Introduction to Non Commutative Algebraic Geometry

Ordinary commutative algebraic geometry is based on commutative polynomial algebras over an algebraically closed field k. Here we make a natural generalization to matrix polynomial k-algebras which are non-commutative coordinate rings of non-commutative varieties

College Students’ Attitudes Toward Condom Use in Pornography: Associations with Sexual History, Sexually Transmitted Infections, and Pornography Use

The depiction of condomless sex in pornography has significant public health implications for adult film (pornography) actors and potentially for its consumers. Previous research suggests that most consumers of pornography are in favor of condom use in pornography; however, available research on attitudes toward condom use in pornography has surveyed mostly White, male, American undergraduate students. Currently, there is a need to explore viewers’ attitudes toward condom use in pornography among women and racially/ethnically diverse individuals. The current study investigated United States (US) college students’ attitudes toward condom use in pornography using the Pornography Actors’ Condom Use Attitudes Questionnaire (PACUAQ). Participants included 601 heterosexual US college students (n=326 women and n=275 men) over 18 years of age who reported using pornography in the past 12 months. First, I conducted an item analysis to examine the skewness and kurtosis of the PACUAQ items. Second, I completed an inter-item correlation to examine the scale for highly and weakly correlated items. Third, I conducted a confirmatory factor analysis (CFA) to verify the factor structure of the PACUAQ. Next, I explored measurement invariance with the configural model by gender. Lastly, I examined mean differences in Condom Supportive and Critical Attitudes across gender, race/ethnicity, pornography history characteristics, and sexual history characteristics. CFA supported a two-factor model, comprised of ten items reflecting two subscales: Condom Supportive Attitudes and Condom Critical Attitudes. The PACUAQ achieved strict invariance by gender. Results indicated that overall, participants had higher mean scores on the Condom Supportive Attitudes subscale compared to the Condom Critical Attitudes subscale. Men, relative to women, demonstrated higher endorsement of Condom Critical Attitudes, while women reported higher endorsement of Condom Supportive Attitudes compared to men. Condom Critical Attitude scores were positively associated with pornography viewing frequency and duration, meeting the suggested clinical cutoff score on a measure assessing problematic pornography use, and number of hookup partners. Condom Critical Attitude scores were negatively correlated with the age of first viewing pornography. Moreover, those who viewed pornography less frequently and for less duration also reported higher endorsement on the Condom Supportive Attitudes subscale. Notably, those who reported not using condoms during hookup sex endorsed higher Condom Critical Attitudes than those who reported using condoms during hookup sex. Results from the present study provide a validated questionnaire to explore attitudes toward condom use among men and women. Study findings may also be used to inform practitioners of the implications of increased pornography viewing on safe sex practices and highlight the need for sex education surrounding pornography use

Mono-anabelian Reconstruction of Solvably Closed Galois Extensions of Number Fields

A theorem of Uchida asserts that every continuous isomorphism between the Galois groups of solvably closed Galois extensions of number fields arises from a unique isomorphism between the solvably closed Galois extensions. In particular, the isomorphism class of a solvably closed Galois extension of a number field is completely determined by the isomorphism class of the associated Galois group. On the other hand, neither the statement of this theorem nor the proof of this theorem yields an "explicit reconstruction" of the given solvably closed Galois extension. In the present paper, we establish a functorial "grouptheoretic" algorithm for reconstructing, from the Galois group of a solvably closed Galois extension of a number field, the given solvably closed Galois extension equipped with the natural Galois action

On The Geometry Of Elliptic Pairs

An elliptic pair $(X, C)$ is a projective rational surface $X$ with log terminal singularities, and an irreducible curve $C$ contained in the smooth locus of $X$, with arithmetic genus one and self-intersection zero. They are a useful tool for determining whether the pseudo-effective cone of $X$ is polyhedral, and interesting algebraic and geometric objects in their own right. Especially of interest are toric elliptic pairs, where $X$ is the blow-up of a projective toric surface at the identity element of the torus. In this paper, we classify all toric elliptic pairs of Picard number two. Strikingly, it turns out that there are only three of these. Furthermore, we study a class of non-toric elliptic pairs coming from the blow-up of $\mathbb{P}^2$ at nine points on a nodal cubic, in characteristic $p$. This construction gives us examples of surfaces where the pseudo-effective cone is non-polyhedral for a set of primes $p$ of positive density, and, assuming the generalized Riemann hypothesis, polyhedral for a set of primes $p$ of positive density.Comment: 23 pages, 8 figure

HAL/S-360 compiler system specification

A three phase language compiler is described which produces IBM 360/370 compatible object modules and a set of simulation tables to aid in run time verification. A link edit step augments the standard OS linkage editor. A comprehensive run time system and library provide the HAL/S operating environment, error handling, a pseudo real time executive, and an extensive set of mathematical, conversion, I/O, and diagnostic routines. The specifications of the information flow and content for this system are also considered

Surface Brightness and Intrinsic Luminosity of Ellipticals

{Abridged} We show that the surface brightness (SB) profiles of elliptical galaxies can be parametrized using a linear superposition of 2-3 components, described by functions developed in Dhar & Williams as the 2D projections of a 3D Einasto profile. For a sample of 23 ellipticals with -24 < Mv < -15, our multi-component models span a range of up to 10^6 in SB and 10^5 in radius, have a median rms of 0.032 mag arcsec^-2, and are statistically justified at >3{\sigma}. Our models indicate that i) the central component is more concentrated than the outer component; and ii) the central component of 'core' galaxies is much more luminous, extended and concentrated than that of 'cuspy' galaxies, with their near exponential central profiles indicating disk-like systems whose existence must be verified spectroscopically. While such central excess components are not necessarily contrary to the notion of a mass deficit in 'core' galaxies, we show that the existence, amount, radial extent and sign of mass deficits disagree substantially in the literature, both for a given galaxy and on an average over a sample. We discuss possible implications and suggest that SMBH binaries are unlikely to be the sole mechanism for producing the large 'cores'. We also deduce conditions under which the 3D light density can be described with a multi-component Einasto model for both cuspy and core galaxies; indicating an universality in the functional form of the 3D density of light in galaxies and dark matter in LCDM N-body haloes. Finally, we show that our result - the outer component of the SB profiles of massive galaxies has 5 < n < 8 - could imply i) a common feature of collisionless systems; and ii) that galaxies with such n for their outer component are dark matter dominated.Comment: Accepted to MNRAS 12th December, 2011 (40 pages, 39 figures); in original form 2nd June, 201

Banking on agriculture:an assessment of Absa Bank’s Shared Growth Strategy for Agriculture.

Masters Degree. University of KwaZulu-Natal, Durban.The study assesses whether Absa Bank lives up to its Shared Growth Strategy for Agriculture. The objectives of this study are to examine how Absa Bank is supporting and contributing strategically to the development of the agriculture sector in KwaZulu-Natal (KZN); establish whether Absa’s products and services are assisting black commercial farmer clients to escape from poverty and succeed in running sustainable businesses; to assess how Absa Bank is supporting black commercial farmers financially and non-financially; and whether Absa Bank’s Shared Growth Strategy is realised through agricultural sector financing and advisory in KZN. The research method was scheduled in-depth qualitative interviews with eight Absa clients, who are black commercial farmers. The study uses the multidimensional equity framework (MDEF) to assess the impact of Absa agricultural funding, assessing whether access to finance has transferred equity and empowered the clients. The MDEF shaped the interview content with clients to delineate whether they thought about equity issues beyond the current state of their businesses and at the same time government representatives interviewed reflected on the equity issues of the farmers’ businesses in terms of longevity and sustainability. In examining Absa Bank’s Shared Growth Strategy in specific reference to agricultural sector financing to black commercial farmers, it is clear that the funding system is not strategically focused to pay attention to this segment. It was poignantly clear that providing finance to black commercial farmers was not sufficient, therefore there was a legitimate need to provide non-financial business support to the clients as well. These lessons can also be applied to other commercial banks who provide finance to agriculture and specifically black commercial farmers. Absa has not risen to the occasion in as far as using its technical expertise; in as far as the role of the bank in black commercial farming is concerned. Clients and government representatives, including industry body representatives, revealed that the bank should be more than just a financier. The technical capability of the bank is in demand in agriculture, combined with the training and development of black farmers. The strategic challenge is to be differentiated in a competitive market by using enterprise development. The role of a bank in providing loan finance is not enough, therefore its clients, specifically black farmers emphasised the fact that a deeper engagement with Absa Bank was required in order for the relationship to be more nuanced. This is in line with the bank’s strategy to shape its operations to help small and medium-sized businesses to succeed and grow through enterprise development, therefore the bank is expected to offer innovative financial solutions and business support services to small businesses. At the centre of this, is reinventing itself in order for more people to have access to financial services to achieve financial inclusion

Special Geometry and the swampland

In the context of 4d effective gravity theories with 8 supersymmetries, we propose to unify, strenghten, and refine the several swampland conjectures into a single statement: the structural criterion, modelled on the structure theorem in Hodge theory. In its most abstract form the new swampland criterion applies to all 4d N = 2 effective theories (having a quantum-consistent UV completion) whether supersymmetry is local or rigid: indeed it may be regarded as the more general version of Seiberg-Witten geometry which holds both in the rigid and local cases.As a first application of the new swampland criterion we show that a quantum-consistent N = 2 supergravity with a cubic pre-potential is necessarily a truncation of a higher-Nsugra. More precisely: its moduli space is a Shimura variety of 'magic' type. In all other cases a quantum-consistent special Kahler geometry is either an arithmetic quotient of the complex hyperbolic space SU(1, m)/U(m) or has no local Killing vector.Applied to Calabi-Yau 3-folds this result implies (assuming mirror symmetry) the validity of the Oguiso-Sakurai conjecture in Algebraic Geometry: all Calabi-Yau 3-folds X without rational curves have Picard number rho = 2, 3; in facts they are finite quotients of Abelian varieties. More generally: the Kahler moduli of X do not receive quantum corrections if and only if X has infinite fundamental group. In all other cases the Kahler moduli have instanton corrections in (essentially) all possible degrees

Femtosecond-laser induced dynamics of CO on Ru(0001): Deep insights from a hot-electron friction model including surface motion

Theoretical Chemistr