Miracle-dz/UniFAR-FTUs huggingface dataset:
Uniform Estimates of Entire Functions by Logarithmic Sums

Abstract We give uniform estimates in the whole complex plane of entire functions of exponential type less than a certain numerical constant (approximately equal to 0.44) having sufficiently small logarithmic sums. In these estimates the entire dependence on the function is through its type and logarithmic sum. This result extends a theorem of Koosis about polynomials and gives a new proof of that theorem. The proof is based on material related to multiplier theorems, first obtained by Beurling and Malliavin.
Confidence Intervals and Tests for Two Exponential Scale Parameters Based On Order Statistics in Compressed Samples

We construct confidence intervals for the ratio of two exponential scale parameters and present a test of hypothesis concerning these parameters. The procedures are based on the selection of subsets of two independent ordered samples from exponential populations. The discussion centers around the distribution of the ratio of the BLUE's (the ABLE's in large samples) of these parameters, and a simple approximation to that distribution. Optimal selection of the data is discussed. In an example, the power function of the proposed test is compared with the power function of the same test based on complete samples.
Detecting dependence between marks and locations of marked point processes

Summary. We introduce two characteristics for stationary and isotropic marked point proces‐ ses, E(h) and V(h), and describe their use in investigating mark–point interactions. These quantities are functions of the interpoint distance h and denote the conditional expectation and the conditional variance of a mark respectively, given that there is a further point of the process a distance h away. We present tests based on E and V for the hypothesis that the values of the marks can be modelled by a random field which is independent of the unmarked point process. We apply the methods to two data sets in forestry.
An Asymptotic Expansion for Posterior Distributions

(0.1) po(x) = C(+) exp [OR(x)] with respect to a a-finite measure , over a Euclidean sample space. Now assume that the parameter 4 has a prior density p(4). The posterior density of 4), given (Xi, X2 , . , Xn) = (xl, x2, *. *, xn), is proportional to (0.2) [C(Q)e',]np(0) where r = 57=l R(x)/n. The expression (0.2) is proportional to a density function and hence defines a random variable 4 whose density depends on r. But since r 3 i '=l R(xi)/n, the distribution of X when 4 = 40 generates a sequence (xl, x2, ) and a sequence (R (xi), '[R (xi) + R(x2)], ***) and ultimately an infinite sequence of posterior densities of 4. It is the asymptotic form of this sequence with which we shall be concerned. Neglecting for the moment the stochastic aspect of r, we see that if r is held fixed, perhaps at the expected value of R(x), the density proportional to (0.2) is exactly of the form considered in Johnson (1966, 1967). Accordingly, after suitably centering and scaling, we obtain an asymptotic expansion having the standard normal cdf as the leading term. Closely related to this approach is the work by Bernstein and von Mises. Their results are for the Bernoulli situation, and both use the usual parameter p rather than the 4 = log [p/(l p)] which results if the density is cast into the form (0.2). von Mises actually holds r fixed as he passes to the limit. Their results, which give only the limiting normal term, are reproduced in Bernstein (1934), page 406, and von Mises (1964), Chapter VIII, Section C. von Mises also gives the multinomial generalization. A more recent work following the same line of attack is given in Gnedenko (1962), Section 65. LeCam, in two basic papers (1953) and (1958), takes into account the stochastic nature of (xl, x2, . ), and his Theorem 7 (1953) and Lemma 5 (1958) show that under very general conditions, the scaled posterior distribution converges to the normal distribution for almost all sequences (xl, x2, * * * ) with respect to the infinite product measure generated by (0.1). His conditions include a more general likelihood than ours and the case where the parameter is
Probing high-Reynolds-number effects in numerical boundary layers

We study the high-Reynolds-number behavior of a turbulent boundary layer in the low supersonic regime through very-large-scale direct numerical simulation (DNS). For the first time a Reynolds number is attained in DNS (Reτ=δ/δv≈4000, where δ is the boundary layer thickness and δv is the viscous length scale) at which theoretical predictions and experiments suggest the occurrence of phenomena pertaining to the asymptotic Reynolds number regime. From comparison with previous DNS data at lower Reynolds number we find evidence of a continuing trend toward a stronger imprint of the outer-layer structures onto the near-wall region. This effect is clearly manifested both in flow visualizations, and in energy spectra. More than a decade of nearly-logarithmic variation is observed in the mean velocity profiles, with log-law constants k ≈ 0.394, C ≈ 4.84, and a trend similar to experiments. We find some supporting evidence for the debated existence of a k−1 region in the power spectrum of streamwise velocity fluctu.
Modular Invariants of Parabolic Subgroups of General Linear Groups

Let p be a prime number and let A be an elementary abelian p-group of rank m. The purpose of this paper is to determine a full system for the invariants of parabolic subgroups of the general linear group GL(m, Fp) in H*(A, Fp). A relation between these invariants and Dickson ones is also obtained.
Evaporation of a Sessile Microdroplet on a Heated Hydrophobic Substrate

We investigated evaporation of sessile water microdroplets on heated hydrophobic glass substrate. An in-house, experimentally validated finite-element numerical model was employed to simulate internal fluid flow and heat transfer during the evaporation. We also validated the non-uniform evaporative flux for water droplets having different initial wetting angles with theoretical results from literature. During evaporation, the fluid flow is radially outward due to the largest evaporative flux near the wetting line. The isotherms are almost horizontal which indicates that the conduction between the droplet and substrate dominates over internal convection during the evaporation. The evolution of wetted radius and wetting angle indicates a two-stage evaporation process:during the first stage of the evaporation, wetted radius remains constant and wetting angle decreases with time; while in the second stage, wetting angle remains constant and wetted radius decreases with time. The droplet volume shows a linear .
EXTREME-ULTRAVIOLET SPECTROSCOPY OF Fe vi–Fe xv AND ITS DIAGNOSTIC APPLICATION FOR ELECTRON BEAM ION TRAP PLASMAS

Extreme-ultraviolet spectra of intermediately ionized iron ions (Fe vi–Fe xiv) in the wavelength range of 125.0–265.0 Å have been measured at the Heidelberg electron beam ion trap. Emission spectra were recorded sequentially while varying the electron energy over the range of 75–544 eV in steps of 5 eV. The observed spectra clearly show the evolution of each ionic stage as a function of the electron energy, allowing to distinguish the emission lines from neighboring ion charge species and helping to disentangle possible line blends. The collisional-radiative modeling satisfactorily reproduces the measurement. A comparison with previous astrophysical observations (Sun) reveals that some weak emissions may originate from Fe vi and Fe vii, resulting in incorrect assignment of transition lines. The calculated polarization effects due to nonthermal (monoenergetic) electrons are found to be negligible for most of the emission lines at low-energy electron impact, except for a few lines whose polarization can be over 20%. By line ratio technique, the effective electron density in the trap was estimated to be 7.1+2.4−3.0 × 109–3.4+0.5−0.5 × 1010 cm−3, slightly depending on the ion charge state.
An Experimental Investigation of Performance and Exergy Analysis of a Counterflow Vortex Tube Having Various Nozzle Numbers at Different Inlet Pressures of Air, Oxygen, Nitrogen, and Argon

An experimental investigation has been carried out to determine the thermal behavior of cooling fluid as it passes through a vortex tube and the effects of the orifice nozzle number and the inlet pressure on the heating and cooling performance of the counterflow type vortex tube (RHVT). Experiments have been performed using oxygen (O 2 ), nitrogen (N 2 ), and argon (Ar). Five orifices have been fabricated and used during the experimental study with different nozzle numbers of 2, 3, 4, 5, and 6. The orifices used at these experiments are made of the polyamide plastic material. The thermal conductivity of polyamide plastic material is 0.25 W/m K. To determine the energy separation, the inlet pressure values were adjusted from 150 kPa to 700 kPa with 50 kPa increments for each one of the orifices and each one of the studied fluids. The vortex tube that was used during the experiments has L/D ratio of 15 and the cold mass fraction was held constant at 0.5. As a result of the experimental study, it is determined that the temperature gradient between the cold and hot exits is decreased depending on the orifice nozzle number increase. Exergy analyses have been realized for each one of the studied fluids under the same inlet pressures with the experiments (P i = 150-700). The exergy efficiency of the vortex tube is more affected by inlet pressure than nozzle number.
Optimal reinsurance: minimize the expected time to reach a goal

In this paper, we consider an optimal reinsurance problem. The surplus model of the insurance company is approximated by a diffusion model with the drift coefficient . The insurance company employs reinsurance to reduce the risk. is the proportion of each claim paid by the company and the remainder proportion of the claim is paid by the reinsurer. is the rate at which the premiums are diverted to the reinsurer, thus it holds in general. We discuss two cases: (i) non-cheap reinsurance (when ), (ii) cheap reinsurance (when ). The objective of the insurance company is to make an optimal decision on reinsurance to reach a goal (a given surplus level) in minimal expected time. We disclose that for some case it is not suitable to search optimal decisions by minimizing the expected time to reach a goal. In order to deal with this case, we study two other methodologies (ruin probability minimization and expected discount factor maximization) for the optimal strategy selection problem in reinsurance decision.
A highly sensitive radio survey of symbiotic stars at 3.6 centimeters

We present the results of a highly sensitive VLA survey of symbiotic stars at 3.6 cm. We searched for radio emission in 99 stars, and detected emission in 50, showing that symbiotic stars are one of the more prolific stellar radio emitters. The median sensitivity (3 σ) of the survey is 110 μJy. We have combined our measurements with other data, primarily in the infrared (IR) and ultraviolet (UV) to extend the study of the collective radio properties in Seaquist & Taylor. As in earlier work, the radio emission is consistent with thermal bremsstrahlung from the ionized portion of the envelopes of symbiotic stars, presumed to be associated with their mass outflow
On Sensitivity of Structural Equation Modeling to Latent Relation Misspecifications

By giving counterexamples where the covariance matrix provides crucial information about consequential model misspecifications, this article cautions researchers about overinterpreting Rogosa and Willett's (1985, p. 104) conclusion that "the covariance matrix is a severe summary of the longitudinal data, one that may discard crucial information about growth. "
Role of Initial Conditions in Establishing Asymptotic Flow Behavior

The role of the details of initial (or upstream) conditions in establishing asymptotic behavior is reviewed. The traditional view that at least simple shear flows reach universal asymptotic states is shown to be inconsistent with the abundant experimental and direct-numerical-simulation data. Even though scaled mean velocity profiles collapse, the streamwise (or temporal) variation of the scaling parameters and spreading rates can vary widely for different upstream (or initial) conditions. Equilibrium similarity theory shows why the traditional view has arisen: normalized mean velocity profiles can be universal, even though the other moment profiles and scaling parameters are not. Decaying isotropic turbulence and applications of the proper orthogonal decomposition to free shear flows are used to show what parameters might control the downstream development. It is argued that Reynolds-averaged Navier‐Stokes cannot account for these dependencies, but large-eddy simulation can.
Using pseudometrics in kernel density estimation

Common kernel density estimators (KDE) are generalised, which involve that assumptions on the kernel of the distribution can be given. Instead of using metrics as input to the kernels, the new estimators use parameterisable pseudometrics. In general, the volumes of the balls in pseudometric spaces are dependent on both the radius and the location of the centre. To enable constant smoothing, the volumes of the balls need to be calculated and analytical expressions are preferred for computational reasons. Two suitable parametric families of pseudometrics are identified. One of them has common KDE as special cases. In a few experiments, the proposed estimators show increased statistical power when proper assumptions are made. As a consequence, this paper describes an approach, where partial knowledge about the distribution can be used effectively. Furthermore, it is suggested that the new estimators are adequate for statistical learning algorithms such as regression and classification.
Broadband calibration of radio-frequency magnetic induction probes

We describe broadband calibration of a magnetic induction probe using a network analyzer. Our procedure uses a small driver coil and the scattering matrix associated with the coil-probe pair. This allows rapid, high-resolution measurements of the amplitude and phase of the probe’s response to oscillating magnetic fields. Our setup gives high accuracy between 100kHz and 100MHz and less accuracy outside this range. We present over 1800 sensitivity measurements between 30kHz and 1GHz. The ideal probe response is compared to calibrations done with two different driver coils. We discuss several hurdles in probe design and calibration, as well as several high-frequency effects.
A SIMPLIFIED ANALYTICAL METHOD FOR SOIL PENETRATION ANALYSIS

SUMMARY A new one-dimensional model for penetration analysis of a rigid projectile into a soil target is presented. The soil medium is represented by a set of discs of constant thickness, responding in the radial direction under plain strain regime. When penetration through a typical disc occurs, the projectile displaces soil material and a radial plastic shock wave propagates in the disc. The interaction pressure between the projectile and soil material is compatible with the motion of the contact boundary between them. The instantaneous resistive force is obtained by summation of the contributions of all the discs which are in contact with the nose surface of the projectile. Soil is considered as a 'floating' ideally locking material, in which the locking volumetric strain is adjusted to the physical stress-strain properties of the soil material. Friction between projectile and soil is assumed to be negligible. Comparison is made with both twodimensional computer program results and experimental data, and very good agreement is observed. Comparison with other analytical methods reveals that the present model most closely resembles existing experimental results and permits further analysis of the problem as predictions of target response and of stress distribution on the projectile nose. The calculations require very small amounts of computer time. Analysis with the present model yields an efficient and comprehensive means to analyse penetration and perform parameter analysis.
PREDICTIVE VALIDITY OF A LINEAR REGRESSION EQUATION

The squared correlation coefficient, w2, between an empirically chosen linear function of predictors, B0 + B′x, and a criterion, y, is employed as a measure of predictive precision. This coefficient is defined over the entire population but is conditional on B. Assuming a multinormal distribution for x and y, approximations for the expected value and variance of w2 are derived. If too many predictors are employed, precision of prediction can decrease. This is illustrated by means of an example of a sequence of values of ℰ (w2). A function of the sample squared multiple correlation coefficient, r2, is proposed as an estimator of w2. Results of Monte Carlo experiments are employed to give an impression of the precision of the estimates of w2, and the accuracy of the approximations for ℰ (w2) and var (w2).
Multiplier Hopf algebras

In this paper we generalize the notion of Hopf algebra. We consider an algebra A , with or without identity, and a homomorphism A from A to the multiplier algebra M(A ® A) of A ® A . We impose certain conditions on A (such as coassociativity). Then we call the pair {A, A) a multiplier Hopf algebra. The motivating example is the case where A is the algebra of complex, finitely supported functions on a group G and where (Af)(s, t) = f(st) with s, t £ G and f € A . We prove the existence of a counit and an antipode. If A has an identity, we have a usual Hopf algebra. We also consider the case where A is a *-algebra. Then we show that (a large enough) subspace of the dual space can also be made into a *-algebra.
Ultrafilter invariants in topological spaces

ABSTRAcr. Let m > mo and X = HirXi. Then X is [xo, m]-compact if and only if isj,X, is [IK, m]-compact for all J C I with IJI No, (xC: ( < m) a net in X,p E X, and 6D EE I(m). Thenp = limC<m xf if {( < m: xC E U) E 6D for every neighborhood U of p. Every topological space is characterized by its 6D-limits. Several topological properties are described using ultrafilter invariants, including compactness and perfect maps. If X is a Hausdorff space and D is a discrete space equipotent with a dense subset of X, then X is a continuous perfect image of a subspace of ,D which contains D if and only if X is regular.
The wave normals of ELF hiss emissions observed onboard GEOS 1 at the equatorial and off-equatorial regions of the plasmasphere

The wave normal directions of plasmaspheric ELF hiss have been determined at the equatorial and offhequatorial regions of the plasmasphere by using the data observed by GEOS 1 satellite. Two different methods of direction findings have been utilizedc l1r the maximum entropy method for estimating the wave distribution functions and l2r the maximum likelihood method to estimate the propagation peaks. Three equatorial events have been analyzed, and it is found that just inside the plasmapause, the wave normal θ of ELF hiss is nearly aligned with the magnetic field, and when the observing position is 0.3–0.5 RE inside from the plasmapause, there are two different groups of wave normal angless one is a medium wave normal angle ranging from 20° to 60° and the other is a large wave normal in a range from 70° to 80°, slightly smaller the Gendrin angle. Then, offhequatorial observations have been made at geomagnetic latitudes 30° to 24° for L e 4.66 to 2.90 inside the plasmasphere. The direction findings have yielded that the waves are always composed of two plane wavess both main and secondary peaks take very large wave normal angles, θ e 80°–85°. The present direction finding results of equatorial ELF hiss have been extensively compared with the previous theoretical model to discuss the generation mechanism of plasmaspheric ELF hiss. Then, it is concluded that some of the plasmaspheric hiss emissions are generated by the cyclotron instability with θ ≅ 0°, initially proposed by Thorne et al. l1973r, but majority of ELF hiss emissions are generated at large wave normals.
Coupled Random Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces

Abstract Let (X, ≤) be a partially ordered set and suppose there is a metric d on X such that (X, d) is a complete separable metric space and (Ω, Σ) be a measurable space. In this article a pair of random mappings F: Ω × (X × X) → X and g: Ω × X → X, where F has a mixed g-monotone property on X, and F and g satisfy the non-linear contractive condition (5) below, are introduced and investigated. Two coupled random coincidence and coupled random fixed point theorems are proved. These results are random versions and extensions of recent results of Lakshmikantham and Ćirić [V. Lakshmikantham and Lj. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. —Theor. 70(12) (2009): 4341–4349] and include several recent developments.
A GENERALIZED DIFFERENTIAL TRANSFORM METHOD FOR COMBINED FREE AND FORCED CONVECTION FLOW ABOUT INCLINED SURFACES IN POROUS MEDIA

In this article, we apply the differential transform method (DTM) to obtain approximate analytical solutions of combined free and forced (mixed) convection about inclined surfaces (or wedges) in a saturated porous medium. Both aiding and opposing flows are considered. It is found that the parameter mixed convection from inclined surfaces in porous media is Gr/Re, where Gr is the local Grashof number and Re is the local Reynolds number. DTM solutions are obtained for mixed convection from an isothermal vertical flat plate as well as an inclined plate with constant heat flux having an inclination of 45°. Temperature and velocity profiles for these two cases at different values of Gr/Re are presented. The similarity transformations are applied to reduce the governing partial differential equations (PDEs) to a set of nonlinear coupled ordinary differential equations (ODEs) in dimensionless form. DTM is used to solve the nonlinear differential equations governing the problem in the form of series with easily computable terms. Thereafter a Padé approximant is applied to the solutions to increase the convergence of the given series. Excellent correlation between DTM-Padé and numerical quadrature (shooting) solutions is achieved. The DTM-Padé simulation is shown to be a robust benchmarking tool providing an excellent means of validation of numerical methods. The study has applications in geothermal energy systems, chemical engineering filtration systems, and packed beds.