This work is motivated by Nathanson’s recent paper on relatively prime sets and a phi function for subsets of {1, 2, 3, . . . , n}. We establish enumeration formulas for the number of relatively prime subsets and the number of relatively prime subsets of cardinality k of {1, 2, 3, . . . , n} under various constraints. Further, we show how this work links up with the study of multicompositions. ...

Let n ≥ k ≥ l ≥ 2 be integers, and let F be a family of k-element subsets of an n-element set. Suppose that l divides the size of the intersection of any two (not necessarily distinct) members inF . We prove that the size ofF is at most (⌊n/l⌋ k/l ) provided n is sufficiently large for fixed k and l.

Let X be an abstract set and L a lattice of subsets of X such that ;; X 2 L. In this paper we extend smoothness characterizations of L regular measures 2 MR(L) to the general case of 2 M (L), by considering different outer measures associated with and the induced measure on a Wallman space.

This paper distinguishes a rare subset of myeloid dendritic-like cells found in mouse spleen from conventional (c) dendritic cells (DC) in terms of phenotype, function and gene expression. These cells are tentatively named "L-DC" since they resemble dendritic-like cells produced in longterm cultures of spleen. L-DC can be distinguished on the basis of their unique phenotype as CD11bhiCD11cloMHC...

OBJECTIVE To evaluate the effect of growth hormone treatment on growth, levels of insulin-like growth factor I (IGF-I) and lymphocyte subsets in immunosuppressed renal allograft recipients. METHODS 18 children (aged 8.0-16.6 years) received growth hormone 1 IU/Kg/week daily for two years. Height, IGF-I levels and in 11/18 patients, lymphocyte subsets were evaluated serially. RESULTS Standar...

A subset X of a lattice L with 0 is called CDW-independent if (1) it is CDindependent, i.e., for any x, y ∈ X , either x ≤ y or y ≤ x or x ∧ y = 0 and (2) it is weakly independent, i.e., for any n ∈ N and x, y1, . . . , yn ∈ X the inequalityx ≤ y1∨· · ·∨yn implies x ≤ yi for some i. A maximal CDW-independent subset is called a CDW-basis. With combinatorial examples and motivations in the backgr...

human brucellosis is a major health problem in developing countries. a number of patients with human brucellosis do not recover from the acute stage of the disease and pass into the chronic form. since the pathophysiology of this change is not well understood, we studied the t-cell subsets during the acute, subacute and chronic forms of human brucellosis. in this study we found alterations in t...

In this paper, the P-connectedness of L-subsets in L-topological spaces is introduced and studied. It preserves some fundamental properties of connected sets in general topological spaces. Especially, the famous K. Fan’s Theorem holds for P-connectivity.