Killing Goliath? Elhanan the Bethlehemite and the Text of 2 Samuel 21:19

The text of 2 Sam 21:19 states in summary fashion that a certain Elhanan, son of Jaare-oregim the Bethlehemite, killed Goliath the Gittite in battle (thus, in apparent contradiction to the famous extended pericope of 1 Sam 17). A text-critical reconstruction of the verse is presented which accounts for the relationship between “the Bethlehemite” in 2 Sam 21:19 and the name “Lahmi” which is recorded as belonging to Goliath’s brother in 1 Chr 20:5. Along these lines it is further argued that a text-critical analysis is a viable option for resolving the tension with 1 Sam 17, without the need to resort to additional literary or source-critical solutions.

Newton-type methods near critical solutions of piecewise smooth nonlinear equations

It is well-recognized that in the presence of singular (and in particular nonisolated) solutions of unconstrained or constrained smooth nonlinear equations, the existence of critical solutions has a crucial impact on the behavior of various Newton-type methods. On the one hand, it has been demonstrated that such solutions turn out to be attractors for sequences generated by these methods, for wide domains of starting points, and with a linear convergence rate estimate. On the other hand, the pattern of convergence to such solutions is quite special, and allows for a sharp characterization which serves, in particular, as a basis for some known acceleration techniques, and for the proof of an asymptotic acceptance of the unit stepsize. The latter is an essential property for the success of these techniques when combined with a linesearch strategy for globalization of convergence. This paper aims at extensions of these results to piecewise smooth equations, with applications to corresponding reformulations of nonlinear complementarity problems.

Potential, Prospects and Challenges Associated with the Implementation of Photovoltaic Solar Energy in Zimbabwe

Renewable energy is one of the critical solutions to address the ever-increasing demand for energy. In developing countries such as Zimbabwe where the conventional generation hardly sustains half of the nation’s energy demands, renewable energy solutions are compensating for the deficit. Among these renewables, solar energy technologies have witnessed rapid growth. In most cases, solar energy installers assume to have all the knowledge required in the field. However, many technical barriers still exist within the field of solar energy systems. For solar energy systems which are synchronized to the grid, the integration of these renewables pose a serious stability and protection threat to the already unstable and even stable grids. In this paper, some of the technical problems being faced are discussed. Policy issues as well as the possible solutions needed in order to realize full, unhindered growth of solar energy are addressed.

Critical Casimir interactions of colloids in micellar critical solutions

We study the temperature-dependence of critical Casimir interactions in a critical micellar solution of the nonionic surfactant C12E5 dissolved in water.

On perturbation theory and critical exponents for self-similar systems

Gravitational critical collapse in the Einstein-axion-dilaton system is known to lead to continuous self-similar solutions characterized by the Choptuik critical exponent $$\gamma $$ γ . We complete the existing literature on the subject by computing the linear perturbation equations in the case where the axion-dilaton system assumes a parabolic form. Next, we solve the perturbation equations in a newly discovered self-similar solution in the hyperbolic case, which allows us to extract the Choptuik exponent. Our main result is that this exponent depends not only on the dimensions of spacetime but also the particular ansatz and the critical solutions that one started with.

Constrained Lipschitzian Error Bounds and Noncritical Solutions of Constrained Equations

For many years, local Lipschitzian error bounds for systems of equations have been successfully used for the design and analysis of Newton-type methods. There are characterizations of those error bounds by means of first-order derivatives like a recent result by Izmailov, Kurennoy, and Solodov on critical solutions of nonlinear equations. We aim at extending this result in two directions which shall enable, to some extent, to include additional constraints and to consider mappings with reduced smoothness requirements. This leads to new necessary as well as sufficient conditions for the existence of error bounds.

Cloud Computing Recent Trends And Emerging Technologies

With invent of IoT technologies, it is easier to connect people residing at geographically distant locations for information exchange. The ease in sharing of data across global boundaries has led to increased mooring of traffic for extracting services that are IT based. This has presented challenges before providers of these services to cope up with user expectations. Therefore, with emergence of cloud in the market, the models of fog and edge computing necessitates delivery of solutions that can cater heterogeneous user needs without constraints of latency and time-sensitive service delivery. It becomes imperative in such a scenario to offer viable solutions in the direction of provisioning security mechanisms to put a constraint on unauthorized user access to such services. Hence, technologies like multi-access edge computing (MEC) and cloudlet plays a vital role in comprehending security critical solutions. Therefore, the focus of this paper has been directed to discuss such emerging technologies pertaining to implementations in cloud that are capable of increasing confidence of user in distributed paradigm.