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Original title in Czech: Aplikovaná matematikaFSIAbbreviation: D-APMAcad. year: 2018/2019
Programme: Applied Natural Sciences
Length of Study: 4 years
Accredited from: 1.1.1999Accredited until: 31.12.2020
Profile
Creative research conducted in a field of applied mathematics and co-operation with experts in other engineering and scientific fields are major focuses of the study that the students should master. They are encouraged in a maximum degree possible to engage in research projects of the Institute of Mathematics at the BUT Faculty of Mechanical Engineering. Computers are available to students as standard equipment.
Guarantor
prof. RNDr. Jan Čermák, CSc.
Issued topics of Doctoral Study Program
Tutor: Bednář Josef, Ing., Ph.D.
Recently, significant fluctuations of climatological factors, mainly long-lasting hot seasons without precipitation, results in worsening living conditions from city themal regime point of view. Recent airborne imaging spectorscopy in reflective (VNIR, SWIR) and thermal (TIR) bands of electromagnetic spectrum together with LiDAR scanning offer sources for description of state and structural city quantities and their relations. The aims of the work are: 1/ a development of algorithms and mathematical models for urban thermal properties simulations using mentioned geoinformational data; 2/ assessment of impact of urban greenery on mitigation of weveheat at different spatial scales. The suggested topic is in the focus of long-term research activities of the RS group, Global Change Research Institute CAS and CzechGlobe varanties both data/soft. availability and part time job..
Tutor: Zemek František, doc. Ing. Mgr., Ph.D.
The aim is to extend the use of geometric algebras, particularly the conformal geometric algebra, to various tasks of image processing. Indeed, correction of radial distortions caused by lens curvature seems to be a promising topic.
Tutor: Vašík Petr, doc. Mgr., Ph.D.
The theme is focused on the application of the theory of jets and Weil algebras for materials corresponding with Cosserat continuum and generalizations. It is a new use of methods of commutative algebra and modern differential geometry in applications.
Tutor: Kureš Miroslav, doc. RNDr., Ph.D.
The topic is focused on the application of a screw calculus in the sense of F. M. Dimentberg in mechanics and generalizations for other local algebras.
Some dynamical systems exhibit a complex behavior known as deterministic chaos. The topic is focused on analysis of suitable chaotic models (with respect to a widest set of system's parameters). This analysis can be extended on models of non-integer (fractional) order as well.
Tutor: Nechvátal Luděk, doc. Ing., Ph.D.
In an automated data collection environment, this large amount of data should be organized and sorted for further analysis. For this, various mining methods, including cloud analysis, are used. The use of these methods, including finding a possible new approach for a special type of data, will address a listed topic.
Tutor: Žák Libor, doc. RNDr., Ph.D.
We shall study qualitative properties of various second order and higher order nonlinear differential equations, which arise from applications (including, e.g., the equations with a (generalized) Laplacian). The research will be focused, for example, on obtaining asymptotic formulae for solutions or establishing new oscillation criteria. We shall deal not only with differential equations but also with their discrete (or time scale) analogues. This will enable us, among others, to compare (and explain) similarities and/or discrepancies between a continuous case and some of its discretization. We plan to utilize various (modifications of and combinations of) standard tools, but also to develop new techniques.
Tutor: Řehák Pavel, prof. Mgr., Ph.D.
Functional differential equations generalize ordinary differential equations. The research of theirs properties is much more difficult than it is for the ordinary differnetial equations. We shall analyze qualitative properties of the particular functional differential equations, which may appear in real models.
Tutor: Opluštil Zdeněk, doc. Mgr., Ph.D.
The goal is the system analysis, mathematic model and developing of software tools to control industrial robots (manipulators) by menas of geometric (Clifford) algebras. In the implementation of selected algorithms, our goal is to use the object orented approach and computational complexity based on algebraic properties of Clifford algebras.
Tutor: Hrdina Jaroslav, doc. Mgr., Ph.D.
Assessment of data quality is a crucial and meaningful stage in the processing of hyperspectral airborne data. In practice, existing methodologies used for quality assessment are moreover only providing rough quality tags or recommendations without proposing practial methodologies. The objective of the work is to develop a methodology (in an automatic and generic fashion) on hyperspectral airborne data quality assessment, which covers the complete data processing chain. The quality of each step has to be investigated: ranging from sensor calibration up to mapping results. All data, software will be available at the Global Change Research Institute, CAS (CzehGlobe) where Ph.D. candidate will be trained and will get a part time job.
The aim of this work is to improve mathematical methods of solar corona image analysis which enable to measure electron temperature in the solar corona. These methods are based on coronal brightness measurement in several wavelength intervals by means of narrow-band interference filters. The results must be compared with mathematical model of free electrons light scattering in the solar corona. This model already exists however it contains a lot of questionable asumptions and simplifications. Improving of this mathematical model is the main task of the work. This PhD topic is a part of our participation on NASA ONSET spacecraft project in which the PhD work supervisor is on the position of co-investigator for image processing methods and data analysis. The launch of this spacecraft for research of solar corona is planned during 2024 year.
Tutor: Druckmüller Miloslav, prof. RNDr., CSc.
Dynamical systems theory provides a useful tool for description and qualitative investigation of many engineering problems. There is a need of profound problem analysis for a construction of adequate mathematical model. Considering too many details is generally leading to complications in the model investigation whereas a negligence of fundamental factors can depreciate obtained analysis. Therefore it is necessary to compare the model analysis with real data (if it is possible). The work consists in applying mathematical and numerical analysis in engineering problems modelling and proper interpretation of obtained results.
Tutor: Tomášek Petr, doc. Ing., Ph.D.
Many recent logistic problems are related to large-scale mathematical programs. They are often specific by their specialized distributed structure. Such a structure influences theoretical properties of models and also efficiency of classical techniques to modelling and solving. Hence, the key role is often played by approximation-based and decomposition approaches in model building, modifications of existing algorithms, and development of new solution techniques. Therefore, the proposed research goal is to develop new and modify existing methods in both modeling and solution areas of studied problems together with their implementation and application.
Tutor: Popela Pavel, RNDr., Ph.D.
Since intial boundary value problems for evolutionary mainly partial differential equations in technology often do not admit classical solution, various generalized formulations of these problems were proposed. The aim of the study will be comparison of these formulations and studying existence and uniqueness of their solutions. Then the theory will be applied to particular problems occuring in technology and alternatively to carry out numerical experiments.
Tutor: Franců Jan, prof. RNDr., CSc.
The aim of this work is development of numerical methods for motion analysis in digital images which enable to measure local shifts with sub-pixel precision. These algorithms will be used for SDO AIA and HMI images. The main task is solar differential rotation measurement and analysis of motions in the photosphere in the neighbourhood of sunspots.
The aim is to solve the optimal trajectories of robotic snakes by geometric control theory. The advance differential geometry, Lie group, Lie algebras and its representations are assumed to be used.
The theoretical part will focus on existing atmospheric correction of airborne hyperspectral thermal data and separation of emissivity from temperature. The improvements of following algorithms are expected: 1/ an algorithm for atmospheric correction of the HS thermal data, including specification and data source for proper parametrization; 2/ algorithm for separation of emissivity from temperature. The practical aspect of the thesis will be payed to implementation of the improved algorithms in the form of software modules which would became an important part of the whole processing chain for the airborne data acquired by TASI hyperspectral sensor. All data, software will be available at the Global change research institute, ASCR (CzechGlobe) where the Ph.D. candidate will be trained and will get a part time job.
In order to facilitate proper functioning of spectroradiometers is necessary regular spectral and radiometric calibration of instruments. Calibrations are necessary for numerical as well as imaging spectroradiometers, The objective of the work is to develop a methodology for calibration of multispectral and hyperspectral spectroradiometers. Alternatively, to verify methodology recommended by producer of instrument. Expected outcome of work is calibration methodology including scripts for practical use. Example of instruments for calibration: FieldSpec-4, CASI-1500. All data, software will be available at the Global Change Research Institute, CAS (CzechGlobe) where Ph.D. candidate will be trained and will get a part time job.
The study will be focused on analysis of continuous and discrete dynamic systems. These systems appear in many engineering and natural science branches and model equations are supposed to by analyzed with respect to these applications. The other studied topics are stabilization of unstable dynamic systems by use of a suitable delayed feedback control, stabilizing (or destabilizing) effect of time delays on dynamics of a system, asymptotics of solutions and relationship between continuous and discrete models. These models can involve also modern types of dynamic systems, including chaotic and fractional ones.
Tutor: Čermák Jan, prof. RNDr., CSc.
The aim is the autonomous control of the chosen mechanism (inverse kinematics) based on the information received from two or more visual sources (cameras). The theory of conformal geometric algebras is assumed to be used.
The aim of the work is development of new numerical method for object 3D reconstruction in confocal microscopy. This method is using lens deliberate aberration which enables to increase resolution within one optical cut. The method will be applied to a twin-line confocal microscope based on a rotating Nipkow disc.
Tutor: Štarha Pavel, doc. Ing., Ph.D.
Study plan wasn't generated yet for this year.