Finite Constant Research Articles

Ruin probability approximation for bidimensional Brownian risk model with tax

Let B(t)=(B1(t),B2(t)), t≥0 be a two-dimensional Brownian motion with independent components and define the γ-reflected process X(t)=(X1(t),X2(t))=B1(t)−c1t−γ1infs1∈[0,t](B1(s1)−c1s1),B2(t)−c2t−γ2infs2∈[0,t](B2(s2)−c2s2),with given finite constants c1,c2∈R and γ1,γ2∈[0,2). The goal of this paper is to derive the asymptotics of the ruin probability P∃t∈[0,T]:X1(t)>u,X2(t)>auas u→∞ for T>0.

Quantum geometrical properties of topological materials

The momentum space of topological insulators and topological superconductors is equipped with a quantum metric defined from the overlap of neighboring valence band states or quasihole states. We investigate the quantum geometrical properties of these materials within the framework of Dirac models and differential geometry. Their momentum space is found to be always a maximally symmetric space with a constant Ricci scalar, and the vacuum Einstein equation is satisfied in 3D with a finite cosmological constant. For linear Dirac models, several geometrical properties are found to be independent of the band gap, including a peculiar straight line geodesic, constant volume of the curved momentum space, and the exponential decay form of the nonlocal topological marker, indicating the peculiar yet universal quantum geometrical properties of these models.

Holographic Gauss-Bonnet transport

We extend the computational framework of [1] to analysis of shear and bulk viscosities in generic strongly coupled holographic Gauss-Bonnet gauge theories. The finite Gauss-Bonnet coupling constant encodes holographic plasma with non-equal central charges c≠a at the ultraviolet fixed point. In a simple model we discuss transport coefficients within the causality window −12≤c−ac≤12 of the theory.

The finite Jung constant in Banach spaces

AbstractWe study in this paper the finite Jung constant, its interplay with Kottman’s constant and its meaning regarding the geometry of Banach spaces.

ОБҐРУНТУВАННЯ ПАРАМЕТРІВ МЕТОДУ РОЗРАХУНКУ ХАРАКТЕРИСТИК ЕЛЕКТРОМАГНІТНОГО РОЗСІЮВАННЯ МЕТАЛЕВОЇ НАНОЧАСТИНКИ У ОПТИЧНОМУ ДІАПАЗОНІ

Structures of nanoparticles of noble metals in the optical range are of great interest in solving practical problems of building and using optical antennas and sensors for communication, creating solar cells, coatings for masking objects in the optical range and their detection. Currently, intensive research is being carried out on resonance effects during the scattering and absorption of light by such nanosized particles. There are both experimental methods of studying the characteristics of electromagnetic scattering of nanostructures in the optical range, and methods of mathematical modeling. Mathematical methods are subject to strict requirements regarding accuracy and ensuring the convergence of calculation results. The method of integral equations is widely used to model scattering from various objects with finite dielectric constants. At the same time, in the optical range, scattering on nanoparticles, as homogeneous resonant objects, has its own characteristics that affect the accuracy and convergence of the calculation algorithm. The article examines the issue of choosing and justifying the parameters of the method for calculating the characteristics of electromagnetic scattering of nanoparticles of noble metals of different sizes in the optical range, which are based on the application of a system of Müller integral equations. The internal convergence of the algorithm for calculating electromagnetic scattering characteristics depends on the size and shape of nanoparticles. When calculating according to the proposed numerical method, the number of nodes in which the current density was calculated was chosen in such a way that there was an internal convergence of the algorithm characterized by a given value . The required number of current nodes and the discretization step on the surface of one nanoparticle of two sizes (75x75x25 and 100x100x20) were obtained, which ensure internal convergence and the best accuracy of the proposed computational algorithm. Nanoparticles of these sizes will be used as the basis for the construction of various structures. The direction of further research is obtaining and analyzing the characteristics of electromagnetic scattering of various structures made of silver nanoparticles under different conditions of irradiation and polarization of the incident electromagnetic wave.

Effect of local active fluctuations on structure and dynamics of flexible biopolymers.

Active fluctuations play a significant role in the structure and dynamics of biopolymers (e.g. chromatin and cytoskeletal proteins) that are instrumental in the functioning of living cells. For a large range of experimentally accessible length and time scales, these polymers can be represented as flexible chains that are subjected to spatially and temporally varying fluctuating forces. In this work, we introduce a mathematical framework that correlates the spatial and temporal patterns of the fluctuations to different observables that describe the dynamics and conformations of the polymer. We demonstrate the power of this approach by analyzing the case of a point fluctuation on the polymer with an exponential decay of correlation in time with a finite time constant. Specifically, we identify the length and time scale over which the behavior of the polymer exhibits a significant departure from the behavior of a Rouse chain and the range of impact of the fluctuation along the chain. Furthermore, we show that the conformation of the polymer retains the memory of the active fluctuation from earlier times. Altogether, this work sets the basis for understanding and interpreting the role of spatio-temporal patterns of fluctuations in the dynamics, conformation, and functionality of biopolymers in living cells.

Active correction of window Faraday effects for ITER laser diagnostics

Measurement of the change in polarization of a laser beam traversing a magnetized plasma is a standard diagnostic technique for extracting key plasma parameters, including density and current profile. Depending on the polarization orientation of the incident laser beam relative to theplasma magnetic field, the polarization change is denoted as either Faraday rotation or Cotton-Mouton effect. On ITER three laser diagnostics will make use of this effect to make their measurements. Unfortunately, this effect is also evident when the laser beam passes through the vacuum window. The large magnetic field and finite verdet constant of the window material mean that on ITER this effect — in particular faraday rotation — is non-negligible, and needs to be disentangled from the desired measurement parameter. The Toroidal Interferometer-Polarimeter (TIP) and Density Interferometer-Polarimeter (DIP), in particular, are affected. Both diagnostics use lasers in the 5–10 μm range, and will use zinc-selenide (ZnSe) as the vacuum window material. In order to compensate for the unwanted window distortion a sensor is being developed to monitor the magnetic field perpendicular to the window and activelycorrectfor the faraday rotation in real time. The sensor consists of an inductive coil closely fitted just in front of the window disc. It comprises several turns of fine wire in center-tap configuration. Both the raw voltage signal, as well as the integrated signal, will be monitored to estimate the magnetic field through the window disk. The system is designed to measure fields up to B <1 T with an accuracy of 0.01 T, at frequencies of D.C. to 1 kHz. The backend electronics will leverage off similar technology developed for other ITER magnetics systems. Using the real-time magnetic field information, in conjunction with published and/or measured data on the verdet constant of the ZnSe window material, in-house developed software will estimate the faraday rotation induced by passing through the window.An initial prototype of the sensor has been fabricated and results from preliminary characterization trials of the system are presented. Detailed testing is planned for the future using the DIP system prototype currently under development.

Does the Hartman effect exist in triangular barriers

We study the phase, Larmor and dwell times of a particle scattered off triangular barriers (TBs). It is interesting that the dependences of dwell, reflective phase and Larmor times on the wave number, barrier width and height for a pair of mirror-symmetric (MS) exact triangular barriers (ETBs) are quite different, as the two ETBs have quite distinct scattering surfaces. In comparison, the dependence of the transmitted phase or Larmor times is exactly the same, since the transmitted amplitudes are the same for a pair of MS TBs. We further study the Hartman effect by defining the phase and Larmor velocities associated with the phase and Larmor times. We find no barrier width saturation effect for the transmitted and reflected times. This is indicated by the fact that all the velocities approach finite constants that are much smaller than the speed of light in vacuum for TBs with positive-slope impact faces. As for ETBs with vertical left edges, the naive velocities seem to also indicate the absence of the Hartman effect. These are quite distinct from rectangular barriers and may shed new light on the clarification of the tunneling time issues.

Special theory of relativity for a graded index fibre

The speed of light (c) in a vacuum is independent of the choice of frames to describe the propagation, according to the theory of relativity. We consider how light is characterised in a material, where the speed of light is different from that in a vacuum due to the finite dielectric constant. The phase velocity in a material is smaller thanc, such that the speed of a moving frame can be larger than the phase velocity, such that the frame can move faster than the speed of light in a material. Consequently, an unusual Doppler effect is expected, and the wavelength in the moving frame changes from the red-shift to the blue-shift upon increasing the speed of the frame. The corresponding energy of the light also changes sign from positive to negative, while momentum is always positive, leading to the changes of signs for the phase velocity and the helicity. In a graded index fibre, where the exact solution is available, even more complicated phenomena are expected, due to the finite effective mass of photons. Upon the increase of the energy gap, generated by optical confinements and optical orbital angular momentum, the effective mass of photons increases. If the gap is large enough, momentum starts to change the sign upon increasing the frame velocity, while the energy of photons is always positive. In this case, the phase velocity diverges if momentum is in agreement with the fame velocity. Contrary to the unusual behaviours of the phase velocity, the group velocity is always belowc. This thought experiment might be useful for considering insight into the polarisation state of light.

Efficient Client Selection Based on Contextual Combinatorial Multi-Arm Bandits

To overcome the challenge of limited bandwidth, client selection has been considered an effective method for optimizing Federated Learning (FL). However, since the volatility of the learning environment, the available clients exhibit some volatility over the training process in terms of client population, client data, training status, and transmitting status, which greatly increases the difficulty of client selection. To find a practical solution, we explore a client selection problem in volatile federated learning (Volatile FL). Specifically, we first derive the convergence analysis for non-convex and strongly convex cases to illustrate the main factors affecting the convergence speed. Then, we introduce the client utility to quantify the client’s contribution to model training and discuss the key problems of client selection in Volatile FL. For an efficient settlement, we propose CU-CS, a Combinatorial Multi-Arm Bandit (C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> MAB) based decision scheme for the proposed selection problem. Theoretically, we prove that the regret of CU-CS is strictly bounded by a finite constant, justifying its theoretical feasibility. The experimental results demonstrate that our method significantly boosts FL by speeding up model convergence, promoting model accuracy, and reducing energy consumption.

Group velocity and dispersion of Buchwald and Adams shelf waves. A new analytical approach

In this paper, a new analysis of the known topographic models of Rossby waves for piecewise exponential topography profiles is performed. A mathematical method is proposed that allows us to find analytically the group velocity and variance. A numerical comparison is made of the relations presented in the study of Buchwald and Adams and the dependencies obtained within the framework of a new analytical approach. Numerical comparative analysis showed that the discrepancy for the phase velocities lies in the range of five percent. For group speeds, the discrepancy reaches nineteen percent for the first mode and decreases for higher mode numbers. We also consider long-wave asymptotics of eigenfunctions. It is established that the long-wave limit for Rossby shelf waves has specifics: the longitudinal wave number tends to zero, and the transverse wave number reaches a certain finite positive constant, which is the greater the higher the mode number. It is shown that in the long-wave limit, Rossby shelf waves transform into shelf topographic currents, while there is a certain self-similarity for the phase and group velocities of shelf currents depending on the value of the topography gradient.

Quantifying Charge Extraction and Recombination Using the Rise and Decay of the Transient Photovoltage of Perovskite Solar Cells.

The extraction of photogenerated charge carriers and the generation of a photovoltage belong to the fundamental functionalities of any solar cell. These processes happen not instantaneously but rather come with finite time constants, e.g., a time constant related to the rise of the externally measured open circuit voltage following a short light pulse. Herein, a new method to analyze transient photovoltage measurements at different bias light intensities combining rise and decay times of the photovoltage. The approach uses a linearized version of a system of two coupled differential equations that are solved analytically by determining the eigenvalues of a 2×2 matrix. By comparison between the eigenvalues and the measured rise and decay times during a transient photovoltage measurement, the rates of carrier recombination and extraction as a function of bias voltage are determined, and establish a simple link between their ratio and the efficiency losses in the perovskite solar cell.

Scale invariant curvature perturbations from a spontaneously decaying scalar field

The evolution of superhorizon curvature perturbations in a two-component interacting Universe is considered. It is found that adiabatic modes conserve the total curvature perturbation , unless there are stages in which the rate of dissipation of one component into another is not constant. Moreover, our result shows that when the rate is varying it is possible for ‘isocurvature’ perturbations generated during reheating to alter the amplitude of an adiabatic curvature mode even when the mode is outside the horizon. Specifically, if an indefinitely large rate Γ for massive particles decaying into photons develops rapidly amid vanishingly small initial values (before decay) of the total curvature and Newtonian potential , such that the product and become a pair of finite and universal constants for all superhorizon scales afterwards, Harrison–Zel’dovich scale-invariant power spectrum could be synthesized from a homogeneous state without inflation at all.

Heterogeneous Integration of Freestanding Bilayer Oxide Membrane for Multiferroicity.

Transition metal oxides exhibit a plethora of electrical and magnetic properties described by their order parameters. In particular, ferroic orderings offer access to a rich spectrum of fundamental physics phenomena, in addition to a range of technological applications. The heterogeneous integration of ferroelectric and ferromagnetic materials is a fruitful way to design multiferroic oxides. The realization of freestanding heterogeneous membranes of multiferroic oxides is highly desirable. In this study, epitaxial BaTiO3 /La0.7 Sr0.3 MnO3 freestanding bilayer membranes are fabricated using pulsed laser epitaxy. The membrane displays ferroelectricity and ferromagnetism above room temperature accompanying the finite magnetoelectric coupling constant. This study reveals that a freestanding heterostructure can be used to manipulate the structural and emergent properties of the membrane. In the absence of the strain caused by the substrate, the change in orbital occupancy of the magnetic layer leads to the reorientation of the magnetic easy-axis, that is, perpendicular magnetic anisotropy. These results of designing multiferroic oxide membranes open new avenues to integrate such flexible membranes for electronic applications.

Reprint of: Testing for unit roots in heterogeneous panels

This paper proposes unit root tests for dynamic heterogeneous panels based on the mean of individual unit root statistics. In particular it proposes a standardized t-bar test statistic based on the (augmented) Dickey–Fuller statistics averaged across the groups. Under a general setting this statistic is shown to converge in probability to a standard normal variate sequentially with T (the time series dimension) →∞, followed by N (the cross sectional dimension) →∞. A diagonal convergence result with T and N→∞ while N/T→k,k being a finite non-negative constant, is also conjectured. In the special case where errors in individual Dickey–Fuller (DF) regressions are serially uncorrelated a modified version of the standardized t-bar statistic is shown to be distributed as standard normal as N→∞ for a fixed T, so long as T ¿ 5 in the case of DF regressions with intercepts and T ¿ 6 in the case of DF regressions with intercepts and linear time trends. An exact fixed N and T test is also developed using the simple average of the DF statistics. Monte Carlo results show that if a large enough lag order is selected for the underlying ADF regressions, then the small sample performances of the t-bar test is reasonably satisfactory and generally better than the test proposed by Levin and Lin (1993).

VFedCS: Optimizing Client Selection for Volatile Federated Learning

Federated learning (FL) has shown great potential as a privacy-preserving solution to training a centralized model based on local data from available clients. However, we argue that, over the course of training, the available clients may exhibit some volatility in terms of the client population, client data, and training status. Considering these volatilities, we propose a new learning scenario termed volatile federated learning (volatile FL) featuring set volatility, statistical volatility, and training volatility. The volatile client set along with the dynamic of clients’ data and the unreliable nature of clients (e.g., unintentional shutdown and network instability) greatly increase the difficulty of client selection. In this article, we formulate and decompose the global problem into two subproblems based on alternating minimization. For an efficient settlement for the proposed selection problem, we quantify the impact of clients’ data and resource heterogeneity for volatile FL and introduce the cumulative effective participation data (CEPD) as an optimization objective. Based on this, we propose upper confidence bound-based greedy selection, dubbed UCB-GS, to address the client selection problem in volatile FL. Theoretically, we prove that the regret of UCB-GS is strictly bounded by a finite constant, justifying its theoretical feasibility. Furthermore, experimental results show that our method significantly reduces the number of training rounds (by up to 62%) while increasing the global model’s accuracy by 7.51%.

On thermodynamic and ultraviolet stability bounds for bosonic lattice QCD models in Euclidean dimensions d = 2,3,4

We prove thermodynamic and ultraviolet stable stability bounds for lattice scalar QCD quantum models, with multiflavor real or complex scalar Bose matter fields and a compact, connected gauge Lie group [Formula: see text], [Formula: see text] with Lie algebra dimension [Formula: see text]. Our models are defined on a finite hypercubic lattice [Formula: see text], [Formula: see text], [Formula: see text], with [Formula: see text], even, sites on a side, [Formula: see text] sites, and with free boundary conditions. The models action is a sum of a minimally coupled Bose-gauge part and a Wilson pure-gauge plaquette action. We use local, scaled scalar multiflavor Bose fields. The scaling is global, [Formula: see text]-dependent and noncanonical, and corresponds to an a priori renormalization. The Wilson action is a sum over positive plaquette actions times a factor [Formula: see text], with the gauge coupling [Formula: see text] in [Formula: see text], [Formula: see text]. By local gauge invariance, to eliminate the excess of gauge variables, sometimes we use an enhanced temporal gauge, leaving only [Formula: see text] for [Formula: see text], retained bonds. Fixing this gauge does not alter the value of the partition function. Considering the original physical, unscaled partition function [Formula: see text], where [Formula: see text] is the unscaled (bare) hopping parameter and [Formula: see text] are the boson fields bare masses, and letting [Formula: see text] and [Formula: see text], we show that the scaled partition function [Formula: see text] satisfies the thermodynamic and ultraviolet stable stability bounds [Formula: see text], with finite constants [Formula: see text], independent of the lattice size [Formula: see text] of [Formula: see text] and the spacing [Formula: see text]. For the normalized finite-lattice free energy [Formula: see text], a finite thermodynamic limit ([Formula: see text]) for [Formula: see text], and then the continuum limit [Formula: see text], both exist in the sense of subsequences. They give the model normalized free energies [Formula: see text]. The finiteness of [Formula: see text] is the only question addressed here! The use of the Weyl integration formula is essential in showing these bounds. It allows us to replace the gauge integral over [Formula: see text] gauge bond matrix elements by the integration over its [Formula: see text] eigenvalues. A new global upper bound on the Wilson plaquette action is obtained, which is quadratic in the gluon fields. Our method bypasses the use of diamagnetic inequality and can be extended to treat more general lattices and Lie gauge groups.

Pulverized coal combustion computational modeling approach: A review

CFD (Computational fluid dynamics) is a tool, through which, the entire combustion process for pulverized coal combustion (PCC) can be predicted. The solid fuel combustion modeling is not as simple as gaseous or liquid fuel combustion modeling. In the solid fuel combustion process, various physical transformations and chemical reactions occur simultaneously. Therefore in the computational modeling approach for PCC, basic physical and chemical processes such as; turbulence, radiation, devolatilization, gas-phase combustion, char reaction and soot formation/reduction are integrated to obtain the desired results. However, in order to reach the desired accuracy, different computational models should be chosen carefully. In this review, various common models that are widely used in PCC simulation are discussed scientifically along with their modeling aspects. The basic advantages and disadvantages of these models are also discussed in this study. Moreover, different models preferred by various authors for pulverized coal combustion simulation process are also summarized. From the review, it has been observed that the eddy viscosity based two-equation turbulent models and Eulerian-Lagrangian multiphase approach are mostly preferred due to better computational economy. Two competing rate devolatilization model from various finite rate models and FG-DVC devolatilization model from various phenomenological models are mostly used for PCC. Diffusion kinetic control and Intrinsic char combustion models are mostly chosen to predict the char reaction. Finite reaction rate models are preferred when the computational economy is a concern, whereas phenomenological models provide results with better accuracy because in phenomenological models realistic inputs are given as input for simulation whereas, in finite rate models, finite rate constants are mostly empirical. Most of the gas phase models are given almost equal importance. Discrete ordinate (DO) is mostly used for PCC due to its ability of volumetric radiation calculation and the ability to evaluate radiation effect on the particle phase.

Periodic solutions of nonlinear ordinary differential equations computed by a boundary shape function method and a generalized derivative-free Newton method

In the paper, the period of an n-dimensional nonlinear dynamical system is computed by a formula derived in an (n+1)-dimensional augmented state space. The periodic conditions and nonlinear first-order ordinary differential equations constitute a specific periodic boundary value problem within a time interval, whose length is an unknown finite constant. Two periodic problems are considered: (I) boundary values are given and (II) boundary values are unknown. A boundary shape function method (BSFM), using the derived shape functions, is devised to an initial value problem with the initial values of new variables given, whereas the terminal values and period are determined by iterative algorithms. The periodic solutions obtained by the BSFM satisfy the periodic conditions automatically. For the sake of comparison, the iterative algorithms based on the shooting method are developed, directly implementing the Poincaré map with the fictitious time integration method to determine the periodic solutions, where the periodic conditions are transformed to a mathematically equivalent scalar equation. Owing to the implicit, non-differentiable and nonlinear property of the scalar equation, we develop a generalized derivative-free Newton method (GDFNM) to solve the periodic problem of case (I), which can pick up very accurate period through a few iterations. In numerical examples the computed order of convergence displays the merit of the proposed iterative algorithms. The BSFM and GDFNM are better than the shooting method from the aspects of convergence speed, accuracy and stability. A conventional Poincaré mapping method is introduced to solve the periodic problems with the same parameters. The BSFM converges faster and more accurate than the Poincaré mapping method and is less sensitive to the initial guesses of initial values and period.

Martingale Wasserstein inequality for probability measures in the convex order

It was shown by the authors that two one-dimensional probability measures in the convex order admit a martingale coupling with respect to which the integral of |x−y| is smaller than twice their W1-distance (Wasserstein distance with index 1). We showed that replacing |x−y| and W1 respectively with |x−y|ρ and Wρρ does not lead to a finite multiplicative constant. We show here that a finite constant is recovered when replacing Wρρ with the product of Wρ times the centred ρ-th moment of the second marginal to the power ρ−1. Then we study the generalisation of this new martingale Wasserstein inequality to higher dimension.