It is shown that Ramanujan could have proved a special case of his conjecture that his tau function is multiplicative without any recourse to modularity results.

We investigate relaxation and correlations in a class of mean-reverting models for stochastic variances. derive closed-form expressions the correlation functions leverage general form term. also discuss three specific models— multiplicative, Heston (Cox-Ingersoll-Ross) combined multiplicative-Heston—whose steady-state probability density are Gamma, Inverse Gamma Beta Prime respectively, latter ...

due to damaging effects of speckle noise to information of radar images, reduction of these effects has been considered by many researchers. we discussed speckle reduction of radar images based on curvelet transformation. more specifically we discussed the speckle reduction with emphasizing on preservation of the edges by hard thresholding of curvelet transformation. in this algorithm, first mu...

Most findings from genome-wide association studies (GWAS) are consistent with a simple disease model at a single nucleotide polymorphism, in which each additional copy of the risk allele increases risk by the same multiplicative factor, in contrast to dominance or interaction effects. As others have noted, departures from this multiplicative model are difficult to detect. Here, we seek to quant...

In [9], the notion of c-differentials was introduced as a potential expansion differential cryptanalysis against block ciphers utilizing substitution boxes. Drawing inspiration from technique higher order cryptanalysis, in this paper we propose c-derivatives and differentials investigate their properties. Additionally, consider how several classes functions, namely multiplicative inverse functi...

A time-delayed tumor cell growth model with correlated noises is investigated. In the condition of small delay time, the stationary probability distribution is derived and the stationary mean value (〈x〉st ) and normalized variance λ2 of the tumor cell population and state transition rate (κ) between two steady states are numerically calculated. The results indicate that: (i) The delay time (τ )...

In this work, the definition of first and second types multiplicative Chebyshev differential equations is given solutions these are investigated with help power series. Also, properties type polynomials proved. Finally, studies supported numerical examples.

Corrupting the input and hidden layers of deep neural networks (DNNs) with multiplicative noise, often drawn from the Bernoulli distribution (or ‘dropout’), provides regularization that has significantly contributed to deep learning’s success. However, understanding how multiplicative corruptions prevent overfitting has been difficult due to the complexity of a DNN’s functional form. In this pa...

We show existence of measure attractors for 2-D stochastic Navier-Stokes equations with general multiplicative noise.

In this paper, we develop an energy method to study finite speed of propagation and waiting time phenomena for the stochastic porous-media equation with linear multiplicative noise in up to three spatial dimensions. Based on a novel iteration technique and on stochastic counterparts of weighted integral estimates used in the deterministic setting, we formulate a sufficient criterion on the grow...