A Hermite interpolatory subdivision scheme for C2C^2-quintics on the Powell-Sabin 12-split

In order to construct a $C^1$-quadratic spline over an arbitrary triangulation, one can split each triangle into 12 subtriangles, resulting in a finer triangulation known as the Powell-Sabin 12-split. It has been shown previously that the corresponding spline surface can be plotted quickly by means of a Hermite subdivision scheme. In this paper we introduce a nodal macro-element on the 12-split for the space of quintic splines that are locally $C^3$ and globally $C^2$. For quickly evaluating any such spline, a Hermite subdivision scheme is derived, implemented, and tested in the computer algebra system Sage. Using the available first derivatives for Phong shading, visually appealing plots can be generated after just a couple of refinements.Comment: 17 pages, 7 figure

B-spline-like bases for C2C^2 cubics on the Powell-Sabin 12-split

For spaces of constant, linear, and quadratic splines of maximal smoothness on the Powell-Sabin 12-split of a triangle, the so-called S-bases were recently introduced. These are simplex spline bases with B-spline-like properties on the 12-split of a single triangle, which are tied together across triangles in a B\'ezier-like manner. In this paper we give a formal definition of an S-basis in terms of certain basic properties. We proceed to investigate the existence of S-bases for the aforementioned spaces and additionally the cubic case, resulting in an exhaustive list. From their nature as simplex splines, we derive simple differentiation and recurrence formulas to other S-bases. We establish a Marsden identity that gives rise to various quasi-interpolants and domain points forming an intuitive control net, in terms of which conditions for $C^0$-, $C^1$-, and $C^2$-smoothness are derived

A sampling strategy based on B-wavelets decomposition

Finding optimal sampling strategy is a central problem in surface reconstruction. In this paper a sampling strategy on different scales of a free-form surface is proposed. Non-Uniform Rational B-spline (NURBS) surfaces are used to represent the nominal shape; the decomposition is performed through the orthogonal B-wavelet basis. A sampling based on each level of the shape decomposition is then proposed to detect the points of interest that reflect the variations between different levels. The number of the samples is selected according to the complexity of the shape, which is represented by the number of the internal knots

QUARTERLY ECONOMETRIC MODEL AND FORECASTS OF THE MINNESOTA AND U.S. IRON MINING INDUSTRY

The Report projects quarterly production and stock levels for the Minnesota and U.S. iron mining industry to the year 2000. Projections of Minnesota's iron industry employment are subsequently derived from the production forecasts. Ordinary least squares regression techniques are used to analyze the seasonality patterns that existed between 1955 and 1978. The regression equations, based on the quarterly data, were calibrated so they could be used to seasonalize the annual iron ore consumption, production and import projections developed by the U.S. Bureau of Mines. Alternate industry forecast series are presented to facilitate comparison with the yearly baseline projection series.Community/Rural/Urban Development, Resource /Energy Economics and Policy,

A note on the Oslo algorithm

Journal ArticleThe Oslo algorithm is a recursive method for updating the B-spline representation of a curve or tensor product surface when extra knots are added. In the present note the derivation of this method is simplified

Beregninger av nitrogenbalansen på 50 gårdsbruk i kommunene Midsund, Fræna, Gjemnes, Surnadal og Rindal

Landbruk Nordvest har gjennomført nitrogenbalanse-beregninger på 50 gårdsbruk ikommunene Midsund, Fræna, Gjemnes, Surnadal og Rindal. Dette er et ledd i ”klima-arbeidet” i de fem kommunene. På samtlige melke-produksjonsbruk i undersøkelsen ble det kjøpt inn langt mer nitrogen og fosfor enn hva som ble solgt ut igjen, slik at gårdene tilførte flere næringsstoffer enn hva de fjernet. Det er en betydelig variasjon mellom enkeltbruk. Nitrogen-balanseberegningene for de 4 sauebrukene med økologisk drift viser at det også her er overskudd på nitrogen

Of Fear and Fright: Reminiscences from the Bangladesh Sundarbans in Colonel Ershad's Time

In these reminiscences from the Bangladesh Sundarbans in the early 1980s, I recall the climate of fear that reigned in the area. Among the poor, every spring presented the threat of starvation and death, as their rice stocks became depleted and the price of rice became impossibly high. Rice became scarce, too, since much was smuggled to India at an even "better" price. For those who had a little land, there was the danger that rich neighbours would dispossess them by bribing the village accountant to change the title to the land. For the land-grabbers, there was the fear of vengeance from the Mukti Bahini, the clandestine freedom fighters from the time of the war of independence, who would sometimes kill the wrongdoers. For those who sympathised with the Mukti Bahini, there was the fear of the police. Even the schoolmasters were afraid, for the state coffers would run dry in the summer, and they would not get paid until the arrival of foreign aid money in January. And yet, in the midst of all this, there was the Jatra, the folk theatre, whose rehearsals were held clandestinely in spite of the curfew - proof of the people’s determination to enjoy life and art in spite of everything. This article, then, is a reflection on the courage exhibited by the residents of the Sundarbans in defiance of the omnipresent spectre of fear

English Teachers’ Beliefs and Practices of Oral Skills Assessment in Norwegian Primary School

Denne studien retter søkelys mot engelsklæreres oppfatning av og praksis med muntlige ferdigheter og vurdering på mellomtrinnet i grunnskolen. Med fornyelsen av den nasjonale læreplanen (LK20), er lærere overlatt med høy grad av autonomi og et stort ansvar for å realisere læreplanens intensjon, nemlig å legge til rette for et læringsmiljø der alle elever kan nå sitt læringspotensial og oppnå ferdigheter og kompetanse basert på kjerneelementer og det enkelte fagets kompetansemål. Vurdering for læring skal gjennomsyre hele skolegangen på barneskolen, som betyr at lærere må ta utgangspunkt i elevenes nåværende kunnskapsnivå for å kunne veilede dem videre til økt faglig kunnskap og sosial kompetanse. Data for denne studien ble samlet inn gjennom semi-strukturerte intervju med fire engelsklærere som delte sine oppfatninger av muntlige ferdigheter og undervisnings- og vurderingspraksiser. De rapporterte om bruk av varierte typer muntlige aktiviteter for å fremme muntlig ferdigheter, men opplever at de har for lite tid og for store klasser til å sikre at alle elever får deltatt i muntlig aktivitet som kan danne et vurderingsgrunnlag. For å møte disse utfordringene, har tre av lærerne tatt i bruk taleopptak, hvor elevene leser inn tekster digitalt. Dette gir både lesetrening for elevene, innslag av egenvurdering, danner grunnlag for vurdering og sparer lærere for tid. På tross av dette er vurdering en sammensatt øvelse, og bruk av vurderingskriterier og strategier ser ut til å skje sporadisk. Funn i studien viser også at læreres erfaringer fra egen skolegang og utdanning har betydning for deres egen undervisningspraksis av muntlige ferdigheter. Ytre rammefaktorer påvirker også hvordan lærere planlegger, tilrettelegger og gjennomfører muntlige aktiviteter i klassen. I tillegg ser det ut til at lærere mangler både terminologi, kunnskap og kompetanse om vurdering og strategier for å vurdere muntlige ferdigheter. I likhet med funn fra studier om vurdering av muntlige ferdigheter fra ungdoms- og videregående skoler (se bl.a. Bøhn, 2015; Johannessen, 2018; Kaldahl, 2022), strever lærerne i denne studien med å vite hva og hvordan de skal vurdere og savner retningslinjer og felles standarder for å unngå å mislykkes i å tilrettelegge og tilpasse opplæringen. Kort oppsummert er det behov for mer forskning på barneskolelæreres vurderingspraksiser, og å jobbe systematisk for å utvikle felles terminologi og retningslinjer for vurdering for alle nivåer i opplæringen.This thesis addresses English teachers’ beliefs and practices of oral skills and assessment in Norwegian primary school (levels 5-7). The renewal of the National curriculum (LK20) leaves teachers with autonomy and great responsibility to realize it’s intentions, namely to facilitate a learning environment in which all pupils can reach their learning potential and develop skills and competences according to core elements and competence aims in the various subjects. Assessment for learning is a fundamental principal in primary school, which means that teachers must provide guidance based on pupils’ present knowledge, in order to help each student to advance both related to content knowledge and social competence. Data for this study was collected through four semi-structured interviews with English teachers, who shared their perceptions about oral skills and reported teaching and assessment practices. They reported to use a variety of activities to facilitate oral skills, however, due to both time constraints and large groups of pupils, they find it challenging to enable all pupils to take part in oral production that form a basis for assessment. To accommodate this demand, three of the teachers have practiced voice-recordings of pupils’ readings. This provides reading practice for pupils, elements of self-assessment, form a foundation for assessment and saves time for teachers. However, assessment of oral skills is complex, and assessment criteria and strategies appear to be randomly conducted. Findings also suggests that teachers’ beliefs related to teachers’ own language learning experience and language education influence their practice of oral skills teaching. Contextual factors, such as institutional and instructional parameters also impact how they plan, facilitate and carry out oral activities in class. Furthermore, teachers seem to lack both terminology and knowledge about assessment and competence and strategies of how to assess oral skills. Similar to findings from research on oral skills assessment in higher levels (see Bøhn, 2015; Johannessen, 2018; Kaldahl, 2022), teachers in this study struggle to know what and how to assess, and call for guidelines and shared standards to avoid failing to facilitate and adapt learning. In short, there is a need for further research on assessment practices in primary school, and to work systematically towards developing a shared terminology and common guidelines for assessment for all levels of education