<p>Planar Turán number, denoted by $ \mathrm{ex}_{\mathcal{P}}(n, H) $, is the maximum number of edges in an n $-vertex planar graph which does not contain H as a subgraph. Ghosh, Győri, Paulos and Xiao initiated topic for double stars. There were two stars S_{3, 4} 5} that remained unknown. In this paper, we give exact value 4}) $.</p>

With the development of end-to-end control based on deep learning, it is important to study new system modeling techniques realize dynamics with high-dimensional inputs. In this paper, a novel Koopman-based convolutional network, called CKNet, proposed identify latent from raw pixels. CKNet learns an encoder and decoder play role Koopman eigenfunctions modes, respectively. The eigenvalues can be approximated by learned state transition matrix. deterministic network (DCKNet) variational...

In recent years, BP neural network is widely used in the field of nonlinear prediction. This paper proposes a variable step size algorithm for forecast investment on inventory clearance and framework to improve prediction accuracy reduce risks.

INTRODUCTION: With the continuous advancement of urbanization, urban landscape sculpture plays an increasingly important role in modern planning. Traditional planning and design methods make it challenging to demonstrate three-dimensional sense artistry fully; therefore, this study explores a new method designing based on virtual reconstruction.OBJECTIVES: This aims enhance through reconstruction technology meet needs development better. By using advanced technical means, can be made more...

The planar Tur\'{a}n number of a graph $H$, denoted by $ex_{\mathcal{P}}(n,H)$, is the maximum edges in an $n$-vertex $H$-free graph. Recently, D. Ghosh, et al. initiated topic double stars and prove that $ex_{\mathcal{P}}(n,S_{2,5})\leq \frac{20}{7}n$. In this paper, we continue to study give sharp upper bound \frac{19}{7}n-\frac{18}{7}$ for all $n\geq 1$, with equality when $n=12$. This improves Ghosh's result.

The planar Tur$\acute{a}$n number of a graph $H$, denoted by $ex_{\mathcal{P}}(n,H)$, is the maximum edges in an $n$-vertex $H$-free graph. Recently, D. Ghosh, et al. initiated topic double stars and prove that $ex_{\mathcal{P}}(n,S_{2,5})\leq \frac{20}{7}n$. In this paper, we continue to study give sharp upper bound \frac{19}{7}n-\frac{18}{7}$ for all $n\geq 1$, with equality when $n=12$. This improves Ghosh's result.

Planar Tur\'an number $ex_{\mathcal{P}}(n,H)$ of $H$ is the maximum edges in an $n$-vertex planar graph which does not contain as a subgraph. Ghosh, Gy\H{o}ri, Paulos and Xiao initiated topic for double stars. In this paper, we prove that $ex_{\mathcal{P}}(n,S_{2,4})\leq \frac{31}{14}n$ $n\geq 1$, show equality holds infinitely many integers $n$.

In this paper, we investigate an optimization scheme for extreme learning machine (ELM) regression, named OELR, to overcome the limitation of ELM that it may lead overfitting on large training data sets. OELR amounts minimization ε-insensitive loss and norm output weights single hidden layer feedforward networks (SLFNs). Compared support vector regression (SVR), has less constraints. Empirical results benchmark sets show competitive performance over state-ofthe-art algorithms.