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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]

In this paper we obtain solutions in closed form for some special cases of the Toeplitz plus Hankel integral equation on the whole real line with the help of a new Hartley–Fourier cosine generalized convolution. [ABSTRACT FROM AUTHOR]

In this paper, we construct and study a new polyconvolution for the Hartley, Fourier cosine and Fourier sine transforms. Here, it is the first time that four different integral transforms appear in the factorization equalities. Next, we get the norm inequalities for this polyconvolution operator in the function spacesL1(ℝ) andLp(ℝ). The applications in solving integral equations and systems of two integral equations are presented. [ABSTRACT FROM AUTHOR]

The Fourier exchange theorem is generalized to 𝒮′-convolvable kernels, i.e. temperate distributions K(x, y) ∈ 𝒮′(ℝ2n ) for which K(x − y, y) is semitemperate with respect to x and partially summable with respect to y. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce some basic concepts of microlocal analysis suitable to the notion of R-regularity within Colombeau algebra. Main result is an extension of the well-known Hormander's theorem on the wave front set of the product of two distributions. [ABSTRACT FROM AUTHOR]

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in Levy and stochastic volatility models. [ABSTRACT FROM AUTHOR]

The current waterhammer models coupled with friction models cannot adequately represent the pressure wave attenuation observed in real-world pipe systems, because the pressure wave damping is affected by additional effects not accounted for. One such effect is pipe visco-elasticity from the material behaviour of pipe-wall to be investigated herein. The numerical results indicate that the pressure head attenuation attributable to unsteady friction is comparable to the visco-elastic effect during the initial transient stage, while the visco-elastic effect becomes dominant both in terms of damping and phase shift at later stages. An analytical analysis shows that the visco-elastic effect is more critical if the visco-elastic retardation time is less than the wave travel time along the entire pipeline length. In addition, it is demonstrated that the visco-elastic term in waterhammer models is wrongly referred to in the literature as energy dissipation instead of energy transfer between fluid and pipe-wall by the work done by the pressure force. [ABSTRACT FROM AUTHOR]

The theory of Fourier transform on spaces of Boehmians is well known. Several spaces of Boehmians are constructed, and the Fourier transform on these spaces are defined and investigated in the recent literature. Most recently, Dennis Nemzer introduced a new space of Boehmians [image omitted] called the space of integrable Boehmians, which is properly larger than the space [image omitted] of all integrable functions on [image omitted] (the real axis) and investigates the theory of Fourier transform on this space. In this article, we shall find a necessary and sufficient condition for a continuous function to be the Fourier transform of some integrable Boehmian. This answers a question raised by Nemzer. [ABSTRACT FROM AUTHOR]

This paper investigates a multi-resolution digital Earth model called PYXIS, which was developed by PYXIS Innovation Inc. The PYXIS hexagonal grids employ an efficient hierarchical labeling scheme for addressing pixels. We provide a recursive definition of the PYXIS grids, a systematic approach to the labeling, an algorithm to add PYXIS labels, and a discussion of the discrete Fourier transform on PYXIS grids. [ABSTRACT FROM AUTHOR]

The C L classes including analytic and Gevrey ones are the basis of a microlocal analysis developed by Hörmander and refining the C ∞ one. To extend this analysis to the framework of 𝒢, the sheaf of the simplified Colombeau algebra, we begin to embed C L into 𝒢 L constructed as a subpresheaf of 𝒢 ∞ , the subsheaf of ‘regular sections’ of 𝒢. Then, by means of a special estimate for the Fourier transform of some sequence of generalized functions, we can give a microlocal description of the singularities related to 𝒢 L . [ABSTRACT FROM AUTHOR]

We consider the problem of recovering the surface temperature history of a two-layer composite body from interior measurements. The problem is ill-posed. We shall use the Fourier transform and the method of truncated integration to regularize the problem. Error estimate is given. [ABSTRACT FROM AUTHOR]

In this article, we prove an inversion formula for the distributional Fourier transform on the space , k ∈ ℤ, k < 0. This result is applied to obtain a representation on &Sscr;′ for any distribution of , as a limit of a sequence of ordinary functions. [ABSTRACT FROM AUTHOR]

We consider the study of an eigenvalue problem obtained by linearizing about solitary wave solutions of a Boussinesq equation. Instead of using the technique of Evans functions as done by Pego and Weinstein in [R. Pego and M. Weinstein, Convective Linear Stability of Solitary Waves for Boussinesq equation. AMS , 99, 311-375] for this particular problem, we perform Fourier analysis to characterize solutions of the eigenvalue problem in terms of a multiplier operator and use the strong relationship between the eigenvalue problem for the linearized Boussinesq equation and the eigenvalue problem associated with the linearization about solitary wave solutions of a special form of the KdV equation. By using a generalization of the Rouché Theorem and the asymptotic behavior of the Fourier symbol corresponding to the eigenvalues problem for the Boussinesq equation and the Fourier symbol corresponding to the eigenvalues problem for the KdV equation, we show nonexistence of eigenvalues with respect to weighted space in a planar region containing the right-half plane. [ABSTRACT FROM AUTHOR]

The aim of this study was to document the effects of the local anesthetic agent bupivacaine on individual fibers of peripheral nerve. To accomplish this objective, compound action potentials (CAPs) were recorded from isolated frog sciatic nerves treated with bupivacaine for seven individual concentration levels. Numerical and fast Fourier transform (FFT) analysis were performed on these recordings. The areas, latency periods, maximum and minimum derivatives, and power spectrums of the CAPs were computed. The results show that the area and the absolute values of maximum and minimum derivatives decrease linearly as bupivacaine concentration increases. The power spectrum of the CAPs, which resides in the 0-1000 Hz interval, initially shifts to higher frequencies then returns to lower frequency region again with increasing bupivacaine concentration. Due to this result, it is thought that bupivacaine inhibits nerve fibers in a dose-dependent manner. It primarily affects the fibers having the least myelin sheets (motor fibers), then it begins to depress the fast conducting (neurosensorial) fibers as the bupivacaine concentration increases, and finally blocks the unmyelinated C-fibers.­­­ [ABSTRACT FROM AUTHOR]

This paper presents three recurrent neural networks to estimate the spectral content of (noisy) periodic waveforms that are common in many engineering processes. The presented (structured) networks, which are based on the recursive discrete Fourier transform, are especially useful in computing high-order derivaties of such waveforms. Unlike conventional differentiating techniques, the proposed networks perform differentiation in the frequency domain and thus are immune to uncorrelated measurement noise. Furthermore, due to moving-average based correlation scheme, which is inherent to the recursive transform, the presented networks can handle composite waveforms without a detailed signal model in the frequency domain. The performance of the proposed network architectures in a number of simulation and experimental cases has also been evaluated in this paper. [ABSTRACT FROM AUTHOR]