Ridigity of Ricci solitons with weakly harmonic Weyl tensors

In this paper, we prove rigidity results on gradient shrinking or steady Ricci solitons with weakly harmonic Weyl curvature tensors. Let be a compact gradient shrinking Ricci soliton satisfying with constant. We show that if satisfies , then is Einstein. Here denotes the Weyl curvature tensor. In the case of noncompact, if M is complete and satisfies the same condition, then M is rigid in the sense that M is given by a quotient of product of an Einstein manifold with Euclidean space. These are generalizations of the previous known results in 10 , 14 and 19 . Finally, we prove that if is a complete noncompact gradient steady Ricci soliton satisfying , and if the scalar curvature attains its maximum at some point in the interior of M, then either is flat or isometric to a Bryant Ricci soliton. The final result can be considered as a generalization of main result in 3 .     

NPK 2.0: Introducing tensor decompositions to the kinetic analysis of gas–solid reactions

A method for deriving kinetic models of gas–solid reactions for reactor and process design is presented. It is based on the nonparametric kinetics (NPK) method and resolves many of its shortcomings by applying tensor rank-1 approximation methods. With this method, it is possible to derive kinetic models based on the general kinetic equation from any combination of experiments without additional a priori assumptions. The most notable improvements over the original method are that it is computationally much simpler and that it is not limited to two variables. Two algorithms for computing the rank-1 approximation as well as a tailored initialization method are presented, and their performance is assessed. Formulae for the variance estimation of the solution values are derived to improve the accuracy of the model identification and to provide a tool for diagnosing the quality of the kinetic model. The methods effectiveness and performance are assessed by applying it to a simulated data set. A Matlab implementation is available as Supporting Information.     

Scalar Tensor Cosmology With Kinetic,Gauss-Bonnet and Nonminimal Derivative Couplings and Supersymmetric Loop Corrected Potential

We discuss a particular four-dimensional cosmology based on non-minimal scalar tensor theories characterized by a supersymmetric loop corrected potential and a Hubble parameter defined as a function of the scalar field. Power-law solutions are obtained in the FRW background giving rise to acceleratedly expanding universe characterized by a scale factor and a scalar field depending both on the non-minimal coupling parameter $\xi$. Based on SNeIa data and on Hubble data X-ray gas mass fraction measurements, we find $0.116<\xi <0.225$ which results on a universe dominated by vacuum energy.     

New Homogeneous Einstein Metrics on SO(7)/T

The authors compute non-zero structure constants of the full flag manifold M = SO(7)/T with nine isotropy summands, then construct the Einstein equations. With the help of computer they get all the forty-eight positive solutions (up to a scale ) for SO(7)/T, up to isometry there are only five G-invariant Einstein metrics, of which one is Kähler Einstein metric and four are non-Kähler Einstein metrics.     

On the modeling of fiber dispersion in fiber-reinforced elastic materials

When an isotropic material is subject to a uniaxial tension, the principal strain transverse to the direction of applied load is always negative. However, in fiber reinforced materials the transverse principal strain can change its sign as the load increases, passing through the zero-points, known as perversions. We investigate how the number of perversions in a material reinforced by two symmetrically aligned families of distributed fibers depends both on the degree of fiber dispersion and the model used for fiber dispersion. Angular integration and three variants of the generalized structure tensor approach are considered and discussed. The study of perversions clearly demonstrates the qualitative difference between these approaches in the case of high dispersion of fibers. The results suggest that this difference is primarily due to the way compressive fibers are modeled.     

The Generalized Order Tensor Complementarity Problems

The main propose of this paper is devoted to studying the solvability of the generalized order tensor complementarity problem. We define two problems: the generalized order tensor complementarity problem and the vertical tensor complementarity problem and show that the former is equivalent to the latter. Using the degree theory, we present a comprehensive analysis of existence, uniqueness and stability of the solution set of a given generalized order tensor complementarity problem.     

13C chemical shift tensors in MOF α-Mg3(HCOO)6: Which component is more sensitive to host-guest interaction?

Metal–organic frameworks (MOFs) are a class of important porous materials with many current and potential applications. Their applications almost always involve the interaction between host framework and guest species. Therefore, understanding of host–guest interaction in MOF systems is fundamentally important. Solid-state NMR spectroscopy is an excellent technique for investigating host–guest interaction as it provides information complementary to that obtained from X-ray diffraction. In this work, using MOF α-Mg₃(HCOO)₆ as an example, we demonstrated that ¹³C chemical shift tensor of organic linker can be utilized to probe the host–guest interaction in MOFs. Obtaining ¹³C chemical shift tensor components (δ₁₁, δ₂₂, and δ₃₃, where δ₁₁ ≥ δ₂₂ ≥ δ₃₃) in this MOF is particularly challenging as there are six coordinatively equivalent but crystallographically non-equivalent carbons in the unit cell with very similar local coordination environment. Two-dimensional magic-angle-turning experiments were employed to measure the ¹³C chemical shift tensors of each individual crystallographically non-equivalent carbon in three microporous α-Mg₃(HCOO)₆ samples with different guest species. The results indicate that the δ₂₂ component (with its direction approximately being co-planar with the formate anion and perpendicular to the C−H bond) is more sensitive to the adsorbate molecules inside the MOF channel due to the weak C−H···O hydrogen bonding or the ring current effect of benzene. The ¹³C isotropic chemical shift, on the other hand, seems much less sensitive to the subtle changes in the local environment around formate linker induced by adsorption. The approach described in this study may be used in future studies on host–guest interaction within MOFs.