Fatou's Lemma for Weakly Converging Probabilities

Fatou's lemma states under appropriate conditions that the integral of the lower limit of a sequence of functions is not greater than the lower limit of the integrals. This note describes similar inequalities when, instead of a single measure, the functions are integrated with respect to different measures that form a weakly convergent sequence

Discretisation for odd quadratic twists

The discretisation problem for even quadratic twists is almost understood, with the main question now being how the arithmetic Delaunay heuristic interacts with the analytic random matrix theory prediction. The situation for odd quadratic twists is much more mysterious, as the height of a point enters the picture, which does not necessarily take integral values (as does the order of the Shafarevich-Tate group). We discuss a couple of models and present data on this question.Comment: To appear in the Proceedings of the INI Workshop on Random Matrix Theory and Elliptic Curve

Random Matrix Theory and the Fourier Coefficients of Half-Integral Weight Forms

Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of conjectures concerning the value-distribution of the Fourier coefficients of half-integral weight modular forms related to these L-functions. Our conjectures may be viewed as being analogous to the Sato-Tate conjecture for integral weight modular forms. Numerical evidence is presented in support of them.Comment: 28 pages, 8 figure

The Study Of Production Regimes And Quality Parameters Of Extruded Feed Additive Based On Corn Seed And Substandard Egg Mass

On the base of practical studies were established the rational parameters of technological processes of production of extruded feed additive. There was determined an expedience of mixture of substandard chicken egg mass and the crushed corn seed in two stages in frame (during 18 s) and blade (during 120…180 s) mixers. There were determined the optimal regimes of mixture extruding: pressure in working zone of extruder 2…3 mPa, consumed force of electric motor 4,0…4,5 kW, temperature on outcome of extruder 110…120 ºС, duration of process 60…120 s, diameter of matrix port 10 mm.There were given the results of study of parameters of quality and nutritive value of extruded feed additive. It was established, that in the process of extruding the quality parameters of food additive are improved at the expense of dextrinization and gelatinization of starch, decrease of bacterial and fungal pollution, disinfection of product.There was proved a possibility to solve problem of utilization of defective eggs at feeding poultry

Estimating emissions of NMVOC from solvent and other product use : Revised model

This report is the end product of a project revising the Norwegian emission calculations of NMVOCs1 from the use of solvents and other products. The development of a new emission model started in 2007, and the results will be used for reporting from the year 2008. According to international emission reporting guidelines, emissions shall be recalculated if new information about emission factors or improved calculation methods is available. The emissions of NMVOC from solvents and other product use were previously calculated using data on import, export and production of solvent-containing substances. The previous solvent balance was developed in 1995, and by the year 2000 the method was considered obsolete. It was thus decided to keep the emission estimates at the year 2000 level until a revised method was developed. A replacement of the solvent balance was due because the assumptions about solvent content and the emission factors were out of date

Unspoken Rules: Using the Game of Mao to Teach Sensemaking and Cultural Approaches to Communication

This interactive classroom activity invites students to interrogate their common sense and taken-for-granted communication practices and assumptions. In the course of playing a “concealed rules” game, students enact the ritual view of communication and the process of sensemaking. The activity provides an experiential model for clarifying complex themes as well as for actively constructing student understanding of the theories. The activity directly challenges norms of classroom communication and interaction and promotes thoughtful and engaged classroom discussion and reflection. Instructors are provided clear instructions, recommended student readings and sample discussion questions. The activity and debrief usually require about one hour of instructional time. Recommendations for ways the activity can be tailored to suit instructor needs allow this dynamic and engaging activity to be effectively adapted

Lower order terms in the full moment conjecture for the Riemann zeta function

We describe an algorithm for obtaining explicit expressions for lower terms for the conjectured full asymptotics of the moments of the Riemann zeta function, and give two distinct methods for obtaining numerical values of these coefficients. We also provide some numerical evidence in favour of the conjecture.Comment: 37 pages, 4 figure