ANIMACIJE IZRAĐENE U MATLAB-U I NJIHOVA PRIMJENA U DIDAKTIČKE SVRHE

     The aim of this paper is to show how dynamic multimedia tool in Matlab (animation) can be made and how the animations and movies can be used for didactic purposes, or to be more precise, how they can be integrated into the teaching process. This paper is a part of a more complex research whose aim is to investigate the impact of the information technology on the quality of mathematical knowledge related to functions.    Analysis of the results of a research conducted on a sample of 30 students before and after performing the innovated teaching with the application of the information technology showed a significant impact of the IT application on the quality of knowledge related to functions. The t-test showed that, with the probability of 99%, it can be concluded that the results of the students after carrying out such type of innovated teaching were significantly better than their results on analogue contents taught through classical teaching. Cilj ovog rada je pokazati kako se može načiniti dinamički multimedijski alat u Matlabu (animacija) i kako se animacije i filmovi mogu koristiti za didaktičke svrhe, ili, da budemo precizniji, kako mogu biti integrirani u nastavni proces. Ovaj rad je dio složenijeg istraživanja čiji je cilj istražiti utjecaj informacijske tehnologije na kvalitetu matematičkih znanja vezanih uz funkcije. Analiza rezultata istraživanja, provedenog na uzorku od 30 studenata prije i nakon izvođenja inovativne nastave uz primjenu informacijskih tehnologija, pokazala je značajan utjecaj primjene informacijskih tehnologija na kvalitetu znanja vezanih uz funkcije. T-test je pokazao da se, uz vjerojatnost od 99%, može zaključiti da su rezultati studenata nakon izvođenja ovog oblika inovativne nastave bili znatno bolji od rezultata iste skupine studenata na analognim sadržajima tijekom klasične nastave

Computer aided (filament winding) tape placement for elbows. Practically orientated algorithm

Filament winding is one of the most used automated techniques for manufacturing of composite objects with different open-end or closed-end structures. Mathematical model for covering an elbow mandrel with composite material is considered. The nature of the comprising equations is elaborated in detail. A practically orientated algorithm for filament winding for elbows is formulated and its open-source implementations in Python and MATLAB are presented. The results from the constructed algorithm are presented and discussed. Keywords: filament winding for elbows, tape placement for elbows, practical algorithm, open-source, CAD

The association of C3435T single-nucleotide polymorphism, Pgp-glycoprotein gene expression levels and carbamazepine maintenance dose in patients with epilepsy

The ABCB1 gene encodes the P-glycoprotein (Pgp) protein, which is thought to transport various antiepileptic drugs. The single nucleotide polymorphism (SNP) (C3435T) in exon 26 of this gene correlates with the altered expression levels of P-glycoprotein, range of drug response and clinical conditions. In order to investigate the influence of this polymorphism on the susceptibility to and efficacy of carbamazepine therapy, we evaluated the allelic frequency and genotype distribution of this variant in 162 epilepsy patients from the Republic of Macedonia. Statistically significant differences were detected neither in the allelic frequency and genotype distribution between carbamazepine-resistant and carbamazepine-responsive epilepsy patients nor between the subgroups of carbamazepine (CBZ)-responsive patients treated with different CBZ doses. However, the T-allele was enriched in CBZ-responsive patients who required higher maintenance CBZ doses, This observation was substantiated by the findings that the median total plasma levels were the lowest in patients with CC (20 μmol/L) followed by CT (23 μmol/L) and TT (29 μmol/L) genotypes. Patients with a CC genotype also had a higher likelihood of response compared to patients with CT or TT genotypes over a wide range (400–1000 mg/day) of initial doses of CBZ. The T allele showed a reduced expression of ~5% compared to the C allele in peripheral blood mononuclear cells in heterozygotes for the variant. This difference might be translated into ~10% difference in homozygotes for the variant, which would explain the trend towards a dose-dependent efficacy of the CBZ treatment in patients with different genotypes. A larger prospective study is warranted to clarify the clinical utility of a genotypespecific individualized CBZ therapy

Didactic principle of visualization in mathematics

Didactic principles are general requirements that must be satisfied by learning to successfully achieve its goals. The principle of visualization is a basic principle in teaching mathematics and helps in the realization of other didactic principles, because the visualization of the external support of mental activity. Didactic principle of visualization in the teaching of mathematics is the search about application for visualization resources in teaching with the aim of achieving a high level of abstraction during the formation of mathematical concepts. The teaching of mathematics in its nature involves the study of concepts, attributes, statements and issues are intrinsically linked with certain dynamic process or situation. Beginning with the introduction of symbolism in the teaching of algebra, a student should begin to think dynamically - what happens to this, what value for that variable. Each geometric task, ask students to question what would happen if one of the geometric objects change. In particular, the study of functions, leading student to a permanent research changes. In essence, the study of functions of the concept of change, especially when it comes to notions of continuity, limes, limit and other essential concepts of mathematical analysis. The principle of visualization should be raised to a higher and more significant level, because visualization refers not only to how to "see " , but the engagement of the whole perceptual apparatus factor of the teaching process. We will show that the perception of the teaching of mathematics should be enriched by all possible means and visualization methods, up to the level where the external review team may replace the internal. Time may be considered at the level of perception, student transferred at the show, after which it should apply the methods that the student will lead to the creation of the concept and form of abstract thinking

Relationship between the extremes of a functional and its variation

Methods to solve variational problems, the tasks for the study for maximum and minimum of functionals are very similar methods to study the maximum and minimum functions. Therefore, appropriate to outline briefly the theory of maximum and minimum functions and in parallel we will introduce similar concepts and prove similar theorems for functional. The variation of functional is primary and linear with respect to a part of the increase of functional. In the study of functional, variation plays the same role played by the differential in the study of functions. We will show that if there is a variation in the basic sense of the linear increase of functional, then there is a variation in the derivative sense of the parameter with initial value, and that both definitions are equivalent and we will give another definition of functional variation. The above we will show in several examples and we will prove a theorem which is a link between the extremes of a functional and its variation

Avoiding heavy computations in inverse calibration procedure for 7 DOF robot manipulator

Procedure for determining commanded coordinates in machine space if desired coordinates are given is inverse calibration. A large amount of data is considered after measurement procedure and it is essential to locate desired point in the real space which is skewed due to measured geometric errors. The machine workspace is divided to cells using measurement points. It is depicted the importance of finding the proper cell in skewed 3D lat- tice, for calibration of translational axes of ATL machine with large workspace. To calibrate 7 DOF robot manipula- tor, this algorithm is extended. The problem of finding the proper cell in 7D skewed grid needs heavy computations and takes significant amount of computational time. Few ideas for avoiding these computations are described and the influence on the final precision of the calibration procedure is explored

Volumetric calibration for improving accuracy of AFP/ATL machines

Automated Fiber Placement (AFP) and Automated Tape Laying (ATL) technologies are mostly used in aerospace industry. Deviations from predefined position and orientation of the AFP/ATL machine’s end-effector may cause defects of the final product like gaps and laps of the laminate ply, tow end placement errors, pressure and temperature variations, etc. That makes clear the importance of accuracy of AFP/ATL machines. Calibration is needed to enhance accuracy. Development and implementation of a comprehensive procedure for volumetric calibration of three linear axes is described in this paper. According to ISO 230-1:2012 and ISO 230-2:2014 standards, 18 position dependent and 3 position independent (in total 21) errors of the 3 linear axes are considered. Measurements are performed using laser interferometer on ATL machine produced by company Mikrosam. Obtained data are used for calibration of that machine and validity of the results is verified by comparison with the calibration results obtained by TRAC-CAL software developed by ETALON AG

Algorithmic approach to geometric solution of generalized Paden–Kahan subproblem and its extension

Kinematics as a science of geometry of motion describes motion by means of position, orientation, and their time derivatives. The focus of this article aims screw theory approach for the solution of inverse kinematics problem. The kinematic elements are mathematically assembled through screw theory by using only the base, tool, and workpiece coordinate systems—opposite to conventional Denavit–Hartenberg approach, where at least n þ 1 coordinate frames are needed for a robot manipulator with n joints. The inverse kinematics solution in Denavit–Hartenberg convention is implicit. Instead, explicit solutions to inverse kinematics using the Paden–Kahan subproblems could be expressed. This article gives step-by-step application of geometric algorithm for the solution of all the cases of Paden–Kahan subproblem 2 and some extension of that subproblem based on subproblem 2. The algorithm described here covers all of the cases that can appear in the generalized subproblem 2 definition, which makes it applicable for multiple movement configurations. The extended subproblem is used to solve inverse kinematics of a manipulator that cannot be solved using only three basic Paden–Kahan subproblems, as they are originally formulated. Instead, here is provided solution for the case of three subsequent rotations, where last two axes are parallel and the first one does not lie in the same plane with neither of the other axes. Since the inverse kinematics problem may have no solution, unique solution, or many solutions, this article gives a thorough discussion about the necessary conditions for the existence and number of solutions. Keywords Screw motion, Paden–Kahan subproblem, geometric algorithm, inverse kinematics, mathematical foundation