For relatively hyperbolic groups, we investigate conditions under which the subgroup generated by two quasiconvex subgroups Q1 and Q2 is quasiconvex and isomorphic to Q1 ∗Q1∩Q2 Q2. Our results generalized known combination theorems for quasiconvex subgroups of word-hyperbolic groups. Some applications are presented. In addition, it is proved that the intersection of quasiconvex subgroups is qua...

Let q1 and q2 be univalent in ∆ := {z : |z| < 1} with q1(0) = q2(0) = 1. We give some applications of first order differential subordination and superordination to obtain sufficient conditions for a normalized analytic functions f with f(0) = 0 , f ′(0) = 1 to satisfy q1(z) ≺ zf ′(z) f(z) λ ≺ q2(z).

One of the fascicles of the posterior commissure of the embryonic grasshopper is pioneered by an individually identifiable neuron named Q1. Q1 initially grows along a longitudinal pathway established by another pioneer neuron, MP1, and then crosses to the midline, where it meets and fasciculates with the axon of the contralateral Q1. The Q1 growth cone follows the contralateral Q1 axon to the c...

A recent study among 13,707 postmenopausal women without benign breast disease (BBD) from the Breast Cancer Detection Demonstration Project (BCDDP) cohort found breast cancer risk associated with greater total fat, unsaturated fat, and oleic acid intake. We assessed the associations between cumulative averaged dietary intake from 1980, 1984, 1986, and 1990 with breast cancer risk through 1994 a...

OBJECTIVE The hypothesis of carotenoid having a preventive role in diabetes is suggested by their antioxidant properties. In this report, we investigated the relationship between baseline total plasma carotenoid levels and 9-year onset of dysglycemia (impaired fasting glucose or type 2 diabetes) in a healthy elderly population. RESEARCH DESIGN AND METHODS The Epidemiology of Vascular Ageing S...