Our brief Journey with some properties and patterns of the Mulatu Numbers

The Mulatu numbers were introduced by Mulatu Lemma in [1]. The Mulatu numbers are integral sequences of numbers of the form: 4, 1, and 5,6,11,17,28,45...These numbers have wonderful and amazing properties and patterns. In mathematical terms, the sequence of the Mulatu numbers is defined by the following recurrence relation: The first number of the sequence is 4, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself. That is, after two starting values, each number is the sum of the two preceding numbers. In [1] some properties and patterns of the numbers were considered. In this paper, we more deeply examine additional properties and patterns of these fascinating and mysterious numbers. Many beautiful mathematical identities involving the Mulatu numbers, the Fibonacci numbers, and the Lucas numbers will be explored. 2000 Mathematical Subject Classification:  1

The Fascinating Gamma Function in actions

The gamma function has several properties that define it. In this paper, I will present proofs for those properties and give example using real numbers. The properties I will prove are as followed

The Fascinating Mathematical Beauty Of The Fibonacci Numbers

 The Fibonacci numbers are sequences of numbers of the form: 0,1,1,2,3,5,8,13,...  Among numerical sequences, the Fibonacci numbers Fn have achieved a kind of celebrity status. These numbers are famous for possessing wonderful and amazing properties. Mathematicians have been fascinated for centuries by the properties and patterns of Fibonacci numbers. In mathematical terms, it is defined by the following recurrence relation: The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself. That is, after two starting values, each number is the sum of the two preceding numbers. In this paper, we give excellent summary of basic properties of Fibonacci numbers as well as and its patterns.  This is a paper which is very helpful for quick reference on Fibonacci numbers

The Mulatu Numbers, The Newly Celebrated Numbers of Pure Mathematics

The Mulatu numbers are sequences of numbers of form 4, 1, 5, 6, 11, 17, 28, 45, ….  The numbers have wonderful and amazing properties and patterns. In mathematical terms, it is defined by the following recurrence relation: The first number of the sequence is 4, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself. That is, after two starting values, each number is the sum of the two preceding numbers. In this paper, we give summary of some important properties and patterns of Mulatu numbers. Its relations to the Fibonacci and Lucas numbers are also investigated. 2010 Mathematical Subject Classi8fications:  1

ESMD Space Grant Faculty Report

The strength of the Exploration Systems Mission Directorate ESMD Faculty Project lies in its ability to meet National Aeronautics Space Administration NASA's Strategic Educational Outcome 1 by developing a sustainable and long-term integration of student involvement at academic institutions with all NASA Centers. This outcome is achieved by a three-fold approach: 1) by collecting Senior Design projects pertaining to Constellation work performed at each of the ten NASA Centers, 2) by engaging students at Minority Serving Institutions in the art of systems engineering and systems design of technologies required for space exploration, and 3) by identifying potential internships at each Center relative to exploration that provide students who are supported by their institutional Space Grant to engage in on-going mission-level and explorative systems designs. The objectives of the ESMD Faculty Project are to: 1. Aid the Centers (both Education Offices and associated technical organizations) in providing relevant opportunities for the ESMD Space Grant Program to support student and faculty in Senior Design projects 2. Enable better matches between the ESMD work required and what the Space Grant Consortia can do to effectively contribute to NASA programs 3. Provide the Space Grant Consortia an opportunity to strengthen relations with the NASA Centers 4. Develop better collective understanding of the U.S. Space Exploration Policy by the Center, Space Grant, faculty, Education Office, and students 5. Enable Space Grant institution faculty to better prepare their students to meet current and future NASA needs 6. Enable the Center Education Offices to strengthen their ties to their technical organizations and Space Grant Consortia 7. Aid KSC in gaining a greater and more detailed understanding of each of the Center activities Senior Design projects are intended to stimulate undergraduate students on current NASA activities related to lunar, Mars, and other planetary missions and to bring out innovative and novel ideas that can be used to complement those currently under development at respective NASA Centers. Additionally, such academic involvement would better the prospects for graduating seniors to pursue graduate studies and to seek careers in the space industry with a strong sense for systems engineering and understanding of design concepts. Internships, on the other hand, are intended to provide hands-on experience to students by engaging them in diverse state-of-the-art technology development, prototype bread-boarding, computer modeling and simulations, hardware and software testing, and other activities that provide students a strong perspective of NASA's vision and mission in enhancing the knowledge of Earth and space planetary sciences. Ten faculty members, each from a Space Grant Consortium-affiliated university, worked at ten NASA Centers for five weeks between June 2 and July 3, 2008. The project objectives listed above were achieved. In addition to collecting data on Senior Design ideas and identifying possible internships that would benefit NASA/ESMD, the faculty fellows promoted and collected data when required for other ESMD-funded programs and helped the Center's Education Office, as,needed.

Thoracic Operations for Pulmonary Nodules Are Frequently Not Futile in Patients with Benign Disease

IntroductionPulmonary nodules often require operative resection to obtain a diagnosis. However, 10 to 30% of operations result in a benign diagnosis. Our purpose was to determine whether negative thoracic operations are futile by describing the pathological diagnoses; determining new diagnoses and treatment changes initiated based on operative findings; and assessing morbidity, mortality, and cost of the procedure.MethodsAt our academic medical center, 278 thoracic operations were performed for known or suspected cancer between January 1, 2005, and April 1, 2009. We collected and summarized data pertaining to preoperative patient and nodule characteristics, pathologic diagnosis, postoperative treatment changes resulting from surgical resection, perioperative morbidity and mortality, and hospital charges for patients with benign pathology.ResultsTwenty-three percent (65/278) of patients who underwent surgical resection for a suspicious nodule had benign pathology. We report granulomatous disease in 57%, benign tumors in 15%, fibrosis in 12%, and autoimmune and vascular diseases in 9%. Definitive diagnosis or treatment changes occurred in 85% of cases. Surgical intervention led to a new diagnosis in 69%, treatment course changes in 68% of benign cases, medication changes in 38%, new consultation in 31%, definitive treatment in 9%, and underlying disease management in 34%. There was no intraoperative, in-hospital, or 30-day mortality. Postoperative in-hospital events occurred in seven patients. The mean total cost was $25,515 with a mean cost per day of$7618.ConclusionsPatients with a benign diagnosis after surgical resection for a pulmonary nodule received a new diagnosis or had a treatment course change in 85% of the cases

2008 ESMD Space Grant Faculty Project

Objectives of this project was to: Gather senior design project ideas and internship opportunities: Relative to space explorationnd In support of the ESMD Space Grant Student Project Support NASAs Educational Framework Outcome 1: Contribute to the development of the STEM workforc

Enhanced Lifetime Of Excitons In Nonepitaxial Au/cds Core/shell Nanocrystals

The ability of metal nanoparticles to capture light through plasmon excitations offers an opportunity for enhancing the optical absorption of plasmon-coupled semiconductor materials via energy transfer. This process, however, requires that the semiconductor component is electrically insulated to prevent a backward charge flow into metal and interfacial states, which causes a premature dissociation of excitons. Here we demonstrate that such an energy exchange can be achieved on the nanoscale by using nonepitaxial Au/CdS core/shell nanocomposites. These materials are fabricated via a multistep cation exchange reaction, which decouples metal and semiconductor phases leading to fewer interfacial defects. Ultrafast transient absorption measurements confirm that the lifetime of excitons in the CdS shell (tau approximate to 300 ps) is much longer than lifetimes of excitons in conventional, reduction-grown Au/CdS heteronanostructures. As a result, the energy of metal nanoparticles can be efficiently utilized by the semiconductor component without undergoing significant nonradiative energy losses, an important property for catalytic or photovoltaic applications. The reduced rate of exciton dissociation in the CdS domain of Au/CdS nanocomposites was attributed to the nonepitaxial nature of Au/CdS interfaces associated with low defect density and a high potential barrier of the interstitial phase

The James Webb Space Telescope

The James Webb Space Telescope (JWST) is a large (6.6m), cold (50K), infrared-optimized space observatory that will be launched early in the next decade. The observatory will have four instruments: a near-infrared camera, a near-infrared multi-object spectrograph, and a tunable filter imager will cover the wavelength range, 0.6 to 5.0 microns, while the mid-infrared instrument will do both imaging and spectroscopy from 5.0 to 29 microns. The JWST science goals are divided into four themes. The End of the Dark Ages: First Light and Reionization theme seeks to identify the first luminous sources to form and to determine the ionization history of the early universe. The Assembly of Galaxies theme seeks to determine how galaxies and the dark matter, gas, stars, metals, morphological structures, and active nuclei within them evolved from the epoch of reionization to the present day. The Birth of Stars and Protoplanetary Systems theme seeks to unravel the birth and early evolution of stars, from infall on to dust-enshrouded protostars to the genesis of planetary systems. The Planetary Systems and the Origins of Life theme seeks to determine the physical and chemical properties of planetary systems including our own, and investigate the potential for the origins of life in those systems. To enable these observations, JWST consists of a telescope, an instrument package, a spacecraft and a sunshield. The telescope consists of 18 beryllium segments, some of which are deployed. The segments will be brought into optical alignment on-orbit through a process of periodic wavefront sensing and control. The JWST operations plan is based on that used for previous space observatories, and the majority of JWST observing time will be allocated to the international astronomical community through annual peer-reviewed proposal opportunities.Comment: 96 pages, including 48 figures and 15 tables, accepted by Space Science Review

Design of composite structures using knowledge-based and case-based reasoning

Ph.D.Charles Um