Miracle-dz/UniFAR-FTUs huggingface dataset:
On the Connection between Residual Distribution Schemes and Flux Reconstruction

In this short paper, we are considering the connection between the \emph{Residual Distribution Schemes} (RD) and the \emph{Flux Reconstruction} (FR) approach. We demonstrate that flux reconstruction can be recast into the RD framework and vice versa. Because of this close connection we are able to apply known results from RD schemes to FR methods. In this context we propose a first demonstration of entropy stability for the FR schemes under consideration and show how to construct entropy stable numerical schemes based on our FR methods. Simultaneously, we do not restrict the mesh to tensor structures or triangle elements, but rather allow polygons. The key of our analysis is a proper choice of the correction functions for which we present an approach here.
Monotonicity and local uniqueness for the Helmholtz equation

This work extends monotonicity-based methods in inverse problems to the case of the Helmholtz (or stationary Schrodinger) equation $(\Delta + k^2 q) u = 0$ in a bounded domain for fixed non-resonance frequency $k>0$ and real-valued scattering coefficient function $q$. We show a monotonicity relation between the scattering coefficient $q$ and the local Neumann-Dirichlet operator that holds up to finitely many eigenvalues. Combining this with the method of localized potentials, or Runge approximation, adapted to the case where finitely many constraints are present, we derive a constructive monotonicity-based characterization of scatterers from partial boundary data. We also obtain the local uniqueness result that two coefficient functions $q_1$ and $q_2$ can be distinguished by partial boundary data if there is a neighborhood of the boundary where $q_1\geq q_2$ and $q_1\not\equiv q_2$.
Econophysics of interest rates and the role of monetary policy

This paper presents empirical evidence using recently developed techniques in econophysics suggesting that the degree of long-range dependence in interest rates depends on the conduct of monetary policy. We study the term structure of interest rates for the US and find evidence that global Hurst exponents change dramatically according to Chairman Tenure in the Federal Reserve Board and also with changes in the conduct of monetary policy. In the period from 1960's until the monetarist experiment in the beginning of the 1980's interest rates had a significant long-range dependence behavior. However, in the recent period, in the second part of the Volcker tenure and in the Greenspan tenure, interest rates do not present long-range dependence behavior. These empirical findings cast some light on the origins of long-range dependence behavior in financial assets.
Circle patterns with obtuse exterior intersection angles.

Thurston's Circle Pattern Theorem studies existence and rigidity of circle patterns of a given combinatorial type and the given non-obtuse exterior intersection angles. Using topological degree theory, variational principle, Teichmuller theory, and Sard's Theorem, this paper generalizes Circle Pattern Theorem to the case of obtuse exterior intersection angles.
s-process nucleosynthesis-nuclear physics and the classical model

Among the various processes responsible for the formation of the heavy elements in stars, the slow neutron capture process (s-process) is distinguished by the fact that it involves mostly stable isotopes. Therefore, the relevant nuclear physics data can be determined by experiments. With this rather reliable data basis, s-process nucleosynthesis offers an important testground of models for the late stages of stellar evolution, which are supposed to be the s-process site. The empirical counterpart for such models is the so-called classical s-process, a purely phenomenological picture, that is successfully used to derive the resulting abundances as well as information on the physical conditions during the s-process. The status of this classical approach is reviewed with emphasis on the implications for various stellar models of the s-process and in the light of results obtained by stellar spectroscopy. A brief account of the potential s-process chronometers is also presented.
Synoptic-Scale Flow and Valley Cold Pool Evolution in the Western United States

Abstract Valley cold pools (VCPs), which are trapped, cold layers of air at the bottoms of basins or valleys, pose a significant problem for forecasters because they can lead to several forms of difficult-to-forecast and hazardous weather such as fog, freezing rain, or poor air quality. Numerical models have historically failed to routinely provide accurate guidance on the formation and demise of VCPs, making the forecast problem more challenging. In some case studies of persistent wintertime VCPs, there is a connection between the movement of upper-level waves and the timing of VCP formation and decay. Herein, a 3-yr climatology of persistent wintertime VCPs for five valleys and basins in the western United States is performed to see how often VCP formation and decay coincides with synoptic-scale (∼200–2000 km) wave motions. Valley cold pools are found to form most frequently as an upper-level ridge approaches the western United States and in response to strong midlevel warming. The VCPs usually last as .
Herman–Kluk allows analysis of quantum discrete breathers in higher dimensional systems

Discrete breathers (DBs) provide an important example of spatial localization of energy encountered in non-linear many-body systems. Studying the quantum equivalent of DBs has always been restricted to small or simple systems. We show that Herman–Kluk (HK), a well studied semi-classical method, can be used successfully to observe the dynamics of a quantum state for systems that are too large for conventional quantum mechanical methods. HK reduces the growth of computational cost that comes with increase of system size. We show that HK performs very well for a quartic potential, when compared to exact quantum dynamics. As an application of the approach, we compute and analyse the spectrum of quantum DBs in a seven-dimensional potential. This result advances our ability to model experimental systems in many fields, including solar energy harvesting, quantum computing, nano-science, medicine, etc.
Universality in the Hubbard model

A new viewpoint of universality is introduced in strongly correlated electron systems; Our description relies on the operator theoretic correlation inequalities. We explain the Marshall-Lieb-Mattis theorem and Lieb\rq{}s theorem from a viewpoint of universality; in addition, from the new perspective, we prove that Lieb\rq{}s theorem still holds true even if the electron-phonon and electron-photon interactions are taken into account. We also study Nagaoka-Thouless\rq{} theorem and its stabilities in terms of universality.
A Fourth-Order Accurate Compact Difference Scheme for Solving the Three-Dimensional Poisson Equation With Arbitrary Boundaries

This paper presents an efficient high-order sharp-interface method for solving the three-dimensional (3D) Poisson equation with Dirichlet boundary conditions on a nonuniform Cartesian grid with irregular domain boundaries. The new approach is based on the combination of the fourth-order compact finite difference scheme and the preconditioned stabilized biconjugate-gradient (BiCGSTAB) method. Contrary to the original immersed interface method by LeVeque and Li [1], the new method does not require jump corrections, instead, the (regular) compact finite difference stencil is adjusted at the irregular grid points (in the vicinity of the interfaces of the immersed bodies) to obtain a solution that is sharp across the interface while keeping the fourth-order global accuracy. The contribution of the present work is the design of a fourth-order-accurate 3D Poisson solver whose accuracy and efficiency does not deteriorate in the presence of an immersed boundary. This is attributed to (i) the modification of the discrete operators near immersed boundaries does not lead to a wide grid stencil due to the compact nature of the discretization and (ii) a preconditioning technique whose efficiency and cost are independent of the complexity of the geometry and the presence or not of an immersed boundary. The accuracy and computational efficiency of the proposed algorithm is demonstrated and validated over a range of problems including smooth and irregular boundaries. The test cases show that the new method is fourth-order accurate in the maximum norm whether an immersed boundary is present or not, on uniform or nonuniform grids. Furthermore, the efficiency of the preconditioned BiCGSTAB is demonstrated with regard to convergence rate and `extra' floating-point operation ($FLOP_{extra}$) which is due to the presence of immersed boundaries.
Toward microscale Cu(In,Ga)Se2 solar cells for efficient conversion and optimized material usage: Theoretical evaluation

We develop a model to predict the performances of microscale Cu(In,Ga)Se2 (CIGS) solar cells under concentrated sunlight, based on the study of the influence of the window spread sheet resistance, which is the first limiting factor for concentration on CIGS solar cells. This model can be used to extract the value of the sheet resistance from simple current-voltage or electroluminescence measurements. The scaling benefits associated with the operation of microscale CIGS solar cells are studied. The optimum concentration ratio, linked to the best efficiency, is calculated for different cell sizes. It is predicted that an increase from 20% efficiency, for current CIGS solar cells under 1 sun illumination, up to 30% efficiency can be expected for microscale cells under concentrated sunlight.
An overview of time-domain diffuse fluorescence imaging: instrumentation and applications

Rapidly pulsed laser excitation with high-rate signal detection allows the dispersion of emitted fluorescent signals through tissue to be measured. This “time-domain” approach to measuring diffuse fluorescence data offers a wide range of advantages over conventional “continuous-wave” fluorescence imaging. While continuous-wave imaging provides a measure of only fluorescence intensity at each source-detector pairing, time-domain approaches provide fluorescence intensity throughout the whole temporal response to the pulsed-laser excitation, adding a whole new dimension to the dataset. This paper introduces the instrumentation required to collect time-domain data, dealing with complications and nuances of system and data calibration, as well as the major current applications of time-domain diffuse fluorescence imaging.
Ultrasonic Velocity around the Successive Phase Transition Points of CsPbBr3

Sound velocities in perovskite-type crystal CsPbBr 3 have been measured around the structural phase transition points at 88 and 130°C. “Detwinned” samples were used, which made it possible to relate the measured velocities to the elastic constants in each phase. The velocities of c 11 and c 11 – c 12 modes exhibit large anomalies above and below the two transition points, whereas that of c 44 mode is almost independent of temperature throughout the transition region. The results are compared with the consequences of phenomenological and fluctuation theories. Temperature dependence of the velocity of c 11 mode just above the higher transition point is shown to be consistent with the prediction from the fluctuation theory,
SUPPORTS UNIPOTENTS DE FAISCEAUX CARACTÈRES

Soit $G$ un groupe algébrique réductif sur la clôture algébrique d’un corps fini $\mathbb{F}_q$ et défini sur ce dernier. L’existence du support unipotent d’un caractère irréductible du groupe fini $G(\mathbb{F}_q)$, ou d’un faisceau caractère de $G$, a été établie dans différents cas par Lusztig, Geck et Malle, et le second auteur. Dans le présent article, nous démontrons que toute classe unipotente sur laquelle la restriction du caractère ou du faisceau caractère donné est non nulle est contenue l’adhérence de Zariski du support unipotent de ce dernier. Pour établir ce résultat, nous étudions certaines représentations des groupes de Weyl, dites “bien supportées”. Let $G$ be a reductive algebraic group over the algebraic closure of a finite field $\mathbb{F}_q$, and defined over the latter. The existence of a unipotent support for an irreducible character of the finite group $G(\mathbb{F}_q)$, or for a character sheaf on $G$, has been established in several cases by Lusztig, Geck and Malle, and the second author. In this paper, we prove that any unipotent class on which the restriction of the given character or character sheaf does not vanish is contained in the Zariski closure of its unipotent support. In order to establish this result, we study some representations of Weyl groups, which are called ‘well supported’.
Approximate Solutions to Complete Elliptic Integrals for Practical Use in Water Engineering

Complete elliptic integrals have many applications in water engineering. Examples can be found in different fields such as hydrodynamics, water wave mechanics, groundwater engineering, sediment transport, irrigation and drainage engineering, and shallow water and deep water engineering. In practice, these integrals are evaluated from lookup tables or closed-form solutions (infinite series). Most tables use discrete values of the modulus, which makes accurate interpolation difficult. On the other hand, a series expansion can only be applied to a limited range of the modulus, and is not suitable for manual calculations. Consequently, it is of interest to approximate complete elliptic integrals by simple and accurate algebraic formulas over the entire practical range of the modulus. In current research, the undetermined coefficients method is used for this purpose. Various techniques can be used to determine the unknown coefficients of this method, but most of these do not depend on the integrand. Curve fitt.
Discrepancy of Generalized LS-Sequences

Abstract The LS-sequences are a parametric family of sequences of points in the unit interval. They were introduced by Carbone [4], who also proved that under an appropriate choice of the parameters L and S, such sequences are lowdiscrepancy. The aim of the present paper is to provide explicit constants in the bounds of the discrepancy of LS-sequences. Further, we generalize the construction of Carbone [4] and construct a new class of sequences of points in the unit interval, the generalized LS-sequences.
Using the SNOMED CT Error Taxonomy to Maximize the SNOMED CT Content Request System

Background SNOMED CT (Systematized Nomenclature of Medicine--Clinical Terms) is a comprehensive clinical terminology, currently distributed by the International Health Terminology Standards Development Organisation (IHTSDO). The National Library of Medicine (NLM) acts as the National Release Center for SNOMED CT for the US. Recently, NLM developed a new system for submitting requests for changes to SNOMED CT, the US SNOMED CT Content Request System (USCRS). Objective To create a taxonomy that describes the types and causes of errors occurring in SNOMED CT in order to inform the further development of the request system, as well as general research on quality assurance in SNOMED CT. Methods To achieve these ends, we examined requests submitted via the original email method. We also tested the SNOMED CT request submission system beta version to gain insight into its current functions and design, and we reviewed relevant literature and SNOMED CT documentation. The SNOMED CT error taxonomy was created through a gradual process of successive reviews of submissions and literature alternating with refinements to the growing error taxonomy. Eventually the taxonomy was used to formally code the requests examined.
On symplectic fillings of small Seifert
3–manifolds

In this paper, we investigate the minimal symplectic fillings of small Seifert 3-manifolds with a canonical contact structure. As a result, we classify all minimal symplectic fillings of small Seifert 3-manifolds satisfying certain conditions. Furthermore, we also demonstrate that every such a minimal symplectic filling is obtained by a sequence of rational blowdowns from the minimal resolution of the corresponding weighted homogeneous complex surface singularity.
The Szlenk power type and tensor products of Banach spaces

We prove a formula for the Szlenk power type of the injective tensor product of Banach spaces with Szlenk index at most $\omega$. We also show that the Szlenk power type as well as summability of the Szlenk index are separably determined, and we extend some of our recent results concerning direct sums.
Travelling corners for spatially discrete reaction-diffusion systems

We consider reaction-diffusion equations on the planar square lattice that admit spectrally stable planar travelling wave solutions. We show that these solutions can be continued into a branch of travelling corners. As an example, we consider the monochromatic and bichromatic Nagumo lattice differential equation and show that both systems exhibit interior and exterior corners. Our result is valid in the setting where the group velocity is zero. In this case, the equations for the corner can be written as a difference equation posed on an appropriate Hilbert space. Using a non-standard global center manifold reduction, we recover a two-component difference equation that describes the behaviour of solutions that bifurcate off the planar travelling wave. The main technical complication is the lack of regularity caused by the spatial discreteness, which prevents the symmetry group from being factored out in a standard fashion.
Proof of some conjectures on cohomological dimension

Introduction. Let k be a field of characteristic q (= prime or 0) and let r be a non-negative integer. Then k is said to be Cr if and only if every (homogeneous) form of degree d in n variables over k has a nontrivial zero over k if n > dr. In Serre [3, Chap. II, Corollary to Proposition 8] the following result is obtained: If k is C1 then dim (k) 1, the existence of fields of dimension r which are not Cr. But the situation is worse than that: R is quasifinite in the sense of Serre [2, Chap. XIII, ? 2], and for all r, R is not Cr. The interest in these considerations stemmed from a possible relation with Artin's conjecture which states: If k1 is the maximal abelian extension of the rationals then k1 is C1; if k2 is a totally imaginary number field or a p-adic field then k2 is C2. Indeed, dim(ki) = 1 and dim(k2)=2 as follows from Serre [Cor. to Prop. 9, Cor. to Prop. 12, Prop. 13]. We denote by Gk, the galois group of an algebraic closure i of k over k. We also denote the cohomological p-dimension of Gk by cd,(Gk). In ? 2 we solve the problem raised in the following remark of Serre [3, Chap. II, ? 4.2]: "Supposons que cd,(Gk) = 00II est probable que l'on a alors cd,(Gk') = 0o pour toute extension transcendante pure k' of k, mais je ne vois pas comment le demontrer. " Serre then raises the corresponding problem for a field complete
Precise measurement of the transverse piezoelectric coefficient for thin films on anisotropic substrate

In this study, we propose a reliable measurement method for the effective transverse piezoelectric coefficient for thin films especially on anisotropic substrate. This coefficient for piezoelectric Pb(Zr, Ti)O3 (PZT) thin films was calculated by measuring the electric field-induced tip displacement of unimorph cantilevers composed of PZT thin films and Si substrates. We evaluated the reliability of the proposed measurement method by comparing it with numerical analysis and confirmed that the relative error of the piezoelectric coefficient (e31, f) was less than 1%. We prepared 16 different unimorph cantilevers composed of identical PZT films on different Si beam geometries that had various substrate thicknesses and cantilever widths. Although the effective transverse piezoelectric coefficient e31, f of PZT thin films ranged from −6.5 to −14 C/m2 as a function of the applied voltage, the difference among the 16 samples with an applied voltage of 25 V was within 10%. These results demonstrate that the propo.
Biplanar Foldings.

We are introducing a general framework for the construction of polyhedra and simplicial comlexes that are {\em bifoldable}, i.e. foldable into two two different planes. This vastly generalizes Origami folds known as the Miura pattern, the Eggbox pattern. After describing the framework and its basic features, we give several new examples of infinite triply periodic and fractal bifoldable polyhedra.
A brief review on hardware structure of AC electric spring

Decarbonizing power generation and reducing greenhouse gas emissions require renewable energy sources. Intermittent nature of renewable energy sources can cause blackouts, fluctuation in voltage, grid-connected inverter usage, inability to predict power generation, fluctuations in voltage and frequency. It is possible to balance between the supply and demand of power to overcome these problems by using an electric spring (ES). It is necessary to study its work, types, and controlling actions for realizing the benefits of the electric spring. This paper reviews the hardware structure of an ES based on voltage-source inverter (VSI) and current-source inverter (CSI) topologies, in single-phase and three-phase AC power distribution systems with renewable energy sources. The structure, control strategies, operating modes, advantages and disadvantages of each ES topology are elaborated to make it a suitable alternative for resolving different power quality issues caused due to the high penetration of renewable energy sources.
Transverse-Mode Characteristics of InGaAs/GaAs Vertical-Cavity Surface-Emitting Lasers Considering Gain Offset

We have fabricated InGaAs/GaAs vertical-cavity surface-emitting lasers with modulation-doped graded distributed Bragg reflectors (DBRs) grown by metal-organic chemical vapor deposition (MOCVD). The threshold current was 3.2 mA. By observing the spontaneous emission through DBRs, we found that transverse mode behavior depends on gain characteristics. Single fundamental transverse-mode lasing is achieved at a negative gain offset and multiple transverse-mode lasing is achieved at a positive gain offset.
Navier-Stokes equations, symmetric and uniform analytic solutions in phase space

For incompressible Navier-Stokes equations, Necas-Ruzicka-Sverak proved that self-similar solution has to be zero in 1996. Further, Yang-Yang-Wu find symmetry property plays an important role in the study of ill-posedness. In this paper, we consider two types of symmetry property. We search special symmetric and uniform analytic functions to approach the solution and establish global uniform analytic and symmetric solution with initial value in general symmetric Fourier-Herz space. For two kinds of symmetry of initial data, we prove that the solution has also the same symmetric structure. Further, we prove that the uniform analyticity is equivalent to the convolution inequality on Herz spaces. By these ways, we can use symmetric and uniform analytic functions to approximate the solution.
A universal exponent for Brownian entropic repulsion

We investigate the extent to which the phenomenon of Brownian entropic repulsion is universal. Consider a Brownian motion conditioned on the event $\mathcal{E}$ -- that its local time is bounded everywhere by 1. This event has probability zero and so must be approximated by events of positive probability. We prove that several natural quantities, in particular the speed of the process, are highly sensitive to the approximation procedure, and hence are not universal. However, we also propose an exponent $\kappa$ -- which measures the strength of the entropic repulsion by evaluating the probability that a particular point comes close to violating the condition $\mathcal{E}$. We show that $\kappa=3$ for several natural approximations of $\mathcal{E}$, and conjecture that $\kappa=3$ is universal in a sense that we make precise.