Miracle-dz/UniFAR-FTUs huggingface dataset:
On norm closed ideals in L(\ell_p\oplus\ell_q)

It is well known that the only proper non-trivial norm-closed ideal in the algebra L(X) for X=\ell_p (1 \le p < \infty) or X=c_0 is the ideal of compact operators. The next natural question is to describe all closed ideals of L(\ell_p\oplus\ell_q) for 1 \le p,q < \infty, p \neq q, or, equivalently, the closed ideals in L(\ell_p,\ell_q) for p < q. This paper shows that for 1 < p < 2 < q < \infty there are at least four distinct proper closed ideals in L(\ell_p,\ell_q), including one that has not been studied before. The proofs use various methods from Banach space theory.
Focusing Molecular Beams of NH3

The problem of forming molecular beams for use in ammonia masers is examined. It is shown theoretically and experimentally that through the use of a new type of parabolic focuser with a ``point source'' effuser, the molecular flow may either be reduced by a factor of 8, for the same power output, or the power output may be increased by a factor of 2 for the same molecular flow. A theory of beam formation in a multitube effuser is described. This shows that the most intense molecular beam is formed by an effuser of small overall diameter. Design considerations are discussed for parabolic, upper‐state focusers, and for coaxial, lower‐state focusers. The operation of a system is described, using a lower‐state focuser and an ionization detector, in which lower‐state molecules produced by maser oscillation may be detected.
The existence of designs via iterative absorption

In a recent breakthrough, Keevash proved the Existence conjecture for combinatorial designs, which has its roots in the 19th century. We give a new proof, based on the method of iterative absorption. Our main result concerns $K^{(r)}_{q}$-decompositions of hypergraphs whose clique distribution fulfils certain uniformity criteria. These criteria offer considerable flexibility. This enables us to strengthen the results of Keevash as well as to derive a number of new results, for example a resilience version and minimum degree version.
Random laser scattering pulse signal analysis in laser particle counter with lognormal distribution

The statistical distribution of natural phenomena is of great significance in studying the laws of nature. Here, in this paper, based on laser scattering particle counter, a simple random pulse signal generating and testing system is designed for studying the counting distributions of three typical objects including particles suspended in the air, standard particles, and background noises. Moreover, in order to have a deep understanding of the experimental results from laser scattering particle counter, a random process model is also proposed theoretically to study the random law of measured results. Both normal and lognormal distribution fittings are applied to analyze the experimental results, and we have proved that statistical amplitude and width distributions of particles suspended in the air, standard particles, and background noise match well with lognormal distribution when natural numbers are used as the variables. This study is an important reference for statistical data processing for laser scattering particle counter, moreover, it will also be a useful guide for designing laser scattering particle counter with high accuracy and processing speed.
The geometry of maximal components of the PSp(4, ℝ) character variety

In this paper we describe the space of maximal components of the character variety of surface group representations into PSp(4,R) and Sp(4,R). For every rank 2 real Lie group of Hermitian type, we construct a mapping class group invariant complex structure on the maximal components. For the groups PSp(4,R) and Sp(4,R), we give a mapping class group invariant parameterization of each maximal component as an explicit holomorphic fiber bundle over Teichmuller space. Special attention is put on the connected components which are singular, we give a precise local description of the singularities and their geometric interpretation. We also describe the quotient of the maximal components for PSp(4,R) and Sp(4,R) by the action of the mapping class group as a holomorphic submersion over the moduli space of curves. These results are proven in two steps, first we use Higgs bundles to give a non-mapping class group equivariant parameterization, then we prove an analogue of Labourie's conjecture for maximal PSp(4,R) representations.
An equal 18‐way low‐profile power divider for sparse antenna arrays using amplitude equalization network

An equal 18‐way power divider, using a half‐air‐filled stripline technique, is presented in this letter. An amplitude equalization network is designed to mitigate the amplitude imbalance of the multiplexed planar/quasi‐planar power‐division network. Optimized transmission paths are obtained based on a combination of 1‐6‐3 power division and a multilayer structure, which effectively reducing transmission losses. To validate the design, this power divider, which is used to feed a sparse antenna array, is designed, optimized, fabricated, and measured. The measured return loss was better than 18 dB, and the measured insertion loss was better than 1.55 dB over the range 7–10 GHz. The amplitude imbalance is better than 0.4 dB, and the phase imbalance is better than 7.3°. The measured results are in good agreement with the simulation results.
Pulse propagation in quantum wells with multiple valence subband structure

Using the Luttinger formulations, we have analyzed the propagation characteristics of an ultrashort (femtosecond) coherent radiation pulse in the transverse plane of a direct gap semiconductor quantum well waveguide structure (QWWS). The semiconductor QWWS is considered to possess degenerate valence subbands near the centre of the Brillouin zone. The photoinduced resonant transitions below the band edge to both 1s and 2s excitonic states from the light hole (lh) and heavy hole (hh) subbands have been considered. The cross-over betwen the lh and hh bands occurs in case of transverse plane where the light holes are found to play more dominant role than the heavy holes. We have analyzed the transient pulse propagation characteristics like pulse break-up and optical nutation. The transverse electric mode propagation is also studied in the QWWS assuming the same to behave as a three-layer asymmetric planar waveguide. Numerical analysis made for GaAs/AlGaAs QWWS duly shined by a 150 fs Ti:Sapphire laser shows good qualitative agreement of the present results with those available in literature.
Relationship between CME velocity and active region magnetic energy

We find an empirical relationship between the initial speed of Coronal Mass Ejection (CME) and the potential magnetic field energy of the associated active region (AR) that closely resembles the Sedov relation between the speed of a blast wave and the blast energy. We conclude that it is the magnetic energy of an AR that drives the CME. The restructuring of the AR field lines in the corona which can push material with Alfven speed and thus inject energy into the plasma on a time scale shorter than the dynamical time of the corona, is a likely process that can drive the CME. The empirical relationship allows the prediction of the maximum speed of a CME that can result from an AR of a given magnetic energy.
Time-Consistent Risk Measures for Continuous-Time Markov Chains

We develop an approach to time-consistent risk evaluation of continuous-time processes in Markov systems. Our analysis is based on dual representation of coherent risk measures, differentiability concepts for multivalued mappings, and a refined concept of time consistency. We prove that the risk measures are defined by a family of risk evaluation functionals (transition risk mappings), which depend on state, time, and the transition function. Their dual representations are risk multikernels of the Markov system. We introduce the concept of a semi-derivative of a risk multikernel and use it to generalize the concept of a generator of a Markov process. Using these semi-derivatives, we derive a system of ordinary differential equations that the risk evaluation must satisfy, which generalize the classical backward Kolmogorov equations for Markov processes. Additionally, we construct convergent discrete-time approximations to the continuous-time risk measures.
Complex-exponential fuzzy logic systems

By mapping information used by a fuzzy logic system (FLS) from Euclidean to Riemann space, we are able to obtain a formulation of the FLS on the complex plane, and thus exploit the properties of vector manipulations. This enables us to express an FLS in a complex-exponential summation form, and derive an expression for the recall error, using concepts from n-dimensional geometry. We also examine the performance of the complex-valued FLS in a system identification example, and compare it with that of an equivalent real-valued FLS.
EXPLICIT SOLUTION PROCESSES FOR NONLINEAR JUMP-DIFFUSION EQUATIONS

Recent studies have shown that the nonlinear jump-diffusion models give results which are in agreement with financial data. Here we provide linearization criteria together with transformations which linearize the nonlinear jump-diffusion models with compound Poisson processes. Furthermore, we introduce the stochastic integrating factor to solve the linear jump-diffusion equations. Extended Cox–Ingersoll–Ross, Brennan–Schwartz and Epstein models are shown to be linearizable and their explicit solutions are presented.
Fatou-type theorems and boundary value problems for elliptic systems in the upper half-space

We survey recent progress in a program aimed at proving general Fatou-type results and establishing the well-posedness of a variety of boundary value problems in the upper half-space ${\mathbb{R}}^n_{+}$ for second-order, homogeneous, constant complex coefficient, elliptic systems $L$, formulated in a manner that emphasizes pointwise nontangential boundary traces of the null-solutions of $L$ in ${\mathbb{R}}^n_{+}$.
Approximation and reconstruction of the electrostatic field in wire-plate precipitators by a low-order model

The numerical computation of the ionic space charge and electric field produced by corona discharge in a wire–plate electrostatic precipitator (ESP) is considered. The electrostatic problem is defined by a reduced set of the Maxwell equations. Since self-consistent conditions at the wire and at the plate cannot be specified a priori, a time-consuming iterative numerical procedure is required. The efficiency of all numerical solvers of the reduced Maxwell equations depends in particular on the accuracy of the initial guess solution. The objectives of this work are two: first, we propose a semianalytical technique based on the Karhunen–Loeve (KL) decomposition of the current density field J, which can significantly improve the performance of a numerical solver; second, we devise a procedure to reconstruct the complete electric field from a given J. The approximate solution of the current density field is based on the derivation of an analytical approximation J, which, added to a linear combination of few KL basis functions, constitutes an accurate approximation of J. In the first place, this result is useful for optimization procedures of the current density field, which involve the computation of many different configurations. Second, we show that from the current density field we can obtain an accurate estimate for the complete electrostatic field which can be used to speed up the convergence of the iterative procedure of standard numerical solvers.
Security Analysis of Triangle Channel-Based Physical Layer Key Generation in Wireless Backscatter Communications

Ambient backscatter communication (AmBC) enables ultra-low-power communications by backscattering ambient radio frequency (RF) signals and harvesting energy simultaneously. It has emerged as a cutting-edge technology for supporting a variety of Internet of Things (IoT) applications. However, existing research lacks effective secret key sharing schemes for safeguarding communications between resource-constrained backscatter devices (BDs) in AmBC systems. In this paper, we present, Tri-Channel, a novel physical layer key generation scheme between two BDs by multiplying downlink signals and backscatter signals to obtain the information of a triangle channel as a shared random secret source for key generation. In particular, we analyze the security of our scheme under both passive and active attacks, concretely Eavesdropping Attack (EA), Control Channel Attack (CCA), Signal Manipulative Attack (SMA), and Untrusted RF-Source Attack (URSA). Through theoretical analysis and simulations by comparing with a traditional scheme (named Tradi-Channel), we found that our scheme consistently outperforms the Tradi-Channel under the EA and two active attacks (CCA and SMA). In addition, it shows better security performance under URSA, which is proposed based on the unauthenticated characteristic of BDs in Tri-Channel, even though URSA is more vital than SMA. Concretely, Tri-Channel’s secret key rate (SKR) outperforms Tradi-Channel’s under the above four passive and active attacks. This implies that our scheme is advanced in terms of both security and efficiency of key generation. Numerous extensive simulations further prove our theoretical analysis results.
Twin paradox in compact spaces

Twins travelling at constant relative velocity will each see the other's time dilate leading to the apparent paradox that each twin believes the other ages more slowly. In a finite space, the twins can both be on inertial, periodic orbits so that they have the opportunity to compare their ages when their paths cross. As we show, they will agree on their respective ages and avoid the paradox. The resolution relies on the selection of a preferred frame singled out by the topology of the space.
Bandwidth-Enhanced Compact Circularly-Polarized Wearable Antenna With a Magneto-Electric Dipole

A compact broadband circularly-polarized wearable antenna is presented for wireless body area network (WBAN) off-body communications. The proposed antenna comprises two substrates, a semi-rigid substrate with low loss-tangent and a textile substrate, that can boost the antenna performance while maintaining wearer comfort. Initially, a crossed-dipole as a fundamental radiator that radiates a circularly polarized (CP) wave is printed on the semi-rigid substrate. A pair of L-shaped slits are loaded into crossed-dipole arm, which significantly miniaturizes the antenna size. A magneto-electric dipole as a parasitic element is loaded to widen axial ratio bandwidth (ARBW) and impedance bandwidth (IBW). A conductive textile is attached to the textile substrate as the ground plane to minimize the specific absorption rate (SAR). The simulated SAR at 5.85 GHz is below the US and EU limit standards. The proposed antenna has solved typical issues in wearable antenna design such as low gain, low radiation efficiency, large size, and narrow IBW and ARBW, while still providing comfortability to wearers.
Real numbers with polynomial continued fraction expansions

In this paper we show how to apply various techniques and theorems (including Pincherle's theorem, an extension of Euler's formula equating infinite series and continued fractions, an extension of the corresponding transformation that equates infinite products and continued fractions, extensions and contractions of continued fractions and the Bauer-Muir transformation) to derive infinite families of in-equivalent polynomial continued fractions in which each continued fraction has the same limit. This allows us, for example, to construct infinite families of polynomial continued fractions for famous constants like $\pi$ and $e$, $\zeta{(k)}$ (for each positive integer $k\geq 2$), various special functions evaluated at integral arguments and various algebraic numbers. We also pose several questions about the nature of the set of real numbers which have a polynomial continued fraction expansion.
A Hybrid Alternating Least Squares-TT-Cross Algorithm for Parametric PDEs

We consider the approximate solution of parametric PDEs using the low-rank Tensor Train (TT) decomposition. Such parametric PDEs arise for example in uncertainty quantification problems in engineering applications. We propose an algorithm that is a hybrid of the alternating least squares and the TT cross methods. It computes a TT approximation of the whole solution, which is beneficial when multiple quantities of interest are sought. This might be needed, for example, for the computation of the probability density function (PDF) via the maximum entropy method [Kavehrad and Joseph, IEEE Trans. Comm., 1986]. The new algorithm exploits and preserves the block diagonal structure of the discretized operator in stochastic collocation schemes. This disentangles computations of the spatial and parametric degrees of freedom in the TT representation. In particular, it only requires solving independent PDEs at a few parameter values, thus allowing the use of existing high performance PDE solvers. In our numerical experiments, we apply the new algorithm to the stochastic diffusion equation and compare it with preconditioned steepest descent in the TT format, as well as with (multilevel) quasi-Monte Carlo and dimension-adaptive sparse grids methods. For sufficiently smooth random fields the new approach is orders of magnitude faster.
Relationship between Social Anxiety Symptoms and Behavioral Impairment in Adolescents: The Moderating Role of Perfectionism and Learning Motivation

Numerous studies have found that adolescents with social anxiety disorder experience greater difficulty in school adjustment and show higher dropout rates. Perfectionism and learning motivation are known to be significant predictors of academic achievement; these factors may enhance or diminish behavioral impairment within the school setting. The purpose of the present study was to examine the relationship between social anxiety, learning motivation, perfectionism, and behavioral impairment within a community sample of adolescents. Five hundred ninety-four German middle school students aged 12-17 years (mean age = 14.60, SD=1.64; 59.4% female) were recruited through their schools to respond to a questionnaire package consisting of Spence Children’s Anxiety Scale, the Child and Adolescent Perfectionism Scale, impact supplement of the Strengths and Difficulties Questionnaire, and intrinsic values subscale of Motivational Strategies for Learning Questionnaire. Results of correlational and multiple regression analysis showed that social anxiety symptoms were a significant predictor of distress and behavioral impairment, especially in friendship and classroom learning domains. It was shown that intrinsic learning motivation promotes classroom learning in students with high levels of social anxiety, whereas perfectionism interferes with domains outside the classroom, such as friendships and leisure activities. Limitations and implications for future research were discussed.
Limiting Si/SiO2 interface roughness resulting from thermal oxidation

The changes effected by oxidation on purposely roughened and initially smooth Si surfaces are followed via atomic force microscopy and spectroscopic ellipsometry and a technique called spectroscopic immersion ellipsometry. Initially, rough and smooth Si surfaces yield opposite roughening trends upon thermal oxidation. Rough surfaces become smoother, and smooth surfaces become rougher, ultimately yielding a limiting roughness of about 0.3 nm root-mean square. A consideration of the distribution of surface roughness features plus the thermodynamics of small features are used to explain these trends. It is also reported that the changes of interface roughness are primarily the result of the oxidation reaction and not from the high temperatures.
Ho on Pt(111) as a single-atom memory bit: A quantum master equation analysis

Due to underlying symmetries the two degenerate angular-momentum ground states of a single holmium atom (with $J=8$) on a Pt(111) surface have exceptionally long lifetimes, as observed in recent scanning tunneling microscopy studies. This opens perspectives for the application as a single-atom memory bit. For control and read-out the atom is coupled to electronic contacts. Hence the spin dynamics of the system is governed by a quantum master equation. In general it cannot be reduced to a classical master equation in the basis of the unperturbed crystal-field Hamiltonian. Rather, depending on parameters and control fields, "environment induced superselection" principles choose the appropriate set of basis states, which in turn determines the specific relaxation channels and lifetimes. Our results suggest that in ideal situations the lifetimes should be even longer than observed in the experiment. We, therefore, investigate the influence of various perturbations. We also study the initialization process of the state of the Ho atom by applied voltage pulses and conclude that fast, high fidelity writing into the memory, on a 100ns timescale, should be possible.
Numerical computation of internal & external flows: fundamentals of numerical discretization

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Enumeration of Seidel matrices

In this paper Seidel matrices are studied, and their spectrum and several related algebraic properties are determined for order n ≤ 13. Based on this Seidel matrices with exactly three distinct eigenvalues of order n ≤ 23 are classified. One consequence of the computational results is that the maximum number of equiangular lines in R with common angle 1/5 is exactly 20.
Metamaterial‐based highly isolated MIMO antenna system for 5G smartphone application

A two‐port multiple‐input‐multiple‐output (MIMO) antenna system operating in the mm‐wave band for 5G applications is presented. The two elements of MIMO structure are separated from each other by 19 mm (1.9 λ ) and excited by microstrip feed. The MIMO elements are circular patches with round cuts at the edges to improve impedance bandwidth. Quadrilateral slot in the ground plane is designed to improve the radiation characteristics of the radiating element having size 18 ×19× 0.8 mm3. The MIMO design is simulated through CST. The proposed antenna works in 27–29 GHz range, providing a potential bandwidth of 2 GHz. Furthermore a gain is improved from 8.2 to 8.75 dB and efficiency increase from 85% to 88% and high isolation of 64 dB is achieved by placing 4‐elements of metamaterial with size 4.5 × 18 mm2 in the middle of two circular monopole antennas. The metamaterial gives us a band stop response and act as decoupler and enhance the isolation to reduce mutual coupling. By analyzing the radiation characteristics of the proposed design, in term of reflection coefficient, surface currents, reduced mutual coupling, suitable gain, envelope correlation coefficient (ECC), diversity gain (DG) and radiation pattern, the recommended antenna can be considered a good candidate for 5G applications.