Survival Chances of Mutants Starting With One Individual

A simple theoretical model of a Darwinian system (a periodic system with a multiplication phase and a selection phase) of entities (initial form of polymer strand, primary mutant and satellite mutants) is given. First case: one mutant is considered. One individual of the mutant appears in the multiplication phase of the first generation. The probabilities to find N individuals of the mutant after the multiplication phase M of the n-th generation (with probability δ of an error in the replication, where all possible errors are fatal errors) and after the following selection phase S (with probability β that one individual survives) are given iteratively. The evolutionary tree is evaluated. Averages from the distributions and the probability of extinction are obtained. Second case: two mutants are considered (primary mutant and new form). One individual of the primary mutant appears in the multiplication phase of the first generation. The probabilities to find N _p individuals of the primary mutant and N _m individuals of the new form after the multiplication phase M of the n-th generation (probability ɛ of an error in the replication of the primary mutant giving the new form) and after the following selection phase S (probabilities β _p and β _m that one individual each of the primary mutant and of the new form survives) are given iteratively. Again the evolutionary tree is evaluated. Averages from the distributions are obtained. The online version of the original article can be found at .     

Effect of fungal infection on reproductive potential and survival time of <Emphasis Type="Italic">Tetranychus urticae</Emphasis> (Acari: Tetranychidae)

The effect of fungal infection on the reproductive potential of two-spotted spider mite, Tetranychus urticae, was evaluated as part of the full biocontrol potential of three entomopathogenic fungi by modeling of fecundity probability. Female mites (≤2-day-old) on leaves were exposed to the sprays of Beauveria bassiana, Paecilomyces fumosoroseus and Metarhizium anisopliae at the concentrations of 1.13 × 10³, 1.55 × 10³ and 0.95 × 10³ deposited conidia mm⁻² and then individually reared at 25°C and 12:12 L:D for oviposition. Mite mortalities 10 days after spraying were 73.1, 75.4 and 67.9% in the fungal treatments versus 15.5% in control. On average, females infected by the three fungal species survived 5.8, 6.2 and 6.3 days, and laid 3.1, 4.0 and 4.0 eggs per capita, respectively. These were 3–4 fold lower than the control fecundity at 12.3. The cumulative probabilities [P(m ≤ N)] for the counts of infected and non-infected (control) females laying m eggs per capita (m ≤ N) during 10 days fit very well the equation P(m ≤ N) = 1/[1 + exp(a + bm)] (r ² ≥ 0.98), yielding a solution to the probability for the female mites to achieve a specific fecundity {P(m ≤ N)−P[m ≤ (N − 1)]}. Consequently, the infected mites had 71–78% chance to lay ≤5 eggs per capita but only 5–8% to deposit >10 eggs despite some variation among the tested fungi. In contrast, the chances for the non-infected mites to achieve the low and high fecundities were 23 and 55%. The fitted probabilities provide a full coverage of the fecundity potential of infected versus non-infected mites and are more informative than the mean fecundities.     

Rhizobium etli cytochrome mutants with derepressed expression of cytochrome terminal oxidases and enhanced symbiotic nitrogen accumulation

 A method to isolate mutants with derepressed expression of cytochrome oxidases and better symbiotic performance is presented. A mutant of Rhizobium etli, CFN030, isolated by its azide-resistant phenotype, was obtained by transposon Tn5-mob mutagenesis. This mutant has a derepressed expression of cytochrome aa₃, higher respiratory activities when cultured microaerobically and an improved symbiotic nitrogen fixation capacity. This phenotype was similar to the previously described mutant CFN037, which was isolated by its increased capacity to oxidize N,N,N′,N′-tetramethyl-p-phenylenediamine (TMPD) [Soberón M et al. (1990) J Bacteriol 172:1676–1680]. We show here that although both mutants have a similar symbiotic phenotype, they are affected in different genes. Strain CFN030 has the Tn5 inserted in the chromosome while in strain CFN037 the transposon was located in plasmid b. Cytochrome spectral analysis of both mutant strains in the post-exponential phase of growth, showed the expression of an additional terminal oxidase (cbb₃) that is not expressed in the wild-type strain. Received: 10 April 1995/Received revision: 21 August 1995/Accepted: 7 September1995     

Isolation and characterization of Pichia stipitis mutants with enhanced xylanase activity

Pichia stipitis strain NRRL Y-11,543 was mutagenized with N-methyl-N′-nitro-N-nitrosoguanidine (NTG) to improve xylanolytic activity. A total of 20,000 mutants were screened for xylanase overproduction by observing the clear zones around the colonies on remazol-briliant-blue-xylan (RBB-xylan)-containing agar. Of 94 mutants isolated 11 of them were found to have enhanced xylanase activity compared to the parental strain. The most active mutant NP54376 had superior properties to the wild type which included: double the enzyme activity of wild type, a shorter generation time of 2.22 h compared to 3.13 h when grown on xylan, and an enhanced growth and yield of xylanase when low levels of xylose were added to the medium. Zymogram analysis of the crude enzyme preparations from both NP54376 and the wild type by isoelectric focusing showed multiple bands ranging between pI 4.2 and 7.4. No significant difference was observed in the K _m and V _max values of the parental strain and NP54376. K _m and V _max values of xylanase for birchwood xylan were 4.2 mg ml⁻¹ and 0.08 μmol min⁻¹ mg⁻¹ of protein, respectively. This revised version was published online in July 2006 with corrections to the Cover Date.     

Seasonal relationships between leaf nitrogen content (photosynthetic capacity) and leaf canopy light exposure in peach (Prunus persica)

Abstract Field gas exchange measurements on intact peach (Prunus persica (L.) Batsch) leaves indicate that leaf nitrogen content (N_L) and leaf weight per unit leaf area (W_a) are highly correlated with CO₂ assimilation rate (A) and mesophyll conductance (g_m). Therefore, N_L and W_a were used to study seasonal relationships between leaf carboxylation capacity and natural light exposure in tree canopies. From mid-season onwards, N_L and W_a were linearly correlated with light exposure expressed as the amount of time during a clear day that a leaf was exposed to a photosynthetic photon flux density (Q) of ≥ 100 μmol m^?2 s^?1. The data support the hypothesis that whole-tree photosynthesis is optimized by partitioning of photosynthetic capacity among leaves in deciduous tree canopies with respect to natural light exposure.     

Microsolvation of aminoethanol: a study using DFT combined with QTAIM

The microsolvation of aminoethanol (AE) with one, two, three or four water molecules was investigated using a density functional theory (DFT) approach. Quantum theory of atoms in molecules (QTAIM) analyses were employed to elucidate the hydrogen-bonding characteristics of AE–(H₂O) _n (n = 1–4) complexes. The results showed that AE tends to break its intramolecular OH^AE···N^AE hydrogen bond (H-bond) upon microsolvation and form intermolecular H-bonds with water molecules, while complexes that retain the intramolecular OH^AE···N^AE H-bond show reduced stabilities. The intermolecular H-bond that forms between the nitrogen atom of AE and the hydroxyl of a water molecule is the strongest one for the most stable AE–(H₂O) _n (n = 1–4) complexes, and as n increases from 1 to 4 they grow stronger. The partial covalent character of this H-bond was confirmed by QTAIM analyses. Many-body interaction analysis showed that the relaxation energies and two- and three-body energies make significant contributions to the binding energies of the complexes.     

Improvement of a useful enzyme (subtilisin BPN′) by an experimental evolution system

In order to improve a natural enzyme so as to fit industrial purposes, we have applied experimental evolution techniques comprised of successive in vitro random mutagenesis and efficient screening systems. Subtilisin BPN, a useful alkaline serine protease, was used as the model enzyme, and the gene was cloned to an Escherichia coli host-vector system. Primary mutants with reduced activities of below 80% of that of the wild type were first derived by hydroxylamine mutagenesis directly applied to subtilisin gene DNA, followed by screening of clear-zone non-forming transformant colonies cultured at room temperature on plates containing skim-milk. Then, secondary mutants were derived from each primary mutant by the same mutagenic procedure, but screened by detecting transformant colonies incubated at 10°C with clear zones that were greater in size than that of the wild type. One such secondary mutant, 12–12, derived from a primary mutant with 80% activity, was found to gain 150% activity (k _cat/K _m value) of the wild-type when the mutant subtilisin gene was subcloned to a Bacillus subtilis host-vector system, expressed to form secretory mutant enzyme in the medium, and the activity measured using N-succinyl-l-Ala-l-Ala-l-Pro-l-Phe-p-nitroanilide as the substrate. When N-succinyl-l-Ala-l-Ala-l-Pro-l-Leu-p-nitroanilide was used, 180% activity was gained. Genetic analysis revealed that the primary and secondary mutations corresponded to D197N and G131D, respectively. The activity variations found in these mutant subtilisins were discussed in terms of Ca²⁺-binding ability. The thermostability was also found to be related to the activity.     

Transferase and hydrolytic activities of the laminarinase from rhodothermus marinus and its M133A, M133C, and M133W mutants

Comparative studies of the transglycosylation and hydrolytic activities have been performed on the Rhodothermus marinus β-1,3-glucanase (laminarinase) and its M133A, M133C, and M133W mutants. The M133C mutant demonstrated near 20% greater rate of transglycosylation activity in comparison with the M133A and M133W mutants that was measured by NMR quantitation of nascent β(1-4) and β(1-6) linkages. To obtain kinetic probes for the wild-type enzyme and Met-133 mutants, p-nitrophenyl β-laminarin oligosaccharides of degree of polymerisation 2–8 were synthesized enzymatically. Catalytic efficiency values, k _cat/K _m, of the laminarinase catalysed hydrolysis of these oligosaccharides suggested possibility of four negative and at least three positive binding subsites in the active site. Comparison of action patterns of the wild-type and M133C mutant in the hydrolysis of the p-nitrophenyl-β-D-oligosac- charides indicated that the increased transglycosylation activity of the M133C mutant did not result from altered subsite affinities. The stereospecificity of the transglycosylation reaction also was unchanged in all mutants; the major transglycosylation products in hydrolysis of p-nitrophenyl laminaribioside were β-glucopyranosyl-β-1,3-D-glucopy- ranosyl-β-1,3-D-glucopyranose and β-glucopyranosyl-β-1, 3-D-glucopyranosyl-β-1,3-D-glucpyranosyl-β-1,3-D- glucopyranoxside. In a memoriam of Dr. Kirill N. Neustroev. All we, his friends and colleagues, mourn for his sudden death. He was a bright and talented scientist, brilliant manager and good friend.     

Purification and Properties of an <Emphasis Type="Italic">N</Emphasis>-acetylglucosaminidase from <Emphasis Type="Italic">Streptomyces cerradoensis</Emphasis>

An N-acetylglucosaminidase produced by Streptomyces cerradoensis was partially purified giving, by SDS-PAGE analysis, two main protein bands with Mr of 58.9 and 56.4 kDa. The K_m and V_max values for the enzyme using p-nitrophenyl-β-N-acetylglucosaminide as substrate were of 0.13 mM and 1.95 U mg⁻¹ protein, respectively. The enzyme was optimally activity at pH 5.5 and at 50 °C when assayed over 10 min. Enzyme activity was strongly inhibited by Cu²⁺ and Hg²⁺ at 10 mM, and was specific to substrates containing acetamide groups such as p-nitrophenyl-β-N-acetylglucosaminide and p-nitrophenyl-β-D-N,N′-diacetylchitobiose.     

Relationships between dynamics of nitrogen uptake and dry matter accumulation in maize crops. Determination of critical N concentration

The concept of critical nitrogen concentration(%N _c) has been proposed as the minimum%N in shoots required to produce the maximum aerial biomassat a given time. Several authors have shown that%N _c declines as a function of aerial biomassaccumulation (W) and the %N _c –W relationship has been proposed as a diagnostic tool of N statusin different crops, excluding maize. From data obtained in five nitrogenfertilisation experiments in irrigated maize crops, 26 critical data-pointswere selected with a precise statistical procedure. An allometric relationwas fitted and a critical %N−W relationshipmodel is proposed in maize as: If W < 1 t ha^-1%N _c = 3.40 If 1 t ha^-1≤ W ≤ 22 t ha^-1%N _c = 3.40(W)^−0.37 The model is applicable to maize crop development between emergenceand silking + 25 days. The model was tested and validated with dataobtained in a network of 17 N fertilisation experiments conducted inFrance under contrasting pedoclimatic conditions. In only nineout of 280 data-points (3.2%), the plant N status was mispredictedwhen ±5% error around %N _c wasallowed. A critical N uptake model (Nu_c, kg Nha^-1) is proposed as Nu_c = 34 (W)^0.63 A comparison between Nu_c and N uptake observedin N treatments giving the maximal grain yields has shown that maizecrops assimilate at least 30 kg N ha^-1 in a storage N poolat the silking stage. The significance of the critical%N−W and Nu−W relationships is discussed in relation to theoretical models proposed inwhole plant ecophysiology. Different relationships calculated betweenleaf area index and aerial biomass accumulation, and between N uptakeand leaf area were consistent with previous results for other crops.This strengthens the interest of the critical%N−W relationship for use as diagnostictool of nitrogen status in maize crops. This revised version was published online in June 2006 with corrections to the Cover Date.     

Moisture adsorption capacity and surface area as deduced from vapour pressure isotherms in relation to hygroscopic water of soils

Six calcareous and alluvial soil profiles differing in their texture, CaCO₃ and salinity were chosen from west and middle Nile Delta for the present study. The 1^st and 2^nd profiles from Borg El-Arab area were sandy loam in texture and > 30% CaCO₃, while the 3^rd and 4^th profiles (from Nubaria area) were sandy clay loam and < 30% CaCO₃. The 2^nd and 4^th profiles were taken from cultivated area with maize. The 5^th profile from Epshan area was non-saline clay alluvial soil and the 6^th from El-Khamsen was saline clay alluvial soil. The relation between soil moisture content (W%) and water vapour pressure (P/P _o) was established for the mentioned soils. Data showed that the specific surface area (S) values were 34–53 and 44–60 m²/g for calcareous soils of Borg El-Arab and Nubaria areas, 206–219 and 206–249 m²/g for non-saline and saline clay alluvial soils of Epshan and El-Khamsen areas, respectively. The corresponding values of the external specific surface area (S _e) were 16–21, 14–22, 72–86 and 92–112 m²/g. Submitting W _m+W _me as an adsorption boundary of moisture films (W _c) (where W _m is mono-adsorbed layer of water vapour on soil particles and W _me is the external mono-adsorbed layer), the maximum water adsorption capacity (W _a) was found to be W _c + W _me or W _m + 2W _me. It was ranged from 1.88 to 2.70%, 1.97 to 2.95%, 9.70–10.70% and 10.80 to 13.12% while the maximum hygroscopic water (M _H) values were 2.43–3.78%, 2.91–4.65%, 16–17% and 18.30–21.9% for the studied soil profiles respectively. The residual moisture content (θ _r) at pF 7 and P/P _o = 0 was ranged from 0.0005–0.0010%, 0.0007–0.0019% and 0.0043–0.0048% in Borg El-Arab, Nubaria and Epshan soil profiles, respectively. The inter-relations between the surface area and the hygroscopic moisture parameters of the soils under investigation were as follows Calcareous soils; W _m = 0.40 M _H, W _c = 0.55 M _H, W _a = 0.70 M _H, S = 14 M _H Non-saline soil; W _m = 0.35 M _H, W _c = 0.49 M _H, W _a = 0.63 M _H, S = 13 M _H Saline soil; W _m = 031 M _H, W _c = 0.45 M _H, W _a = 0.59 M _H, S = 12 M _H These relations give possibility to deduce the soil moisture adsorption capacities and specific surface area via maximum hygroscopic water, which can be obtained through the experimental determination of water vapor adsorption isotherms.     

Photosynthetic Response of Carrots to Varying Irradiances

Response to irradiance of leaf net photosynthetic rates (P _N) of four carrot cultivars: Cascade, Caro Choice (CC), Oranza, and Red Core Chantenay (RCC) were examined in a controlled environment. Gas exchange measurements were conducted at photosynthetic active radiation (PAR) from 100 to 1 000 μmol m⁻² s⁻¹ at 20 °C and 350 μmol (CO₂) mol⁻¹(air). The values of P _N were fitted to a rectangular hyperbolic nonlinear regression model. P _N for all cultivars increased similarly with increasing PAR but Cascade and Oranza generally had higher P _N than CC. None of the cultivars reached saturation at 1 000 μmol m⁻² s⁻¹. The predicted P _N at saturation (P _Nmax) for Cascade, CC, Oranza, and RCC were 19.78, 16.40, 19.79, and 18.11 μmol (CO₂) m⁻² s⁻¹, respectively. The compensation irradiance (I _c) occurred at 54 μmol m⁻² s⁻¹ for Cascade, 36 μmol m⁻² s⁻¹ for CC, 45 μmol m⁻² s⁻¹ for Oranza, and 25 μmol m⁻² s⁻¹ for RCC. The quantum yield among the cultivars ranged between 0.057–0.033 mol(CO₂) mol⁻¹(PAR) and did not differ. Dark respiration varied from 2.66 μmol m⁻² s⁻¹ for Cascade to 0.85 μmol m⁻² s⁻¹ for RCC. As P _N increased with PAR, intercellular CO₂ decreased in a non-linear manner. Increasing PAR increased stomatal conductance and transpiration rate to a peak between 600 and 800 μmol m⁻² s⁻¹ followed by a steep decline resulting in sharp increases in water use efficiency. This revised version was published online in August 2006 with corrections to the Cover Date.     

Extinction probabilities in branching processes: A note on holgate and Lakhani's paper

Within the class of offspring distributions with given meanm>1 and probability of no offspringp _o, the probabilityq of ultimate extinction in a Galton-Watson branching process starting from one individual satisfiesp ₀<q(m,p₀)≤q<1. A short table illustrates the lower boundq(m,p ₀). Work done at the Mathematics Department, University of Washington, Seattle, U.S.A.     

Sex-related differences in thermoregulatory responses while wearing protective clothing

This study examined the thermoregulatory responses of men (group M) and women (group F) to uncompensable heat stress. In total, 13 M [mean (SD) age 31.8 (4.7) years, mass 82.7 (12.5) kg, height␣1.79␣(0.06) m, surface area to mass ratio 2.46␣(0.18) m² · kg⁻¹ · 10⁻², Dubois surface area 2.01 (0.16) m², %body fatness 14.6 (3.9)%, V˙O_2peak 49.0 (4.8) ml · kg⁻¹ · min⁻¹] and 17 F [23.2 (4.2) years, 62.4 (7.7) kg, 1.65 (0.07) m, 2.71 (0.14) m² · kg⁻¹ · 10⁻², 1.68 (0.13) m², 20.2 (4.8)%, 43.2 (6.6) ml · kg⁻¹ · min⁻¹, respectively] performed light intermittent exercise (repeated intervals of 15 min of walking at 4.0 km · h⁻¹ followed by 15 min of seated rest) in the heat (40°C, 30% relative humidity) while wearing nuclear, biological, and chemical protective clothing (0.29 m² ·°C · W⁻¹ or 1.88 clo, Woodcock vapour permeability coefficient 0.33 i _m). Group F consisted of eight non-users and nine users of oral contraceptives tested during the early follicular phase of their menstrual cycle. Heart rates were higher for F throughout the session reaching 166.7 (15.9) beats · min⁻¹ at 105 min (n = 13) compared with 145.1 (14.4) beats · min⁻¹ for M. Sweat rates and evaporation rates from the clothing were lower and average skin temperature () was higher for F. The increase in rectal temperature (T _re) was significantly faster for the F, increasing 1.52 (0.29)°C after 105 min compared with an increase of 1.37 (0.29)°C for M. Tolerance times were significantly longer for M [142.9 (24.5) min] than for F [119.3 (17.3) min]. Partitional calorimetric estimates of heat storage (S) revealed that although the rate of S was similar between genders [42.1 (6.6) and 46.1 (9.7) W · m⁻² for F and M, respectively], S expressed per unit of total mass was significantly lower for F [7.76 (1.44) kJ · kg⁻¹] compared with M [9.45 (1.26) kJ · kg⁻¹]. When subjects were matched for body fatness (n = 8 F and 8 M), tolerance times [124.5 (14.7) and 140.3 (27.4) min for F and M, respectively] and S [8.67 (1.44) and 9.39 (1.05) kJ · kg⁻¹ for F and M, respectively] were not different between the genders. It was concluded that females are at a thermoregulatory disadvantage compared with males when wearing protective clothing and exercising in a hot environment. This disadvantage can be attributed to the lower specific heat of adipose versus non-adipose tissue and a higher percentage body fatness. Accepted: 31 October 1997     

Using a Normal Approximation to Test for the Binomial Distribution

The commonly used method to test for the binomial distribution is the x²-test. In this paper, we introduce an alternative method to test for the binomial distribution. Suppose N is the number of sample groups with n individuals each, x_ij is the jth sample in ith group, a Bernoulli variable with parameter and VVI=s²/[m(1 - m)/n]. Then it is well know that the asymptotic distribution of the statistic (N - 1) VVI is x²(N - 1) under the hypothesis p₁ = p₂ = … = p_N. Here we find that VVI has an asymptotic normal distribution N(1, 2(1 - 1/n)/(N - 1)). Unlike the x²-statistic, the variance of the normal test statistic is a function of n. This method is convenient in detecting spatial patterns and dispersion in the study of diseased organisms (e.g., plants) in field samples.     

Heat and mass exchange processes between the surface of the human body and ambient air at various altitudes

 The rates of convection and evaporation at the interface between the human body and the surrounding air are expressed by the parameters convective heat transfer coefficient h _c, in W m^–2°C^–1 and evaporative heat transfer coefficient h _e, W m^–2 hPa^–1. These parameters are determined by heat transfer equations, which also depend on the velocity of the airstream around the body, that is still air (free convection) and moving air (forced convection). The altitude dependence of the parameters is represented as an exponential function of the atmospheric pressure p: h _c∼p ⁿ and h _e∼p ^1–n, where n is the exponent in the heat transfer equation. The numerical values of n are related to airspeed: n=0.5 for free convection, n=0.618 when airspeed is below 2.0 ms^–1 and n=0.805 when airspeed is above 2.0 ms^–1. This study considers the coefficients h _c and h _e with respect to the similarity of the two processes, convection and evaporation. A framework to explain the basis of established relationships is proposed. It is shown that the thickness of the boundary layer over the body surface increases with altitude. As a medium of the transfer processes, the boundary layer is assumed to be a layer of still air with fixed insulation which causes a reduction in the intensity of heat and mass flux propagating from the human body surface to its surroundings. The degree of reduction is more significant at a higher altitude because of the greater thickness of the boundary layer there. The rate of convective and evaporative heat losses from the human body surface at various altitudes in otherwise identical conditions depends on the following factors: (1) during convection – the thickness of the boundary layer, plus the decrease in air density, (2) during evaporation (mass transfer) – the thickness of the boundary layer, plus the increase with altitude in the diffusion coefficient of water vapour in the air. The warming rate of the air volume due to convection and evaporation is also considered. Expressions for the calculation of altitude dependences h _c (p) and h _e (p) are suggested. Received: 23 June 1998 / Accepted: 10 February 1999     

Study of the parameters of hydrogen-titanium plasma in a pulsed reflective discharge

The parameters of a dense (10¹³–10¹⁴ cm⁻³) plasma produced by ionization of a H₂ + Ti mixture in a moderate-power (W ≤ 10 MW) pulsed reflective discharge are investigated. The dynamics of the plasma density, the elemental composition of the generated plasma, the radial distribution of the electron density, the rotation velocity and frequency of the plasma layer with n _p ≥ n _cr, the radial electric field, the coefficient of plasma particle separation, and the coefficient of plasma recombination in the stage of plasma decay are determined.     

Site-directed mutagenesis of cysteine residues of <Emphasis Type="Italic">Luciola mingrelica</Emphasis> firefly luciferase

Single mutants (C62S, C62V, C86S, C146S, C164S), double mutants (C62/146S, C62/164S, C86/146S, C146/164S), and triple mutant C62/146/164S of the Luciola mingrelica firefly luciferase carrying C-terminal His6-tag were obtained on the basis of plasmid pETL7 by site-directed mutagenesis. Bioluminescence and fluorescence spectra were not altered by the introduced mutations. In the case of mutants C86S, C86/146S, C62/164S, and the triple mutant C62/146/164S, the K _m^ATP and K_m^LH₂ K_m^{LH_2 } values were increased by a factor of ∼1.5–1.9. Their expression level, specific activity, and thermal stability were significantly decreased. The other mutations had almost no effect on the K _m^ATP and K_m^LH₂ K_m^{LH_2 } values, specific activity, and thermal stability of the enzyme. Thermal stability of the C146S mutant was increased by a factor of ∼2 and 1.3 at 37 and 42°C, respectively. The possible mechanism of the influence of these mutations on properties and structure of the enzyme is discussed.     

Note on an inequality for the coefficients in legendre polynomial expansions and its application to the theory of liquid phase transitions

It is shown that if themth derivative of a function is positive, and it has a Legendre polynomial expansion with coefficients,A _n, then (A _m)/(2m+1)≧(A _n)/(2n+1) forn>m. This result is applied to the theory of liquid phase transitions.     

Biofiltration of paint solvent mixtures in two reactor types: overloading by hydrophobic components

Steady-state performance characteristics of a trickle bed reactor (TBR) and a biofilter (BF) in loading experiments with increasing toluene/xylenes inlet concentrations while maintaining a constant loading rate of hydrophilic components (methyl ethyl and methyl isobutyl ketones, acetone, and n-butyl acetate) of 4 g m⁻³ h⁻¹ were evaluated and compared, along with the systems’ dynamic responses. At the same combined substrate loading of 55 g m⁻³ h⁻¹ for both reactors, the TBR achieved more than 1.5 times higher overall removal efficiency (RE_W) than the BF. Increasing the loading rate of aromatics resulted in a gradual decrease of their REs. The degradation rates of acetone and n-butyl acetate were also inhibited at higher loads of aromatics, thus revealing a competition in cell catabolism. A step-drop in loading of aromatics resulted in an immediate increase of RE_W with variations in the TBR, while the new steady-state value in the BF took 6–7 h to achieve. The TBR consistently showed a greater performance than BF in removing toluene and xylenes. Increasing the loading rate of aromatics resulted in a gradual decrease of their REs. The degradation rates of acetone and n-butyl acetate were also lower at higher OL_AROM, revealing a competition in the cell catabolism. The results obtained are consistent with the proposed hypothesis of greater toxic effects under low water content, i.e., in the biofilter, caused by aromatic hydrocarbons in the presence of polar ketones and esters, which may improve the hydrocarbon partitioning into the aqueous phase.