The Students’ Perspective of Geometry Teaching and Learning in High School

The purpose of this article is to present the results obtained from a questionnaire applied to Costa Rican high school students, in order to know their perspectives about geometry teaching and learning. The results show that geometry classes in high school education have been based on a traditional system of teaching, where the teacher presents the theory; he presents examples and exercises that should be solved by students, which emphasize in the application and memorization of formulas. As a consequence, visualization processes, argumentation and justification don’t have a preponderant role. Geometry is presented to students like a group of definitions, formulas, and theorems completely far from their reality and, where the examples and exercises don’t possess any relationship with their context. As a result, it is considered not important, because it is not applicable to real life situations. Also, the students consider that, to be successful in geometry, it is necessary to know how to use the calculator, to carry out calculations, to have capacity to memorize definitions, formulas and theorems, to possess capacity to understand the geometric drawings and to carry out clever exercises to develop a practical ability.

Investigation of novel methodologies for the MCNP geometry preparation: application on the Upper Launcher BSM of ITER

La tesi si divide in due macroargomenti relativi alla preparazione della geometria per modelli MCNP. Il primo è quello degli errori geometrici che vengono generati quando avviene una conversione da formato CAD a CSG e le loro relazioni con il fenomeno delle lost particles. Il passaggio a CSG tramite software è infatti inevitabile per la costruzione di modelli complessi come quelli che vengono usati per rappresentare i componenti di ITER e può generare zone della geometria che non vengono definite in modo corretto. Tali aree causano la perdita di particelle durante la simulazione Monte Carlo, andando ad intaccare l' integrità statistica della soluzione del trasporto. Per questo motivo è molto importante ridurre questo tipo di errori il più possibile, ed in quest'ottica il lavoro svolto è stato quello di trovare metodi standardizzati per identificare tali errori ed infine stimarne le dimensioni. Se la prima parte della tesi è incentrata sui problemi derivanti dalla modellazione CSG, la seconda invece suggerisce un alternativa ad essa, che è l'uso di Mesh non Strutturate (UM), un approccio che sta alla base di CFD e FEM, ma che risulta innovativo nell'ambito di codici Monte Carlo. In particolare le UM sono state applicate ad una porzione dell' Upper Launcher (un componente di ITER) in modo da validare tale metodologia su modelli nucleari di alta complessità. L'approccio CSG tradizionale e quello con UM sono state confrontati in termini di risorse computazionali richieste, velocità, precisione e accuratezza sia a livello di risultati globali che locali. Da ciò emerge che, nonostante esistano ancora alcuni limiti all'applicazione per le UM dovuti in parte anche alla sua novità, vari vantaggi possono essere attribuiti a questo tipo di approccio, tra cui un workflow più lineare, maggiore accuratezza nei risultati locali, e soprattutto la possibilità futura di usare la stessa mesh per diversi tipi di analisi (come quelle termiche o strutturali).

Advanced numerical modeling of masonry vaulted structures based on BIM parametric geometry generation

Vaults are an architectural element which during construction history have been built with a great variety of different materials, shapes, and sizes. The shape of these structural elements was often dependent by the necessity to cover complex spaces, by the needed loading capacity, or by architectural aesthetics. Within this complex scenario masonry patterns generates also different effects on loading capacity, load percolation and stiffness of the structure. These effects were been extensively investigated, both with empirical observations and with modern numerical methods. While most of them focus on analyzing the load bearing capacity or the texture effect on vaulted structures, the aim of this analysis is to investigate on the effects of the variation of a single structural characteristic on the load percolation in the vault. Moreover, an additional purpose of the work is related to the coding of a parametrical model aiming at generating different masonry vaulted structures. Nevertheless, proposed script can generate different typology of vaulted structure basing on some structural characteristics, such as the span and the length to cover and the dimensions of the blocks.

The three-dimensional single-bin-size bin packing problem: combining metaheuristic and machine learning approaches

The Three-Dimensional Single-Bin-Size Bin Packing Problem is one of the most studied problem in the Cutting & Packing category. From a strictly mathematical point of view, it consists of packing a finite set of strongly heterogeneous “small” boxes, called items, into a finite set of identical “large” rectangles, called bins, minimizing the unused volume and requiring that the items are packed without overlapping. The great interest is mainly due to the number of real-world applications in which it arises, such as pallet and container loading, cutting objects out of a piece of material and packaging design. Depending on these real-world applications, more objective functions and more practical constraints could be needed. After a brief discussion about the real-world applications of the problem and a exhaustive literature review, the design of a two-stage algorithm to solve the aforementioned problem is presented. The algorithm must be able to provide the spatial coordinates of the placed boxes vertices and also the optimal boxes input sequence, while guaranteeing geometric, stability, fragility constraints and a reduced computational time. Due to NP-hard complexity of this type of combinatorial problems, a fusion of metaheuristic and machine learning techniques is adopted. In particular, a hybrid genetic algorithm coupled with a feedforward neural network is used. In the first stage, a rich dataset is created starting from a set of real input instances provided by an industrial company and the feedforward neural network is trained on it. After its training, given a new input instance, the hybrid genetic algorithm is able to run using the neural network output as input parameter vector, providing as output the optimal solution. The effectiveness of the proposed works is confirmed via several experimental tests.

Computational tool for three-point hitch geometry optimization

The weight-transfer effect, consisting of the change in dynamic load distribution between the front and the rear tractor axles, is one of the most impairing phenomena for the performance, comfort, and safety of agricultural operations. Excessive weight transfer from the front to the rear tractor axle can occur during operation or maneuvering of implements connected to the tractor through the three-point hitch (TPH). In this respect, an optimal design of the TPH can ensure better dynamic load distribution and ultimately improve operational performance, comfort, and safety. In this study, a computational design tool (The Optimizer) for the determination of a TPH geometry that minimizes the weight-transfer effect is developed. The Optimizer is based on a constrained minimization algorithm. The objective function to be minimized is related to the tractor front-to-rear axle load transfer during a simulated reference maneuver performed with a reference implement on a reference soil. Simulations are based on a 3-degrees-of-freedom (DOF) dynamic model of the tractor-TPH-implement aggregate. The inertial, elastic, and viscous parameters of the dynamic model were successfully determined through a parameter identification algorithm. The geometry determined by the Optimizer complies with the ISO-730 Standard functional requirements and other design requirements. The interaction between the soil and the implement during the simulated reference maneuver was successfully validated against experimental data. Simulation results show that the adopted reference maneuver is effective in triggering the weight-transfer effect, with the front axle load exhibiting a peak-to-peak value of 27.1 kN during the maneuver. A benchmark test was conducted starting from four geometries of a commercially available TPH. As result, all the configurations were optimized by above 10%. The Optimizer, after 36 iterations, was able to find an optimized TPH geometry which allows to reduce the weight-transfer effect by 14.9%.

Quantum Riemannian geometry on graphs for gauge field theory

In questo lavoro estendiamo concetti classici della geometria Riemanniana al fine di risolvere le equazioni di Maxwell sul gruppo delle permutazioni $S_3$. Cominciamo dando la strutture algebriche di base e la definizione di calcolo differenziale quantico con le principali proprietà. Generalizziamo poi concetti della geometria Riemanniana, quali la metrica e l'algebra esterna, al caso quantico. Tutto ciò viene poi applicato ai grafi dando la forma esplicita del calcolo differenziale quantico su $\mathbb{K}(V)$, della metrica e Laplaciano del secondo ordine e infine dell'algebra esterna. A questo punto, riscriviamo le equazioni di Maxwell in forma geometrica compatta usando gli operatori e concetti della geometria differenziale su varietà che abbiamo generalizzato in precedenza. In questo modo, considerando l'elettromagnetismo come teoria di gauge, possiamo risolvere le equazioni di Maxwell su gruppi finiti oltre che su varietà differenziabili. In particolare, noi le risolviamo su $S_3$.

Molecular Variations In Aromatic Cosolutes: Critical Role In The Rheology Of Cationic Wormlike Micelles.

Wormlike micelles formed by the addition to cetyltrimethylammonium bromide (CTAB) of a range of aromatic cosolutes with small molecular variations in their structure were systematically studied. Phenol and derivatives of benzoate and cinnamate were used, and the resulting mixtures were studied by oscillatory, steady-shear rheology, and the microstructure was probed by small-angle neutron scattering. The lengthening of the micelles and their entanglement result in remarkable viscoelastic properties, making rheology a useful tool to assess the effect of structural variations of the cosolutes on wormlike micelle formation. For a fixed concentration of CTAB and cosolute (200 mmol L(-1)), the relaxation time decreases in the following order: phenol > cinnamate> o-hydroxycinnamate > salicylate > o-methoxycinnamate > benzoate > o-methoxybenzoate. The variations in viscoelastic response are rationalized by using Mulliken population analysis to map out the electronic density of the cosolutes and quantify the barrier to rotation of specific groups on the aromatics. We find that the ability of the group attached to the aromatic ring to rotate is crucial in determining the packing of the cosolute at the micellar interface and thus critically impacts the micellar growth and, in turn, the rheological response. These results enable us for the first time to propose design rules for the self-assembly of the surfactants and cosolutes resulting in the formation of wormlike micelles with the cationic surfactant CTAB.

Brij Detergents Reveal New Aspects Of Membrane Microdomain In Erythrocytes.

Membrane microdomains enriched in cholesterol, sphingolipids (rafts), and specific proteins are involved in important physiological functions. However their structure, size and stability are still controversial. Given that detergent-resistant membranes (DRMs) are in the liquid-ordered state and are rich in raft-like components, they might correspond to rafts at least to some extent. Here we monitor the lateral order of biological membranes by characterizing DRMs from erythrocytes obtained with Brij-98, Brij-58, and TX-100 at 4 °C and 37 °C. All DRMs were enriched in cholesterol and contained the raft markers flotillin-2 and stomatin. However, sphingomyelin (SM) was only found to be enriched in TX-100-DRMs - a detergent that preferentially solubilizes the membrane inner leaflet - while Band 3 was present solely in Brij-DRMs. Electron paramagnetic resonance spectra showed that the acyl chain packing of Brij-DRMs was lower than TX-100-DRMs, providing evidence of their diverse lipid composition. Fatty acid analysis revealed that the SM fraction of the DRMs was enriched in lignoceric acid, which should specifically contribute to the resistance of SM to detergents. These results indicate that lipids from the outer leaflet, particularly SM, are essential for the formation of the liquid-ordered phase of DRMs. At last, the differential solubilization process induced by Brij-98 and TX-100 was monitored using giant unilamellar vesicles. This study suggests that Brij and TX-100-DRMs reflect different degrees of lateral order of the membrane microdomains. Additionally, Brij DRMs are composed by both inner and outer leaflet components, making them more physiologically relevant than TX-100-DRMs to the studies of membrane rafts.

Crystal Structure Of (3e)-3-[(4-nitro-phen-oxy)-meth-yl]-4-phenyl-but-3-en-2-one.

In the title compound, C17H15NO4, the conformation about the C=C double bond [1.348 (2) Å] is E with the ketone group almost co-planar [C-C-C-C torsion angle = 7.2 (2)°] but the phenyl group twisted away [C-C-C-C = 160.93 (17)°]. The terminal aromatic rings are almost perpendicular to each other [dihedral angle = 81.61 (9)°] giving the mol-ecule an overall U-shape. The crystal packing feature benzene-C-H⋯O(ketone) contacts that lead to supra-molecular helical chains along the b axis. These are connected by π-π inter-actions between benzene and phenyl rings [inter-centroid distance = 3.6648 (14) Å], resulting in the formation of a supra-molecular layer in the bc plane.

Finite-element Analysis Of 3 Situations Of Trauma In The Human Edentulous Mandible.

Maxillofacial trauma resulting from falls in elderly patients is a major social and health care concern. Most of these traumatic events involve mandibular fractures. The aim of this study was to analyze stress distributions from traumatic loads applied on the symphyseal, parasymphyseal, and mandibular body regions in the elderly edentulous mandible using finite-element analysis (FEA). Computerized tomographic analysis of an edentulous macerated human mandible of a patient approximately 65 years old was performed. The bone structure was converted into a 3-dimensional stereolithographic model, which was used to construct the computer-aided design (CAD) geometry for FEA. The mechanical properties of cortical and cancellous bone were characterized as isotropic and elastic structures, respectively, in the CAD model. The condyles were constrained to prevent free movement in the x-, y-, and z-axes during simulation. This enabled the simulation to include the presence of masticatory muscles during trauma. Three different simulations were performed. Loads of 700 N were applied perpendicular to the surface of the cortical bone in the symphyseal, parasymphyseal, and mandibular body regions. The simulation results were evaluated according to equivalent von Mises stress distributions. Traumatic load at the symphyseal region generated low stress levels in the mental region and high stress levels in the mandibular neck. Traumatic load at the parasymphyseal region concentrated the resulting stress close to the mental foramen. Traumatic load in the mandibular body generated extensive stress in the mandibular body, angle, and ramus. FEA enabled precise mapping of the stress distribution in a human elderly edentulous mandible (neck and mandibular angle) in response to 3 different traumatic load conditions. This knowledge can help guide emergency responders as they evaluate patients after a traumatic event.

Molecularly Imprinted Solid Phase Extraction Of Fluconazole From Pharmaceutical Formulations.

This work encompasses a direct and coherent strategy to synthesise a molecularly imprinted polymer (MIP) capable of extracting fluconazole from its sample. The MIP was successfully prepared from methacrylic acid (functional monomer), ethyleneglycoldimethacrylate (crosslinker) and acetonitrile (porogenic solvent) in the presence of fluconazole as the template molecule through a non-covalent approach. The non-imprinted polymer (NIP) was prepared following the same synthetic scheme, but in the absence of the template. The data obtained from scanning electronic microscopy, infrared spectroscopy, thermogravimetric and nitrogen Brunauer-Emmett-Teller plot helped to elucidate the structural as well as the morphological characteristics of the MIP and NIP. The application of MIP as a sorbent was demonstrated by packing it in solid phase extraction cartridges to extract fluconazole from commercial capsule samples through an offline analytical procedure. The quantification of fluconazole was accomplished through UPLC-MS, which resulted in LOD≤1.63×10(-10) mM. Furthermore, a high percentage recovery of 91±10% (n=9) was obtained. The ability of the MIP for selective recognition of fluconazole was evaluated by comparison with the structural analogues, miconazole, tioconazole and secnidazole, resulting in percentage recoveries of 51, 35 and 32%, respectively.

Synthesis, characterization, DFT and Td-dfT study of the [Fe(mnt)(L)(t-BuNC) 2] octahedral complex (L = phen, bipy)

FeBr2 has reacted with an equivalent of mnt2- (mnt = cis-1,2-dicyanoethylene-1,2-dithiolate) and the α-diimine L (L = 1,10'-phenantroline, 2,2'-bipyridine) in THF solution, and followed by adding of t-butyl-isocyanide to give [Fe(mnt)(L)(t-BuNC)2] neutral compound. The products were characterized by infrared, UV-visible and Mössbauer spectroscopy, besides thermogravimetric and conductivity data. The geometry in the equilibrium was calculated by the density functional theory and the electronic spectrum by the time-dependent. The experimental and theoretical results in good agreement have defined an octahedral geometry with two isocyanide neighbours. The π→π* intraligand electronic transition was not observed for cis-isomers in the near-IR spectral region.

Caracterização físico-química de filmes comestíveis de amido adicionado de acerola (Malphigia emarginata D.C.)

Edibles films are an alternative to synthetic materials used for packing food products. Barbados cherry is rich in vitamin C and carotenoids. The aim of this study was to characterize and develop films by casting from cassava starch, lyophilized Barbados cherry pulp and glycerol. The films were characterized with respect to thickness, water vapor permeability (WVP), water solubility, vitamin C, carotene and mechanical properties. The interaction of pulp and glycerol reduced film thickness. An increase in pulp concentration up to 60% increased WVP but beyond this concentration reduced both WVP and solubility leading to an increased level of vitamin C and β carotene in the films.

Avaliação de danos mecânicos causados em banana Nanicão durante as etapas de beneficiamento, transporte e embalagem

This study had as objective the evaluation of mechanical damages occurred in banana Nanicão during the improvement process, packing and distribution, identifying the probable critical points. The mechanical damages caused by transport, first cleaning; cleanness and sorting; preservation in the packing, transport, and mature were evaluated. The studied packing had been: torito wooden packing (18 kg), wood type ½ box, (13 kg) and cardboard (18 kg). The stage of preservation and transport of the fruits to the distribution center duplicated the light defects and quintupled the serious defects, causing rottenness after the acclimatization. The cardboard packing did not support the piling up and presented deformations, that resulted in the kneading the fruits of the inferior packing, causing a significant increase of the serious defects. The fruits conditioned in the involved packing of plastic bubble had presented an inferior number of serious damages when compared with the others packing, without the plastic.