[9] **viXra:1810.0216 [pdf]**
*submitted on 2018-10-13 16:33:06*

**Authors:** Toshiro Takami

**Comments:** 2 Pages.

I calculated ζ (5) and ζ (7).
ζ (5), ζ (7) tended to converge quickly.
In particular, convergence of ζ (7) was fast.

**Category:** General Mathematics

[8] **viXra:1810.0195 [pdf]**
*replaced on 2018-10-13 00:58:02*

**Authors:** Toshiro Takami

**Comments:** 11 Pages.

I calculated ζ (3),ζ(5). ζ (7),ζ(9)……… ζ (23).
And the formula indicated.

**Category:** General Mathematics

[7] **viXra:1810.0186 [pdf]**
*submitted on 2018-10-11 08:57:08*

**Authors:** John Smith

**Comments:** 6 Pages.

basic economics

**Category:** General Mathematics

[6] **viXra:1810.0152 [pdf]**
*submitted on 2018-10-09 07:46:04*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

En esta nota recordamos una serie trigonométrica que involucra a la constante de Catalan.

**Category:** General Mathematics

[5] **viXra:1810.0150 [pdf]**
*submitted on 2018-10-09 08:05:47*

**Authors:** Edgar Valdebenito

**Comments:** 15 Pages.

This note presents a collection of mathematical formulas.

**Category:** General Mathematics

[4] **viXra:1810.0122 [pdf]**
*submitted on 2018-10-08 22:09:22*

**Authors:** Wendong Wang, Feng Zhang, Jianjun Wang

**Comments:** 10 Pages.

In this paper, we theoretically investigate the low-rank matrix recovery problem in the context of the unconstrained regularized nuclear norm minimization (RNNM) framework. Our theoretical findings show that, one can robustly recover any matrix X from its few noisy measurements b=A(X)+n with a bounded constraint ||n||_{2}<ε via the RNNM, if the linear map A satisfies restricted isometry property (RIP) with δ_{tk}<√(t-1)/t for certain fixed t>1. Recently, this condition with t≥4/3 has been proved by Cai and Zhang (2014) to be sharp for exactly recovering any rank-k matrices via the constrained nuclear norm minimization (NNM). To the best of our knowledge, our work first extends nontrivially this recovery condition for the constrained NNM to that for its unconstrained counterpart. Furthermore, it will be shown that similar recovery condition also holds for regularized l_{1}-norm minimization, which sometimes is also called Basis Pursuit DeNoising (BPDN).

**Category:** General Mathematics

[3] **viXra:1810.0121 [pdf]**
*replaced on 2018-10-14 08:59:07*

**Authors:** Feng Zhang, Wendong Wang, Jianwen Huang, Jianjun Wang

**Comments:** 22 Pages.

The essential task of multi-dimensional data analysis focuses on the tensor decomposition and the corresponding notion of rank. However, most tensor ranks are not well defined with a tight convex relaxation. In this paper, by introducing the notion of tensor singular value decomposition (t-SVD), we establish a regularized tensor nuclear norm minimization (RTNNM) model for low tubal rank tensor recovery. In addition, the tensor nuclear norm within the unit ball of the tensor spectral norm here has been shown to be a convex envelop of tensor average rank. On the other hand, many variants of the restricted isometry property (RIP) have proven to be crucial frameworks and analysis tools for recovery of sparse vectors and low-rank tensors. So, we initiatively define a novel tensor restrict isometry property (t-RIP) based on t-SVD. Besides, our theoretical results show that any third-order tensor X∈R^{n_{1}× n_{2}× n_{3}} whose tubal rank is at most r can stably be recovered from its as few as measurements y = M(X)+w with a bounded noise constraint ||w||_{2}≤ε via the RTNNM model, if the linear map M obeys t-RIP with δ_{tr}^{M}<√（t-1）/(n_{3}^{2}+t-1) for certain fixed t>1. Surprisingly, when n_{3}=1, our conditions coincide with T. Cai and A. Zhang's sharp work in 2013 for low-rank matrix recovery via the constrained nuclear norm minimization. We note that, as far as the authors are aware, such kind of result has not previously been reported in the literature.

**Category:** General Mathematics

[2] **viXra:1810.0023 [pdf]**
*submitted on 2018-10-02 11:05:44*

**Authors:** Peter J. Nolan, Shane D. Ross}

**Comments:** 8 Pages. In preparation for journal submission

Lagrangian analysis using techniques such as the finite-time Lyapunov exponent (FTLE) field or Lagrangian coherent structures can be very informative as to the dynamics of a system, however these methods can be time consuming to integrate and tricky to interpret. Recent developments in dynamical systems theory have generated new Eulerian methods, such as objective Eulerian coherent structures (OECS), for the anaylsis of dynamical systems. In this paper we will build upon this previous work by connecting OECS to FTLE, and providing a new method for the visualization of OECS.

**Category:** General Mathematics

[1] **viXra:1810.0018 [pdf]**
*submitted on 2018-10-02 16:30:39*

**Authors:** Surapati Pramanik, Rama Mallick

**Comments:** 13 Pages.

VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) is a popular strategy for multi- attribute decision making (MADM). We extend the VIKOR strategy for multi- attribute group decision making (MAGDM) problems in trapezoidal neutrosophic number environment. In decision making situation, the attribute values are expressed in terms of single-valued trapezoidal neutrosophic numbers. Then we develop an extended VIKOR strategy to deal with MAGDM with single-valued trapezoidal neutrosophic numbers. The influence of decision-making mechanism coefficient is presented. To illustrate and validate the proposed VIKOR strategy, we solve an illustrative numerical example of MAGDM problem in trapezoidal fuzzy neutrosophic number environment.

**Category:** General Mathematics