In this paper, we study the evolution of L p-forms under Ricci flow with bounded curvature on a complete non-compact or a compact Riemannian manifold. We show that under curvature pinching conditions on such a manifold, the L norm of a smooth p-form is non-increasing along the Ricci flow. The L∞ norm is showed to have monotonicity property too.

Let G be a Lie group and K a compact subgroup of G. Then the homogeneous space G/K has an invariant Riemannian metric and an invariant volume form ΩG. Let M and N be compact submanifolds of G/K, and I(M ∩ gN) an “integral invariant” of the intersection M ∩ gN . Then the integral

We prove that noncommutative solenoids are limits, in the sense of the Gromov-Hausdorff propinquity, of quantum tori. From this observation, we prove that noncommutative solenoids can be approximated by finite dimensional quantum compact metric spaces, and that they form a continuous family of quantum compact metric spaces over the space of multipliers of the solenoid, properly metrized.

Due to the high density and the low consumption power in the digital integrated circuits, mostly technology of CMOS is used. During the past times, the Metal oxide silicon field effect transistors (MOSFET) had been used for the design and implementation of the digital integrated circuits because they are compact and also they have the less consumption power and delay to the other transistors. B...

We give some estimates of the first eigenvalue of the Laplacian for compact and non-compact submanifold immersed in the Euclidean space by using the square length of the second fundamental form of the submanifold merely. Then some spherical theorems and a nonimmersibility theorem of Chern and Kuiper type can be obtained.

We characterize hyperbolic metrics on compact triangulated surfaces with boundary using a variational principle. As a consequence, a new parameterization of the Teichmüller space of compact surface with boundary is produced. In the new parameterization, the Teichmüller space becomes an open convex polytope. It is conjectured that the Weil-Petersson symplectic form can be expressed explicitly in...

NADPH-cytochrome P450 reductase is a key component of the P450 mono-oxygenase drug-metabolizing system. There is evidence for a conformational equilibrium involving large-scale domain motions in this enzyme. We now show, using small-angle X-ray scattering (SAXS) and small-angle neutron scattering, that delivery of two electrons to cytochrome P450 reductase leads to a shift in this equilibrium f...

We show that there are no automorphic Banach spaces of the form C(K) with K continuous image of Valdivia compact except the spaces c0(Γ). Nevertheless, when K is an Eberlein compact of finite height such that C(K) is not isomorphic to c0(Γ), all isomorphism between subspaces of C(K) of size less than אω extend to automorphisms of C(K).

Extending work of [14, 16, 26], we show there is a model of set theory in which normal spaces are collectionwise Hausdorff if they are either first countable or locally compact, and yet there are no first countable L-spaces or compact S-spaces. The model is one of the form PFA(S)[S], where S is a coherent Souslin tree.

A k-form ω is called multi-symplectic, if Iω is a monomorphism. The classification (under the action ofGl(V )) of multi-symplectic 3-forms in dimension 7 has been done by Bures and Vanzura [B-V2002]. There are together 8 types of these forms, among them there two generic classes of G2-form ω 3 1 and G̃2-form ω 3 2 . They are generic in the sense of Gl(V )-action, more precisely the orbits Gl(V )...