Resolution in propositional calculus

Tema ovog završnog rada je rezolucija za propozicijsku logiku. Kako bi se lakše objasnila rezolucija, na početku je pojašnjena propozicijska logika, objašnjene su njena sintaksa i semantika. Opisana je metoda rezolucije, kao i pojam klauzula koji se koristi u primjerima, dokazima i objašnjenjima. Metoda kojom se dolazi do logičkog izvoda pomoću rezolucije naziva se rezolucijsko pravilo koje je potrebno slijediti kako bi rješavanje rezolucijom bilo valjano. Valjanost formule opisuje njeno stanje odnosno je li formula istinita ili lažna

The influence of flat plate length on the drag coefficient for a flat plate

U radu se razmatra utjecaj duljine ravne ploče na koeficijent otpora trenja za ravnu ploču. U prvom dijelu rada definiran je granični sloj uzduž ravne ploče, te proračun za laminarni i turbulentni režim strujanja. Kroz tekstualne formulacije, grafičke prikaze te jednadžbe objašnjeno je značenje Reynolds-ovog broja i efekta geometrije, procjene integracijom zakona o očuvanju količine gibanja, jednadžbi graničnog sloja, te koeficijenta trenja. U nastavku rada slijedi prikaz rezultata proračuna koeficijenta otpora trenja. Rezultati analitičkih proračuna uspoređeni su s rezultatima numeričkog proračuna koji je proveden primjenom modela „Boundary Layer Applet“. Rezultati su pokazali kako manje vrijednosti koeficijenta otpora trenja odgovaraju većim vrijednostima duljine ravne ploče, a veće vrijednosti koeficijenta trenja manjim vrijednostima duljine ravne ploče.The paper deals with the influence of flat plate length on the drag coefficient for a flat plate. Firstly, the paper defines boundary layer along the flat plate and the calculation for the laminar and turbulent flow regime. The meaning of Reynolds number and geometry effects, momentum integral estimates, the boundary layer equations and drag coefficient. The following is a presentation of the results of the drag coefficient calculation. The results of the analytical calculations were compared with the results of the numerical calculation. The numerical calculation was performed using the „Boundary Layer Applet“ model. The results showed that lower values of the drag coefficient correspond to higher values of the length of the flat plate, and higher values of the drag coefficient correspond to lower values of the length of the flat plate

Resolution in propositional calculus

Tema ovog završnog rada je rezolucija za propozicijsku logiku. Kako bi se lakše objasnila rezolucija, na početku je pojašnjena propozicijska logika, objašnjene su njena sintaksa i semantika. Opisana je metoda rezolucije, kao i pojam klauzula koji se koristi u primjerima, dokazima i objašnjenjima. Metoda kojom se dolazi do logičkog izvoda pomoću rezolucije naziva se rezolucijsko pravilo koje je potrebno slijediti kako bi rješavanje rezolucijom bilo valjano. Valjanost formule opisuje njeno stanje odnosno je li formula istinita ili lažna

evidence from a frontier market

When looking at the simulation of the stock price, the Geometric Brownian motion model is a widely used share price prediction model in various countries. But, in the Sri Lankan context, the use of the Geometric Brownian Motion model in stock price prediction is not observable. As a filling of the gap and identifying the validity of the Geometric model in Sri Lanka were the main purposes of conducting this research To obtain the validity of the GBM model was checked by using two hundred and fifty (250) companies in the Colombo Stock Exchange, which analyzed was forecasted from 2014 to 2018. The accuracy was verified by using the Mean Absolute Percentage Error (MAPE) value. A number of scholars used the MAPE-based judgment method to evaluate the accuracy of the forecast resulted from GBM. Since the MAPE values are between 0% and 10%, it implies that the GBM model is a highly accurate model for forecasting stock prices on the Colombo Stock Exchange in Sri Lanka. The forecast was limited only for one day. The mean value of the MAPE of the sample of 250 companies is 4.49 %. Further, 97.2% of the sample, the MAPE value was below 10%. It implies that a one-day price forecast is highly accurate in the Sri Lankan context. Geometric Brownian motion model has been developed in the study to predict stock price behaviour, and the model has subsequently been used to exchange. The results of the simulated or forecasted prices were subsequently compared to the actual prices obtained. The results show that the model consistently predicts stock behaviour in more than 95% of the cases. A procedure to mathematically examine the probabilistic distribution of stocks has also been provided. It is expected that this scholarly work will help investors and other stakeholders, especially on the stock market in Colombo, to make informed decisions on trading and valuation. However, in this study, the forecast is limited only for one day. In other words, utilizing historical data until trading day t, someone can forecast the price of the trading day t+1. Key Words

Geotechnical analyzes of the right bank levee of the river Glina damaged in the earthquake

U radu se razmatraju geotehničke analize desnoobalnog nasipa rijeke Gline oštećenog u potresu koji je pogodio Sisačko-moslavačku županiju u prosincu 2020. godine. U prvom dijelu rada definiran je pojam likvefakcije te su navedene su glavne aktivnosti kojima će se sanacije oštećenog nasipa. U nastavku slijedi pregled istražnih radova izvedenih na predmetnoj lokaciji, razrada podloga i odabir relevantnih parametara tla. Kroz tekstualne formulacije, grafičke prikaze te jednadžbe prikazani su geotehnički proračuni. Rađene su analize procjeđivanja i analize stabilnosti predmetnog nasipa prije i poslije sanacije oštećenja primjenom programskog paketa GeoStudio. Rezultati analiza su pokazali zadovoljavajuće vrijednosti hidrauličkih gradijenata i faktora sigurnosti čime je potvrđena uspješnost sanacije pokosa nasipa zasijecanjem uz zamjenu materijala i ugradnjom geomreža, uz ojačanje temeljnog tla mlaznim injektiranjem.The thesis deals with the geotechnical analysis of the right-bank levee of the Glina river damaged in the earthquake that hit Sisačko-Moslavačka county in December of 2020. In the first part of the thesis, the concept of liquefaction is defined, as well as the main activities that will be conducted to rehabilitate the damaged levee. An overview of the investigation works carried out follows, as well the selection of the relevant soil parameters. Through text, graphics and equations, geotechnical calculations are presented. Analysis of water seepage and analysis of levee stability are evaluated before and after the rehabilitation measures, and were carried out using the GeoStudio software package. The results of the analysis show satisfactory values of hydraulic gradients and safety factors, which confirmes the success of the levee rehabilitation by replacement of materials and installation of geosynthetics, along with foundation soil strengthening by jet grouting

Starogrčka geometrijska algebra

U radu opisujemo probleme vezane uz geometriju kojima su se bavili starogrčki matematičari, a koji se moderno mogu interpretirati algebarski. U pokušajima rješavanja koristili su razne metode, no valjana geometrijska konstrukcija dopuštala je samo korištenje konstrukcija ravnalom i šestarom. U prvom poglavlju navodimo neke klasične konstrukcije ravnalom i šestarom koje su bile poznate među grčkim matematičarima. Drugo poglavlje opisuje neke pokušaje rješavanja tri klasična problema. U trećem poglavlju naglasak je na drugoj knjizi Euklidovih Elemenata. Četvrto poglavlje sadrži dokaz nesumjerljivosti stranice i dijagonale kvadrata te način na koji je Apolonije opisivao konike. Rad završava opisom Descartesovog povezivanja geometrije i algebre, dokazom ekvivalencije konstrukcija ravnalom i šestarom s rješavanjem algebarskih kvadratnih jednadžbi te dokazom da tri klasična problema nisu rješivi konstrukcijama ravnalom i šestarom.This thesis describes geometric problems that ancient Greek mathematicians were trying to solve and which can be interpreted geometrically. In their attempts they used different methods, but only solutions that used straightedge and compass were considered valid. In the first chapter we describe some of the classical straightedge and compass constructions that were known to Greek mathematicians. The second chapter describes some attempts to solve three classical problems. In the third chapter the emphasis is on the second book of Euclid’s Elements. The fourth chapter contains a proof of the incommensurability of the side and diagonal of a square and Appolonius’ approach to conics. The thesis concludes with Descartes’ connection of geometry and algebra, with proof that straightedge and compass constructions are equivalent to solving algebraic quadratic equations and with proofs of the impossibility of solving the three classical problems with ruler and compass constructions

Starogrčka geometrijska algebra

U radu opisujemo probleme vezane uz geometriju kojima su se bavili starogrčki matematičari, a koji se moderno mogu interpretirati algebarski. U pokušajima rješavanja koristili su razne metode, no valjana geometrijska konstrukcija dopuštala je samo korištenje konstrukcija ravnalom i šestarom. U prvom poglavlju navodimo neke klasične konstrukcije ravnalom i šestarom koje su bile poznate među grčkim matematičarima. Drugo poglavlje opisuje neke pokušaje rješavanja tri klasična problema. U trećem poglavlju naglasak je na drugoj knjizi Euklidovih Elemenata. Četvrto poglavlje sadrži dokaz nesumjerljivosti stranice i dijagonale kvadrata te način na koji je Apolonije opisivao konike. Rad završava opisom Descartesovog povezivanja geometrije i algebre, dokazom ekvivalencije konstrukcija ravnalom i šestarom s rješavanjem algebarskih kvadratnih jednadžbi te dokazom da tri klasična problema nisu rješivi konstrukcijama ravnalom i šestarom.This thesis describes geometric problems that ancient Greek mathematicians were trying to solve and which can be interpreted geometrically. In their attempts they used different methods, but only solutions that used straightedge and compass were considered valid. In the first chapter we describe some of the classical straightedge and compass constructions that were known to Greek mathematicians. The second chapter describes some attempts to solve three classical problems. In the third chapter the emphasis is on the second book of Euclid’s Elements. The fourth chapter contains a proof of the incommensurability of the side and diagonal of a square and Appolonius’ approach to conics. The thesis concludes with Descartes’ connection of geometry and algebra, with proof that straightedge and compass constructions are equivalent to solving algebraic quadratic equations and with proofs of the impossibility of solving the three classical problems with ruler and compass constructions

Starogrčka geometrijska algebra

U radu opisujemo probleme vezane uz geometriju kojima su se bavili starogrčki matematičari, a koji se moderno mogu interpretirati algebarski. U pokušajima rješavanja koristili su razne metode, no valjana geometrijska konstrukcija dopuštala je samo korištenje konstrukcija ravnalom i šestarom. U prvom poglavlju navodimo neke klasične konstrukcije ravnalom i šestarom koje su bile poznate među grčkim matematičarima. Drugo poglavlje opisuje neke pokušaje rješavanja tri klasična problema. U trećem poglavlju naglasak je na drugoj knjizi Euklidovih Elemenata. Četvrto poglavlje sadrži dokaz nesumjerljivosti stranice i dijagonale kvadrata te način na koji je Apolonije opisivao konike. Rad završava opisom Descartesovog povezivanja geometrije i algebre, dokazom ekvivalencije konstrukcija ravnalom i šestarom s rješavanjem algebarskih kvadratnih jednadžbi te dokazom da tri klasična problema nisu rješivi konstrukcijama ravnalom i šestarom.This thesis describes geometric problems that ancient Greek mathematicians were trying to solve and which can be interpreted geometrically. In their attempts they used different methods, but only solutions that used straightedge and compass were considered valid. In the first chapter we describe some of the classical straightedge and compass constructions that were known to Greek mathematicians. The second chapter describes some attempts to solve three classical problems. In the third chapter the emphasis is on the second book of Euclid’s Elements. The fourth chapter contains a proof of the incommensurability of the side and diagonal of a square and Appolonius’ approach to conics. The thesis concludes with Descartes’ connection of geometry and algebra, with proof that straightedge and compass constructions are equivalent to solving algebraic quadratic equations and with proofs of the impossibility of solving the three classical problems with ruler and compass constructions

The influence of flat plate length on the drag coefficient for a flat plate

U radu se razmatra utjecaj duljine ravne ploče na koeficijent otpora trenja za ravnu ploču. U prvom dijelu rada definiran je granični sloj uzduž ravne ploče, te proračun za laminarni i turbulentni režim strujanja. Kroz tekstualne formulacije, grafičke prikaze te jednadžbe objašnjeno je značenje Reynolds-ovog broja i efekta geometrije, procjene integracijom zakona o očuvanju količine gibanja, jednadžbi graničnog sloja, te koeficijenta trenja. U nastavku rada slijedi prikaz rezultata proračuna koeficijenta otpora trenja. Rezultati analitičkih proračuna uspoređeni su s rezultatima numeričkog proračuna koji je proveden primjenom modela „Boundary Layer Applet“. Rezultati su pokazali kako manje vrijednosti koeficijenta otpora trenja odgovaraju većim vrijednostima duljine ravne ploče, a veće vrijednosti koeficijenta trenja manjim vrijednostima duljine ravne ploče.The paper deals with the influence of flat plate length on the drag coefficient for a flat plate. Firstly, the paper defines boundary layer along the flat plate and the calculation for the laminar and turbulent flow regime. The meaning of Reynolds number and geometry effects, momentum integral estimates, the boundary layer equations and drag coefficient. The following is a presentation of the results of the drag coefficient calculation. The results of the analytical calculations were compared with the results of the numerical calculation. The numerical calculation was performed using the „Boundary Layer Applet“ model. The results showed that lower values of the drag coefficient correspond to higher values of the length of the flat plate, and higher values of the drag coefficient correspond to lower values of the length of the flat plate