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Let \(G=(V,E)\) be a simple connected undirected graph. In this paper, we define generalized the Liouville’s and Möbius functions of a graph \(G\) which are the sum of Liouville \(λ\) and Möbius \(μ\) functions of the degree of the vertices of a graph denoted by \(\bigwedge(G)=\sum_{v\inV(G)}λ(deg(v))\) and \(M(G)=\sum_{v\inV(G)}μ(deg(v))\)respectively. We also determine the Liouville’s and Möbius functions of some standard graphs as well as determining the relationships between the two functions with their proofs. The sum of generalized the Liouville and Möbius functions extending over the divisor d of degree of vertices of graphs is also given.

The increasing concentration of carbon dioxide (CO2) in the atmosphere is considered to be one of the main causes of the global warming problem. Moreover, there is an international movement to reduce the emission of CO2 by imposing different measures such as carbon tax. Biological CO2 fixation has been extensively investigated as part of efforts to solve the global warming problem. Microalgae are fast growing systems that can consume high quantities of CO2 to produce different types of biomass. The efficiency of microalgae is highly related to the concentration of CO2 in the growth atmosphere and the higher the concentration of CO2 the better is the growth and hence productivity. The present review aimed at shedding some light upon microalgal capability to sustain their viability and propagate under high CO2 concentration.

The photosynthetic bacteria, Rodospirillum rubrum, produced hydrogen when grown in cheese whey in presence of light. The production increased three times as much when whey was used after being incubated in presence of Escherichia coli at 37℃ for 5 days, giving a total of 3600 ml of H2 in 10 days. The presence of Fe ions (5 mg/L) enhanced H2 production of treated whey to about 6000 ml in 10 days. Mo ions (0.3 and 1.6 mg/l) did not affect achieved H2 production of treated whey. However, when Fe and Mo ions were present together, the production was comparable with that of Mo ions alone, i.e. Mo prevented Fe of producing any enhancing effect. The addition of Mn ions (7.68 mg/L) to treated whey containing Fe (5 mg/L) and Mo ions (8 mg/L) increased H2 production to give about 9500 ml/10 days.

Intensity of the 662-keV gamma ray from cesium-137 was closely monitored in a variety of foods and beverages, including milk, flavored milk, fruit juices, infant foods, cooking oil, biscuits and fish. Nuclear facilities in the region, and the proximity of Oman to India and Pakistan (where nuclear material exists) played an important role in influencing our investigation. Relevant food items were obtained at appropriate intervals from January to December 2003 and 2004, and subjected to high-resolution gamma-ray measurement with a 28-cm 2 high-purity germanium detector. Each sample was prepared in a suitable Marinelli beaker and counted for 12 h. The recorded specific activities in milk, fruit juices and oil were generally

Low-level actinium contamination (228Ac) of petroleum sludge is reported. The sludge is earmarked for road-building and soil enrichment, hence long-term radiation in low doses is not desirable. We subsequently investigated the distribution of this radioactivity over a one-year period. Collection was conducted at different sites, and the sludge was subjected to high-resolution gamma-ray measurement with a Geenlarge this page detector. Samples of 1 kg dry weight were prepared in suitable Marinelli beakers and counted for 12 h. The approximate literature guideline for this radioistope in soil and regular sludge is about 60 Bq/kg. The levels in many of our samples were several times higher, and activities up to 600 Bq/kg were observed. The general distribution was studied; and suggestions for possible preventative remediation to deplete the activity levels in the sludge prior to its use as a building material and on sludge-farms are outlined. The study, therefore, formed an interesting contribution to research associated with radioactivity in the environment.

The presence of flavored colorants (peach and raspberry), flavors (caramel, citric acid and vanilla) and food preservatives (sodium nitrite, sodium nitrate, sodium benzoate, benzoic acid, potassium sorbate and sodium chloride) in Escherichia coli suspension during exposure to sunlight did not change the extent of cell survival. No effect on viability and mutation induction (kanamycin resistant) was also seen when cells were kept in contact with any of the additives for 80 min in the dark. However, when the relevant additive was present in cell suspension during sunlight exposure the number of induced mutations was increased to varying extents over that seen with sunlight alone. Raspberry and peach increased the number of mutations in a dose dependent manner, while vanilla produced mutations in an additive fashion. Nitrite, nitrate, benzoate, sorbate and benzoic acid increased mutation somewhat additively over that of sunlight. Sodium chloride and citric acid were not effective. The impact of this investigation reflects the significance of combination of sunlight and chemical food additives as potential risk, which requires special attention and necessitates further investigations to evaluate the risk.

Elevated levels of 214Pb and 214Bi activity were observed in oily sludge samples and the possible risk they could pose to the environment are investigated. 214Pb and 214Bi levels can be used to estimate indirectly the prominence of radon (222Rn), which is considered to be significant ecological hazard at abnormal levels. The sludge itself is regarded as prospective building material for constructing pavements, carparks and shopping malls; and is also disposed off on ‘sludge‐farms’ to enrich soil. The approximate literature guideline for these radioistopes in soil and regular sludge is around 200 Bq/kg. Levels in the samples investigated were more than four times this level. The distribution of this radioactivity was subsequently investigated over a one‐year period extending from January 2004 to December 2004.

Radium in oily sludge is unexplored, and this investigation could serve as a baseline study. We report elevated levels of 224Ra and 226Ra in 55 oily sludge samples that were collected from different sites and subjected to high-resolution gamma-ray measurement. The levels in our samples were more than five times higher than the estimated guidelines for soil and regular sludge. The period of investigation extended from January 2003 to January 2004. Both radium isotopes were identified by their characteristic gamma rays, whilst the short-lived one (224Ra) was also identified by its half-life. Samples (1 kg dry weight) were counted for 12 hours, and activities between 150–1000 Bq/kg were recorded. The sludge is regarded as a useful building material and as an additive for soil enrichment, and remediation procedures are suggested to deplete the activity levels in the sludge prior to its use for these purposes.

Background/Purpose: Vitamin D3 plays important roles in the absorption of calcium and phosphorus from the gastrointestinal tract and in the treatment of rickets; in addition, it facilitates the deposition of minerals in bones, thus minimizing the possibility of developing osteomalacia. Sunlight naturally induces vitamin D3 photosynthesis. Such a process is affected by a number of factors such as age, geographical location, skin color, sunscreen application and clothing. It is intended in the present investigation to study in vitro the effect of clothing on the solar photoproduction of vitamin D3. Methods: Fifteen different fabric samples were tested for their effect on the efficiency of the in vitro solar conversion of 7-dehydrocholesterol (7-DHC) to vitamin D3. 7-DHC was dissolved in methanol to give a concentration of 2.6×10−4 M. Solutions were exposed to sunlight in quartz containers for predetermined periods either uncovered or covered with the fabric sample under test. Changes in the concentrations of 7-DHC and the photoproducts were monitored by HPLC. Fabrics were graded as the number of threads per square inch (in2), and their sunlight attenuation was determined. Results: 7-DHC is transformed to previtamin D3 upon exposure to sunlight, and the amount generated exhibited an almost linear relationship. When fabric-covered samples of 7-DHC were irradiated, photoproducts were also detected and their concentrations depended on the degree of sunlight attenuation imposed by the fabric. Generally, the higher the number of threads per in2 the more the light attenuation produced. Conclusion: Clothing plays an important role in attenuating sunlight, thus leading to diminished vitamin D3 production to an extent that would require dietary compensation.

A mathematical model was formulated that will facilitate the prediction of solar disinfection by analyzing the effect of sunlight exposure (x(1)) and the load of bacterial contamination (x(2)), as predictor variables, on the efficiency of solar disinfection (y). Aliquots of 0.1 ml containing average numbers of E. coli, ranging between 1 and 5 x 10(3)cells/ml raw water, were introduced into each of the 96 wells of polystyrene microtitre plates. Plates, with the lid on, were exposed to sunlight for varying exposures ranging between 1.04 x 10(3) and 8.40 x 10(3)kJ m(-2). Double strength nutrient broth was then added. After 48 h incubation wells containing visible contamination were considered as containing one cell or more that survived the exposure. Data showed that disinfection is dependent both on the load of bacterial contamination and sunlight exposure. This relationship is characterized by curves having shoulders followed by a steep decline and then tailing off in an asymptotic fashion. The shoulder size increased with the increase of the contamination load, however, the slope remains the same. Statistical analysis indicates a positive correlation among the variables (R(2) = 0.893); the mathematical model, y=1-(1-e(-kx(1)))(x(2)), represents the relationship, with k being the solar inactivation constant. The exposure required to produce a given decontamination level can be predicted using the equation: x(1)=-1/kln[1-(1-y)(-1/x(2))]e(-micro/rho.m/A), where micro is the linear attenuation coefficient (m(-1)), rho is the density, m is the mass and A is the area of the exposed part of the sample. The predictor variables (x(1), x(2)) strongly influence the efficiency of solar disinfection, which can be predicted using the suggested mathematical model. The present data provides a means to predict the efficiency of solar disinfection as an approach to improve the quality of drinking water mainly in developing countries with adequate sunshine all year-round.

The study comprised several co-investigations, each of which formed an original contribution to bilirubin research. Variation in the bioanalytical concentration of the unconjugated specimen and its reversion to other products was examined in each case. The contributions of the different components of the study are broadly summarized as follows: (i) photolysis by sunlight and phototherapy illumination; (ii) the effect of ionizing radiation; (iii) solvent effects and chromatographic studies; (iv) kinetic studies; (v) thermal and chemical effects. Initially, in vitro studies in dilute aqueous NaOH compared the efficiency of sunlight with illumination from a phototherapy unit. The data indicated that at comparable light intensities the phototherapy unit was as effective as sunlight in reducing the bilirubin levels to less than 10% of its original value. This work was extended by subjecting dilute non-aqueous solutions (chloroform) of bilirubin to 137Cs gamma irradiation. It was found that the ionizin...

This study examined the depletion and growth of bilirubin and biliverdin, respectively, after exposing dilute solutions of the unconjugated specimen of bilirubin to light and heat. Firstly, the solar photolysis of bilirubin in CHCl3 resembled a chemical reaction of bilirubin in CDCl3. Secondly, at temperatures up to about 70°C, appreciable yields of biliverdin were converted from bilirubin in NaOH, before and after irradiation with cool white light produced from a phototherapy facility. This derivation augurs well for purposes of separating suitable quantities of biliverdin for implementation as precursors in biochemical studies. The aspect of the study associated with CDCl3 demonstrated that the systematic decrease in the characteristic bilirubin peak at 453 nm, via a chemical reaction, emulated the photolysis of bilirubin with sunlight in regular chloroform. The respective rate constants of the photochemical and chemical reactions were approximately 0.15 s−1 and 0.17 s−1. The temperature depen...

The chemistry of bilirubin with deuterated compounds is a relatively underexplored area of research. In this study, biliverdin was observed as a product of the reaction of unconjugated bilirubin with CDCl3. The reaction was investigated in the presence of oxygen and under anaerobic conditions using pure N2 gas, with no perceptible changes in the biliverdin yields. Subsequently, the feasibility was examined of isolating the by-products of the reaction mixture on a simple glass column using Al2O3 as the stationary phase. Separation was achieved by eluting at regular intervals with 5% acetic acid and petroleum ether. The presence of the biliverdin component was confirmed spectrophotometrically, producing intense characteristic absorbance maxima at 365 and 660 nm. A sequel to this study involved the photolysis of bilirubin by solar irradiation. The unconjugated specimen was dissolved in regular chloroform (5.2 × 10−2mM) and exposed to sunlight for 30 min. The absorption spectrum of the irradiated sample produ...

The removal and destruction of a tri-phenyl methane dye, Acid Violet 17 (AV17), from aqueous solution by adsorption and electrochemical regeneration was studied using a graphite intercalation compound (GIC) adsorbent. It was demonstrated that the adsor­bent could be regenerated by anodic oxidation of the adsorbed dye in a simple electro­chemical cell. The GIC adsorbent recovered its initial adsorption capacity after 40 to 60 min of treatment at a current density of 10 mA cm - 2 , corresponding to a charge of 12 to 18 C g - 1 of adsorbent. The charge passed is consistent with that expected for mine­rali­sation of the dye, suggesting that the dye was removed and destroyed with high charge efficiency. The energy cost of the regeneration was found to be around 120 J per g of adsorbent regenerated or 115 J per mg of the AV17 dye removed and destroyed. A model describing the process of wastewater treatment by multiple cycles of adsorption and electrochemical regeneration, based on adsorption isotherm data, has been deve­loped and validated. It was found that relatively modest improvements in the adsorption capacity of the adsorbent material could significantly improve the process performance.

Flow-through ion-selective electrodes were constructed from compressed pellets (8-10 mm thick, 13 mm diameter, 10 tons/cm(2) pressure) of Ag(2)S/AgX (X = Cl(-), Br(-) or I(-)) drilled longitudinally (1.5 mm diameter hole) to be suitable for use in flow-injection analysis. A column of AgCl (5.5 cm long, 2-3 mm i.d.) was included in the Cl(-)-electrode manifold to remove interferences from 10(-4)M Br(-) and 3 x 10(-5)M I(-) and S(2-). A column of amalgamated lead (2-3 cm long, 2-3 mm i.d.) was used in the Br(-) electrode manifold to remove interference from 2 x 10(-5)M I(-), 3 x 10(-5)M S(2-) and 7 x 10(-4)M Cl(-). These columns and the addition of ascorbic acid were not required when I(-) was determined with the iodide electrode. The carrier stream was 0.1M sodium perchlorate (pH 4) at a flow-rate of 0.5 ml/min. The sample pH could be 4-7. Simultaneous determination of Cl(-) and I(-), Cl(-), I(-) and Br(-) and Cl(-), I(-), Br(-) and F(-) ions was possible with combinations of the corresponding electrodes and columns in series and/or parallel in specially designed manifolds. Calibration plots were linear, with almost theoretical slopes, down to 10(-6)M I(-), 5 x 10(-6)M Br(-), 10(-4)M Cl(-) and 5 x 10(-6)M F(-), with precision better than 1%. Sampling rates for single-ion determinations were 72, 102, 90 and 80 per hr for the one-, two-, three- and four-electrode systems respectively. Determinations of these ions in water samples by the recommended procedure and by established batch methods showed no significant difference at the 95% confidence limits in a paired comparison t-test.

A new thermometric sensor, which is a transistor (OC71), has been introduced to follow thermometric titrations successfully to clear end points. The sensor was suitable in both normal and differential modes of titration. It is possible to titrate down to 1.32micromol of HCl and 26.4micromol of H(3)BO(3)in a final 20ml solution with accuracy and precision of 1%, 2.2% and 1.4%, 2.2%, respectively. The sensor, in association with a pH glass electrode, was used for the determination of pK values of some well established weak acids such as, acetic acid (4.77), phosphoric acid (pK(1)=2.18, pK(2)=7.20 and pK(3)=12.32) as well as for a very weak acid of uncertain pK values H(3)BO(3) (pK(1)=9.20, pK(2)=12.7 and pK(3)=13.80). The sensor was also examined for kinetic catalytic determination of iron(III) in water, milk and pharmaceuticals.

The effect of the nature of solvent on the properties of biomedically important compounds is of particular importance. The conversion of certain biomedical compounds with deuterated solvents is an area of research that has not been accorded adequate recognition in the literature. We explored this area in the interest of shedding some light on the possible effects of solvent on the nature of the solute. The transformation of specific medically important compounds such as bilirubin, thymine, uracil, dehydrocholesterol (7-DHC) and vitamin D(3) was observed in the presence of deuterated solvents such as heavy water and deuterated chloroform. The products of the relevant reactions were confirmed spectrophotometrically. An additional feature to our investigation involved the photolysis of the aforementioned compounds by solar irradiation. The pure samples were dissolved in solutions of the deuterated solvents, corresponding to concentrations of typically 10(-2) mM, and exposed to sunlight for about 15-30 min. The deuterated solvents caused chemical transformation in all chemical compounds tested, and produced intense characteristic absorbance maxima between 200 and 700 nm. Sunlight exposure was also effective in either augmenting the effects of deuterated solvent as in bilirubin and 7-DHC or reducing it as with thymine or having no effect as with uracil or completely changing it as in vitamin D(3). It has been shown that the use of deuterated solvents produces unique chemical and photochemical conversions of bilirubin, 7-DHC, thymine, uracil and vitamin D(3). This was attributed to the fact that deuterated compounds display a somewhat different chemistry to their ordinary counterparts and that possibly thermodynamic considerations could be responsible for the novel transformations.

Background/Aim: Light can be efficiently used for the treatment of neonatal jaundice. Sunlight, which covers a large portion of the light spectrum including the bilirubin-absorbing range, is abundant in the Middle East. Such advantages prompted the present study to investigate the efficiency of sunlight in isomerizing bilirubin. This may introduce a practical source of light for the treatment of hyperbilirubinic infants in areas where phototherapy units are not available. Methods: The efficiency of sunlight was quantified by a comparison with a phototherapy unit. Aqueous bilirubin solutions were exposed to periodic sunlight over the entire year and the reduction of bilirubin concentration was monitored spectrophotometrically. Bilirubin solutions were also exposed to a phototherapy unit intensity comparable to that of sunlight (17 cm away from the source). Results: The data indicated that at this comparable light intensity, the phototherapy unit was as effective as sunlight. However, for the treatment of neonatal jaundice, phototherapy units are usually operated at a distance of 50 cm (where the light intensity is six times less than that of sunlight). When this distance was tested, only 16% of bilirubin was isomerized in the first 5 min of exposure. In contrast, about 65% of bilirubin was isomerized when the phototherapy unit was placed at a distance of 17 cm and when the bilirubin solutions were exposed to sunlight for the same time period. The hourly and seasonal changes in sunlight intensity affected the reduction in bilirubin concentration significantly. Conclusion: Data revealed that sunlight is almost 6.5 times more effective than a phototherapy unit when operating at the ward geometry after taking isomerization efficiency and area of exposure into consideration. Moreover, sunlight is still more effective during the winter season, when its intensity is lower. Thus, sunlight may be considered an alternative phototherapy source for the treatment of neonatal jaundice, particularly in areas where conventional phototherapy units are unavailable.

Aromatic polyarene-phosphochloridates were prepared by condensation of various bis-phenols (4,4'-isopropylidenediphenol,4,4'-dihydroxydiphenyl sulphone, and 4,4'-dihydroxybi-phenyl) with phosphorus oxychloride in pyridine medium. These polymers were characterized by IR spectrophotometry. The isothermal decomposition of these polymers and their 2% mixtures with PVC were studied.

Molar ratios of Ag2S/AgI between 3:1 to 1:3 have been studied as Hg(II) ion selective electrode. It was found that the molar ratio 1:3 WBB the best ratio to be used as Hg(II) electrode after one hour conditioning in a solution of 10−2M Hg(II) ion and in the pH range between 1.5–4.5. Interferences from anions (Cl−, Br−, S− and CN−) were quite serious if concentration of the interfering ion exceeded that of Hg(II) ion. Cations except Ag+ ion did not interfere. Dynamic response of the electrode showed that the equilibrium response time of the electrode is between 30–50 seconds at different concentrations of Hg(II) ion. Potentiometric titrations and antomatic titrations using Cl− or Br− as titrants gave sharp end points down to 10−3M Hg(II) ion. Analysis of pure inorganic Hg(II) ion gave an error of 0.5% or less and a coefficient Of variation of better than 0.1%.

Misonidazole sensitized anoxic spores of Bacillus megaterium against the lethal action of gamma radiation to an extent amounting to about 30% of the level achieved by O2. An enhancement by misonidazole, equal in magnitude to that occurring in anoxia, was seen in spores at an O2 concentration obtained by equilibrating with 1.2 or 2.2% O2 in N2 gas. At these two concentrations of 02 the enhancing actions of O2 and misonidazole were additive. No effect of misonidazole was observed with spores equilibrated with 3.0 or 4.1% O2 in N2 gas. At high O2 concentrations (equilibration with air or 100% O2) misonidazole protected the spores to a small extent against lethal action of radiation. The mechanistic implications of the enhancing action of O2 in spores are given.

Anodic stripping voltammetry with a hanging-drop mercury electrode is used for determination of traces of Zn, Cd, Pb and Cu in white sugar. The sample (1.5 g) is decomposed by ignition in oxygen in a specially modified system.

An ion exchange method to determine the alkalinity of water-soluble tea ash containing high levels of manganese is described. A chromatographic column containing a strong cation exchange resin (20–50 mesh) in Na+ form, with a bed volume of 5 mL is used. The present ion exchange method is compared to pH titrations and also to the official AOAC methods (31.012, 31.015, 31.016). Results with the new method are accurate and precise.