Middle school students’ proportional reasoning in real life contexts in the domain of geometry and measurement

The purpose of this study was to examine middle school students’ proportional reasoning, solution strategies and difficulties in real life contexts in the domain of geometry and measurement. The underlying reasons of the difficulties were investigated as well. Mixed research design was adopted for the aims of the study by collecting data through an achievement test from 935 sixth, seventh and eighth grade students. The achievement test included real life problems that required proportional reasoning, and were related to the measurement of length, perimeter, area and volume concepts. In addition, task-based interviews were conducted on 12 of these students to collect more comprehensive data and to support the findings of the achievement test. Findings revealed that although students were mostly successful in giving correct answers, their reasoning lacked a clear argument of the direct and indirect proportional relationships between the variables and that they approached the problems by superficial characteristics of the problems.     

Design and kinematic optimization of a novel underactuated robotic hand exoskeleton

This study presents the design and the kinematic optimization of a novel, underactuated, linkage-based robotic hand exoskeleton to assist users performing grasping tasks. The device has been designed to apply only normal forces to the finger phalanges during flexion/extension of the fingers, while providing automatic adaptability for different finger sizes. Thus, the easiness of the attachment to the user’s fingers and better comfort have been ensured. The analyses of the device kinematic pose, statics and stability of grasp have been performed. These analyses have been used to optimize the link lengths of the mechanism, ensuring that a reasonable range of motion is satisfied while maximizing the force transmission on the finger joints. Finally, the usability of a prototype with multiple fingers has been tested during grasping tasks with different objects.     

Analytical study of the splitting process of a multiply-quantized vortex in a Bose–Einstein condensate and collaboration of the zero and complex modes

We study the dynamics of a trapped Bose–Einstein condensate with a multiply-quantized vortex, and investigate the roles of the fluctuations in the dynamical evolution of the system. Using the perturbation theory of the external potential, and assuming the situation of the small coupling constant of self-interaction, we analytically solve the time-dependent Gross–Pitaevskii equation. We introduce the zero mode and its adjoint mode of the Bogoliubov–de Gennes equations. Those modes are known to be essential for the completeness condition. We confirm how the complex eigenvalues induce the vortex splitting. It is shown that the physical role of the adjoint zero mode is to ensure the conservation of the total condensate number. The contribution of the adjoint mode is exponentially enhanced in synchronism with the exponential growth of the complex mode, and is essential in the vortex splitting.     

Particle formation in the hydrolysis of tetraethyl orthosilicate in pH buffer solution

Particle formation in the hydrolysis and condensation of tetraethyl orthosilicate (TEOS) was studied by varying pH (9.5-11) with the basic catalysts NH3, methylamine (MA), and dimethylamine (DMA) in the presence of 5 mol/m3 CH3COOH, which was chosen to suppress time variations of pH and ionic strength during the reaction. Spherical particles were formed for MA and DMA at catalyst concentrations of 0.02-0.2 kmol/m3 and for NH3 at catalyst concentrations of 0.1-1.5 kmol/m3. In a common range of catalyst concentrations for spherical particle formation, average particle size was largest for DMA and smallest for NH3. Hydrolysis rate of TEOS could be quantified by the use of buffer systems as a function of TEOS and OH- concentrations. A specific relation was not found between the hydrolysis and the particle size. The zeta potential of silica particles measured in the reaction solvent was in the order DMA < MA < NH3, and ionic strength, estimated from pH in the reactions, was in the order DMA approximately equal to MA > NH3. This suggested that the particle sizes were controlled by electrostatic particle interactions.     

Quantum field theoretical description of unstable behavior of a Bose-Einstein condensate with a highly quantized vortex in a harmonic potential

The Bogoliubov-de Gennes equations are used for a number of theoretical works to describe quantum and thermal fluctuations of trapped Bose-Einstein condensates. We consider the case in which the condensate has a highly quantized vortex. It is known that these equations have complex eigenvalues in this case. We give the complete set including a pair of complex modes whose eigenvalues are complex conjugates to each other. The expansion of the quantum fields which represent neutral atoms in terms of the complete set brings the operators associated with the complex modes, which are simply neither bosonic nor fermionic ones. The eigenstate of the Hamiltonian is given. Introducing the notion of the physical states, we discuss the instability of the condensates in the context of Kubo’s linear response theory.     

Fractional knapsack problems

The fractional knapsack problem to obtain an integer solution that maximizes a linear fractional objective function under the constraint of one linear inequality is considered. A modification of the Dinkelbach's algorithm [3] is proposed to exploit the fact that good feasible solutions are easily obtained for both the fractional knapsack problem and the ordinary knapsack problem. An upper bound of the number of iterations is derived. In particular it is clarified how optimal solutions depend on the right hand side of the constraint; a fractional knapsack problem reduces to an ordinary knapsack problem if the right hand side exceeds a certain bound.     

Evidence for an oscillatory signature in atmospheric neutrino oscillations

Muon neutrino disappearance probability as a function of neutrino flight length L over neutrino energy E was studied. A dip in the L/E distribution was observed in the data, as predicted from the sinusoidal flavor transition probability of neutrino oscillation. The observed L/E distribution constrained nu(micro)<-->nu(tau) neutrino oscillation parameters; 1.9x10(-3)0.90 at 90% confidence level.     

Search for electron neutrino appearance in a 250 km long-baseline experiment

We present a search for electron neutrino appearance from accelerator-produced muon neutrinos in the K2K long-baseline neutrino experiment. One candidate event is found in the data corresponding to an exposure of 4.8 x 10(19) protons on target. The expected background in the absence of neutrino oscillations is estimated to be 2.4+/-0.6 events and is dominated by misidentification of events from neutral current pi(0) production. We exclude the nu(micro) to nu(e) oscillations at 90% C.L. for the effective mixing angle in the 2-flavor approximation of sin((2)2theta(microe)( approximately 1/2sin((2)2theta(13))>0.15 at Deltam(2)(microe)=2.8 x 10(-3) eV(2), the best-fit value of the nu(micro) disappearance analysis in K2K. The most stringent limit of sin((2)2theta(microe)<0.09 is obtained at Deltam(2)(microe)=6 x 10(-3) eV(2).