In 1941 Sumner Myers proved that if the Ricci curvature of a complete Riemann manifold has a positive infimum then the manifold is compact and its diameter is bounded in terms of the infimum. Subsequently the curvature hypothesis has been weakened, and in this paper we weaken it further in an attempt to find the ultimate, sharp result.

For time series discrimination,the main idea behind the proposed approach is to use a variance/covariance criterion to strengthen or weaken aligned observations according to their contribution to the variability within and between classes. To this end, the classical variance/covariance expression is extended to a set of time series, as well as to a partition of time series.

Combining several previously known arguments, we prove marked length spectrum rigidity for surfaces with nonpositively curved Riemannian metrics away from a finite set of cone-type singularities with cone angles > 2π. With an additional condition, we can weaken the requirement on one metric to ‘no conjugate points.’

Nuclear medicine uses radiation to provide diagnostic information about the functioning of a person's specific organs, or to treat them. Diagnostic procedures are now routine.. Radiotherapy can be used to treat some medical conditions, especially cancer, using radiation to weaken or destroy particular targeted cells. Millions of nuclear medicine procedures are performed each year, and demand fo...

The decline of oak stands is a phenomenon that has been observed since the beginning 20th century in many European countries. It can be caused both with abiotic factors such as drought and fluctuations groundwater levels, well biotic infestations by insects, fungi bacteria. Acute Oak Decline (AOD) an dangerous disease trees which was first XX century. From moment symptoms were noticed, able to ...

To reduce the negative impact of informal recycling on environment, we consider competition in industry to explore manufacturer's collection channel choice and optimal points-exchange level. In this paper, a closed-loop supply chain model including manufacturer an recycler (IR) is constructed. Stackelberg game theory used as theoretical guide. addition, study decision problem under profit maxim...

BACKGROUND Trichoepithelioma is a rare benign skin lesion that originates from hair follicles. Trichoepitheliomas are mostly seen in the scalp, nose, forehead, and upper lip. METHODS We present a large family of Iranian origin with 15 individuals affected with multiple familial trichoepithelioma in four generations, and treated with three different methods. RESULTS Trichoepithelioma is his...

Recent surveys found that an increasing number of parents are concerned that infants receive too many vaccines. Implicit in this concern is that the infant's immune system is inadequately developed to handle vaccines safely or that multiple vaccines may overwhelm the immune system. In this review, we will examine the following: 1) the ontogeny of the active immune response and the ability of ne...

This paper contains a critical examination of the prospects for analyses knowledge that weaken factivity condition so implies only approximate truth.

Recently, I put forth the hypothesis that the signaling molecule, norepinephrine (NE), is an etiological factor in a number of types of cancer. In this brief commentary, I summarize evidence that NE plays a role in cancer and describe details involved in testing the hypothesis in humans through epidemiological investigation of existing medical records of persons who have taken pharmaceutical dr...