A contact covariant approach to optimal control with applications to sub-Riemannian geometry

We discuss contact geometry naturally related with optimal control problems (and Pontryagin Maximum Principle). We explore and expand the observations of [Ohsawa, 2015], providing simple and elegant characterizations of normal and abnormal sub-Riemannian extremals.Comment: A small correction in the statement and proof of Thm 6.15. Watch our publication: https://youtu.be/V04N9X3NxYA and https://youtu.be/jghdRK2IaU

The effective algorithm for solving the quadratic diofantic equation with three unknowns

The article is devoted to the problem of finding the triples of integer numbers generating equal sums of the squares in the linear combination. At first the theorem giving the conditions of existing two equal sums of the squares is presented. Based on it the algorithm for finding the triples of the integer numbers generating equal sums of the squares is built. The time complexity is calculated and the effectiveness for different size of the input parameters is verified

Controllability of second order infinite dimensional dynamical systems with delays

The article is devoted to analysing the approximate absolute and approximate relative controllability of a given type second order infinite dimensional system. The considered dynamical system is governed by the evolution equation with three damping terms and three terms without derivatives. Following this aim, spectral theory for linear unbounded operators is involved. At first the representation of considered infinite dimensional dynamical system by the infinite series of finite dimensional systems is given. Next, two theorems on necessary and sufficient conditions of approximate absolute and approximate relative controllability of the considered system are formulated and proved. Finally, proven theorems are applied to the analysis of the elastic beam

Controllability of second order infinite dimensional dynamical systems with delays

The article is devoted to analysing the approximate absolute and approximate relative controllability of a given type second order infinite dimensional system. The considered dynamical system is governed by the evolution equation with three damping terms and three terms without derivatives. Following this aim, spectral theory for linear unbounded operators is involved. At first the representation of considered infinite dimensional dynamical system by the infinite series of finite dimensional systems is given. Next, two theorems on necessary and sufficient conditions of approximate absolute and approximate relative controllability of the considered system are formulated and proved. Finally, proven theorems are applied to the analysis of the elastic beam

A parallel implementation in the investigations of the controllability of an infinite dimensional system in the three dimensional rectangular prism

The article is devoted to the parallel implementation of an algorithm for finding triplesgenerating equal sums of the squares. Based on a known single thread algorithm, the parallelalgorithm is built. The obtained improvement of the time performance is verified on a multi-coreserver

Methodologies For Attaching Polypyridyl Ligands Into Amino Acids And Synthesis And Biological Evaluation Of Novel Light Activated Peptidomimetic Cysteine Protease Inhibitors Caged By Ruii(bpy)2

Two separate subjects are described in this dissertation. The first part describes novel methodologies for attaching polypyridyl ligands into unnatural amino acids. The first chapter describes the different possibilities for attaching metal ligands to peptides and their applications as potential imaging and therapeutic agents covered so far in the literature. It is followed in the second chapter by the description of a new method for the construction of metal-peptide conjugates through the use of three unnatural amino acids, and their adaptation to solid phase synthesis. The third chapter describes the synthesis of a novel, optimal substrate for the enantioselective alkylation reaction of benzophenone glycine imine derivatives. Optimization of the enantiomeric excess, scope and compatibility with acid-labile containing protecting groups are disclosed. The second chapter presents the synthesis of the first caged cysteine protease inhibitor. After an introductory survey of different Ru and Pt complexes used as potential therapeutic cancer agents, cysteine protease inhibitors are described. The syntheses of RuII(bpy)2 complexes caging cathepsin inhibitors are revealed with full characterization in the following chapters. The stability of the complexes in the dark in aqueous solutions and their ability to release the inhibitors upon irradiation with visible light are shown, followed by cathepsin activity inhibition studies, in vitro and in cellulo. Finally, the toxicity of the complexes is evaluated in cell viability studies

Correction of 'J. Laderman, V. Pan, X. H. Sha, On practical Algorithms for Accelerated Matrix Multiplication, Linear Algebra and its Applications. Vol. 162-164 (1992) pp. 557-588'

In this article we corrected the trilinear formula for triple disjoint matrix multiplication given in the article 'J. Laderman, V. Pan, X. H. Sha, On practical Algorithms for Accelerated Matrix Multiplication, Linear Algebra and its Applications. Vol. 162-164 (1992) pp. 557-588', which is incorrect for matrix dimensions equal to two or greater. That formula is a base of two algorithms, for disjoint and single matrix multiplication. The necessary correction made the amount of non scalar products raise, slightly increasing the algorithm time complexity. We also corrected explicit formulas, in the bilinear form, for triple disjoint matrix multiplication. They are explicit, thus convenient for practical use of fast matrix multiplication algorithms in question

Conic nonholonomic constraints on surfaces and control systems

This paper addresses the equivalence problem of conic submanifolds in the tangent bundle of a smooth 2-dimensional manifold. We deal with this problem under the prism of feedback equivalence of control systems, both control-affine and fully nonlinear. We also give equivalence results for a special class of conic submanifolds via the study of the Lie algebra of infinitesimal symmetries of the corresponding control systems. Then we consider the classification problem of conic submanifolds, which is achieved via feedback classification of nonlinear control system. Our results describe and completely characterise conic systems, and include several normal and canonical forms.Comment: 42 pages, 5 appendices, preprin