Matrices of 3iet preserving morphisms

We study matrices of morphisms preserving the family of words coding 3-interval exchange transformations. It is well known that matrices of morphisms preserving sturmian words (i.e. words coding 2-interval exchange transformations with the maximal possible factor complexity) form the monoid $\{\boldsymbol{M}\in\mathbb{N}^{2\times 2} | \det\boldsymbol{M}=\pm1\} = \{\boldsymbol{M}\in\mathbb{N}^{2\times 2} | \boldsymbol{M}\boldsymbol{E}\boldsymbol{M}^T = \pm\boldsymbol{E}\}$, where $\boldsymbol{E} = (\begin{smallmatrix}0&1 -1&0\end{smallmatrix})$. We prove that in case of exchange of three intervals, the matrices preserving words coding these transformations and having the maximal possible subword complexity belong to the monoid $\{\boldsymbol{M}\in\mathbb{N}^{3\times 3} | \boldsymbol{M}\boldsymbol{E}\boldsymbol{M}^T = \pm\boldsymbol{E},\ \det\boldsymbol{M}=\pm 1\}$, where$\boldsymbol{E} = \Big(\begin{smallmatrix}0&1&1 -1&0&1 -1&-1&0\end{smallmatrix}\Big)$.Comment: 26 pages, 4 figure

Structural and Surface Modifications of Nanomaterials for Energy Applications

While renewable energy systems are currently on the rise, there are many projections stating that fossil fuels will still remain the dominant energy source for the next few decades. In order for the energy transition to take place promptly, the cost of generating energy from renewable sources has to be in line or lower compared to fossil fuels. Of the renewable energy alternatives that are available, solar energy is by far the most abundant and widely distributed source of energy generation. However, this type of energy is intermittent and has to be combined with energy storage technology, which has, in the last decade, developed significantly. In this thesis, research has focused on materials modification, synthesis, and utilization for solar cells. At first, TiO2 1D (one-dimensional) nanomaterials were synthesized, which are n-type materials, typically used for charge transportation (electron extraction) in a solar device configuration. Properties of these nanomaterials were modified by the addition of <12 nm gold nanoparticles (NPs), which can further improve energy conversion efficiency. The choice of using NPs for TiO2 modification was additionally expanded towards lanthanum and lithium metal ions, which were separately combined for the creation of a composite material. Characterisation was then performed using techniques that are widely employed for materials science research. In addition, nanomaterials were implemented for solar devices, and two different types were fabricated: dye-sensitized, and perovskite solar cells. Finally, research was expanded towards the synthesis of perovskite nanocrystals, which were produced using a novel, low energy, and scalable approach. In this thesis, challenges in the field of photovoltaics are addressed by exploiting the field of nanotechnology, with the aim to improve the performance of solar cells

Investigation and Production of Furniture for Villa Tugendhat 2009–2012

Villa Tugendhat is an expression of “gesamtkunstwerk”, where every detail is subordinated to the whole. Mies van der Rohe devoted the same amount of attention to the furnishings of the house as to its design. The furniture designed and placed according to his conception is such an important aspect of the house that without it the Villa is only half complete. The system governing the organization of all parts of the building – ratios, proportions, whole areas and details – is visible also in the precise placement of the house contents, which only allowed the owner limited variability in the use of space. The Villa became world famous not long after its completion, but Fritz and Grete Tugendhat were not destined to spend many happy years there. Even before the Munich Pact had been signed, signifying the de facto end of democratic Czechoslovakia, they left Brno forever. At the end of the summer of 1938 two removal vans came to take part of the furnishings to St. Gallen in Switzerland. Today the main body of the original equipment is, except for several pieces, still in the possession of the family. The Villa was, after two years of general reconstruction, reopened to the public in February this year. For the first time since 1938 it was equipped with all the furnishings Mies van der Rohe had designed for it. The most significant event was the return after seventy years of the original curved wall of the dining area to its original location. This famous Makassar wall had been considered lost for many decades

The Interaction of New and Old Magnetic Fluxes at the Beginning of Solar Cycle 23

The 11-year cycle of solar activity follows Hale's law by reversing the magnetic polarity of leading and following sunspots in bipolar regions during the minima of activity. In the 1996-97 solar minimum, most solar activity emerged in narrow longitudinal zones - `active longitudes' but over a range in latitude. Investigating the distribution of solar magnetic flux, we have found that the Hale sunspot polarity reversal first occurred in these active zones. We have estimated the rotation rates of the magnetic flux in the active zones before and after the polarity reversal. Comparing these rotation rates with the internal rotation inferred by helioseismology, we suggest that both `old' and `new' magnetic fluxes were probably generated in a low-latitude zone near the base of the solar convection zone. The reversal of active region polarity observed in certain longitudes at the beginning of a new solar cycle suggests that the phenomenon of active longitudes may give fundamental information about the mechanism of the solar cycle. The non-random distribution of old-cycle and new-cycle fluxes presents a challenge for dynamo theories, most of which assume a uniform longitudinal distribution of solar magnetic fields.Comment: 4 pages, 5 figures; accepted for publication in ApJ Letter

Niche with a Relief of St. Helen - a Contribution to the Romanesque Style in the Town of Hvar

Romanički, srpasti luk koji je sekundarno upotrijebljen kao niša za reljef sv. Jelene Križarice na kući Novak-Koga jedan je od rijetkih sačuvanih detalja stambene romanike u gradu Hvaru. Sekundarna upotreba romaničkog detalja potkrepljuje pretpostavke o široj rasprostranjenosti ovog stila na stambenoj arhitekturi grada. Srpasti luk niše je naknadno goticiziran, što pokazuje jedan od načina prodora gotike u stambenu arhitekturu.The niche on the house of Novak-Koga family in the town of Hvar, with a relief of St. Helen the "Cross-Finder", is a secondarily utilized Romanesque "sickle-like" arch. The relief itself goes back to the second half of the 15th c. Exceedingly scarce Romanesque elements in the preserved house architecture of this town give special meaning to the arch here described. Its secondary reusage confirms the supposition of a far wider presence of that style in the past than it could be inferred from its actual scarcity. The same can be said in regard of the typological diversity of Romanesque remnants. The sickle-like arch of the niche in question has been Gothicised in the manner that its inner tip was later sharpened, while its upper outer end was reshaped in mortar into a pointed form, thus giving to the whole of the niche a new, Gothic character. A similar "sharpening" can be observed on some other semi-circular Romanesque arches in the house architecture of Hvar, which probably means that they have been Gothicised in the same way

SOME NEW ARCHIVAL INFORMATION ABOUT PETAR HEKTOROVIĆ

Autor donosi, osim dosada poznatih vijesti o imanjima Petra Hektorovića na Visu, i vise izvornih, neobjavljenih dokumenata medu kojima se ističe opis njegovog ljetnikovca na predjelu Luka u Visu iz 1704. godine.The life of the celebrated Renaissance poet Petar Hektorović is mostly associated with Stari Grad and its Tvrdalj, fortified mansion, and Hvar, which in its time created vigorous discussion; however, documents from the Hektorović archives show that his estates, like most of the landed estates of the gentry, were scattered over the area of the entire commune. It is little known that the poet had a highly organised large estate on the island of Vis, which he inherited from his father, Marin Hektorović. The Hektorovićes had been a presence on Vis right from their progenitor, Hektor Golubinić. The last Hektorovićes too were recorded on Vis. During his lifetime, the poet leased out his Vis estate. In 1558 he leased a house, a hut with a cellar, garden and several items of land in Luka, Vis, to Nikola Šoltić. He contracted a similar lease with Ivan Balci in 1552. Petar Hektorović mentioned the Vis estate in several places in his will in 1559, without any precise descriptions of the real estate. He stipulated that the land and houses be leased out, as he had himself been accustomed to do, and that the revenues be deposited in the Hvar commune chancellery. The revenues were to be applied to the execution of his bequests, above all to the completion of Tvrdalj. One provision of the will was particularly important, that touching the combining of the lands and houses into a fidei commissum, or entail, an inalienable and inseparable whole that was to be inherited by the legitimate male members of the Hektorović family. The Hektorović fidei commissum, that is, the matter of his estate, led to what was probably the longest civil suit in the history of the commune of Hvar, and lasted, in various forms, from the first split of 1595 until the mid-19th century. At the beginning of the 17th century, the Vis summer residence and the house and garden at Cojno polje mainly belonged to the Korcula family of the Arneris. In the mid-17th century the Hvar Benedictines had an ongoing suit against the Arneris to do with boundary rights, while Matij and his sun Marcantun Hektorović had a suit against the Arneris concerning the inheritance of the poet\u27s fidei commissum on Vis from the end of the 17th century to the middle of the 18th. The documents relating to these disputes are kept in the Croatian Academy Historical Science institute in Dubrovnik, in the Hektorović Archives. Among these documents, particular importance must be attached to the drawing of the poet\u27s complex in Vis of 1647, the description of the complex with measurements of 1704, and a letter of 1752 in which the poet\u27s ownership over the house and garden in the area of Cojno polje in the interior of the island is definitely borne out. The same set of documents also includes drawings from the mid-18th century of the lands belonging to the poet Petar Hektorović, giving the precise location of the lands, with the names of the surrounding proprietors and the year in which the Hektorović family acquired them