953 research outputs found
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
Contact systems and corank one involutive subdistributions
We give necessary and sufficient geometric conditions for a distribution (or
a Pfaffian system) to be locally equivalent to the canonical contact system on
Jn(R,Rm), the space of n-jets of maps from R into Rm. We study the geometry of
that class of systems, in particular, the existence of corank one involutive
subdistributions. We also distinguish regular points, at which the system is
equivalent to the canonical contact system, and singular points, at which we
propose a new normal form that generalizes the canonical contact system on
Jn(R,Rm) in a way analogous to that how Kumpera-Ruiz normal form generalizes
the canonical contact system on Jn(R,R), which is also called Goursat normal
form.Comment: LaTeX2e, 29 pages, submitted to Acta applicandae mathematica
Nilpotentization of the kinematics of the n-trailer system at singular points and motion planning through the singular locus
We propose in this paper a constructive procedure that transforms locally,
even at singular configurations, the kinematics of a car towing trailers into
Kumpera-Ruiz normal form. This construction converts the nonholonomic motion
planning problem into an algebraic problem (the resolution of a system of
polynomial equations), which we illustrate by steering the two-trailer system
in a neighborhood of singular configurations. We show also that the n-trailer
system is a universal local model for all Goursat structures and that all
Goursat structures are locally nilpotentizable.Comment: LaTeX2e, 23 pages, 4 figures, submitted to International journal of
contro
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
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