A note on the integrable discretization of the nonlinear Schr\"odinger equation

We revisit integrable discretizations for the nonlinear Schr\"odinger equation due to Ablowitz and Ladik. We demonstrate how their main drawback, the non-locality, can be overcome. Namely, we factorize the non-local difference scheme into the product of local ones. This must improve the performance of the scheme in the numerical computations dramatically. Using the equivalence of the Ablowitz--Ladik and the relativistic Toda hierarchies, we find the interpolating Hamiltonians for the local schemes and show how to solve them in terms of matrix factorizations.Comment: 24 pages, LaTeX, revised and extended versio

Utilization of Low Cost Waste Material Bagasse Fly Ash in Removing of CU2+, NI2+, ZN2+ and CR3+ from the Industrial Waste Water

Bagasse fly ash, a waste material generated in sugar industry, collected from a local sugar Firm at Kom-Ombo district (42Km - distance, on the northern direction, from the mid city of Aswan ), Aswan Governorate, Egypt was utilized as a low cost and effective adsorbing surface for the removal of Cu2+, Ni2+, Zn2+ and Cr3+ from the industrial wastewater. The adsorption capacity was followed as a function of pH, adsorbent dose, metal ion concentration, shaking time and divers ions. Under the optimum conditions used, more than 95% of some of the ions under study were successfully removed. The data were fitted utilizing both Freundlich and Langmuir isotherms

Interaction of Nonlinear Schr\"odinger Solitons with an External Potential

Employing a particularly suitable higher order symplectic integration algorithm, we integrate the 1-$d$ nonlinear Schr\"odinger equation numerically for solitons moving in external potentials. In particular, we study the scattering off an interface separating two regions of constant potential. We find that the soliton can break up into two solitons, eventually accompanied by radiation of non-solitary waves. Reflection coefficients and inelasticities are computed as functions of the height of the potential step and of its steepness.Comment: 14 pages, uuencoded PS-file including 10 figure

Pollination and serological studies on Egyptian grapes

White Roumi grape (Vitis vinifera L.) produces low yield when planted alone. Both pollination and serological tests indicated that this problem appears to be due to the presence of partial self-incompa·tibility in its flowers. Cross-pollination is necessary in White Roumi vineyards in order to obtain abundant yields and to improve berry quality.Different degrees of cross-compatibility were found between White Roumi flowers and four grape pollina.tors. Evaluating these pollinators indicated that Red Roumi and Thompson Seedless pollen gave the highest berry set and fruiting. BezEl-N akah resulted in early ripening berries possessing the largest weight and size. Ghariby proved to be an unsuitable pollinator of White Roumi flowers. It decreased  berry-set percentage and fruiting and increased percentage qf preharvest berry drop. Moreover, the berries were of poor quality.Bestäubungsversuche und serologische Untersuchungen an ägyptischen RebenDie Rebsorte White Roumi (Vitis vinifera L.) bringt allein gepflanzt nur niedrige Traubenerträge. Sowohl Bestäubungsexperimente als auch die serologische Prüfung zeigten, daß es sich hierbei um eine partielle Selbstinkompatibilität handeln dürfte. In Rebanlagen mit White Roumi ist Fremdbestäubung erforderlich, um reichliche Ernten zu erzielen und die Beerenqualität zu verbessern.Zwischen den Blüten von White Roumi und vier Pollenspendern wurden unterschiedliche Grade der Fremdverträglichkeit festgestellt. Bei Bestäubung mit Pollen von Red Roumi und Thompson Seedless waren der Beerenansatz und Fruchtertrag am höchsten. Pollen von Bez-El-Nakah hatte eine frühe Beerenreife zur Folge; die Beeren dieser Kreuzung waren am schwersten und größten. Die Sorte Ghariby erwies sich als ungeeigneter Pollenspender für die White-Roumi-Blüten; der Beerenansatz und Traubenertrag waren vermindert und der Anteil der vor der Ernte abgefallenen Beeren erhöht. Überdies waren die Beeren von geringer Qualität

Can a foreign body migrate against natural body barriers?

Pericardial foreign bodies (FBs) are a rare cause of chest pain in children. They can reach the pericardium through several routes including direct or iatrogenic implantation, transbronchial or transesophageal migration of inhaled or swallowed FBs. We reported a case of a 4-year-old girl presenting with persistent chest pain for 1 month. The child described the pain as ‘stitching’ in nature localized on the left side of the sternum. The child presented with increased pain intensity and a new onset of fever and cough. No history of chocking or swallowing of FB and no signs of trauma or child abuse were noted. Chest radiography revealed a needle in the left side of the chest. Computed tomography scan and echocardiography were used to precisely localize the needle and exclude intracardiac extension. ECG showed elevated ST segment and cardiac enzymes were normal. Removal of the needle was carried out surgically under fluoroscopic guidance. A small portion of the needle was found intrapericardially complicated by localized purulent pericarditis. The child had uneventful recovery and was discharged from the hospital on postoperative day 3.Keywords: foreign bodies, pain, pediatrics, pericardium, thoracic surger

Contribution of 3-D electrical resistivity tomography for landmines detection

Landmines are a type of inexpensive weapons widely used in the pre-conflicted areas in many countries worldwide. The two main types are the metallic and nonmetallic (mostly plastic) landmines. They are most commonly investigated by magnetic, ground penetrating radar (GPR), and metal detector (MD) techniques. These geophysical techniques however have significant limitations in resolving the non-metallic landmines and wherever the host materials are conductive. In this work, the 3-D electric resistivity tomography (ERT) technique is evaluated as an alternative and/or confirmation detection system for both landmine types, which are buried in different soil conditions and at different depths. This can be achieved using the capacitive resistivity imaging system, which does not need direct contact with the ground surface. Synthetic models for each case have been introduced using metallic and non-metallic bodies buried in wet and dry environments. The inversion results using the L1 norm least-squares optimization method tend to produce robust blocky models of the landmine body. The dipole axial and the dipole equatorial arrays tend to have the most favorable geometry by applying dynamic capacitive electrode and they show significant signal strength for data sets with up to 5% noise. Increasing the burial depth relative to the electrode spacing as well as the noise percentage in the resistivity data is crucial in resolving the landmines at different environments. The landmine with dimension and burial depth of one electrode separation unit is over estimated while the spatial resolutions decrease as the burial depth and noise percentage increase

On-resin N-methylation of cyclic peptides for discovery of orally bioavailable scaffolds.

Backbone N-methylation is common among peptide natural products and has a substantial impact on both the physical properties and the conformational states of cyclic peptides. However, the specific impact of N-methylation on passive membrane diffusion in cyclic peptides has not been investigated systematically. Here we report a method for the selective, on-resin N-methylation of cyclic peptides to generate compounds with drug-like membrane permeability and oral bioavailability. The selectivity and degree of N-methylation of the cyclic peptide was dependent on backbone stereochemistry, suggesting that conformation dictates the regiochemistry of the N-methylation reaction. The permeabilities of the N-methyl variants were corroborated by computational studies on a 1,024-member virtual library of N-methyl cyclic peptides. One of the most permeable compounds, a cyclic hexapeptide (molecular mass = 755 Da) with three N-methyl groups, showed an oral bioavailability of 28% in rat

A L\'evy input fluid queue with input and workload regulation

We consider a queuing model with the workload evolving between consecutive i.i.d.\ exponential timers $\{e_q^{(i)}\}_{i=1,2,...}$ according to a spectrally positive L\'evy process $Y_i(t)$ that is reflected at zero, and where the environment $i$ equals 0 or 1. When the exponential clock $e_q^{(i)}$ ends, the workload, as well as the L\'evy input process, are modified; this modification may depend on the current value of the workload, the maximum and the minimum workload observed during the previous cycle, and the environment $i$ of the L\'evy input process itself during the previous cycle. We analyse the steady-state workload distribution for this model. The main theme of the analysis is the systematic application of non-trivial functionals, derived within the framework of fluctuation theory of L\'evy processes, to workload and queuing models

Latent tuberculosis among pregnant mothers in a resource poor setting in Northern Tanzania: a cross-sectional study

Untreated latent TB infection (LTBI) is a significant risk factor for active pulmonary tuberculosis, hence predisposing to adverse pregnancy outcomes and mother to child transmission. The prevalence of latent tuberculosis in pregnancy and its association, if any, with various socio-demographic, obstetric and clinical characteristics was evaluated. Northern Tanzania was chosen as the study site. In a cross-sectional study, a total of 286 pregnant women from 12 weeks gestational age to term were assessed. Screening was undertaken using an algorithm involving tuberculin skin testing, symptom screening in the form of a questionnaire, sputum testing for acid fast bacilli followed by shielded chest X-rays if indicated. HIV serology was also performed on consenting participants.\ud Prevalence of latent infection ranged between 26.2% and 37.4% while HIV sero prevalence was 4.5%. After multivariate logistic analysis it was found that age, parity, body mass index, gestational age, and HIV sero status did not have any significant association with tuberculin skin test results. However certain ethnic groups were found to be less vulnerable to LTBI as compared to others (Chi square = 10.55, p = 0.03). All sputum smears for acid fast bacilli were negative. The prevalence of latent tuberculosis in pregnant women was found to be relatively high compared to that of the general population. In endemic areas, socio-demographic parameters alone are rarely adequate in identifying women susceptible to TB infection; therefore targeted screening should be conducted for all pregnant women at high risk for activation (especially HIV positive women). As opposed to the current policy of passive case detection, there appears to be an imminent need to move towards active screening. Ethnicity may provide important clues into genetic and cultural differences which predispose to latent tuberculosis, and is worth exploring further

Pomegranate (Punica graantum) Peels as an Agricultural Waste for Removing of CD(II), CR(VI), CU(II), NI(II), PB(II) and ZN(II) from Their Aqueous Solutions

Pomegranate (Punica graantum) peels as an agricultural waste was used as an adsorbent for removal of Cd, Cr, Cu, Ni, Pb and Zn ions from simulated aqueous solutions. The adsorption process was carried out using the batch method. Various effective parameters such as pH, initial metal ion concentration, and adsorbent dose, shaking time, particle size and temperature were investigated. Fourier Transform Infrared (FTIR) and Scanning Electron Microscopy (SEM) of Punica graantum peels were done. The efficiency of Punica graantum peels toward removal of metal ions was ordered as Pb2+ \u3c Cr6+ \u3c Cu2+ \u3c Cd2+ \u3c Zn2+ \u3c Ni2+, with the corresponding values of 92.8%, 84.6%, 52.8%, 38%, 25.4% and 22.8%, respectively