Tridendriform structures

We first study tensor products of tridendriform algebras in order to introduce the notion of tridendriform bialgebra. We shall need for this a notion of augmented tridendriform algebras. Inspired by the work of J-L. Loday and M. Ronco, we build free tridendriform algebras over reduced trees and show that they have a coproduct satisfying some compatibilities with the tridendriform products. Such an object will be called a (3, 1)--dendriform algebra. Studying the free (3, 1)--dendriform bialgebra over one generator, we describe its products and coproduct in a combinatorial way. The products are described by branches shuffle and the coproduct by admissible cuts. We compare it with quasi-shuffle algebras over words. Its graded dual is the bialgebra TSym introduced by N. Bergeron and al which is described by the lightening splitting of a tree. As a consequence, this shows that TSym has a (1, 3)--dendriform bialgebra structure. This means that its coproduct can be split in three parts with convenient compatibilities. This can be extended to (3, 1)-bialgebras over an arbitrary number of generators. Finally, we introduce the notion of (3, 2)--dendriform bialgebra. This is a Hopf algebra, where we can split the product in three pieces and the coproduct in two with Hopf compatibilities. We give an example of such an algebra built on the free (3, 1)-dendriform bialgebra with one generator. We describe and generate its codendriform primitives and count its coassociative primitives thanks to L. Foissy's work. We end this paper by showing that a quotient of this (3, 2)-dendriform bialgebra is the Loday-Ronco bialgebra

Developing Modified ADS-33D Helicopter Maneuvers for the Shipboard Environment

The Office of the Secretary of Defense chartered the Joint Shipboard Helicopter Integration Process (JSHIP), Joint Test and Evaluation (JT&E) Program to improve Joint interoperability between U.S. Navy ships and U.S. Army/Air Force helicopters. One effort of the JSHIP JT&E Program was to improve the modeling and simulation tools and fidelity levels associated with conducting Joint shipboard helicopter operations, for both testing agencies and operational users. The UH-60A helicopter and the LHA class ship were identified as the highest priority helicopter-ship pair for operational forces and also allowed JSHIP to enhance models that currently existed. Enhancing the visual model of an LHA ship was a primary effort for the research and testing community in order to accurately replicate the shipboard visual cueing environment. Evaluating enhanced visual models in a research flight simulator in order to reduce actual shipboard flight testing or expand wind launch/recovery envelopes required the use of more aggressive and precise flight maneuvers than standard shipboard takeoffs and landings. The U.S. Army’s Aeronautical Design Standard 33D (ADS-33D) contained flight test industry accepted maneuvers of sufficient aggressiveness and precision, but were not designed for, or intended to be flown from the deck of a ship at sea. The methodology and procedure used to modify selected ADS-33D flight maneuvers so that they could safely be executed aboard an LHA class ship is presented in this thesis, along with the final maneuver descriptions, locations, and flight tolerances. The results of the shipboard test program and follow-on simulator assessment are not presented here, as they fall outside the scope of this thesis. However, conclusions from the at-sea flight tests relating to development of the modified ADS-33D were included. The flight test philosophy, methodology, and lessons learned while developing the modified ADS-33D maneuvers for the shipboard environment are the primary conclusions drawn

Educational Policy Decisions Effect Upon Same-Gender Public Education

The No Child Left Behind (NCLB) Act of 2001, with emphasis on greater choice and flexibility for parents and students in public education, to include the provision for same-gender public schools and classrooms, led to a resurgence in same-gender public education in the United States. With the results of the research on same-gender education presenting conflicting evidence and mixed-perspectives on the outcomes of same-gender education in improving academic achievement or attainment, there are still questions to be answered, not only to the effectiveness of same-gender education, but also to policy decisions to establish same-gender public education programs. While proponents of same-gender public education advocate that same-gender schooling supports increased educational opportunity and achievement while freeing students from gender stereotypes, opponents claim separate but equal is discriminatory and unconstitutional. As a result, public policy decisions by local educational agencies to establish same-gender public education programs, no matter how well intentioned, and irrespective of the provisions for same-gender schools and classrooms within NCLB, can be left open to questions on the rationales, justifications, and resources behind such decisions. This non-experimental, mixed methods study gathered and analyzed data on same-gender public education programs in the United States using a descriptive cross sectional survey with telephone interviews to question principals of 92 K-12 same-gender public schools on the proponents, rationales, justifications, resources, and metrics behind decisions to establish and maintain same-gender public education programs. Fifty-four respondents agreed the establishment and maintenance of same-gender public education programs results from actions of local educational agencies and the leadership of the same-gender school, and they agreed this leadership is knowledgeable on the requirements for same-gender public education programs. Respondents to the study also agreed school choice for low-income students is a key reason for the establishment of same-gender public schools. Respondents to the study further agreed that supplementary funding, whether federal, state, or local, was not critical in the establishment and maintenance of same-gender public education programs

Provably Secure Mobile Key Exchange: Applying the Canetti-Krawczyk Approach

info:eu-repo/semantics/publishe

Molecular Resolvent Operator for H2 + molecule

We present a theoretical method to extract photoelectron and nuclear kinetic energy spectra of molecules under intense ultrashort laser pulses. The method is applied to H2+ photoionization and dissociation within a 3D model of the H2+ molecule. This method is an extension to molecules of the resolvent technique originally proposed for atoms, which was recently implemented to extract absolute values of photoelectron and nuclear kinetic energy spectr