Miracle-dz/UniFAR-FTUs huggingface dataset:
Locally compact groups: maximal compact subgroups and N-groups

Abstract If G is a locally compact group such that G/G0 contains a uniform compactly generated nilpotent subgroup, then G has a maximal compact normal subgroup K such that G/G is a Lie group. A topological group G is an N-group if, for each neighbourhood U of the identity and each compact set C ⊂G, there is a neighbourhood V of the identity such that for each g∈G. Several results on N-groups are obtained and it is shown that a related weaker condition is equivalent to local finiteness for certain totally disconnected groups.
136-MHz/400-MHz radio-sky maps

A radio-sky map, covering the whole celestial sphere, is helpful for determining the system noise temperature of an earth-based satellite receiving system. Detailed sky maps for the 136- and 400-MHz space research (space-to-earth) satellite frequency bands have been generated, using a computer, by the National Aeronautics and Space Administration (NASA).
What we know on Central Bank Digital Currencies (so far)

A central bank digital currency (CBDC) is a topic that is only going to gain importance as a couple of nations have recently went line with a retail CBDC system, dozens of them are piloting it and there are even more who actively research the topic. In the process, many studies have already identified several important potential benefits of a CBDC as well as potential risks and costs. As is already well understood, a CBDC introduction can have a profound impact on all three monetary policy, financial stability and payment systems. This paper, trying to be a go-to starting point for those just exposed to the topic, thoroughly reviews all the benefits and risks/costs associated with a CBDC in the current literature as well as underlines key areas of this topic that need more research. In addition, we try to lay some ground for systematizing three-dimensional linkages between benefits, costs/risks and design choices by (i) discussing probable design choices needed for each item in the list of benefits and costs/risks to-be-mitigated and (ii) overviewing what other benefits and cost/risk-mitigation aims these design choices may be in conflict with. JEL Codes: E42, E50, G20
Stokes profile analysis and vector magnetic fields. VI: Fine scale structure of a sunspot

The vector magnetic field structure of a small, symmetric sunspot observed very close to disk center has been explored using data from the High Altitude Observatory/National Solar Observatory Advanced Stokes Polarimeter (ASP). This instrument provides, for the first time, quantitative information on sunspot photospheric vector magnetic fields with high angular resolution, as derived from full Stokes profiles of the Zeeman-sensitive Fe I line pair at 630 nm
Parameterized lifetime of radiation belt electrons interacting with lower‐band and upper‐band oblique chorus waves

In order to evaluate the electron lifetimes from quasi‐linear bounce‐averaged diffusion coefficients, a large amount of CPU time is required to compute scattering rates. To reduce computation time, we assume that the electron loss rates are a function of L shell and electron energy, allowing us to derive the parameterization of electron lifetime using a linear regression technique. We also present the parameterizations of lifetimes as a function of electron energy and ratios of plasma frequency to electron gyrofrequency at a fixed L shell. By considering the net loss rates due to lower‐band (0.05–0.5 |Ωce|) and upper‐band (0.5–0.7 |Ωce|) chorus waves propagating obliquely with respect to the ambient magnetic field, the parameterizations of electron lifetime for energies between 1 keV and 2 MeV are investigated in the outer radiation belt. The parameterized lifetimes indicate a strong functional dependence on electron energy, L shell, and the level of geomagnetic activity (Kp index), and are also dependent on the ratios of plasma frequency to electron gyrofrequency. During the storm time, the lifetimes for higher energy (>100 keV) electrons range from hours to days in the heart of the radiation belts. In contrast, the lifetimes for lower energy (<100 keV) electrons are mainly in the range from minutes to hours. Such parameterization efforts of radiation belt electron lifetimes are very significant for multi‐dimensional simulations of the dynamics of the radiation belt and ring current electrons.
Harmonic structure of Pc 3–5 magnetic pulsations observed at the Syowa‐Husafell conjugate pair

Strong evidence for the harmonic structure of Pc 3–5 magnetic pulsations observed on the ground has been provided by extracting coherent oscillations from magnetic pulsation data recorded at the Syowa-Husafell conjugate pair near L = 6 and then calculating the phase difference of the H components between the conjugate points as a function of local time. The model calculation suggests that the Pc 4/5 band observed in the frequency range ∼3–10 mHz is the fundamental mode of standing shear Alfven waves near L = 6, while the Pc 3 band with multiple harmonic structure observed in the frequency range ∼20–100 mHz is the higher harmonics (usually third to sixth harmonics). The second harmonic is not notable in comparison with other harmonics. It is found further that the fundamental mode and the higher harmonics are not always excited simultaneously. Therefore it is likely that when the frequency of the external driving source is in the Pc 3 range, it excites higher harmonics of standing shear Alfven waves near L = 6, while when the frequency of the external driving source is in the Pc 4/5 range, it excites the fundamental mode.
Nebular properties from far-infrared spectrosopy

We describe a semiempirical methodology-based on measurements of far-infrared (FIR) lines-that yields information on electron densities in regions where various ionic species exist, effective temperatures (T(sub eff)) for stars ionizing H II regions, and gas-phase heavy element abundances. Although this capability has long been available via optical data, the special features of FIR lines-relative insensitivity to extinction and electron temperature variations-extend the analysis ability. Several line ratios serve as diagnostics of electron density, N(sub e), probing different ionization conditions and different density regimes. The more N(sub e)-diagnostic observations made, the more reliable will be the deciphering of the actual variation in density throughout a nebula. A method to estimate T(sub eff) from the FIR (N III)/(N II) line ratio requires that the nebula be ionization bounded and that substantially all of the flux from the revevant lines be observed. However, to estimate T(sub eff) by a second method that uses the ratio of FIR (S III)/(O III) lines, an ionization-bounded nebula is a sufficient, but not necessary, condition. These restrictions are unnecessary for estimating densities and heavy element abundances. We show that a fairly general determination of metallicity, via the S/H ratio, may be made for H II regions with observations of just two lines-(S III) 19 micron and a hydrogen recombination line (or appropriate substitute). These techniques are applied to recent FIR data for the G333.6-0.2 H II region, including application to the recently measured (N II) 122 and 205 micron lines.
Effect of Surface Roughness on Room-Temperature Wafer Bonding by Ar Beam Surface Activation

Using Ar beam etching in vacuum, strong bonding of Si wafers is attained at room temperature. With appropriate etching time, the bonding occurs spontaneously without any load to force two wafers together. However, surface roughness of the wafers increases during Ar beam etching. Because surface roughness has a strong influence on wafer bonding, long etching time degrades the bonding strength. Using atomic force microscope, we measured surface roughness enhancement caused by Ar beam etching, and investigated the relationship between surface roughness and bonding properties such as strength and interfacial voids. The results agree well with theoretical predictions using elastic theory and energy gain by bond formation. A guideline for successful room-temperature bonding is proposed from these results.
Multiple channel queues in heavy traffic. II: sequences, networks, and batches

This paper is a sequel to [7], in which heavy traffic limit theorems were proved for various stochastic processes arising in a single queueing facility with r arrival channels and s service channels. Here we prove similar theorems for sequences of such queueing facilities. The same heavy traffic behavior prevails in many cases in this more general setting, but new heavy traffic behavior is observed when the sequence of traffic intensities associated with the sequence of queueing facilities approaches the critical value (ρ = 1) at appropriate rates.
On cyclic maps

Throughout X will denote a connected, finite C.W. complex. Let G be a subgroup of ∑n, the symmetric group, which acts transitively on the Cartesian product, Xn, of the space X. A map f:Xn→X is G-symmetric if it commutes with the action of G. If x0εX is a base point let i:X→Xn denote the inclusion, i(x) = (x,x0, …,x0). In ((6); (7); (11)–(13)) the following problem is posed: if X is an orientable topological n-manifold, what is the set of integers which may be obtained as the degree of(f.i) where f is a G-symmetric map? The degree of(f.i) is called the James number of f. If G = ∑n(G = Zn) a G-symmetric map will be called a symmetric map (a cyclic map). If X = Sn, the n-sphere, this problem has been studied in ((6)–(8), (11)–(13))
On groups with decomposable commutator subgroups

Let G be a group. We define λ(G) to be the smallest integer n such that every element of the commutator subgroup G′ is a product of n commutators. Ito [4] has shown that λ (An)= 1 for all n. Thompson [7] has shown that λ (SLn(q))= 1 for all n and q. In fact, there is no known simple group G such that λ(G)>1. However, there do exist such perfect groups (cf. [7]).
UNIFYING A MULTITUDE OF COMMON FIXED POINT THEOREMS EMPLOYING AN IMPLICIT RELATION

A general common fixed point theorem for two pairs of weakly compatible mappings using an implicit function is proved without any continuity requirement which generalizes the result due to Popa (20, Theorem 3). In process, several previously known results due to Fisher, Kannan, Jeong and Rhoades, Imdad and Ali, Imdad and Khan, Khan, Shahzad and others are derived as special cases. Some related results and illustrative examples are also discussed. As an application of our main result, we prove an existence theorem for the solution of simultaneous Hammerstein type integral equations. As established in Jungck (12), a common fixed point theorem in metric spaces generally involves conditions on contraction, commutativity and continuity of the involved mappings besides a suitable containment of range of one mapping into the range of other. To prove a new metrical common fixed point theorem one is always required to improve one or more of these conditions. Of all these four conditions, the means of improving contraction condition to prove new results on fixed and common fixed point is much discussed which continue to attract the attention of the researchers of this domain. But in this paper we use an implicit function due to Popa (20). The tradition of improving commutativity condition in common fixed point theorems was initiated by Sessa (21). Inspired by the definition of weak com- mutativity of Sessa (21), researchers of this domain, introduced several def- initions of weak commutativity such as: Compatible mappings, Compatible mappings of type (A), Compatible mappings of type (B), Compatible map- pings of type (P), Compatible mappings of type (C), Biased maps, R-weakly commuting mappings and some others whose lucid comparison and illustration
On the large‐eddy simulation of transitional wall‐bounded flows

The structure of the subgrid‐scale fields in plane channel flow has been studied at various stages of the transition process to turbulence. The residual stress and subgrid‐scale dissipation calculated using velocity fields generated by direct numerical simulations of the Navier–Stokes equations are significantly different from their counterparts in turbulent flows. The subgrid scale dissipation changes sign over extended areas of the channel, indicating energy flow from the small scales to the large scales. This reversed energy cascade becomes less pronounced at the later stages of transition. Standard residual stress models of the Smagorinsky type are excessively dissipative. Rescaling the model constant improves the prediction of the total (integrated) subgrid scale dissipation, but not that of the local one. Despite the somewhat excessive dissipation of the rescaled Smagorinsky model, the results of a large‐eddy simulation of transition on a flat‐plate boundary layer compare quite well with those of a direct simulation, and require only a small fraction of the computational effort.
Applications of a computer implementation of Poincaré’s theorem on fundamental polyhedra

PoincarCs Theorem asserts that a group F of isometries of hyperbolic space H is discrete if its generators act suitably on the boundary of some polyhedron in H, and when this happens a presentation of F can be derived from this action. We explain methods for deducing the precise hypotheses of the theorem from calculation in F when F is "algorithmi- cally defined", and we describe a file of Fortran programs that use these methods for groups F acting on the upper half space model of hyperbolic 3-space H. We exhibit one modest example of the application of these programs, and we summarize computations of repesenta- tions of groups PSL(2, 0) where 6 is an order in a complex quadratic number field. In the early 1880's H. Poincare discovered a general theorem allowing one to deduce the discreteness of, and a presentation for, a group G of isometries of hyperbolic space from its action on a hyperbolic polyhedron under certain condi- tions. Theorems of this sort are part of the foundations of his theories of Fuchsian and Kleinian groups that have become very popular again, and H. Seifert has recently given us a modern proof of a fairly general version of Poincare's Theorem in (12); see also (7). This theorem has been little used over the past century, perhaps partly because its hypotheses have seemed very difficult to verify for a given group G except in very special circumstances. One reason for doubting that Poincare's Theorem is unreasonably difficult to apply to fairly general discrete groups is that no general alternative method for accomplishing its tasks has been proposed. The present paper is devoted to demonstrating that Poincare's Theorem can indeed be applied to given groups in apparently difficult cases and that much of the work can be done by a computer. Our experience suggests that the theorem is really very helpful in guiding the user to an understanding of the details of the action of G starting from a state of near ignorance. An outline of this paper is as follows. In Section 1 we begin by stating Seifert's version of Poincare's Theorem and explaining how we would apply it to an " algorithmically defined" group G of isometries of hyperbolic space H 'o. In Section 2 we specialize to the situation, 00 , for which we wrote our file, Poincare', of Fortran
Invariant Sullivan–De Rham Forms on Cyclic Sets

Let Y be a topological space; and suppose that the circle group, S1, which will be denoted by G throughout this paper, is acting on Y. Then the equivariant cohomology HG*(Y) of Y is defined to be H*(YG), where YG=(EG×Y)/G, the Borel construction. Because of the bundle map YG→BG, the cohomology HG*(Y) is an H*(BG)‐module. With rational coefficients H*(BG; Q)=Q[u], where deg(u) = 2. And, when Y is a reasonably nice finite‐dimensional space, for example, a finite‐dimensional G‐CW‐complex, then the localized module HG*(Y;Q)[u‐1] is isomorphic to HG*(Y;Q)[u‐1] via the restriction homomorphism, where YG⊆Y is the fixed point set. (See, for example, [2].) That this very useful Localization Theorem does not generalize to infinite dimensional spaces can be seen by taking Y=EG, for example.
Experimental study of interfacial solitary waves

A small-scale experiment was conducted (in a 3 m long flume) to study interfacial long-waves in a two-immiscible-fluid system (water and petrol were used). Experiments and nonlinear theories are compared in terms of wave profiles, phase velocity and mainly frequency–amplitude relationships. As expected, the KdV solitary waves match the experiments for small-amplitude waves for all layer thickness ratios. The characteristics of ‘large’-amplitude waves (that is when the crest is close to the critical level – approximately located at mid-depth) asymptotically tend to be predicted by a ‘KdV-mKdV’ equation containing both quadratic and cubic nonlinear terms. In addition a numerical solution of the complete Euler equations, based on Fourier series expansions, is devised to describe solitary waves of intermediate amplitude. In all cases, solitary interfacial waves in this numerical theory tally with the experimental data. When the layer thicknesses are almost equal (ratio of lower layer to total depth equal to 0.4 or 0.63) both the KdV-mKdV and the numerical solutions match the experimental points.
Time series models with univariate margins in the convolution-closed infinitely divisible class

A unified way of obtaining stationary time series models with the univariate margins in the convolution-closed infinitely divisible class is presented. Special cases include gamma, inverse Gaussian, Poisson, negative binomial, and generalized Poisson margins. ARMA time series models obtain in the special case of normal margins, sometimes in a different stochastic representation. For the gamma and Poisson margins, some previously defined time series models are included, but for the negative binomial margin, the time series models are different and, in several ways, better than previously defined time series models. The models are related to multivariate distributions that extend a univariate distribution in the convolution-closed infinitely divisible class. Extensions to the non-stationary case and possible applications to modelling longitudinal data are mentioned.
The interaction between waves in the ion cyclotron range of frequencies and the plasma boundary

The interaction between the ion cyclotron resonance heating and the plasma edge is a vast and interlinked domain: the edge affects the radio frequency heating and the radio frequency heating affects the edge. This interaction between the radio frequency heating and the edge is-in view of the relation between the edge and overall plasma properties and performance-of utmost importance. The paper gives an overview of the topic, emphasizing basic concepts and recent results. The identification of the sheath rectification mechanism as the main cause for the influence of the RF on the edge, has permitted a better understanding of this domain and significant progress in the avoidance of the effects.
DEVELOPMENT OF POTATO-BORO-T. AMAN RICE CROPPING PATTERN AGAINST FALLOW-BORO-T. AMAN RICE CROPPING PATTERN AT MYMENSINGH

The experiment was conducted at Multiplication Testing Site (MLT) Trishal of On-Farm Research Division, Bangladesh Agricultural Research Institute, Mymensingh during 2017-18 and 2018-19 to evaluate the agro-economic performance of improved cropping pattern for increasing cropping intensity and system productivity as compared to farmers’ existing cropping pattern. The experiment was laid out in randomized complete block design with six dispersed replications. Two cropping patterns viz. improved pattern Potato (BARI Alu-25)-Boro (BRRI dhan28)-T. Aman rice (BRRI dhan49) and farmers existing cropping pattern Fallow-Boro (BRRI dhan29)- T. Aman rice (BRRI dhan49) were treatments variables of the experiment. Two years mean data showed that Potato-Boro-T. Aman rice cropping pattern produced higher tuber/grain yield as well as higher rice equivalent yield (30.53 t ha -1 yr -1 ), production efficiency (149 kg ha -1 day -1 ), land utilization index (74 %) and labour employment (367man-days ha -1 yr -1 ) than Fallow-Boro-T. Aman rice cropping pattern. This pattern also increased system productivity, production efficiency, land utilization index and labour employment by 158, 166, 26 and 51% higher over exiting pattern. The mean gross return (Tk. 481800 ha -1 ) and gross margin (Tk.235329 ha -1 ) of improved cropping pattern were 139 and 237% higher, respectively compared to existing pattern with 87% extra cost. The mean marginal benefit cost ratio (2.45) indicated superiority to improved cropping pattern over existing pattern. Experimental findings revealed that there is potential for greater adoption of intensified cropping systems with increased productivity and profitability as compared to rice–rice systems in Mymensingh.
Linear convective patterns in cylindrical geometry for unipolar injection

Linear stability theory is used to discriminate between the possible convective structures (axisymmetric rolls, axially independent columns, and general three‐dimensional patterns) in the case of unipolar injection between coaxial cylinders of arbitrary radii. The cases of weak, strong, and arbitrary finite injection, either from the inner or outer cylinder, are considered. In all cases three‐dimensional modes are found to be the least stable. Physical mechanisms involved are discussed thoroughly.
Lattice wave emission from a moving dislocation

A dislocation moving in a lattice accelerates and decelerates due to the lattice periodicity and emits lattice waves. Simulations of this process in square and triangular lattices have been presented. Under a small stress, less than 70-80% of the Peierls stress, a dislocation moving from an unstable position cannot overcome the next Peierls hill because it loses energy by emitting lattice waves. With a larger stress a long-distance motion of a dislocation is possible. When a dislocation moves slowly, lattice waves of dipolar type are emitted in the direction perpendicular to the motion of the dislocation. When the dislocation velocity is about half of the shear wave velocity, a V-shaped pattern of strong lattice vibration forms behind the moving dislocation because of the restricted propagation directions of the excited lattice waves. When the dislocation velocity exceeds 70% of the shear wave velocity, pair creation of dislocations occurs, which leads to dislocation cascading. A dislocation can move faster than the shear wave velocity in the square lattice, and there is no discontinuous change between subsonic and supersonic motions. The dislocation velocity is not proportional to the applied stress. The energy loss of the moving dislocation is about one order of magnitude larger than the theoretical value estimated by phonon-scattering mechanisms, even at room temperature.
The mathematical theory of non-uniform gases

The classic work on the mathematical theory of viscosity, thermal conduction and diffusion in non-uniform gases, based on the solution of the Maxwell-Boltzmann equations. This edition has been reset in an up-to-date format, and revised to include recent develop-ments of the theory in relation to molecular forces, the effects of internal energy, and phenomena in dense gases and plasmas.
High-temperature continuous-wave 3–6.1 μm “W” lasers with diamond-pressure-bond heat sinking

Optically pumped type-II W lasers emitting in the mid-infrared exhibited continuous-wave (cw) operating temperatures of 290 K at λ=3.0 μm and 210 K at λ=6.1 μm. Maximum cw output powers for 78 K were 260 mW at λ=3.1 μm and nearly 50 mW at λ=5.4 μm. These high maximum temperatures were achieved through the use of a diamond-pressure-bonding technique for heat sinking the semiconductor lasers. The thermal bond, which is accomplished through pressure alone, permits topside optical pumping through the diamond at wavelengths that would be absorbed by the substrate.