Dimensional reduction of Lattice Gauge Theory in (2+1)D

This is my Ph.D. thesis defended earlier this year. It contains mostly information already presented in previous Bielefeld/Saclay papers on this subject, though in more detailed form. It also includes actual calculations and some unpublished material on phase structure of the reduced model.Comment: ph.d. thesi

Regression Filtration with Resetting to Provide Exponential Convergence of MRAC for Plants with Jump Change of Unknown Parameters

This paper proposes a new method to provide the exponential convergence of both the parameter and tracking errors of the composite adaptive control system without the requirement of the regressor persistent excitation (PE). Instead, the composite adaptation law obtained in this paper requires the regressor to be finitely exciting (FE) to guarantee the above-mentioned properties. Unlike known solutions, not only does it relax the PE requirement, but also it functions effectively under the condition of a jump change of the plant uncertainty parameters. To derive such an adaptation law, an integral filter of regressor with damping and resetting is proposed. It provides the required properties of the control system, and its output signal is bounded even when its input is subjected to noise and disturbances. A rigorous analytical proof of all mentioned properties of the developed adaptation law is presented. Such law is compared with the known composite ones relaxing the PE requirement. The wing-rock problem is used for the modeling of the developed composite MRAC system. The obtained results fully support the theoretical analysis and demonstrate the advantages of the proposed method.Comment: 12 pages, 3 figure

Law in Judicial Practice of the Grand Duchy of Lithuania and the Grand Duchy of Moscow in the First Half of the 16th Century

Introduction. Analysis of preserved legal texts is an important instrument in studying the past which provides an opportunity to make conclusions on the level of social and legal development of the society. The modern scientists tend to attribute to legal texts of the past the same meaning that the modern laws have. The objective of this study is to consider to what extent the Lithuanian Statute of 1529 and the Moscow Code of Law (Sudebnik) of 1497 were mandatory for judges. Methods. To study the level of social and legal development of the society, investigators traditionally use the approach associated with the study of application of legal provisions in practical life. In such event, the investigator inevitably undertakes the role of a judge as they need to understand the provision of law in order to determine how it is applied. Consequently, one cannot be sure that modern interpretation of the provision is the same as interpretation of judges in the past. This study tries to find out how often the judges refer to the Statute of 1529 and the Sudebnik of 1497 in their judicial decisions. Results. The data for the Grand Duchy of Lithuania are based on the study of the judicial decisions by Vitebsk voivode M.V. Klochko for the period 1533–1540: he took 6 decisions containing accurate citations from the Statute of 1529 and 9 decisions referring to the provisions of the Statue from nearly 200 decisions. The conclusions for the Grand Duchy of Moscow have been made based on the studies conducted: from the preserved 160 documents dating to the first half of the 16th century in the Grand Duchy of Moscow the judges referred to the provisions of the Sudebnik in 31 cases. Conclusions. The Grand Duchy of Lithuania considerably developed enforcement mechanisms in the first half of the 16th century. This allowed establishing a rule in the Statute of 1529 that a custom could be applied in cases where a suitable provision of law (Statute) was absent. By contrast, the provisions of the Sudebnik of 1497 were mandatory for actions of judges, otherwise the provisions of the Sudebnik were advisory in nature