Miracle-dz/UniFAR-FTUs huggingface dataset:
The influence of surface roughness on the capacitance between a sphere and a plane

The problem of capacitance between a rough sphere and a rough plane very close to each other is studied. The problem is simplified by gathering the roughness of both members onto the plane. We begin by considering the case where the sphere and the plane are both ideally smooth. Starting from a known exact formula of the capacitance involving an infinite sum, we derive a simple and easy to use approximate expression. Then we consider the case where the sphere is smooth and the plane rough. The new formula for the capacitance involves an integral in which the weighting function is the height distribution. To validate this formula, the results of two experiments, during which the derivative of the capacitance with respect to the separation has been recorded, are considered. Comparison of the measurements with theoretical calculations indicates the approach is valid.
Deformation of Dirac Structures via L∞ Algebras

The deformation theory of a Dirac structure is controlled by a differential graded Lie algebra that depends on the choice of an auxiliary transversal Dirac structure; if the transversal is not involutive, one obtains an $L_\infty $ algebra instead. We develop a simplified method for describing this $L_\infty $ algebra and use it to prove that the $L_\infty $ algebras corresponding to different transversals are canonically $L_\infty $–isomorphic. In some cases, this isomorphism provides a formality map, as we show in several examples including (quasi)-Poisson geometry, Dirac structures on Lie groups, and Lie bialgebras. Finally, we apply our result to a classical problem in the deformation theory of complex manifolds; we provide explicit formulas for the Kodaira–Spencer deformation complex of a fixed small deformation of a complex manifold, in terms of the deformation complex of the original manifold.
Visibility of Shafarevich-Tate group of abelian varieties over number field extensions

Given an abelian variety J and an abelian subvariety A of J over a number field K, we study the visible elements of the Shafarevich-Tate group of A with respect to J over certain number field extension M of K. The notion of visible elements in Shafarevich-Tate group of an abelian variety was introduced by Mazur. In this article, we study the image of Visible elements of A with respect to J under the natural restriction map of the Galois cohomology of A over K to the Galois cohomology of A over M. In particular, for a fixed odd prime p, we investigate the conditions under which visible elements of order p can be produced over a quadratic extension or a degree p extension M of K.
Existence and Asymptotics of Abstract Functional Differential Equations

It is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear abstract functional differential equations in both, the finite and infinite delay case. A generalization of the integral solution will provide regularity results. Moreover, this method applies to derive uniform convergence on the halfline, and therefore general results on boundedness and various types of asymptotic almost periodicity.
Magnetic Properties of some Cubic Rare‐Earth‐Iron Compounds of the Type RFe2 and RxY1−xFe2

Magnetic measurements in fields up to 30 kOe and for temperatures between 4.2° and 1000°K have been performed for cubic Laves phase compounds RFe2 (R=Gd, Tb, Dy, Ho, Er, and Y) and RxY1−xFe2 (R=Gd, Tb, and Er). The Curie temperatures and saturation moments at 4.2°K are given. A compensation in the temperature dependence of the magnetization is only observed for the various compounds in a certain range of x values. Conditions for the occurrence of a compensation point are derived. For the compounds RxY1−xFe2 the iron moment remains constant for 0≤x≤0.8. Above x=0.8 the iron moment increases strongly. The variation of the Fe moments with x is discussed in terms of a nonlocalized moment associated with the iron ions. The moments shown by Er and Tb in ErFe2 and TbFe2 are both 8.3 μB. For most of the compounds RFe2 the lattice constants are given.
Spatial-Temporal characteristics of ion beamlets in the plasma sheet boundary layer of magnetotail

[1] The processes of nonadiabatic ion acceleration occurring in the vicinity of magnetic neutral lines produce highly accelerated (up to 2500 km/s) field-aligned ion beams (beamlets) with transient appearance streaming earthward in the plasma sheet boundary layer (PSBL) of the Earth’s magnetotail. Previous studies of these phenomena based on single spacecraft (s/c) missions supported the view that beamlets are temporal transients, since the typical time of a beamlet observation at a given s/c very rarely exceeds ∼1–2 min. Now multipoint Cluster observations have led to a new understanding of these phenomena with a spatial rather than a temporal structure. On the basis of 3-year Cluster measurements made in the PSBL, we present statistical evaluation of the beamlet duration (at least 5–15 min) and confirm well-manifested localization of the beamlet along Z and in some cases along Y directions, i.e., approximately across the lobe magnetic field. Earlier results reporting shorter beamlet observations could be understood by invoking not only PSBL flapping motions but also of an additional effect revealed by Cluster: earthward propagation of kink-like perturbations along the beamlet filaments. Phase velocity of these perturbations is of the order of the local Alfven velocity (V ∼ 600–1400 km/s) and related fast flappings of localized beamlet structures in the Y-Z direction significantly decreasing the time of their observation at a given spacecraft. Multipoint observations of beamlets revealed that they represent long-living (∼5–15 min) plasma filaments elongated along the lobe magnetic field (∼60–100RE) and strongly localized in direction perpendicular to the PSBL-lobe boundary (∼0.2–0.7RE). In some cases, it was also possible to estimate the width of beamlet in dawn-dusk direction which was of the order of fractions of RE.
Models of Twenty Asteroids from Photometric Data

We present models of the shapes and rotational states of selected asteroids based on data from the Uppsala Asteroid Photometric Catalogue. The results show a wide variety of shapes especially among the smaller asteroids. Few asteroids show clear signs of significant albedo variegation. Most rotational states are in reasonable agreement with those previously estimated with rough models. We discuss some practical aspects of photometric analysis and present a simple way of building one-spot models.
On spherically symmetric stellar models in general relativity

R ecently H . R . B eyer [1 ] a n d S . S . L in [7 ] investigated th e linearized equation fo r sm all perturbations near spherically sym m etric equilibria of a self-gravitating gas in th e Newtonian i. e . , non-relativistic theory o f stellar s t r u c tu r e . F o r a lo n g tim e a s tro p h y s ic is ts h a d b e e n b e lie v in g th a t the a sso c ia te d d iffe re n tia l e q u a tio n re d u c e s to a S tru m -L io u v ille eigenvalue p ro b le m , a lr e a d y f ro m t h e Eddington's w o r k in 1 9 1 9 , w ithou t any m athem atical proof. B ut th is w as not obvious, since the coefficients of the equation a r e q u ite s in g u la r . H . R . B ey e r h a s c lo sed th is g ap i n [1 ], and independently S. S. Lin has in [7] in a wider c o n te x t. T h e aim of th is article is to carry their results to the corresponding problem in general relativity. In order to do that, w e must investigate the qualitative properties of the s t r u c tu r e o f s o lu t io n s f o r th e e q u a tio n w h ic h g o v e rn s t h e spherically sym m etric static configurations of self-gravita ting gas in general relativity, since th e cefficients o f th e linearized equation fo r sm all perturbations are determined by these equilibrium configurations. The equation which governs spherically sym m etric equilibria in genera l re la tiv ity is form ulated by J. P. Oppenheimer and G . M. Volkoff i n [11], 1939, and th is has been fam iliar in astrophysical textbooks a s th e TOV e q u a tio n . B u t s till n o w no qualitative ana lysis o f th e s t ru c tu re o f th is e q u a tio n c a n b e fo u n d i n mathematical lite ra tu re s . E v e n in th e non-relativistic theory, in w hich th e equation for equilibria under th e equation o f state p = const.pr reduces to th e wellknown Lane-Emden equation, no fully mathematically rigorous treatments were found untill in 1972/73 the w o rk [6] by D. D. Joseph and T. S. Lundgren appeared, although many numerical computations and good intuitive analogies had been obtained a s found in th e Chandrasekhar's fam ous textbook [ 2 ] . Moreover when the relation p = const.pr holds only in asymptotic sense, for example in the equation of state for white dwarfs, there were no mathematical proof of the elementary fact that the radius of a solution obtained by the shooting methods is fin ite untill th e w o rk [8 ] b y th e author, 1 9 8 4 . In general relativity, the author did not know any mathematically rigorous study of the structure of the
Rough flows

We introduce in this work a concept of rough driver that somehow provides a rough path-like analogue of an enriched object associated with time-dependent vector fields. We use the machinery of approximate flows to build the integration theory of rough drivers and prove well-posedness results for rough differential equations on flows and continuity of the solution flow as a function of the generating rough driver. We show that the theory of semi-martingale stochastic flows developed in the 80's and early 90's fits nicely in this framework, and obtain as a consequence some strong approximation results for general semimartingale flows and provide a fresh look at large deviation theorems for 'Gaussian' stochastic flows.
Spectral discrimination of healthy and Ganoderma-infected oil palms from hyperspectral data

Although hyperspectral remote sensing has been used to study many agricultural phenomena such as crop stress and diseases, the potential use of this technique for detecting Ganoderma disease infestations and damage to oil palms under field conditions has not been explored to date. This research was conducted to investigate the feasibility of using a portable hyperspectral remote-sensing instrument to identify spectral differences between oil-palm leaves with and without Ganoderma infections. Reflectance spectra of samples representative of three classes of disease severity were collected. The most significant bands for spectral discrimination were selected from reflectance spectra and first derivatives of reflectance spectra. The significant wavelengths were identified using one-way analysis of variance. Then, a Jeffries–Matusita (JM) distance measurement was used to determine spectral separability between the classes. A maximum likelihood classifier method was used to classify the three classes based on the most significant wavelength spectral responses, and an error matrix was finally used to assess the accuracy of the classification.
VLBI OBSERVATIONS OF THE TYPE I b/c SUPERNOVA 2009bb

We report on VLBI as well as Very Large Array radio observations of the Type I b/c supernova 2009bb. The high radio luminosity of this supernova seems to require relativistic outflow, implying that the early radio emission was “engine-driven,” that is, driven by collimated outflow from a compact object, even though no gamma-ray emission was seen. The radio light curve shows a general decline, with a “bump” near t = 52 d, seen most prominently at 5 GHz. The light-curve bump could be either engine-driven or it might represent the turn-on of the normal radio emission from a supernova, driven by interaction with the circumstellar material rather than by the engine. We undertook VLBI observations to resolve SN 2009bb's relativistic outflow. Our observations constrain the angular outer radius at an age of 85 d to be <0.64 mas, corresponding to <4 × 1017 cm and an average apparent expansion speed of <1.74 c. This result is consistent with the moderately relativistic ejecta speeds implied by the radio luminosity and spectrum.
An application of the Duistermaat–Heckman
theorem and its extensions in Sasaki geometry

Building on an idea laid out by Martelli--Sparks--Yau, we use the Duistermaat-Heckman localization formula and an extension of it to give rational and explicit expressions of the volume, the total transversal scalar curvature and the Einstein--Hilbert functional, seen as functionals on the Sasaki cone (Reeb cone). Studying the leading terms we prove they are all proper. Among consequences we get that the Einstein-Hilbert functional attains its minimal value and each Sasaki cone possess at least one Reeb vector field with vanishing transverse Futaki invariant.
Internet of Things Based Chinese Whisper Jensen-Shannon Boost Node Clustering for Energy Efficient Routing in Wireless Sensor Networks

Wireless Sensor Networks (WSN) is a heterogeneous network that contains a lot of small gadgets called sensors which collect the physical or environmental conditions for example temperature, sound, vibration, weight, and so on, and transfers it to the base station. A machine's ability to mimic intelligent human behavior is broadly defined as machine learning, a branch of artificial intelligence which plays a significant role in WSN. In WSN, the method of routing is transferring the data between the sensor nodes and the base station. Many kinds of research were carried out for energy-efficient routing in WSN. But, the network lifetime and higher data delivery were not achieved by existing routing techniques. For the purpose of enhancing energy-efficient routing, an Internet of Things based Chinese Whisper Jensen-Shannon Boost Node Clustering (IoT-CWJSBNC) technique is introduced in WSN. This technique performs three processes, namely data collection, clustering, and routing. Initially, for sensing and gathering patient data at a distance, IoT devices are employed in sensor nodes. After the data collection process, sensor nodes are clustered into two groups, namely higher performance sensor nodes, and lesser performance sensor nodes by using the Chinese Whisper Jensen-Shannon Boosting technique. In IoT-CWJSBNC Technique, the Chinese Whisper Clustering method is considered as the weak cluster to partition the sensor nodes into two groups based on the Ruzicka similarity measure. Jensen-Shannon Boost method combines the results of weak learners to increase the clustering performance for efficient routing. After the clustering process, only higher-performance sensor node is considered. Then, the source node finds the neighbouring sensor node with higher signal strength for reducing the delay and packet loss rate during the routing process. WSN routing is carried out in this fashion to be energy-efficient. The simulation is administered on factors such as energy consumption, packet delivery ratio, packet loss rate, and therefore the end-to-end delay in relation to a number of patient data packets and sensor nodes. The results of the simulation show that the IoT-CWJSBNC technique effectively enhances the delivery of data packets and lowers energy consumption, packet loss rate, and delay than the traditional routing strategies.
Molecular genetic identi�cation of Opisthorchiidae cercariae from Bithyniidae snails of Chany Lake (South-Western Siberia, Russia)

The studies of the opisthorchiids larval stages associated with Вithyniidae snails can provide the important and the most reliable data for opisthorchiidoses foci characterization due to the least mobility of the snails among opisthorchiids host species. Since the foci of opisthorchiosis (caused by Opisthorchis felineus) and metorchiosis (caused by Metorchis bilis) are overlapping in the basins of the Ob and Irtysh rivers the obstacles in determining the species of cercariae signi�cantly reduce the accuracy of epidemiological conclusions regarding opisthorchiosis, which has a much higher medical signi�cance. Moreover, the di�culties with identi�cation are complicated by the fact that the focus of metorchiosis caused by Metorchis xanthosomus infecting birds of prey occur in the same territory. In this study we for the �rst time carried out the molecular genetic identi�cation of West-Siberian opisthorchiid cercariae to verify morphological identi�cation and con�rmed O. felineus main association with Bithynia troschelii snail and M. bilis ‒ with B. tentaculata snail. Thus, our study applied an integrated approach combining �rst the morphological identi�cation of opisthorchiid cercariae in Bithynia snails with subsequent molecular genetic identi�cation of the cercarial samples.
COMPARISON OF METHODS OF ISOLATION AND QUANTIFICATION OF CELL FREE DNA FROM PLASMA OF PATIENTS WITH BREAST CANCER

Objective: Cell-free DNA (cfDNA) released in response to necrosis in cancer patients The objective of this study was to compare the efficiency of two commercial and two manual methods for cell-free DNA extraction. as well as to search for a method that is easy to extract the DNA from the plasma and cost-effective. Methods : Plasma samples seven in number of patients of Breast Cancer was taken. We evaluated DNA quantity and its subsequent amplification obtained by four different cfDNA isolation methods; Modified Phenol Chloroform Isoamyl, Triton Heat Phenol, EpiQUik Circulating Cell-Free DNA isolation Easy kit” (EpiGentek) and “Nucleospin cfDNA kit”. Extracted DNA was quantified using Qubit and quantitative real-time PCR. Results: Quantity of cf DNA varied between different extractions methods of a total of seven samples analyzed. The highest quantity was found from the samples extracted from the Nucleospin XS kit and the extraction efficiency was significantly higher in a pairwise comparison with the other three methods (p-value <0.0001). The concentration of the cfDNA obtained by all four methods was assessed on a Qubit fluorometer. The concentration was higher for the Nucleospin ˃ MPC ˃ THP ˃ Epiquik kit The qPCR values were consistently higher for Nucleospin XS as compared to all others. This indicates good amplifiability of Nucleospin XS Conclusion: We tested four methods of cf DNA extraction. In our hands, Nucleospin XS gave the best yield and amplifiability. It is a quick and cost-effective method and sensitive for quantification of cfDNA on Real-time PCR. Therefore, it is highly recommended for clinical use of plasma as a liquid biopsy.
An inverse theorem for the Gowers U^{s+1}[N]-norm (announcement)

In this note we announce the proof of the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s => 3; this is new for s => 4, the cases s = 1,2,3 having been previously established. More precisely we outline a proof (details of which will appear in a forthcoming paper) that if f : [N] -> [-1,1] is a function with || f ||_{U^{s+1}[N]} => \delta then there is a bounded-complexity s-step nilsequence F(g(n)\Gamma) which correlates with f, where the bounds on the complexity and correlation depend only on s and \delta. From previous results, this conjecture implies the Hardy-Littlewood prime tuples conjecture for any linear system of finite complexity. In particular, one obtains an asymptotic formula for the number of k-term arithmetic progressions p_1 3.
The B0.5IVe CoRoT target HD 49330 - I. Photometric analysis from CoRoT data

Context. Be stars undergo outbursts producing a circumstellar disk from the ejected material. The beating of non-radial pulsations has been put forward as a possible mechanism of ejection. Aims. We analyze the pulsational behavior of the early B0.5IVe star HD 49330 observed during the first CoRoT long run towards the Galactical anticenter (LRA 1). This Be star is located close to the lower edge of the β Cephei instability strip in the HR diagram and showed a 0.03 mag outburst during the CoRoT observations. It is thus an ideal case for testing the aforementioned hypothesis. Methods. We analyze the CoRoT light curve of HD 49330 using Fourier methods and non-linear least square fitting. Results. In this star, we find pulsation modes typical of β Cep stars (p modes) and SPB stars (g modes) with amplitude variations along the run directly correlated with the outburst. These results provide new clues about the origin of the Be phenomenon as well as strong constraints on the seismic modelling of Be stars.
Characteristic polynomial patterns in difference sets of matrices

We show that for every subset E of positive density in the set of integer square‐matrices with zero traces, there exists an integer k⩾1 such that the set of characteristic polynomials of matrices in E-E contains the set of all characteristic polynomials of integer matrices with zero traces and entries divisible by k . Our theorem is derived from results by Benoist–Quint on measure rigidity for actions on homogeneous spaces.
The energy balance in coronal holes and average quiet-sun regions

In this paper we construct emission measure curves for average coronal hole and quiet-Sun spectra taken during the Skylab mission with the Harvard College Observatory spectroheliometer. These curves are then used to discuss the implications for the energy balance in each region. We find that the coronal hole spectrum shows a smaller slope in the emission measure distribution, consistent with the expected expect effects of outflows. Models of constant cross section coronal loops with radiative losses balanced by the divergence of the thermal conduction flux predict an emission measure rise between 10/sup 5/ K and 10/sup 6/ K, consistent with the average quiet-Sun observations, but not with the cell center or network emission measure distributions.
Primitive forms and Frobenius structures on the Hurwitz spaces

The main goal of this paper is to introduce the notion of a primitive form for a generic family of Hurwitz covers of $\mathbb{P}^1$ with a fixed ramification profile over infinity. We prove that primitive forms are in one-to-one correspondence with semi-simple Frobenius structures on the base of the family. Furthermore, we introduce the notion of a polynomial primitive form and show that the corresponding class of Frobenius manifolds contains the Hurwitz Frobenius manifolds of Dubrovin. Finally, we apply our theory to investigate the relation between the Eynard--Orantin recursion and Frobenius manifolds.
On rigidity of trinomial hypersurfaces and factorial trinomial varieties

Trinomial varieties are affine varieties given by some special system of equations consisting of polynomials with three terms. Such varieties are total coordinate spaces of normal rational varieties with torus action of complexity one. For an affine variety X we consider the subgroup SAut(X) of the automorphism group generated by all algebraic subgroups isomorphic to the additive group of the ground field. An affine variety X is rigid if SAut(X) is trivial. In opposite an affine variety is flexible if SAut(X) acts transitively on the regular locus. Arzhantsev proved a criterium for a factorial trinomial hypersurface to be rigid. We give two generalizations of Arzhantsev's result: a criterium for an arbitrary trinomial hypersurface to be rigid and a criterium for a factorial trinomial variety to be rigid. Also a sufficient condition for a trinomial hypersurface to be flexible is obtained.
Minimum-clock-cycle Itoh-Tsujii algorithm hardware implementation for cryptography applications over GF(2m) fields

Inversion over finite fields is the most costly basic operation for diverse cryptographic applications, such as elliptic curve cryptography and others. The Itoh-Tsujii algorithm (ITA) provides high performance implementations for the inversion operation in standard bases through diverse versions like squarer-ITA, parallel squarer-ITA or quad-ITA. A new modification of the ITA algorithm allows the inversion over finite fields in a minimal number of clock cycles. The proposed implementations complete the inversion over GF(2233) or GF(2409) from only 10 clock cycles.