Abstract:
Studien unders ker vilken betydelse goda gymnasiala f rkunskaper i matematik har f r studieresultatet p en kurs i grundl ggande statistik p h gskoleniv . S rskilt fokus r p betydelsen av studenternas gymnasiala f rkunskaper 1) i s dan matematik som ing r i beh rig-hetskraven och 2) i form av extra kurser matematik som l sts ut ver beh righetskraven. Data erh lls genom att p individniv l nka samman tentamensresultat p en statistikkurs med uppgifter kring studenternas gymnasiala meriter i mnet matematik. N got f rv nande – och i kontrast till tidigare studier – r det inget i resultaten som indikerar att extra kurser i matematik ut ver beh righetskraven har betydelse f r studieresultatet p statistikkursen. Ist llet tycks det vara vilket betyg studenterna har p de mer element ra matematikkurserna som ing r i beh righetskraven som r viktigt. En tolkning av resultaten r att en grundl ggande h gskolekurs i statistik inte kr ver s rskilt mycket matematiskt kunnande, utan att det r allm nna kognitiva f rm gor som intuition, logiskt t nkande och probleml sningsf rm ga som r viktiga och att betygen p de mest element ra matematikkurserna p gymnasiet speglar s dana f rm gor.

Abstract:
Experimental data suggest that a tissue renin-angiotensin system is present in the pancreatic islets of several species, including man. However, the physiological role for this local renin-angiotensin system remains largely unknown. In vitro findings argue against a direct effect of angiotensin II on alpha- and beta-cells. In contrast, when the influence of angiotensin II on the pancreatic islets has been evaluated in the presence of an intact vascular system either in vivo or in the perfused pancreas, a suppression of insulin release has been observed, also in man. These discrepancies may be explained by the profound effects of the renin-angiotensin system on pancreatic islet blood perfusion. Alterations in the systemic renin-angiotensin system and an increased vascular sensitivity for its components have been observed in diabetes mellitus and hypertension. Whether changes occur also in the pancreatic islet renin-angiotensin system during these conditions remains unknown. Future research may help to provide an answer to this question, and to elucidate to what extent the renin-angiotensin system may contribute to beta-cell dysfunction in these diseases.

Abstract:
This article aims to join the contemporary effort to promote a psychoanalytic renaissance within cinema studies, post Post-Theory. In trying to shake off the burden of the 1970s film theory's distortion of the Lacanian Gaze, rejuvenating it with the strength of the Real and fusing it with Freudian thoughts on the uncanny, hopefully this new dawn can be reached. I aspire to conceptualize the Gaze in a straightforward manner. This in order to obtain an instrument for the identification of certain strategies within the filmic realm aimed at depicting the subjective destabilizing of diegetic characters as well as thwarting techniques directed at the spectorial subject. In setting this capricious Gaze against the uncanny phenomena described by Freud, we find that these two ideas easily intertwine into a draft description of a powerful, potentially reconstitutive force worth being highlighted.

Abstract:
This thesis is concerned with two topics in Hamiltonian lattice gauge theory: improvement and the application of analytic techniques. On the topic of improvement, we develop a direct method for improving lattice Hamiltonians for gluons, in which linear combinations of gauge invariant lattice operators are chosen to cancel the lowest order discretisation errors. On the topic of analytic methods, we extend the techniques that have been used in 2+1 dimensional SU(2) variational calculations for many years, to the general case of SU(N). For this purpose a number of group integrals are calculated in terms of Toeplitz determinants. As generating functions these group integrals allow the calculation of all matrix elements appearing in variational glueball mass calculations in 2+1 dimensions. Making use of these analytic techniques, glueball masses in various symmetry sectors are calculated with N as large as 25 allowing extrapolations to infinite N to be performed. We finish with a feasibility study of applying analytic Hamiltonian techniques in 3+1 dimensional calculations.

Abstract:
Thermal ions in spherical tokamaks have two adiabatic invariants: the magnetic moment and the longitudinal invariant. For hot ions, variations in magnetic-field strength over a gyro period can become sufficiently large to cause breakdown of the adiabatic invariance. The magnetic moment is more sensitive to perturbations than the longitudinal invariant and there exists an intermediate regime, super-adiabaticity, where the longitudinal invariant remains adiabatic, but the magnetic moment does not. The motion of super-adiabatic ions remains integrable and confinement is thus preserved. However, above a threshold energy, the longitudinal invariant becomes non-adiabatic too, and confinement is lost as the motion becomes chaotic. We predict beam ions in present-day spherical tokamaks to be super-adiabatic but fusion alphas in proposed burning-plasma spherical tokamaks to be non-adiabatic.

Abstract:
We construct a notion of derived completion which applies to homomorphisms of commutative S-algebras. We study the relationship of the construction with other constructions of completions, and prove various invariance properties. The construction is expected to have applications within algebraic K-theory.

Abstract:
The Nekrasov partition function in supersymmetric quantum gauge theory is mathematically formulated as an equivariant integral over certain moduli spaces of sheaves on a complex surface. In ``Seiberg-Witten Theory and Random Partitions'', Nekrasov and Okounkov studied these integrals using the representation theory of ``vertex operators'' and the infinite wedge representation. Many of these operators arise naturally from correspondences on the moduli spaces, such as Nakajima's Heisenberg operators, and Grojnowski's vertex operators. In this paper, we build a new vertex operator out of the Chern class of a vector bundle on a pair of moduli spaces. This operator has the advantage that it connects to the partition function by definition. It also incorporates the canonical class of the surface, whereas many other studies assume that the class vanishes. When the moduli space is the Hilbert scheme, we present an explicit expression in the Nakajima operators, and the resulting combinatorial identities. We then apply the vertex operator to the above integrals. In agreeable cases, the commutation properties of the vertex operator result in modularity properties of the partition function and related correlation functions. We present examples in which the integrals are completely determined by their modularity, and their first few values.

Abstract:
Let $E$ be the bundle defined by applying a polynomial representation of $GL_n$ to the tautological bundle on the Hilbert scheme of $n$ points in the complex plane. By a result of Haiman, the Cech cohomology groups $H^i(E)$ vanish for all $i>0$. It follows that the equivariant Euler characteristic with respect to the standard two-dimensional torus action has nonnegative coefficients in the torus variables $z_1,z_2$, because they count the dimensions of the weight spaces of $H^0(E)$. We derive a very explicit asymmetric formula for this Euler characteristic which has this property, by expanding known contour integral formulas for the Euler characteristic stemming from the quiver description in $z_2$, and calculating the coefficients using Jing's Hall-Littlewood vertex operator with parameter $z_1$.

Abstract:
Let $X = \bigcup_k X_k$ be the ind-Grassmannian of codimension $n$ subspaces of an infinite-dimensional torus representation. If $\cE$ is a bundle on $X$, we expect that $\sum_j (-1)^j \Lambda^j(\cE)$ represents the $K$-theoretic fundamental class $[\cO_Y]$ of a subvariety $Y \subset X$ dual to $\cE^*$. It is desirable to lift a $K$-theoretic "projection formula" from the finite-dimensional subvarieties $X_k$, but such a statement requires switching the order of the limits in $j$ and $k$. We find conditions in which this may be done, and consider examples in which $Y$ is the Hilbert scheme of points in the plane, the Hilbert scheme of an irreducible curve singularity, and the affine Grassmannian of $SL(2,\C)$. In the last example, the projection formula becomes an instance of the Weyl-Ka\c{c} character formula, which has long been recognized as the result of formally extending Borel-Weil theory and localization to $Y$ \cite{S}. See also \cite{C3} for a proof of the MacDonald inner product formula of type $A_n$ along these lines.