On the Lie symmetries of a class of generalized Ermakov systems

The symmetry analysis of Ermakov systems is extended to the generalized case where the frequency depends on the dynamical variables besides time. In this extended framework, a whole class of nonlinearly coupled oscillators are viewed as Hamiltonian Ermakov system and exactly solved in closed form

Equitable opportunities in economic environments

In this paper, we extend the axiomatic analysis of equitable opportunities developed in Kranich [6] from finite to continuous opportunity sets. This extended framework is amenable to economic applications. The main results establish conditions under which an ordinal ranking of profiles of opportunity sets can be represented by a cardinal advantage function which describes both the extent of inequality and the distribution of advantage among the agents

Enterprise information security policy assessment - an extended framework for metrics development utilising the goal-question-metric approach

Effective enterprise information security policy management requires review and assessment activities to ensure information security policies are aligned with business goals and objectives. As security policy management involves the elements of policy development process and the security policy as output, the context for security policy assessment requires goal-based metrics for these two elements. However, the current security management assessment methods only provide checklist types of assessment that are predefined by industry best practices and do not allow for developing specific goal-based metrics. Utilizing theories drawn from literature, this paper proposes the Enterprise Information Security Policy Assessment approach that expands on the Goal-Question-Metric (GQM) approach. The proposed assessment approach is then applied in a case scenario example to illustrate a practical application. It is shown that the proposed framework addresses the requirement for developing assessment metrics and allows for the concurrent undertaking of process-based and product-based assessment. Recommendations for further research activities include the conduct of empirical research to validate the propositions and the practical application of the proposed assessment approach in case studies to provide opportunities to introduce further enhancements to the approach

Cosmological implications of a viable non-analytical f(R) model

Power-law corrections (having the exponent strictly between 2 and 3) to the Einstein-Hilbert action yield an extended theory of gravity which is consistent with Solar-System tests and properly reproduces the main phases of the Universe thermal history. We find two distinct constraints for the characteristic length scale of the model: a lower bound from the Solar-System test and an upper bound by requiring the existence of the matter-dominated era. We also show how the extended framework can accommodate the existence of an early de Sitter phase. Within the allowed range of characteristic length scales, the relation between the expansion rate and the energy scale of inflation is modified, yielding a value of the rate several orders of magnitude smaller than in the standard picture. The observational implication of this fact is that a tiny value of the tensor-to-scalar ratio is expected in the extended framework. The suppression of primordial tensor modes also implies that the inflationary scale can be made arbitrarily close to the Planck one according to the current limits. Finally, an analysis of the propagation of gravitational waves on a Robertson-Walker background is addressed.Comment: 10 pages, 5 figure

Priority-Based Conflict Resolution in Inconsistent Relational Databases

We study here the impact of priorities on conflict resolution in inconsistent relational databases. We extend the framework of repairs and consistent query answers. We propose a set of postulates that an extended framework should satisfy and consider two instantiations of the framework: (locally preferred) l-repairs and (globally preferred) g-repairs. We study the relationships between them and the impact each notion of repair has on the computational complexity of repair checking and consistent query answers

Fourier Series Formalization in ACL2(r)

We formalize some basic properties of Fourier series in the logic of ACL2(r), which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r). Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.Comment: In Proceedings ACL2 2015, arXiv:1509.0552

Qualitative constraint satisfaction problems: An extended framework with landmarks

Dealing with spatial and temporal knowledge is an indispensable part of almost all aspects of human activity. The qualitative approach to spatial and temporal reasoning, known as Qualitative Spatial and Temporal Reasoning (QSTR), typically represents spatial/temporal knowledge in terms of qualitative relations (e.g., to the east of, after), and reasons with spatial/temporal knowledge by solving qualitative constraints. When formulating qualitative constraint satisfaction problems (CSPs), it is usually assumed that each variable could be "here, there and everywhere".1 Practical applications such as urban planning, however, often require a variable to take its value from a certain finite domain, i.e. it is required to be 'here or there, but not everywhere'. Entities in such a finite domain often act as reference objects and are called "landmarks" in this paper. The paper extends the classical framework of qualitative CSPs by allowing variables to take values from finite domains. The computational complexity of the consistency problem in this extended framework is examined for the five most important qualitative calculi, viz. Point Algebra, Interval Algebra, Cardinal Relation Algebra, RCC5, and RCC8. We show that all these consistency problems remain in NP and provide, under practical assumptions, efficient algorithms for solving basic constraints involving landmarks for all these calculi. © 2013 Elsevier B.V