The purpose of this paper is to develop the shooting method as a technique for approximating the solution to the two-point boundary value problem on the interval [a,b] with the even order differential equation {i.e. n is even) u(n)(t) + f(t, u(t), u(i)(t, ),..., u(n-1)(t)) = 0 and boundary conditions u(a) = A u(b) = B and with at most n-2 other boundary conditions specified at either a or b. The basic proceedure will be illustrated by the following example. Consider the two-point boundary value problem (0.1) (0.2) (0.3) with the additional boundary conditions u(i)(a) = mi for i = 1, ... ,k-1,k+l, ... ,n-1. The first step is to find values m1 and m2 such that the solutions or "shots", u1(t) and u2(t), to (0.1) that satisfy the initial conditions u(a) = A u(k-1)(a)= mk-1 u(k)(a) = m1 u(k+1)(a) = mk+l u(n-1)(a) = mn-1 with 1 = 1,2, respectively, with the property that u1(b) < B < u2(b). The interval [m1,m2] is then searched by seccussive bisection to find the value, m, such that the solution or "shot", u(t), to the initial value problem with (0.1) and initial conditions u(a) = A u(k-1)(a)= mk-1 u(k)(a) = m1 u(k+1)(a) = mk+l u(n-1)(a) = mn-1 has the property that u(b) = B.

The thesis is divided in three parts based largely on published articles or on manuscripts submitted for publication. First we propose a new method which is called the shooting-bead method. This method is a fast and easy experimental technique for evaluating cantilever stiffness and flexural rigidity of semi-flexible to semi-rigid rod-like biological and nano-filaments based on the measurement of just two distances. The method is based on applying a force normal to the filament with a microsphere bead trapped in the laser tweezer followed by its sudden release. Through a simple measurement of the distances that the bead moves, the flexural rigidity of the filament can be found from the formula derived in this paper. Then we take into account the effects of the viscous drag force exerted on the filament itself. To this end, we have defined a key variable, called the filament energy-loss factor (or filament drag factor) that accounts for all the energy-loss effects. It has been shown that the effect due to the consideration of filament energy-loss factor on calculation of the flexural rigidity increases with increasing the flexibility of the filament. Finally, in the third part we discuss the effect of ultrasound on the microtubules. Here we have analytically solved equations of motion for the vibrational dynamics of an MT that is attached at its two ends. This is especially relevant for MTs during mitosis when they attach to chromosomes and centrosomes. Our analysis applies to MTs present inside a viscous solution and when driven by an ultrasound plane wave. We have shown that with using ultrasound plane waves the resonance condition for the MT treated as a rigid rod cannot be provided, and in order to achieve resonance we should excite a single mode of the MT with a harmonic number larger than a threshold value introduced in this thesis. Single mode excitation not only helps to transfer the minimum amount of energy to the surrounding medium compared with multi-mode excitation but it also allows for a simultaneous high-amplitude and high-quality factor which is impossible when using plane waves.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / No leaf vii so pagination is misnumbered. Typescript. Vita. Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / No leaf vii so pagination is misnumbered. Typescript. Vita. Includes bibliographical references. Also available on the Internet.

Syfte Syftet med studien är att analysera tillslagsprecision i fotboll och jämföra eventuella skillnader mellan juniorer och seniorer på både herr- och damsidan. Metod Totalt 30 elitspelare varav 16 herrar och 14 damer utförde tester i tillslagsprecision. De färdigheter som testades var passning och skott. Upplägget var 60 skott (30 stillaliggande och 30 halvvolley) och 80 passningar (20 stillaliggande bästa fot, 20 rullande bästa fot, 20 stillaliggande näst bästa fot och 20 rullande näst bästa fot). Testresultaten analyserades via Excel och Kinovea, där kunde medelvärden och standardavvikelser för varje testperson och testgrupp räknas ut. Resultat Resultatet visar att det endast var signifkant skillnad på ett av sex moment vad gäller tillslagsprecisionen på herrsidan. På damsidan var det ingen signifikant skillnad på något moment. Slutsatser Författarna har i denna studie identifierat en platå mellan spelare i åldrarna 16-18 år och seniorspelare vad gäller tillslagsprecision. Spelare i åldrarna 16-18 är lika bra som seniorspelare på de individuella färdigheterna passning och skott. Denna platå kan vara resultatet av för lite individuell träning, sk isolerad träning vad det gäller tillslagsprecision, på föreningsträningarna. Om föreningstränarna följer den utbildning SvFF ger dem ska endast två minuter per träning gå till varje individuell färdighet (13 st enligt SvFF). Bristen av tid för dessa färdigheter kan vara en avgörande faktor för att utvecklingen av tillslagsprecision står stilla idag. / The aim of this study is to analyze if the precision of a shot and a pass differs between professional youth players (16-18 years) and senior players (22+ or older). Method A total of 30 elite players which were 16 males and 14 females performed tests in shooting and passing precision. The set-up on the test days were a total of 60 shots(30 lying still and 30 half volley) and 80 passes (20 lying still best foot, 20 rolling best foot, 20 lying still next best foot and 20 rolling next best foot). The test results were analyzed using Excel and Kinovea. In these programs the mean value and standard deviation for each player and test group could be calculated. Results The result shows that there were only significant differences in one of six parts regarding precision on the men's side. On the women's side, there was no significant difference in any of the six moments. Conclusions The authors of this study identified a plateau between players aged 16-18 and senior players in terms of accuracy in passing and shooting. Players between the ages of 16-18 is as good as a senior player at the individual skills passing and shooting. This plateau can be the result of too little individual training so called isolated training in terms of precision. If the club coaches follow the training SvFF educate, only two minutes per training session goes to each individual skill (SvFF names 13 skills). The lack of time for these skills can be a decisive factor for why the development of precision stands still today.

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Thesis (Ph. D.)--University of Chicago, Dept. of Anthropology. / Includes bibliographical references. Also available on the Internet.

Thesis (M.S. in Operations Research)--Naval Postgraduate School, 2005. / Title from title screen (viewed Jan. 31, 2006). "June 2005." Includes bibliographical references (p. 89-90). Also issued in paper format.

Thesis (M.S. in Operations Research)--Naval Postgraduate School, June 2005. / Thesis Advisor(s): Thomas W. Lucas, Richard Spainhour. Includes bibliographical references (p. 89-90). Also available online.

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