Tato práce se zabývá měřením aerodynamických charakteristik modelu závodního vozu Formula SAE v aerodynamickém tunelu, v měřítku 1:4. V první části je představen projekt Formula SAE a popsána role aerodynamiky v rámci této soutěže. Následuje přehled teoretického pozadí, které je relevantní k provedenému experimentu. Ve druhé části práce je popsán samotný experiment a prezentovány jeho výsledky. Součástí je návrh, výroba a kalibrace šestikomponentní tenzometrické váhy pro měření aerodynamického zatížení. Testy v aerodynamickém tunelu byly provedeny ve čtyřech konfiguracích, aby bylo možné určit vliv přítlačných křídel a podlahy s difuzorem na výsledné aerodynamické charakteristiky vozu.

Formula Student is a global engineering competition where university students collaborate to design, construct, and race formula-style cars. Aerodynamics is one aspect in the vehicle design that can improve on-track performance by increasing cornering and straight-line speed. To improve the aerodynamics of KTH Formula Student's DeV18 vehicle, the side structure is being redesigned. The current model, DeV17, features an underperforming tunnel-based side structure. To address this issue, this had the goal to investigate a new multi-element wing design that utilizes ground effect. The design study of the DeV18 vehicle is conducted using Siemens NX 2212 for 3D modelling and Simcenter Star-CCM+ 17.06.008-R8 for airflow simulations. To quickly investigate certain design parameters effect on the results, Design Manager Project inside Simcenter Star-CCM+ is used. The resulting side structure produces a total of 26 N of downforce and 6 N of drag at 40 kph, more than twice that of DeV17’s side structure while also producing less drag. Although this significant improvement compared to DeV17, it is believed that further increases in performance are necessary to compete with top teams. By using a more sophisticated method to optimize the multi-element wing, such as adjoint optimization, the concept could be improved. However, the overall potential of the concept is still considered too limited to achieve the desired performance goals, which is why it will no longer be investigated further.

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We obtain a generalization of the Sokhotskii formula for the forth degree by means of methods of theory of residues. We obtain relations of Mikusinskii and Gonzalez – Dominguez type that connect distributions and hyperdistributions. We obtain an analog of the Sokhotskii formula for an arbitrary positive integer. / Получены обобщения формулы Сохоцкого для четвертой степени методами теории вычетов. Получены соотношения типа Микусинского и Гонсалеса – Домингеса, связывающие распределения и гиперраспределения. Было получено обобщение формулы Сохоцкого для любого натурального числа.

After an introduction to Brownian motion, Hausdorff dimension, nonstandard analysis and Loeb measure theory, we explore the notion of a nonstandard formulation of Hausdorff dimension. By considering an adapted form of the counting measure formulation of Lebesgue measure, we find that Hausdorff dimension can be computed through a counting argument rather than the traditional way. This formulation is then applied to obtain simple proofs of some of the dimensional properties of Brownian motion, such as the doubling of the dimension of a set of dimension smaller than 1/2 under Brownian motion, by utilising Anderson's formulation of Brownian motion as a hyperfinite random walk. We also use the technique to refine a theorem of Orey and Taylor's on the Hausdorff dimension of the rapid points of Brownian motion. The result is somewhat stronger than the original. Lastly, we give a corrected proof of Kaufman's result that the rapid points of Brownian motion have similar Hausdorff and Fourier dimensions, implying that they constitute a Salem set. / Mathematical Sciences / D. Phil. (Mathematical Sciences)

The current study employed a Monte Carlo design to examine whether samplebased and formula-based estimates of cross-validated R2 differ in accuracy when predictor selection is and is not performed. Analyses were conducted on three datasets with 5, 10, or 15 predictors and different predictor-criterion relationships. Results demonstrated that, in most cases, a formula-based estimate of the cross-validated R2 was as accurate as a sample-based estimate. The one exception was the five predictor case wherein the formula-based estimate exhibited substantially greater bias than the estimate from a sample-based cross validation study. Thus, formula-based estimates, which have an enormous practical advantage over a two sample cross validation study, can be used in most cases without fear of greater error.

Undersökningen genomförs baserat på finansiell data från tidsperioden 2005-2015 påStockholmsbörsen, genom fiktiva aktieportföljer som skapas efter Graham och Greenblattsstrategier. Portföljerna får ett tillskott på 50 000 kr vid två fasta datum årligen där de mest köpvärdaaktierna enligt respektive strategi inhandlas. I tillägg till dessa portföljer skapas ytterligare tvåportföljer med den skillnaden att halva placeringen årligen investeras i obligationsfonder.Resterande investeras i enlighet med Grahams respektive Greenblatts strategier. Undersökningenvisar att båda värdeinvesteringsstrategierna gav en hög avkastning. Bäst resultat fick Greenblattsportfölj som påvisade en genomsnittlig årlig avkastning på hela 19,37 procent! och ett betavärdejämfört med populationen på 0,79. Grahams strategi gav en genomsnittlig årsavkastning på 10,71procent och hade ett något lägre betavärde på 0,7. Samtidigt gav de alternativa portföljerna enavkastning på 10,93 respektive 7,52 procent med viktade betavärden om 0,39 och 0,35 jämfört medpopulationen som helhet. Stockholmsbörsen avkastade under perioden 9,44 procent.

The Fibonacci Numbers are one of the most intriguing sequences in mathematics. I present generalizations of this well known sequence. Using combinatorial proofs, I derive closed form expressions for these generalizations. Then using Markov Chains, I derive a second closed form expression for these numbers which is a generalization of Binet’s formula for Fibonacci Numbers. I expand further and determine the generalization of Binet’s formula for any kth order linear recurrence.

acase@tulane.edu / Modular-type transformation formulas are the identities that are invariant under the transformation α → 1/α, and they can be represented as F (α) = F (β) where α β = 1. We derive a new transformation formula of the form F (α, z, w) = F (β, z, iw) that is a one-variable generalization of the well-known Ramanujan-Guinand identity of the form F (α, z) = F (β, z) and a two-variable generalization of Koshliakov’s formula of the form F (α) = F (β) where α β = 1. The formula is generated by first finding an integral J that is comprised of an invariance function Z and evaluating the integral to give F (α, z, w) mentioned above. The modified Bessel function K z (x) appearing in Ramanujan-Guinand identity is generalized to a new function, denoted as K z,w (x), that yields a pair of functions reciprocal in the Koshliakov kernel, which in turn yields the invariance function Z and hence the integral J and the new formula. The special function K z,w (x), first defined as the inverse Mellin transform of a product of two gamma functions and two confluent hypergeometric functions, is shown to exhibit a rich theory as evidenced by a number of integral and series representations as well as a differential-difference equation. The second topic of the thesis is 2-adic valuations of integer sequences associated with quadratic polynomials of the form x 2 +a. The sequence {n 2 +a : n ∈ Z} contains numbers divisible by any power of 2 if and only if a is of the form 4 m (8l+7). Applying this result to the sequences derived from the sums of four or fewer squares when one or more of the squares are kept constant leads to interesting results, that also points to an inherent connection with the functions r k (n) that count the number of ways to represent n as sums of k integer squares. Another class of sequences studied is the shifted sequences of the polygonal numbers given by the quadratic formula, for which the most common examples are the triangular numbers and the squares. / 1 / Aashita Kesarwani

Aerodynamic devices, such as wings, are used in higher levels of motorsport (Formula-1 etc.) to increase the contact force between the road and tyres (i.e. to generate downforce). This in turn increases the performance envelope of the race car. However the extra downforce increases aerodynamic drag which (apart from when braking) is generally detrimental to lap-times. The drag acts to slow the vehicle, and hinders the effect of available drive power and reduces fuel economy. Wings, in automotive use, are not constrained by the same parameters as aircraft, and thus higher angles of attack can be safely reached, although at a higher cost in drag. Variable geometry aerodynamic devices have been used in many forms of motorsport in the past offering the ability to change the relative values of downforce and drag. These have invariably been banned, generally due to safety reasons. The use of active aerodynamics is currently legal in both Formula SAE (engineering compet ition for university students to design, build and race an open-wheel race car) and production vehicles. A number of passenger car companies are beginning to incorporate active aerodynamic devices in their designs. In this research the effect of ground proximity on the lift, drag and moment coefficients of inverted, two-dimensional aerofoils was investigated. The purpose of the study was to examine the effect ground proximity on aerofoils post stall, in an effort to evaluate the use of active aerodynamics to increase the performance of a race car. The aerofoils were tested at angles of attack ranging from 0° - 135°. The tests were performed at a Reynolds number of 2.16 x 105 based on chord length. Forces were calculated via the use of pressure taps along the centreline of the aerofoils. The RMIT Industrial Wind Tunnel (IWT) was used for the testing. Normally 3m wide and 2m high, an extra contraction was installed and the section was reduced to form a width of 295mm. The wing was mounted between walls to simulate 2-D flow. The IWT was chosen as it would allow enough height to reduce blockage effect caused by the aerofoils when at high angles of incidence. The walls of the tunnel were pressure tapped to allow monitoring of the pressure gradient along the tunnel. The results show a delay in the stall of the aerofoils tested with reduced ground clearance. Two of the aerofoils tested showed a decrease in Cl with decreasing ground clearance; the third showed an increase. The Cd of the aerofoils post-stall decreased with reduced ground clearance. Decreasing ground clearance was found to reduce pitch moment variation of the aerofoils with varied angle of attack. The results were used in a simulation of a typical Formula SAE race car.