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We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of Kátai's orthogonality cri ...
The topic of this thesis is vanishing theorems in positive characteristic. In particular, we use "the covering trick of Ekedahl" to investigate the vanishing of H1(X,OX(−D)) for a big and nef Weil divisor D on a normal projective variety w ...
Byzantine resilience emerged as a prominent topic within the distributed machine learning community. Essentially, the goal is to enhance distributed optimization algorithms, such as distributed SGD, in a way that guarantees convergence despite the presence ...
This letter proposes the application of a hybrid numerical technique to two cases of interest in the space business: the reallocation of radiators and scatters on satellite platforms; and the analysis of antennas for mobile communications. It is based on t ...
During the last twenty years, Random matrix theory (RMT) has produced numerous results that allow a better understanding of large random matrices. These advances have enabled interesting applications in the domain of communication. Although this theory can ...
The operators of power distribution systems strive to lower their operational costs and improve the quality of the power service provided to their customers. Furthermore, they are faced with the challenge of accommodating large numbers of Distributed Energ ...
We consider the following class of fractional Schrodinger equations: (-Delta)(alpha)u + V(x)u = K(x)f(u) in R-N, where alpha is an element of (0, 1), N > 2 alpha, (-Delta)(alpha) is the fractional Laplacian, V and K are positive continuous functions which ...
How can we explain consciousness? This question has become a vibrant topic of neuroscience research in recent decades. A large body of empirical results has been accumulated, and many theories have been proposed. Certain theories suggest that consciousness ...
Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of an analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is applied to calcul ...
We prove an identity relating the permanent of a rank 2 matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the possibility that t ...
