Methods of Variations and Their Applications

In this review article, we begin with reviewing Calculus of variations giving few examples on its use to solve a large number of problems in geometry, physics, and other branches of knowledge. Afterwards, we direct our attention to different methods of variations which evolved during the last century and which include their use in eigenvalue problems and in finite difference methods and those adopted in classical and quantum mechanics. The methods used in evaluating products and quotients of functionals are also discussed along with variational iteration methods. Later on, a good number of applications in different areas are presented and discussed;then a concluding discussion is given.

The Cumulative Method for Multiplication and Division

This paper provides a method of the process of computation called the cumulative method, it is based upon repeated cumulative process. The cumulative method is being adapted to the purposes of computation, particularly multiplication and division. The operations of multiplication and division are represented by algebraic formulas. An advantage of the method is that the cumulative process can be performed on decimal numbers. The present paper aims to establish a basic and useful formula valid for the two fundamental arithmetic operations of multiplication and division. The new cumulative method proved to be more flexible and made it possible to extend the multiplication and division based on repeated addition/subtraction to decimal numbers.

<i>In Vitro</i>Antibacterial Activity of Flavonoid Extracts of Two Selected Libyan Algae against Multi-Drug Resistant Bacteria Isolated from Food Products

This study aimed to evaluate the antibacterial activity of flavonoids extracted from two Libyan brown algae namely Cystoseira compressa and Padina pavonica using microwave-assisted extraction method against pathogenic bacteria isolated from meat, meat products, milk and dairy products (Staphylococcus aureus subsp. aureus (5 isolates), Bacillus cereus (3 isolates), Bacillus pumilus (1 isolate), Salmonella enterica subsp. enteric (4 isolates) and Enterohaemor-rhagic Escherichia coli O157 (EHEC O157) (4 isolates)). All of these isolates were muti-drug resistant with high MAR index. The results showed that C. compressa extract exhibited better and stronger antibacterial activities against the seventeen tested isolates with inhibition zones diameter ranged from 14 - 22 mm compared to P. pavonica extract which showed positive effect against 9 isolates with low inhibition zone ranged from 11 - 16.5 mm. Flavonoids extracted from C. compressa also displayed the best spectrum of bactericidal effect with a ratio MBC/MIC ≤ 4 obtained on all susceptible tested bacterial strains. Flavonoids and proanthocyanidins significantly contributed to the antibacterial properties. The mode of action of these active extracts is under investigation.

Anticancer and Antioxidant Activities of Some Algae from Western Libyan Coast

Seaweeds are considered as one of the largest biomass producers in marine environment that is rich in bioactive metabolites and a source of natural ingredients for functional foods. The potential antioxidant activity and the potential inhibition of Caco2 cell proliferation, of crude extracts of: Chlorophyta (Ulva lactuca, and Codium tomentosum), Phaeophyta (Cystoseira crinita, Cystoseira stricta, and Sargassum vulgare), and Rhodophyta (Gelidium latifolium, Hypnea musciformis, and Jania rubens) were collected from western Libyan coast and evaluated in vitro. The antioxidant activity was determined by reducing power and DPPH assays while cell proliferation, morphological changes and the cell cycle arrest were assessed by MTT, inverted light microscope and flow cytometry methods respectively. The polyphenols and flavonoids rich extracts showed remarkable reducing power and antiradical properties. After exposure of Caco2 cells to various concentrations of extracts (50, 100, 150 and 200 μg/mL) especially from brown algae for 72 h, cell proliferation was reduced significantly. The antiproliferative effect of algae extracts was correlated with their polyphenol and flavonoid contents. Cell cycle analysis further showed that cells were arrested in G phases along with an increment in sub-diploidal cell population (sub-G) after extract application. These results imply that seaweeds which are rich in bioactive compounds may be used in anticancer drug research programs. However, further investigations are essential to reveal the molecular mechanisms of the anticancer activities of these algae.

Effect of Ciprofloxacin on S.aureus and E.coli Growth in Presence of Vitamin C Using Cup Cut Diffusion Method

Ciprofloxacin is a second-generation of fluoroquinolone,broad-spectrum antibiotic with bactericidal activity against Gram-positive and Gram-negative organisms.It is one of the most widely used antibiotics,because of its efficacy,safety,and relatively low cost.Ascorbic acid(vitamin C)is water-soluble monosaccharide antioxidant;it is essentially required by the body for its various biochemical and physiological processes.S.aureus is Gram-positive cocci;widely distributed in the environment,it is a member of the normal flora of the body.S.aureus is not always pathogenic;it is a common cause of skin infections including abscesses,respiratory infections such as sinusitis,and food poisoning.E.coli is Gram-negative bacteria,found in the environment,foods,and intestines.Most E.coli strains are harmless;it is part of the normal microbiota of the gut.However,some serotypes of E.coli cause serious food poisoning in their hosts;it can cause diarrhea,while others cause urinary tract infections,respiratory illness and pneumonia,and other illnesses.Method:Cup cut diffusion method was applied.Experiment I:is carried out to choose the concentration of vitamin C to be used in experiment II.The negative control is normal saline,added in cup in each plate,vitamin C(100 mg/mL,200 mg/mL,400 mg/mL)was added,the volume in each cup was 100μL.Experiment II:Eight groups of treatments were applied.The first is the negative control(1%normal saline),the second group is the positive control of vitamin C(200 mg/mL).The third,fourth and fifth groups are ciprofloxacin with different concentrations(10 mg/mL,20 mg/mL,40 mg/mL);the sixth,seventh and eighth are the combination of vitamin C with each concentration of ciprofloxacin(10 mg/mL,20 mg/mL,40 mg/mL).Each group includes six petri dishes.Bacterial plates were incubated at 37 oC for 24 h and 48 h.Zone of inhibition is measured in mm.Results and conclusion:Ciprofloxacin produces dose dependent increase in zone of inhibition of S.aureus and E.coli growth,after 24 and 48 hours incubation.While vitamin C in the concentration used produced inhibitory effect on the growth of S.aureus and E.coli,after 24 hours incubation,vitamin C effect was not changed after 48 hours incubation.After 24 hours incubation,vitamin C potentiated the effect of ciprofloxacin at low concentration(10 mg/mL);while vitamin C antagonized the effect of ciprofloxacin at higher concentrations(20 and 40 mg/mL)on S.aureus growth.In the same time,ciprofloxacin antagonized the inhibitory effect of vitamin C on S.aureus growth.After 48 hours incubation,S.aureus produced resistance against ciprofloxacin alone,and that combined with vitamin C compared to zone of inhibition after 24 hours.Ciprofloxacin produced dose dependent inhibition of E.coli growth after incubation for 24 and 48 hours.Vitamin C potentiated the inhibitory effect induced by ciprofloxacin(additive effect).The inhibitory effect of ciprofloxacin,vitamin C and the combination was not changed after 48 hours compared to 24 hours.

Comparative Evaluation of Antioxidant Enzymes and Serum Selenium Levels in Libyan Atherosclerotic Patients

Introduction: Atherosclerosis is the major source of morbidity and mortality in the developed countries like Libya. Oxidative stress represents a risk factor and plays a key role at several steps of atherosclerosis. Formation of atherosclerotic plaques is the main reason for coronary artery disease. Aim: This study is aimed to assess the impact of the imbalance between body oxidants and antioxidants (oxidative stress) and its involvement in developing and severity of atherosclerosis in atherosclerotic with and without diabetes Libyan patients. Methods: The study sample comprised of atherosclerosis with and without diabetes patients (n = 73), as well as healthy controls (n = 27). Blood samples were collected to determine the levels of malonaldehyde (MDA) as oxidative biomarker, serum selenium level, total antioxidant status (TAS) level and some antioxidant enzymes including glutathione peroxidase (GPx), Catalase (Cat) and superoxide dismutase (SOD). Additionally, oxidant/antioxidant status was compared between atherosclerotic patients with and without diabetes in comparison to controls. Results: The results indicated a significant increase in MDA level among atherosclerotic patients compared to healthy subjects (P Conclusion: Determination of antioxidative defense markers contributes to understanding the effect of oxidative stress on the development and the prevention of cardiovascular disease.

Removal of Some Heavy Metals from Wastewater by Using of Fava Beans

The Fava Beans were used in this work as low cost adsorbent material for removal of Pb(II), Cd(II) and Zn(II) ions from aqueous solutions. The samples were prepared without farther treatment and sorted according to the particles diameter by standard sieves 250 - 500 μm. Batch adsorption experiments were carried out to study the adsorption process, several parameters such as Initial pH of adsorbent, effect of contact time, effect of adsorbent amount and effect of metal concentration were conducted in these experiments. The effects of any one of those previously mentioned parameters on the adsorption capacity were studied while the other parameters were kept constant. It was found that the obtained maximum adsorption capacities of Fave beans for the removal of selected heavy metals were very high. This provide us to use Fava beans as a low coast adsorbent material to clean up the water in the environment from toxic heavy metals such as Pb(II), Cd(II) and Zn(II) ions.

Evaluation of Low Saline “Smart Water” Enhanced Oil Recovery in Light Oil Reservoirs

With the depletion of natural driving forces responsible for pushing the oil from reservoirs & declination of oil recovery after secondary stage, the emphasis is now on EOR techniques. The low saline flooding is a type of EOR which gains the attention of researchers due to its easiness to use implications, less cost & environment-friendly nature. Though the low salinity effect has been seen in various labscale core flooding experiments as well as field pilot projects, the mechanism which actually leads to this enhancement in recovery is still the area of research among researchers which is wide open and needs to gain consensus. Seeing the wide mechanisms taking place under different scenarios, it is certain that more than one mechanism is actually supplementing each other in reducing the residual oil saturation while LSW flooding. This study has been undertaken investigations on the low saline flooding in unconsolidated Ottawa sandpack cores with two different, Weyburn & Pelican crude oil, to find out the optimum salinity, LSW Slug Size & underlying mechanisms during LSW flooding. Several core flooding experiments were performed under secondary as well as tertiary recovery stage by unsteady state method. With the reduction of brine salinity from 5000 PPM to 1500 PPM, the oil recovery increased in secondary stage & decreased further upon reduction in salinity to 500 PPM gaining the peak at 1500 PPM. Small enhancement in tertiary recovery of 2.24% observed upon switching to 1500 NaCl PPM brine after injection of formation brine in secondary stage for Weyburn Oil, though large tertiary recoveries of the order of 9.95% for effective oil viscosity of 4 cP and 7.32% for 29.7 cP were observed for n-dodecane diluted Pelican Oil. LSW slug size of 25% pore volume was found to be effective in producing Weyburn Oil in secondary stage.

Epidemiological characterization and geographic distribution of human immunodeficiency virus/acquired immunodeficiency syndrome infection in North African countries

BACKGROUND Human immunodeficiency virus(HIV)infection is a major global public health concern.North African countries carry a disproportionate burden of HIV representing one of the highest rates in Africa.AIM To characterize the epidemiological and spatial trends of HIV infection in this region.METHODS A systematic review was carried out on all the published data regarding HIV/acquired immunodeficiency syndrome in North African countries over ten years(2008-2017)following the PRISMA guidelines.We performed a comprehensive literature search using Medline PubMed,Embase,regional and international databases,and country-level reports with no language restriction.The quality,quantity,and geographic coverage of the data were assessed at both the national and regional levels.We used random-effects methods,spatial variables,and stratified results by demographic factors.Only original data on the prevalence of HIV infection were included and independently evaluated by professional epidemiologists.RESULTS A total of 721 records were identified but only 41 that met the criteria were included in the meta-analysis.There was considerable variability in the prevalence estimates of HIV within the countries of the region.The overall prevalence of HIV ranged from 0.9%[95%confidence interval(CI)0.8-1.27]to 3.8%(95%CI 1.17-6.53).The highest prevalence was associated with vulnerable groups and particularly drug abusers and sexually promiscuous individuals.The dense HIV clustering noted varied from one country to another.At least 13 HIV subtypes and recombinant forms were prevalent in the region.Subtype B was the most common variant,followed by CRF02_AG.CONCLUSION This comprehensive review indicates that HIV infection in North African countries is an increasing threat.Effective national and regional strategies are needed to improve monitoring and control of HIV transmission,with particular emphasis on geographic variability and HIV clustering.

Optimal Design and Simulation of Solar Photovoltaic Powered Cathodic Protection for Underground Pipelines in Libya

In Libya,pipelines are being used as means of transferring hydrocarbon from wellheads to export sea ports,refineries,storage tanks,steel factory and power plants.Steel pipeline is widely used because it is the safest means of transporting hydrocarbon and other oil products as well as its cost effective.However,one of the challenges facing oil and gas sector is corrosion on infrastructure facilities and processing units.Cathodic-protection(CP)is an electrical method used to protect metallic body in contact with the earth from corrosion.A photovoltaic(PV)provides a reliable solution for powering remote CP stations,enabling the placing of CP units in any location along the underground pipeline,thus ensuring optimal current distribution for the exact protection requirements.In this paper the sizing of the system is determined based on the electrical power needed for the catholic protection,characteristics of the used PV module and the meteorological data of the installation site.Matlab/Simulink and PVsyst V6.43 software are used as tools for optimal design,sizing and simulation of the PV powered cathodic protection system components.In addition to that estimation of system cost was investigated and compared with the conventional system.The results show that using solar energy powered cathodic protection system for underground pipelines is practical and very beneficial besides being economical,especially considering the rapid decreasing in the prices of PV systems components and the increasing of its efficiencies and reliability.

Numerical Solutions of Finite Well in Two Dimensions Using the Finite Difference Time Domain Method

The higher excited states for two dimensional finite rectangular well potential are calculated numerically,by solving the Schrödinger equation using the finite difference time domain method.Although,this method is suitable to calculate the ground state of the quantum systems,it has been improved to calculate the higher excited states directly.The improvement is based on modifying the iterative process involved in this method to include two procedures.The first is known as cooling steps and the second is known as a heating step.By determining the required length of the cooling iteration steps using suitable excitation energy estimate,and repeating these two procedures using suitable initial guess function for sufficient times.This modified iteration will lead automatically to the desired excited state.In the two dimensional finite rectangular well potential problem both of the suitable excitation energy and the suitable initial guess wave function are calculated analytically using the separation of variables technique.

On the Use of Perturbation Theory in Eigenvalue Problems

The importance of perturbation theory in many fields is very clear through almost a century or even more. Its importance was exemplified in solving many problems in physics and other applied fields. A great deal of applications arose in dealing with eigenvalue problems especially in quantum mechanics in conjunction with the field of atomic physics. Accordingly, it came to our mind to write a brief review article on the subject. At the beginning, we give some important definitions to do with various eigenvalue problems;then we introduce concepts that have to do with perturbation theory and the techniques used in such a theory, beginning with the algebraic perturbation theory giving a good number of examples from the literature on the use of the theory in solving integral equation, algebraic equations and differential equations. Few applications are then given in applied fields such as classical mechanics, quantum mechanics and fluid mechanics. Finally, a concluding discussion is given which is related to the use of the theory.

Removal of Aniline Blue from Aqueous Solutions Using Ce_1-xBi_xCrO₃(x = 0, 0.5, 1)

The removal of aniline blue dye from aqueous solutions using the A-site doped perovskite Ce1-xBixCrO3 (x = 0, 0.5, 1) was investigated. The perovskite oxides were synthesised using Sol-Gel method and characterised by conventional powder X-ray diffraction technique. The X-ray diffraction measurements suggested that doping with Bismuth Ion influences both the crystal structure and the particle size of the oxides, and consequently affects the adsorption properties. It was found that both CeCrO3 and Ce0.5Bi0.5CrO3 compounds are orthorhombic and have approximate particle size of 87 and 36 nm respectively, whereas BiCrO3 oxide has rhombohedral space group symmetry and the particle sizes are less than 49 nm. The batch mode study demonstrated that the removal capacities of Aniline Blue at 150 min and pH = 4.3 for Ce0.5Bi0.5CrO3, CeCrO3 and BiCrO3 are 779.67, 705.45 and 440.18 mg/g respectively. The results reflect the influence of the A site doping on the adsorption properties of the oxides. The removal of Aniline Blue was found to be negatively correlated with temperature and pH.

Petrophysical interpretations of subsurface stratigraphic correlations,Baram Delta,Sarawak,Malaysia

Petrophysical well log data help to predict hydrocarbon reserves before field development which involves huge financial commitment.In this study,reservoir characterization was performed with a view to obtain information on the geological formation type and petrophysical parameters.Wireline log data obtained from five wells were used to develop a 3D model of X-field in the Baram Delta which was in turn evaluated using the PETREL software.Suites of gamma ray,sonic,density,resistivity and neutron logs aided the delineation and correlation of the sandstone formation.Fourteen hydrocarbon-bearing sands were defined from well log data and divided into two-reservoir zones,shallow and deep.Well correlation assisted in the delineation of the reservoir sands across the wells.The quality of the reservoir formation was evaluated from average petrophysical properties:with an average thickness of 62 m,an average porosity of 0.19,an average net-to-gross ratio of 0.068,an average V-shale of 0.45,and an average water saturation of 0.95.A rollover anticline structure was identified across the field using the fault as a description tool.Variation of petrophysical parameters and uncertainty in the reservoir properties were included to predict the effect on the volume of oil in place.This study revealed that the discovered hydrocarbon reserve resource accumulations in the Field X for the fourteen-mapped reservoir sands have a total proven reserve resource estimate of 740MMSTB at P90,655MMSTB at P50 and 593MMSTB at P10.Reservoirs A and B are the only intervals with the highest recoverable oil,a volume of 256MMSTB at P90,215MMSTB at P50 and 181MMSTB at P10,respectively.These analyses facilitated an improved reservoir description of shaly sandstone,which contributes to better planning of hydrocarbon re-development and future recovery,and thereby improving the energy supply security of the regions.

A Cross-Sectional Study on Current Practice of the Management of Pregnancy Induced Hypertension and Its Maternal and Foetal Complications and Outcome in the Western Part of the State of Libya

Background: Maternal and perinatal mortality and morbidity are mainly affected by hypertension during pregnancy (pre-eclampsia). Haemorrhage and cerebral bleeding are the primary and significant complications of pre-eclampsia. Abruption of the placenta and renal failure are among the major complications caused by this disease. The perinatal complications include Intrauterine Growth Restriction (IUGR), Intrauterine Foetal Death (IUFD), neonatal death, and prematurity. Objective: The purpose of the present study was to examine the incidence of Pregnancy-Induced Hypertension (PIH), pre-eclampsia, the management of PIH, including the early diagnosis, the pharmacological drug management used, and the prevalence of maternal and perinatal complications. Methods and Patients: This cross-sectional study took place in Aljalaa maternity hospital, which represented the west of the state of Libya in the period from 1st January 2012 to 31st December 2012, with patients who were diagnosed, managed, and terminated according to protocol management of the hospital. Results: In the present study, from the total deliveries in Aljalaa Maternity hospital, the incidence of PIH is 8.4% and pre-eclampsia is 5.1%. No maternal mortality, CNS haemorrhaged, hepatic failure, or renal failure. The reported maternal complications included: Eclampsia, HELLP syndrome (Haemolysis, Elevated Liver enzymes and Low platelets), abruption placenta, and pulmonary oedema see in eighteen percent, six percent, nine percent, four percent and less than one percent, respectively. The foetal complications were preterm babies and Intrauterine Growth Restriction (IUGR) in nineteen percent, Low Birth Weight (LBW) in twenty-five percent, Intrauterine Foetal Death (IUFD) in five percent, neonatal death in two percent and, perinatal death in six percent. In the PIH patients, the presence of associated symptoms such as headache, blurred vision, irritability, and the presence of signs such as severe hypertension, generalized oedema, exaggerated reflexes, and abnormal investigations (protein urea, high uric acid, abnormal LFT, haemoconcentration, and low pits) increased the risk of maternal and foetal complications. Conclusion: To decrease mother and newborn mortality and morbidity in PIH patients, a rigorous management protocol is required to implement evidence-based guidelines.