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The two‐way propagation of a certain class of long‐crested water waves is governed approximately by systems of equations of the Boussinesq type. These equations have been put forward in various forms by many authors and their higher‐order generalizations arise when modeling the propagation of waves on large lakes, ocean, and in other contexts. Considered here is a class of such system which couple two higher‐order Korteweg–de‐Vries type equations. Our aim is to investigate the controllability properties of the linearized model posed on a periodic interval. By using the classical duality approach and some theorems on nonharmonic Fourier series, we prove that the system is exactly controllable in certain well‐chosen Sobolev spaces by means of suitable boundary controls. [ABSTRACT FROM AUTHOR]

We examine the house price convergence across 12 OECD countries over the period 1905–2016. Using novel quantile unit root tests which allow for smooth breaks via a Fourier expansion series, we find that nine countries show the presence of relative house price convergence at all the quantiles. Focusing on several specific quantiles, 11 countries have significant convergence tendencies. Moreover, there are four definite patterns related to shocks in the relative house prices across quantiles. [ABSTRACT FROM AUTHOR]

We consider viscous steady streaming induced by oscillatory flow past a cylinder between two plates, where the cylinder's axis is normal to the plates. While this phenomenon was first studied in the 1930s, it has received renewed interest recently for possible applications in particle manipulations and non-Newtonian flows. The flow is driven at the ends of the channel by the boundary condition which is a series solution of the oscillating flow problem in a rectangular channel in the absence of a cylinder. We use a combination of Fourier series and an asymptotic expansion to study the confinement effects for steady streaming. The Fourier series in time naturally simplifies to a finite series. In contrast, it is necessary to truncate the Fourier series in, which is in the direction of the axis of the cylinder, to solve numerically. The successive equations for the Fourier coefficients resulting from the asymptotic expansion are then solved numerically using finite element methods. We use our model to evaluate how steady streaming depends on the domain width and distance from the cylinder to the outer walls, including the possible breaking of the four-fold symmetry due to the domain shape. We utilize the tangential steady streaming velocity along the radial chord at an angle of π/4 to analyze our solutions over an extensive range of oscillating frequencies and multiple levels in the -direction. Finally, higher-order solutions are computed and an asymptotic correction to steady streaming is included. [ABSTRACT FROM AUTHOR]

The paper deals with the boundary controllability of a family of nonlinear Boussinesq systems introduced by J. L. Bona, M. Chen and J.-C. Saut to describe the two-way propagation of small amplitude gravity waves on the surface of water in a canal. By combining the classical duality approach and a careful spectral analysis of the operator associated with the state equations, we first obtain the exact controllability of the linearized system in suitable Hilbert spaces. Then, by means of a contraction mapping principle, we establish the local exact controllability for the original nonlinear system. [ABSTRACT FROM AUTHOR]

Based on the explicit formula of the pointwise error of Fourier projection approximation and by applying van der Corput-type Lemma, optimal convergence rates for periodic functions with different degrees of smoothness are established. It shows that the convergence rate enjoys a decay rate one order higher in the smooth parts than that at the singularities. In addition, it also depends on the distance from the singularities. Ample numerical experiments illustrate the perfect coincidence with the estimates. [ABSTRACT FROM AUTHOR]

In this paper we study point processes on the complex plane and illustrate their uses in several statistical areas, where the quantities of interest requiring estimation involve Fourier expansions. In particular, for any problem where we can describe a quantity in terms of its Fourier expansion, we propose modeling the coefficients of the expansion using a point process on the complex plane. We utilize the Poisson complex point process and model its intensity function using log-linear and mixture models. The proposed models are exemplified via applications to general density approximation, via modeling of the characteristic function, and time series analysis, via modeling of the spectral density. [ABSTRACT FROM AUTHOR]

This paper presents a high‐order Fourier‐expansion based differential quadrature method with isothermal and thermal lattice Boltzmann flux solvers (LBFS‐FDQ and TLBFS‐FDQ) for simulating incompressible flows. The numerical solution in the present method is approximated via trigonometric basis. Therefore, both periodic and non‐periodic boundary conditions can be handled straightforwardly without the special treatments as required by polynomial‐based differential quadrature methods. The incorporation of LBFS/TLBFS enables the present methods to efficiently simulated various types of flow problems on considerably coarse grids with spectral accuracy. The high‐order accuracy, efficiency and competitiveness of the proposed method are comprehensively demonstrated through a wide selection of isothermal and thermal flow benchmarks. [ABSTRACT FROM AUTHOR]

For some so-called computationally difficult problems, using the method of Boolean logic is fundamentally inefficient. For example, the vertex coloring problem looks very simple, but the number of possible solutions increases sharply with the increase of graph vertices. This is the difficulty of the problem. This complexity has been widely studied because of its wide applications in the fields of data science, life science, social science, and engineering technology. Consequently, it has inspired the use of alternative and more effective non-Boolean methods for obtaining solutions to similar problems. In this paper, we explore the research on a new generation of computers that use local active memristors coupling. First, we study the dynamics of the memristor coupling network. Then, the simplified system phase model is obtained. This research not only clarifies a physics-based calculation method but also provides a foundation for the construction of customized analog computers to effectively solve NP-hard problems. [ABSTRACT FROM AUTHOR]

This paper examines the tourism markets' convergence hypothesis across South Korea's major source markets. In doing so, we use monthly data of visitor arrivals over the period July 1995 to June 2019 and adopt a novel quantile unit root tests that allows for multiple structural breaks via a Fourier expansion series. Our results indicate that seven countries out of 10 show firm convergence tendencies at most of the quantiles, and two countries have weak but significant converging trends at some quantiles. [ABSTRACT FROM AUTHOR]

For some so-called computationally difficult problems, using the method of Boolean logic is fundamentally inefficient. For example, the vertex coloring problem looks very simple, but the number of possible solutions increases sharply with the increase of graph vertices. This is the difficulty of the problem. This complexity has been widely studied because of its wide applications in the fields of data science, life science, social science, and engineering technology. Consequently, it has inspired the use of alternative and more effective non-Boolean methods for obtaining solutions to similar problems. In this paper, we explore the research on a new generation of computers that use local active memristors coupling. First, we study the dynamics of the memristor coupling network. Then, the simplified system phase model is obtained. This research not only clarifies a physics-based calculation method but also provides a foundation for the construction of customized analog computers to effectively solve NP-hard problems.

• An advanced unconditional multi-channel signal processing algorithm is proposed. • Algorithm can reconstruct section contour and determine its engineering center. • Introduction of transform matrix concept adapts to various measuring challenges. • Advanced feature: Enables measurement without any predetermined section parameter. In mechanical engineering the standard method to assess the geometric tolerances of rotational parts is by analysing parts' rotational motion in relation to the measuring system. Traditional tolerance compliance measurement models are conditional signal processing models that require pre-defined contour parameters of measured sections. However, due to part diversity and complexity, pre-determining and pre-setting the section parameters before each measurement process is very time-consuming and, in some cases, unachievable. To address this challenge, this paper proposes an advanced unconditional signal processing model, which uses multi-channel measurements for cross-section contour reconstruction that operates without predefined section parameters. This model can handle multi-point measurement signals and accurately estimate the contour shape and engineering center coordinates of measured sections through circumferential Fourier expansion and an approximated signal-contour transform matrix. An efficient iterative algorithm then reconstructs the contour and precisely locates the engineering center. The computational accuracy and robustness of the proposed model have been confirmed through rigorous theoretical analysis and comprehensive experimental validation. Due to its inherent unconditional advantage, the proposed signal processing model can achieve intelligent monitoring of rotational parts throughout their entire life, which not only adapts and remains stable across a wide variety of cross-section types but also significantly improves measurement efficiency, ensuring precise and accurate results. [ABSTRACT FROM AUTHOR]

The wave field created by a pulsed point source of sound in a uniform homogeneous flow with an arbitrary value of the Mach number is theoretically studied. The aim of research is to obtain an analytical dependence of the sound field on physical parameters. The space-waveguide Fourier expansion of the sound field is used to solve the Cauchy problem for the wave equation in a reference frame moving together with the medium. It is only necessary to transform the spatiotemporal dependence of the source, given in a fixed frame of reference, to a dependence in a moving frame of reference. The transition to the description of the solution in the frame of reference, relative to which the medium moves at a constant velocity, is made taking into account the main properties of the generalized Dirac d-function. Analytical dependences of the sound field on physical parameters are obtained for both subsonic and supersonic flows. A comparison is made with the results of calculations for the case of a pulsed point source moving in a medium at rest. The solution obtained in this work for the case of an impulsive source moving in a medium at rest made it possible to trace its connection with the Green's function for a stationary source in a moving medium. The analytical dependence of the obtained solution for the Green's function makes it possible to write down the explicit form of the «characteristic solution surface», that is, the «wave front». It is shown that the difference between the solutions for subsonic and supersonic motion is characterized by the position of the source relative to the moving wavefront. The calculation results can be used to describe the sound field created by an arbitrary spatiotemporal distribution of sound sources. [ABSTRACT FROM AUTHOR]

A correction to the article "The Fourier Expansion of Hecke Operators for Vector-Valued Modular Forms" that was published in a previous journal of the issue is presented.

To investigate the dynamic response of a submerged floating tunnel (SFT) under the action of waves, a modal superposition method in the frequency domain was established, and the amplitudes of the modals were determined using the generalized wave loads and hydrodynamic coefficients of the structural modals. In this model, the SFT was simplified as a constant-cross-section Euler–Bernoulli beam with multiple anchor cables, and its structural modals were resolved using the finite element method (FEM). The generalized wave loads and generalized hydrodynamic coefficients were obtained using the Fourier expansion strategy of the modal function, by which the hydrodynamic problem can be converted into 2D problems with the modified Helmholtz controlling equation and solved using the matched higher-order boundary element method (HOBEM) and eigenfunction expansion. The effects of the diameter of the anchor cables and length of the SFT on the stiffness of the structure and the dynamic response of an SFT with anchor cables under wave action were investigated. Furthermore, the effects of different added mass calculation methods on the structural response were studied. In addition, the wave exciting forces were calculated using potential flow theory or linearized Morison equations according to the wave scale. Finally, the effects of the incident wave frequencies and incident angles were investigated in detail to reveal the combined resonance mechanism. • A modal superposition method in the frequency domain is established to investigate the dynamic response of a submerged floating tunnel (SFT) under the action of waves. • The finite element method (FEM) and high order matched boundary element method (HOBEM) are used for the dry modal and hydrodynamic analysis of an SFT. • The generalized exciting forces and hydrodynamic coefficients of an SFT are constructed through Fourier series transformation of modal functions. • The wave exciting forces are calculated using diffraction theory or Morison equation based on the ratio of the SFT cross-sectional size to wave length. • The influence of the cable diameter and SFT spanwise length on the dynamic behavior of the structure are studied. The influence of incident wave frequencies and angles on the dynamic response of an SFT are studied. [ABSTRACT FROM AUTHOR]

This research tests the mean reversion properties of the U.S. EPU (economic policy uncertainty) index and its 11 sub-categories using the Fourier non-linear quantile unit root test over the period 1985M1-2020M12. The results indicate the following. (1) The U.S. EPU index responds asymmetrically to shocks, in which positive shocks are more long-lasting than negative shocks. (2) Monetary, fiscal, and trade policies and also national security and regulation series behave like unit root processes in all quartiles, whereas by contrast financial regulation and sovereign debt exhibit stationary behaviour over all quantiles. (3) Government spending, health care, national security, and entitlement programmes present stationary processes in low/high quantiles. [ABSTRACT FROM AUTHOR]

In this paper, a new approach is developed for the identification of Wiener–Hammerstein model structures. Unlike several other papers, the transfer functions of linear elements are of unknown structure. Indeed, the linear subsystems are not necessarily parametric or FIR. Furthermore, the function of nonlinear block can be nonparametric and noninvertible. The main challenge in identifying a Wiener–Hammerstein system lies in the separation of the dynamics over the input and the output LTI elements. Presently, this issue does not arise, without any conditions being imposed on the frequency band. Then, a two‐stage identification method is suggested. Firstly, the system is excited by a set of constant inputs to capture the system nonlinearity. In the second stage, an identification approach based on the spectral analysis and using periodic input signals is developed to determine the linear elements parameters. In the present method, very interesting concepts are used, like the Fourier decomposition, the frequency approach and the spectrum analysis. Simulations demonstrate that the proposed identification method is both effective and efficient. [ABSTRACT FROM AUTHOR]

The goal of this paper is to investigate the method outlined by one of us (P. R.) in Cherubini, U., Della Lunga, G., Mulinacci, S. and Rossi, P. [Fourier Transform Methods in Finance, 2009 (John Wiley & Sons Inc.).] to compute option prices. We name it the SINC approach. While the COS method by Fang, F. and Oosterlee, C.W. [A novel pricing method for european options based on Fourier-cosine series expansions. SIAM. J. Sci. Comput., 2009, 31(2), 826–848.] leverages the Fourier-cosine expansion of truncated densities, the SINC approach builds on the Shannon Sampling Theorem revisited for functions with bounded support. We provide several results which were missing in the early derivation: (i) a rigorous proof of the convergence of the SINC formula to the correct option price when the support grows and the number of Fourier frequencies increases; (ii) ready to implement formulas for put, Cash-or-Nothing, and Asset-or-Nothing options; (iii) a systematic comparison with the COS formula for several log-price models; iv) a numerical challenge against alternative Fast Fourier specifications, such as Carr, P. and Madan, D. [Option valuation using the fast Fourier transform. J. Comput. Finance, 1999, 2(4), 61–73.] and Lewis, A.L. [Option Valuation Under Stochastic Volatility with Mathematica Code, 2000 (Newport Beach: Finance Press).]; (v) an extensive pricing exercise under the rough Heston model of Jaisson, T. and Rosenbaum, M. [Limit theorems for nearly unstable Hawkes processes. Ann. Appl. Probab., 2015, 25(2), 600–631.]; (vi) formulas to evaluate numerically the moments of a truncated density. The advantages of the SINC approach are numerous. When compared to benchmark methodologies, SINC provides the most accurate and fast pricing computation. The method naturally lends itself to price all options in a smile concurrently by means of Fast Fourier techniques, boosting fast calibration. Pricing requires resorting only to odd moments in the Fourier space. [ABSTRACT FROM AUTHOR]

Subject and Purpose. The wave field produced by a spatial-temporal distribution of sound sources in a uniform subsonic flow is theoretically studied in an effort to obtain an analytical dependence of the sound field on physical parameters. Method and Methodology. Cauchy problem for wave equation in a moving medium is solved using a spatial-waveguide Fourier expansion of the sound field. A Fourier representation of the Green's function of a point-like pulse sound source is constructed whose inverse transform allows us to obtain the Green's function spatial-temporary representation. Results. With the Green’s function obtained, the wave fields from arbitrarily shaped sources have been represented in the “wave potential” form, which is a convolution type integral of the density of spatial-temporal distribution of the sound sources and the Green’s function. Conclusion. The calculation results give a clear idea of the propagation of sound waves excited by a point-like pulse source in a uniform homogeneous flow. The wave front of the sound field represents a sphere whose center “drifts” from the source at a speed equal to the speed of the flow in its movement direction, and the radius of the sphere grows in the course of time at a speed equal to the speed of sound. The obtained Green’s function allows for the analytic continuation to the supersonic flow case that, in contrast to the subsonic case, satisfies the causality principle not in all unlimited space but only at the observation points within the Mach cone. The wave field from a monochromatic source is the limiting case of the rectangular pulse solution.

Abstract The main purpose of this paper is to investigate the Fourier series representation of the generalized Apostol-type Frobenius–Euler polynomials, and using the above-mentioned series we find its integral representation. At the same time applying the Fourier series representation of the Apostol Frobenius–Genocchi and Apostol Genocchi polynomials, we obtain its integral representation. Furthermore, using the Hurwitz–Lerch zeta function we introduce the formula in rational arguments of the generalized Apostol-type Frobenius–Euler polynomials in terms of the Hurwitz zeta function. Finally, we show the representation of rational arguments of the Apostol Frobenius Euler polynomials and the Apostol Frobenius–Genocchi polynomials.

Abstract Fourier expansions of higher-order Apostol–Genocchi and Apostol–Bernoulli polynomials are obtained using Laurent series and residues. The Fourier expansion of higher-order Apostol–Euler polynomials is obtained as a consequence.

A simple semi-analytical approach relying on Fourier-type finite expansions and boundary collocation is proposed to solve an inverse problem for the fully nonlinear two-dimensional, steady, free-surface, wave-free gravity fluid flow in an infinite channel with topography of finite extent. The fluid is of constant density, and the flow is assumed irrotational. The coefficients involved in the series representation for the streamfunction are determined from a linear system of algebraic equations. Results are plotted for four cases belonging to two main classes of the flow. [ABSTRACT FROM AUTHOR]

A theoretical formulation is presented for the displacements, temperature and stresses in a 3 D transversely isotropic thermoelastic solid under arbitrary mechanical loads and heat flux. By using two scalar potential functions, 3 D patch-load, patch-heat source, point-load and point-heat source Green's functions are given for the displacements, temperature and stresses. Basic governing equations of coupled thermoelasticity in transversely isotropic solids are presented in the cylindrical coordinates system. By means of two scalar potential functions, the four coupled governing equations for this class of problems are uncoupled into a 6th order and a 2nd order partial differential equations. Applying the Fourier expansions and Hankel transforms, the angular and radial variables are suppressed and 6th and 2nd order ordinary differential equations are obtained. By solving the ordinary differential equations, the potential functions, displacements, temperature and stresses are obtained in the Fourier-Hankel transformed space. By applying the Hankel inversion theorem, all responses are presented in the physical time-spatial space. To prove the validity of the analytical and numerical solutions, our results are compared with existing solutions reported in the literature. Numerical results are also included to show the effects of material anisotropy, elastic and thermal properties; and frequency of excitation on the responses. [ABSTRACT FROM AUTHOR]

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This short note aims at revisiting the causal links among urbanization, coal consumption and CO2 emissions in China using a newly developed Bootstrap Fourier Granger Causality in Quantile test over the period of 1969–2019. The quantile causality approach evaluates causal relationships in a more detailed and flexible way than the conditional mean causality analysis. While the causality definition of Granger (Econometrica 37:424–438, 1969) cannot provide information about a tail causal relation or nonlinear causalities, the Causality in Quantiles test allows us to determine whether extremely low or high changes matter for the urbanization-coal consumption- CO2 emission nexus. Granger causality test based on our proposed model indicates one-way Granger causality running from urbanization to both CO2 emissions (within 0.2 quantile) and coal consumption (within 0.4, 0.6 and 0.8 quantiles) in China. These empirical results have important policy implications for the government conducting urbanization and energy policies in China. [ABSTRACT FROM AUTHOR]

This paper is devoted to solve the steady monoenergetic Fokker-Planck equation in the 1D slab when the incoming fluxes and the source term are allowed to depend on the azimuth θ. The problem is split into a collection of θ-independent problems for the Fourier coefficients of the full solution. The main difficulty is that, except for the zeroth Fourier coefficient, each of these problems contains an artificial absorption coefficient which is singular at the poles. Two numerical schemes capable of dealing with the singularities are proposed: one that is considered as the main scheme, and a second 'security' scheme which is used to verify that the results obtained by means of the first one are reliable. Numerical experiments showing second order of convergence are conducted and discussed. [ABSTRACT FROM AUTHOR]

We consider time-optimal problem for the heat dynamics in a rod. Taking the first two terms of Fourier expansion and using the method of coupling terms the problem is reduced to two-dimensional linear control system. Solving the last system it is obtained an approximate solution of the posed problem. [ABSTRACT FROM AUTHOR]

The ratio of O number density to N2 number density (O/N2) is an important parameter to describe thermospheric composition changes and its effects on the ionosphere. Based on Global Ultraviolet Imager (GUVI) limb measurements, we investigate the seasonal behaviors of O/N2 volume density ratio on different constant pressure levels during geomagnetically quiet periods. The global O/N2 shows the prominent annual and semiannual variations with solar activity dependence. An empirical model considering the solar activity and annual/semiannual variations can reasonably reproduce the original O/N2. The modeled O/N2 captures the hemispheric asymmetry of the annual variations in both length and magnitude. Global maps of the seasonal harmonic components of the modeled O/N2 indicate the latitudinal and altitudinal dependence of O/N2 seasonal variations. The annual component dominates over the semiannual component at mid‐latitudes, but it is smaller than the semiannual component at low latitudes. In the Northern Hemisphere, and at low geomagnetic latitudes of the Southern Hemisphere, the annual component peaks around December solstice at all altitudes, whereas at middle geomagnetic latitudes of the Southern Hemisphere, it peaks around June solstice. The semiannual component peaks at the equinoxes in almost all regions over the globe at all altitudes. The annual and semiannual amplitudes both increase with altitude. In addition, O/N2 annual variations and solar activity dependence are more influenced by the thermal expansion and contraction. Key Points: The global O/N2 volume density ratio shows the prominent annual and semiannual variations with solar activity dependenceO/N2 annual/semiannual variations have latitudinal and altitudinal dependence and exhibit hemispheric asymmetryO/N2 annual variations and solar activity dependence are more affected by the thermal expansion and contraction [ABSTRACT FROM AUTHOR]

Fourier expansions of higher-order Apostol–Genocchi and Apostol–Bernoulli polynomials are obtained using Laurent series and residues. The Fourier expansion of higher-order Apostol–Euler polynomials is obtained as a consequence. [ABSTRACT FROM AUTHOR]

We generalize Merel's work on universal Fourier expansions to Bianchi modular forms over Euclidean imaginary quadratic fields, under the assumption of the nondegeneracy of a pairing between Bianchi modular forms and Bianchi modular symbols. Among the key inputs is a computation of the action of Hecke operators on Manin symbols, building upon the Heilbronn–Merel matrices constructed by Mohamed. [ABSTRACT FROM AUTHOR]

This study presents an effective strategy to optimize the hydrodynamic shape for sea-crossing bridge piers towards minimal wave force. The bridge pier is parameterized using a shape model based on Fourier expansion and collaborated with the frequency-domain boundary element method to resolve the hydrodynamic wave force. The optimization is driven by generalized pattern search algorithm and integrates the parametric shape model with the hydrodynamic solver, exploring the optimal geometry to gain the minimal wave force. A case study is investigated and the effect of two major constraint conditions, i.e., the cross-sectional area and aspect ratio are examined. The reduction mechanism of the optimized shape is clarified. The results show that the presented approach can provide optimal cross-sections that reduce 25%–40% wave force under different conditions compared to the circular cross-sectional bridge pier and outperform most commonly used cross-sections, e.g., stadium, rectangle, hexagon, and ellipse. The optimizer suggests the optimal cross-sections as quasi-ellipse or quasi-rectangle styles, highly depending on the specific user-defined constraint conditions. The mechanics of wave force reduction reveals that the optimized shapes successfully reduce the wave force by altering scattered waves around the pier, which changes the amplitude and phase of diffraction wave forces but negligibly affects the Froude-Krylov force, thereby reducing the overall wave force. • An effective approach to optimize the hydrodynamic shape for sea-crossing bridge piers towards minimal wave force is proposed. • A Fourier expansion-based shape model is integrated with boundary element method to resolve hydrodynamic shape optimization problem. • The optimal cross-sections of bridge pier and the mechanism of wave force reduction are revealed and discussed. [ABSTRACT FROM AUTHOR]

This study presents a novel and efficient framework that leverages machine learning to predict wave forces acting on truncated cylinders with arbitrary cross-section, with a particular emphasis on their application to piers and caps of sea-crossing bridges. A reduced-order shape model based on Fourier expansion is presented for geometry parameterization. A neural network model is developed to establish a complex mapping from parameterized structure profiles to hydrodynamic wave loads. Automatic meshing techniques and frequency-domain boundary element method are integrated to resolve hydrodynamic problems and generate datasets efficiently. A parallel modeling strategy is employed to reduce the training cost of the force transfer function. This is achieved by partitioning the wave force transfer functions into multiple sub-regions and training them independently as sub-models. Evaluations on the test set show favorable model performance that the predicted wave forces are in remarkably high agreement with the ground truth with a correlation coefficient R 2 of over 0.999. The prediction Mean Absolute Percentage Error is 2.66% and 1.39% for Fx and Fy , respectively. Over 90% of the wave force predictions resulted in an Absolute Percentage Error within 5%. The presented method exhibits a favorable predictive capability and provides significant advantages in terms of computational efficiency while maintaining high accuracy. • A novel and efficient machine learning model for predicting wave loads on bridge substructures with arbitrary cross-sectional shapes is proposed. • A Fourier expansion-based shape model and frequency-domain boundary element method are integrated to parameterize arbitrary geometries and generate datasets efficiently. • Tests on a variety of shapes show excellent agreement between predicted and ground truth for modeling verification. [ABSTRACT FROM AUTHOR]

The hydrodynamic behaviour of floating regular polygonal platforms under wave action was studied by conducting parametric studies. Considering triangular, square, hexagonal, and circular platforms of similar size and draft, the results show that their added mass, radiation damping, and RAOs are similar. However, the wave exciting forces are slightly different, particularly the horizontal forces. The polygonal platforms oriented with one of its corners in line with the prevailing wave direction can lead to a reduction in the horizontal force on the platform, a feature that helps in reducing the cost of a mooring system. Moreover, such oriented platforms are able to disperse the waves better in multiple directions and hence will not pose problems for ships or marine vessels passing by the platform on the weather side. Thus, the orientation of a polygonal platform is an important design consideration. From the comparison study among different polygonal platforms, their wave attenuation performances are slightly similar. The hydrodynamic analyses performed herein for the parametric studies were sped up considerably by using a significantly lesser number of Fourier coefficient sets for the series functions that define the velocity potentials when compared to those used by previous researchers in their analytical approaches. The adoption of the radius function defined by cosine-type radial perturbation does not only generate the geometric boundaries of polygonal platforms, but it also simplifies the formulation and quickens the computations.

In this paper we are concerned with a Boussinesq system for small-amplitude long waves arising in nonlinear dispersive media. Considerations will be given for the global well-posedness and the time decay rates of solutions when the model is posed on a periodic domain and a general class of damping operator acts in each equation. By means of spectral analysis and Fourier expansion, we prove that the solutions of the linearized system decay uniformly or not to zero, depending on the parameters of the damping operators. In the uniform decay case, the result is extended for the full system. [ABSTRACT FROM AUTHOR]

We consider the inverse problem of determining an unknown vectorial source current distribution associated with the homogeneous Maxwell system. We propose a novel non-iterative reconstruction method for solving the aforementioned inverse problem from multi-frequency far-field measurements. The method is based on recovering the Fourier coefficients of the unknown source. A key ingredient of the method is to establish the relationship between the Fourier coefficients and the multi-frequency far-field data. Uniqueness and stability results are established for the proposed reconstruction method. Numerical experiments are presented to illustrate the effectiveness and efficiency of the method. [ABSTRACT FROM AUTHOR]

Real interest rate differentials usually exhibit two properties; structural breaks and asymmetric dynamics. In this paper, we use various types of Quantile Unit Root Test (QURT) which accounts for both properties. Unlike previous research, we reject the unit root in the real interest rate differentials in 18 out of 21 OECD countries as well as in 4 out of 5 BRICS countries using QURT with sharp and smooth breaks. [ABSTRACT FROM AUTHOR]

A 1D analytical model for slag infiltration during continuous casting of steel is developed to investigate the slag behavior in the mold–strand gap. The superposition principle and Fourier expansion are applied to obtain the analytical solution for transient slag flow under arbitrary mold oscillation including non-sinusoidal oscillation mode. The validated model using literature data partially explains several controversies such as slope of slag film channel, mechanism of non-sinusoidal mold oscillation, and timing of slag infiltration. The model shows that a converging slag film into the casting direction is required to open the mold–strand gap if compression is applied in between. Also, model calculations imply that higher slag consumption is achievable from non-sinusoidal mold oscillation by means of the increase of film thickness through longer positive pressure with higher peak pressure. The model demonstrates a time difference between slag flow and pressure near the meniscus and the discrepancy in timing of infiltration between previous works is attributed to the mismatch. The model provides a concise but reliable tool to understand slag infiltration behavior and design mold oscillation settings.