Converting renewable energy into ammonia has been recognized as a promising way to realize "green hydrogen substitution" in the chemical industry. However, power (RePtA) requires an essential investment facilities provide buffer against strong volatility of and limited flexibility synthesis, which involves three main stakeholders, namely, power, hydrogen, ammonia. Therefore, sizing pricing RePtA play core role balancing interest demands investors. This article proposes optimal method for...

Abstract In this paper, we consider a bi‐quadratic homogeneous polynomial optimization problem over two unit spheres arising in nonlinear elastic material analysis and entanglement studies quantum physics. The is equivalent to computing the largest M ‐eigenvalue of fourth‐order tensor. To solve problem, propose practical method whose validity guaranteed theoretically. make sequence generated by converge good solution also develop an initialization scheme. given numerical experiments show...

In this paper, we show that for a symmetric tensor, its best rank-$1$ approximation is approximation. Based on result, positive lower bound the ratio of tensor given. Furthermore, higher order polynomial spherical optimization problem can be reformulated as multilinear problem. Then, present modified power algorithm solving homogeneous Numerical results are presented, illustrating effectiveness proposed algorithm.

Abstract In this paper, we present a novel approach to the low rank matrix recovery (LRMR) problem by casting it as group sparsity problem. Specifically, propose flexible sparse regularizer (FLGSR) that can any number of columns unit, whereas existing methods each column unit. We prove equivalence between and FLGSR under some mild conditions, show LRMR with either them has same global minimizers. also establish relaxed penalty formulations FLGSR. then an inexact restarted augmented...

In this paper, the cubic spherical optimization problems, including one-spherical/two-spherical/three-spherical are discussed. We first show that two-spherical problem is a special case of three-spherical problem. Then we one-spherical and have same optimal value when tensor symmetric. addition, NP-hardness them established. For problem, discuss conditions under which polynomial time solvable if approximation scheme (PTAS) exists. present relative quality bound by finding largest singular...

A real symmetric tensor is said to be copositive if the associated homogeneous form greater than or equal zero over nonnegative orthant. The problem of detecting copositivity NP-hard. This paper proposes a complete semidefinite relaxation algorithm for tensor. If it copositive, can get certificate copositivity. not, point that refutes We show detection done by solving finite number relaxations all tensors. As special case, also applied detect matrix

Three conjugated polymers based on the thieno[3,2-<italic>b</italic>]indole (TI) unit as electron-donor block and benzothiadiazole (BT) electron-accepting thiophene rings spacers. Their photovoltaic performance were finely tuned by

Comon's Conjecture claims that for a symmetric tensor, its rank and coincide. We show this conjecture is true under an additional assumption the of tensor not larger than order. Moreover, if less order, then all decompositions are necessarily decompositions.

Abstract Low Tucker rank tensor completion has wide applications in science and engineering. Many existing approaches dealt with the by unfolding matrix rank. However, a to would destroy data's original multi‐way structure, resulting vital information loss degraded performance. In this article, we establish relationship between ranks of factor matrices decomposition. Then, reformulate low problem as multilinear problem. For reformulated problem, symmetric block coordinate descent method is...

Hexagonal close packed Cr₂O₃, fabricated by an electrospinning technique combined with a heating method, is adopted for the first time as catalyst non-aqueous lithium–oxygen (Li–O₂) batteries.

A linear map between real symmetric matrix spaces is positive if all semidefinite matrices are mapped to ones. separable it can be written as a summation of Kronecker products matrices. This paper studies how check or not and not. We propose numerical algorithms, based on Lasserre's type relaxations, for solving such questions. To the positivity map, we construct hierarchy relaxations minimizing associated biquadratic form over unit spheres. show that detected by finite number relaxations....

Motivated by the Tucker decomposition, in this paper we introduce a new tensor decomposition for third order tensors, which decomposes to three factor tensors. Each has two low dimensions. We call such triple and corresponding rank rank. The of is not greater than middle value number parameters bilevel form standard less substantial cases. theoretical discovery confirmed numerically. Numerical tests show that data from practical applications as internet traffic image are ranks. A recovery...

Shape memory alloys exhibit superelasticity and shape properties by virtue of a reversible phase transformation between austenite martensite. Here, 14% recoverable strain is reported in Heusler-type Ni52.87Mn23.82Ga23.32 microwire, fabricated rapid solidification via the Taylor method, with diameter 110 µm. The microwire exhibits superelastic ~11%, very low Young's modulus ~5.5 GPa, critical stress ~110 MPa mechanical stability during cyclic tensile test. We attribute this enhanced ductility...

In this paper, an SDP relaxation algorithm is proposed to test the copositivity of higher order tensors. By solving finitely many relaxations, can determine Furthermore, for any copositive but not strictly tensor, also check it exactly. Some numerical results are reported show efficiency algorithm.

SUMMARY In this paper, we consider the NP‐hard problem of finding global minimum quadratically constrained multivariate bi‐quadratic optimization. We present some bounds considered via approximately solving related bi‐linear semidefinite programming (SDP) relaxation. Based on SDP relaxation, also establish approximation solution methods, which generalize methods for quadratic polynomial optimization in ( SIAM J. Optim. 2003; 14 :268–283). Finally, a special form, whose relaxation can be...

Rice grain yield and quality are negatively impacted by high temperature stress. Irrigation water significantly affects rice growth development, thus influencing quality. The role of cooler irrigation in counteracting induced damages not explored. Hence, the present study two hybrids, Liangyoupeijiu (LYPJ) IIyou 602 (IIY602) were exposed to heat stress irrigated with having different temperatures a split-split plot experimental design. was imposed starting from heading until maturity under...