In this paper, we study the boundary behaviors of compact manifolds with nonnegative scalar curvature and nonempty boundary. Using a general version Positive Mass Theorem Schoen-Yau Witten, prove following theorem: For any manifold curvature, if it is spin its can be isometrically embedded into Euclidean space as strictly convex hypersurface, then integral mean cannot greater than image hypersurface in space. Moreover, equality holds only isometric domain Conversely, under assumption that...

Aim : Immunohistochemical analysis of protein expression is central to most clinical translational studies and defines patient treatment or selection criteria for novel drugs. Interobserver variation rarely analysed despite recognition that this a key area potential inaccuracy. Therefore our aim was examine observer suggest the revision current standards. Methods results We inter‐ intra‐observer variation, by interclass correlation coefficient (ICCC) κ statistics, in 8661 samples....

This paper is motivated by previous work of the authors [18] and its application to study structure complete Kahler manifolds in a subsequent first author [16].Roughly speaking main theorem relates infinity geometric certain class theory harmonic functions.Let us recall precise setting.Let M be noncompact manifold without boundary.Suppose sectional curvature K nonnegative outside some compact subset M. Without loss generality, we may assume that contained geodesic ball radius 1.By using...

The main cause of prostate cancer-related mortality is the development hormone-refractory disease. Circulating serum levels IL-6 are raised in cancer patients and evidence from cell line studies suggests that IL-6R/JAK/STAT3 pathway may be involved this In current study we investigate if expression these family members implicated cancer. Immunohistochemistry using IL-6R, JAK1, STAT3, pSTAT3(Tyr705) pSTAT3(Ser727) antibodies was performed on 50 matched hormone-sensitive tumours pairs. An...

In this paper, we will study the limiting behavior of Brown-York mass coordinate spheres in an asymptotically flat manifold.Limiting behaviors volumes regions related to are also obtained, including a discussion on isoperimetric introduced by Huisken [14].We expansions and Hawking geodesic with center at fixed point p 3-manifold.Some geometric consequences be derived.

Soit M une variete de Riemann a n dimensions courbure Ricci non negative. On suppose que le volume des boules geodesiques rayon r centrees en un point x∈M satisfait V(B x (r))=O(r h ). Alors la dimension l'espace fonctions harmoniques croissance lineaire sur doit etre ≤k

Introduction The purpose of this paper is to study some uniqueness and regularity properties the Dirichlet problem at infinity for proper harmonic maps between hyperbolic spaces. In general, if metrics two complete noncompact manifolds Mm N' are given locally by ds2 = iMj gij dxzdxj dsy -En h:,3 du'du$, respectively, then energy-density function a C1 map u: M -N defined

On demontre d'une facon constructive que l'operateur de Laplace admet une fonction Green symetrique G(x,y) sur variete Riemann complete

Ever since the technique of Kalman–Bucy filter was popularized, there has been an intense interest in finding new classes finite dimensional recursive filters. In late seventies, concept estimation algebra a filtering system introduced. It proven to be invaluable tool study nonlinear problems. this paper, simple algebraic necessary and sufficient condition is established for special class systems finite-dimensional. Also presented rigorous proof Wei–Norman program which allows one construct...

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a constant. alttext="script upper M Subscript gamma Superscript <mml:msubsup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">M</mml:mi> </mml:mrow> <mml:mi>γ</mml:mi>...

In this paper, we study global properties of continuous plurisubharmonic functions on complete noncompact Kähler manifolds with nonnegative bisectional curvature and their applications to the structure such manifolds. We prove that reasonable growth rate can be approximated by smooth through heat flow deformation. Optimal Liouville type theorem for as well a splitting in terms harmonic holomorphic are established. The results then applied several theorems or sectional curvature.

3), (2.4), and the assumption that s(R 2 ) -i(R x > 0, we have

Abstract Perelman established a differential Li-Yau-Hamilton (LYH) type inequality for fundamental solutions of the conjugate heat equation corresponding to Ricci flow on compact manifolds. As an application LYH inequality, proved pseudolocality result In this article we provide details proofs these results in case complete noncompact Riemannian manifold. Using prove that under certain conditions, finite time singularity must form within set. The conditions are satisfied by asymptotically...

In the first part of this work, Poisson equation on complete noncompact manifolds with nonnegative Ricci curvature is studied. Sufficient and necessary conditions for existence solutions certain growth rates are obtained. Sharp estimates also derived. second part, these results applied to study decay Kähler manifolds. particular, Poincaré-Lelong holomorphic bisectional Several applications then derived, which include Steinness flatness a class satisfying pinching condition. Liouville type...

Estimation algebra turns out to be a crucial concept in the investigation of finite-dimensional nonlinear filters. In an earlier paper by authors, necessary and sufficient algebraic condition was derived for exact estimation finite-dimensional. this paper, properties algebras is continued, some structure partial classification theorems such are proved.

This paper concerns some stability properties of higher dimensional catenoids in $\mathbb {R}^{n+1}$ with $n\ge 3$. We prove that have index one. use $\delta$-stablity for minimal hypersurfaces and show the catenoid is $\frac 2n$-stable a complete hypersurface or hyperplane provided second fundamental form satisfies decay conditions.

In this paper, we obtain some rigidity theorems on compact manifolds with nonempty boundary. The results may be related to the positivity of quasi-local mass Brown–York type. main argument is use monotonicity quantities similar in a foliation quasi-spherical metrics. Together hyperbolic version quantity, our results.

We prove directly without using a density theorem that (i) the ADM mass defined in usual way on an asymptotically flat manifold is equal to intrinsically Ricci tensor; (ii) Hamiltonian formulation of center and tensor are same.