Miracle-dz/UniFAR-FTUs huggingface dataset:
Transitively-saturated property, Banach recurrence and Lyapunov regularity

The topological entropy of upper recurrent, lower recurrent points and Birkhoff regularity were considered in Tian (2016 Adv. Math. 288 464–526) but Banach upper recurrence points are not considered. In this paper we mainly consider whether the points that are Banach upper recurrent but not upper recurrent can carry full topological entropy. Moreover, we use statistical -limit sets to obtain entropy results on the refined orbit distribution of Banach recurrence. In this process, we strengthen Pfister and Sullivan’s result of Pfister and Sullivan (2007 Ergod. Theor. Dynam. Syst. 27 929–56) from saturated property to transitively-saturated property (and from single-saturated property to transitively-convex-saturated property). We also establish an abstract framework on the combination of Banach recurrence and multifractal analysis of general observable functions and in particular, how these results can be applied in the combination of Banach recurrence Lyapunov regularity to obtain a generalized and refined theory of Barreira and Doutor (2009 J. Math. Pures Appl. 92 1–17); Barreira and Gelfert (2006 Commun. Math. Phys. 267 393–418); Barreira and Saussol (2001 Trans. Am. Math. Soc. 353 3919–44); Feng and Huang (2010 Commun. Math. Phys. 297 1–43); Feng (2003 J. Math. 138 353–76); Feng (2009 Israel J. Math. 170 355–94); Feng and Lau (2002 Math. Res. Lett. 9 363–78) etc, on mixed Lyapunov multifractal analysis such as irregular sets and level sets of Lyapunov exponents.
Publications of the Astronomical Society of the Pacific 91:642-647, October 1979 A REDDENING-FREE MAIN SEQUENCE FOR THE PLEIADES CLUSTER

The effects of differential reddening on the UBV colors of Pleiades members have been removed for stars earlier than (B—V)0 = 1*T 00, and the dereddened colors have been found to exhibit an ultraviolet excess of 8(U — B) = + 0"K)3 with respect to Hyades stars. A correction of -t-0'"15 in A/r at constant {B—V) has been derived for the Hyades main sequence to adjust it to Pleiades metallicity, and this has been fit to Pleiades late-tvpe dwarfs in order to define a new photometric ZAMS for typical solar neighborhood stars of spectral types A, F, and G. A zero-point of 3.15 was adopted for the Hyades distance modulus based upon a review of available astrometric data, and the corresponding Pleiades distance modulus is 5.56.
On the Fenchel Duality between Strong Convexity and Lipschitz Continuous Gradient

We provide a simple proof for the Fenchel duality between strong convexity and Lipschitz continuous gradient. To this end, we first establish equivalent conditions of convexity for a general function that may not be differentiable. By utilizing these equivalent conditions, we can directly obtain equivalent conditions for strong convexity and Lipschitz continuous gradient. Based on these results, we can easily prove Fenchel duality. Beside this main result, we also identify several conditions that are implied by strong convexity or Lipschitz continuous gradient, but are not necessarily equivalent to them. This means that these conditions are more general than strong convexity or Lipschitz continuous gradient themselves.
Application of Continuous Dynamic Grid Adaption Techniques to Meteorological Modeling. Part II: Efficiency

Abstract The continuous dynamic adaptive grid (CDGA) technique has been shown to yield significant improvements in solution accuracy over equivalent fixed-grid methods. In this paper we consider the related question of efficiency; for a given degree of solution accuracy is the CDGA method faster than the fixed-grid approach, and if so, by how much? A new grid-generation algorithm based on discrete equidistribution principles is proposed, which, while it has the disadvantage of producing nonorthogonal grids, is extremely simple to implement and fast to execute. The algorithm is applied to a barotropic model designed to examine the motion of interacting multiple vortices. Numerical tests confirm the efficacy of the proposed algorithm and show that the CDGA method can produce solutions as accurate as those obtained from a fixed-grid model in only one-third the time.
Maximal Function Characterizations of Musielak-Orlicz-Hardy Spaces Associated to Non-negative Self-adjoint Operators Satisfying Gaussian Estimates

Let $L$ be a non-negative self-adjoint operator on $L^2(\mathbb{R}^n)$ whose heat kernels have the Gaussian upper bound estimates. Assume that the growth function $\varphi:\,\mathbb{R}^n\times[0,\infty) \to[0,\infty)$ satisfies that $\varphi(x,\cdot)$ is an Orlicz function and $\varphi(\cdot,t)\in {\mathbb A}_{\infty}(\mathbb{R}^n)$ (the class of uniformly Muckenhoupt weights). Let $H_{\varphi,\,L}(\mathbb{R}^n)$ be the Musielak-Orlicz-Hardy space introduced via the Lusin area function associated with the heat semigroup of $L$. In this article, the authors obtain several maximal function characterizations of the space $H_{\varphi,\,L}(\mathbb{R}^n)$, which, especially, answer an open question of L. Song and L. Yan under an additional mild assumption satisfied by Schr\"odinger operators on $\mathbb{R}^n$ with non-negative potentials belonging to the reverse H\"older class, and second-order divergence form elliptic operators on $\mathbb{R}^n$ with bounded measurable real coefficients.
Structure and energetics of stoichiometric TiO 2 anatase surfaces

We present an ab initio density-functional investigation of the structure and energetics of several stoichiometric $1\ifmmode\times\else\texttimes\fi{}1$ low-index surfaces of anatase, a ${\mathrm{TiO}}_{2}$ polymorph $\ensuremath{\sim}9%$ less dense and $\ensuremath{\sim}1.2$ kcal/mol less stable than rutile. Although our calculations do not reproduce the relative ordering of the two phases that is observed experimentally, the calculated bulk structural and elastic properties of both polymorphs are in excellent agreement with the experiment, suggesting that surface relaxations are correctly described as well. As expected, the surface energies of anatase appear to be related to the presence of undercoordinated Ti atoms: the surfaces with fourfold-coordinated Ti atoms have a larger energy than those with fivefold-coordinated Ti. Furthermore, we find that the average surface energy of a ${\mathrm{TiO}}_{2}$ anatase macroscopic crystal is smaller than that of rutile. Finally, patterns in the relaxation of the surface atoms which are common to different surfaces are analyzed.
The magnetic field and magnetosphere of Ganymede

Within Jupiter's magnetosphere, Ganymede's magnetic field creates a mini‐magnetosphere. We show that the magnetic field measured during Galileo‧s second pass by Ganymede, with closest approach at low altitude almost directly over the moon's polar cap, can be understood to a large measure in terms of the structure of a vacuum superposition model of a uniform field and a Ganymede‐centered dipole field. Departures from the simple model can be attributed principally to magnetopause currents. We show that the orientation of the observed magnetopause normal is qualitatively consistent with expectations from the vacuum superposition model. The magnetopause currents inferred from the inbound boundary crossing are closely related to expected values, and the magnetic structure of the boundary is similar to that observed at the magnetopause of Earth. We use the vacuum magnetic field model to infer the magnetic field near Ganymede's surface, and thereby predict the particle loss cones that should be present along the spacecraft trajectory. By mapping a fraction of the corotation electric field into the polar cap, we determine expected flow velocities near closest approach to Ganymede as a function of reconnection efficiency. We conclude by discussing prospects for measurements on Galileo's remaining passes by Ganymede.
Soil Permittivity Estimation Over Croplands Using Full and Compact Polarimetric SAR Data

Soil permittivity estimation using polarimetric synthetic aperture radar (PolSAR) data has been an extensively researched area. Nonetheless, it provides ample scope for further improvements. The vegetation cover over the soil surface leads to a complex interaction of the incident polarized wave with the canopy and subsequently with the underlying soil surface. This article introduces a novel methodology to estimate soil permittivity over croplands with vegetation cover using the full polarimetric (FP) and compact polarimetric (CP) modes. The proposed method utilizes the FP and CP scattering-type parameters, <inline-formula> <tex-math notation="LaTeX">$\theta _{\text {FP}}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\theta _{\text {CP}}$ </tex-math></inline-formula>, respectively. These scattering type parameters are a function of the soil permittivity and the Barakat degree of polarization. The method considers the extended Bragg (X-Bragg) scattering model for the soil surface. In particular, these scattering-type parameters explicitly account for the depolarizing structure of the scattered wave while characterizing targets. Thus, the depolarization information in terms of surface roughness in the X-Bragg model gets inherent importance while using <inline-formula> <tex-math notation="LaTeX">$\theta _{\text {FP}}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\theta _{\text {CP}}$ </tex-math></inline-formula>, unlike existing scattering-type parameters. Therefore, the proposed technique enhances the expected value of the inversion accuracies. This study validated the major phenology stages of four crops using the UAVSAR full-pol and simulated compact pol SAR data and the ground-truth data collected during the SMAPVEX12 campaign over Manitoba, Canada. The proposed method estimated permittivity with a root mean square error (RMSE) of 2.2–4.69 for FP and 3.28–5.45 for CP SAR data along with a Pearson coefficient, <inline-formula> <tex-math notation="LaTeX">$r\ge 0.62$ </tex-math></inline-formula>.
On large subsets of F nq with no three-termarithmetic progression

In this note, we show that the method of Croot, Lev, and Pach can be used to bound the size of a subset of F n q Fqn with no three terms in arithmetic progression by c n cn with c<q c<q . For q=3 q=3 , the problem of finding the largest subset of F n 3 F3n with no three terms in arithmetic progression is called the cap set problem. Previously the best known upper bound for the affine cap problem, due to Bateman and Katz, was on order n −1−ϵ 3 n n−1−ϵ3n .
The effect of aerosol composition and concentration on the development and anvil properties of a continental deep convective cloud

A 3‐D cloud‐resolving model including an explicit aerosol module is used to examine the influence of a range of hygroscopic (CCN) and hydrophobic (IN) aerosol concentrations on the development of a mid‐latitude, continental deep convective cloud. The model reproduces a response to changes in CCN which is in agreement with previous studies of continental convection, i.e. lower precipitation rates and a later onset of deep convection for high CCN concentrations. However, the response is non‐linear and for low increments of CCN, coalescence and graupel formation becomes more efficient, which increases the total precipitation, i.e. a response similar to what has been obtained for oceanic deep convection. This result indicates the importance of using a range of CCN concentrations when examining aerosol influence on deep convection. The simulations show that an increased IN concentration has a substantial influence on the convective cloud development. Higher IN concentrations generally result in higher updraught velocities, a prolonged precipitation event and larger total precipitation amounts. The radiative forcing exerted by the cloud is determined by the anvil extent and ice crystal size. The anvil area is linked to the average updraught velocity which in turn is found to be correlated with the IN concentration. Homogeneously nucleated ice crystals dominate the total anvil ice mass formed, but heterogeneously formed ice crystals may significantly alter the homogeneous freezing process. For the simulated case, a key parameter for determining whether the number of homogeneously nucleated ice crystals will decrease or increase with increasing IN concentration is the initial updraught velocity. This dependence makes the results sensitive to the amount of heterogeneously formed ice crystals. Copyright © 2007 Royal Meteorological Society
Star formation efficiency patterns in the spiral arms of M51

We have studied the distribution of ionized, molecular, and atomic hydrogen in the disk and especially along the spiral arms of the Whirlpool galaxy, M51, by combining recently published maps of the H-alpha, H-2, and H I surface densities, and we report a twofold result. First, we note the existence of a symmetric pattern of peaks and dips in the arm/interarm ratio of the massive star formation efficiency [measured using L(H-alpha)/sigma(H-2 + H I), where sigma is the surface density] along the two main arms, similar to the patterns previously found in NGC 3992 and NGC 628. The pattern is due to enhanced on-arm star formation at specific radii in the disk. These radii correspond to antiresonances of a density wave system, as identified by Elmegreen et al., suggesting that the resonance pattern locally affects the process of star formation. Second, we find that the high peaks in the H-alpha distribution along the arms are not reproduced in H-2, which is by far the most abundant form of neutral hydrogen in the inner disk. The peaks do seem to show up, although less strongly in the H I surface density along the arms.
A note on implementation of boundary variation diminishing algorithm to high-order local polynomial-based schemes

A novel approach for selecting appropriate reconstructions is implemented to the hyperbolic conservation laws in the high-order local polynomial-based framework, e.g., the discontinuous Galerkin (DG) and flux reconstruction (FR) schemes. The high-order polynomial approximation generally fails to correctly capture a strong discontinuity inside a cell due to the Runge phenomenon, which is replaced by more stable approximation on the basis of a troubled-cell indicator such as that used in the total variation bounded (TVB) limiter. This paper examines the applicability of a new algorithm, so-called boundary variation diminishing (BVD) reconstruction, to the weighted essentially non-oscillatory (WENO) methodology in the FR framework including the nodal type DG method. The BVD reconstruction adaptively chooses a proper approximation for the solution function so as to minimize the jump between values at the left- and right-side of cell boundaries without any ad hoc constant such as the TVB parameter. Several numerical tests are conducted for a linear advection equation as well as the selection of an appropriate reconstruction, where the results of the BVD algorithm are comparable to those using the conventional TVB limiter. Note that the present work is limited to third or lower order polynomials, leaving the implementations for higher-order schemes a future work.
A broadband and wide beam circular polarization LTCC microstrip antenna analysis and design with characteristic modes theory

In this paper, characteristic modes theory was used in analysis and design of a broad axial ratio band circular polarization LTCC microstrip antenna. An ellipse slot couple structure was proposed to take the place of traditional circular slot couple structure for enlarging circular polarization broadband. And the theory of how to improve the axial ratio band was researched in detail by characteristic mode method. The characteristic angle phase difference of two orthogonal characteristic modes and the phase difference of feed line in whole frequencies are the key points in these kind of designs. Finally, the designed broadband axial ratio band circular polarization LTCC microstrip antenna was been successfully implemented, and the experimental results are presented and discussed. Good agreement between simulation and testing was achieved.
Local minimizers of semi-algebraic functions

Consider a semi-algebraic function $f\colon\mathbb{R}^n \to {\mathbb{R}},$ which is continuous around a point $\bar{x} \in \mathbb{R}^n. $ Using the so--called {\em tangency variety} of $f$ at $\bar{x},$ we first provide necessary and sufficient conditions for $\bar{x}$ to be a local minimizer of $f,$ and then in the case where $\bar{x}$ is an isolated local minimizer of $f,$ we define a ``tangency exponent'' $\alpha_* > 0$ so that for any $\alpha \in \mathbb{R}$ the following four conditions are always equivalent: (i) the inequality $\alpha \ge \alpha_*$ holds; (ii) the point $\bar{x}$ is an $\alpha$-order sharp local minimizer of $f;$ (iii) the limiting subdifferential $\partial f$ of $f$ is $(\alpha - 1)$-order strongly metrically subregular at $\bar{x}$ for $0;$ and (iv) the function $f$ satisfies the \L ojaseiwcz gradient inequality at $\bar{x}$ with the exponent $1 - \frac{1}{\alpha}. $ Besides, we also present a counterexample to a conjecture posed by Drusvyatskiy and Ioffe in [Math. Program. Ser. A, 153(2):635--653, 2015].
A System‐Oriented Approach for the Optimal Control of Process Chains under Stochastic Influences

Process chains in manufacturing consist of multiple connected processes in terms of dynamic systems. The properties of a product passing through such a process chain are influenced by the transformation of each single process. There exist various methods for the control of individual processes, such as classical state controllers from cybernetics or function mapping approaches realized by statistical learning. These controllers ensure that a desired state is obtained at process end despite of variations in the input and disturbances. The interactions between the single processes are thereby neglected, but play an important role in the optimization of the entire process chain. We divide the overall optimization into two phases: (1) the solution of the optimization problem by Dynamic Programming to find the optimal control variable values for each process for any encountered end state of its predecessor and (2) the application of the optimal control variables at runtime for the detected initial process stat.
Stability and convergence analysis of the kinematically coupled scheme and its extensions for the fluid-structure interaction

In this work we analyze the stability and convergence properties of a loosely-coupled scheme, called the kinematically coupled scheme, and its extensions for the interaction between an incompressible, viscous fluid and a thin, elastic structure. We consider a benchmark problem where the structure is modeled using a general thin structure model, and the coupling between the fluid and structure is linear. We derive the energy estimates associated with the unconditional stability of an extension of the kinematically coupled scheme, called the $\beta$-scheme. Furthermore, for the first time we present \textit{a priori} estimates showing optimal, first-order in time convergence in the case when $\beta=1$. We further discuss the extensions of our results to other fluid-structure interaction problems, in particular the fluid-thick structure interaction problem. The theoretical stability and convergence results are supported with numerical examples.
Jacobi's Inversion Problem for Genus Two Hyperelliptic Integral

Hinted by the elliptic parameterization of the Ising model, the addition formula of the elliptic function forms to give the integrable SU(2) group relation in the previous paper. We then expect that the addition formula of the Abelian function with any genus will form to give some integrable Lie group structure. In this paper, we study Jacobi's inversion problem for hyperelliptic integral with genus two and we expect some SU(2) structure for the addition formula of the hyperelliptic theta function with genus two.
Strict comparison of projections and positive combinations of projections in certain multiplier algebras

In this paper we investigate whether positive elements in the multiplier algebras of certain finite C*-algebras can be written as finite linear combinations of projections with positive coefficients (PCP). Our focus is on the category of underlying C*-algebras that are separable, simple, with real rank zero, stable rank one, finitely many extreme traces, and strict comparison of projections by the traces. We prove that the strict comparison of projections holds also in the multiplier algebra of the stabilizer algebra. Based on this result and under the additional hypothesis that the multiplier algebra has real rank zero, we characterize which positive elements of the multiplier algebra are PCP.
5G Magnetic Resonance Coupling Planar Spiral Coil Wireless Power Transfer

Wireless Power Transfer in the 5G frequency band is the most promising technology to power up ubiquitous small electronic devices as well as IoT devices. A strongly coupled magnetic resonance WPT technique that focuses on near-field electromagnetic energy has been proposed in this paper. However, most Magnetic Resonance Coupling Wireless Power Transfer (MRC WPT) applications have been designed in kHz and MHz frequency spectrum. This paper demonstrates Planar Spiral Coil Magnetic Resonance Coupling (PSC MRC) WPT designs at 5G (GHz) frequencies. Also, the transformation technique of the low frequency (kHz and MHz) magnetic resonance circuit model equations to high frequency (GHz) circuit model equations to achieve a high-efficiency power transfer. PSC MRC WPT designs structure antennas are designed at 3.4 - 3.5 GHz in the form of circular and square shapes with 1 turn coil. The proposed antenna structures are firstly being optimized in a full-wave electromagnetic simulator, CST Microwave Studio to resonate at the 3.4 - 3.5 GHz band. Then, the close-loop equations to determine the efficiency of 5G Magnetic Resonance Coupling Planar Spiral Coil Wireless Power Transfer is designed. Lastly, the results are compared with the simulation and calculated parts. The highest efficiency of the PSC MRC circular antenna is 31.58 % when the distance is at 2 mm, and 31.26 and 31.02 % when the distance is at 3 and 4 mm, respectively. The efficiency of circular PSC MRC is found to be 25 % better than the efficiency of square shape design. HIGHLIGHTS IoT devices need to be charged and maintained as the network system has massive numbers of sensors. Wireless power transfer is a promising technology to power up IoT devices This paper proposed, a WPT technique based on strongly coupled magnetic resonance which focuses on the near-field electromagnetic energy. This technique can extend the distance of the power transfer between the transmitter and the receiver The transformation technique of the low frequency (kHz and MHz) magnetic resonance circuit model equations to high frequency (GHz) circuit model equations to achieve a high-efficiency PSC MRC WPT design structure is introduced in this paper This novel technique can be applied to effectively design PSC MRC Antenna WPT for 5G applications. Most reported Magnetic Resonance Coupling Wireless Power Transfer (MRC WPT) applications have been designed in kHz and MHz frequency spectrum GRAPHICAL ABSTRACT
Codimension one partially hyperbolic diffeomorphisms with a uniformly compact center foliation

We consider a partially hyperbolic C1-diffeomorphism f on a smooth compact manifold M with a uniformly compact f-invariant center foliation. We show that if the unstable bundle is one-dimensional and oriented, then the holonomy of the center foliation vanishes everywhere, the quotient space of the center foliation is a torus and f induces a hyperbolic automorphism on it, in particular, f is centrally transitive. We actually obtain further interesting results without restrictions on the unstable, stable and center dimension: we prove a kind of spectral decomposition for the chain recurrent set of the quotient dynamics, and we establish the existence of a holonomy invariant family of measures on the unstable leaves (Margulis measure).