In this paper we consider a nonlocal boundary value problem with an integral condition for the McKendrick von Foerster loaded equation with the Caputo operator. The existence and uniqueness theorem for the solution of the problem is proved.
The paper addresses an extended (1+1)-dimensional Sawada-Kotera (SK) equation. The Lie symmetry analysis leads to many plethora of solutions to the equation. The non-linear self-adjointness condition for the SK equation established and subsequently used to construct simplified independent conserved vectors. In particular, we also get conservation laws of the equation with the corresponding Lie symmetry
We consider the boundary-value problem for a third-order equation of parabolic type with the fractional derivative of Caputo. By the method of energy inequalities an a priori estimate of the solution of the analogue of the second boundary value problem for an equation with multiple characteristics.
We present some new sharp estimates concerning distance function in some new mixed norm and Lizorkin-Triebel type spaces in the unit ball.This leads at the same time to direct generalizations of our recent results on extremal problems in such Bergman type spaces. In addition new sharp results in this direction in Hardy-Morrey, and some new weighted Hardy classes in the unit ball and mixed norm Hardy type spaces and Herz type spaces in polyball will be provided and discussed.
The question of the coincidence of estimates of reliability parameters with their true values is considered, when planning maintenance and determining estimates of the reliability parameters of operated systems. The main attention is paid to the problem of constructing models that simulate the behavior of systems during operation in the future. Establishing such a connection consists in using the Bayesian approach and estimating the parameters of the reliability model, covering systems with partially known reliability parameters, which are specified by a priori distributions.
The paper describes the developed software that allows you to model planned investment decisions without losing financial resources, compare several projects and provide the necessary accounting documentation to potential investors and creditors, justify the economic efficiency of participation in an investment project.
We propose a new clustering method for partitioning of finite sets from Rn, which is based on the application of averaging aggregating functions and an iterative re-weighing method for searching cluster centers.
Mechanism of geomagnetic jerks evident from the model of the hot Earth magnetic field is discussed here. Similar in their principle, reversals, excursions and jerks result from auto adjusting of temperature of the phase change (PC) “evaporation-condensation” at the F-layer of the Earth inner core border. In our model both magnitude and polarity of the geomagnetic field as its generation are governed by PC temperature. Reversals, excursions and jerks synchronism at the F-layer appears to be due to quantum entangling of the core matter.
Climate variation during the last 700 – 800 kyr is known to reveal some periods of the temperature fluctuation. It is during about 100 kyr when temperature is slowly lowering, glaciation, and then it quickly raises resulting in ice melting. Some short period temperature fluctuations usually interpreted by Milancovich theory [1] are argued here to be a well known flicker noise. This approach allows a new insight into climate mechanism and prognosis of its variation.
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