Here we get the desired bound for an algebraic rank and give a bound for the number of S integral points on E in terms of its conductor. Due to the results of the previous section we have

In this paper we give an upper bound for the number of integral points on an elliptic curve E over F_q[T] in terms of its conductor N and q. We proce…

We provide novel random surface density functional theory (RSDFT) formulation in the case of geometric heterogeneous surface of solid media which is …

Symmetric informationally complete positive operator valued measures (SIC-POVMs) are studied within the framework of the probability representation o…

Modeling interactions between features improves the performance of machine learning solutions in many domains (e.g. recommender systems or sentiment …

This work demonstrates the possibility of magnetic field topology investigations using microwave polarimetric observations. We study a solar flare of…

Perturbation theory is an indispensable tool in quantum mechanics and electrodynamics that handles weak effects on particle motion or fields. However…

In this work, a new modification of an adaptive stochastic mirror descent algorithm was proposed to solve the randomized version of the convex minimization problems in the case of Lipschitz-continuous objective function and several convex functional…

The paper is devoted to a new modification of recently proposed adaptive stochastic mirror descent algorithm for convex optimization problems in the …

A method to increase the precision of feedforward networks is proposed. It requires a prior knowledge of a target function derivatives of several ord…

We study linear perturbations of classically stable Q-balls in theories admitting analytic solutions. Although the corresponding boundary value probl…

The simplest model for non-congruent phase transition of gas-liquid type was developed in frames of modified model with no associations of a binary i…

Surface plasmon polaritons (SPPs) give an opportunity to break the diffraction limit and design nanoscale optical components, however their practical…

We discuss the two-dimensional Grassmannian $SU(N)/S(U(N-2)\times U(2))$ and the flag $SU(N)/S(U(N-2)\times U(1)\times U(1))$ sigma models on a finit…

We investigate the sound absorption in quark matter due to the interaction of the sound wave with the precritical fluctuations of the diquark-pair fi…

Travelling modes of single-photon-added coherent states (SPACS) are characterized via optical homodyne tomography. Given a set of experimentally meas…

Comprehensive analysis of space debris rotational dynamics is vital for active debris removal missions that require physical capture or de-tumbling o…

We consider optimization methods for convex minimization problems under inexact information on the objective function. We introduce inexact model of …

We propose a novel autoencoding model called Pairwise Augmented GANs. We train a generator and an encoder jointly and in an adversarial manner. The g…

We tackle the problem of unsupervised visual descriptors compression, which is a key ingredient of large-scale image retrieval systems. While the dee…

Nowadays, deep neural networks (DNNs) have become the main instrument for machine learning tasks within a wide range of domains, including vision, NL…

Learning useful representations is a key ingredient to the success of modern machine learning. Currently, representation learning mostly relies on em…

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