Maple

Taking into account the economic importance of Acer species and their frequent use in landscape architecture, both nationally and internationally, it is necessary to develop an in vitro biotechnology research to propagate some of the most popular and requested Acer varieties. The study presents data on the partial results of in vitro initiation for two varieties of Acer platanoides: 'Globosum' and 'Crimson King'. During the initiation phase, Acer platanoides 'Globosum' showed the best initiation percentage, using the next nutrient composition: MS macroelements, MS microelements, MS vitamins, auxins/citokinine 0.2:1 mg/l, while Acer platanoides 'Crimson King' variety recorded the best results on the nutrient medium with a different composition: MS macroelements, MS microelements, LF vitamins and auxins/citokinine 0.4:1.2 mg/l. Keywords: Acer platanoides‚Globosum, Acer platanoides ‚Crimson King', maple, in vitro culture, explants Cuvinte cheie: Acer platanoides ‚Globosum', Acer platanoides ‚Crimson King', arţar, cultură in vitro, explante

Javor negundovac (Acer negundo L.) je listopadno drvo iz Sjeverne Amerike, a u Hrvatsku je uvezen početkom 20. stoljeća. Cijenjen je u pčelarstvu, šumarstvu, krajobraznom uređenju te je vrlo invazivna vrsta. Od ukrasnih karakteristika vrste mogu se izdvojiti deblo, kora, habitus, grane, listovi, cvjetovi i plodovi. Zbog svoje velike prilagodljivosti podnosi vrlo siromašna tla te položaje koji su izloženi suncu, suši, hladnoći i sjeni. Najrasprostranjeniji je u kontinentalnom i submediteranskom dijelu Hrvatske. A. negundo se s vremenom dosta raširio tako da je na području Hrvatske svrstan u invazivnu alohtonu vrstu. Prema literaturnim izvorima navedena vrsta za sada ne pričinjava ozbiljnije štete autohtonoj vegetaciji. Negundovac (Acer negundo L.) slabo je zastupljena dendrološka vrsta na gradskim krajobraznimpovršinama Knina, kao soliter, u drvoredu ili u skupinama. Metodom promatranja je također uočeno da u pogledu održavanja i njege stabala A. negundo na krajobraznim površinama nužno posvetiti više pažnje u formiranju krošnje. Nisu uočena njegova stabla van gradskih krajobraznih površina. Anketno istraživanje je provedeno tijekom druge polovice 2017. godine na uzorku od 50 ispitanika s područja grada Knina i okolice. Temeljem anketnog istraživanja ispitanici su dodijelili vrlo dobre ocijene ukrasnim karakteristikama i ugodnosti prisustva A. negundo na krajobraznim površinama Knina. Ponešto su lošije ocijenili ulogu navede vrste u pčelarstvu, šumskim melioracijama i urbanom šumarstvu. Veći broj ispitanika ne zna da je A. negundo vrlo invazivna vrsta. Ash-leaf maple or boxelder (Acer negundo L.) is a deciduous tree that originates from North America. It was imported into Croatia at the beginning of the 20th century. It is highly valued in bee-keeping, forestry and landscape architecture and it is a highly invasive species. Amongst the ornamental characteristics it is important to highlight its tree trunk, tree bark, habitus, branches, leaves, flowers and fruits. Due to its high adaptability it tolerates very poor soils and positions exposed to the sunlight, drought, cold and shade. It is the most widespread in the continental and sub-Mediterranean parts of Croatia. In time A. negundo became considerably widespread and hence, it was considered as an invasive alien species in Croatia. According to the references provided from professional literature, the previously mentioned tree species does not currently do any serious damage to the autochthonous vegetation. Ash-leaf maple (Acer negundo L.) is a sparsely distributed woody species in urban landscape surfaces of Knin, as a solitary tree, in tree lines or in groups of trees. Moreover, using the observation method concerning maintenance and care of A. negundo on landscape surfaces, it was noted that more attention needs to be paid to the formation of the tree top. These trees have not been found outside the urban landscapes. The survey research was conducted in the second half of 2017 on a sample comprising of 50 respondents originating from the city of Knin and its outskirts. Based on the findings of the survey research the respondents gave very good grades to ornamental characteristics and the comfort of the presence of A. negundo on the landscape surfaces of Knin. The role of the previously mentioned tree species received slightly lower grades in bee-keeping, forest meliorations and urban forestry. A considerable number of those surveyed was unaware of the fact that A. negundo is a highly invasive tree species.

This paper shows a model of teacher training developed by the Department of Mathematics of the University of Turin, aimed at introducing teachers to the use of innovative methodologies for learning Mathematics and for developing disciplinary and cross-cutting competences. The learning methodologies proposed are mainly based on Problem Posing and Problem Solving, the use of an Advanced Computing Environment, of a Virtual Learning Environment and of an Automated Assessment System. The training model, designed in blended modality, mainly relies on the creation of an online community of practice, where teachers, supported by tutors, collaborate in the creation of interactive learning materials for their classes. They acquire competences not only in the use of learning technologies, but also on sharing and collaborating in virtual environments; they learn how to develop self-tailored didactic methodologies. The key strengths of this model are highlighted and the results, achieved after the experimentation in several projects, are discussed, showing the effectiveness of the model. Teacher training: a model for introducing innovative digital methodologies for learning Mathematics

The mathematical models used in intermediate
macroeconomics have become increasingly more
sophisticated and challenging for students to learn. This
paper demonstrates how mathematics software, such as
Maple, can be used to design a simulation as a pedagogical
aid. The paper proceeds by developing a system of
equations to model the economy, simulating the system with
Maple, and illustrating the impacts of fiscal and monetary
policy changes. A pilot test of the simulation was performed
to see if higher levels of mathematical rigor could be
introduced in a principles course. The results indicate that
symbolic mathematics software can be an effective teaching
and student learning tool.

This work presents the nonlinear analysis of forced harmonic oscillation system using differential transformation method-Padé approximant techniques. Without any series expansion of the included sine and cosine of the angular displacement in the nonlinear model of the system, an improved analytical solution of the dynamic model is presented. The high level of accuracy and validity of the analytical solutions obtained by the differential transformation method are shown through comparison of the results of the solution with the corresponding numerical solutions obtained by fourth-fifth-order Runge-Kutta method, homotopy perturbation method and energy balance methods. Also, with the aid of the analytical solutions, parametric studies are carried to study the impacts of the model parameters on the dynamic behavior of the large-amplitude nonlinear oscillation system. The method avoids any numerical complexity and it is very simple, suitable and useful as a mathematical tool for dealing the nonlinear problems.