The production planning problem, that is, to determine the production rate of a factory in the future, requires an aggregate model for the production flow through a factory. The canonical model is the clearing function model based on the assumption that the local production rate instantaneously adjusts to the one given by the equilibrium relationship between production rate (flux) and work in p...

We discuss the generalization of the connection between the determinant of an operator entering a quadratic form and the associated Gaussian path-integral valid for grassmann variables to the paragrassmann case [θp+1 = 0 with p = 1 (p > 1) for grassmann (paragrassamann) variables]. We show that the q-deformed commutation relations of the paragrassmann variables lead naturally to consider qdefor...

To the problem of no overall optimal merger for one-way merger in the segmentation algorithm proposed by Wang Yongzhong, et al., in this paper, we propose a method of overall optimal search and merger. At the same time, to the unreasonable problem of merging a segment which has non-value (value-segment) and a segment which values are zeros entirely (zeros-segment) to a large segment in Wang’s m...

The functional bases of the first-order differential invariants for the splitting subgroups of the Poincaré group P (1, 4) are constructed. Some of the results obtained are presented. The differential invariants of Lie groups of point transformations play an important role in geometry (see, for example, [14]), group analysis of differential equations (see, for example, [12, 14, 15]), etc. In pa...

We consider a certain class of Herglotz-Nevanlinna matrix-valued functions which can be realized as the Weyl-Titchmarsh matrix-valued function of some symmetric operator and its self-adjoint extension. New properties of Weyl -Titchmarsh matrixvalued functions as well as a new version of the functional model in such realizations are presented. In the case of periodic Herglotz-Nevanlinna matrix-v...

This paper is devoted to the analysis of covariant canonical formalism $F(R)$ gravity in Einstein frame. We also find transformation between formulation F(R) Jordan frame and frames we determine corresponding generating function.