Search results for: secondary electrons

Authors: Maurizio Dapor, Isabel Abril, Pablo de Vera, Rafael Garcia-Molina

Abstract:

The ionization yield of ion tracks in polymers and bio-molecular systems reaches a maximum, known as the Bragg peak, close to the end of the ion trajectories. Along the path of the ions through the materials, many electrons are generated, which produce a cascade of further ionizations and, consequently, a shower of secondary electrons. Among these, very low energy secondary electrons can produce damage in the biomolecules by dissociative electron attachment. This work deals with the calculation of the energy distribution of electrons produced by protons in a sample of polymethylmethacrylate (PMMA), a material that is used as a phantom for living tissues in hadron therapy. PMMA is also of relevance for microelectronics in CMOS technologies and as a photoresist mask in electron beam lithography. We present a Monte Carlo code that, starting from a realistic description of the energy distribution of the electrons ejected by protons moving through PMMA, simulates the entire cascade of generated secondary electrons. By following in detail the motion of all these electrons, we find the radial distribution of the energy that they deposit in PMMA for several initial proton energies characteristic of the Bragg peak.

Keywords: Monte Carlo method, secondary electrons, energetic ions, ion-beam cancer therapy, ionization cross section, polymethylmethacrylate, proton beams, secondary electrons, radial energy distribution.

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Authors: Hamid Reza Pakzad

Abstract:

Ion-acoustic solitary waves in a plasma with nonthermal electrons, thermal positrons and warm ions are investigated using Sagdeev-s pseudopotential technique. We study the effects of non-thermal electrons and ion temperature on solitons and show both negative and positive potential waves are possible.

Keywords: Ion acoustic waves, Solitons, Nonlinear phenomena, Sagdeev potential

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Authors: Basudev Ghosh, Sreyasi Banerjee

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Using the pseudopotential technique the Sagdeev potential equation has been derived in a plasma consisting of twotemperature nonisothermal electrons, negatively charged dust grains and warm positive ions. The study shows that the presence of nonisothermal two-temperature electrons and charged dust grains have significant effects on the excitation and structure of the ionacoustic double layers in the model plasma under consideration. Only compressive type double layer is obtained in the present plasma model. The double layer solution has also been obtained by including higher order nonlinearity and nonisothermality, which is shown to modify the amplitude and deform the shape of the double layer.

Keywords: Two temperature non-isothermal electrons and charged dust grains.

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Authors: Basudev Ghosh, Sreyasi Banerjee

Abstract:

Using pseudo potential method arbitrary amplitude ion-acoustic solitary waves have been theoretically studied in a collisionless plasma consisting of warm drifting positive ions, Boltzmann positrons and nonthermal electrons. Ion-acoustic solitary wave solutions have been obtained and the dependence of the solitary wave profile on different plasma parameters has been studied numerically. Lower and higher order compressive and rarefactive solitary waves are observed in presence of positrons, nonthermal electrons, ion drift velocity and finite ion temperature. Inclusion of higher order nonlinearity is shown to have significant correction to the solitary wave profile for the same values of plasma parameters.

Keywords: Ion-acoustic waves, Nonthermal electrons, Sagdeev potential, Solitary waves.

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Authors: Djemai Bara, Mohamed Faouzi Mahboub, Djamila Bennaceur-Doumaz

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In this work, the role of the preformed plasma created on the front face of a target, irradiated by a high intensity short pulse laser, in the framework of ion acceleration process, modeled by Target Normal Sheath Acceleration (TNSA) mechanism, is studied. This plasma is composed of cold ions governed by fluid equations and non-thermal & trapped with densities represented by a "Cairns-Gurevich" equation. The self-similar solution of the equations shows that electronic trapping and the presence of non-thermal electrons in the pre-plasma are both responsible in ion acceleration as long as the proportion of energetic electrons is not too high. In the case where the majority of electrons are energetic, the electrons are accelerated directly by the ponderomotive force of the laser without the intermediate of an accelerating plasma wave.

Keywords: Cairns-Gurevich Equation, ion acceleration, plasma expansion, pre-plasma.

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Authors: S.N.Paul, G.Pakira, B.Paul, B.Ghosh

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Nonlinear propagation of ion-acoustic waves in a selfgravitating dusty plasma consisting of warm positive ions, isothermal two-temperature electrons and negatively charged dust particles having charge fluctuations is studied using the reductive perturbation method. It is shown that the nonlinear propagation of ion-acoustic waves in such plasma can be described by an uncoupled third order partial differential equation which is a modified form of the usual Korteweg-deVries (KdV) equation. From this nonlinear equation, a new type of solution for the ion-acoustic wave is obtained. The effects of two-temperature electrons, gravity and dust charge fluctuations on the ion-acoustic solitary waves are discussed with possible applications.

Keywords: Charge fluctuations, gravitating dusty plasma, Ionacoustic solitary wave, Two-temperature electrons

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Authors: N. Kekelidze, B. Kvirkvelia, E. Khutsishvili, T. Qamushadze, D. Kekelidze, R. Kobaidze, Z. Chubinishvili, N. Qobulashvili, G. Kekelidze

Abstract:

On the basis of InAs, InP and their InP_xAs_1-x solid solutions, the technologies were developed and materials were created where the electron concentration and optical and thermoelectric properties do not change under the irradiation with Ф = 2∙10¹⁸ n/cm² fluences of fast neutrons high-energy electrons (50 MeV, Ф = 6·10¹⁷ e/cm²) and 3 MeV electrons with fluence Ф = 3∙10¹⁸ e/cm². The problem of obtaining such material has been solved, in which under hard irradiation the mobility of the electrons does not decrease, but increases. This material is characterized by high thermal stability up to T = 700 °C. The complex process of defects formation has been analyzed and shown that, despite of hard irradiation, the essential properties of investigated materials are mainly determined by point type defects.

Keywords: InAs, InP, solid solutions, irradiation.

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Authors: Hamid Reza Pakzad

Abstract:

Dust acoustic solitary waves are studied in warm dusty plasma containing negatively charged dusts, nonthermal ions and Boltzmann distributed electrons. Sagdeev pseudopotential method is used in order to investigate solitary wave solutions in the plasmas. The existence of compressive and rarefractive solitons is studied.

Keywords: Nonthermal, Soliton, Dust, Sagdeev potential

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Authors: S. N. Ekbote, G. K. Padam, Manju Arora

Abstract:

Electron spin resonance (ESR) spectroscopic investigations of (Bi, Pb)2Sr2Ca2Cu3O10-x (Bi-2223) bulk samples were carried out in both the normal and superconducting states. A broad asymmetric resonance signal with side signals is obtained in the normal state, and all of them disappear in the superconducting state. The temperature and angular orientation effects on these signals suggest that the broad asymmetric signal arises from electron spin resonance of conduction electrons (CESR) and the side signals from exchange interactions as Platzman-Wolff type spin waves. The disappearance of CESR and spin waves in a superconducting state demonstrates the role of exchange interactions in Cooper pair formation.

Keywords: Bi-2223 superconductor, electron spin resonance of conduction electrons, electron spin resonance, Exchange interactions, spin waves.

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Authors: Sherif S. Nafee, Amir K. Al-Ramady, Salem S. Shaheen

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Evaluated nuclear decay data for the 217Po nuclide is presented in the present work. These data include recommended values for the half-life T1/2, α-, β-- and γ-ray emission energies and probabilities. Decay data from 221Rn α and 217Bi β—decays are presented. Q(α) has been updated based on the recent published work of the Atomic Mass Evaluation AME2012. In addition, the logft values were calculated using the Logft program from the ENSDF evaluation package. Moreover, the total internal conversion electrons and the K-shell to L-shell and L-shell to M-shell and to N-shell conversion electrons ratios K/L, L/M and L/N have been calculated using Bricc program. Meanwhile, recommendation values or the multi-polarities have been assigned based on recently measurement yield a better intensity balance at the 254 keV and 264 keV gamma transitions.

Keywords: Atomic Mass Evaluation, Nuclear Data Evaluation, Total Electron Conversion Electrons.

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Authors: Hoang Van Ngoc, Nguyen Vu Nhan, Nguyen Quang Bau

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The light-effect in cylindrical quantum wire with an infinite potential for the case of electrons, optical phonon scattering, is studied based on the quantum kinetic equation. The density of the direct current in a cylindrical quantum wire by a linearly polarized electromagnetic wave, a DC electric field, and an intense laser field is calculated. Analytic expressions for the density of the direct current are studied as a function of the frequency of the laser radiation field, the frequency of the linearly polarized electromagnetic wave, the temperature of system, and the size of quantum wire. The density of the direct current in cylindrical quantum wire with an infinite potential for the case of electrons – optical phonon scattering is nonlinearly dependent on the frequency of the linearly polarized electromagnetic wave. The analytic expressions are numerically evaluated and plotted for a specific quantum wire, GaAs/GaAsAl.

Keywords: The light-effect, cylindrical quantum wire with an infinite potential, the density of the direct current, electrons - optical phonon scattering.

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Authors: Nikol Žižková, Šárka Keprdová, Rostislav Drochytka

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The paper focuses on the study of the properties of cement-based composites produced using secondary crystallization (crystalline additive). In this study, cement mortar made with secondary crystallization was exposed to an aggressive environment and the influence of secondary crystallization on the degradation of the cementitious composite was investigated. The results indicate that the crystalline additive contributed to increasing the resistance of the cement-based composite to the attack of the selected environments (sodium sulphate solution and ammonium chloride solution).

Keywords: Secondary crystallization, cement-based composites, durability.

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Authors: N. Basanta Singh, Sanjoy Deb, G. P Mishra, Subir Kumar Sarkar

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Carrier mobility has become the most important characteristic of high speed low dimensional devices. Due to development of very fast switching semiconductor devices, speed of computer and communication equipment has been increasing day by day and will continue to do so in future. As the response of any device depends on the carrier motion within the devices, extensive studies of carrier mobility in the devices has been established essential for the growth in the field of low dimensional devices. Small-signal ac transport of degenerate two-dimensional hot electrons in GaAs quantum wells is studied here incorporating deformation potential acoustic, polar optic and ionized impurity scattering in the framework of heated drifted Fermi-Dirac carrier distribution. Delta doping is considered in the calculations to investigate the effects of double delta doping on millimeter and submillimeter wave response of two dimensional hot electrons in GaAs nanostructures. The inclusion of delta doping is found to enhance considerably the two dimensional electron density which in turn improves the carrier mobility (both ac and dc) values in the GaAs quantum wells thereby providing scope of getting higher speed devices in future.

Keywords: Carrier mobility, Delta doping, Hot carriers, Quantum wells.

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Authors: Ioan Rusu

Abstract:

Let us consider that the entire universe is composed of a single hydrogen atom within which the electron is moving around the proton. In this case, according to classical theories of physics, radiation, photons respectively, should be absorbed by the electron. Depending on the number of photons absorbed, the electron radius of rotation around the proton is established. Until now, the principle of photons absorption by electrons and the electron transition to a new energy level, namely to a higher radius of rotation around the proton, is not clarified in physics. This paper aims to demonstrate that radiation, photons respectively, have mass and negative electrostatic charge similar to electrons but infinitely smaller. The experiments which demonstrate this theory are simple: thermal expansion, photoelectric effect and thermonuclear reaction.

Keywords: Electrostatic, electron, proton, photon, radiation.

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Authors: Nguyen Quang Bau, Nguyen Thu Huong, Dang Thi Thanh Thuy

Abstract:

The analytic expression for the Hall Coefficient (HC) caused by the confined electrons in the presence of a strong electromagnetic wave (EMW) including the effect of phonon confinement in rectangular quantum wires (RQWs) is calculated by using the quantum kinetic equation for electrons in the case of electron - optical phonon scattering. It is because the expression of the HC for the confined phonon case contains indexes m, m’ which are specific to the phonon confinement. The expression in a RQW is different from that for the case of unconfined phonons in a RQW or in 2D. The results are numerically calculated and discussed for a GaAs/GaAsAl RQW. The numerical results show that HC in a RQW can have both negative and positive values. This is different from the case of the absence of EMW and the case presence of EMW including the effect of phonon unconfinement in a RQW. These results are also compared with those in the case of unconfined phonons in a RQW and confined phonons in a quantum well. The conductivity in the case of confined phonon has more resonance peaks compared with that in case of unconfined phonons in a RQW. This new property is the same in quantum well. All results are compared with the case of unconfined phonons to see differences.

Keywords: Hall coefficient, rectangular quantum wires, electron-optical phonon interaction, quantum kinetic equation, confined phonons.

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Authors: N. Kulakova

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Thisresearch paper is dedicated to an actual issue in Latvia and in the whole European Union – development of the secondary materials management. The goal of this paper is to research the development of the secondary materials management in Latvia as a result to point out its main positive aspects and problems. In this research paper the author regards following issues: significance of the secondary materials management, current situation of the waste generation and utilization in Latvia comparing with other EU Member States, main problems and positive aspects of the secondary materials management in Latvia. The research author concludes that in last ten years a great work is done to develop the secondary materials market. Nevertheless following improvements are necessary: implementation of the packaging deposit system, development of the separate waste collection, increasing of the recycling capacity.

Keywords: sustainable development, secondary materials, separate waste collection, packaging deposit system.

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Authors: Salem El-tohami Ashoor

Abstract:

Here, we have shown the reaction of [Cr(ArN(CH2)3NAr)2Cl2] (1) where (Ar = 2,6-Pri 2C6H3) and in presence of NaCp (2) (Cp= C5H5 = cyclopentadien), with a center coordination η5 interaction between Cp as co-ligand and chromium metal center, for optimization we used density functional theory (DFT), under methods, explicitly including electrons correlations, for the final calculations as MB3LYP (Becke) (Lee–Yang–Parr) level of theory we used to obtain more exact results. This complex was calculated as electronic energy for molecular system, because the calculation accounting all electrons correlations interactions. The optimised of [Cr(ArN(CH2)3NAr)2(η5-Cp)] (Ar = 2,6-Pri2C6H3 and Cp = C5H5) was found to be thermally stable. By using Dewar-Chatt-Duncanson model, as a basis of the molecular orbital (MO) analysis and showed the highest occupied molecular orbital (HOMO) and lowest occupied molecular orbital LUMO.

Keywords: Chromium (III) cyclopentadienyl complexes, DFT, MO, HOMO, LUMO.

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Authors: M. J. Park, S. H. Lee, C. H. Lee, O. M. Kwon

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This paper studies a secondary voltage control framework of the microgrids based on the consensus for a communication network of multiagent. The proposed control is designed by the communication network with one-way links. The communication network is modeled by a directed graph. At this time, the concept of sampling is considered as the communication constraint among each distributed generator in the microgrids. To analyze the sampling effects on the secondary voltage control of the microgrids, by using Lyapunov theory and some mathematical techniques, the sufficient condition for such problem will be established regarding linear matrix inequality (LMI). Finally, some simulation results are given to illustrate the necessity of the consideration of the sampling effects on the secondary voltage control of the microgrids.

Keywords: Microgrids, secondary control, multiagent, sampling, LMI.

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Authors: Sapan Mohan Saini

Abstract:

We report the electronic structure and optical properties of NdF3 compound. Our calculations are based on density functional theory (DFT) using the full potential linearized augmented plane wave (FPLAPW) method with the inclusion of spin orbit coupling. We employed the local spin density approximation (LSDA) and Coulomb-corrected local spin density approximation, known for treating the highly correlated 4f electrons properly, is able to reproduce the correct insulating ground state. We find that the standard LSDA approach is incapable of correctly describing the electronic properties of such materials since it positions the f-bands incorrectly resulting in an incorrect metallic ground state. On the other hand, LSDA + U approximation, known for treating the highly correlated 4f electrons properly, is able to reproduce the correct insulating ground state. Interestingly, however, we do not find any significant differences in the optical properties calculated using LSDA, and LSDA + U suggesting that the 4f electrons do not play a decisive role in the optical properties of these compounds. The reflectivity for NdF3 compound stays low till 7 eV which is consistent with their large energy gaps. The calculated energy gaps are in good agreement with experiments. Our calculated reflectivity compares well with the experimental data and the results are analyzed in the light of band to band transitions.

Keywords: FPLAPW Method, optical properties, rare earthtrifluorides LSDA+U

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Authors: Daniel Santos, Bruno Ribeiro, Marco Amato, Antonio Fonseca

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In this paper we discuss the behaviour of the longitudinal modes of a magnetized non collisional plasma subjected to an external electromagnetic field. We apply a semiclassical formalism, with the electrons being studied in a quantum mechanical viewpoint whereas the electromagnetic field in the classical context. We calculate the dielectric function in order to obtains the modes and found that, unlike the Bernstein modes, the presence of radiation induces oscillations around the cyclotron harmonics, which are smoothed as the energy stored in the radiation field becomes small compared to the thermal energy of the electrons. We analyze the influence of the number of photon involved in the electronic transitions between the Landau levels and how the parameters such as the external fields strength, plasma density and temperature affect the dispersion relation

Keywords: Collective oscillations, External fields, Dispersion relation.

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Authors: Shih-Yi Chao

Abstract:

The similarity comparison of RNA secondary structures is important in studying the functions of RNAs. In recent years, most existing tools represent the secondary structures by tree-based presentation and calculate the similarity by tree alignment distance. Different to previous approaches, we propose a new method based on maximum clique detection algorithm to extract the maximum common structural elements in compared RNA secondary structures. A new graph-based similarity measurement and maximum common subgraph detection procedures for comparing purely RNA secondary structures is introduced. Given two RNA secondary structures, the proposed algorithm consists of a process to determine the score of the structural similarity, followed by comparing vertices labelling, the labelled edges and the exact degree of each vertex. The proposed algorithm also consists of a process to extract the common structural elements between compared secondary structures based on a proposed maximum clique detection of the problem. This graph-based model also can work with NC-IUB code to perform the pattern-based searching. Therefore, it can be used to identify functional RNA motifs from database or to extract common substructures between complex RNA secondary structures. We have proved the performance of this proposed algorithm by experimental results. It provides a new idea of comparing RNA secondary structures. This tool is helpful to those who are interested in structural bioinformatics.

Keywords: Clique detection, labeled vertices, RNA secondary structures, subgraph, similarity.

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Authors: J. Kosikova, B. Vacenovska, M. Vyhnankova

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The paper reports on the subject of recycling and further use of secondary raw materials obtained from solar panels, which is becoming a very up to date topic in recent years. Recycling these panels is very difficult and complex, and the use of resulting secondary raw materials is still not fully resolved. Within the research carried out at the Brno University of Technology, new polymer materials used for industrial floors are being developed. Secondary raw materials are incorporated into these polymers as fillers. One of the tested filler materials was glass obtained from solar panels. The following text describes procedures and results of the tests that were performed on these materials, confirming the possibility of the use of solar panel glass in industrial polymer flooring systems.

Keywords: Fillers, industrial floors, recycling, secondary raw material, solar panel.

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Authors: Hezlina Mohd Hashim, Abdul Mutalib Embong, Zullina H. Shaari

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This study analyses the perceptions of secondary school students about the accounting profession in Malaysia. Fifty five form three and form four students who are taking accounting/commerce subjects were met. Individual-s perception data were collected through questionnaires. The results at the secondary school level suggest that the stereotypical negative image of the accountant ends, with students expressing the positive view of the work of an accountant. There were also gender differences in perceiving the accounting profession. Overall, the results of the study suggest that we are now in line in projecting positive and accurate perceptions of the accounting profession to secondary school students.

Keywords: Perceptions, secondary school students, accounting profession, Malaysia.

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Authors: Verónica Diaz Quezada

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This research examines the teaching models used by secondary math teachers when teaching logarithmic, quadratic and exponential functions. For this, descriptive case studies have been carried out on 5 secondary teachers. These teachers have been chosen from 3 scientific-humanistic and technical schools, in Chile. Data have been obtained through non-participant class observation and the application of a questionnaire and a rubric to teachers. According to the results, the didactic model that prevails is the one that starts with an interactive strategy, moves to a more content-based structure, and ends with a reinforcement stage. Nonetheless, there is always influence from teachers, their methods, and the group of students.

Keywords: Teaching models, math teachers, functions, secondary education.

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Authors: Douangmala Kounsana, Xiang Wen, Toru Takahashi

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After a strong earthquake occurs, a secondary disaster due to strong aftershocks, flood, landslide or heavy snow can possible to occur and the secondary disaster due to resident-s action also can possible to happen. However, until now seldom researchers have paid attention at it. This paper focused on the Inhabitant-s action after the strong earthquake occurs when a terrible even becomes calm. An inappropriate behavior of people with disadvantaged climate after the worse earthquake can bring a tragedy to their life.

Keywords: Sichuan Earthquake, Secondary Disaster, Inhabitant's Action, inappropriate behavior.

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Authors: Pamela L. Knox, Linda R. Guthrie

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Trauma in early life is widely regarded as a cause for adult mental health problems. This study explores the role of secondary trauma on later functioning in a sample of 359 university students enrolled in undergraduate psychology classes in the United States. Participants were initially divided into four groups based on 1) having directly experienced trauma (assaultive violence), 2) having directly experienced trauma and secondary traumatization through the unanticipated death of a close friend or family member or witnessing of an injury or shocking even), 3) having no experience of direct trauma but having experienced indirect trauma (secondary trauma), or 4) reporting no exposure. Participants completed a battery of measures on concepts associated with psychological functioning which included measures of psychological well-being, problem solving, coping and resiliency. Findings discuss differences in psychological functioning and resilience based on participants who experienced secondary traumatization and assaultive violence versus secondary traumatization alone.

Keywords: Psychological Functioning, Resiliency, Trauma, Abuse

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Authors: Ellen. A. Kalinga

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Moodle is an open source learning management system that enables creation of a powerful and flexible learning environment. Many organizations, especially learning institutions have customized Moodle open source LMS for their own use. In general open source LMSs are of great interest due to many advantages they offer in terms of cost, usage and freedom to customize to fit a particular context. Tanzania Secondary School e- Learning (TanSSe-L) system is the learning management system for Tanzania secondary schools. TanSSe-L system was developed using a number of methods, one of them being customization of Moodle Open Source LMS. This paper presents few areas on the way Moodle OS LMS was customized to produce a functional TanSSe-L system fitted to the requirements and specifications of Tanzania secondary schools’ context.

Keywords: LMS, Moodle, e-Learning, Tanzania, Secondary school.

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Authors: V. Paployan, K. Madoyan, A. Melikyan, H. Minassian

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In this paper, we calculate the two-photon ionization (TPI) cross-section for pump-probe scheme in Ag neutral cluster. The pump photon energy is assumed to be close to the surface plasmon (SP) energy of cluster in dielectric media. Due to this choice, the pump wave excites collective oscillations of electrons-SP and the probe wave causes ionization of the cluster. Since the interband transition energy in Ag exceeds the SP resonance energy, the main contribution into the TPI comes from the latter. The advantage of Ag clusters as compared to the other noble metals is that the SP resonance in silver cluster is much sharper because of peculiarities of its dielectric function. The calculations are performed by separating the coordinates of electrons corresponding to the collective oscillations and the individual motion that allows taking into account the resonance contribution of excited SP oscillations. It is shown that the ionization cross section increases by two orders of magnitude if the energy of the pump photon matches the surface plasmon energy in the cluster.

Keywords: Resonance enhancement, silver clusters, surface plasmon, two-photon ionization.

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Authors: Cory A. Bennett

Abstract:

Teaching and learning through the use of discourse support students’ conceptual understanding by attending to key concepts and relationships. One discourse structure used in primary classrooms is number talks wherein students mentally calculate, discuss, and reason about the appropriateness and efficiency of their strategies. In the secondary mathematics classroom, the mathematics understudy does not often lend itself to mental calculations yet learning to reason, and articulate reasoning, is central to learning mathematics. This qualitative case study discusses how one secondary school in the Middle East adapted the number talk protocol for secondary mathematics classrooms. Several challenges in implementing ‘reasoning talks’ became apparent including shifting current discourse protocols and practices to a more student-centric model, accurately recording and probing student thinking, and specifically attending to reasoning rather than computations.

Keywords: Discourse, reasoning, secondary mathematics, teacher development.

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Authors: Rui Yin, Ming Yin, Yang Wang

Abstract:

For a rotational reference frame of the theory of special relativity, the critical radius is defined as the distance from the axis to the point where the tangential velocity is equal to the speed of light, and the critical cylinder as the set of all points separated from the axis by this critical radius. Based on these terms, two relativistic effects of rotation are discovered: (i) the tangential velocity in the region of Outside Critical Cylinder (OCC) is not superluminal, due to the existence of space-time exchange; (ii) some of the physical quantities of the rotational body have an opposite mathematic sign at OCC versus those at Inside Critical Cylinder (ICC), which is termed as the Critical Cylindrical Effect (CCE). The laboratory experiments demonstrate that the repulsive force exerted on an anion by electrons will change to an attractive force by the electrons in precession while the anion is at OCC of the precession. 36 screenshots from four experimental videos are provided. Theoretical proofs for both space-time exchange and CCE are then presented. The CCEs of field force are also discussed.

Keywords: Critical radius, critical cylindrical effect, special relativity, space-time exchange.

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