSTIs) caused by mycobacteria are rare and difficult to diagnose and treat. Furthermore, systematic treatment protocols for mycobacterial SSTIs have not been established. This study introduces a strategy with radical resection and resurfacing using thoracodorsal artery perforator (TDAP) free flaps.Methods: From December 2013 to February 2022, 13 patients with mycobacterial SSTIs underwent radical resection and reconstruction using TDAP free flaps. Exact mapping of the lesion extent was performed preoperatively with magnetic resonance imaging. When the extent was limited to soft tissue, resection and reconstruction were performed in a single stage. However, in cases with bone or joint involvement, two-stage reconstruction was applied with radical resection and negative-pressure wound therapy followed by resurfacing with a flap. Complex defects formed after resection were filled with a musculocutaneous or chimeric flap. All patients were administered antimycobacterial medications.Results: Mycobacterial infection recurred in one patient; therefore, a total of 14 cases of reconstruction were performed. Reconstruction was performed with a TDAP free flap alone in 10 cases, with a chimeric flap in three cases, and with a musculocutaneous flap in one case. The flaps ranged in size from 7×5 cm2 to 25×12 cm2 (mean, 97.2 cm2). The mycobacterial species identified were Mycobacterium tuberculosis (n=8) and nontuberculous mycobacteria (n=5). Conclusion: For mycobacterial SSTIs, radical resection followed by resurfacing and reconstruction using TDAP free flaps can be an effective surgical treatment strategy.
Soap films with gravity and almost-minimal surfaces

Motivated by the study of the equilibrium equations for a soap film hanging from a wire frame, we prove a compactness theorem for surfaces with asymptotically vanishing mean curvature and fixed or converging boundaries. In particular, we obtain sufficient geometric conditions for the minimal surfaces spanned by a given boundary to represent all the possible limits of sequences of almost-minimal surfaces. Finally, we provide some sharp quantitative estimates on the distance of an almost-minimal surface from its limit minimal surface.
Energy Distribution of Electrons in High Frequency Gas Discharges

In this paper an equation for the energy distribution of electrons in a gas subject to a spatially constant high frequency field is obtained. The domain of applicability of the equation is limited (a) to situations in which the densities of electrons, ions, and excited molecules are very small compared to the density of normal molecules, (b) to electron energies such that the elastic collision cross section for electron-molecule collisions is large compared to the inelastic cross section, (c) to linear dimensions of the discharge region large compared to the mean free path for elastic collision, and (d) to frequencies of the impressed electric field larger than a certain lower limit determined by the pressure, type of gas, and linear dimensions of the discharge region. Methods for the solution of the distribution equation are presented in Section 5; simplified examples illustrating these methods are given in Section 7. The distribution equation for the d.c. case is also derived (Section 6); it agrees with those obtained by other authors. A comparison of the high frequency and d.c. distribution equations suggests a useful correlation between the two cases.
Deletion of large-conductance calcium-activated potassium channels promotes vascular remodelling through the CTRP7-mediated PI3K/Akt signaling pathway

The large-conductance calcium-activated potassium (BK) channel is a critical regulator and potential therapeutic target of vascular tone and architecture, and abnormal expression or dysfunction of this channel is linked to many vascular diseases. Vascular remodelling is the early pathological basis of severe vascular diseases. Delaying the progression of vascular remodelling can reduce cardiovascular events, but the pathogenesis remains unclear. To clarify the role of BK channels in vascular remodelling, we use rats with BK channel α subunit knockout (BK α ‒/‒). The results show that BK α ‒/‒ rats have smaller inner and outer diameters, thickened aortic walls, increased fibrosis, and disordered elastic fibers of the aortas compared with WT rats. When the expression and function of BK α are inhibited in human umbilical arterial smooth muscle cells (HUASMCs), the expressions of matrix metalloproteinase 2 (MMP2), MMP9, and interleukin-6 are enhanced, while the expressions of smooth muscle cell contractile phenotype proteins are reduced. RNA sequencing, bioinformatics analysis and qPCR verification show that C1q/tumor necrosis factor-related protein 7 ( CTRP7) is the downstream target gene. Furthermore, except for that of MMPs, a similar pattern of IL-6, smooth muscle cell contractile phenotype proteins expression trend is observed after CTRP7 knockdown. Moreover, knockdown of both BK α and CTRP7 in HUASMCs activates PI3K/Akt signaling. Additionally, CTRP7 is expressed in vascular smooth muscle cells (VSMCs), and BK α deficiency activates the PI3K/Akt pathway by reducing CTRP7 level. Therefore, we first show that BK channel deficiency leads to vascular remodelling. The BK channel and CTRP7 may serve as potential targets for the treatment of cardiovascular diseases.
Resolvent Estimates on Asymptotically Hyperbolic Spaces

We extend Vasy's results on semiclassical high energy estimates for the meromorphic continuation of the resolvent for asymptotically hyperbolic manifolds to metrics that are not necessarily even. Vasy's method gives the meromorphic continuation of the resolvent and high energy estimates in strips, assuming that the geodesic flow is non-trapping, without having to construct a parametrix. We prove that the size of the strip to which the resolvent can be extended meromorphically is the same obtained by Guillarmou.
Mobile Human Capital and Diffusion of Ideas Across Cities ∗

I study how internal migration of inventors affects local and aggregate growth through technological diffusion across cities. I propose a quantitative spatial theory of growth and knowledge diffusion through internal migration. My model highlights two mechanisms in which productivity growth can be higher in one city than another: (1) agglomeration forces driven by city size and (2) knowledge inﬂows through internal migration. I estimate the model using data on U.S. cities and ﬁnd that large cities have signiﬁcantly beneﬁted from better access to technology through migration inﬂows from other cities. This migration effect explains approximately 40% of the cross-sectional variation in local productivity changes.
On weakly 2-absorbing ideal of commutative rings

Let R be a commutative ring with identity 1 6 0. Various generalizations of prime ideals have been studied. For example, a proper ideal I of R isweakly prime if a;b2 R with 06 ab2 I, then either a2 I or b2 I. Also a proper ideal I of R is said to be 2-absorbing if whenever a;b;c 2 R and abc 2 I, then either ab 2 I or ac 2 I or bc 2 I. In this paper, we introduce the concept of a weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing ideal of R if whenever a;b;c2 R and 0 6 abc 2 I, then either ab 2 I or ac 2 I or bc 2 I. For example, every proper ideal of a quasi-local ring (R;M) with M 3 =f0g is a weakly 2-absorbing ideal of R. We show that a weakly 2-absorbing ideal I of R with I 3 6 0 is a 2-absorbing ideal of R. We show that every proper ideal of a commutative ring R is a weakly 2-absorbing ideal if and only if either R is a quasi-local ring with maximal ideal M such that M 3 =f0g or R is ring- isomorphic to R1 F where R1 is a quasi-local ring with maximal ideal M such that M 2 =f0g and F is a eld or R is ring-isomorphic to F1 F2 F3 for some elds F1;F2;F3.
Uniform reduction error analysis

By taking advantage of asymptotic results from the statistical literature, it is possible to develop marginal confidence intervals and joint confidence regions for hypocentral parameters derived from Jeffrey's uniform reduction earthquake location algorithm. The method currently used to compute confidence intervals is ad hoc and can result in substantial errors. Monte Carlo experiments have been used to indicate typical deviations from the asymptotic distribution for finite numbers of observations. Also, the statistical theory can be applied to estimating the efficiency of the uniform reduction algorithm when applied to various models of the travel-time residual probability density function. Further, the nonuniqueness of the uniform reduction algorithm can be understood and eliminated by appealing to well-known results from robust statistical theory. Finally, it is possible to derive a weighting function which is asymptotically efficient for any presumed residual model.
Generation of entanglement outside of the light cone

The Feynman propagator has nonzero values outside of the forward light cone. That does not allow messages to be transmitted faster than the speed of light, but it is shown here that it does allow entanglement and mutual information to be generated at space-like separated points. These effects can be interpreted as being due to the propagation of virtual photons outside of the light cone or as a transfer of pre-existing entanglement from the quantum vacuum. The differences between these two interpretations are discussed.
Short Geodesics of Unitaries in the L 2 Metric

Abstract Let $\mathcal{M}$ be a type $\text{I}{{\text{I}}_{1}}$ von Neumann algebra, $\tau$ a trace in $\mathcal{M}$ , and ${{L}^{2}}\left( \mathcal{M},\tau \right)$ the GNS Hilbert space of $\tau$ . We regard the unitary group ${{U}_{\mathcal{M}}}$ as a subset of ${{L}^{2}}\left( \mathcal{M},\tau \right)$ and characterize the shortest smooth curves joining two fixed unitaries in the ${{L}^{2}}$ metric. As a consequence of this we obtain that ${{U}_{\mathcal{M}}}$ , though a complete (metric) topological group, is not an embedded riemannian submanifold of ${{L}^{2}}\left( \mathcal{M},\tau \right)$