We show that assuming lower bounds on the Ricci curvature and injectivity radius absolute value of certain characteristic numbers a Riemannian manifold, including all Pontryagin Chern numbers, is bounded proportionally to volume. The proof relies Chern–Weil theory applied connection constructed from Euclidean connections charts in which metric tensor harmonic has Hölder norm. generalize this th...

A non-probabilistic generalization of Aumann’s (1976) agreement theorem is proved. Early attempts at such a theorem were based on a version of the sure-thing principle which assumes an intrapersonal-interstate comparison of knowledge. But such comparisons are impossible in partition structures. The theorem proved here is based on a new version of the sure-thing principle that makes an interpers...

A non-probabilistic generalization of Aumann’s (1976) agreement theorem is proved. Early attempts at such a theorem were based on a version of the sure-thing principle which assumes an intrapersonal-interstate comparison of knowledge. But such comparisons are impossible in partition structures. The theorem proved here is based on a new version of the sure-thing principle that makes an interpers...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...