Celestial holography provides a promising avenue to studying bulk scattering in flat spacetime from the perspective of boundary celestial conformal field theory (CCFT). A key ingredient connecting two sides is amplitude, which given by Mellin transform momentum space amplitude energy. As such, amplitudes can be identified with correlation functions theory. In this paper, we introduce further no...

It is known that Heston’s stochastic volatility model exhibits moment explosion, and that the critical moment s+ can be obtained by solving (numerically) a simple equation. This yields a leading order expansion for the implied volatility at large strikes: σBS(k, T ) T ∼ Ψ(s+ − 1) × k (Roger Lee’s moment formula). Motivated by recent “tail-wing” refinements of this moment formula, we first deriv...

The goals of the proposed research are: 1) To obtain additional concrete computational evidence §2.1 of the unknown structure on the imaginary parts of the non-trivial zeros of the Riemann zeta function, called herein the Riemann spectrum, following the method from [1]; specifically, the PI will compute correlations between histograms of random variables Xp (§2); 2) To prove the that the densit...

The paper presents a registration algorithm based on the Analytical Fourier-Mellin Transform (AFMT). In the Fourier Mellin registration algorithm, the estimation of the geometrical transformation is only done in the Fourier Transform phase domain which is known by containing the shape information. The proposed algorithm will be used to estimate homography since in the vicinity of key points, we...

In this paper it has been developed an algorithm for cryptography, using the Mellin's transform. Cryptography is very important to protect data to ensure that two people, using an insecure channel, may communicate in a secure way. In the present age, ensure the communications will essential to shared data that have to be protected. The original message is a plain text, and the encrypted form as...

The paper develops multiplicative compensation for complex-valued semimartingales and studies some of its consequences. It is shown that the stochastic exponential any semimartingale with independent increments becomes a true martingale after when such meaningful. This generalization L\'evy--Khintchin formula fills an existing gap in literature. allows, example, computation Mellin transform sig...

We describe a non-commutative generalization of the complex Fourier-Mellin transform to Clifford algebra valued signal functions over the domain Rp,q taking values in Cl(p,q), p+q = 2.