Design considerations of depressed clad W-shaped single mode dispersion compensating fibers

Dispersion compensating fibers (DCFs) are being widely used as dispersion compensation techniques because of its superior characteristics. This work reports the theoretical modelling of a single mode DCF having W-shaped shallow as well as deeply depressed clad profile. The DCFs have been designed and optimized by suitable adjusting different fiber parameters such as, central relative index difference (Δ⁺), inner core radius (a), depression depth parameter (ρ), normalized end position of the depressed clad (p), etc. at a given spot size . The figure of merit (FOM) characteristics including the bend loss as well as other losses associated with fiber manufacturing technique have been thoroughly investigated. Performances of these DCFs for recent wavelength division multiplexing (WDM) transmission system have also been discussed. By adjusting different fiber parameters, the effective core area (A_eff) of the above DCFs can be controlled to minimize the effect of non-linearities on them.     

求一类多元多峰函数全局极小的区间斜率方法

Based on the interval analysis, an interval slope method is proposed for finding all global minimizers of a several peaks function f on domain X^0包含于R^n, which is given by interval slope discard tests and interval extension of objective function.Numerical results of representative test functions show that this method is practical and effective.     

Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

Effective reaction rates of a thin catalyst layer

The catalyst layer in a fuel cell can be described with a system of reaction diffusion eq uations for the oxygen concentration and the protonic overpotential. The Tafel law gives an exponential expression for the reaction rate, and the Tafel slope is a coefficient in this law. We present a rigorous thin layer analysis for two reaction regimes. In the case of thin catalyst layers and bounded potentials, the original Tafel law enters as an effective boundary condition. Instead, in the case of large protonic overpotentials, we derive an exponential law that contains the doubled Tafel slope. Copyright © 2009 John Wiley & Sons, Ltd.     

Effects of inclined impermeable bed on the turbulent characteristics of the flow using particle image velocimetry

In this study, the turbulent characteristics of the flow in an open channel with horizontal and inclined impermeable beds were studied experimentally using two-dimensional particle image velocimetry (PIV). The experiments were conducted in a channel of 6.5 m in length, 7.5 cm in width and 25 cm in height. The slope of the channel was S = 0 for the horizontal impermeable bed and for S = ?0.002, S = ?0.004 and S = ?0.006 for the inclined impermeable bed. Hydraulic characteristics such as distributions of velocities, turbulent intensities and Reynolds stress are investigated at a fine resolution using the PIV. Velocity is measured above the horizontal and inclined impermeable bed for the same different heights (h = 5, 7, 9, 11 and 13 cm) and for the same different discharges (Q = 0.735, 0.845 and 0.970 lt/s). Results show that the channel slope influences significantly near the impermeable bed but not near the free surface the variation of turbulent characteristics of the flow and also the alteration of the channel slope from ?0.002 to ?0.006 doesn't influence the variation of turbulent characteristics of the flow, which are the longitudinal turbulent intensity u′U_*, the vertical turbulent intensity v′/U_* and the turbulent kinetic energy. The channel slope doesn't influence the Reynolds stress.     

Laser Light and X-Ray Diffraction Studies of Oriented Isotactic Polypropylene (iPP) Prepared by Temperature Slope Crystallization

Isotactic polypropylene (iPP) film was melt-crystallized in a temperature gradient. The iPP film showed well oriented α- and β-crystalline textures along the gradient. The crystalline structure, phase transition boundary and lamellar twisting were examined by X-ray diffraction and laser light diffraction (LLD). On the α-β boundary, LLD shows a sharp streak perpendicular to the boundary, where the a-axis of the β-crystal is oriented perpendicular to the temperature gradient. Apart from the boundary, the a-axis of the β-crystal becomes parallel to the gradient. The β-crystal shows lamellar twisting with a pitch of 200 μm at room temperature. When heated the β-crystal, the lamellar distance of 295Å at room temperature decreases to 285Å at 80–100°C and then increases to more than 300Å above 120°C. During the heating, the value of the twist period increases from 200 to 210 μm at 90–100°C, and then to above 224 μm at 140°C. The increase of the twist period is related to the increasing crystalline thickness of the β-lamellae.     

Exploring mathematical connections of pre-university students through tasks involving rates of change

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures, representations or meanings or with other disciplines or the real-world. Four tasks were proposed to the 33 pre-university students that participated in this research; the central concept of the first task is the slope, the last three tasks contain concepts like velocity, speed and acceleration. Task-based interviews were conducted to collect data and later analysed with thematic analysis. Results showed most of the students made mathematical connections of the procedural type, the mathematical connections of the common features type are made in smaller quantities and the mathematical connection of the generalization type is scarcely made. Furthermore, students considered slope as a concept disconnected from velocity, speed and acceleration.     

pH-sensing properties of PbO<Subscript>2</Subscript> thin film electrodeposited on carbon ceramic electrode

In this paper, a new highly sensitive potentiometric pH electrode is proposed based on the solid-state PbO₂ film electrodeposited on carbon ceramic electrode (CCE). Two different crystal structures of PbO₂, α and β were examined and the similar results were obtained. Moreover, the experimental results obtained for the proposed pH sensor and a conventional glass pH electrode were in good agreement. The electromotive force (emf) signal between the pH-sensitive PbO₂-coated CCE and SCE reference electrode was linear over the pH range of 1.5–12.5. Near-Nernstian slopes of −64.82 and −57.85 mV/pH unit were obtained for α- and β-PbO₂ electrodes, respectively. The interferences of some mono-valence and multi-valence ions on potentiometric response of the sensor were studied. The proposed pH sensor displayed high ion selectivity with respect to K⁺, Na⁺, Ca²⁺, and Li⁺, with log values around −12 and has a working lifetime of about 30 days. Key parameters important for the pH sensor performance, including kind of PbO₂ film, selectivity, response time, stability, and reproducibility, have been characterized. The proposed electrode showed a good efficiency for direct pH-metry after calibration and pH-metric titrations without calibration step. The response time was about 1 s in acidic medium and less than 30 s in alkaline solutions. The pH values of complex matrix samples such as fruit juices measured by the proposed sensor and a conventional glass pH electrode were in good agreement.     

New figuring model based on surface slope profile for grazing‐incidence reflective optics

Surface slope profile is widely used in the metrology of grazing‐incidence reflective optics instead of surface height profile. Nevertheless, the theoretical and experimental model currently used in deterministic optical figuring processes is based on surface height, not on surface slope. This means that the raw slope profile data from metrology need to be converted to height profile to perform the current height‐based figuring processes. The inevitable measurement noise in the raw slope data will introduce significant cumulative error in the resultant height profiles. As a consequence, this conversion will degrade the determinism of the figuring processes, and will have an impact on the ultimate surface figuring results. To overcome this problem, an innovative figuring model is proposed, which directly uses the raw slope profile data instead of the usual height data as input for the deterministic process. In this paper, first the influence of the measurement noise on the resultant height profile is analyzed, and then a new model is presented; finally a demonstration experiment is carried out using a one‐dimensional ion beam figuring process to demonstrate the validity of our approach.     

Steep pulsed electric fields modulate cell apoptosis through the change of intracellular calcium concentration

A steep electric pulsed field with low intensity (150–250 V/cm) and relative long time (10 min) was applied to adherent liver cancer cell line SMMC-7721 and the liver cell line HL-7702. Results showed that the electric field with intensity of 200 and 250 V/cm could trigger cell apoptosis, whereas the SMMC-7721 cell was more sensitive to the electric stimulation than the HL-7702 cell. Laser Scanning Confocal Microscope (LSCM) was used to measuring the real-time change of cytosolic free Ca²⁺ concentration. When cells were exposed electric pulses with 100 V/cm intensity for 10 min, there was no significant change of intracellular calcium concentration. With the intensity increased to 200 and 250 V/cm, intracellular calcium concentration decreased significantly. Results demonstrated the relationship between the apoptosis and change of intracellular calcium concentration. And the steep electric pulsed field can be used to the cancer therapy.