A Vector Field Texture Generation Method without Convolution Calculation

In the LIC algorithm process, symmetrical streamline tracing is used to symmetrically convolve the original values of all the primitive values that pass by to obtain the resulting texture. In this process, streamline tracking and convolution consume a lot of computing resources. To generate more expressive textures for vector fields with less time consumption, a novel method named random increment streamline (RIS) is put forward, which can generate streamline textures without convolution calculations. First, the mesh unit filling preprocessing (MUFP) method is presented to transform an undressed irregular grid into a special kind of regular grid named a “texture pixel”, and the point location and interpolation processes of all sampling points in the texture pixels are calculated before streamline tracking. Second, the random increment streamline method is used to generate line integral convolution style textures without any convolution calculations, thus greatly reducing the algorithm’s time consumption. Third, the vector directions at each point in the static vector field are clearly expressed using the periodic cyclic animation method. Finally, several simplifications of the RIS algorithm are discussed, which help to achieve a better visual effect with faster speed. The programming results show that the method is faster and more applicable than the traditional LIC method and provides clearer expression of the vector field.

Random Measure Algebras Under O-dot Product and Morse-Transue Integral Convolution

In this article, we consider two operations of random measures: O-dot product and the convolution product by Morse-Transue integral. With these two operations, we construct algebras of random measures. Also we investigate further on the explicit forms of the products of Wiener processes by O-dot operation and by Morse-Transue integral convolution.

Random Measure Algebras Under O-dot Product and Morse-Transue Integral Convolution

In this article, we consider two operations of random measures: O-dot product and the convolution product by Morse-Transue integral. With these two operations, we construct algebras of random measures. Also we investigate further on the explicit forms of the products of Wiener processes by O-dot operation and by Morse-Transue integral convolution.

Another Look at the Hartman-Watson Distributions

The article deals with the Hartman-Watson distributions and presents a new approach to them by investigating a special function u. The function u is strictly related to the distribution of the exponential functional of Brownian motion appearing in the mathematical finance framework. The study of the latter leads to new explicit representations for the function u. One of them is through a new parabolic PDE. Integral relations of convolution type between Hartman-Watson distributions and modified Bessel functions are presented. It turns out that u can be represented as an integral convolution of itself and the modified Bessel function K0. Finally, excursion theory and a subordinator connected to the hyperbolic cosine of Brownian motion are involved in order to obtain yet another representation for u. Possible applications of the resulting explicit formulas are discussed, among others Monte Carlo evaluations of u.

DECISION-MAKING IN THE MANAGEMENT OF THE TAX AUTHORITIES ON THE BASIS OF INTEGRATED PERFORMANCE INDICATORS

The paper highlights the results of applying the methodology of integral convolution of key indicators of economic efficiency of territorial subdivisions of the tax authority of the state: results of tax collection, productivity, cost, dynamics of indicators. The criteria for grouping of territorial tax divisions according to the values of the indicator of effectiveness for the purpose of making tactical and strategic management decisions are formed. The paper formulates recommendations on the use of the proposed approach in goal- setting when making managerial decisions based on the "sigma" management.