Proximal Point Algorithms for Finding a Zero of a Finite Sum of Monotone Mappings in Banach Spaces

We introduce an iterative process which converges strongly to a zero of a finite sum of monotone mappings under certain conditions. Applications to a convex minimization problem are included. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings

First Amendment Constraints of Public School Administrators to Regulate Off-campus Students' Speech in the Technology Age

In a world where students and teachers both rely on technology in the process of education, understanding the constraints of public school administrators to regulate off-campus student's speech is a vital issue. This dissertation focuses on ways to evaluate legal analysis of cases involved in off campus speech. The methodology of legal analysis is used to identify judicial reasoning concerning established legal principles pertaining to the constitutional right of public school students to freedom of expression, and the application of those principles to off-campus student expression delivered by electronic means. This research produces a number of key findings: Many lower court cases have favored with the students unless the school district could prove substantial disruption to the learning environment or a true threat existed due to the off campus speech. In addition, it is crucial for the districts to have concrete policies in place to educate the students about acceptable usage of technology. The main conclusions drawn from this research are that current approaches to punishing students for their offensive off campus speech does not uphold in the courts and administrators must be resilient to speech that may be unpleasant to them. This research also includes several recommendations for administrators such as guidelines on how to write their acceptable usage policy. It also provides a chart with a summary of critical cases of importance to administrators

Convergence of Mann’s type iteration method for generalized asymptotically nonexpansive mappings

AbstractLet C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ti:C→H,i=1,2,…,N, be a finite family of generalized asymptotically nonexpansive mappings. It is our purpose, in this paper to prove strong convergence of Mann’s type method to a common fixed point of {Ti:i=1,2,…,N} provided that the interior of common fixed points is nonempty. No compactness assumption is imposed either on T or on C. As a consequence, it is proved that Mann’s method converges for a fixed point of nonexpansive mapping provided that interior of F(T)≠0̸. The results obtained in this paper improve most of the results that have been proved for this class of nonlinear mappings

Strong Convergence Theorems for a Common Fixed Point of a Family of Asymptotically k

We provide an iterative process which converges strongly to a common fixed point of finite family of asymptotically k-strict pseudocontractive mappings in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators

Comparative evaluation of extraction methods for apoplastic proteins from maize leaves

Proteins in the plant apoplast are essential for many physiological processes. We have analysed and compared six different infiltration solutions for proteins contained in the apoplast to recognize the most suitable method for leaves and to establish proteome maps for each extraction. The efficiency of protocols was evaluated by comparing the protein patterns resolved by 1-DE and 2-DE, and revealed distinct characteristics for each infiltration solution. Nano-LC-ESI-Q-TOF MS analysis of all fractions was applied to cover all proteins differentially extracted by infiltration solutions and led to the identification of 328 proteins in total in apoplast preparations. The predicted subcellular protein localisation distinguished the examined infiltration solutions in those with high or low amounts of intracellular protein contaminations, and with high or low quantities of secreted proteins. All tested infiltration solution extracted different subsets of proteins, and those implications on apoplast-specific studies are discussed

Assessing The Impact of Medical Treatment and Fumigation on The Superinfection of Malaria: A Study of Sensitivity Analysis

Malaria is a disease caused by the parasite Plasmodium, transmitted by the bite of an infected female Anopheles. In general, five species of Plasmodium that can cause malaria. Of the five species, Plasmodium falciparum and Plasmodium vivax are two species of Plasmodium that can allow malaria superinfection in the human body. Typically, the popular intervention for malaria eradication is the use of fumigation to control the vector population and provide good medical services for malaria patients. Here in this article, we formulate a mathematical model based on a host-vector interaction. Our model considering two types of plasmodium in the infection process and the use of medical treatment and fumigation for the eradication program. Our analytical result succeeds in proving the existence of all equilibrium points and how their existence and local stability criteria depend not only on the control reproduction number but also in the invasive reproduction number. This invasive reproduction number represent how one plasmodium can dominate other plasmodium. Our sensitivity analysis shows that fumigation is the most influential parameter in determining all control reproduction numbers. Furthermore, we find that the order in which numerous intervention measures are taken will be very crucial to determine the level of success of our malaria eradication program