The way super- and sub-additive transformations of aggregation functions are introduced involve suprema and infima taken over simplexes whose dimensions may grow arbitrarily. Exact values of such transformations may thus be hard to determine in general. In this note we discuss methods of algorithmic approximation of such transformations.

We found Fuchs–Garnier pairs in 3×3 matrices for the first and second Painlevé equations which are linear in the spectral parameter. As an application of our pairs for the second Painlevé equation we use the generalized Laplace transform to derive an invertible integral transformation relating two its Fuchs–Garnier pairs in 2×2 matrices with different singularity structures, namely, the pair du...

Although considerable attention in recent years has been given to the problem of symmetry detection in general shapes, few methods have been developed that aim to detect and quantify the intrinsic symmetry of a shape rather than its extrinsic, or pose-dependent symmetry. In this paper, we present a novel approach for efficiently computing symmetries of a shape which are invariant up to isometry...

We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature —in this paper on hyperboloids—, which returns the correct marginals and has the covariance of the Shapiro functions under SO(D, 1) transformations. To the free systems obeying the Laplace-Beltrami equation on the hyperboloid, we add a conic-oscillator potential in the hyperbolic c...

In this paper, we tackle the problem of generalizing conformal maps to volumetric meshes. Current methods seek for harmonicity but unfortunately, no computational methods optimize conformality in the volumetric context. As it is proven that conformal maps do not exist for general volume transformations, we seek to optimize shape preservation with a generalization of the CauchyRiemann equations....

Introduction: Transformations are vital to any engineering subject, in particular, to electrical engineering. Fourier series, Laplace transform, Fourier transform and their counterparts in the discrete-time domain, are the fundamental tools for signal processing, communication and control engineering. Recently, the discrete Pascal transform (DPT) has been introduced to process discrete signals ...

The probability of a Brownian motion with drift to remain between two constant barriers (for some period of time) is known explicitly. In mathematical finance, this and related results are required, e.g., for the pricing of singleand double-barrier options in a Black-Scholes framework. One popular possibility to generalize the Black-Scholes model is to introduce a stochastic time-scale. This eq...

The paper is concerned with testing uniformity versus a monotone density. This problem arises in two important contexts, after transformations, testing whether a sample is a simple random sample or a biased sample, and testing whether the intensity function of a nonhomogeneous Poisson process is constant against monotone alternatives. A penalized likelihood ratio test (P-test) and a Dip likelih...

reduced differental transform method (rdtm), which isone of the useful and effective numerical method, is applied to solve nonlinear time-dependent foam drainage equation (fde) with different initial conditions. we compare our method with the famous adomian decomposition and laplace decomposition methods. the obtained resultsdemonstrated that rdtm is a powerful tool for solving nonlinear par...