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Rice grain yield and quality are negatively impacted by high temperature stress. Irrigation water temperature significantly affects rice growth and development, thus influencing yield and quality. The role of cooler irrigation water in counteracting high temperature induced damages in rice grain yield and quality are not explored. Hence, in the present study two rice hybrids, Liangyoupeijiu (LYPJ) and IIyou 602 (IIY602) were exposed to heat stress and irrigated with water having different temperatures in a splitsplit plot experimental design. The stress was imposed starting from heading until maturity under field-based heat tents, over two consecutive years. The maximum day temperature inside the heat tents was set at 38°C. For the irrigation treatments, two different water sources were used including belowground water with cooler water temperature and pond water with relatively higher water temperature. Daytime mean temperatures in the heat tents were increased by 1.2–2.0°C across two years, while nighttime temperature remained similar at both within and outside the heat tents. Cooler belowground water irrigation did have little effect on air temperature at the canopy level but decreased soil temperature (0.2–1.4°C) especially under control. Heat stress significantly reduced grain yield (33% to 43%), panicles m-2 (9% to 10%), spikelets m-2 (15% to 22%), grain-filling percentage (13% to 26%) and 1000-grain weight (3% to 5%). Heat stress significantly increased chalkiness and protein content and decreased grain length and amylose content. Grain yield was negatively related to air temperature at the canopy level and soil temperature. Whereas grain quality parameters like chalkiness recorded a significantly positive association with both air and soil temperatures. Irrigating with cooler belowground water reduced the negative effect of heat stress on grain yield by 8.8% in LYPJ, while the same effect was not seen in IIY602, indicating cultivar differences in their response to irrigation water temperature. Our findings reveal that irrigating with cooler belowground water would not significantly mitigate yield loss or improve grain quality under realistic field condition. The outcome of this study adds to the scientific knowledge in understanding the interaction between heat stress and irrigation as a mitigation tool. Irrigation water temperature regulation at the rhizosphere was unable to counteract heat stress damages in rice and hence a more integrated management and genetic options at canopy levels should be explored in the future. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel regularization with a truncated difference of nuclear norm and Frobenius norm of form Lt,*--αF with an integer t and parameter a for rank minimization problem. The forward-backward splitting (FBS) algorithm is proposed to solve such a regularization problem, whose subproblems are shown to have closed-form solutions. We show that any accumulation point of the sequence generated by the FBS algorithm is a first-order stationary point. In the end, the numerical results demonstrate that the proposed FBS algorithm outperforms the existing methods. [ABSTRACT FROM AUTHOR]

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

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

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

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

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

In this paper, the cubic spherical optimization problems, including the cubic one-spherical/two-spherical/three-spherical optimization problems, are discussed. We first show that the two-spherical optimization problem is a special case of the three-spherical optimization problem. Then we show that the one-spherical optimization problem and the two-spherical optimization problem have the same optimal value when the tensor is symmetric. In addition, NP-hardness of them are established. For the cubic three-spherical optimization problem, we discuss the conditions under which the problem is polynomial time solvable and if the polynomial time approximation scheme (PTAS) exists. Then we present a relative quality bound by finding the largest singular values of matrices. Finally, a practical method for solving the cubic three-spherical optimization problem is proposed and preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

This paper studies the relationship between the so-called bi-quadratic optimization problem and its semidefinite programming (SDP) relaxation. It is shown that each r-bound approximation solution of the relaxed bi-linear SDP can be used to generate in randomized polynomial time an $${\mathcal{O}(r)}$$-approximation solution of the original bi-quadratic optimization problem, where the constant in $${\mathcal{O}(r)}$$ does not involve the dimension of variables and the data of problems. For special cases of maximization model, we provide an approximation algorithm for the considered problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider a bi-quadratic homogeneous polynomial optimization problem over two unit spheres arising in nonlinear elastic material analysis and in entanglement studies in quantum physics. The problem is equivalent to computing the largest M-eigenvalue of a fourth-order tensor. To solve the problem, we propose a practical method whose validity is guaranteed theoretically. To make the sequence generated by the method converge to a good solution of the problem, we also develop an initialization scheme. The given numerical experiments show the effectiveness of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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