Miracle-dz/UniFAR-FTUs huggingface dataset:
The probability function of the product of two normally distributed variables.

Let $x$ and $y$ follow a normal bivariate probability function with means $\bar X, \bar Y$, standard deviations $\sigma_1, \sigma_2$, respectively, $r$ the coefficient of correlation, and $\rho_1 = \bar X/\sigma_1, \rho_2 = \bar Y/\sigma_2$. Professor C. C. Craig [1] has found the probability function of $z = xy/\sigma_1\sigma_2$ in closed form as the difference of two integrals. For purposes of numerical computation he has expanded this result in an infinite series involving powers of $z, \rho_1, \rho_2$, and Bessel functions of a certain type; in addition, he has determined the moments, semin-variants, and the moment generating function of $z$. However, for $\rho_1$ and $\rho_2$ large, as Craig points out, the series expansion converges very slowly. Even for $\rho_1$ and $\rho_2$ as small as 2, the expansion is unwieldy. We shall show that as $\rho_1$ and $\rho_2 \rightarrow \infty$, the probability function of $z$ approaches a normal curve and in case $r = 0$ the Type III function and the Gram-Charlier Type A series are excellent approximations to the $z$ distribution in the proper region. Numerical integration provides a substitute for the infinite series wherever the exact values of the probability function of $z$ are needed. Some extensions of the main theorem are given in section 5 and a practical problem involving the probability function of $z$ is solved.
Numerical Investigation of Phase Distribution and Liquid Turbulence Modulation in Dilute Particle-Laden Flow

Studies on the motion of particles in turbulence and interactions between particles and turbulence are extremely significant, which can help us to improve the efficiency of industrial processes. In this article, we investigated the particle distribution and particle-turbulence interaction in a solid-liquid channel flow with the Euler-Lagrange two-way model. The liquid phase was solved using direct numerical simulation (DNS), and the particle motion was tracked by Newtonian equations of motion considering effects of drag force, pressure gradient force, and gravity. Two-way coupling was used to explain the effect of particles on the turbulence structure. The results show that the local void fraction of particles indicates the wall-peaked profile, particles scatter uniformly in the spanwise direction, and the injection of particles suppresses the turbulence activities in the near wall region. Suppression of the liquid turbulence is mainly caused by vortexes decay of different sizes.
Equivalence of connectivity maps and peripherally continuous transformations

In [1 ] and 12 ] 0. H. Hamilton and J. Stallings have shown that a local connectivity mapping, and hence a connectivity mapping, of a locally peripherally connected polyhedron into a regular Hausdorff space is peripherally continuous. The purpose of this paper is to prove the converse of this theorem. Some definitions will now be recalled. A mapping f: S-*T is a connectivity mapping if for every connected set A in S, the set g(A) is connected, where g: S->SX T is the graph map of f defined by g(p)-(p, f(p)) [1, p. 750]. The mapping f is a local connectivity mapping if there is an open covering { Ua } of S such that fj Ua is a connectivity mapping for every a [2, p. 249]. The mappingf is peripherally continuous if for every point p in S and for every pair of open sets U and V containing p and f(p), respectively, there is an open set NC U and containing p such that f(F(N)) C V, where F(N) is the boundary of N [1, p. 751 ]. A space S is locally peripherally connected if every point has arbitrarily small neighborhoods with connected boundary [2, p. 252]. In this paper S will denote a connected, locally connected, locally peripherally connected, unicoherent metric space and T a space such that SX T is completely normal. The following lemma, proved by Stallings [2, p. 255], is used in the proof of Theorem 1.
Interface traps generated by internal photoemission in Al‐SiO2‐Si structures

Generation of interface traps by internal photoemission of electrons from both the Al interface and the Si interface of an Al‐SiO2‐Si structure has been studied. The generation rate differs significantly between steam oxide and dry oxide samples, and among the dry oxide samples, the post‐metal‐anneal (PMA) treatment results in an appreciable reduction of this rate. A characteristic peak in the interface trap distribution, similar to the one generated by ionizing radiation, has been observed for all samples. For a given injection condition, the magnitude of this peak depends on the oxidation and PMA treatments, and is in the order (steam oxide)>(dry oxide/no PMA)>(dry oxide/PMA). For a given sample, the peak increases with the applied electric field and the total injected charge for either polarity. When the injection is made from the Si interface, the generation rate also depends on the energy of the incident photons, while no such dependence is observed for injection from the Al interface. A qualitative .
Flow and Thermal Errors in Current National Weather Service Wind Chill Models

The two National Weather Service (NWS) wind chill models in operation since 2001 have inherent errors. The first model attempted and failed to make a facial surface temperature correction on the existing Siple and Passel model. The second model, intended as an improvement on the first, erred by mistakenly defining the wind chill temperature in terms of an internal body temperature rather than the facial surface temperature. To account for a boundary-layer reduction in the free-stream velocity at head level, both models incorrectly apply a constant high-percentage reduction to this velocity as measured at the NWS 10 m level. As a result of these errors, both models predict wind chill temperatures much warmer than the actual values. These warmer temperatures can instill a public complacency whereby facial freezing is viewed as a remote possibility when in reality it may be imminent.
RESÍDUOS DE SERRARIAS NA PRODUÇÃO DE PAINÉIS DE MADEIRA AGLOMERADA DE EUCALIPTO

This research paper was developed aiming to evaluate the feasibility of utilization of the woods of Eucalyptus maculata, E. grandis and E. tereticornis, deriving from saw mill processing residues to particleboard manufacture. Was manufactured 24 boards, being eight treatments, defined in function of three species and its mixture, and two resin levels (8 and 12%). The processing variables were: board density = 0,75g.cm-3, press temperature = 140° C, pressing time = 8 min and pressure = 40 kg.cm-2. The following physical and mechanical properties were evaluated: water absorption (AA-2 and 24 h), thickness swelling (IE-2 and IE24 h), internal bond (LI), modulus of elasticity (MOE) and modulus of rupture (MOR) in bending strenght. Boards manufactured with these eucaliptus species showed satisfctory physical and mechanical properties in comparison to some referentials species as Pinus elliottii, Mimosa scabrella and Eucalyptus dunnii presented in the literature. The boards manufactured with 12% of resin level showed better results than boards with 8%. Based in the mechanical properties, the Eucalyptus maculata showed the best behavior for particleboard manufacture.
Signal waveform restoration by wavelet denoising

In this paper, we first establish an approximated sampling theorem for an arbitrary continuous signal which is essential for wavelet analysis. The differences and similarities between quadrature mirror filter decomposition and wavelet decomposition are contrasted. We then propose an efficient way to recover a source signal buried in white noise by using wavelet denoising. The method is capable of reducing the mean square error bound from O(log/sup 2/(n)) to O(log(n)), where n is the number of samples. It is also shown that the new estimator is asymptotically unbiased if the source signal is a piece-wise polynomial.
Set convergence for discretizations of the attractor

We consider the discretization of a dynamical system given by a C 0 -semigroup S(t), defined on a Banach space X, possessing an attractor A. Under certain weak assumptions, Hale, Lin and Raugel showed that discretizations of S(t) possess local attractors, which may be considered as approximations to A. Without further assumptions, we show that these local attractors possess convergent subsequences in the Hausdorff or set metric, whose limit is a compact invariant subset of A. Using a new construction, we also consider the Kloeden and Lorenz concept of attracting sets in a Banach space, and show under mild assumptions that discretizations possess attracting sets converging to A in the Hausdorff metric.
Self-Sustained Oscillations in a Ring Array of Coupled Lossless Transmission Lines

Abstract In this paper, we derive a neutral difference-differential system with diffusion which arises from a ring array of coupled lossless transmission lines. We investigate the problem of self-sustained oscillations of the considered transmission lines and apply a global Hopf bifurcation theorem to establish the existence of multiple large amplitude phase-locked periodic solutions in the corresponding neutral system.
VLBI Observations of Southern Hemisphere ICRF Sources. I.

We present 8.4 GHz very long baseline interferometry (VLBI) observations of 69 southern hemisphere extragalactic sources in the International Celestial Reference Frame. These are the first in a series of observations intended to image all such sources at milliarcsecond resolution in order to determine their continued suitability for reference-frame use based on intrinsic structure. We use the resultant images to calculate a core fraction, that is, the ratio of core flux density to total flux density, for all observed sources. The resulting distribution, with a mean value of 0.83, suggests that most sources are relatively compact. However, just over half the observed sources show significant extended emission in the form of multiple compact components. These sources are probably poorly suited for high-accuracy reference-frame use unless intrinsic structure and potential variability can be taken into account. Our observations represent the first large, comprehensive VLBI imaging survey in the southern hemisphere, significantly extending the existing limited VLBI surveys and, along with some well-known objects, containing many sources that have never been imaged at milliarcsecond resolution. The overlap with Very Long Baseline Array images of sources between 0° and -35° declination helps determine the limits to imaging with the southern hemisphere–accessible telescopes.
Fast and Slow Rotation of Asteroids

Abstract We present an analysis of the distribution of asteroid spin rates vs. size. The existence of significant populations of both slow and fast rotators among asteroids smaller than D=40 km, and especially below 10 km (where our sample is mostly near-Earth asteroids), is shown. We have found that the excess of slow rotators is present at spin rates below ≈0.8 rev/day, and the group of fast rotators occupies the range of spin rates >7 rev/day. The fast rotators show interesting characteristics: The lack of objects rotating faster than 2.2 h period among asteroids with absolute magnitude H
Methane on Triton and Pluto: new CCD spectra

Spectra of Triton and of Pluto from 4553-9558 A at 25 A resolution are presented. Both spectra show the methane absorption near 8900 A; its equivalent width was 16 times greater on Pluto than on Triton at the time of the observations. This is the first published observation of the 8900 A feature in Triton's spectrum. The previously reported 27 m-amagat abundance of the Pluto atmosphere ignored contributions due to methane ice and should therefore be regarded as an upper limit. The observations of the Pluto spectrum discussed here show sharp structure in the 8900 and 8600 A bands; the case for an atmosphere on Pluto may turn on whether new laboratory measurements show that such structure is present in methane ice.
A comparison of models for clustered binary outcomes: analysis of a designed immunology experiment

The lymphocyte proliferative assay (LPA) of immune competence was conducted on 52 subjects, with up to 36 processing conditions per subject, to evaluate whether samples could be shipped or stored overnight, rather than being processed on fresh blood as currently required. The LPA study resulted in clustered binary data, with both cluster level and cluster‐varying covariates. Two modelling strategies for the analysis of such clustered binary data are through the cluster‐specific and population‐averaged approaches. Whereas most research in this area has focused on the analysis of matched pairs data, in many situations, such as the LPA study, cluster sizes are naturally larger. Through considerations of interpretation and efficiency of these models when applied to large clusters, the mixed effect cluster‐specific model was selected as most appropriate for the analysis of the LPA data. The model confirmed that the LPA response is significantly impaired in individuals infected with the human immunodeficiency virus (HIV). The LPA response was found to be significantly lower for shipped and overnight samples than for fresh samples, and this effect was significantly stronger among HIV‐infected individuals. Surprisingly, an anticoagulant effect was not detected.
AN IMAGING STUDY OF THE GALACTIC DIFFUSE SOFT X-RAY BACKGROUND

In the soft energy regime < 1 keV, the Galactic background is a significant component of the celestial diffuse X-ray radiation and carries important information about hot gas in the disk and in the corona of the Galaxy. We have conducted a study of the Galactic diffuse soft X-ray background with the data collected with the Imaging Proportional Counter on board the Einstein X-ray Observatory. The high sensitivity and spatial resolution of the data enable us to detect and subtract discrete sources to a flux level < 1013 erg cm-2 s-1, to measure the background with minmized confusion between various components in the radiation, and to study arcmin-scale fluctuation of the background. The results reported here demonstrate the value of imaging data in studying the background. At high Galactic latitudes, the Galactic background, indicated by the global enhancement of the X-ray radiation intensity toward the Galactic center, could arise in the corona of the galaxy. We have measured the intensity of the radiation in the 0.2-0.8 keV band in the latitude interval 30 degrees < |b|< 70 degrees and have compared the distribution of the intensity with a simple emission model of the Galactic corona. This comparison suggests that the corona probably accounts for more than half of the radiation in the energy band. The estimated density and pressure in the coronal gas are consistent with both theoretical arguments and UV observations made with IUE, HST, and rocket experiments. The intensity and spectrum of the Galactic background at the Galactic plane are measured with a deep image of the plane. The spectrum in the 0.2-3.5 keV band can be characterized by the emission from optically-thin, thermal coronal gas of a temperature at 4 x 106 K, and the M-band intensity is Ix(0.5 - 1 keV) 3 X 10-8 erg cm-2 s-1 sr-1. An angular autocorrelation analysis of the imaging data leads to the conclusion that no known stellar population is likely responsible for the bulk of the background. A hot gas model seems consistent with the observation; but a satisfactory fit to the observed spectrum requires X-ray emission from hot gas beyond the 106 K Local Bubble. We further point out that the X-ray background, enhanced in the M-band at the Galactic plane, is apparently not related to the Galactic ridge emission inferred from observations in the higher energy 2-10 keV regime.
Periodic solutions of nonlinear periodic differential systems with a small parameter

We deal with nonlinear periodic differential systems depending on a small parameter. The unperturbed system has an invariant manifold of periodic solutions. We provide sufficient conditions in order that some of the periodic orbits of this invariant manifold persist after the perturbation. These conditions are not difficult to check, as we show in some applications. The key tool for proving the main result is the Lyapunov--Schmidt reduction method applied to the Poincare--Andronov mapping.
More (Inclusive) Entrepreneurship in South Africa: The Role of Franchising

This paper explores franchising in South Africa, and its potential to help resolve the economy’s challenges of low entrepreneurship and concentrated ownership. South Africa features a large franchising sector, with half a million formal workers and a large number of small businesses owners competing directly with vertically integrated chains. Traditional franchising may not have much space for further growth as a percentage of the economy, but it can be made more inclusive with innovations in franchise finance that broaden the base of potential franchisees, as well as enforcement of consumer protections to ensure franchisee-franchisor relationships are balanced. The expansion of the franchising model to less capital-intensive business concepts and serving lower-income consumers (micro-franchising) is one area with expanding growth potential for the country, while the application of the franchising model to public services and socially driven organizations is less promising. Finally, while the franchising model is only directly applicable to particular sectors, there are features of franchising and the capabilities built up around the franchising that could be applied to other priority areas of the economy, in particular to smallholder agriculture. The success of traditional franchising shows the power of a menu of standardized proposals and contracts in a marketplace with a range of franchisors (in this case up- and downstream agriculture corporates) offering different opportunities to potential franchisees (in this case smallholder farming communities), along with training and technology transfer at scale.
Band gap design of thiophene polymers based on density functional theory

Hybrid density functional theory calculations are carried out to investigate the band gaps of thiophene derivatives. We carry out density functional theory (DFT) calculations for finite-length oligomers and estimate the band gaps of infinite-length polymers using an extrapolation scheme. The calculated band gaps of polythiophene, poly(3-hexylthiophene) (P3HT), poly(2-ethenylthiophene), and polyisothianaphthene (PITN) are close to experimental values. We predict the band gap of poly(2-ethenyl-3-hexylthiophene). The calculated band gaps of various thiophene derivatives in this study are 1.10–1.81 eV; therefore, we have demonstrated that the band gaps can be controlled using thiophene derivatives. We discuss the mechanism of band gap decrease in derivatives, which is useful for the band gap design of thiophene derivatives.
Two-dimensional warm gas kinematics in interacting galaxy systems

Gas reservoirs, internal or acquired, play an important role in the secular evolution of interacting galaxies, since they are able to enhance/trigger star formation episodes and, probably, feed the activity of active galactic nuclei. Using Fabry‐Perot observations, we have mapped, in the Hα line, the warm (T ≈ 10 4 )g as distribution and the velocity fields of the galaxy members of five interacting, gas-rich galaxy systems. We investigated two M51-like systems (Arp 70 and Arp 74), two systems containing highly disrupted members (WBL 366 and RR 24) and a case of merging in progress (Arp 299, one of the nearest luminous infrared objects). We detected gas motions following the elongated arm/tail of Arp 70b, while in the fainter member of the pair of galaxies, Arp 70a, the gas distribution is off-centred with respect to the stellar isophotes, suggesting an external acquisition. Our kinematic data highlighted noncircular motions in the velocity field of one of the members of Arp 74 (Arp 74a). The two galaxies of the RR 24 system are connected by one tidal tail, through which the kinematically disturbed component RR 24b seems to supply warm gas to RR 24a. In spite of the nearly irregular gas distribution and perturbed morphology, WBL 366a (the star-forming galaxy VV523) and WBL 366b have nearly regular velocity fields. The velocity field in the Arp 299 system is irregular, and gas flow between the two nuclei is detected. The present observations, discussed in the light of model predictions and complementary observations from the literature, suggest that all these systems are still probably in an early phase of the encounter. However, the ionized gas distribution and kinematics are strongly influenced by tidal forces. In particular, cross-fuelling mechanisms between galaxies are in action. In Arp 299 the warm and cold gaseous components show similar kinematic properties, although the cold gas seems to maintain a still better organized motion with respect to the warm gas. Ke yw ords: galaxies: general ‐ galaxies: interactions ‐ galaxies: kinematics and dynamics.
Comparative study of dynamical critical scaling in the auroral electrojet index versus solar wind fluctuations

Based on an analysis of auroral electrojet (AE) index data, we demonstrate that the temporal evolution of magnetospheric perturbations exhibits non‐trivial power‐law relations consistent with the behavior of a general class of statistical physical models in the vicinity of a stationary critical point. We show that the ensemble average dynamics of the activity bursts in the AE index is essentially scale‐free and can be characterized in terms of spreading critical exponents η and δ. The lifetime T and the size S of the bursts show strong algebraic correlation that is approximated by the dependence S ∼ T1+η+δ. For times shorter than 3.5 hours, we find scaling features in the AE index that are independent of the solar wind input, thus indicating the internal magnetospheric origin of the revealed effects.
A note on changes in channel geometry at tributary junctions

Evidence is presented to justify the assumption that channel width varies stochastically about an approximately constant mean width within a stream link of an alluvial channel. Adjustments of channel width occur predominantly at junctions, but Miller's (1958) simple model describing such changes is misleading, and an alternative is proposed whose implication is that channel width (and probably other channel dimensions) is a power function of link magnitude. It is suggested that an alternative to conventional hydraulic geometry is provided by the combination of a step function describing changes at junctions and a stochastic model of variation within individual links.
Production of a collisionless conduction front by rapid coronal heating and its role in solar hard X-ray bursts.

The theoretical and observational evidence for and against an impulsively heated thermal bremsstrahlung source of solar hard X-ray bursts is briefly reviewed. In particular, it is noted that in a collision-dominated plasma of any reasonable density the collisional relaxation time would be much longer, and the conductive cooling time much shorter, than typical burst durations (cf. Kahler). It is then shown, however, that free expansion of impulsively heated electrons into a cool surrounding plasma will generate an ion-sound turbulent front which efficiently scatters the electrons, thus bottling up their heat flux. The conductive cooling time is thus increased by a factor approx. (m/sub i//m/sub e/)/sup 1/2/ over its free expansion limit, compatible with observations. The front thickness is less than about 1 km. Interaction with the turbulence permits the bulk of the electrons to reach a relaxed distribution, without the need for high densities, hence providing an efficient source of hard X-rays. Electrons of U> or =2.6U/sub e/, however, are not scattered by the ion-sound turbulence but do not necessarily escape freely either, because of the action of the thermoelectric field present.Finally, some brief remarks are directed to the mechanism of heating and to the compatibility of these conditions in themore » hard X-ray source with other flare observations. « less