Teaching European mathematics in the Ottoman Empire during the eighteenth and nineteenth centuries: between admiration and rejection

The purpose of this study is to examine the modernizing process in the teaching of mathematics in three countries that were part of the Ottoman Empire, namely Turkey, Egypt and Tunisia, during the eighteenth and nineteenth centuries. In each case, a permanent state of war and continued European pressures made the need of reforms of military structures a vital necessity for the preservation of the state. Some of the military reforms proposed, although they met with rejection and resulted in revolts and in the dismissal of most of their initiators, did sow wholesome seeds into the educational system which would be transformed first in Muhammad Ali??s Egypt, then in Mahm??d II??s Turkey and finally in Khayr al-D??n??s Tunisia who introduced important and comprehensive reforms under which the teaching of modern mathematics played a non-negligible part. The second part outlines the transformations of the educational institutions and their role in the introduction of the new imported Western mathematics. Finally, we detail the type of mathematics taught into the newly founded military and engineering schools and insist on the efforts made by the Egyptians for translating into Arabic French textbooks.     

Convergence of distributed optimal control problems governed by elliptic variational inequalities

First, let u _g be the unique solution of an elliptic variational inequality with source term g. We establish, in the general case, the error estimate between $u_{3}(\mu)=\mu u_{g_{1}}+ (1-\mu)u_{g_{2}}$ and $u_{4}(\mu)=u_{\mu g_{1}+ (1-\mu) g_{2}}$ for ????[0,1]. Secondly, we consider a family of distributed optimal control problems governed by elliptic variational inequalities over the internal energy g for each positive heat transfer coefficient h given on a part of the boundary of the domain. For a given cost functional and using some monotony property between u ₃(??) and u ₄(??) given in Mignot (J.?Funct. Anal. 22:130?C185, 1976), we prove the strong convergence of the optimal controls and states associated to this family of distributed optimal control problems governed by elliptic variational inequalities to a limit Dirichlet distributed optimal control problem, governed also by an elliptic variational inequality, when the parameter h goes to infinity. We obtain this convergence without using the adjoint state problem (or the Mignot??s conical differentiability) which is a great advantage with respect to the proof given in Gariboldi and Tarzia (Appl. Math. Optim. 47:213?C230, 2003), for optimal control problems governed by elliptic variational equalities.     

Magnetic and structural studies on CoFe2O4 nanoparticles synthesized by co-precipitation,normal micelles and reverse micelles methods

Cobalt ferrite nanoparticles were synthesized by the chemical co-precipitation, normal micelles and reverse micelles methods of iron and cobalt chlorides. X-ray diffraction analysis, Fourier Transform Infrared (FTIR) and Vibrating Sample Magnetometer were carried out at room temperature to study the structural and magnetic properties. X-ray patterns revealed the production of a broad single cubic phase with the average particle sizes of ∼12 nm, 5 nm and 8 nm for co-precipitation, normal micelles and reverse micelles methods, respectively. The FTIR measurements between 400 and 4000 cm⁻¹ confirmed the intrinsic cation vibrations of spinel structure for each one of the three methods. Moreover, the average particle sizes were lower than the single domain size (128 nm) and higher than the super-paramagnetic size (2–3 nm) at room temperature. The results revealed that the magnetic properties depend on the particle size and cation distribution, whereas the role of particle size is more significant.     

The effect of doping three Al and N atoms on the chemical shielding tensor parameters of the boron phosphide nanotubes: A DFT study

In this work, an armchair model of the (4,4) boron phosphide nanotubes (BPNTs) with a 1-nm length and consisting of 32 B and 32 P atoms is considered to study the influence of doping three atoms of aluminum in sites of boron (B_3AlPNTs) and three atoms of nitrogen in sites of phosphors (BP_3NNTs) on the electrostatic structure properties. The mouths of nanotubes are capped by hydrogen atoms in order to saturate the dangling bonds of the boundaries and to decrease the calculation time. The structures of BPNTs, B_3AlPNTs and BP_3NNTs are optimized by performing the level of density functional theory (DFT) using 6-31G^? basis set. The optimized structures are used for calculating the chemical shielding (CS) tensors and nuclear magnetic resonance parameters such as isotropic chemical shielding (CS^I) and anisotropic chemical shielding (CS^A). The results reveal that in both models of B_3AlPNTs and BP_3NNTs by doping N atoms the chemical shielding parameters of P and B atoms, which are directly connected to the Al and N atoms decreased and the other sites significantly changed.     

Improving the characteristics of the modulation response for fiber Bragg grating Fabry–Perot lasers by optimizing model parameters

A unified and comprehensive study on the small-signal intensity and frequency modulation characteristics of a fiber Bragg grating Fabry–Perot (FBG–FP) laser are numerically investigated. The effect of injection current, temperature, external optical feedback (OFB), nonlinear gain compression factor, fiber grating (FG) parameters and spontaneous emission factor on modulation response characteristics are presented. The rate equations of the laser model are presented in the form that the effect of temperature (T) and external optical feedback (OFB) are included. The temperature dependence (TD) of laser response is calculated according to the TD of laser cavity parameters instead of directly using the well-known Parkove equation. It is shown that the optimum external fiber length (L_ext) is 3.1 cm and the optimum range of working temperature for FGFP laser is within ±2 °C from the FBG reference temperature (T_o). Also, the antireflection (AR) coating reflectivity and the linewidth enhancement factor have no significant effect on the modulation spectra. It is also show that modulation response is extremely sensitive to the OFB level, high injection current and gain compression factor. The study indicates clearly that good dynamic characteristic can be obtained by system parameters optimization.     

Comment on: “Theoretical calculation of turn-on delay time of VCSEL and effect of carriers recombination” [Opt. Laser Technol. 39 (2007) 997–1001]

Zhang et al. [Opt. Laser Technol. 39 (2007) 997–1001], through theoretical calculation, have shown that the turn-on time delay can be reduced by increasing any of the non-radiative (A_nr), radiative (B), and/or Auger recombination (C) coefficients at a constant injection current over threshold current. Here, we explain that the results presented by that paper are incorrect and the turn-on time delay increases by increasing any of the carrier recombination rate coefficients.     

Broad spectral sliced multiwavelength source with a mode locked fiber laser

A simple multi-wavelength source is demonstrated based on spectral slicing of supercontinuum (SC) light using a Sagnac loop mirror. A mode locked fiber laser with pulse width of 800 fs is employed to generate the SC in photonic crystal fiber (PCF). The SC light extending from 1200 nm up to the wavelength region above 1750 nm is obtained at the amplified pulse pump power of 30 dBm. By slicing the SC with a loop mirror, a multiwavelength comb spectrum is obtained with different channel spacing for different operating wavelength region. Spacings of 1.5, 2.3, and 2.9 nm are shown at wavelength regions of 1220, 1450, and 1730 nm, respectively. It is also observed that the signal to noise ratio (SNR) increases from 15 to 20 dB as the operating wavelength increases from 1220 to 1730 nm region.     

Stable double spacing multiwavelength Brillouin-Erbium doped fiber laser based on highly nonlinear fiber

A double frequency spaced multiwavelength Brillouin-Erbium doped fiber laser (BEDFL) with figure-of-eight cavity have been successfully developed and tested. Double frequency spacing is achieved by using a piece of 2 km of highly nonlinear fiber (HNLF) as a gain medium. Figure-of-eight configuration removes the odd order Stokes signals via a four-port circulator. Fifteen Stokes channels are simultaneously generated with a spacing of 0.154 nm that is around 20 GHz, when the Brillouin pump and 980 nm pump powers are fixed at the optimized values of 6 dBm and 40 mW, respectively. Fourteen anti stoke channels are also obtained, which are generated through four wave mixing (FWM) process in the laser cavity. The output is smooth triangular comb. The BEFL can also be tuned from 1526.5 to 1567.5 nm.     

Time delay reduction in low power ultrashort pulse and pulse stream propagation with overlapping soliton pair

Propagation of temporal 50 femtosecond pulse and pulse stream, which is realized by substituting each input pulse with reduced-order overlapping soliton pair, is investigated through short standard single-mode fiber. For the pulse stream the initial inter-pulse delay is selected to be 227 fs and the pulses are to be perturbed to avoid collision with the neighboring pulses. This method reduces the pulse time delay and properly retains the amplitude despite tradeoff between these two. This is a significant improvement in the low power femtosecond pulse and pulse stream propagation.     

Impact of Green Chitosan Nanoparticles Fabricated from Shrimp Processing Waste as a Source of Nano Nitrogen Fertilizers on the Yield Quantity and Quality of Wheat (Triticum aestivum L.) Cultivars

Waste from crustaceans has adverse effects on the environment. In this respect, shrimp waste was valorized for producing chitosan nanoparticles as a source for eco-friendly nano-nitrogen fertilizer. The application of nano-nitrogen fertilizers is a valuable alternative approach in agriculture due to its potential for reducing the application of mineral nitrogen fertilizers and increasing yield quality and quantity, thereby helping to reduce the worldwide food shortage. Chitosan nanoparticles were foliar sprayed at three volumes (0, 7, and 14 L/ha) and compared with mineral nitrogen fertilizer (M-N) sprayed at three volumes (0, 120, and 240 kg N/ha) and their combination on two wheat cultivars (Misr-1 and Gemaiza-11) during two consecutive seasons (2019/2020 and 2020/2021) in order to evaluate the agronomic response. The synthesized chitosan nanoparticles displayed characteristic bands of both Nan-N and urea/chitosan from 500–4000 cm⁻¹. They are stable and have a huge surface area of 73.21 m² g⁻¹. The results revealed significant differences among wheat cultivars, fertilization applications, individual or combined, and their interactions for yield-contributing traits. Foliar application of nano-nitrogen fertilizer at 14 L/ha combined with mineral fertilizer at 240 kg/ha significantly increased total chlorophyll content by 41 and 31% compared to control; concerning plant height, the two cultivars recorded the tallest plants (86.2 and 86.5 cm) compared to control. On the other hand, the heaviest 1000-grain weight (55.8 and 57.4 g) was recorded with treatment of 120 kg Mn-N and 14 L Nan-N/ha compared to the control (47.6 and 45.5 g). The Misr-1 cultivar achieved the highest values for grain yield and nitrogen (1.30 and 1.91 mg/L) and potassium (9.87 and 9.81 mg/L) in the two studied seasons when foliarly sprayed with the combination of 120 kg Mn-N/ha + 14 L Nan-N/ha compared to the Gemaiza-11 cultivar. It can be concluded that Misr-1 exhibited higher levels of total chlorophyll content, spike length, 100-grain weight, grain yield in kg/ha, and nitrogen and potassium. However, Gemaiza-11 displayed higher biomass and straw yield values, plant height, and sodium concentration values. It could be economically recommended to use the application of 120 kg Mn-N/ha + 14 L Nan-N/ha on the Misr-1 cultivar to achieve the highest crop yield.