Semi-positive line bundles over compact Kahler manifolds have been the focus of studies for decades. Among them, there are several straddling vanishing theorems such as the Kodaira-Nakano Vanishing Theorem, Vesentini-Gigante-Girbau Vanishing Theorems and KawamataViehweg Vanishing Theorem. As a corollary of the above mentioned vanishing theorems one can easily show that a line bundle over compa...

The necessary and sufficient Horn inequalities which determine the nonvanishing Littlewood-Richardson coefficients in the cohomology of a Grassmannian are recursive in that they are naturally indexed by non-vanishing Littlewood-Richardson coefficients on smaller Grassmannians. We show how non-vanishing in the Schubert calculus for cominuscule flag varieties is similarly recursive. For these var...

We consider scalar-vector-tensor (SVT) theories with second-order equations of motion and tensor propagation speed equivalent to the light. Under sub-horizon quasi-static approximations we find analytical formulae for an effective dark energy fluid, i.e., sound speed, anisotropic stress as well density pressure. took advantage our general, fluid description showed that it is possible design SVT...

We prove the instability of $d$-dimensional conformal field theories (CFTs) having in operator-product expansion two fundamental fields a primary operator scaling dimension $h=d/2+i r$, with non-vanishing $ r\in\mathbb{R}$. From an AdS/CFT point view, this corresponds to well-known tachyonic instability, associated violation Breitenlohner-Freedman bound AdS${}_{d+1}$; we derive it here directly...

The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end along a line segment. The condition on the existence of these hypersurfaces is the vanishing of the sum of certain integral moments of the spheres with respe...

A scheme is proposed to achieve chaos synchronization for mutual coupled systems via partial stability theory. Under this scheme, three criteria are given to ensure chaos synchronization. The first criterion applies to the case without system perturbation and the other two apply to systems possessing vanishing and nonvanishing perturbations, respectively. Finally, coupled Lorenz systems are sim...