Miracle-dz/UniFAR-FTUs huggingface dataset:
Some applications of the Stone-Weierstrass theorem to planar rational approximation

The Stone-Weierstrass theorem is used to prove two general results about algebras of continuous functions, and each of these yields a necessary and sufficient condition for the planar function algebras R(K) and C(K) to be coincident. We begin with a result which slightly extends the Stone-Weierstrass theorem. THEOREM 1. (Almost selfadjoint algebras are selfadjoint.) Let X be a compact Hausdorff space, and let f E C(X ). Suppose m and n are relatively prime positive integers. Let A be the closed subalgebra of C(X) generated by fam, fnl, and the constant functions. Then A = { g o f: g E C (f (X ))}. In particular, iff separates the points of X, then A = C(X). PROOF. Let K = f (X) and let B be the closed subalgebra of C(K) generated by zm, zn, and the constant functions. We claim B = C(K). By the usual Stone-Weierstrass theorem, it suffices to show that z E B and z E B. Now m B and n E B imply (Zm)n(zn)m E B, or rz2mn E B. Since the function h(u) = ul/2mn is uniformly approximable by polynomials on the interval [0, ||zj|2Kmn] and B is closed, it follows that Izl E B. Since (m, n) = 1, we can find integers a and b with am + bn = 1. Without loss of generality, we can assume that a > 0, b < 0. Then on K {0} we have Z = zam+bn = (zm)a/(zn)-b = (zm)a(zn)-b/lzl-2bn
Functional differences between the tonotopic and periodic cues in discrimination of melodic pitch intervals under a diatonic context

perceptual cues for melodic identities, it is impor- tant to clarify the role of tonotopicity and periodicity. A sequence of rippled noises (RN) and band-noises (BN) were used to com- pose melodic intervals. In RN stimuli, the delay time with which a white noise was added back to itself corresponded to the inverse of the target fundamental frequencies. With the RN stimuli, the main cue is assumed to be the periodic one. In the BN stimuli, the center frequencies corresponded to the fundamental frequencies of the target melodies. With this type of stimulus, the main cue is assumed to be the tonotopic one. Six musically trained listeners were asked to discriminate two melodic pitch intervals preceded by a diatonic scale with three response categories, i.e., "narrower," "equal," and "wider. " The standard interval started with either the tonic or the leading note of the tonal context provided by the preceding scale. Comparison intervals were either equal to, smaller, or larger than each standard interval by 20 cents. The position and width of discriminal dispersions were estimated on the basis of the ratios of three responses. BN were not. This suggests difficulty in identifying the size relation of melodic pitch intervals in the case of BN. Sec- ond, whole-tone standard intervals starting with the tonic in the diatonic context exhibited steeper dispersions with the RN stimuli than with the BN stimuli. This result indi- cates that melodic intervals of RN can yield the sense of "equality" more strongly on melodic interval discrimina- tion under a diatonic context than can that of BN.
Divisia price and quantity indices: 80 years after

This paper reviews and extends the theory of price and quantity indices which are defined as line integrals, the two types being those of Divisia and Montgomery. The properties of these indices are systematically explored, whereby in particular attention is paid to the path‐(in)dependency issue. Two sections discuss the problem of how to approximate the line integral indices when only data at discrete points of time are available. It appears that every bilateral index can be conceived as the outcome of a line integral index over a particular curve in price–quantity space. The classical position is that chained bilateral indices are rationalized by Divisia indices. This rationalization is only interesting when the Divisia indices themselves possess a proper foundation in economic theory. The final sections are therefore devoted to the role played by the Divisia indices in micro‐economic theory.
Adsorption-driven tuning of the electrical resistance of nanoporous gold

The electrical resistance of nanoporous gold prepared by dealloying is tuned by charging the surfaces of the porous structure in an electrolyte. Reversible variations in the resistance up to approximately 4% and 43% occur due to charging in the regimes of double layer charging and specific adsorption, respectively. Charging-induced variations in the electron density or of the volume cannot account for the resistance variation, indicating that this variation is primarily caused by charge-induced modifications of the charge carrier scattering at the solid-electrolyte interface. The relative resistance variation in nanoporous Au with surface charging is found to be much higher than reported for porous nanocrystalline Pt. This is due to the lesser resistance contribution from internal grain boundaries. The resistance variation in nanoporous Au is also higher than that found in thin films owing to the stronger surface scattering in the ligament structure compared to plan surfaces. We argue that the strong resi.
Analytical solutions for tsunami runup on a plane beach: single waves, N-waves and transient waves

In the literature it has so far been common practice to consider solitary waves and N-waves (composed of solitary waves) as the appropriate model of tsunamis approaching the shoreline. Unfortunately, this approach is based on a tie between the nonlinearity and the horizontal length scale (or duration) of the wave, which is not realistic for geophysical tsunamis. To resolve this problem, we first derive analytical solutions to the nonlinear shallow-water (NSW) equations for the runup/rundown of single waves, where the duration and the wave height can be specified separately. The formulation is then extended to cover leading depression N-waves composed of a superposition of positive and negative single waves. As a result the temporal variations of the runup elevation, the associated velocity and breaking criteria are specified in terms of polylogarithmic functions. Finally, we consider incoming transient wavetrains generated by monopole and dipole disturbances in the deep ocean. The evolution of these wavetrains, while travelling a considerable distance over a constant depth, is influenced by weak dispersion and is governed by the linear Korteweg–De Vries (KdV) equation. This process is described by a convolution integral involving the Airy function. The runup on the plane sloping beach is then determined by another convolution integral involving the incoming time series at the foot of the slope. A good agreement with numerical model results is demonstrated.
2.5D forward for the transient electromagnetic response of a block linear resistivity distribution

This paper presents a 2.5-dimensional finite element forward algorithm for calculating transient electromagnetic responses by a magnetic source when the conductivity varies continuously within each block. The main differences between this method and those in previous works are as follows: the conductivity parameter in a mesh cell varies linearly but is not a uniform value; in modelling transient electromagnetic method (TEM) data, the electromagnetic field is separated into a primary (background) and a secondary (scattered) field to avoid a source singularity. The background field is solved by an analytical method where only the components of electric and magnetic fields along-strike of a geoelectric structure are computed, and the secondary field caused by anomalous bodies is computed numerically. Finally, numerical checks of several typical examples against analytical solutions show that the solution provides accurate results.
The estimations of neutron star mass and radius by the kHz QPOs

The kHz quasi-periodic oscillations (QPOs) have been detected by the RXTE satellite in about thirty neutron stars (NSs) in low mass X-ray binaries (LMXBs), which are usually interpreted to be related to the Keplerian motions in the orbit close to NS surface where the accreted matter is sucked onto the star. Based on the MHD Alfven wave oscillation model and the relativistic precession model for the neutron star (NS) kHz QPOs, estimations of mass M and radius R of some NSs are given, which can give clues to evaluate the models. Furthermore, comparisons with theoretical M -R relations by stellar equations of state (EOSs) are presented (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling of the space invariant optical systems with a spatially incoherent illumination

A study of imaging in an isoplanatic optical setup with a spatially incoherent illumination is presented. In such optical setups a light intensity distribution in an image plane can be calculated by a convolution of an input field with a Point Spread Function (PSF). Additionally a numerical simulation of incoherent monochromatic illumination is done by an integration of intensity images obtained with different random initial phase distributions (equivalent to a long exposure with a rotating diffuser in an optical setup). When an optical system is non space-invariant the point source image changes in various regions of the image plane and imaging simulation becomes complicated. Method with a simple convolution with PSF distribution cannot be applied because there is no one well defined PSF for the whole optical setup. This second method needs a bigger computational effort but can provide imaging modelling for both isoplanatic and non space invariant situations. In this contribution we compare the two mentioned methods in terms of imaging quality and its agreement with theoretical expectations. We give some statistical analysis of a contrast and noise level of the obtained pictures. We discuss the advantages and limitations of both modelling techniques for typical greyscale test patterns.
Sources and sinks of radiative energy from 30 to 90 km

The absorption of solar radiation and the exchange of long-wave terrestrial radiation are computed for the 30 to 90 km region for all latitudes using the climatological mean temperatures given by Murgatroyd (1957). Over most of the earth's surface (approximately 30° in the winter hemisphere to 60° in the summer hemisphere) there is a close approach to radiative equilibrium at all the levels considered. In the polar regions, however, there is a significant departure from radiative equilibrium with excess heating during the summer and excess cooling during the winter.
An Evaluation of the Safety Effectiveness and Cost of Autonomous Vehicles Based on Multivariable Coupling

There is a need for in-depth studies of autonomous vehicle safety that evaluate the effectiveness of safety functions and different “atomic” technology combinations for vehicles and roads. In this paper, we provide a crash avoidance effectiveness evaluation model for autonomous vehicles enabled with different sensor combinations based on multiple variables of 14 different “atomic” sensing technologies on the vehicle side and road side, 52 safety functions, and 14 accident types. Meanwhile, a cost-sharing model is developed based on the traveled distance during the life cycle of vehicles and based on the traffic flow over the life cycle of roads to evaluate the unit cost per km of different “atomic” technology combinations. The results clearly show that the cost increases with the addition of “atomic” sensing technologies on the vehicle side, while an increase in crash avoidance effectiveness decreases. It is necessary to switch to V2X and to introduce roadside “atomic” technology combinations to realize better safety effectiveness at a lower cost for vehicles. In addition, a map that covers the safety effectiveness and cost per kilometer of all “atomic” technology combinations is calculated for decision-makers to select combinations under the preconditions of cost and safety.
Algorithm 489: the algorithm SELECT—for finding the ith smallest of n elements [M1]

SELECT will rearrange the values of array segment X[L: R] so that X[K] (for some given K; L ≤ K ≤ R) will contain the (K-L+1)-th smallest value, L ≤ I ≤ K will imply X[I] ≤ X[K], and K ≤ I ≤ R will imply X[I] ≥ X[K. While SELECT is thus functionally equivalent to Hoare's algorithm FIND [1], it is significantly faster on the average due to the effective use of sampling to determine the element T about which to partition X. The average time over 25 trials required by SELECT and FIND to determine the median of n elements was found experimentally to be: n 500 1000 5000 10000 SELECT 89 ms. 141 ms. 493 ms. 877 ms. FIND 104 ms. 197 ms. 1029 ms. 1964 ms. The arbitrary constants 600, . 5, and . 5 appearing in the algorithm minimize execution time on the particular machine used. SELECT has been shown to run in time asymptotically proportional to N + min (I, N-I), where N = L - R + 1 and I = K - L + 1. A lower bound on the running time within 9 percent of this value has also been proved [2]. Sites [3] has proved SELECT terminates.
Effects of anode materials on the performance of explosive field emission diodes

Explosive field-emission cathodes have been the electron emitter of choice, and often necessity, for high-power microwave (HPM) tubes for many years. The materials typically used for these cathodes range from polymer and cotton velvets, to metals such as stainless steel, and to carbon materials such as bulk carbon and carbon fibers. With several notable exceptions, the issues of the anode and its composition have been largely ignored. Generally, the diode performance, such as current levels, impedance collapse, and out-gassing, have been attributed to the cathode alone rather than to the combination of the cathode and anode. In this paper, we investigate the affects of various anode materials on the performance of explosive field emission cathodes. We show that bipolar flow significantly and rapidly alter diode performance at lower voltage and energy densities than usually observed. We show also the effects of anode material choice on out-gassing, and diode conditioning. Experiments have shown that bipolar flow is a significant issue in diode performance for even short pulses. The theoretical aspects of the diodes are discussed, with a comparison of experiment to theory.
Design of nonlinear regulators for linear plants

A procedure for designing stable nonlinear control laws for linear plants is presented. The design is based on an inverse optimal control problem with the closed form controller being directly given by the solution of a set of linear algebraic equations. The nonlinear controllers can be used to produce saturation effects on particular states, and an example is included to illustrate the results.
Nanomedicine: New Frontiers in Fighting Microbial Infections

Microbes have dominated life on Earth for the past two billion years, despite facing a variety of obstacles. In the 20th century, antibiotics and immunizations brought about these changes. Since then, microorganisms have acquired resistance, and various infectious diseases have been able to avoid being treated with traditionally developed vaccines. Antibiotic resistance and pathogenicity have surpassed antibiotic discovery in terms of importance over the course of the past few decades. These shifts have resulted in tremendous economic and health repercussions across the board for all socioeconomic levels; thus, we require ground-breaking innovations to effectively manage microbial infections and to provide long-term solutions. The pharmaceutical and biotechnology sectors have been radically altered as a result of nanomedicine, and this trend is now spreading to the antibacterial research community. Here, we examine the role that nanomedicine plays in the prevention of microbial infections, including topics such as diagnosis, antimicrobial therapy, pharmaceutical administration, and immunizations, as well as the opportunities and challenges that lie ahead.
Streaming Data Processing

Aims: The data which is continuously being produced by hundreds of thousands of data sources is recognized as streamed data. The data which is processed via this kind of source is relatively smaller in size and is being sent at the same time it is generated. Study Design: In streaming data, the data range is so wide like the telemetry from interconnected devices or other such forms of data with the inclusion of certain web applications. This information should be handled consecutively and steadily on a record-by-record premise or throughout sliding time windows and utilized for a wide assortment of examinations including relationships, totals, separating, and inspecting. Place and Duration of Study: Service usage (for metering and billing), server activity, website clicks, and the geo-location of devices, people, and physical goods are just a few of the many aspects of a company's business and customer activity that can be seen through this type of analysis. It also enables companies to respond quickly to new arising situations. Methodology: The research methodology is used for the current research work is the qualitative method through which the research studies of a similar domain are studied thoroughly. It has been analyzed that the specified changes in the large volumes of data can better be managed through stream data processing. Results: The flaws of batch data processing are better dealt with through the usage of streaming data processing agenda. Real-time monitoring as well as response functionality are the keys to success in the given method of data processing. Conclusion: Stream data processing connects analytics and applications. Because multiple systems can be constructed using the same architecture, this makes the construction of the infrastructure a similar architecture. It additionally allows designers to fabricate applications that utilize scientific outcomes to straightforwardly answer information experiences and make a move.
Systematic Mapping of the Social Construction of Learning (2015-2020): Challenges for Online Learning Environments

The purpose of this study is to identify and characterize the state of social construction of learning in virtual communities within online learning environments and to identify the advances and research challenges of social learning. The method was a systematic mapping to analyze the evidence published on the topic in 2015-2020. We automatically searched the Scopus and Web of Science databases, applying inclusion and exclusion criteria to obtain the maximum relevant information. The pre-designed search strategy resulted in 187 articles. The main research topic addressed in most of these is learning as a social construction in training contexts, primarily virtual communities. In higher education, the United States is the country with the most active researchers on this topic. In addition, the most significant findings show that in a virtual learning community, social and cognitive interactions with teaching presence are crucial for students to build knowledge and achieve a higher level of learning. This study describes challenges related to the various methodologies, geographical scope, and types of social construction learning in virtual learning communities. This research is intended to be of value to teachers, decision-makers, designers of research and researchers interested in the social construction of learning in online learning environments.
Characterization of the First Animal Toxin Acting as an Antagonist on AT1 Receptor

The renin-angiotensin system (RAS) is one of the main regulatory systems of cardiovascular homeostasis. It is mainly composed of angiotensin-converting enzyme (ACE) and angiotensin II receptors AT1 and AT2. ACE and AT1 are targets of choice for the treatment of hypertension, whereas the AT2 receptor is still not exploited due to the lack of knowledge of its physiological properties. Peptide toxins from venoms display multiple biological functions associated with varied chemical and structural properties. If Brazilian viper toxins have been described to inhibit ACE, no animal toxin is known to act on AT1/AT2 receptors. We screened a library of toxins on angiotensin II receptors with a radioligand competition binding assay. Functional characterization of the selected toxin was conducted by measuring second messenger production, G-protein activation and β-arrestin 2 recruitment using bioluminescence resonance energy transfer (BRET) based biosensors. We identified one original toxin, A-CTX-cMila, which is a 7-residues cyclic peptide from Conus miliaris with no homology sequence with known angiotensin peptides nor identified toxins, displaying a 100-fold selectivity for AT1 over AT2. This toxin shows a competitive antagonism mode of action on AT1, blocking Gαq, Gαi3, GαoA, β-arrestin 2 pathways and ERK1/2 activation. These results describe the first animal toxin active on angiotensin II receptors.
Breast Tuberculosis: A Case Report

Breast tuberculosis (BTB) is a rare manifestation of tuberculosis (TB), and it is more common in countries with a high incidence of TB. We describe a case of a 36-year-old Angolan woman, who had a history of breast reduction surgery, presenting with right breast enlargement, pain, purulent discharge through multiple skin openings, fever, and abdominal pain, progressively worsening in the past year. She had already undergone several surgical drainages and six months of treatment with ciprofloxacin, with no improvement. Breast ultrasound and MRI were performed, which revealed a large fluid collection, with several small abscesses and surrounding adenopathies, complicated by multiple fistulae. The fluid was drained through needle aspiration, which was found to be sterile for bacteria, mycobacteria, and fungi. A lymph node biopsy showed necrosis without granulomas, and the biopsy culture was positive for Mycobacterium tuberculosis (Mt). This case shows how a rare manifestation can simulate bacterial breast abscesses or cancer, and hence a high index of suspicion is necessary to reach the correct diagnosis and ensure appropriate treatment delivery in these patients.
The anomaly of convex bodies

I write X for the point (x1, x2, …, xn) of n-dimensional Euclidean space Rn. The coordinates x1, x2, …, xn are real numbers. The origin (0, 0,…, 0) is denoted by O. If t is a real number, tX denotes the point (tx1, tx2, …, txn); in particular, − X is the point (−x1, −x2,…, −xn). Also X + Y denotes the point {x1 + y1, x2 + y2, …, xn + yn).
Experimental study of force-free, collinear plasma structures

Detailed measurements of the trapped magnetic fields and currents in plasma structures generated by conical theta-pinches are reported. Studies of these structures interacting with a magnetic barrier, and with each other in a collision at the centre of a magnetic mirror, are reported. The magnetic well formed by the collision has been studied by simultaneous use of several diagnostic techniques. The measurements are in agreement with a force-free, collinear magnetic field configuration (Wells 1972). Arguments relating superposability and collinearity of flow fields to these observations are given.