**Seminar on
Applied Mathematics**

**PROGRAM**

Matematički fakultet

Fakultet organizacionih nauka

JUPIM

IEEE Computer Chapter, Srbija

MI SANU, Knez Mihailova 36, sala 305

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Utorak, 03.11.2009. u 14:15, Sala 301f, MI SANU:
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Srdjan Krco, Fakultet
organizacionih nauka
FP7 SENSEI - ARCHITECTURE OF A UBIQUITOUS SENSING AND ACTUATION FRAMEWORK IN
THE CONTEXT OF THE NETWORK OF THE FUTURE
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Abstract: Internet and the mobile network infrastructures have
become the technological backbone of our society, with a large
number of businesses, social interactions and public services such
as government, health and education, heavily relying on it on a
daily basis. More recently, sensing and interacting with the
physical world have gained a lot of attention, which has resulted
in a range of useful application proposals that have exploited the
context of a person, an object or an area, to provide novel
services to users or enterprizes. These applications often served
immediate and specialized needs (e.g. maps showing nearby
restaurants or busy intersections) and hence were designed as
isolated enclaves, i.e. as closed, vertical, stand-alone systems
built with one specific purpose in mind. In the realm of the
network of the future, people, sensors, objects, and spaces will
be intertwined in both virtual and physical realms while
collaborating and sharing information in an unobtrusive manner.
Wireless sensor and actuator networks will enable inclusion of the
physical world context into the new intelligent, invisible and
autonomous applications and services as well as enhancement and
enrichment of the existing communication services (person-person,
person-machine, mobile-machine, person-content, and
machine-machine). The role of the sensor networks, and more
general of Internet of Things, in the network of the future is
thus to provide the missing link between the virtual and the
physical world. Therefore, it is necessary to take into account
the physical world factors when developing new service and network
infrastructures and to embed interfaces to the physical world,
regardless of how interaction with the physical world is realized.
A number of challenges like design of an open sensor and actuator
framework, design of horizontal solutions reusable across multiple
applications, platforms and domains, business enablers,
scalability, inter-operability, security, have to be overcome
before such a ubiquitous communication, computing, sensing and
actuation environment can be created.
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In this presentation the work done in FP7 SENSEI project on
architecture of a ubiquitous sensing and actuation framework in
the context of the Network of the Future addressing the
challenges mentioned above is described. The main user scenarios
are presented first, followed by a description of the framework
components. Finally, a brief outline of the SENSEI's pan-European
test bed is given.
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Pttak, 10.11.2009. u 14:15, sala 301f, MI:
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Milica Selmic, Saobracajni fakultet, Beograd
BEE COLONY OPTIMIZATION FOR SCHEDULING INDEPENDENT
TASKS TO IDENTICAL PROCESSORS
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Abstract: The problem of static scheduling independent tasks on
homogeneous multiprocessor systems is presented. This problem is
solved by the Bee Colony Optimization (BCO). The BCO algorithm
belongs to the class of stochastic swarm optimization methods
inspired by the foraging habits of bees in the nature. Our BCO
algorithm was able to obtain optimal value of the objective
function in most test examples known from the literature. The CPU
times required to find the best solutions by the BCO are
significantly smaller than the corresponding times required by the
CPLEX optimization solver.
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This is joint work with dr Tatjana Davidovic and prof. Dusan
Teodorovic.
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Utorak, 17.11.2009. u 14:15, sala 301f, MI SANU:
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Anastasija Andreevna Vasiljeva, Katedra opstih problema
upravljanja, Mehanicko-matematihki fakultet, Moskovski
drzavni univerzitet
KOLMOGOROV WIDTHS OF WEIGHTED SOBOLEV CLASSES
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Abstract: For a wide class of weight functions estimates of
Kolmogorov n-widths of weighted Sobolev classes in a weighted
$L_p$ space are obtained. Using Mayorov method of discretization,
Pietcsh - Stesin - Kashin - Gluskin estimates of Kolmogorov widths
of finite-dimensional balls and Stepanov's estimates of norms of
weighted Riemann - Liouville operators and choosing an appropriate
partition of an interval, we can obtain generalization and
refinement of known results. In a case of multidimensional domains
we obtain some embedding theorems and estimates of Kolmogorov
n-widths.
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Docent PhD Alexandr Saveljevich Kochurov, Katedra opstih problema
upravljanja
Mehanicko-matematicki fakultet
Moskovski drzavni univerzitet
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ON SOLUTIONS OF SOME MULTIVARIATE OPTIMAL CONTROL PROBLEMS

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Abstract. This is still unknown, whether Pontryagin's maximum
principle holds for multivariate optimal control problems.
We present three examples, where the maximum principle is
applicable for solutions. In each of those problems the sharp
solution can be computed and analized.
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Utorak, 24.11.2009. u 14:15, sala 301f, MI SANU:
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Katica R. (Stevanović) Hedrih
THE OPTIMAL CONTROL IN ENGINEERING NONLINEAR SYSTEMS WITH TRIGGER OF
COUPLED SINGULARITIES Katica R. (Stevanović) Hedrih
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Abstract. Short main idea of the phase plane method applied to the
optimal control in nonlinear dynamical systems with triggers of a
coupled singularities, and with one degree of freedom, is
reconsidered. Paper present a short review of the author’s previous
published results containing series of the special cases of the
optimal control in nonlinear dynamical systems with trigger of
coupled singularities important for engineering applications.
This paper analyses the controllability of motion of conservative or
noconservative nonlinear dynamical systems in which triggers of
coupled singularities exist or appear. It is shown that the phase
plane method is useful for the analysis of nonlinear dynamics of
conservative and no conservative systems with one degree of freedom
of control strategies and also shows the way it can be used for
controlling the relative motion in rheonomic systems having
equivalent scleronomic conservative or noconservative system.
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For the system with one generalized coordinate described by
nonlinear differential equation of nonlinear dynamics with triggers
of coupled singularities, the functions of system potential energy
and conservative force must satisfy some conditions defined by a
Theorem on the existence of a trigger of coupled singularities and
the separatrix in the form of number eight. Task of the defined
dynamical conservative system optimal control is: by using
controlling force acting to the system, transfer initial state of
the nonlinear dynamics of the system into the final terminate state
of the nonlinear dynamics in the minimal time for that optimal
control task.
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Some research results of fascinating nonlinear dynamics of a heavy
material particle along circles with coupled rotations with many
different properties of nonlinear dynamics and optimal control of
this dynamics are presented. A visualizations of nonlinear dynamical
processes in such rheonomic systems were made.
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RUKOVODIOCI SEMINARA
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Vera Kovačević-Vujčić
Milan Dražić
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