We analyze supersymmetric solutions of M-theory based an a seven-dimensional internal space with SU(3) structure and a four-dimensional maximally symmetric space. The most general supersymmetry conditions are derived and we show that a non-vanishing cosmological constant requires the norms of the two internal spinors to differ. We find explicit local solutions with singlet flux and the space be...

We study the rigidity and flexibility of symplectic embeddings of simple shapes. It is first proved that under the condition r n ≤ 2r 1 the symplectic ellipsoid E(r1, . . . , rn) with radii r1 ≤ · · · ≤ rn does not embed in a ball of radius strictly smaller than rn. We then use symplectic folding to see that this condition is sharp and to construct some nearly optimal embeddings of ellipsoids a...

In this work, we investigated the social media streams to understand their characteristics and their temporal aspects. We assumed that each blogger has different temporal preference for posting. To investigate this hypothesis, we analyzed a massive dataset, nearly 700,000 blog articles, with the consideration of two factors which are day of the week and time of the day. The comparison was done ...

Wiegerinck has shown that a separately subharmonic function need not be subharmonic. Improving previous results of Lelong, Avanissian, Arsove, and of us, Armitage and Gardiner gave an almost sharp integrability condition which ensures a separately subharmonic function to be subharmonic. Completing now our recent counterparts to the cited results of Lelong, Avanissian and Arsove for so-called qu...

First-principles molecular-dynamics simulations on models of a-Si:H and a-Si reveal the existence of a quasicontinuous manifold of nearly degenerate and conformationally distinct metastable minima which are accessible to each other at moderate simulation temperatures in the microcanonical ensemble. Other lowenergy excitations were also observed: elastic modes with anomalously low frequencies, w...

We consider the existence of spots and stripes for a class of NLS-type equations in the presence of nearly one-dimensional localized potentials. Under suitable assumptions on the potential, we construct various types of waves which are localized in the direction of the potential and have singleor multihump, or periodic profile in the perpendicular direction. The analysis relies upon a spatial d...

We study the Witten–Reshetikhin–Turaev SU(2) invariant for the Seifert manifold S/Γ where Γ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of the modular forms with half-integral weight, and we give an exact asymptotic expansion of the invariants by use of the nearly modular property of the Eichler integral. We further discuss that...

We study the dimensional reduction of the N = 1, ten-dimensional Heterotic Supergravity to four dimensions, at leading order in α′, when the internal space is a coset manifold. Then we apply the formalism using as internal manifolds all possible six-dimensional nonsymmetric coset spaces, namely G2/SU(3), Sp4/(SU(2)× U(1))non−max and SU(3)/U(1)× U(1), which moreover are nearly-Kähler manifolds a...

We collect the recent results on invariant f -structures in the generalized Hermitian geometry. Here the canonical f -structures on homogeneous k-symmetric spaces play a remarkable role. Specifically, these structures provide a wealth of invariant examples for the classes of nearly Kähler f -structures, Hermitian f -structures and some others. Finally, we consider all invariant f structures on ...

For any triple (M, g,∇) consisting of a Riemannian manifold and a metric connection with skew-symmetric torsion we introduce an elliptic, second order operator Ω acting on spinor fields. In case of a naturally reductive space and its canonical connection, our construction yields the Casimir operator of the isometry group. Several non-homogeneous geometries (Sasakian, nearly Kähler, cocalibrated...