Smarandache Non-Associative (SNA-) rings

In this paper we introduce the concept of Smarandache non-associative rings, which we shortly denote as SNA-rings as derived from the general definition of a Smarandache Structure (i.e., a set A embedded with a week structure W such that a proper subset B in A is embedded with a stronger structure S

Fixed point theorems for α\alpha--contractive mappings of Meir--Keeler type and applications

In this paper, we introduce the notion of $\alpha$--contractive mapping of Meir--Keeler type in complete metric spaces and prove new theorems which assure the existence, uniqueness and iterative approximation of the fixed point for this type of contraction. The presented theorems extend, generalize and improve several existing results in literature. To validate our results, we establish the existence and uniqueness of solution to a class of third order two point boundary value problems

Computed Chaos or Numerical Errors

Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical chaotic solution is currently available. Using the well-known Lorenz equations as an example, it is demonstrated that numerically computed results and their associated statistical properties are time-step dependent. There are two reasons for this behavior. First, chaotic differential equations are unstable so that any small error is amplified exponentially near an unstable manifold. The more serious and lesser-known reason is that stable and unstable manifolds of singular points associated with differential equations can form virtual separatrices. The existence of a virtual separatrix presents the possibility of a computed trajectory actually jumping through it due to the finite time-steps of discrete numerical methods. Such behavior violates the uniqueness theory of differential equations and amplifies the numerical errors explosively. These reasons imply that, even if computed results are bounded, their independence on time-step should be established before accepting them as useful numerical approximations to the true solution of the differential equations. However, due to these exponential and explosive amplifications of numerical errors, no computed chaotic solutions of differential equations independent of integration-time step have been found. Thus, reports of computed non-periodic solutions of chaotic differential equations are simply consequences of unstably amplified truncation errors, and are not approximate solutions of the associated differential equations.Comment: pages 24, Figures

Cyclic (Noncyclic) ϕ-condensing operator and its application to a system of differential equations

We establish a best proximity pair theorem for noncyclic ϕ-condensing operators in strictly convex Banach spaces by using a measure of noncompactness. We also obtain a counterpart result for cyclic ϕ-condensing operators in Banach spaces to guarantee the existence of best proximity points, and so, an extension of Darbo’s fixed point theorem will be concluded. As an application of our results, we study the existence of a global optimal solution for a system of ordinary differential equations

Existence of the solution to a nonlocal-in-time evolutional problem

This work is devoted to the study of a nonlocal-in-time evolutional problem for the first order differential equation in Banach space. Our primary approach, although stems from the convenient technique based on the reduction of a nonlocal problem to its classical initial value analogue, uses more advanced analysis. That is a validation of the correctness in definition of the general solution representation via the Dunford-Cauchy formula. Such approach allows us to reduce the given existence problem to the problem of locating zeros of a certain entire function. It results in the necessary and sufficient conditions for the existence of a generalized (mild) solution to the given nonlocal problem. Aside of that we also present new sufficient conditions which in the majority of cases generalize existing results.Comment: This article is an extended translation of the part of Dmytro Sytnyk's PhD Thesi

Compound orbits break-up in constituents: an algorithm

In this paper decomposition of periodic orbits in bifurcation diagrams are derived in unidimensional dynamics system $x_{n+1}=f(x_{n};r)$, being $f$ an unimodal function. We proof a theorem which states the necessary and sufficient conditions for the break-up of compound orbits in their simpler constituents. A corollary to this theorem provides an algorithm for the computation of those orbits. This process closes the theoretical framework initiated in (Physica D, 239:1135--1146, 2010)

Tenure reform and presidential power: The single, six-year term proposal"

During the twentieth century, a series of rapid changes transformed the office of the presidency, affecting not only its raw power and influence upon other political institutions but also, crucially for an office defined as much by image as by constitutional authority, its status in the eyes of the American public and news media. From the turn-of-the-century administration of Theodore Roosevelt to the Lyndon Johnson presidency in the 1960s, George Reedy notes, “commitment to the presidential concept” by politicians, voters and the news media became so pronounced that Americans were "virtually incapable of thinking of the United States in other terms."1 Progressives frequently encouraged the trend toward greater presidential influence as a useful means of bypassing entrenched conservatism in national and state legislatures but many on the political right were disturbed by the expansion of executive power, viewing it as both cause and consequence of liberal interventionism and as a threat to the equilibrium of constitutional government

Open versus closed surgical exposure of canine teeth that are displaced in the roof of the mouth

Background: Palatal canines are upper permanent canine (eye) teeth that have become displaced in the roof of the mouth. They are a frequently occurring anomaly, present in 2% to 3% of the population. Management of this problem is both time consuming and expensive and involves surgical exposure (uncovering) followed by fixed braces for 2 to 3 years to bring the canine into alignment within the dental arch. Two techniques for exposing palatal canines are routinely used in the UK: one method (the closed technique) involves orthodontically moving the canine into its correct position beneath the palatal mucosa and the second method (the open technique) involves orthodontically moving the canine into its correct position above the palatal mucosa. Objectives: To establish if clinical, patient centred and economic outcomes are different according to whether an ’open’ or ’closed’ technique is employed for uncovering palatal canines. Search strategy: MEDLINE, EMBASE, the Cochrane Central Register of Controlled Trials (CENTRAL) and the Cochrane Oral Health Group’s Trials Register were searched (to 29th February 2008). There were no restrictions with regard to publication status or language. Selection criteria: Patients receiving surgical treatment to correct upper palatally impacted canines.Therewas no restriction for age, presenting malocclusion or the type of active orthodontic treatment undertaken. Unilateral and bilaterally displaced canines were included. Trials including participants with craniofacial deformity/syndrome were excluded. Data collection and analysis: Two review authors independently and in duplicate assessed studies for inclusion. The Cochrane Collaboration statistical guidelines were to be followed for data synthesis