Программная реализация редуцированной вычислительной схемы численного интегрирования системы линейных дифференциальных уравнений на основе методов Эйлера
The paper considers the implementation of the basic algorithms for constructing the reduced computational schemes for the numerical integration of the system of linear differential equations by Euler's method. Shows the time and construction costs reduced by calculation scheme as compared with conventional numerical methods. Payment scheme for computing large mathematical models occurs at 2-3 orders of magnitude faster used in specialized software techniques.
The tutorial deals with the application of the basic principles of structured programming in complex software systems in the high-level C ++ language, which are demonstrated with meaningful examples.
1. Description of the problem. Instrumental analysis makes it possible to find the arguments of adjudication on the bounders and structure of corpus delicti, its correlation to criminal and filling-up legislation. 2. Initial theses. Corpus delicti is regarded as that expressed in criminal law doctrine result of reorganization of orders of criminal law into other practically necessary form. That happens in the process of theory and practical experience accumulation. The construction of corpus delicti is transformed for practical needs, textually expressed system of features, regulated by criminal law and characterizing deeds as a crime of a definite type. Correlation of construction of corpus delicti with law and doctrine. Corpus delicti, its algorithm. Transition from law regulations to corpus delicti can be done: 1) prog-nostically; 2) within constant analysis of law; 3) in the process of law application. 3. Stages of instrumental building of corpus delicti: prognostic, doctrinal, law applicatory. Instrumental approach to corpus delicti includes within each stage: 1) based on criminal law decision of classification of corpus delicti and its borders; 2) objective description of a factual model; 3) acception of meaning correlated with legal notions and constructions; 4) choice of the construction of the corpus delicti and disposal of characteristics; 5) verification of legitimacy, necessity and adequacy of foundation. 4. Instrumental analysis of disputable questions of understanding and application of constructions of corpus delicti. A. Functions and purposes of application of construction of corpus delicti. Functions of corpus delicti: a) modeling; b) communicative; c) identificatory; d) technological. B. Contents of corpus delicti. Contents of corpus delicti as it is traditionally regarded does not correspond to indications of crime, does not characterize features of social danger; sign of danger of penalty also does go into corpus delicti. Two variants are proposed for the discussion: widening of the borders of corpus delicti by means of introduction of signs of social danger and signs, defining individualization of penalty and to limitate corpus delicti by characteristic of criminally punished act, separating it from contents of guilt and contents of social danger. C. Structure of corpus delicti. There are two problems: division of elements of crime seems to be extremely harsh and inadequate - it is expedient to include signs of special and time limits of act, causal links, crossing signs of objective and subjective sides, first of all consequences and an object of crime, into the structure of corpus delicti. Forms of committing a criminally punished act is a crime commitment in complicity, ideal system, not finished crime.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability
The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.