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In this paper, we propose a novel dual-user image authentication algorithm based on the double fractional Mellin transform. We perform a security analysis of the nonlinear cryptosystem based on the fractional Mellin transform and show its vulnerability. In the proposed algorithm, polar decomposition and sparse multiplexing are additionally applied to generate a ciphertext. During the encryption process, polar decomposition generates two private keys that can be utilized on the dual-user authentication platform. The proposed scheme has a large key space and is robust against several attacks such as contamination attacks (noise and occlusion), brute force attacks, plain-text attacks, and special iterative attacks. In addition, we carry out a comparison with a similar existing scheme for the proposed algorithm. Simulated results indicate that the proposed authentication algorithm is feasible and robust.

In a large number of applications, different types of descriptors have been implemented to identify and recognize textured objects in grayscale images. Their classification must be carried out independently of their position, orientation and scale. The property of completeness of descriptors which guarantees their uniqueness for a given shape is also a sought-after property. It is known in the literature that such a property is difficult to obtain. It was possible to achieve it in rare cases for planar curves using for instance Fourier descriptors or the curvature. In grayscale images, we know at least three cases of complete descriptors: Those based on Zernike moments, those computed from the analytical Fourier–Mellin transform or obtained from the complex moments. To our current knowledge, in the case of curved surfaces and 3D volume images, there are yet no complete descriptors invariant to the 3D rigid motions. The property of invertibility of invariants, introduced recently and which implies completeness, allows the reconstruction of the object shape up to a similarity. The two sets of descriptors that we propose here verify on the one hand the invariance and the invertibility and on the other hand, the notion of stability which was introduced to guarantee the fact that the descriptors vary slightly during small variations in the shape. Their construction based on the Radon transform allows a certain robustness with respect to noise. In this article, we rigorously demonstrate the properties of invariance, invertibility and convergence for the two sets of proposed invariants. To evaluate the stability and robustness with respect to noise, experimental studies are carried out on different well-known datasets, namely Kimia 99 and MPEG7. We introduced our own face dataset, which we named FSTEF for further evaluation. On the other hand, several types and levels of noise were added to test the robustness to noise. Therefore, the effectiveness of the suggested sets of invariants are demonstrated by the different studies proposed in the present work.

This work investigates the interplay between the Mellin transform and Lambert transforms to derive several novel results. In particular, we establish new inversion formulae for the Lambert transforms along with a Plancherel-type identity. Additionally, we explore the implications of these findings, highlighting their relevance to Salem’s equivalence and potential connections with the Riemann hypothesis.

For recursively generated shifts, we provide definitive answers to two outstanding problems in the theory of unilateral weighted shifts: the Subnormality Problem ( SP ) (related to the Aluthge transform) and the Square Root Problem ( SRP ) (which deals with Berger measures of subnormal shifts). We use the Mellin Transform and the theory of exponential polynomials to establish that ( SP ) and ( SRP ) are equivalent if and only if a natural functional equation holds for the canonically associated Mellin transform. For p -atomic measures with p ≤ 6 , our main result provides a new and simple proof of the above-mentioned equivalence. Subsequently, we obtain an example of a 7-atomic measure for which the equivalence fails. This provides a negative answer to a problem posed by Exner (J Oper Theory 61:419–438, 2009), and to a recent conjecture formulated by Curto et al. (Math Nachr 292:2352–2368, 2019).

Integral transforms play a fundamental role in science and engineering. Above all, the Fourier transform is the most vital, which has some specifications—Laplace transform, Mellin transform, etc., with their inverse transforms. In this paper, we restrict ourselves to the use of a few versions of the Mellin transform, which are best suited to the treatment of zeta functions as Dirichlet series. In particular, we shall manifest the underlying principle that automorphy (which is a modular relation, an equivalent to the functional equation) is intrinsic to lattice (or Epstein) zeta functions by considering some generalizations of the holomorphic and non-holomorphic Eisenstein series as the Epstein-type Eisenstein series, which have been treated as totally foreign subjects to each other. We restrict to the modular relations with one gamma factor and the resulting integrals reduce to a form of the modified Bessel function. In the H-function hierarchy, what we work with is the second simplest H[sub.1,1] [sup.1,1]↔H[sub.0,2] [sup.2,0], with H denoting the Fox H-function.

In this paper, in order to serve credit risk management, we introduce a pricing model for a vulnerable Bull Spread options in a Mixed Modified Fractional Hull-White-Vasicek stochastic volatility and stochastic interest rate model. We use Milstein scheme to find the sample paths of asset price and its volatility, and the sample paths of interest rates of asset price movement. We use the double Mellin transform to obtain an analytical vulnerable bull spread call option formula and an analytical vulnerable bull spread put option formula under fractional stochastic volatility and fractional stochastic interest rates.

The family of Generalized Gaussian (GG) distributions has received considerable attention from the engineering community, due to the flexible parametric form of its probability density function, in modeling many physical phenomena. However, very little is known about the analytical properties of this family of distributions, and the aim of this work is to fill this gap. Roughly, this work consists of four parts. The first part of the paper analyzes properties of moments, absolute moments, the Mellin transform, and the cumulative distribution function. For example, it is shown that the family of GG distributions has a natural order with respect to second-order stochastic dominance. The second part of the paper studies product decompositions of GG random variables. In particular, it is shown that a GG random variable can be decomposed into a product of a GG random variable (of a different order) and an independent positive random variable. The properties of this decomposition are carefully examined. The third part of the paper examines properties of the characteristic function of the GG distribution. For example, the distribution of the zeros of the characteristic function is analyzed. Moreover, asymptotically tight bounds on the characteristic function are derived that give an exact tail behavior of the characteristic function. Finally, a complete characterization of conditions under which GG random variables are infinitely divisible and self-decomposable is given. The fourth part of the paper concludes this work by summarizing a number of important open questions.

This paper introduces extensions H4,p and X8,p of Horn’s double hypergeometric function H4 and Exton’s triple hypergeometric function X8, taking into account recent extensions of Euler’s beta function, hypergeometric function, and confluent hypergeometric function. Among the numerous extended hypergeometric functions, the primary rationale for choosing H4 and X8 is their comparable extension type. Next, we present various integral representations of Euler and Laplace types, Mellin and inverse Mellin transforms, Laguerre polynomial representations, transformation formulae, and a recurrence relation for the extended functions. In particular, we provide a generating function for X8,p and several bounding inequalities for H4,p and X8,p. We explore the utilization of the H4,p function within a probability distribution. Most special functions, such as the generalized hypergeometric function, the Beta function, and the p-extended Beta integral, exhibit natural symmetry.

In this paper, we present a fresh perspective on the fractional power of the Bessel operator using the Mellin transform. Drawing inspiration from the work of Pagnini and Runfola, we develop a new approach by employing Tato’s type lemma for the Hankel transform. As an application, we establish a new intertwining relation between the fractional Bessel operator and the fractional second derivative, emphasizing the important role of the Mellin transform in the domain of fractional calculus associated with the Bessel operator.

In this article, we consider the asymptotic behaviour of the modified Mellin transform , , of the Riemann zeta-function using weak convergence of probability measures in the space of analytic functions defined by means of shifts , where is a real increasing to differentiable function with monotonically decreasing derivative satisfying a certain estimate connected to the second moment of . We prove in this case that the limit measure is concentrated at the point . This result is applied to the approximation of by shifts