We consider a situation in which the forecaster has available M individual forecasts of a univariate target variable. We propose a 3‐step procedure designed to exploit the interrelationships among the M forecast‐error series (estimated from a large time‐varying parameter VAR model of the errors, using past observations) with the aim of obtaining more accurate predictions of future forecast errors.

This paper presents a new fuzzy time series forecasting model based on technical analysis, AP clustering and SVR model. Technical analysis indicators are divided into three categories to construct multivariate fuzzy logical relationships. AP clustering without specifying the number of clusters is used to obtain a suitable partition for the universe of discourse, and the representative exemplars are

We introduce the Tensor Auto‐Regressive (TAR) model for modeling time series data which is robust to model misspecification, seasonality and non‐linear trends. We develop a parameter estimation algorithm for the proposed model by using the 𝑡‐product, which allows us to model a three‐dimensional block of parameters. We use the Fast‐Fourier Transform, which allows for efficient and parallelizable computations

In natural rock masses, the shapes of three‐dimensional (3‐D) blocks cut by arbitrary fracture networks may be very complex. Owing to the geometric complexity and difficulty of mesh discretization of 3‐D blocks and fracture facets, explicit consideration of fracture networks in flow analysis of fractured porous medium (FPM) is very challenging. Using the numerical manifold method based on independent

This contribution is addressing the ultimate limit state design of massive three‐dimensional reinforced concrete structures based on a finite‐element implementation of yield design theory. The strength properties of plain concrete are modeled either by means of a tension cutoff Mohr Coulomb or a Rankine condition, while the contribution of the reinforcing bars is taken into account by means of a homogenization

The response presents three comments, which (i) explain theoretical background for the success of the explicit front advancing scheme by Zia and Lecampion (comment 1), (ii) suggest possible extensions (comment 2), and (iii) pay attention on expected limitations of the scheme to be checked by the authors in numerical experiments (comment 3). The response does not intend to present novel results: it

This study provides a retrospective of the Journal of Forecasting (JoF) between 1982 and 2019. Evidence shows a considerable increase in JoF’s productivity and influence since 1982. For example, a JoF article, on average, receives more than 18 citations and contributions from 65 nations appear in the journal. All articles have a forecasting implication but JoF encourages a wide range of contexts recently

For a nonorientable surface, the twist subgroup is an index 2 subgroup of the mapping class group generated by Dehn twists about two-sided simple closed curves. In this paper, we consider involution generators of the twist subgroup and give generating sets of involutions with smaller number of generators than the ones known in the literature using new techniques for finding involution generators.

We prove that for a free product G with free factor system 𝒢, any automorphism ϕ preserving 𝒢, atoroidal (in a sense relative to 𝒢) and none of whose power send two different conjugates of subgroups in 𝒢 on conjugates of themselves by the same element, gives rise to a semidirect product G⋊ϕℤ that is relatively hyperbolic with respect to suspensions of groups in 𝒢. We recover a theorem of Gautero–Lustig

The most popular algorithm for the nonuniform fast Fourier transform (NUFFT) uses the dilation of a kernel ϕ to spread (or interpolate) between given nonuniform points and a uniform upsampled grid, combined with an FFT and diagonal scaling (deconvolution) in frequency space. The high performance of the recent FINUFFT library is in part due to its use of a new “exponential of semicircle” kernel ϕ(z)=eβ1−z2

This paper explores essence of the fractional (0

We introduce Ψec(Rn), a discretization of Cartan's exterior calculus of differential forms using wavelets. Our construction consists of differential r-form wavelets with flexible directional localization that provide tight frames for the spaces Ωr(Rn) of forms in R2 and R3. By construction, the wavelets satisfy the de Rahm co-chain complex, the Hodge decomposition, and that the k-dimensional integral

SIAM Journal on Numerical Analysis, Volume 58, Issue 5, Page 2934-2952, January 2020. This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo technique for sampling the probability space, a continuation method with respect

SIAM Journal on Mathematical Analysis, Volume 52, Issue 5, Page 5001-5035, January 2020. This paper rigorously establishes the stabilization effect of a background magnetic field on electrically conducting fluids, a phenomenon that has been widely observed in physical experiments and numerical simulations. This study is based on a 2 dimensional (2D) magnetohydrodynamic (MHD) system in which the velocity

SIAM Journal on Mathematical Analysis, Volume 52, Issue 5, Page 4971-5000, January 2020. We prove that the time-harmonic solutions to Maxwell's equations in a three-dimensional exterior domain converge to a certain static solution as the frequency tends to zero. We work in weighted Sobolev spaces and construct new compactly supported replacements for Dirichlet--Neumann fields. Moreover, we even show

In 2006, Dafermos and Holzegel formulated the so-called AdS instability conjecture, stating that there exist arbitrarily small perturbations to AdS initial data which, under evolution by the Einstein vacuum equations for Λ < 0 with reflecting boundary conditions on conformal infinity ℐ, lead to the formation of black holes. The numerical study of this conjecture in the simpler setting of the spherically

Let (𝒳, d, μ) be a space of homogeneous type, in the sense of Coifman and Weiss, with the upper dimension ω. Assume that η ∈(0, 1) is the smoothness index of the wavelets on 𝒳 constructed by Auscher and Hytönen. In this article, via grand maximal functions, the authors introduce the Hardy–Lorentz spaces H*p,q(𝒳) with the optimal range p∈(ωω+η,∞) and q ∈ (0, ∞]. When and p∈(ωω+η,1]q ∈ (0, ∞], the

When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional 𝓗 in terms of the stream function and the thermocline. We also compute the second variation of the constrained

We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes equations for the velocity v, coupled with a diffusive variant of a combination of the Oldroyd-B and the Giesekus models for a tensor 𝔹. By a proper choice of the constitutive

This paper discusses equivalence conditions on entire solutions to eikonal-type nonlinear partial differential equations uz12+uz22=p(z1,z2)eg(z1,z2) in C2 for polynomials g(z1,z2),p(z1,z2). All our results are supplemented by examples for accuracy.

We deal with the characterization of entire solutions to the generalized parabolic 2-Hessian equation of the form ut=μ(F2(D2u)1/2) in Rn×(−∞,0]. We prove that any strictly 2-convex-monotone solution u=u(x,t)∈C4,2(Rn×(−∞,0]) must be a linear function of t plus a quadratic polynomial of x, under some assumptions on μ:(0,∞)→R, some growth conditions on u and the boundedness of the 3-Hessian of u from

We consider a linear system coming from a population dynamics model with age structuring and nonlocal boundary conditions. Our population dynamics model is a four-stage model with a second derivative with respect to the age variable. Using Banach fixed point theorem, we show the existence and unicity of a non negative solution and illustrations of numerical simulations are given.

In this paper, we investigate the following Chern-Simons-Schrödinger system{−Δu+V(x)u+A0u+A12u+A22u=f(x,u),x∈R2,∂1A2−∂2A1=−12u2,∂1A1+∂2A2=0,∂1A0=A2u2,∂2A0=−A1u2. where V is the potential, ∂1=∂∂x1,∂2=∂∂x2 for x=(x1,x2)∈R2, Aj:R2→R is the gauge field (j=0,1,2) and the nonlinearity f(x,s)∈C(R2×R,R) behaves like e4πs2 as |s|→+∞. If V and f are both asymptotically periodic at infinity, we prove the existence

Supposing that A(z) is an exponential polynomial of the formA(z)=H0(z)+H1(z)eζ1zn+⋯+Hm(z)eζmzn, where Hj's are entire and of order

We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch. As a consequence, we give very general conditions for these spaces to be nuclear. In particular, we obtain the corresponding results

The transonic channel flow problem is one of the most important problems in mathematical fluid dynamics. The structure of solutions near the sonic curve is a key part of the whole transonic flow problem. This paper constructs a local classical hyperbolic solution for the 3-D axisymmetric steady compressible full Euler equations with boundary data given on the degenerate hyperbolic curve. By introducing

In this paper, we consider the following nonlinear Schrödinger equation:

The Quasi-Newton method is one of the most effective methods using the first derivative for solving all unconstrained optimization problems. The Broyden family method plays an important role among the quasi-Newton algorithms. However, the study of the convergence of the classical Broyden family method is still not enough. While in the special case, BFGS method, there have been abundant achievements

In this paper, we consider the solutions of the non-homogeneous quasilinear elliptic obstacle problems involving measure data. At first we prove the existence of approximable solutions to these problems. Then we establish pointwise and oscillation estimates for the gradients of solutions via the nonlinear Wolff potentials, and these yield results on C1,α-regularity of solutions.

We study elliptic equations with quasilinear perturbation{Δu+12κuΔu2+ε∑i,j=1N(aij(u)Diju+12Dzaij(u)DiuDju)+f(u)+εh(u)=0,inΩ,u=0,on∂Ω, where Ω⊂RN,N≥3 is a smooth bounded domain, κ∈{0,1}, ε is a small parameter. Multiplicity result is proved by elliptic regularization method.

In this note, we consider the radial symmetry property of rotating vortex patches for the 2D incompressible Euler equations in the unit disk. By choosing a suitable vector field to deform the patch, we show that each simply-connected rotating vortex patch D with angular velocity Ω, Ω≥max⁡{1/2,(2l2)/(1−l2)2} or Ω≤−(2l2)/(1−l2)2, where l=supx∈D⁡|x|, must be a disk. The main idea of the proof, which has

We study the problem of inverting a restricted transverse ray transform on symmetric tensor fields in R3 using microlocal analysis techniques. We show that a symmetric m-tensor field can be recovered up to a known singular term and a smoothing term if its transverse ray transform is known along all lines intersecting a fixed smooth curve satisfying certain geometric conditions.

The aim of this paper is to prove the averaged null controllability property for a wave equation with an unknown velocity of propagation parameter and for parameter-dependent vibrating plate equation under the effect of a boundary control. The choice of the Hilbert uniqueness method seems to be the best-adapted method to our theory, where the key point to prove the desired result is an averaged inverse

Using a recursive formula for the Mellin transform Tn,a(s) of a spherical, principal series GL(n,R) Whittaker function, we develop an explicit recurrence relation for this Mellin transform. This relation, for any n≥2, expresses Tn,a(s) in terms of a number of “shifted” transforms Tn,a(s+Σ), with each coordinate of Σ being a non-negative integer. We then focus on the case n=4. In this case, we use the

We describe the spectrum of degenerate hypoelliptic Ornstein-Uhlenbeck operators A=∑i,j=1nqijDij+∑i,j=1nbijxjDi in Lp(Rn), 1≤p<+∞, and in C0(Rn). We show that the spectrum of A is the sum of (−∞,0] and the spectrum of the drift term. Our result gives a complete picture of the spectral properties of Ornstein-Uhlenbeck operators in Lp spaces.

We prove the existence of a family of non-trivial solutions of the Liouville equation in dimensions two and four with infinite volume. These solutions are perturbations of a finite-volume solution of the same equation in one dimension less. In particular, they are periodic in one variable and decay linearly to −∞ in the other variables. In dimension two, we also prove that the periods are arbitrarily

In an effort to study the stability of contact lines in fluids, we consider the dynamics of a drop of incompressible viscous Stokes fluid evolving above a one-dimensional flat surface under the influence of gravity. This is a free boundary problem: the interface between the fluid on the surface and the air above (modeled by a trivial fluid) is free to move and experiences capillary forces. The three-phase

This paper concerns strong solutions to the 3D viscous liquid–gas two–phase flow model with initial vacuum. Strong solutions are proved to exist globally in time under the assumption that initial data is small in some sense. Compared to previous results, the major step forward is that the initial masses of liquid and gas are allowed to contain some vacuum regions and the higher–order estimates of the

In this work, we consider sub-critical and critical models for viscoelastic flows driven by pure jump Lévy noise. Due to the elastic property, the noise in the equation for the stress tensor is considered in the Marcus canonical form. We investigate existence of a weak martingale solution for stochastic Oldroyd-B models, with full dissipation in whole of Rd,d=2,3. The key ingredients of the proof are

Let A be a symmetric operator. By using the method of boundary triplets we parameterize in terms of a Nevanlinna parameter τ all exit space extensions A˜=A˜⁎ of A with the discrete spectrum σ(A˜) and characterize the Shtraus family of A˜ in terms of abstract boundary conditions. Next we apply these results to the eigenvalue problem for the 2r-th order differential equation l[y]=λΔ(x)y on an interval

In this paper, we are concerned with optimal control problems evolved on Riemannian manifolds, where the initial and final states satisfy some inequality and equality type constraints, and the control set is a separable metric space. We obtain the second order necessary conditions of integral and quasi-pointwise forms, both of which work for Pontryagin type critical controls and involve the curvature

Abstract The article is devoted to the development of a method for solving the inverse problem. We considered the problem of propagation of electromagnetic wave inside the body located in free space. The method of reconstruction of the parameters inhomogeneity from a known field is applied. The numerical results of the inhomogeneity bodies is presented.

Abstract In this paper the computational algorithm for interpreting the results of hydrodynamic and thermohydrodynamic studies in non-linear filtration is proposed. The algorithm allows to determine the conductivity of the reservoir, the limiting pressure gradient, reservoir pressure and the regularization parameter. Temperature and pressure changes data, measured on a vertical well, are taken as the

Abstract The present paper considers the determination of the two-phase region boundary within a simplified version of the wide-range equations of state of water and steam by Nigmatulin–Bolotnova (EOS NB) in the case the determination is based on the temperature-dependence of the saturated vapor pressure. This version of EOS NB can be used when the temperature and pressure ranges under investigation

Abstract This article is devoted to the study of the oblique fall of an acoustic wave from a pure gas to the boundary of a multifraction gas suspension with polydisperse inclusions of different sizes and materials. A mathematical model that allows to determine the reflection coefficient when an acoustic wave falls obliquely on the interface between two media is presented. Dependencies of the reflection

Abstract The mathematical model that determines reflection and transmission of an acoustic wave at different angles of incidence through a medium containing multifractional bubbly liquid is presented. The reflection and transmission coefficients of the wave are calculated for a water–bubble liquid–water mixture. The effect of the volume content of the dispersed phase on the studied coefficients is

Abstract The features of the reflection and refraction of acoustic waves incident at right angles to a layer of a multifractional gas suspension are investigated. Formulas for calculating the reflection and refraction coefficients are obtained. The dependences of the reflection coefficients on the dimensionless frequency for different mass contents of particles and layer thickness are constructed.

Abstract In this work, the heat conduction equations are written out and boundary conditions are set that describe the interphase heat transfer between gas, a viscoelastic shell, and a carrier liquid. For the case of small bubble fluctuations with a small amplitude, analytical solutions for temperatures are found. The total heat flow is determined. The influence of heat transfer is analyzed.

Abstract Acoustic streaming in vibrating cylindrical cavities of different diameters under isothermal boundary conditions is numerically investigated. Two vibration frequencies are considered at various vibration amplitudes. The influence of increasing nonlinearity of the process on the structure of acoustic streaming is determined. The dynamics of an increase in the acoustic streaming velocity with

Abstract The numerical simulation of the flow around the airfoil formed by the moving surface is investigated. The influence of the wall motion into aerodynamic performance of the airfoil is studied in two-dimensional formulation for RANS equations.

Abstract A modification of the well-known wide-range equations of state of Nigmatulin–Bolotnova is proposed for describing the high-speed adiabatic-compression of vapor of tetradecane in the metastable region in physically consistent way. The modification is based on taking into account the effect of delay of vapor condensation processes under high compression rate. It is useful for studying various

Abstract A rectangular resonator with holes embedded in two plane-transverse resonant diaphragms is built in a plane infinite waveguide. The problem of diffraction of the intrinsic wave of a waveguide incident on the diaphragm (hole in the wall of the resonator) is solved. The paired series functional equations of the diffraction problem, by the method of integral-adder identities, are reduced to an

Abstract This paper presents the results of a study of transient temperature distribution in the reservoir during the heat treatment of the producer well. Analytical solutions of the problem for heating the bottomhole zone using a heater with a constant temperature or power are obtained. The analytical solutions are compared with the known approximate solutions. A nonlinear equation is obtained for

Abstract During the development modeling process of an oil reservoir, one of the most important steps is to solve the inverse problem, the solution of which, as a rule, is to select the model parameters for the best matching to the development history. However, the purpose of modeling is not only to repeat development indicators on the historical period, but also to obtain a reliable forecast of the

Abstract The problem of the viscous incompressible fluid flow between two coaxial cylinders is considered in the case when the inner cylinder is rotates and the outer cylinder is stationary. The process of fluid flow is simulated by solving the three-dimensional Navier–Stokes equations. The computational algorithm is based on the finite volume method. The dependences of the dimensionless viscous torque

Abstract In a one-dimensional approximation, the decomposition of gas hydrate in a porous reservoir saturated in the initial state with methane and its hydrate was numerically researched. The upper and lower boundaries of the hydrate-containing reservoir are impervious to the decomposition products of methane hydrate. At the porous reservoir upper boundary, a small increase in temperature occurs, and

Abstract The article is devoted to an inverse problem of reconstruction of inhomogeneity parameters of a body in semi-infinite rectangular waveguide. We suggest a new numerical method for solving this one. The inverse problem is reduced to the solving of volume singular integral equation of first kind and additional procedure of calculation the parameters of inhomogeneity. The numerical results are

Abstract Thin-walled toroidal shells are widely used in the construction and facilities of present-day design. During operation, various defects arise on the surface of the shells, in particular local dependings. The article describes a model of a fragment of the toroidal shell with a local deepening based on three-dimensional finite elements with cubic approximation of the original variables. The

Abstract Different variants of the problem of diffraction of plane electromagnetic wave by the cylindrical body are constructed and researched in the work. These problems are reduced to infinite sets of linear algebraic equations. The conductive bodies and dielectric bodies with thin conductive bands on the non-coordinate boundary are considered. The results of the computational experiment are presented

Abstract The paper is devoted to study of the parametric resonance of torsional vibrations caused by large-amplitude flexural vibrations of cantilevered plates. In this study we considered the first two resonant modes of flexural vibrations. The analytical study of the original problem which is reduced to Hill equation, is based on the WKB approximation. According to the obtained results, we built