On Possibility of Determining Neutrino Mass Hierarchy by the Charged-Current and Neutral-Current Events of Supernova Neutrinos in Scintillation Detectors

One of the unresolved mysteries in neutrino physics is the neutrino mass hierarchy. We present a new method to determine neutrino mass hierarchy by comparing the events of inverse beta decays (IBD), $\bar{\nu}_e + p\rightarrow n + e^+$, and neutral current (NC) interactions, $\nu(\overline{\nu}) + p\rightarrow\nu(\overline{\nu}) + p$, of supernova neutrinos from accretion and cooling phases in scintillation detectors. Supernova neutrino flavor conversions depend on the neutrino mass hierarchy. On account of Mikheyev-Smirnov-Wolfenstein effects, the full swap of $\bar{\nu}_e$ flux with the $\bar{\nu}_x$ ($x=\mu,~\tau$) one occurs in the inverted hierarchy, while such a swap does not occur in the normal hierarchy. In consequence, the ratio of high energy IBD events to NC events for the inverted hierarchy is higher than in the normal hierarchy. Since the luminosity of $\bar{\nu}_e$ is larger than that of $\nu_x$ in accretion phase while the luminosity of $\bar{\nu}_e$ becomes smaller than that of $\nu_x$ in cooling phase, we calculate this ratio for both accretion and cooling phases. By analyzing the change of this event ratio from accretion phase to cooling phase, one can determine the neutrino mass hierarchy.Comment: one column, 16 pages, 3 figure

Solving Lauricella String Scattering Amplitudes through Recurrence Relations

We show that there exist infinite number of recurrence relations valid for all energies among the open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA. Moreover, these infinite number of recurrence relations can be used to solve all the Lauricella SSA and express them in terms of one single four tachyon amplitude. These results extend the solvability of SSA at the high energy, fixed angle scattering limit and those at the Regge scattering limit discovered previously.Comment: 19 pages. v2: Fig.1 adde

String Scattering Amplitudes and Deformed Cubic String Field Theory

We study string scattering amplitudes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. The four-string scattering amplitudes with three tachyons and an arbitrary string state are calculated. The string field theory yields the string scattering amplitudes evaluated on the world sheet of string scattering whereas the coventional method, based on the first quantized theory brings us the string scattering amplitudes defined on the upper half plane. For the highest spin states, generated by the primary operators, both calculations are in perfect agreement. In this case, the string scattering amplitudes are invariant under the conformal transformation, which maps the string world sheet onto the upper half plane. If the external string states are general massive states, generated by non-primary field operators, we need to take into account carefully the conformal transformation between the world sheet and the upper half plane. We show by an explicit calculation that the string scattering amplitudes calculated by using the deformed cubic string field theory transform into those of the first quantized theory on the upper half plane by the conformal transformation, generated by the Schwarz-Christoffel mapping.Comment: 12 pages, 2 figures, references adde

The effects of worked examples presentation on sub-cognitive loads

One promising technique for helping students in fulfilling complex problem solving tasks is through learning with worked example. Although worked example approach is the most prominent technique discussed in the literature of cognitive load theory, there is still very little scientific understanding of managing the students’ sub-cognitive load, namely intrinsic, extraneous and germane load on different complexity of worked example approach especially in engineering domain. Thus, this study was conducted to investigate the effects worked examples presentation on sub-cognitive loads among electrical engineering students. In this research, the worked examples were presented in three different sequences: (i) all examples were of same level of difficulty (ii) from difficult to easy example; (iii) from easy to difficult example. Data were collected from 82 students (Condition (i) =27; Condition (ii) = 34; condition (iii) = 21) of Diploma in Electrical Engineering Program at three selected polytechnics. The inventory tool of sub cognitive load were given to students after each teaching and learning session ends. The findings suggested that worked examples presented in easy to difficult format could be one of the approaches that is more efficient to manage students’ cognitive load and effective to be applied in engineering lesson

Terminal sliding mode control strategy design for second-order nonlinear system

This study mainly focuses on the terminal sliding mode control (TSMC) strategy design, including an adaptive terminal sliding mode control (ATSMC) and an exact-estimator-based terminal sliding mode control (ETSMC) for second-order nonlinear dynamical systems. In the ATSMC system, an adaptive bound estimation for the lump uncertainty is proposed to ensure the system stability. On the other hand, an exact estimator is designed for exact estimating system uncertainties to solve the trouble of chattering phenomena caused by a sign function in ATSMC law in despite of the utilization of a fixed value or an adaptive tuning algorithm for the lumped uncertainty bound. The effectiveness of the proposed control schemes can be verified in numerical simulations.<br /