A family of solutions of certain nonautonomous differential equations by series of exponential functions

Solution of differential equations by series of exponential function

On solutions of differential and functional equations Final report

Solutions of differential and functional equation

Teaching Teachers for the Future (TTF) Project: Development of the TTF TPACK survey instrument

This paper presents a summary of the key findings of the TTF TPACK Survey developed and administered for the Teaching the Teachers for the Future (TTF) Project implemented in 2011. The TTF Project, funded by an Australian Government ICT Innovation Fund grant, involved all 39 Australian Higher Education Institutions which provide initial teacher education. TTF data collections were undertaken at the end of Semester 1 (T1) and at the end of Semester 2 (T2) in 2011. A total of 12881 participants completed the first survey (T1) and 5809 participants completed the second survey (T2). Groups of like-named items from the T1 survey were subject to a battery of complementary data analysis techniques. The psychometric properties of the four scales: Confidence - teacher items; Usefulness - teacher items; Confidence - student items; Usefulness- student items, were confirmed both at T1 and T2. Among the key findings summarised, at the national level, the scale: Confidence to use ICT as a teacher showed measurable growth across the whole scale from T1 to T2, and the scale: Confidence to facilitate student use of ICT also showed measurable growth across the whole scale from T1 to T2. Additional key TTF TPACK Survey findings are summarised

Growth rate degeneracies in kinematic dynamos

We consider the classical problem of kinematic dynamo action in simple steady flows. Due to the adjointness of the induction operator, we show that the growth rate of the dynamo will be exactly the same for two types of magnetic boundary conditions: the magnetic field can be normal (infinite magnetic permeability, also called pseudovacuum) or tangent (perfect electrical conductor) to the boundaries of the domain. These boundary conditions correspond to well-defined physical limits often used in numerical models and relevant to laboratory experiments. The only constraint is for the velocity field u to be reversible, meaning there exists a transformation changing u into −u. We illustrate this surprising property using S2T2 type of flows in spherical geometry inspired by [Dudley and James, Proc. R. Soc. London A 425, 407 (1989)]. Using both types of boundary conditions, it is shown that the growth rates of the dynamos are identical, although the corresponding magnetic eigenmodes are drastically different

Vicious walkers, friendly walkers and Young tableaux II: With a wall

We derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the theory of Young tableaux, and combinatorial descriptions of symmetric functions. For the problem of $n$-friendly walkers, we derive exact asymptotics for the number of stars and watermelons both in the absence of a wall and in the presence of a wall.Comment: 35 pages, AmS-LaTeX; Definitions of n-friendly walkers clarified; the statement of Theorem 4 and its proof were correcte

Application of advanced technologies to small, short-haul aircraft

The results of a preliminary design study which investigates the use of selected advanced technologies to achieve low cost design for small (50-passenger), short haul (50 to 1000 mile) transports are reported. The largest single item in the cost of manufacturing an airplane of this type is labor. A careful examination of advanced technology to airframe structure was performed since one of the most labor-intensive parts of the airplane is structures. Also, preliminary investigation of advanced aerodynamics flight controls, ride control and gust load alleviation systems, aircraft systems and turbo-prop propulsion systems was performed. The most beneficial advanced technology examined was bonded aluminum primary structure. The use of this structure in large wing panels and body sections resulted in a greatly reduced number of parts and fasteners and therefore, labor hours. The resultant cost of assembled airplane structure was reduced by 40% and the total airplane manufacturing cost by 16% - a major cost reduction. With further development, test verification and optimization appreciable weight saving is also achievable. Other advanced technology items which showed significant gains are as follows: (1) advanced turboprop-reduced block fuel by 15.30% depending on range; (2) configuration revisions (vee-tail)-empennage cost reduction of 25%; (3) leading-edge flap addition-weight reduction of 2500 pounds

Scope and Predictive Genetic/Phenotypic Signatures of Bicarbonate (NaHCO3) Responsiveness and β-Lactam Sensitization in Methicillin-Resistant Staphylococcus aureus.

Addition of sodium bicarbonate (NaHCO3) to standard antimicrobial susceptibility testing medium reveals certain methicillin-resistant Staphylococcus aureus (MRSA) strains to be highly susceptible to β-lactams. We investigated the prevalence of this phenotype (NaHCO3 responsiveness) to two β-lactams among 58 clinical MRSA bloodstream isolates. Of note, ∼75% and ∼36% of isolates displayed the NaHCO3 responsiveness phenotype to cefazolin (CFZ) and oxacillin (OXA), respectively. Neither intrinsic β-lactam MICs in standard Mueller-Hinton broth (MHB) nor population analysis profiles were predictive of this phenotype. Several genotypic markers (clonal complex 8 [CC8]; agr I and spa t008) were associated with NaHCO3 responsiveness for OXA

Small ball probability, Inverse theorems, and applications

Let $\xi$ be a real random variable with mean zero and variance one and $A={a_1,...,a_n}$ be a multi-set in $\R^d$. The random sum $$S_A := a_1 \xi_1 + ... + a_n \xi_n$$ where $\xi_i$ are iid copies of $\xi$ is of fundamental importance in probability and its applications. We discuss the small ball problem, the aim of which is to estimate the maximum probability that $S_A$ belongs to a ball with given small radius, following the discovery made by Littlewood-Offord and Erdos almost 70 years ago. We will mainly focus on recent developments that characterize the structure of those sets $A$ where the small ball probability is relatively large. Applications of these results include full solutions or significant progresses of many open problems in different areas.Comment: 47 page