We consider a , rst-order partial di, erential equation with constant irreversible co-e, cients in a Banach space in the regular case. The equation is split into equations in subspaces, in which non-degenerate subsystems are obtained. We obtain an ana-lytical solution of each system with Showalter-type conditions. Finally, an example is given to illustrate the theoretical results.

Recently, one-two Descriptor has been defined and it has been shown that it is a good predictor of the heat capacity at P constant (CP) and of the total surface area (TSA). In this paper, we analyze its generalizations by replacing the value 2 by arbitrary positive value α . We show that these analyses may be on interest, because even good predictions of CP and TSA can be slightly improved. Furthermore, it can be expected that this more general Descriptor can find a wider range of application than the original one. The extremal values of trees have been found for all values of α .

Singular systems have been studied extensively during the last two decades due to their many practical applications. Such systems possess numerous properties not shared by the well-known state variable systems. This paper considers the linear tracking problem for the continuous-time singular systems. The Hamilton-Jacobi theory is used in order to compute the optimal control and associated trajectory. Two methods are presented for solving these trajectories. The first method uses the concept of the Drazin inverse, and the second involves the derivation and solution of a Riccati equation. Similar to the linear regulator problem, necessary and sufficient conditions for existence and uniqueness of a solution are stated.

The Bertz indices, derived by counting the number of connecting edges of line graphs of a molecule were used in deriving the QSPR models for the physicochemical properties of alkanes. The inability of these indices to identify the hetero centre in a chemical compound restricted their applications to hydrocarbons only. In the present work, a novel molecular Descriptor has been derived from the weighted line graph of the molecular structure and applied in correlating the physicochemical properties of alkane isomers with these Descriptors. A weight is tagged at the vertex of the line graph, which consequently modifies the weight of the edge. These Descriptors were found to classify the alkane isomers and served well in deriving the QSPR models for various physicochemical properties. The mathematical calculations include the quantitative treatment on the role of substituents (alkyl) in governing the properties under study of the alkane isomers. Further, the use of weighted line graph in the enumeration of the topological index opens up a new vista on application to heteroatomic systems.

This paper presents a novel Texture-Edge Descriptor, TED, for background modeling and pedestrian detection in video sequences which models texture and edge information of each image block simultaneously. Each block is modeled as a group of adaptive TED histograms that are calculated for pixels of the block over a rectangular neighborhood. TED is an 8-bit binary code which is independent of the neighborhood size. Experimental results over real-world sequences from PETS database clearly show that TED outperforms LBP.