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INSTITUTE OF MATHEMATICS

• Section of applied algebra and geometry
• 1 professor, 3 associate professors, 6
  lecturers
• Section of computer graphics and geometry
• 1 professor, 1 associate professor, 5 lecturers
• Section of applied analysis
• 1 professor, 3 associate professors, 7 lecturers
• Section of stochastic and optimization methods
• 1 professor, 2 associate professors, 4 lecturers

Sections
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INSTITUTE OF MATHEMATICS

• Basic mathematical courses offered at the Faculty
  of Mechanical Engineering including
• linear algebra
• analytic geometry
• calculus
• numerical methods
• constructive geometry and computer graphics
• differential equations
• infinite series
• probability and statistics
• Special field of Mathematical Engineering
• for engineers with extended theoretical
  background based on mathematics and computer
  science
• Other disciplines of applied mathematics
• for individual specializations of Masters degree
  programmes at the Faculty of Mechanical
  Engineering

Teaching
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INSTITUTE OF MATHEMATICS Section of applied
algebra and geometry

• Applied linear algebra
• Differential geometry and its applications
• Coalgebras and their applications
• Digital topology
• Local algebras
• Methods of commutative algebra in differential
  geometry
• General algebraic systems and their applications
  in computer science
• Topological structures on categories

Research
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INSTITUTE OF MATHEMATICS Section of applied
algebra and geometry

• GACR Grant GA201/00/1466 Continuous and
  Set-Theoretic Methods in Topological and
  Algebraic Structures
• GACR Grant GA201/03/0933 Set-Theoretic and
  Categorial Methods in Topological and Algebraic
  Structures
• MŠMT Research Plan MSM0021630518 Simulation
  Modelling of Mechatronic Systems
• GACR Grant GA201/02/0225 (2002-2004) Elongation
  of Geometric structures
• GACR Grant GA201/05/0523 (2005-2007) Geometric
  Structures on Fibred Varieties
• GACR Grant GA201/04/0381 (2004-2006) Methods of
  Theory of Numbers

Projects implemented
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INSTITUTE OF MATHEMATICS Section of applied
algebra and geometry

• Masaryk University in Brno
• Technische Universität Wien (Austria)
• Universität Potsdam (Germany)
• Universita degli Studi dell'Aquila (Italy)
• Dalhousie University in Halifax (Canada)
• Science University of Tokyo (Japan)

Cooperation
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INSTITUTE OF MATHEMATICS Section of applied
algebra and geometry
Samples of problems investigated
Modelling the structuring of a digital plane
using a new Alexandrov topology closed points
are encircled. This topology offers a range of
Jordan curves which is wider than that based on
the commonly used Khalimsky topology. In
particular, it lets curves bend at an angle of
?/4.
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INSTITUTE OF MATHEMATICS Section of applied
algebra and geometry
Samples of problems investigated
Finding the minimum route on a smooth variety
with respect to a given metric is among the basic
variational problems. This is closely related to
parallel transfer of vectors (see the figure) and
eventually leads to the definition of a negative
connection.
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INSTITUTE OF MATHEMATICS Section of Applied
Analysis

• Mathematical problems in modelling composite
  materials using a method of homogenization
• Adapting the method of reliable solution (method
  of the worst scenario) for problems of
  homogenization with uncertain data
• Quasi-periodic and random structures, generating,
  analysis
• Developing tools of functional analysis and
  theory of function spaces for analysing
  mathematical models method of two-scale
  convergence
• Devising numerical methods for flow calculation
• Investigating qualitative properties of the
  solution of functional-differential equations,
  differential and difference equations with a lag
• Theory of dynamic equations on time scales and
  their applications
• Solution of selected problems of optimal control

Research
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INSTITUTE OF MATHEMATICS Section of Applied
Analysis

• GACR Grant GA201/01/0079 (2001-2003) Qualitative
  Theory of Solutions of Differential Equations
• GACR Grant GA201/00/0557 (2000-2002) Mathematical
  Modelling of Some Nonlinear Problems of the
  Mechanics of Continuum
• GACR Grant GA201/03/0570 (2003-2005) Mathematical
  Modelling of Some Nonlinear Problems of the
  Mechanics of Continuum
• GA AVCR Grant IAA1163401 (2004-2006) Limit
  Properties of the Solutions of Differential
  Equations
• MŠMT CR Research Plan MSM0021630518 (2005-until
  now) Simulation Modelling of Mechatronic Systems

Projects implemented
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INSTITUTE OF MATHEMATICS Section of Applied
Analysis

• Université Pierre et Marie Curie, Paris (France)
• Chalmers University of Technology, Göteborg
  (Sweden)
• Technische Universität Hamburg-Harburg (Germany) 
• Universiteit Gent (Belgium)

Cooperation
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INSTITUTE OF MATHEMATICS Section of Applied
Analysis
Homogenization (replacing strongly heterogeneous
material by fictional material homogeneous in
terms of identical macroscopic properties) second
order elliptic equations in 2D with a homogeneous
Dirichlet boundary condition
Samples of problems investigated
Numerical solution corresponding to two-component
periodic composite material with sixteen circular
reinforcements
Corresponding numerical homogenized solution
pertaining to homogeneous material
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INSTITUTE OF MATHEMATICS Section of Applied
Analysis
Samples of problems investigated
The temperature field of the piston of a Diesel
engine (finite-element method)
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INSTITUTE OF MATHEMATICS Section of Stochastic
and Optimization Methods

• Stochastic computing models for determining the
  reliability of systems, statistical models of
  forming processes, generalized regression linear
  models and classification quality
• Estimates of discrete probability distributions
  under external conditions, multi-dimensional
  probability distributions and their properties
• Markov homogeneous and non-homogeneous chains in
  quality
• Fuzzy probability, fuzzy random variables, and
  fuzzy probability distributions, reliability
  models of elements and systems with vague
  information, fuzzy clustering and time series
  prediction in power engineering and finance,
  fuzzy metric spaces and their applications to
  databases with vague information
• Reliability diagnostic supporting nuclear power
  station blocks control
• Stochastic optimization and its application in
  mechanical and civil engineering
• Optimization algorithms and applications in
  technology, foundry, and water management
• Application of statistical methods in metrology,
  production process control, materials
  engineering, and medicine

Research
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INSTITUTE OF MATHEMATICS Section of Stochastic
and Optimization Methods

• MŠMT CR Research 1M06047 Centre for the Quality
  and Reliability of Production (CQR)
• MŠMT CR Research Plan CEZ J22/98 261100009
  Non-traditional Methods of Investigating Complex
  and Uncertain Systems
• GACR Grant GA103/05/0292 Optimizing the Design of
  Progressive Concrete Structures
• State project FF-P114 Research and Development of
  an Advanced Probability Model With Accumulated
  Knowledge Base of an Experienced Industrial
  Operator With Focus on the Operation of the
  VVER-Type Nuclear Power Plants
• IGA MZ CR Grant ND 7134-3 Possibilities of
  Significantly Affecting the Intra-Abdominal
  Pressure After Operations of the Aboral and
  Gastrointestinal Tract By Enteral Feeding Applied
  through a Three-Luminal Probe
• GACR Grant Project GA101/00/0170 Transferability
  of the Fracture Strength In Terms of Evaluating
  the Integrity of Components with Defects
• FRVŠ Project 1746/2002 Materials Science
  interactive textbook
• Cooperation on international projects COST-APOMAT
  OC526, EUREKA COOP 2716, EUREKA E! 2914 FGM, NAZV
  EP 096000 6151

Projects implemented
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INSTITUTE OF MATHEMATICS Section of Stochastic
and Optimization Methods

• University of Malta (stochastic, dynamic and
  integer optimization)
• Molde University College (optimization
  algorithms)
• Nuclear Research Institute at Dukovany
  (development of a supporting diagnostic system of
  the states of a nuclear block)
• BUT FCE Institute of Concrete and Masonry
  Structures (optimization and reliability of
  progressive concrete structures)
• Faculty of Medicine of Masaryk University in Brno
  (statistical modelling of intra-abdominal
  pressure after operation)
• Cardiochronomics Brno (statistical analysis in
  cardiology and chronobiology in cooperation with
  the University of Minnesota)
• Institute of Physics of Material, Academy of
  Sciences CR (stochastic modelling of fracture
  strength characteristics)
• SCC Partner (statistical methods in quality
  control)
• Consulting in mathematical applications for the
  following companies Alcan Decín, Alstom Power,
  Barum Continental, Celestica Czech Republic,
  Invensys Appliance Controls, LG Philips Displays
  Czech, METAL Ústí n.L., Schneider Electric,
  Siemens, Kostal etc.

Cooperation
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INSTITUTE OF MATHEMATICS Section of Stochastic
and Optimization Methods
Research
Estimates of discrete probability distributions
using Hellingers and Shannons quasinorms under
secondary moment conditions determined from real
statistical data
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INSTITUTE OF MATHEMATICS Section of Stochastic
and Optimization Methods
Program for generating fuzzy reliability
characteristics of a fuzzy Weibull type B
distribution
Research
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INSTITUTE OF MATHEMATICS Section of Stochastic
and Optimization Methods
Non-hierarchical clustering of fuzzy objects
Research
Hierarchical clustering of fuzzy objects
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INSTITUTE OF MATHEMATICS Section of Stochastic
and Optimization Methods
Predicting time-dependent energy consumption
using a fuzzy model of a time series
Research
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INSTITUTE OF MATHEMATICS Section of Stochastic
and Optimization Methods
Using fuzzy sets to predict the energy
consumption of the city of Olomouc as compared
with other predictions using other methods
neural networks and statistical methods
Research
Approximating the test strength for determining a
sufficient sample size in an experiment plan n,
U, n to determine object reliabilities
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INSTITUTE OF MATHEMATICS Section of Computer
Graphics and Geometry

• Adaptive filters for visualizing images with high
  dynamic content
• Numerical methods of solar spectrum analysis,
  solar corona images (in cooperation with the
  Úpice Observatory, the Slovak Academy of
  Sciences, and the Ondrejov Observatory)
• Methods of 3D reconstruction of images from the
  classic, confocal, and tunnelling microscope (in
  cooperation with the Faculty of Medicine of
  Masaryk University in Plzen)
• Fast algorithms of computer graphics
• Methods of image registration based on phase
  correlation and their applications
• Applications of digital topology and fractal
  geometry in image analysis
• Numerical methods of human retina analysis
• Engineering applications of constructive
  geometry, multi-valued logic in system control

Research
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INSTITUTE OF MATHEMATICS Section of Computer
Graphics and Geometry

• FRVŠ project 374/2002 Multimedia support of the
  Structure and Composition of Foodstuffs course
• FRVŠ project 855/2005 Interactive textbook for
  the Structure and Composition of Foodstuffs
  course
• FRVŠ project 3323/2006 Electronic support of the
  Mathematical Maple Calculations course

Projects implemented
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INSTITUTE OF MATHEMATICS Section of Computer
Graphics and Geometry

• University of Veterinary and Pharmaceutical
  Sciences Brno (numerical methods of image
  analysis histological examination of
  foodstuffs)
• Faculty of Medicine of Masaryk University in Brno
  (numerical methods of analysis of the human
  retina)
• Institute of Physics at the BUT Faculty of Civil
  Engineering (fractal analysis of the fracture
  surfaces of building materials)
• The Úpice Observatory (numerical methods of solar
  corona analysis)
• Astronomic Institute of the Slovak Academy of
  Sciences at Tatranská Lomnica (numerical methods
  of image analysis)
• Astronomic Institute of the Czech Academy of
  Sciences at Ondrejov (numerical methods of solar
  corona analysis)
• Biological Institute at the Faculty of Medicine
  of Charles University in Plzen (numerical methods
  of confocal microscopy)

Cooperation
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INSTITUTE OF MATHEMATICS Section of Computer
Graphics and Geometry
Samples of problems investigated
The solar corona during the total eclipse of 29th
March 2006 reconstructed from 51 images and
visualised by newly developed adaptive filters.
The image significantly exceeds the capacities of
the state-of-the-art space probes
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INSTITUTE OF MATHEMATICS Section of Computer
Graphics and Geometry
Samples of problems investigated
Dopplergramme of a part of the solar chromosphere
obtained by analyzing a series of images of the
H-alpha absorption line.
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INSTITUTE OF MATHEMATICS Section of Computer
Graphics and Geometry
Samples of problems investigated
A new exact numerical method for determining the
absorption of the light radiated by the solar
photosphere in the hydrogen H-alpha line
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INSTITUTE OF MATHEMATICS Section of Computer
Graphics and Geometry
Samples of problems investigated
New numerical methods for analyzing pictures of
human retina
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INSTITUTE OF MATHEMATICS Section of Computer
Graphics and Geometry
Samples of problems investigated
Numerical methods for identifying and analyzing
bone splinters in meat foodstuff products
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INSTITUTE OF MATHEMATICS Section of Computer
Graphics and Geometry
software reconstruction
Samples of problems investigated
photograph of a real object
Numerical methods developed for processing
optical sections obtained form devices with
narrow sharpness band. Using software tools based
on state-of-the-art numerical methods of image
analysis, not only a sharp image can be obtained
but also a 3D object almost undistinguishable
from the real one.
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INSTITUTE OF MATHEMATICS Section of Computer
Graphics and Geometry
Samples of problems investigated
The new methods of processing transparent optical
sections from a confocal microscope facilitate a
detailed study of the cell morphology and provide
a virtual tour of their interiors
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INSTITUTE OF MATHEMATICS Section of Computer
Graphics and Geometry
Samples of problems investigated
Using measure-theory-based algorithms, the
fractal dimension of microscopic samples can be
determined with increasing precision
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INSTITUTE OF MATHEMATICS
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