We study some problems pertaining to the tournament equilibrium set (τ for short). A tournament H is a τ-retentive tournament if there is a tournament T which has a minimal τ-retentive set R such that T [R] is isomorphic to H. We study τ-retentive tournaments and achieve many significant results. In particular, we prove that there are no τretentive tournaments of size 4, only 2 non-isomorphic τ...

The problem of mixed H2/H1 control is considered for a class of uncertain discrete-time nonlinear stochastic systems. The nonlinearities are described by statistical means of the stochastic variables and the uncertainties are represented by deterministic norm-bounded parameter perturbations. The mixed H2/H1 control problem is formulated in terms of the notion of exponentially mean-square quadra...

Axoplasmic vesicles that translocate on isolated microtubules in an ATP-dependent manner have an associated ATP-binding polypeptide with a previously estimated relative molecular mass of 292 kD (Gilbert, S. P., and R. D. Sloboda. 1986. J. Cell Biol. 103:947-956). Here, data are presented showing that this polypeptide (designated H1) and another high molecular mass polypeptide (H2) can be isolat...

The objective of the study was to investigate the relationship between health and production traits in chickens. The data were obtained from a closed, fully pedigreed, commercial broiler line. Records included measurements of body weight (BW), residual feed intake (RFI), percent breast meat (PBM), and two health traits (H1 and H2) from 13,665 birds and 1,524 hens with progeny records. Productio...

Given a two-dimensional fractional multiplicative process (Ft)t∈[0,1] determined by two Hurst exponents H1 and H2, we show that there is an associated uniform Hausdorff dimension result for the images of subsets of [0, 1] by F if and only if H1 = H2.

In this paper we determine when the join of two graphs is locally homogeneous. It is shown that the Cartesian product of a locally H1 graph and a locally H2 graph is locally (H1∪ H2). All graphs H of order at most 4 for which there are no locally H graphs are determined.

Let G be a graph and A an Abelian group. Denote by F (G,A) the set of all functions from E(G) to A. Denote by D an orientation of E(G). For f ∈ F (G,A), an (A, f)-coloring of G under the orientation D is a function c : V (G) 7→ A such that for every directed edge uv from u to v, c(u) − c(v) 6= f(uv). G is A-colorable under the orientation D if for any function f ∈ F (G,A), G has an (A, f)-color...

Induction of the B7 family molecules by 12-O-tetradecanoyl phorbol 13-acetate (TPA) has been reported, however, the mechanism by which TPA up-regulates these molecules remains poorly understood. In this study, the expression of B7-DC, -H1, -H2, and -H3 in response to TPA was markedly induced in K562 cells. TPA also induced activation of ERK, p38 mitogen-activated protein kinase (MAPK), JNK, pho...