Absence of a consistent classical equation of motion for a mass-renormalized point charge

The restrictions of analyticity, relativistic (Born) rigidity, and negligible O(a) terms involved in the evaluation of the self electromagnetic force on an extended charged sphere of radius "a" are explicitly revealed and taken into account in order to obtain a classical equation of motion of the extended charge that is both causal and conserves momentum-energy. Because the power-series expansion used in the evaluation of the self force becomes invalid during transition time intervals immediately following the application and termination of an otherwise analytic externally applied force, transition forces must be included during these transition time intervals to remove the noncausal pre-acceleration and pre-deceleration from the solutions to the equation of motion without the transition forces. For the extended charged sphere, the transition forces can be chosen to maintain conservation of momentum-energy in the causal solutions to the equation of motion within the restrictions of relativistic rigidity and negligible O(a) terms under which the equation of motion is derived. However, it is shown that renormalization of the electrostatic mass to a finite value as the radius of the charge approaches zero introduces a violation of momentum-energy conservation into the causal solutions to the equation of motion of the point charge if the magnitude of the external force becomes too large. That is, the causal classical equation of motion of a point charge with renormalized mass experiences a high acceleration catastrophe.Comment: 13 pages, No figure

Reading Instruction Activities for Trade Books for Use in Third-Grade Reading Curriculum

Reading instruction activities were developed to be used with trade books in third grade to supplement the basal reading program. Activities developed included comprehension questions and a cloze unit for each selected trade book, as well as general creative and enrichment post-reading·assignments to provide students with reading and writing practice

The Significance of Trauma in the Relationship between Co-Occurring Disorders and Recidivism among Participants of a Community Mental Health\u27s Jail Diversion Program

Abstract Individuals with a psychiatric diagnosis have higher levels of criminal justice involvement compared to the general population. Multiple programs have been developed through grant monies utilizing various models to allow these individuals to be linked to mental health services in the community for the treatment of symptoms which may contribute to recidivism. These programs are designed to provide an encounter with mental health professionals who collaborate with law enforcement and other agencies to intercept these individuals at various points of justice involvement and possibly prevent further entanglements with the legal system. This study explores how trauma may impact justice involvement in individuals with a psychiatric diagnosis. For the diversion program to succeed, it is essential to provide integrated, whole-health treatment to these individuals. More studies are needed to develop diversion programs and reduce recidivism rates in those with a co-occurring psychiatric diagnosis and substance use disorder and to provide education to law enforcement and community agencies to foster collaborative relationships between community mental health agencies and the legal system