the aim of this paper is to study orders over a valuation ring v with arbitrary rank in acentral simple f-algebra q. the relation between all of the orders is explained with a diagram. it is thenshown that inside bezout order, extremal v-orders are precisely semi-hereditary. in the last section, theeffect of henselization on maximal and semi-hereditary orders is examined.

We study two kinds of segment orders, using definitions first proposed by Farhad Shahrokhi. Although the two kinds of segment orders appear to be quite different, we prove several results suggesting that the are very much the same. For example, we show that the following classes belong to both kinds of segment orders: (1) all posets having dimension at most 3; (2) interval orders; and for n ≥ 3...

A finite poset is an angle order if its points can be mapped into angular regions in the plane so that x precedes y in the poset precisely when the region for x is properly included in the region for y. We show that all posets of dimension four or less are angle orders, all interval orders are angle orders, and that some angle orders must have an angular region less than 180” (or more than 180”...

This paper is devoted to the study of contiguity orders i.e. orders having a linear extension L such that all upper (or lower) cover sets are intervals of L. This new class is a strict generalization of both interval orders and N{free orders, and is linearly recognizable. It is proved that computing the number of contiguity extensions is #P{complete, and that the dimension of height one contigu...

let f, g and h be all entire functions of several complex variables. in this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.

in this paper, it is proved that all simple $k_4$-groups of type $l_2(q)$ can be characterized by their maximum element orders together with their orders. furthermore, the automorphism groups of simple $k_4$-groups of type $l_2(q)$ are also considered.

Background. Intravenous aminoglycoside (AG) dosing is complex and highly individualized based on indication, patient’s age, and renal function. Protocols available at study site guide dosing of AGs. This study assesses adherence to current protocols and investigates efforts needed to optimize AG dosing. Methods. 100 consecutive patients who received AG (gentamicin, tobramycin, or amikacin) from...