Let Ir(L) denote the collection of all regular integral operators on L (1 < p <∞) with the regular norm ‖ · ‖r. Then Ir(L) is a Banach function space on X ×X with the Fatou property. In this paper we shall give two distinct descriptions of the order continuous dual, or associate space, of Ir(L). Our first description follows from a result on Ir(L). In [3] we showed that Ir(L) is equal to the Ca...

Robertson and Seymour proved that every graph with sufficiently large treewidth contains a large grid minor. However, the best known bound on the treewidth that forces an l × l grid minor is exponential in l. It is unknown whether polynomial treewidth suffices. We prove a result in this direction. A grid-like-minor of order l in a graph G is a set of paths in Gwhose intersection graph is bipart...

Complexation reactions between methylthymol blue and Fe , A l ,Ga , 1n a nd TI ions have been studied in buffer aqueous solutions of pH 5.0 at 2S°C by a spectrophotometric technique. The conditional stepwise stability constants of the resulting 1:l and 1:2 (metal-to-ligand) complexes were determined from the absorbance-mole ratio data at three different wavelengths of the visible sp...

complexation reactions between methylthymol blue and fe , a l ,ga , 1n a nd ti ions have been studied in buffer aqueous solutions of ph 5.0 at 2s°c by a spectrophotometric technique. the conditional stepwise stability constants of the resulting 1:l and 1:2 (metal-to-ligand) complexes were determined from the absorbance-mole ratio data at three different wavelengths of the visible spectra. the o...

In the study of multi-agent distributed control, containment control is an important problem, which aims to make all following agents enter convex hull formed by leader agents. It has a wide application prospect in UAV information collection and robust control. practical usually experience unknown or uncertain working environment are needed suppress even eliminate adverse effects external distu...

Every m th order cardinal spline wavelet is a linear combination of the functions fN (l) m+l (2x?j); j 2 Zg. Here the function N m is the m th order cardinal B-spline. In this paper we prove that the single function N (l) m+l (2x), or N (l) m+l (2x ? 1) is a wavelet when m and l satisfy some mild conditions. As l decreases, so does the support of the wavelet. When l increases, the smoothness of...

Finding the l Most Probable Explanations (MPE) of a given evidence, S e , in a Bayesian belief network can be formulated as identifying and ordering a set of composite hypotheses, H i s, of which the posterior probabilities are the l largest; i.e., Pr(H 1 jS e) ::: Pr(H l jS e). When an order includes all the composite hypotheses in the network in order to nd all the probable explanations, it b...

In this research, three numerical methods, namely the variational iteration method, Adomian decomposition and homotopy analysis method are considered to achieve an approximate solution for a third-order time-fractional partial differential Equation (TFPDE). The equation is obtained from classical (FW) by replacing integer-order time derivative with Caputo fractional of order η=(0,1] variable co...