Search

Abstract: In this paper, we investigate a specific wave equation which generates the pre-Laguerre system, and prove that the pre-Laguerre system is related to the solution of the partial differential equation with some initial conditions. [Copyright &y& Elsevier]

Abstract: We show that, under adequate norms, the Fourier transform is an isometry over a chain of nested weighted Sobolev spaces. As a result, an infinite number of useful Plancherel-like identities are derived. Possible extensions are discussed, giving rise to some open questions. [Copyright &y& Elsevier]

The harmonic ratio (HR), derived from the Fourier analysis of trunk accelerations, has been described in various ways as a measure of walking smoothness, walking rhythmicity, or dynamic stability. There is an increasing interest in applying the HR technique to investigate the impact of various pathologies on locomotion; however, explanation of the method has been limited. The aim here is to present a clear description of the mathematical basis of HRs and an understanding of their interpretation. We present harmonic theory, the interpretation of the HR using sinusoidal signals, and an example using actual trunk accelerations and harmonic analyses during limb-loading conditions. We suggest that the HR method may be better defined, not as a measure of rhythmicity or stability, but as a measure of step-to-step symmetry within a stride. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the optimal decay rates of solutions for the generalized Benjamin–Bona–Mahony equation in multi-dimensional space (). By using Fourier transform and the energy method, we obtain the convergence rates of the solutions under the condition that the initial data is small. The optimal decay rates obtained in this paper are found to be the same as the decay rate for the Heat equation. [Copyright &y& Elsevier]

Abstract: The Hilbert transform defined via the Hartley transform in contrast with the well-known Fourier transform is mathematically illustrated with a couple of geophysical applications. Although, the 1-D Fourier and Hartley transforms are identical in amplitude with a phase difference of 45°, the Hilbert transform effectively differs when defined as a function of the Hartley transform in certain geophysical applications. It may be noted here that the Hilbert transform defined through Fourier and Hartley transforms while possessing the same magnitude differs in phase by 270°. It is derived and shown mathematically that the evaluation of depth of subsurface targets is directly equal to the abscissa of the point of intersection of the gravity (magnetic) field and the Hartley–Hilbert transform; however, it is not the case with the Fourier–Hilbert transform. The practical applications are illustrated with the interpretation of gravity anomaly due to an inclined sheet-like structure across the Mobrun ore body, Noranda, Quebec, Canada, and the vertical magnetic anomaly due to a cylindrical structure over a narrow band of quartzite magnetite, Karimnagar, India. The entire process can be automated. [Copyright &y& Elsevier]

Abstract: In Kingston and Svalbe [1], a generalized finite Radon transform (FRT) that applied to square arrays of arbitrary size N × N was defined and the Fourier slice theorem was established for the FRT. Kingston and Svalbe asserted that “the original definition by Matúš and Flusser was restricted to apply only to square arrays of prime size,” and “Hsung, Lun and Siu developed an FRT that also applied to dyadic square arrays,” and “Kingston further extended this to define an FRT that applies to prime-adic arrays”. It should be said that the presented generalized FRT together with the above FRT definitions repeated the known concept of tensor representation, or tensor transform of images of size N × N which was published earlier by Artyom Grigoryan in 1984–1991 in the USSR. The above mentioned “Fourier slice theorem” repeated the known tensor transform-based algorithm of 2-D DFT [5–11], which was developed for any order N 1 × N 2 of the transformation, including the cases of N × N, when N =2 r , (r >1), and N = L r , (r ≥1), where L is an odd prime. The problem of “over-representation” of the two-dimensional discrete Fourier transform in tensor representation was also solved by means of the paired representation in Grigoryan [6–9]. [Copyright &y& Elsevier]

Abstract: This paper investigates the space fractional diffusion equation with fractional Feller’s operator. The Green’s function is obtained by using Fourier transform, and the analytical solutions of some space fractional diffusion equations with initial (or initial and boundary) condition are obtained in terms of Green’s function. In addition, numerical simulations are discussed. The results indicate that the effect range of skewness parameter has more effect on probability density than that of parameter . The results also explain the property of the skewness and long tail in the asymmetry diffusion process. [Copyright &y& Elsevier]

Abstract: The problem of non-stationary interference suppression in direct sequence spread-spectrum (DS-SS) systems is considered. The phase of interference is approximated by a polynomial within the considered interval. According to the local polynomial Fourier transform (LPFT) principle, the received signal is dechirped by using the obtained phase approximation and the interference is, in turn, suppressed by excising the corrupted low-pass frequency band. For the estimation of polynomial coefficients, we use the product high-order ambiguity function (PHAF), known for its capability to successfully resolve components of a multicomponent polynomial-phase signal (PPS). The proposed method can suppress interferences with both polynomial and non-polynomial phase. In addition, it can suppress both monocomponent and multicomponent interferences. The simulations show that the proposed method outperforms time-frequency (TF) methods, that successfully deal with multicomponent interferences, in terms of the error probability and computational complexity. [Copyright &y& Elsevier]

Abstract: This paper examines the appropriateness of the Fast Fourier Transform for decomposition and reconstruction of wave records taken at fixed locations and transposed to a different temporal and spatial point. In marine renewable energy, advanced control methods based on the future prediction of waves are being developed. These methods are based on the assumption that a forward looking prediction is available and over the years there has been a conjecture that the FFT may perform this role and that the prediction of wave behaviour at any point on the sea surface should be realizable. The validity of this statement is tested using numerical wave records. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we prove some limit theorems for the Fourier estimator of multivariate volatility proposed by Malliavin and Mancino (2002, 2009) . In a general framework of discrete time observations we establish the convergence of the estimator and some associated central limit theorems with explicit asymptotic variance. In particular, our results show that this estimator is consistent for synchronous data, but possibly biased for non-synchronous observations. Moreover, from our general central limit theorem, we deduce that the estimator can be efficient in the case of a synchronous regular sampling. In the non-synchronous sampling case, the expression of the asymptotic variance is in general less tractable. We study this case more precisely through the example of an alternate sampling. [Copyright &y& Elsevier]

Abstract: In this study we derive the general expression for the entries of the qth power for odd order complex circulant matrices of the type circ n (0, a,0,…, b). [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes three mathematical approaches that can be used to study chemical atmospheric data related to air quality: a) Descriptive statistical analysis, b) Fourier analysis and c) Wavelet analysis. These techniques are used to improve understanding of SO2 pollution in the city of Talcahuano (Chile). The results show high SO2 dispersion values, an annual average standard deviation of 63.5 μg m−3 and a Pearson coefficient of variation of 1.59. The asymmetry and kurtosis coefficients (3.1 and 14.3, respectively) confirm the “non-Gaussianity” of the SO2 concentrations. The main fluctuations of the data studied are due to seasonal and daily cyclical components. Important annual irregularities are detected by the wavelet analysis of daily cycles, especially in winter. This cyclical component is fundamentally due to meteorological factors (because the zonal industrial emissions, mainly emitted by Oil Refining Plant, are roughly constant). Non-negligible correlations, between SO2 concentration and several meteorological variables (vertical wind, temperature, solar radiation, horizontal wind), were also verified (0.49, 0.40, 0.36 and 0.34, respectively). [Copyright &y& Elsevier]

Abstract: A Fourier-transformed eddy current (FTEC) technique has been proposed and developed. This technique employs Fourier transformation analysis to analyze pulsed eddy current signals measured by magnetoresistive sensors. The advantage of this technique is that the intrinsic response, , of a sample material can be extracted without it being affected by the characteristics of the measurement systems. Aluminum plates with an area of and various thicknesses were used as test samples. We examined the relationship between the thickness of the sample and the frequency, when ''s reached 90% of the maximum magnitude. The results indicate that FTEC can be used for non-contact measurements of conductive materials. We also evaluated lift-off effects for for 1- and 5-mm-thick samples. The deviations of the frequencies for the 90% response were and for the 1- and 5-mm-thick samples, respectively. This result indicates that the lift-off effect was reduced by the FTEC analysis. [Copyright &y& Elsevier]

Abstract: Based on the discrete fractional random transform (DFRNT), we present the discrete fractional random cosine and sine transforms (DFRNCT and DFRNST). We demonstrate that the DFRNCT and DFRNST can be regarded as special kinds of DFRNT and thus their mathematical properties are inherited from the DFRNT. Numerical results of DFRNCT and DFRNST for one and two-dimensional functions have been given. [Copyright &y& Elsevier]

Abstract: Many features of natural phenomena can be observed using time records or series of observations. The time records of phenomena such as physiological and economic data or the temperature of a river can display short- and long-term time scales. These signals can also present trends which are an important aspect of their complexity. These trends can lead to difficulties in the analysis of the signals. In this short note we suggest a modified approach for the analysis of low frequency trends added to a noise in time series. We will name this method Fourier-detrended fluctuation analysis, but it is a simple high-pass filter. Using this approach, we will attempt to quantify correlations with trends in a time series. By cutting the first few coefficients of a Fourier expansion, we show that we are able to efficiently remove the globally varying trends. [Copyright &y& Elsevier]

The brain''s memory system can store without any apparent constraint, it recalls stored information efficiently and it is robust against lesion. Existing models of memory do not fully account for all these features. The model due to Hopfield (Proc. Natl. Acad. Sci. USA 79 (1982) 2554) based on Hebbian learning (The Organization of Behaviour, Wiley, New York, 1949) shows an early saturation of memory with the retrieval from memory becoming slow and unreliable before collapsing at this limit. Our hypothesis (Physica A 276 (2000) 352) that the brain might store orthogonalized information improved the situation in many ways but was still constrained in that the information to be stored had to be linearly independent, i.e., signals that could be expressed as linear combinations of others had to be excluded. Here we present a model that attempts to address the problem quite comprehensively in the background of the above attributes of the brain. We demonstrate that if the brain devolves incoming signals in analogy with Fourier analysis, the noise created by interference of stored signals diminishes systematically (which yields prompt retrieval) and most importantly it can withstand partial damages to the brain. [Copyright &y& Elsevier]

The description of the three-dimensional objects independent of size, position and orientation, is an important and difficult problem in scene analysis. The description of moment invariants is recognized as the usual method in this case. In this paper, we intend to derive a stable set of volume descriptors (VDs) for three-dimensional gray-level objects, which are invariant under the group of motions of the three-dimensional Euclidean space. [Copyright &y& Elsevier]

Abstract: The aim of this work is to generalize the methods of Fourier Analysis in order to apply them to a wide class of possibly non-integrable functions, with infinitely many variables. The method consists in distinguishing several levels of observability, with a natural meaning. Mathematical coherence is ensured by the fact that these natural concepts are represented within a sure mathematical framework, that of the relative set theory [Y. Péraire, Théorie relative des ensembles internes, Osaka J. Math. 29 (1992) 267–297; Y. Péraire, Some extensions of the principles of idealization transfer and choice in the relative internal set theory, Arch. Math. Logic 34 (1995) 269–277]. This work is also a step for another approach of the Fourier transform of functionals. It can be related to the one, which use double extensions of standard real numbers, performed by T. Nitta and T.Okada in [T. Okada, T. Nitta, Infinitesimal Fourier transformation for the space of functionals, in: Topics in Almost Hermitian Geometry and Related Fields, World Sci. Publ., 2005; T. Okada, T. Nitta, Poisson summation formula for the space of functionals, Nihonkai Math. J. 16 (2005) 1–21]. [Copyright &y& Elsevier]