Search

We view the (real) Laplace transform through the lens of linear algebra as a continuous analogue of the power series by a negative exponential transformation that switches the basis of power functions to the basis of exponential functions. This approach immediately points to how the complex Laplace transform is a generalisation of the Fourier transform where the pole of the transform realises the linear algebraic intuition. The exponential transformation also motivates the Taylor inversion of the real Laplace transform. [ABSTRACT FROM AUTHOR]

In this paper, we derive some Fourier transforms of confluent hypergeometric functions. We give generalizations of several well-known results involving Fourier transforms of gamma functions. In particular, the generalizations include some Ramanujan's remarkable formulas. [ABSTRACT FROM AUTHOR]

AbstractHigh-throughput mechanical testing based on functionally graded specimens is very promising for accelerating the development of new materials. However, due to the inhomogeneity-induced complexity, most existing analyses on functionally graded materials have recourse to numerical methods to predict their mechanical responses in reaction to external stimuli. This work investigates the surface Green’s functions for an inhomogeneous half-plane with horizontal exponential material gradient subject to both normal and tangential concentrated forces acting on the surface. The governing equations are first simplified by introducing appropriate potential functions, which facilitates the mathematical derivation of displacements via the Fourier transform technique. In the case of normal force, the vertical surface displacement is derived explicitly under the weak gradient assumption while the horizontal surface displacement is derived directly without the same assumption. In particular, the Meijer G-function and Fox H-function are introduced to express and simplify the vertical displacement. In the case of tangential force, the analytical expressions of surface displacements are also derived similarly. It is noted that the surface Green’s functions not only exhibit singularity and asymmetry properties as expected, but also can be reduced to the classical Boussinesq-Flamant solutions for a homogeneous half-plane. In addition, the analytical results are verified through comparison with the finite element analyses. The surface Green’s functions derived here could be a theoretical basis for developing high-throughput mechanical testing methods which use specimens made of functionally graded materials. [ABSTRACT FROM AUTHOR]

Gas turbines play a vital role in gas transportation and power generation, but they are prone to instability phenomena that can lead to vibrations, shorten equipment lifespan, and result in catastrophic failures. To tackle these challenges, a paper introduces an integrated approach that leverages advanced techniques like Fourier transform, Neuro-Fuzzy systems, and wavelet analysis for continuous monitoring of the MS5002C turbine's condition. The proposed method begins by collecting operational data and utilizing the Fourier transform to measure vibratory quantities, accurately representing their evolution through spectral data obtained from the analyzed signals. Adaptive inference-based algorithms of neuro-fuzzy systems are then employed to generate turbine failure indicators. This approach enables the development of a model-based fault detection method that compares the actual turbine operation with the estimated operation derived from a pre-established model, enabling the classification of detected faults. To enhance decision-making quality, evaluation, and validation of the diagnostic strategy's performance, a multi-resolution analysis based on the wavelet transform is applied. The presented results from various implementation and validation tests demonstrate the effectiveness of this intelligent diagnostic approach in detecting and analyzing gas turbine vibrations. The paper exhibits promising outcomes in real-time monitoring, ensuring the operational safety of the turbine. [ABSTRACT FROM AUTHOR]

In this paper, two special-shaped separated heat pipes with different condensation section structures are designed. The working medium is water, and the filling rate is 65%. The evaporation section is placed in the hot water tank, and the condensation section is equipped with a cold water jacket. The effects of different structures of condensing section on the thermal performance of separated heat pipes are experimentally studied, and the temperature changes of the two separated heat pipes during start-up and stable operation under different heating power are analyzed. The results show that the heat transfer characteristics of the two separated heat pipes are different due to the different structures of the condensation section, and the heat transfer capacity of sample 2 is higher. At the same time, the temperature fluctuation in the condensing section of sample 2 is also quite different from that in the condensing section of sample 1, and the temperature fluctuation in the condensing section of sample 2 is greater. The wall temperature fluctuates periodically in a steady-state, and a fast Fourier transform is used to analyze the temperature fluctuation. [ABSTRACT FROM AUTHOR]

The state-space formulation for two-dimensional generalized thermoviscoelasticity has been formulated. In this formulation, the governing equations are transformed into a matrix equation whose solution enables us to write the solution of any two-dimensional problem in terms of the boundary conditions. The resulting formulation is applied to a 2 D problem of a half-space subjected to harmonically varying heating with constant angular frequency. [ABSTRACT FROM AUTHOR]

The delineation of the linear/nonlinear response of bituminous material in the frequency domain is conducted using the small-amplitude oscillatory shear test, wherein only the peak stress and strain are available. In contrast, the large-amplitude oscillatory shear tests provide complete waveform data. Analysis of such data can help to unravel the linear/nonlinear response with greater accuracy. This investigation reports such an exercise. An experimental investigation is conducted on five different materials at different strain amplitudes, frequencies, and temperatures. The geometry-based parameters obtained from the Lissajous plot gave contradictory linear/nonlinear delineation. Analysis of the higher order harmonics did not show any appreciable presence of nonlinearity. However, the orientation of the Lissajous plots differed from the strain amplitude. The elastic and viscous stress could be predicted using the first-order Chebyshev coefficients indicating the linear response, but the coefficients differed with the strain amplitude. The scaling-superposition of the waveform revealed a clear demarcation of the linear/nonlinear response. This indicated that the response of the bituminous material needs to be analysed for a range of frequency and amplitude. The mere analysis of the waveform data at any test condition can help only to establish the necessary condition for linearity but not a sufficient condition. [ABSTRACT FROM AUTHOR]

Calcium is an essential element in our body and plays a vital role in moderating calcium signalling. Calcium is also called the second messenger. Calcium signalling depends on cytosolic calcium concentration. In this study, we focus on cellular calcium fluctuations with different buffers, including calcium-binding buffers, using the Hilfer fractional advection-diffusion equation for cellular calcium. Limits and start conditions are also set. By combining with intracellular free calcium ions, buffers reduce the cytosolic calcium concentration. The buffer depletes cellular calcium and protects against toxicity. Association, dissociation, diffusion, and buffer concentration are modelled. The solution of the Hilfer fractional calcium model is achieved through utilizing the integral transform technique. To investigate the influence of the buffer on the calcium concentration distribution, simulations are done in MATLAB 21. The results show that the modified calcium model is a function of time, position, and the Hilfer fractional derivative. Thus the modified Hilfer calcium model provides a richer physical explanation than the classical calcium model. [ABSTRACT FROM AUTHOR]

We present a gradient-based optimization method that precisely designs simplified isotropic potentials for self-assembly of targeted lattice structures. An ansatz potential and its constraints are constructed to directly reflect the characteristics of a Bravais lattice for the target crystal, and the method is able to design the simplified potential systematically and smoothly. The potential is simplified with a Gaussian function in reciprocal space to minimize the information loss caused by Fourier transform in each design update. Design optimization formulation is derived using design sensitivity to relative entropy, employing a Fourier-Filtered Relative Entropy Minimization (FF-REM) formulation embedded in LAMMPS code to be used as an optimization tool. The potential obtained through this optimization method can successfully self-assemble low-coordinated crystals, such as square, triangle, honeycomb, and Kagome lattices, without further smoothing techniques. It turns out that completely removing the competitive alternative structures is an important condition for improving stability in self-assembling the target lattice in various density ranges. [ABSTRACT FROM AUTHOR]

This paper considers D-optimal designs for linear mixed models involving random effects with unknown distributions. From Bayesian point of view, the Dirichlet process as a prior distribution on the space of all distributions is used. Based on the Dirichlet process as a prior, we give the Bayes estimate of the density function of the response variable, which result in a mixture of two normal distributions. An explicit form of the Fisher information matrix for the proposed model is derived by using the Fourier transform and then D-optimal design is obtained by numerical calculations. [ABSTRACT FROM AUTHOR]

A strip-saturation model is studied to observe the effect of changing polarization axis on an electro-elastic strip, weakened by an eccentrically situated anti-plane semipermeable crack. The model is modified by considering that the saturated limit of electric displacement over rims of the saturation zone is quadratic interpolating polynomial times. The proposed model is formulated and then solved by using the Fourier integral transform technique and integral equations method. Closed-form analytic expressions are derived for developed saturation zone and fracture parameters viz. electric crack condition parameter, crack-sliding displacement, crack-opening potential drop, field intensity factors, energy release rate, etc. The influence of poling angle, prescribed electro-mechanical loadings, crack length, and material constants on fracture parameters are presented and analyzed graphically. [ABSTRACT FROM AUTHOR]

A neural network called sinusoidal decomposition neural network (SDNN) is proposed to reconstruct the digital elevation model (DEM) and orbital velocity field (OVF) of sea surface. According to the linear wave theory, DEM can be regarded as the superposition of a series of sine waves, from which OVF can be obtained. The SDNN adopts a fully connected network (FCN) to fit the DEM, which is similar to the inverse discrete Fourier transform (IDFT) model and regression model. The two-dimensional and three-dimensional SDNN are introduced in detail and their validities are demonstrated. A major advantage of the SDNN is that it requires only one scene of the wave height to reconstruct the OVF. By the applications to wind-driven sea surface and ship wake, respectively, the correctness and efficiency of the reconstruction are verified. [ABSTRACT FROM AUTHOR]

Currently, intelligent systems built on a multimodal basis are used to study the functional state of living objects. Its essence lies in the fact that a decision is made through several independent information channels with the subsequent aggregation of these decisions. The method of forming descriptors for classifiers of the functional state of the respiratory system includes the study of the spectral range of the respiratory rhythm and the construction of the wavelet plane of the monitoring electrocardiosignal overlapping this range. Then, variations in the breathing rhythm are determined along the corresponding lines of the wavelet plane. Its analysis makes it possible to select slow waves corresponding to the breathing rhythm and systemic waves of the second order. Analysis of the spectral characteristics of these waves makes it possible to form a space of informative features for classifiers of the functional state of the respiratory system. To construct classifiers of the functional state of the respiratory system, hierarchical classifiers were used. As an example, we took a group of patients with pneumonia with a well-defined diagnosis (radiography, X-ray tomography, laboratory data) and a group of volunteers without pulmonary pathology. The diagnostic sensitivity of the obtained classifier was 76% specificity with a diagnostic specificity of 82%, which is comparable to the results of X-ray studies. It is shown that the corresponding lines of the wavelet planes are correlated with the respiratory system and, using their Fourier analysis, descriptors can be obtained for training neural network classifiers of the functional state of the respiratory system. [ABSTRACT FROM AUTHOR]

We study approximation properties of multi-resolution analyses in the context of matrix-valued function spaces. Here, we generalize the notions of approximation order and density order given by the reference [de Boor C, DeVore RA, Ron A. Approximation from shift-invariant subspaces of L 2 (R d). Trans Am Math Soc. 1994;341(2):787–806]. Indeed, we prove a characterization of the closed subspaces generated by the shifts of a single matrix-valued function that provide approximation order and/or density order α ≥ 0. To give our conditions, we need the classical notion of approximate continuity. As a consequence, we prove necessary and sufficient conditions on a matrix-valued function to be a scaling function in a multi-resolution analysis. [ABSTRACT FROM AUTHOR]

Abstract The mathematical theory of elasticity helps in the study of physical quantities in the problem of structures. The structures face the problem of crack’s presence, which makes the problem difficult but not impossible to deal. Integral equations are useful in a variety of problems. Integral equations are used to solve problems like fracture mechanics or fracture design. The physical interest in the fracture design criterion is due to stress and crack opening displacement components. We have an accurate form of stress and displacement components for a pair of longitudinal crack propagations in the bone fracture of the human body at the interface of an isotropic and orthotropic half-space that are bounded together in the proposed study. The expression was calculated using the Fourier transform approach near the crack tips, but these components were evaluated using Fredholm integral equations and subsequently reduced to coupled Fredholm integral equations. We employ the Lowengrub and Sneddon problem in this research and reduce it to triple integral equations. The Srivastava and Lowengrub method reduces the solution of these equations to a coupled Fredholm integral equation. The problem is further reduced to a decoupled Fredholm integral equation of the second kind. Triple integral equations are solved, and the problem is reduced to a coupled Fredholm integral equation. The Fredholm integral equation is solved and reduced to a decoupled Fredholm integral equation of the second kind. Stress and crack opening displacement components drive physical interest in fracture design criteria. Finally, the stress and displacement components may be simply calculated in their exact form. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study on developing a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for an infinite thermoelastic half-space under the action of ramp-type thermal loading and due to the influence of a gravitational field. The bounding plane of the half-space is subjected to rough and rigid foundation so that the rough surface prevents the vertical displacement. Due to the shortcomings of power-law distributions, some other forms of derivatives with few other kernel functions are proposed. The present analysis deals with the heat transport which involves the memory-dependent derivative (MDD) on a slipping interval in the context of Lord–Shulman model to describe the physical phenomena which is defined in the form of convolution with the kernels in the form of power functions. Employing the Laplace and the Fourier transform techniques as tools, the analytical expressions for different physical fields have been obtained on the transformed domain. The numerical inversion of the Fourier transforms have been performed analytically, whereas numerical inversion of the Laplace transform is carried out using the Riemann-sum approximation method. Excellent predictive capability is demonstrated due to the presence of MDD, delay time and gravitational field also. [ABSTRACT FROM AUTHOR]

In this paper, sampling Theorems for perfect signal reconstruction using samples of a signal taken below the Nyquist rate involving nonlinear signal reconstruction technique are presented. The presented results are in contrast with the linear time-invariant filtering based signal reconstruction in the celebrated Shannon sampling theory. It is shown that using kth order nonlinearity in the signal reconstruction system, the required sampling rate for perfect signal reconstruction can be reduced by the same factor k for positive odd values of it. The extensions of the proposed sampling expansion to the fractional Fourier transform and linear canonical transform domains are also derived. Simulation results of the proposed technique are given to validate the proposed approach. [ABSTRACT FROM AUTHOR]

The main concern of this article is to deal with the thermoelastic interaction in a functionally graded thermoelastic rod being enlightened by the memory-dependent derivative. This article investigates the transient phenomena due to the influence of an induced magnetic field of constant intensity and due to the presence of a moving heat source of constant velocity in the context of three-phase lag model of generalized thermoelasticity. Employing the Laplace and the Fourier transforms as tool, the problem has been constructed in the transformed domain. The inversions of the Fourier transform have been carried out using residual calculus whereas the numerical inversions of the Laplace transform have been performed employing the Riemann sum approximation method. Numerical computations for stress, displacement, and temperature within the rod are carried out and have been demonstrated graphically. The results also demonstrate how the nonhomogeneity parameter and the speed of the moving heat source influence the thermophysical quantities. It is observed that the temperature, thermally induced displacement, and stress of the rod are found to decrease at large source speed. Also, significant differences on the thermophysical quantities are revealed due to the influence of magnetic field, nonhomogeneity, and memory effect also. [ABSTRACT FROM AUTHOR]

In this paper, we deduct some properties of the Fourier transform on arbitrary time scales. We define the generalized shifting problem and we prove the existence of solutions. We define a generalized convolution on anarbitrary time scale and we deduct and prove the generalized convolution theorem. [ABSTRACT FROM AUTHOR]

Abstract A wide variety of methods have been proposed for clustering of stochastic processes. However, for clustering of periodically correlated processes (PC) it is demanding to introduce some similarity measures that take into account the inherent periodicity of these processes. The frequency-domain based methods seem more desirable to determine groups of PC processes with similar frequency characterizations. In this article, we present new similarity measures based on Hilbert-Schmidt inner product of finite Fourier transforms of PC processes. Based on simulated stochastic processes and a real gene expression dataset we illustrate the accuracy of the methods. [ABSTRACT FROM AUTHOR]

This paper presents the three-dimensional analysis of the stress distribution arising in an isotropic infinite slab with a triaxial ellipsoidal cavity, the surface of which is subjected to the three principal stresses σ 1 , σ 2 , and σ 3 . To satisfy both boundary conditions on the surface of slab and the cavity, harmonic functions in rectangular coordinates are used and double Fourier transform is applied. The problem is reduced to the solution of three integro-differential equations. The existence and uniqueness of the solution is investigated. [ABSTRACT FROM AUTHOR]

Differential privacy mechanisms vary in modalities, and there have been many methods implementing differential privacy on unimodal data. Few studies focus on unifying them to protect multimodal data, though privacy protection of multimodal data is of great significance. In our work, we propose a multimodal differential privacy protection framework. Firstly, we use multimodal representation learning to fuse different modalities and map them to the same subspace. Then based on this representation, we use the Local Differential Privacy (LDP) mechanism to protect data. We propose two protection methods for low-dimensional and high-dimensional fusion tensors respectively. The former is based on Binary Encoding, and the latter is based on multi-dimensional Fourier Transform. To the best of our knowledge, we are the first to propose LDP-based methods for the representation learning of multimodal fusion. Experimental results demonstrate the flexibility of our framework where both approaches show efficient performance as well as high data utility. [ABSTRACT FROM AUTHOR]

The dynamic responses of an unsaturated ground with or without an embankment are analysed using 2.5D finite element method (FEM) to investigate the effects of the soil saturation and the embankment. The Galerkin method is utilised to establish the weak form governing equations for an unsaturated poroviscoelastic medium in the framework of 2.5D FEM. To reduce the reflected waves from the truncated boundaries of the 2.5D FE model, the formulations of the perfectly match layer (PML) technique are coupled with the governing equations of the unsaturated medium. The unsaturated ground vibrations with an embankment under moving loads are analysed by the proposed 2.5D FE approach, to investigate the influences of an embankment on unsaturated ground vibrations. The results of this research found that the PML technique can effectively reduce the reflected waves in the 2.5D FE model of unsaturated grounds. The increased soil saturation would increase the ground vibration amplitude, as well as the pore water pressure. Constructing embankment on the unsaturated ground could reduce the vibrations amplitude under the moving load, however increase the ground vibrations at the foot of the embankment. [ABSTRACT FROM AUTHOR]

The high-power hydraulic rock drill is the key to the development of modern hydraulic drill rig. With the increase of power and frequency of new type rock drill, the rebound of drill tool will be obvious during drilling, which will seriously affect the structural safety and operation efficiency. For this phenomenon, it is necessary to research the characteristics of double damping system to absorb the rebound energy of drill tool. A new model of incident stress wave is revised on the basis of rectangular wave. By combining the reflected stress wave with the model of damping system, the pressure fluctuation of damping system is analysed. Based on the theory of stress wave transmission, the rebound model of drill tool is established, and the transmission law of incident wave and reflection wave in drilling process is analysed. The stress wave experiment was designed and the incident wave shape was obtained by testing. Based on the experimental results, the incident wave in the rebound model is corrected by Fourier transform principle. The accumulator model and the double damping internal structure model are established. The two parameters that can independently change the energy absorption effect of the double damping system are summarised. [ABSTRACT FROM AUTHOR]

Let X be a ball quasi-Banach function space on R n and H X (R n) the associated Hardy space. In this article, under the assumptions that the Hardy–Littlewood maximal operator satisfies some Fefferman–Stein vector-valued inequality on X and is bounded on the associated space of X as well as under a lower bound assumption on the X-quasi-norm of the characteristic function of balls, the authors show that the Fourier transform of f ∈ H X (R n) coincides with a continuous function g on R n in the sense of tempered distributions and obtain a pointwise inequality about g and the Hardy space norm of f. Applying this, the authors further conclude a higher order convergence of the continuous function g at the origin and then give a variant of the Hardy–Littlewood inequality in the setting of Hardy spaces associated with X. All these results have a wide range of applications. Particularly, the authors apply these results, respectively, to mixed-norm Lebesgue spaces, variable Lebesgue spaces, and Orlicz spaces. Even in these special cases, the obtained results for variable Hardy spaces and Orlicz–Hardy spaces are totally new. [ABSTRACT FROM AUTHOR]

The measurement of spatial dependence within a set of observations or the residuals from a regression is one of the most common operations within spatial analysis. However, there appears to be a lack of appreciation for the fact that these measurements are generally based on an a priori definition of a spatial weights matrix and hence are limited to detecting spatial dependence at a single spatial scale. This paper highlights the scale-dependence problem with current measures of spatial dependence and defines a new, multi-scale approach to defining a spatial weights matrix based on a discrete Fourier transform. This approach is shown to be able to detect statistically significant spatial dependence which other multi-scale approaches to measuring spatial dependence cannot. The paper thus serves as a warning not to rely on traditional measures of spatial dependence and offers a more comprehensive, and scale-free, approach to measuring such dependence. [ABSTRACT FROM AUTHOR]

Ground surface settlement (GSS) is one of the major concerns in design and construction of a deep excavation. This paper proposes an analytical approach for the prediction of GSS induced by a braced deep excavation. Considering wall deformation and stress release, the problem investigated is formulated as a system of two second-order partial differential equations (Lame equations) with mixed boundary conditions based on the elastic theory. Taking advantage of the superposition principle, the mixed boundary conditions are decomposed into displacement and stress boundary. The separation of variables method is applied to solve the governing equations with displacement boundary, while the Fourier Transform Method is employed to derive the solution for the governing equations with stress boundary. A novel least-squares based method is proposed to transform the scatter data of wall deflection into a continuous function, which is used to determine the unknown coefficients in the solution. The validity of the proposed solution is checked by predicting the GSS of two well-documented cases and by comparing with some empirical approaches. Parametric studies are conducted to demonstrate the impact of the modulus ratio on the excavation responses. [ABSTRACT FROM AUTHOR]

In this article, we non-trivially prove the higher dimensional version of uniqueness theorem that established by M. M. Dzhrbashyan in the complex plane C . We further prove the growth property involving of the Fourier transform of functions in L 2 in the upper half-space of R n , which partly generalizes the result in Levi [Lectures on entire functions. Providence (RI): American Mathematical Society; 1996]. [ABSTRACT FROM AUTHOR]

In this paper, we price a compound option with log asset price following an extended variance gamma process. The extended variance gamma process can control the skewness and kurtosis. The parameters of the model are estimated via the maximum likelihood method from historical data. We start with finding the risk neutral Esscher measure under which the discounted asset price process is a martingale. Then we derive an analytical pricing formula for compound option in terms of the Fourier integral of the characteristic function of extended variance gamma process, and we use this formula, in combination with the FFT algorithm, to calculate the compound option price across the whole spectrum of the exercise price. Finally, we present some numerical results for illustration. [ABSTRACT FROM AUTHOR]

In this paper, a novel formulation for scattering from one-dimensional (1D) rough surface problem has been presented. The formulation is based on the representation of the scattering field in spectral domain with an unknown spectral coefficient which is solved by applying Taylor series and Fourier Transforms techniques. It is also shown that forward–backward (FB) acceleration technique can be adapted to the spectral formulation to improve the effectiveness in a limited region of convergence. The obtained results are compared with the conventional method of moments (MoM) and the limitations of the formulation are analyzed in detail. [ABSTRACT FROM AUTHOR]

In this paper, an asymmetric cryptosystem with unequal modulus decomposition in the Fourier domain is presented. The input-colour image is decomposed into its red, green, and blue components. Each component is bounded with random phase mask and undergoes Fourier Transform followed by unequal modulus decomposition. One of resulting masks acts as first private key and other one is again Fourier Transformed and undergoes unequal modulus decomposition. Further two masks are obtained, where one acts as second private key and other is phase truncated to obtain encrypted image. Encrypted image is attenuated by a factor and appended with host image to obtain watermarked image. Numerical simulations on MATLAB are performed for authenticating and validating proposed scheme. Statistical, correlation distribution, information entropy and histogram analyses are performed to demonstrate scheme efficacy. The results illustrate that the scheme resists classical cryptographic, special and occlusion attacks. The proposed scheme is also highly sensitive to its private keys and attenuation factor. [ABSTRACT FROM AUTHOR]

In this paper, we present a testing procedure for fractional orders of integration in the context of non-linear terms approximated by Fourier functions. The test statistic has an asymptotic standard normal distribution and several Monte Carlo experiments conducted in the paper show that it performs well in finite samples. Various applications using real life time series, such as US unemployment rates, US GNP and Purchasing Power Parity (PPP) of G7 countries are presented at the end of the paper. [ABSTRACT FROM AUTHOR]

Fourier transform profilometry (FTP) is widely used for real-time three-dimensional (3-D) surface shape measurement with a single frame of projection fringe pattern. The band-pass filter is very important to the shape retrieval accuracy of this technique. On the basis of the Hanning band-pass filter, a cross-shaped Hanning filter is developed in the paper to extract the first-order spectrum of deformed fringe pattern, and the effect of fringe angle on the proposed filter is analysed. The phase retrieval results using the proposed filter and Hanning filter are compared in the simulation and measurement experiment. The results show that the cross-shaped Hanning filter coordinating with the fringe pattern of about 45 degrees holds the higher accuracy of 3-D shape retrieval. [ABSTRACT FROM AUTHOR]