Miracle-dz/UniFAR-FTUs huggingface dataset:
Functional Partial Linear Single‐index Model

This paper deals with the problem of predicting the real‐valued response variable using explanatory variables containing both multivariate random variable and random curve. The proposed functional partial linear single‐index model treats the multivariate random variable as linear part and the random curve as functional single‐index part, respectively. To estimate the non‐parametric link function, the functional single‐index and the parameters in the linear part, a two‐stage estimation procedure is proposed. Compared with existing semi‐parametric methods, the proposed approach requires no initial estimation and iteration. Asymptotical properties are established for both the parameters in the linear part and the functional single‐index. The convergence rate for the non‐parametric link function is also given. In addition, asymptotical normality of the error variance is obtained that facilitates the construction of confidence region and hypothesis testing for the unknown parameter. Numerical experiments including simulation studies and a real‐data analysis are conducted to evaluate the empirical performance of the proposed method.
Scaling of pressure spectrum in turbulent boundary layers

Scaling of pressure spectrum in zero-pressure-gradient turbulent boundary layers is discussed. Spatial DNS data of boundary layer at one time instant (Reθ = 4500) are used for the analysis. It is observed that in the outer regions the pressure spectra tends towards the -7/3 law predicted by Kolmogorov's theory of small-scale turbulence. The slope in the pressure spectra varies from -1 close to the wall to a value close to -7/3 in the outer region. The streamwise velocity spectra also show a -5/3 trend in the outer region of the flow. The exercise carried out to study the amplitude modulation effect of the large scales on the smaller ones in the near-wall region reveals a strong modulation effect for the streamwise velocity, but not for the pressure fluctuations. The skewness of the pressure follows the same trend as the amplitude modulation coefficient, as is the case for the velocity. In the inner region, pressure spectra were seen to collapse better when normalized with the local Reynolds stress than when scaled with the local turbulent kinetic energy
The dynamic velocity of long positive streamers observed using a multi-frame ICCD camera in a 57 cm air gap

The streamer propagation plays an important role in long air gap discharge. In this paper, a multi-frame intensified charge-coupled display (ICCD) camera was used to observe the long positive streamers in a 57 cm air gap. The propagation process of the 20–30 cm long streamers was captured, and the velocity variation in a single streamer was analysed. When applying a +210–290 kV lightning impulse voltage on a rod–plane gap with three different tips, the velocity of a streamer decreases from 8.3 ± 2.7 mm ns−1 at the ignition stage to 0.4 ± 0.1 mm ns−1 at the later stage. The influence of the applied voltage and the electrode size was obtained and analysed. Higher voltage amplitude and larger electrode size lead to a greater velocity. In addition, the relationship between the velocity and the background electric field is discussed here, and the experimental results are compared with an analytical model of different parameters.
Estimation of Monthly Rainfall over Japan and Surrounding Waters from a Combination of Low-Orbit Microwave and Geosynchronous IR Data

Abstract This paper describes a method to combine geosynchronous IR and low-orbit microwave data to estimate mean monthly rainfall useful for climate studies. The IR data have the advantage of high time resolution (important for rapidly changing precipitation patterns and for the detection of diurnal signals) but lack a strong physical connection between the remotely sensed signal and the surface rainfall. The microwave data provide a stronger relation between the radiance and the rainfall but provide poor time sampling of the rainfall signal. The microwave technique uses the brightness temperature at 37 and 86 GHz from the Special Sensor Microwave/Imager instrument on board the Defense Meteorological Satellite Program (DMSP) satellite to define raining areas over water and land and uses the 86-GHz scattering signal to assign rain rate based on cloud model-microwave calculations. The microwave results are generally good for both individual swaths and monthly totals, except for a glaring underestimation of.
Geometry of Membrane Sigma Models

String theory still remains one of the promising candidates for a unification of the theory of gravity and quantum field theory. One of its essential parts is relativistic description of moving multi-dimensional objects called membranes (or p-branes) in a curved spacetime. On the classical field theory level, they are described by an action functional extremalising the volume of a manifold swept by a propagating membrane. This and related field theories are collectively called membrane sigma models. Differential geometry is an important mathematical tool in the study of string theory. It turns out that string and membrane backgrounds can be conveniently described using objects defined on a direct sum of tangent and cotangent bundles of the spacetime manifold. Mathe- matical field studying such object is called generalized geometry. Its integral part is the theory of Leibniz algebroids, vector bundles with a Leibniz algebra bracket on its module of smooth sections. Special cases of Leibniz algebroids are better known Lie and Courant algebroids. This thesis is divided into two main parts. In the first one, we review the foundations of the theory of Leibniz algebroids, generalized geometry, extended generalized geometry, and Nambu- Poisson structures. The main aim is to provide the reader with a consistent introduction to the mathematics used in the published papers. The text is a combination both of well known results and new ones. We emphasize the notion of a generalized metric and of corresponding orthogonal transformations, which laid the groundwork of our research. The second main part consists of four attached papers using generalized geometry to treat selected topics in string and membrane theory. The articles are presented in the same form as they were published.
Recent Developments in the Application of the Generalized Acoustic Analogy to Jet Noise Prediction

The Generalized Acoustic Analogy provides a logical framework for the prediction of aerodynamically generated sound. This paper reviews some recent developments in the use of this analogy for the prediction of noise from high speed air jets. Other approaches to jet noise prediction are not discussed. Recent advances in accounting for non-parallel mean flow and temperature effects are described. The results suggest that the former effect is more important than previously believed. They also suggest that previously neglected coupling between momentum flux and enthalpy flux fluctuations can be an important source of noise in high Mach number heated jets. Some recent improvements in acoustic source modeling are also summarized.
Green Tea Seed Oil Suppressed Aβ1–42-Induced Behavioral and Cognitive Deficit via the Aβ-Related Akt Pathway

The aim of this study was to investigate the availability of seeds, one of the byproducts of green tea, and evaluate the physiological activity of seed oil. The ameliorating effect of green tea seed oil (GTO) was evaluated on H2O2-induced PC12 cells and amyloid beta (Aβ)1–42-induced ICR mice. GTO showed improvement of cell viability and reduced reactive oxygen species (ROS) production in H2O2-induced PC12 cells by conducting the 2′,3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide (MTT) and 2′,7′-dichlorofluorescein diacetate (DCF-DA) analysis. Also, administration of GTO (50 and 100 mg/kg body weight) presented protective effects on behavioral and memory dysfunction by conducting Y-maze, passive avoidance, and Morris water maze tests in Aβ-induced ICR mice. GTO protected the antioxidant system by reducing malondialdehyde (MDA) levels, and by increasing superoxide dismutase (SOD) and reducing glutathione (GSH) contents. It significantly regulated the cholinergic system of acetylcholine (ACh) contents, acetylcholinesterase (AChE) activities, and AChE expression. Also, mitochondrial function was improved through the reduced production of ROS and damage of mitochondrial membrane potential (MMP) by regulating the Aβ-related c-Jun N-terminal kinase (JNK)/protein kinase B (Akt) and Akt/apoptosis pathways. This study suggested that GTO may have an ameliorating effect on cognitive dysfunction and neurotoxicity through various physiological activities.
Symplectic capacities of Hermitian symmetric spaces

Inspired by the work of G. Lu on pseudo symplectic capacities we obtain several results on the Gromov width and the Hofer--Zehnder capacity of Hermitian symmetric spaces of compact type. Our results and proofs extend those obtained by Lu for complex Grassmannians to Hermitian symmetric spaces of compact type. We also compute the Gromov width and the Hofer--Zehnder capacity for Cartan domains and their products.
Angular and Altitude Dependence of Cosmic Ray Muons

Using plastic scintillation detectors, our group produced data to measure the muon flux as a function of altitude, angle, and solid angle subtended by our detectors. This allowed us to compare our data to literature models[2]. Our data showed a high degree of convergence with existing literature models, even those lacking in technical rigour. Improvements could be made by surveying the energy distribution of muons at different altitudes[3], allowing us to use more robust modeling techniques and fit our data more closely. The angular, altitude, and displacement dependence of muon detection was determined by constructing four “Cosmic Watch” muon scintillation detectors. Each scintillation detector utilizes a silicon photomultiplier (SiPM) placed under a 5x5x1 cm BC408 scintillation block. Muons passing through the scintillation block excite electrons, which subsequently return to ground states and release photons in the process. These photons are then received by the SiPM and the signal is processed by an Arduino microcontroller. The voltage produced by the SiPM, muon count number, Arduino uptime/downtime, and analog-to-digital converter are all read to an SD card as a text file (or alternatively displayed on an OLED). Using the 3 mm audio jack of the Cosmic Watch, two muon detectors may be placed in “coincidence mode,” wherein one detector (dubbed “slave”) counts all muons passing through both the second detector (dubbed “master”) and itself. The solid angle subtended by two detectors in coincidence mode may then be manipulated by varying the displacement between them, thereby increasing the accuracy and decreasing precision of the incident angle measurement as displacement is increased. To vary altitude heights, data was collected at different locations (in the Bay Area) with significant and measurable differences in heights. 4 data collection points were ultimately chosen; Mount Rose (2517m), Truckee (1762m), Mount Diablo (1173m) and Clark Kerr UC Berkeley (100m). To vary angular dependance, a precisely calibrated mechanical device was constructed to accurately position detectors at the desired angles of 0°, 30°, 60°. Accurate incisions were cut into two perpendicular wooden struts, and a supporting beam, such that the angle of a supporting wooden beam, upon which the detectors were mounted, could be
Efficient Prime Counting and the Chebyshev Primes

The function where is the logarithm integral and the number of primes up to is well known to be positive up to the (very large) Skewes' number. Likewise, according to Robin's work, the functions and , where and are Chebyshev summatory functions, are positive if and only if Riemann hypothesis (RH) holds. One introduces the jump function at primes and one investigates , , and . In particular, , and for . Besides, for any odd , an infinite set of the so-called Chebyshev primes. In the context of RH, we introduce the so-called Riemann primes as champions of the function (or of the function ). Finally, we find a good prime counting function , that is found to be much better than the standard Riemann prime counting function.
RHEOLOGICAL EQUATIONS IN ASYMPTOTIC REGIMES OF GRANULAR FLOW

This paper assesses the validity of the generalized viscoplastic fluid (GVF) model in light of the established constitutive relations in two asymptotic flow regimes, namely, the macroviscous and grain-inertia regimes. A comprehensive review of the literature on constitutive relations in both regimes reveals that except for some material constants, such as the coefficient of restitution, the normalized shear stress in both regimes varies only with the grain concentration, C. It is found that Krieger-Dougherty's relative viscosity, μ*(C), is sufficiently coherent among the monotonically nondecreasing functions of C used in describing the variation of the shear stress with C in both regimes. It not only accurately represents the C-dependent relative viscosity of a suspension in the macroviscous regime, but also plays a role of the radial distribution function that describes the statistics of particle collisions in the grain-inertia regime. Use of μ*(C) alone, however, cannot link the two regimes. Another par.
Automorphisms of moduli spaces of symplectic bundle

Let X be an irreducible smooth complex projective curve of genus at least 3. Fix a line bundle L on X. Let M_{Sp}(L) be the moduli space of symplectic bundles (E, ExE ---> L) on X, with the symplectic form taking values in L. We show that the automorphism group of M_{Sp}(L) is generated by automorphisms sending E to ExM, where M is a 2-torsion line bundle, and automorphisms induced by automorphisms of X.
Effects of Spin Fluctuations on the Specific Heat in YMn2 and Y0.97Sc0.03Mn2

The specific heat measurements of YMn 2 and Y 0.97 Sc 0.03 Mn 2 , which exhibit giant spin fluctuatuions in the paramagnetic state, were carried out in the temperature range of 13 K to 300 K. The spin fluctuation contribution to the specific heat C m was estimated by subtracting the phonon and electronic parts. The magnetic entropy S m was deduced from C m . Above 120 K, where the the effect of the antiferromagnetic transition vanishes, the entropy curves of two compounds coincide each other, indicating that in the paramagnetic state, YMn 2 has the same amplitude of spin fluctuations as Y 0.97 Sc 0.03 Mn 2 . The absolute value of the entropy was also discussed taking account of results of neutron scattering measurements.
Optimal design of water distribution networks for fuzzy demands

Future water demands being difficult to predict with any certainty are considered herein as fuzzy demands and modelled by trapezoidal possibility distribution function as was done by Xu and Goulter. The fuzzy linear programming model as formulated by Xu and Goulter for minimum cost design of water distribution networks is modified by including loop-head loss constraints in the form of path-head loss constraints. This maintains hydraulic consistency in the network for critical demands and provides network design in a single iteration. Initially, the path concept is used to decide flow directions in various links and also for assuming flow distribution for fuzzy demands. Fuzzy nodal pressure head constraints for the assumed flow distribution are converted to crisp constraints. The proposed method is applied to an example network taken from the literature and the results are compared with those obtained by Xu and Goulter. The modified linear programming model avoids iterative procedure and also provides a cheaper solution.
Formal reduction of differential systems : Singularly-perturbed linear differential systems and completely integrable Pfaffian systems with normal crossings

In this thesis, we are interested in the local analysis of singularly-perturbed linear differential systems and completely integrable Pfaffian systems in several variables. Such systems have a vast literature and arise profoundly in applications. However, their symbolic resolution is still open to investigation. Our approaches rely on the state of art of formal reduction of singular linear systems of ordinary differential equations (ODS) over univariate fields. In the case of singularly-perturbed linear differential systems, the complications arise mainly from the phenomenon of turning points. We extend notions introduced for the treatment of ODS to such systems and generalize corresponding algorithms to construct formal solutions in a neighborhood of a singularity. The underlying components of the formal reduction proposed are stand-alone algorithms as well and serve different purposes (e.g. rank reduction, classification of singularities, computing restraining index). In the case of Pfaffian systems, the complications arise from the interdependence of the multiple components which constitute the former and the multivariate nature of the field within which reduction occurs. However, we show that the formal invariants of such systems can be retrieved from an associated ODS, which limits computations to univariate fields. Furthermore, we complement our work with a rank reduction algorithm and discuss the obstacles encountered. The techniques developed herein paves the way for further generalizations of algorithms available for univariate differential systems to bivariate and multivariate ones, for different types of systems of functional equations.
Bubbly flow model for the dynamic characteristics of cavitating pumps

This paper is concerned with understanding the dynamic behaviour of cavitating hydraulic machines during unsteady or transient operation. The linear transfer matrices which relate the small fluctuating pressures and mass flow rates at inlet and discharge are functions not only of the frequency but also of the mean operating state of the machine, especially the degree of cavitation. The recent experimental transfer matrices obtained by Ng & Brennen (1978) for some axial flow pumps revealed some dynamic characteristics which were unaccounted for by any existing theoretical analysis; their visual observations suggested that the bubbly cavitating flow in the blade passages could be responsible for these effects. A theoretical model of the dynamic response of this bubbly blade-passage flow is described in the present paper. Void-fraction fluctuations in this flow result not only from pressure fluctuations but also because the fluctuating angle of attack causes fluctuations in the rate of production of bubbles near the leading edge. The latter causes kinematic waves which interact through the boundary conditions with the dynamic waves caused by pressure fluctuation. The resulting theoretical transfer functions which result are in good qualitative agreement with the experiments; with appropriate choices of two parameters (the practical values of which are difficult to assess) good quantitative agreement is also obtained. The theoretical model also provides one possible explanation of the observation that the pump changes from an essentially passive dynamic element in the absence of cavitation to a progressively more active element as the extent of cavitation increases.
An introduction to inertial navigation

In most introductory physics courses, the first equations encountered are the kinematic equations. Though the emphasis at this level tends to be on cases of constant acceleration, many real-world examples of motion are not so simple. We describe the use of inexpensive hobbyist-grade accelerometers and spreadsheet software to explore inertial navigation via numerical integration of the measured acceleration.
Replicable one-dimensional non-polarizing guided mode resonance gratings under normal incidence

Polarization-insensitive guided-mode resonance (GMR) filters have significant role in applications such as optical communication systems. Here, we report the design and fabrication of two types of simple-structured one-dimensional (1D) GMR gratings with non-polarizing resonance properties under normal incidence. A single-layer rectangular-profile TiO2 grating is fabricated by electron beam lithography and reactive ion etching, which demonstrates, for the first time in experiment, almost perfect non-polarizing filtering effect with 1D grating under normal incidence. Then, a TiO2-coated polycarbonate 1D GMR grating is fabricated by nanoimprinting and atomic layer deposition, which also exhibits good non-polarizing property and the potential of low-cost mass replication of such functional devices.
Multi-marginal optimal transport on Riemannian manifolds

We study a multi-marginal optimal transportation problem on a Riemannian manifold, with cost function given by the average distance squared from multiple points to their barycenter. Under a standard regularity condition on the first marginal, we prove that the optimal measure is unique and concentrated on the graph of a function over the first variable, thus inducing a Monge solution. This result generalizes McCann's polar factorization theorem on manifolds from two to several marginals, in the same sense that a well-known result of Gangbo and Swiech generalizes Brenier's polar factorization theorem on ${\Bbb R}^n$.
Two-dimensional pseudo-gravity model

We analyze a simple macroscopic model describing the evolution of a cloud of particles confined in a magneto-optical trap. The behavior of the particles is mainly driven by self–consistent attractive forces. In contrast to the standard model of gravitational forces, the force field does not result from a potential; moreover, the non linear coupling is more singular than the coupling based on the Poisson equation. We establish the existence of solutions, under a suitable smallness condition on the total mass, or, equivalently, for a sufficiently large diffusion coefficient. When a symmetry assumption is fulfilled, the solutions satisfy strengthened estimates (exponential moments). We also investigate the convergence of the N-particles description towards the PDE system in the mean field regime.
Unconventional superconductivity in ultrathin superconducting NbN films studied by scanning tunneling spectroscopy

Using scanning tunneling spectroscopy, we address the problem of the superconductor-insulator phase transition in homogeneously disordered ultrathin (2-15 nm) films of NbN. Samples thicker than 8 nm, for which the Ioffe-Regel parameter k(F)l >= 5.6, manifest a conventional superconductivity: a spatially homogeneous BCS-like gap, vanishing at the critical temperature, and a disordered vortex lattice in magnetic field. Upon thickness reduction, however, while k(F)l lowers, the STS reveals striking deviations from the BCS scenario, among which a progressive decrease of the coherence peak height and small spatial inhomogeneities. In addition, the gap below T-C develops on a spectral background, which becomes more and more ``V-shaped'' approaching the localization. The thinnest film (2.16 nm), while not being exactly at the superconductor-insulator transition (SIT) (T-C approximate to 0.4T(C)(bulk)), showed unconventional signatures such as the vanishing of the coherence peaks and the absence of vortices. This behavior suggests a weakening of long-range phase coherence, when approaching the SIT in this quasi-2D limit.