1123 consider N as a continuous variable and seek N* so that aF,/aN = 0. The result is 1-Mp 1-2 which implies N* > M + 1. Although these channels are simple, they constitute a useful model for comparison with the channels studied in the text, which are perhaps of greater practical interest. The special case of N* = M and p = r should be mentioned. The Gram matrix for this channel is given by (B...

A peak effect minimization problem in the free motion of linear systems is considered paper. The paper proposes an iterative procedure for using a combination recently proposed gramian-based approach and theory condition number eigenvectors matrix upper bound estimations system state processes. Minimization control costs based on analysis singular value decomposition gramian costs, followed by ...

We analyze the behavior of a random matrix with independent rows, each distributed according to the same probability measure on R or on 2. We investigate the spectrum of such a matrix and the way the ellipsoid generated by it approximates the covariance structure of the underlying measure. As an application, we provide estimates on the deviation of the spectrum of Gram matrices from the spectru...

A system of linear conditions is presented for Wronskian and Grammian solutions to a (3+1)-dimensional generalized vcKP equation. The formulations of these solutions require a constraint on variable coefficients.

In this paper, it is shown that a refinement of Hölder’s inequality can be established using the positive definiteness of the Gram matrix. As applications, some improvements on Minkowski’s inequality, Fan Ky’s inequality and Hardy’s inequality are given.

While continuous word embeddings are gaining popularity, current models are based solely on linear contexts. In this work, we generalize the skip-gram model with negative sampling introduced by Mikolov et al. to include arbitrary contexts. In particular, we perform experiments with dependency-based contexts, and show that they produce markedly different embeddings. The dependencybased embedding...

In this work, we consider linear and nonlinear fractional stochastic delay systems driven by the Rosenblatt process. With aid of delayed Mittag-Leffler matrix functions representation solutions these systems, derive controllability results as an application. By introducing a Gramian matrix, provide sufficient necessary criteria for systems. Furthermore, employing Krasnoselskii’s fixed point the...

The problem of state dimension reduction and quantizer design under communication constraints is discussed for state estimation in quantized linear systems. Subject to the limited signal power, number and bandwidth of the parallel channels, a differential pulse code modulation (DPCM)-like structure is adopted to generate the quantized innovations as the transmitted signals, and the multi-level ...

This paper is concerned with the exact controllability of linear mean-field stochastic systems deterministic coefficients. With help theory backward differential equations (MF-BSDEs, for short) and some delicate analysis, we obtain a version Gramian matrix criterion general time-variant case, Kalman rank condition special time-invariant case.

In this work, we consider dynamical systems of linear and nonlinear stochastic delay-differential equations driven by the Rosenblatt process. With aid delayed matrix functions these systems, derive controllability results as an application. By using a delay Gramian matrix, provide sufficient necessary criteria for systems. addition, employing Krasnoselskii’s fixed point theorem, present some Ou...