Earls, knights and bastards: a comparative study of the fortunes and misfortunes of two aristocratic families of England c.1135-1267

This thesis analyses and compares the fortunes of two English aristocratic families, the Senlis family and Crevequer family, between the beginning of King Stephen’s reign in 1135 and the closing of the Second Baron’s war in 1267. The first chapter evaluates the duties which the patriarchs of these families performed for either the king or lesser lords. This chapter reveals that, over multiple generations, both families sought to enjoy the benefits which their loyal service could impart. The second chapter examines the political careers of both families during the civil wars of the period. By doing so, it demonstrates that intelligent political opportunism during such times could present great benefits to these families’ power and wealth, but, to the unfortunate aristocrat they could also cause a great loss of land and power. The third chapter explores the estates and religious patronage of the families, looking specifically at the extent of their estates and the methods by which lands were gained and alienated. This chapter also evaluates the motivations for the religious patronage undertaken by these aristocrats and reveals that both spiritual and worldly motivations played a pivotal role in their decisions to fulfil their obligations as founders and benefactors

On the Hojman conservation quantities in Cosmology

We discuss the application of the Hojman's Symmetry Approach for the determination of conservation laws in Cosmology, which has been recently applied by various authors in different cosmological models. We show that Hojman's method for regular Hamiltonian systems, where the Hamiltonian function is one of the involved equations of the system, is equivalent to the application of Noether's Theorem for generalized transformations. That means that for minimally-coupled scalar field cosmology or other modified theories which are conformally related with scalar-field cosmology, like $f(R)$ gravity, the application of Hojman's method provide us with the same results with that of Noether's theorem. Moreover we study the special Ansatz. $\phi\left( t\right) =\phi\left( a\left( t\right) \right)$, which has been introduced for a minimally-coupled scalar field, and we study the Lie and Noether point symmetries for the reduced equation. We show that under this Ansatz, the unknown function of the model cannot be constrained by the requirement of the existence of a conservation law and that the Hojman conservation quantity which arises for the reduced equation is nothing more than the functional form of Noetherian conservation laws for the free particle. On the other hand, for $f(T)$ teleparallel gravity, it is not the existence of Hojman's conservation laws which provide us with the special function form of $f(T)$ functions, but the requirement that the reduced second-order differential equation admits a Jacobi Last multiplier, while the new conservation law is nothing else that the Hamiltonian function of the reduced equation.Comment: 6 pages; minor corrections; accepted for publication by Physics Letters B. arXiv admin note: substantial text overlap with arXiv:1503.0846

Dear Wife : the Civil War letters of Chester K. Leach

Occasional paper (University of Vermont. Center for Research on Vermont) ; no. 20

The Effects of School Board Consolidation and Financing on Student Performance

Over the last 20 years, states and provinces have become increasingly involved in the financing and administration of elementary and secondary education. Local school boards, however, still retain control over key aspects of the provision of education. Historically, these boards were organized at the community level so as to meet the wants of the local community. Today, states and provinces have become more interested in consolidating school boards and moving to a more centralized funding scheme. Do these changes result in improved student achievement? This paper attempts to answer these questions by examining the school board consolidation and funding changes instituted by the province of Ontario. We differentiate the effects of the policy changes based on observed differences in the school boards prior to consolidation. We show that students in previously high wealth school boards perform worse after the policy change compared to students in previously low wealth school boards.school district consolidation; student achievement

Cheng Equation: A Revisit Through Symmetry Analysis

The symmetry analysis of the Cheng Equation is performed. The Cheng Equation is reduced to a first-order equation of either Abel's Equations, the analytic solution of which is given in terms of special functions. Moreover, for a particular symmetry the system is reduced to the Riccati Equation or to the linear nonhomogeneous equation of Euler type. Henceforth, the general solution of the Cheng Equation with the use of the Lie theory is discussed, as also the application of Lie symmetries in a generalized Cheng equation.Comment: 10 pages. Accepted for publication in Quaestiones Mathematicae journa

The interpretation of hard X-ray polarization measurements in solar flares

Observations of polarization of moderately hard X-rays in solar flares are reviewed and compared with the predictions of recent detailed modeling of hard X-ray bremsstrahlung production by non-thermal electrons. The recent advances in the complexity of the modeling lead to substantially lower predicted polarizations than in earlier models and more fully highlight how various parameters play a role in determining the polarization of the radiation field. The new predicted polarizations are comparable to those predicted by thermal modeling of solar flare hard X-ray production, and both are in agreement with the observations. In the light of these results, new polarization observations with current generation instruments are proposed which could be used to discriminate between non-thermal and thermal models of hard X-ray production in solar flares