Simulations of the ion current to a probe in plasma with allowance for ionization and ion-neutral collisions: I. Spherical probe

The ion current to a spherical probe is considered with allowance for volume ionization, ion-neutral collisions, and the ion orbital moment. A model based on the molecular dynamics method and applicable for a wide range of plasma parameters is proposed: r _p/λ_D = 0.001–100, λ _i /λ_D = 0.001–100, ${{\nu _i \lambda _D } \mathord{\left/ {\vphantom {{\nu _i \lambda _D } {\sqrt {{{kT_e } \mathord{\left/ {\vphantom {{kT_e } M}} \right. \kern-0em} M}} }}} \right. \kern-0em} {\sqrt {{{kT_e } \mathord{\left/ {\vphantom {{kT_e } M}} \right. \kern-0em} M}} }} = 0.01 - 1$ , and T _i /T _e = 0.01. A convenient representation of the dependences of the relative ion current density on the Langmuir coefficient α² and a technique for determining the plasma density from simulation results are offered.     

Effects of wind on thermoregulation and energy balance in deer mice (Peromyscus maniculatus)

Summary The effects of various convective and temperature regimes on heat production, evaporative heat loss, and thermal resistance were studied in deer mice,Peromyscus maniculatus. Heat production (measured as oxygen consumption) increased with increasing wind speed (V) and decreasing ambient temperature (T _a), except atT _a=35°C which was thermoneutral for allV from 0.05 through 3.75 m/s. Evaporative water loss ( ) increased with increasingT _a, but wind had little effect on except at highT _a. In the absence of forced convection, the animals' total resistance to heat transfer (r _t) was high and stable atT _a below thermoneutrality. However, at highV ther _t increased steadily with decreasingT _a. Although deer mice rarely experience high wind speeds in natural microhabitats, the convective regime is nevertheless important in determining rates of heat loss, and must be considered in studies of ecological energetics.Symbols and Abbreviations A animal surface area - HP _n net metabolic heat production - EHL evaporative heat loss - MHP metabolic heat production - r _t total resistance to heat transfer - r _ext external resistance component of r_t - RQ respiratory quotient - pc _p volumetric specific heat of air - T _a ambient temperature - t _b body temperature - t _e operative, or equivalent blackbody temperature of the environment - T _sk skin temperature - T _es standard operative temperature - V wind speed - oxygen consumption - carbon dioxide production - evaporative water loss     

Mixing-models applied to industrial batch bioreactors

Mixing models for bioreactors on the basis of the tanks-in-series concept are presented and a suitable parameter-estimation method is introduced. The Monte-Carlo-optimization procedure with the inhomogeneity-curve included in the objective function is used. Results of the parameter optimization procedure are given for stirred-tank-bioreactors equipped with one and three Rushton turbines under aerated conditions. The model designed for the stirredtank with three Rushton turbines is capable to describe the mixing properties, while in case of the stirred-tank with one Rushton turbine the simulated radial circulation time does not correlate with the measured one.List of Symbols a ₀₀...a _XY coefficients in Eq. (9) - d _i m stirrer diameter - D m tank diameter - E relative error - F _AX m³/s axial liquid flow rate - F _G m³/s aeration flow rate - F _RAD m³/s radial liquid flow rate - g m/s² acceleration of gravity - h _l m height of fluid in the tank - i _s(t) simulated inhomogeneity-curve - i _m(t) measured inhomogeneity-curve - k number of sensors - n 1/s stirrer revolutions - N number of tanks in the tanks-of-series-cascade - p number of measured time intervalls - t s time - t _c.AX s axial circulation time - t _c,RAD s radial circulation time - T _i °C temperature of sensors - T °C temperature at the end of the experiment - T ₀ °C temperature before pulse injection - V _tot m³ total liquid volume - V _C m³ liquid volume of circulation cascade, additional index specifications describe the cascade elements (Figs.1 and 2) - V _M m³ liquid volume of well mixed stirrer compartment - w ₀ m/s superficial gas velocity - X, Y exponents in eq. (9) - kg/m³ density - Pas dynamic viscosity - m²/s kinematic viscosity - s time constant (time for 63,2% of T ) of the signal Dimensionless Numbers stirrer Froude number - aeration Froude number     

Tolerance regions with segmented fermentation processes

Many microbial fermentation processes exhibit different phases (e.g. adaption phase, main growth phase, main production phase). The process variables e.g. the biomass vary randomly about their mean. The experimentalist is interested to know the break points of the different phases, and a tolerance region, i.e. a range of possible values of the process variable that can be considered as normal. This paper deals with statistical methods for determining break points and tolerance regions.List of Symbols a _i intercept in phasei - b _i specific growth rate in phasei - e _t deviation of a measurement in timet - tEX expectation of variableX - r number of phases of fermentation - T _i break point of phaseit - t _ij time of measurementj in phasei - t _n–2.1–/2 quantile oft distribution - Y(t) logarithm of measurement at timet Greek Letters 1 – cover probability of tolerance region - 1 – part covered by the tolerance region - ² variance ofe _t - (·) standard normal distribution - quantile of chisquare distribution     

A testcross procedure for selecting exotic strains to improve pure-line cultivars in predominantly self-fertilizing species

Methods for identifying germplasm carrying alleles with the potential to improve a particular single-cross hybrid have been proposed and discussed in recent years. There is a need for similar methods to be used in breeding crops for which pure-line cultivars, rather than hybrids, are the goal. The objective of this research was to develop a method to identify germplasm lines with the potential to contribute favorable alleles not present in a specified pure line or set of pure lines. Given a set of adapted pure lines (A ₁, A ₂ ..., A _m) to be improved and a set of germplasm lines (P ₁ P ₂ ..., P _f), the procedure consists of producing all f x m possible hybrids and evaluating them along with the parents. The testcross statistic T _ij is defined by T _ij=(F _ij–A _j)+(1–) (F _ij–P _i), where A _j, P _i, and F _ij represent the performance of thej ^th adapted line, the i ^th germplasm line, and their hybrid, respectively. The statistic is the mean value of T _ij over all adapted parents A _j. If =(1/2)(1+d), where d = the mean degree of dominance, then T _ij measures the potential for alleles from P _i to improve A _j and measures the potential for alleles from P _i to improve the set A ₁, A ₂ ..., A _m. Use of data on soybean and peanut hybrids published by other researchers suggests that the value assumed for d has little effect on the P _i chosen. The ability of the T _ij and statistics to identify germplasm strains carrying rare favorable alleles should be assessed in empirical studies.Joint contribution: OARDC (Journal Articale No. 161-94), USDAARS, Iowa Agriculture and Home Economics Expriment Station (Journal Paper No. J-16109; Project 2985), and Agreculture and Agri-Food Canada. Salaries and research support for S. K. St. Martin Provided by state and federal funds appropriated to the Ohio Agricultural Research and Development Center, Ohio State University     

Heat transfer in vertical perl mills

A model of heat transfer during grinding in vertical multi-disk perl mills has been proposed. Heat transfer intensity in such mills depends on thermal resistance in a boundary layer formed at the inner surface of mill tank wall. The layer thickness changes depending on process variables. Results obtained are presented in the form of a dimensionless correlation equation.List of Symbols C ball filling of the mill, - c _pw specific heat of cooling water, kJ/(kg K) - d disk diameter, m - d _k ball diameter, m - D inner diameter of the mill tank, m - G _w mass flow rate of cooling water, kg/s - h distance between impeller disks, m - n revolutions frequency of the impeller shaft, s^–1 - q heat flux density, kW/m² - Q _c total heat energy emitted in the mill, W - T temperature, K - T _w1 temperature of cooling water at the cooling jacket inlet, K - T _w2 cooling water temperature at the outlet, K - T _m average temperature inside the mill, K - T _s average temperature of the tank wall, K - u peripheral speed of the impeller disk, m/s - heat transfer coefficient, kW/(m²K) - boundary layer thickness, m - porosity of the lying bed, - _m porosity of the suspended bed, - _c liquid dynamic viscosity, Pa s - _cs liquid dynamic viscosity at wall temperature, Pa s - _c thermal conductivity coefficient of liquid, W/(mK) - _c liquid density, kg/m³ - _s solid density, kg/m³ Dimensionless Numbers Reynolds number for mixing process - Reynolds number for liquid parameters - Nusselt number for liquid parameters - Prandtl number for liquid parameters - modified Euler number     

Suitability of the shaking flask for oxygen supply to microbiological cultures

Due of its simplicity the shaking flask is used in serial studies, e.g. in the screening for secondary metabolites or in the optimization of fermentation processes. Experimental investigations in these small bioreactors are often the first step in developing a large-scale fermentation process.Movement of the flask should produce sufficient mixing, supply of oxygen, and removal of carbon dioxide. In the case of fluids with low or moderate viscosity, gas transport is the most important aspect. This publication summarizes data necessary to calculate the gas transport. These data are derived from the consideration of the gas diffusions through the cotton plug as well as from the substance transport between the gas and liquid phases. As a result suitable fermentation conditions can be selected. Finally, the performance limits of the shaking flask are illustrated using the example of the oxygen supply in a Streptomyces tendae fermentation.List of Symbols A _s Cross section of plug - A Surface area of liquid in flask - a A/V _F specific phase interface area - c Concentration - c ^* Saturation concentration - c Plug diffusion term - D Widest diameter of flask - Diffusion coefficients in multicomponent gas mix tures - Diffusion coefficients in binary gas mixtures - Diffusion coefficient of oxygen in the liquid - d Diameter of neck of flask - e Eccentricity - G Volume-based mass flow - G _m Maximum volume-based mass flow - g Acceleration due to gravity - h Height coordinate - ¯H Mean height of plug - Hy p _i/c ^*, Henry constant - K Consistency index - k D _xy/D _xz, Ratio of diffusion coefficients in binary gas mixtures - k _M Monod constant - k _L a Mass transport coefficient: gas/liquid - M Molecular weight - m Flow exponent - n Speed of shaking - p Pressure - p _i Partial pressure of gas component i - q Area-based flow of volume - R , respiration ratio - Sc , Schmidt number - T Absolute temperature - V Flask volume - V _F Volume of liquid in flask - w Velocity of the Stefan flow - x, y, z Ratios of the partial pressures of the gases O₂, CO₂, N₂ - Rate of shear - Dynamic viscosity of the liquid - Kinematic viscosity of the liquid - Density of the liquid - _x, Density of O₂ gas - Surface tension Indices 0 State in gas volume of shaking flask - 1 State in outside air - G Gas volume - x, y, z O₂, CO₂, N₂     

The human V pre B gene is located on chromosome 22 near a cluster of {\text{V}}_{\lambda _1 } gene segments

The chromosomal location of the human V _pre B gene was determined by Southern blotting analysis of restriction enzyme-digested DNAs from a panel of 17 mouse-human somatic cell hybrids. The pattern of hybridization of a V_preB-specific probe in conjunction with earlier analysis of several marker genes allowed the following conclusions: 1) V _pre B is on human chromosome 22 within band 22q11.2 distal to the bcr-like gene, bcr-2 and proximal to the bcr-like gene, bcr-4. 2) V_preB has been localized relative to several constitutional and tumor-specific breakpoints within 22q 11.2, segregates in hybrids retaining 22q^–chromosomes with some but not with all members of the subgroup of the V genes, and is amplified with these genes in K562 cells. 3) The order of the loci on chromosome 22 is centromerebcr-2, V _preB, .     

Effects of ambient temperature and altitude on ventilation and gas exchange in deer mice (Peromyscus maniculatus)

Summary The effects of different ambient temperatures (T _a) on gas exchange and ventilation in deer mice (Peromyscus maniculatus) were determined after acclimation to low and high altitude (340 and 3,800 m).At both low and high altitude, oxygen consumption ( ) decreased with increasingT _a atT _a from –10 to 30 °C. The was 15–20% smaller at high altitude than at low altitude atT _a below 30 °C.Increased atT _a below thermoneutrality was supported by increased minute volume ( ) at both low and high altitude. At mostT _a, the change in was primarily a function of changing respiration frequency (f); relatively little change occurred in tidal volume (V _T) or oxygen extraction efficiency (O₂EE). AtT _a=0 °C and below at high altitude, was constant due to decliningV _T and O₂EE increased in order to maintain high .At high altitude, (BTP) was 30–40% higher at a givenT _a than at low altitude, except atT _a below 10 °C. The increased at high altitude was due primarily to a proportional increase inf, which attained mean values of 450–500 breaths/min atT _a below 0 °C. The (STP) was equivalent at high and low altitude atT _a of 10 °C and above. At lowerT _a, (STPD) was larger at low altitude.At both altitudes, respiratory heat loss was a small fraction (<10%) of metabolic heat production, except at highT _a (20–30 °C).Abbreviations EHL evaporative heat loss - f respiration frequency - HL _a heat loss from warming tidal air - HL _e evaporative heat loss in tidal air - HL total respiratory heat loss - MHP metabolic heat production - O ₂ EE oxygen extraction efficiency - RQ respiratory quotient - T _a ambient temperature - T _b body temperatureT _lc lower critical temperature - carbon dioxide production - evaporative water loss - oxygen consumption - minute volume - V _T tidal volume     

Graphic analysis of codon usage strategy in 1490 human proteins

The frequencies of bases A (adenine), C (cytosine), G (guanine), and T (thymine) occurring in codon positioni, denoted bya _i ,c _i ,g _i , andt _i , respectively (i=1, 2, 3), have been calculated and diagrammatized for the 1490 human proteins in the codon usage table for primate genes compiled recently. Based on the characteristic graphs thus obtained, an overall picture of codon base distribution has been provided, and the relevant biological implication discussed. For the first codon position, it is shown in most cases that G is the most dominant base, and that the relationshipg ₁>a ₁>c ₁>t ₁ generally holds true. For the second codon position, A is generally the most dominant base and G is the one with the least occurrence frequently, with the relationship ofa ₂>t ₂>c ₂>g ₂. As to the third codon position, the values ofg ₃+c ₃ vary from 0.27 to 1, roughly keeping the relationship ofc ₃>g ₃>a ₃=t ₃ for the majority of cases. Interestingly, if the average frequencies for bases A, C, G, and T are defined as , respectively, we find that is valid almost without exception. Such a characteristic inequality might reflect some inherent rule of codon usage, although its biological implications is unclear. An important advantage by introducing graphic methods is to make it possible to catch essential features from a huge amount of data by a direct and intuitive examination. The method used here allows one to see means and variances, and also spot outliers. This is particularly useful for finding and classifying similarity patterns and relationships in data sets of long sequences, such as DNA coding sequences. The current method also holds a great potential for the study of molecular evolution from the viewpoint of genetic code whose data have been accumulated rapidly and are to continue growth at a much faster pace.On sabbatical leave from Department of Physics, Tianjin University, Tianjin, China.     

Optimal control of continuous fermentation processes

Three layer control structure is proposed for optimal control of continuous fermentation processes. The start-up optimization problems are solved as a first step for optimization layer building. A steady state optimization problem is solved by a decomposition method using prediction principle. A discrete minimum time optimal control problem with state delay is formulated and a decomposition method, based on an augmented Lagrange's function is proposed to solve it. The problem is decomposed in time domain by a new coordinating vector. The obtained algorithms are used for minimum time optimal control calculation of Baker's Yeast fermentation process.List of Symbols x(t) g/l biomass concentration - s(t) g/l limiting substrate concentration - x ⁰ g/l inlet biomass concentration - s ⁰(t) g/l inlet substrate concentration - D(t) h^–1 dilution rate - (t) h^–1 specific growth rate - Y g/g yield coefficient - (t) h^–1 specific limiting substrate consumption rate - k _D h^–1 disappearing constant - w ₁, w ₂ known constant or piece-wise disturbances - _m h^–1 maximum specific growth rate - k _s g/l Michaelis-Menten's parameter - h time delay - x ₀, s ₀ g/l initial concentrations - ¯x, ¯s, ¯D optimal steady state value - V _min , V _max , v=x,s,d,t bounds of variables - t h sampling period - K number of steps in the optimization horison - Js, J _d performance indexes - L _s Lagrange's function - L _d Lagrange's functional - ₀ weighting coefficient for the amount of the limiting substrate throwing out of the fermentor - ₁, ₂ dual variables of Lagrange's function - steps in steady state coordination procedure - errors values for steady state coordination process - _v , v=x, s conjugate variables of Lagrange's functional - _v , v=x,s penalty coefficients of augmented Lagrange's functional - _v , v=x, s interconnections of the time - e _v , v=x,s, D, _x , _s gradients of Lagrange's functional - j, l indexes of calculation procedures - values of errors in calculations The researches was supported by National Scientific Research Foundation under grants No NITN428/94 and No NITN440/94     

Effects of temperature and altitude on ventilation and gas exchange in chukars (Alectoris chukar)

Summary The effects of ambient temperature (T _a) on ventilation and gas exchange in chukar partridges (Alectoris chukar) were determined after acclimation to low and high altitute (LA and HA; 340 and 3,800 m, respectively).At both LA and HA, oxygen consumption ( ) increased with decreasingT _a atT _a from 20 to –20°C. AtT _a of 35 to 40°C, increased above thermoneutral values at HA but remained constant and minimal at LA. Water loss rates increased rapidly atT _a>30°C at both altitudes as birds began to pant. Ventilation rates (f) during panting were 5-to 23-fold greater than the minimalf at thermoneutralT _a.Increased atT _a below thermoneutrality was supported by increased minute volume (V i) at both altitudes. The change inV i was primarily a function of changing tidal volume (V t), althoughf increased slightly asT _a declined. Oxygen extraction ( ) remained fairly constant atT _a below 20°C at both altitudes. BothV t and were considerably lower when birds were panting than at lowerT _a.Chukars showed few obvious ventilatory adaptations to HA. The 35% change in between 340 and 3,800 m was accommodated by a corresponding change inV i (btps), most of which was accomplished by increasedf at HA, along with a slight increase in .Abbreviations and symbols HA high altitude - LA low altitude - rate of evaporative water loss - oxygen extraction efficiency - f respiratory frequency - V t tidal volume - V i minute volume - BMR basal metabolic rate - MHP metabolic heat production     

Thermoregulation,gas exchange,and ventilation in Adelie penguins (Pygoscelis adeliae)

Summary Adelie penguins (Pygoscelis adeliae) experience a wide range of ambient temperatures (T _a) in their natural habitat. We examined body temperature (T _b), oxygen consumption ( ), carbon dioxide production ( ), evaporative water loss ( ), and ventilation atT _a from –20 to 30 °C. Body temperature did not change significantly between –20 and 20°C (meanT _b=39.3°C).T _b increased slightly to 40.1 °C atT _a=30°C. Both and were constant and minimal atT _a between –10 and 20°C, with only minor increases at –20 and 30°C. The minimal of adult penguins (mean mass 4.007 kg) was 0.0112 ml/[g·min], equivalent to a metabolic heat production (MHP) of 14.9 Watt. The respiratory exchange ratio was approximately 0.7 at allT _a. Values of were low at lowT _a, but increased to 0.21 g/min at 30°C, equivalent to 0.3% of body mass/h. Dry conductance increased 3.5-fold between –20 and 30°C. Evaporative heat loss (EHL) comprised about 5% of MHP at lowT _a, rising to 47% of MHP atT _a=30°C. The means of ventilation parameters (tidal volume [VT], respiration frequency [f], minute volume [I], and oxygen extraction [ ]) were fairly stable between –20 and 10°C (VT did not change significantly over the entireT _a range). However, there was considerable inter- and intra-individual variation in ventilation patterns. AtT _a=20–30°C,f increased 7-fold over the minimal value of 7.6 breaths/min, and I showed a similar change. fell from 28–35% at lowT _a to 6% atT _a=30°C.Abbreviations C thermal conductance - EHL evaporative heat loss - oxygen extraction - f respiratory frequency - MHP metabolic heat production - evaporative water loss - LCT lower critical temperature - RE respiratory exchange ratio - T _a ambient temperature - T _b body temperature - rate of oxygen consumption - rate of carbon dioxide production - I inspiratory minute volume - VT tidal volume     

The effect of ambient temperature on the relationship between ventilation and metabolism in a small parrot (Agapornis roseicollis)

Summary Values for basal metabolism, standard tidal volume (V _T), standard minute volume ( ), and mean extraction efficiency (EO₂) in the thermal neutral zone (TNZ) inAgapornis roseicollis (1.84 ml·min^–1; 0.95 ml·br^–1, STPD; and 33.3 ml·min^–1, STPD; and 22.5%; respectively) were all very similar to values for these parameters previously measured inBolborhynchus lineola, a similarly sized, closely related species from a distinctly different habitat.Having both a lower critical temperature (T_lc) below and an upper critical temperature (T_uc) above those ofB. lineola, the TNZ ofA. roseicollis extended from 25° to at least 35°C. The thermal conductance below the TNZ ofA. roseicollis was 14% less than that ofB. lineola. Therefore, at 5°C the standard metabolic rate (SMR) of the former is 17% less than that of the latter, and at 35°C it is 20% less. At 5°CA. roseicollis has a lower EO₂ and at 35°C a higher EO₂ than that ofB. lineola. The patterns of resting energy metabolism and of ventilation ofA. roseicollis and ofB. lineola are consistent with the former species being better suited to living in a more variable thermal environment than the latter.MeanV _T has a weak positive correlation with the rate of oxygen consumption ( ) at a constant ambient temperature (T _a) but a much stronger correlation when resting increases in response to a decrease inT _a.V _t is the only ventilatory parameter which is linearly correlated toT _a from 35° to –25°C. The data suggest thatT _a may have a regulatory effect onV _T somewhat independent of or .     

Studies on a continuous recycle reactor for a lipase-catalysed processing of ricebran oil

The authors have developed a continuous recycle reactor which efficiently performs emulsion type enzymatic reactions. The reactor column is filled with immobilised lipase and the reactions are effected by pumping the pre-prepared oil-water emulsion through the bottom of the reactor. A part of the product was recycled back and this type of recycling greatly improves the productivity of fatty acid compared to continuous once-through reactor without recycling. The recycle reactor could be continuously run for 35 days without decrease in conversions. The performance of the reactor was interpreted by a model and the theoretical conversion was compared with the experimental data.List of Symbols F _AO mol/min feed rate - K _M g/l Michaelis constant - R recycle ratio - r ₅ mol/(ml · min) reaction rate - S ₀ g/l initial substrate concentration - V _max mol/(ml · min) maximum reaction velocity - V _R l void volume of the reactor - x _s fractional conversion - Standard deviation      

Optimal temperature and concentration profiles in a cascade of CSTR's performing Michaelis-Menten reactions with first order enzyme deactivation

A necessary condition is found for the intermediate temperatures and substrate concentrations in a series of CSTR's performing an enzyme-catalyzed reaction which leads to the minimum overall volume of the cascade for given initial and final temperatures and substrate concentrations. The reaction is assumed to occur in a single phase under steady state conditions. The common case of Michaelis-Menten kinetics coupled with first order deactivation of the enzyme is considered. This analysis shows that intermediate stream temperatures play as important a role as intermediate substrate concentrations when optimizing in the presence of nonisothermal conditions. The general procedure is applied to a practical example involving a series of two reactors with reasonable values for the relevant five operating parameters. These parameters are defined as dimensionless ratios involving activation energies (or enthalpy changes of reaction), preexponential factors, and initial temperature and substrate concentration. For negligible rate of deactivation, the qptimality condition corresponds to having the ratio of any two consecutive concentrations as a single-parameter increasing function of the previous ratio of consecutive concentrations.List of Symbols C _E,0 mol.m^–3 Initial concentration of active enzyme - C _E,i mol.m^–3 Concentration of active enzyme at the outlet of the i-th reactor - C _S,0 mol.m^–3 Initial concentration of substrate - C _S,i mol.m^–3 Concentration of substrate at the outlet of the i-th reactor - Da _i Damköhler number associated with the i-th reactor ((V _i.k_v,0.C_E,0)/(Q.C_S,0)) - Da _min Minimum value of the overall Damköhler number - Da _tot Overall Damköhler number - E _d J.mol^–1 Activation energy of the step of deactivation of the enzyme - E _m J.mol^–1 Standard enthalpy change of the step of binding of substrate to the enzyme - E _v J.mol^–1 Activation energy of the step of enzymatic transformation of substrate - i Integer variable - j Dummy integer variable - k Dummy integer variable - k _d,i s^–1 Kinetic constant associated with the deactivation of enzyme in the i-th reactor (k _d,o·exp{–E _d/(R.T _i}) - k _d,0 s^–1 Preexponential factor of the kinetic constant associated with the deactivation of the enzyme - K _m,i mol.m^–3 Equilibrium constant associated with the binding of substrate to the enzyme in the i-th reactor, (k _m,o·exp{–E _m}(R.T _i}) - K _m,0 mol.m^–3 Preexponential factor of the Michaelis-Menten constant associated with the binding of substrate to the enzyme - k _v,i s^–1 Kinetic constant associated with the transformation of the substrate by the enzyme in the i-th reactor (k _v,o·exp{–E _v/(R.T _i})) - k _v,0 s^–1 Preexponential factor of the kinetic constant associated with the transformation of the substrate by the enzyme - N Number of reactors in the series - Q m³.s^–1 Volumetric flow rate of reacting liquid through the reactor network - R J.K^–1.mol^–1 Ideal gas constant - T _i K Absolute temperature at the outlet of the i-th reactor - T ₀ K Initial absolute temperature - V _i m³ Volume of the i-th reactor - v _max mol.m^–3.s^–1 Maximum rate of reaction under saturation conditions of substrate - x _i Normalized concentration of substrate (C_S,i/C_{S, 0}) - x _i,opt Optimum value of the normalized concentration of substrate - y _i Dimensionless temperature (exp{–T ₀/T _i}) - y _i,opt Optimum value of the dimensionless temperature Greek Symbols Dimensionless preexponential factor associated with the Michaelis-Menten constant (K _m,0/C_s,0) - Dimensionless activation energy of the step of enzymatic transformation of substrate (E _v/R.T₀)) - Dimensionless standard enthalpy change of the step of binding of substrate to the enzyme (E _m/(R.T₀)) - Dimensionless activation energy of the step of deactivation of the enzyme (E _d/(R.T₀)) - Dimensionless deactivation preexponential factor ((k _d,0.C_S,0)/(k_v,0.C_E,0)     

A mathematical model of biological evolution

In order to understand generally how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dN _n (t)/dt=(m _n (t-)N _n (t)+N _n-1(t) (n=0,1,2,3...), where N _n (t) and m _n (t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t and is the mutation rate, assumed to be a positive constant. The step number of each replicon is defined as either equal to or larger by one than that of its parent, the latter case occurring when and only when mutation has taken place. The average evolution rate defined by is rigorously obtained for the case (i) m _n (t)=m _n is independent of t (constant fitness model), where m _n is essentially periodic with respect to n, and for the case (ii) (periodic fitness model), together with the long time average m of the average Malthusian parameter . The biological meaning of the results is discussed, comparing them with the features of actual molecular evolution and with some results of computer simulation of the model for finite populations.An early version of this study was read at the International Symposium on Mathematical Topics in Biological held in kyoto, Japan, on September 11–12, 1978, and was published in its Procedings.     

Sequence and age of eruption of deciduous dentition in the baboon (Papio sp)

A detailed eruption sequence and associated age of eruption for deciduous dentition in baboons (Papio sp) are presented in this paper. The sequence was determined by evaluation and comparison of the number and kinds of teeth present in nine age cohorts comprising the study sample of 88 males and 87 females who ranged in age from birth to 763 days. Eruption was assessed visually as present or absent. Several statistical methods used to derive the ages associated with the eruption sequence are described. The basic eruption sequence in the sample population is: i¹ i₁, i₂, i², \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm c}\limits_{\rm -} {\rm,}\mathop {\rm c}\limits^{\rm -} $\end{document} m¹ (m², m₂), M₁, M¹. Both sexes show the same pattern, with the exception of the second deciduous molar, where males show a sequence of m₂, m₂, while females show the opposite. Posterior dentition shows the greatest gender-specific variation in average age of eruption.     

The basic flow equations of electrophysiology in the presence of chemical reactions: I. Development of the equations

Starting from the basic flux equation, it is possible to obtain an integral form relating the current componentsI _i at an arbitrary pointr ₂ to the distribution of mobilities and concentrationsc _i, potential forces\(\bar \mu \), and chemical productivityp _i without any restrictive assumptions such as constant mobilities, constant field, steady state, or electrical neutrality. The equation is

$$\begin{gathered} I_i (r_2 ) = G_i (r_2 )\left[ {\Delta \bar \mu _i - \int_{r_1 }^{r_2 } {z_i } FA\left( {p_i - dc_i /dt} \right)\left( {\frac{1}{{G_i (r)}}} \right)dr} \right]; \hfill \\ G_i (r) = 1/\int_{r_1 }^r {\frac{{dr}}{{z_i^2 F^2 c_i u_i }}.} \hfill \\ \end{gathered} $$     

Theoretical studies on the necessary number of components in mixtures

Summary Theoretical studies on the optimal numbers of components in mixtures (for example multiclonal varieties or mixtures of lines) have been performed according to phenotypic yield stability (measured by the parameter variance). For each component i, i = 1, 2,..., n, a parameter u_i with 0 u_i 1 has been introduced reflecting the different survival and yielding ability of the components. For the stochastic analysis the mean of each u_i is denoted by u ₁ and its variance by _i ² For the character total yield the phenotypic variance V can be explicitly expressed dependent on 1) the number n of components in the mixture, 2) the mean of the _i ² 3) the variance of the _i ² 4) the ratio and 5) the ratio _i ² /² where denotes the mean of the u _i and _u ² is the variance of the u _j. According to the dependence of the phenotypic stability on these factors some conclusions can be easily derived from this V-formula. Furthermore, two different approaches for a calculation of necessary or optimal numbers of components using the phenotypic variance V are discussed: A. Determination of optimal numbers in the sense that a continued increase of the number of components brings about no further significant effect according to stability. B. A reduction of b % of the number of components but nevertheless an unchanged stability can be realized by an increase of the mean of the u _i by 1% (with and _u ² assumed to be unchanged). Numerical results on n (from A) and 1 (from B) are given. Computing the coefficient of variation v for the character total yield and solving for the number n of components one obtains an explicit expression for n dependent on v and the factors 2.-5. mentioned above. In the special case of equal variances, _i ² = _o ² for each i, the number n depends on v, x = (₀/)² and y = (_u/)². Detailed numerical results for n = n (v, x, y) are given. For x 1 and y 1 one obtains n = 9, 20 and 79 for v = 0.30, 0.20 and 0.10, respectively while for x 1 and arbitrary y-values the results are n = 11, 24 and 95.This publication is an extended version of a lecture given at the 1984-EUCARPIA meeting (Section Biometrics in Plant Breeding) in Stuttgart-Hohenheim (Federal Republic of Germany)