The three-dimensional perovskites are known for their wide range of interesting properties including spectral tunability, charge carrier mobility, solution-based synthesis and many others. Such properties make them good candidates for photovoltaics and photodetectors. Low-dimensional perovskites, on the other hand, are good as light emitters due to the quantum confinement originating from their nanoparticle size. Another class of low-dimensional perovskites, also called low-dimensional-networked perovskites (L-DN), is recently reemerging. Those interesting materials combine the advantages of the nanocrystals and the stability of the bulk. For example, zero-dimensional-networked perovskite (0-DN), a special class of perovskites and the focus of this work, consists of building blocks of isolated lead-halide octahedra that could be synthesized into mm-size single crystal without losing their confinement. This thesis focuses on the synthesis and investigation of the optical properties of the 0-DN perovskites through experimental, theoretical and computational tools. The recent discovery of the retrograde solubility of the perovskites family (ABX3), the basis of the inverse temperature crystallization (ITC), inspired the reinvestigation of the low-dimensional-networked perovskites. The results of the optical characterization showed that the absorption and the corresponding PL spectra were successfully tuned to cover the visible spectrum from 410 nm for Cs4PbCl6, to 520 nm and 700 m for Cs4PbBr6 and Cs4PbI6, respectively. Interestingly, the exciton binding energies (Eb) of the 0-DNs were found to be in the order of few hundred meV(s), at least five times larger than their three-dimensional counterpart. Such high Eb is coupled with a few nanoseconds lifetime and ultimately yielded a high photoluminesce quantum yield (PLQY). In fact, the PLQY of Cs4PbBr6 powder showed a record of 45%, setting a new benchmark for solid-state luminescent perovskites. Computational methods were used to calculate the bandgap and study the corresponding excitonic behavior. However, the unexpected mismatch between the calculated and experimental bandgaps questions the origin of the high luminescence, which to date, remains an area of scientific debate that needs further study. Until then, the high PLQY, together with the spectral tunability, insensitivity to particle size and stability all offer a new avenue for more sustainability in light-emitting materials

van der Waals heterostructures meet other low-dimensional materials. Stacking of about 1 nm thick nanosheets with out-of-plane anchor groups functionalized with fullerenes integrates this zero-dimensional material into layered heterostructures with a well-defined chemical composition and without degrading the mechanical properties. The developed modular and highly applicable approach enables the incorporation of other low-dimensional materials, e.g. nanoparticles or nanotubes, into heterostructures significantly extending the possible building blocks.

Title: Homomorphic encryption and coding theory Author: Veronika Půlpánová Department: Department of algebra Supervisor: RNDr. Michal Hojsík, Ph.D., Department of algebra Abstract: The current mainstream in fully homomorphic encryption is the appro- ach that uses the theory of lattices. The thesis explores alternative approaches to homomorphic encryption. First we present a code-based homomorphic encrypti- on scheme by Armknecht et. al. and study its properties. Then we describe the family of cryptosystems commonly known as Polly Cracker and identify its pro- blematic aspects. The main contribution of this thesis is the design of a new fully homomorphic symmetric encryption scheme based on Polly Cracker. It proposes a new approach to overcoming the complexity of the simple Polly Cracker - based cryptosystems. It uses Gröbner bases to generate zero-dimensional ideals of po- lynomial rings over finite fields whose factor rings are then used as the rings of ciphertexts. Gröbner bases equip these rings with a multiplicative structure that is easily algorithmized, thus providing an environment for a fully homomorphic cryptosystem. Keywords: Fully homomorphic encryption, Polly Cracker, coding theory, zero- dimensional ideals

van der Waals heterostructures meet other low-dimensional materials. Stacking of about 1 nm thick nanosheets with out-of-plane anchor groups functionalized with fullerenes integrates this zero-dimensional material into layered heterostructures with a well-defined chemical composition and without degrading the mechanical properties. The developed modular and highly applicable approach enables the incorporation of other low-dimensional materials, e.g. nanoparticles or nanotubes, into heterostructures significantly extending the possible building blocks.

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This thesis consists of six papers. In Paper I, we give an algorithm for merging sorted lists of monomials and together with a projection technique, we obtain a new complexity bound for the Buchberger-Möller algorithm and the FGLM algorithm. In Paper II, we discuss four different constructions of vector space bases associated to vanishing ideals of points. We show how to compute normal forms with respect to these bases and give complexity bounds. As an application we drastically improve the computational algebra approach to the reverse engineering of gene regulatory networks. In Paper III, we introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and, in particular, we give a new algorithm to compute the variety of an ideal of projective dimension zero. In Paper IV, we consider a subset of projective space over a finite field and give a geometric description of the minimal degree of a non-vanishing form with respect to this subset. We also give bounds on the minimal degree in terms of the cardinality of the subset. In Paper V, we study an associative version of an algorithm constructed to compute the Hilbert series for graded Lie algebras. In the commutative case we use Gotzmann's persistence theorem to show that the algorithm terminates in finite time. In Paper VI, we connect the commutative version of the algorithm in Paper V with the Buchberger algorithm. / At the time of doctoral defence, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript. Paper 5: Manuscript. Paper 6: Manuscript

Two-stroke poppet-valved engines may combine the high power density of two - stroke engines and the low emissions of poppet-valved engines. A two-stroke diesel engine can generate the same power as a four-stroke engine of the same size, but at higher (leaner) air/fuel ratios. Diesel combustion at high air/fuel ratios generally means hydrocarbons, soot and carbon monoxide are oxidised more completely to water and carbon dioxide in the cylinder, and the opportunity to increase the rate of exhaust gas recirculation should reduce the formation of nitrogen oxides (NOx). The concept is being explored as a means of economically modifying diesel engines to make them cleaner and/or more powerful. This study details the application of two computational models to this problem. The first model is a relatively simple thermodynamic model created by the author capable of rapidly estimating the behaviour of entire engine systems. It was used to estimate near-optimum engine system parameters at single engine operating points and over a six-mode engine cycle. The second model is a detailed CFD model called KIVA-ERC. It is a hybrid of the KIVA engine modelling package developed at the Los Alamos National Laboratory and combustion and emissions subroutines developed at the University of Wisconsin-Madison Engine Research Center. It was used for detailed scavenging and combustion simulations and to provide estimates of emissions levels. Both models were calibrated and validated for four-stroke cycle operation using experimental data. The thermodynamic model was used to provide initial and boundary conditions to the KIVA-ERC model. Conversely, the combustion simulations were used to adjust zero-dimensional combustion correlations when experimental data was not available. Scavenging simulations were performed with shrouded and unshrouded intake valves. A new two-zone scavenging model was proposed and validated using multidimensional scavenging simulations. A method for predicting the behaviour of the two-stroke engine system based on four-stroke data has been proposed. The results using this method indicate that a four-stroke diesel engine with minor modifications can be converted to a two-stroke cycle and achieve substantially the same fuel efficiency as the original engine. However, emissions levels can not be predicted accurately without experimental data from a physical prototype. It is therefore recommended that such a prototype be constructed, based on design parameters obtained from the numerical models used in this study.

No description available.

Bandgap determines the suitability of materials for device applications such as \cite{lyu2021predictive} light-emitting diodes (LED), solar cells, and photo-detectors. The accuracy of the bandgap predicted using standard LDA or GGA functional is underestimated by density functional theory (DFT) when compared to experimental values. However, DFT combined with Machine Learning (ML) allows computational screening of materials with better accuracy. The training data for the models is obtained from density functional theory calculations which consist of A, B, and X-site elemental properties. The feature importance procedure screens the relative important features among all input features considered in the study. CatBoost(CB) regression model, \cite{Catboost} is an open-source library for gradient boosting. It gives high-perfromance on decision tress as it is based on gradient boosting algorithm and is suitable for small data sets as reduces overfitting, is implemented that can accurately predict the bandgap of $A_2BX_6$ perovskite. Eleven ML techniques were implemented, and their predictions of energy bandgap were compared, such as gradient boosted, random forest, support vector, AdaBoost, linear, K-nearest neighbor, kernel ridge, and decision tree. As per the study, the best performance is achieved by CatBoost regression model.

In his study of spectra of f-rings via pointfree topology, Banaschewski [6] considers lattices of l-ideals, radical l-ideals, and saturated l-ideals of a given f-ring A. In each case he shows that the lattice of each of these kinds of ideals is a coherent frame. This means that it is compact, generated by its compact elements, and the meet of any two compact elements is compact. This will form the basis of our main goal to show that the lattice-ordered rings studied in [6] are coherent frames. We conclude the dissertation by revisiting the d-elements of Mart nez and Zenk [30], and characterise them analogously to d-ideals in commutative rings. We extend these characterisa-tions to algebraic frames with FIP. Of necessity, this will require that we reappraise a great deal of Banaschewski's work on pointfree spectra, and that of Mart nez and Zenk on algebraic frames. / Mathematical Sciences / M. Sc. (Mathematics)