Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature. This report is aiming to solve the scattering and in...
We have recently solved the inverse scattering problem for one parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations conne...
The Pavlov equation is one of the simplest integrable systems of vector fields arising from various problems of mathematical physics and differential geometry which are intensively studied in recent literature. In this report, solving a nonlinear Rie...
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There exist two issues among popular lattice reduction (LR) algorithms that should cause our concern. The first one is Korkine-Zolotarev (KZ) and Lenstra-Lenstra-Lovasz (LLL) algorithms may increase the lengths of basis vectors. The other is KZ reduc...
Noisy intermediate-scale quantum cryptanalysis focuses on the capability of near-term quantum devices to solve the mathematical problems underlying cryptography, and serves as a cornerstone for the design of post-quantum cryptographic algorithms. For...
This article present a concise estimate of upper and lower bound on the cardinality containing shortest vector in a lattice reduced by block Korkin-Zolotarev method (BKZ) for different value of the block size. Paper show how density affect to this ca...
We propose a practical algorithm for block Korkin-Zolotarev reduction, a concept introduced by Schnorr, using CPU arbitrary length Householder QR-decomposition for orthogonalization and double precision OpenCL GPU Finke-Post shortest vector enumerati...
Although "black box" models such as Artificial Neural Networks, Support Vector Machines, and Ensemble Approaches continue to show superior performance in many disciplines, their adoption in the sensitive disciplines (e.g., finance, healthcare) is que...
We introduce a parametrization scheme for $J/ψ(ψ^\prime)\to VP$ where the effects of SU(3) flavor symmetry breaking and doubly OZI-rule violation (DOZI) can be parametrized by certain parameters with explicit physical interpretations. This scheme...
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I'm in Linear Algebra right now and we're mostly just working with vector spaces, but they're introducing us to the basic concepts of fields and groups in preparation taking for Abstract Algebra la...
A generalised Amit-Roginsky vector model in flat space is obtained as the effective dynamics of pertubations around a classical solution of the Boulatov group field theory for 3d euclidean quantum gravity, extended to include additional matter degree...
We establish a sprinkled decoupling inequality for increasing events of Gaussian vectors with an error that depends only on the maximum pairwise correlation. As an application we prove the non-triviality of the percolation phase transition for Gaussi...
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