On recursive averaging processes and Hilbert space extensions of the contraction mapping principle

If T maps a convex domain D_T into itself, and if {ω_n} is a real sequence with range in (0, 1] then the recursive averaging process,

$\text{X}{}_{\mathrm{n+1}}\text{=(1?omega;}{}_{\mathrm{n}}\text{)}\text{X}{}_{\mathrm{n}}\text{+ω}{}_{\mathrm{n}}\text{+ω}{}_{\mathrm{n}}\text{T}\text{x}{}_{\mathrm{n}}\text{,}\text{x}{}_0\text{=ξ?D}{}_{\mathrm{T}}$

generates a sequence {x?_n}; with range in D_T. Under suitable conditions on D_T, T and {ω_n} the sequence {x?_n} will converge in some sense to a fixed point of T. We prove that if D_T is a closed convex subset of a complex Hilbert space H, if Tω = (1 ? ω) I + ωT is a strict contraction for some ω ? (0, 1], and if {ω_n} satisfies the conditions,

$\text{ω}{}_{\mathrm{n}}\text{→ 0}$

and

$\text{∑}\text{n=0}\text{∞}\text{ω}{}_{\mathrm{n}}\text{=∞}$

then, for arbitrary ξ ? D_T, {x?_n} converges strongly to (the unique) fixed point of T. We also prove that if D_T and {ω_n} satisfy the foregoing conditions, if T has at least one fixed point, and if Tω is non-expansive for some ω ? (0, 1], then for all ξ ? D_T, {x?_n} converges at least weakly to some fixed point of T. Finally, we apply these results to linear equations involving bounded normal operators and obtain an extension of the classical Neumann operator series.     

Dielectrophoretic spectra of translational velocity and critical frequency for a spheroid in traveling electric field

An analysis has been made of the dielectrophoretic (DEP) forces acting on a spheroidal particle in a traveling alternating electric field. The traveling field can be generated by application of alternating current signals to an octapair electrode array arranged in phase quadrature sequence. The frequency dependent force can be resolved into two orthogonal forces that are determined by the real and the imaginary parts of the Clausius–Mossotti factor. The former is determined by the gradient in the electric field and directs the particle either toward or away from the tip of the electrodes in the electrode array. The force determined by the imaginary component is in a direction along the track of the octapair interdigitated electrode array. The DEP forces are related to the dielectric properties of the particle. Experiments were conducted to determine the DEP forces in such an electrode arrangement using yeast cells (Saccharomyces cervisiate TISTR 5088) with media of various conductivities. Experimental data are presented for both viable and nonviable cells. The dielectric properties so obtained were similar to those previously reported in literature using other DEP techniques.     

An experimental investigation of forced vibrations

The solution of the differential equation y″ + 2Ry′ + n²y = E cos pt is written in a new form which clearly exhibits many important facts thus far overlooked by theoretical and experimental investigators. Writing s = n ? p, and Δn = n ? √n² ? R², it is found: (a) When s ≠ Δn, there are “beats,” and the first “beat” maximum is greater than any later maximum while the first “beat” minimum is less than any later “beat” minimum. The “beat” frequency is $\text{(s ?}\text{Δ}\text{n)}\text{2π}$. (b) When n² ? p² = R², there are no “beats,” and the resultant amplitude grows monotonically from zero to the amplitude of the forced vibration, (c) At resonance, when n = p, we still have maxima which occur with a frequency $\text{Δ}\text{n}\text{2π}$ in a damped system. (d) The absence of “beats” is neither a sufficient nor a necessary condition for resonance in a damped system.In the experimental investigation the upper extremity of a simple pendulum was moved in simple harmonic motion and photographic records obtained of the motion of the pendulum bob. Different degrees of damping were used, ranging from very small to critical.The experimental results are in excellent agreement with theory.     

The representation of radiation reaction in wave mechanics

It is well known that the wave mechanical ψ equation leads to the conclusion that the centroid of the wave mechanical electron should move according to the classical electrodynamic equation of motion in which, however, the terms representing what is commonly called radiation reaction are absent. If v is the velocity of the electron, the classical rate of change of momentum is $\text{md}\text{dt}\text{{}\text{v}\text{(}\text{I}\text{?}\text{v}{}^2\text{c}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{}}$. The equation of motion including radiation reaction terms may be regarded as obtainable by replacing this quantity by one obtained by operating upon it with the operator P^?1

$\text{P={I?}\text{α}{}_1\text{kd}\text{dt}\text{+}\text{α}{}_2\text{d}\text{dt}\text{(}\text{kd}\text{dt}\text{)?·}}{}^{\mathrm{?}}$

where α₁, α₂, etc., are constants and $\text{k = (}\text{I}\text{?}\text{v}{}^2\text{c}{}^2\text{)}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$. The main purpose of the paper is to show that if there be any relativistically invariant ψ equation which leads to the classical equation of motion without radiation reaction terms, then by replacing the vector and scalar potentials U and ? in that equation by P(U) and P(?), a relativistically invariant equation of motion will be obtained including the radiation reaction terms, provided that the $\text{d}\text{dt}$ in P be now regarded as $\text{?}\text{?t}$ + u · grad, where u is the velocity of the wave mechanical density distribution at a point. The purpose is to use the power to produce the equation of motion as a criterion for suggesting the proper modification of the ψ equation to apply in those cases where, on the classical theory, the electron would suffer great acceleration, as in ionization by rapidly moving corpuscles.     

Eigenvalue localization for the tikhonova model of crystal growth

Matrix A with characteristic polynomial Q(z) is defined positive or negative Hurwitz according to whether Q(z) or Q(-z) is a Hurwitz polynomial. Leading principle sections of the Tikhonova growth matrix have associated characteristic polynomials P_n(-z) which satisfy the recursion

$\text{P}{}_{\mathrm{n+1}}\text{(z)=zP}{}_{\mathrm{n}}\text{(z)+}\text{1}\text{n(n+1)}\text{P}{}_{\mathrm{n-1}}\text{(z),P}{}_0\text{(z)=1,P}{}_1\text{(z)=1+z}$

That the Tikhonova growth matrix is negative Hurwitz is established through applying the Wall-Stieltjes theory of continued fraction expansions to show the P_n(-z) are Hurwitz polynomials. The Kayeya-Enestrom theorem and a procedure for refinement of the Gerschgorin estimate are used to obtain analytical bounds on spectral radii for the Tikhonova model, which provides estimates of maximal growth rates. The theory allows generalization to more complicated growth models.     

Air flow separation at high speed

The resistance coefficient of a body moving in a fluid depends on Reynolds Number R, Mach Number M and the parameter $\text{gL}\text{U}{}^2$, which is customarily neglected in view of small weight of the air. Here L denotes a characteristic length; U denotes the body's speed of translation. The author points that dimensional deduction of this parameter does not limit it to the acceleration of gravity, and that the resistance coefficient is affected by the general acceleration to which the air is subjected. Evaluation of the acceleration of the air flowing about spheres puts this parameter in the form $\text{L}\text{R}$, where the characteristic length L is interpreted as the mean free molecular path. Large and small spheres were found to have widely different values of the pressure coefficient $\text{Δp}\text{q}$ for the same Reynolds Number or Mach Number. Here Δp denotes the difference in pressure between front stagnation point and the rear portion of the sphere, and q denotes the dynamic pressure. The plot of $\text{Δp}\text{q}$ against the parameter $\text{L}\text{R}$ removes this confusion. The low values of $\text{Δp}\text{q}$ are found to be associated with $\text{L}\text{R}$ below a certain critical value, and high values of $\text{Δp}\text{q}$ with $\text{L}\text{R}$ above the critical value, which apparently indicates the condition under which the flow separation takes place. Attention is called to the effect of air pressure on the separation as shown by the parameter $\text{L}\text{R}$, and its possible bearing on the drag in high altitude flying.     

Periodic solutions to systems of reaction-diffusion equations

In this paper, necessary and sufficient conditions are derived for the existence of temporally periodic “dissipative structure” solutions in cases of weak diffusion with the reaction rate terms dominant in a generic system of reaction-diffusion equations ?c_i/?t = D_i?²c_i+Q_i(c), where the enumerator index i runs 1 to n, c_i = c_i(x, t) denotes the concentration or density of the ith participating molecular or biological species, D_i is the diffusivity constant for the ith species and Q_i(c), an algebraic function of the n-tuple c = (c₁,\3., c_n), expresses the local rate of production of the ith species due to chemical reactions or biological interactions.     

Temperature distribution in toroidal electrical coils of rectangular cross section

The essential content of a recent paper by the present writer comprises a comprehensive discussion of the physical bases underlying derivation of formulas for calculating the temperature distribution T, maximum temperature T_m and average temperature T_a in a toroidal electrical coil of rectangular cross section, internally generated heat and change of wire resistance with temperature being taken into account. Illustratively, the solution for the boundary value condition of constant surface temperature and uniform equivalent thermal conductivity was obtained.For the most part, however, problems that arise in practice are not encompassed in the comparatively simple boundary conditions of constant temperature. Experiment shows that in general the boundary condition is $\text{T ? T′ = ?}\text{K?}\text{?n}$; whereof n denotes the outward drawn normal to the coil surface, $\text{K = (}\text{k}{}_{\mathrm{n}}\text{h}\text{)}$ the ratio of the equivalent thermal conductivity in the direction of n to the emissivity of the boundary surface, and T and T′ are the corresponding temperatures in the coil surface and the immediately adjacent ambient medium. Again, it frequently ensues in practice that the thermal conductivity is substantially different in the directions of the two principal axes of the cross section.In the present paper formulas for T, T_m, and T_a are obtained for electrical coils of ratio of external to internal radius greater than (roughly) two whereof (i) the thermal conductivity is different in the directions of the two principal axes of the cross section, (ii) K is different on but constant over each of the four faces of the coil, and (iii) no restriction is made as to T′ except that over each face it be expressible in a generalized Fourier series. Determination of T is posed as a boundary-value problem in the mathematical theory of heat; the formal solution of T effected by expansions in orthogonal functions; and T_m and T_a then determined through use of their known relationships with T. The resulting formulas are in the form of rapidly-converging singly-infinite trigonometric-hyperbolic series. Illustrative of application of these general formulas, the maximum temperatures in a coil of given dimensions subject to two different sets of surface conditions are calculated and found to be in excellent agreement with the known measured values.The just-mentioned formulas encompass practically all cases encountered in practice except those coils which do not satisfy the restriction as to ratio of radii. For these latter formulas for T, T_m, and T_a are obtained pursuant to conditions of (i) equivalent thermal conductivity different in the directions of the two principal axes of the cross section, (ii) K, and likewise T′, different on but constant over each of the four faces of the coil. These formulas are in the form of rapidly-converging singly-infinite trigonometric- Bessel function (of zero order) series: Illustratively, the maximum temperature in a coil of given dimensions is calculated and found to be in excellent agreement with the known measured value.     

An equation of state for a system with a single type of transformation

Based on theory of a previous paper, the writer has developed an equation of state for a system with a single type of transformation. This equation is of the form

$\text{h=A+Bv+Cp+Dpv?T(E+Fv+Gp+Hpv)}$

where h = ε + pv is the total heat, p the pressure, v the specific volume, T the temperature, and p, v, T are considered independent variables. A, B, C, etc., are constants for the system. The latent eat at constant (p, T) is given by

$\text{λp,T=(v}{}_2\text{?v}{}_1\text{)(}\text{?h}\text{?v}\text{)P,T= (v}{}_2\text{?v}{}_1\text{)[(B?TF)+p(D?TH)]}$

. These equations are checked with data on saturated and superheated ammonia, and the agreement is good to within a few tenths of a per cent. Also, checks with data on saturated and superheated steam show agreement within several per cent.     

Smoothed L1/2 regularizer learning for split-complex valued neuro-fuzzy algorithm for TSK system and its convergence results

This paper investigates an evolving split-complex valued neuro-fuzzy (SCVNF) algorithm for Takagi–Sugeno–Kang (TSK) system. In a bid to avoid the contradiction between boundedness and analyticity, splitting technique is traditionally employed to independently process the real part and the imaginary part of weight parameters in the system, which doubles weight dimension and causes oversized structure. For improving efficiency of structural optimization, previous studies have revealed that L_1/2-norm regularizer can be effective in such sparse tasks thus is regarded as a representative of L_q (0?<?q?<?1) regularizer. To eliminate oscillation phenomenon and stabilize training procedure, a smoothed L_1/2 regularizer learning is facilitated by smoothing the original one at the origin flexibly. It is rigorously proved that the real-valued cost function is monotonic decreasing during learning course, and the sum of gradient norm trends closer to zero. Plus some very general condition, the weight sequence itself is also convergent to a fixed point. Experimental results for the SCVNF are demonstrated, which match the theoretical analysis.     

Report on the work of the Bartol Research Foundation, 1933–1934

Using the velocity analyzer of Zartman with improved technique the combined velocity spectrum of Bi atoms and Bi₂ molecules was obtained at 827°, 851°, 875°, 899°, 922°, 947° C. From the spectral distribution curves the relative abundance of Bi atoms and Bi₂ molecules in the beams at the above temperatures could be determined to 1 per cent. The vapor pressure curve of Bi was obtained experimentally by the method of effusion and the values so obtained were combined with the degree of dissociation of the vapor as computed from the beams to give the heat of dissociation. The heat of dissociation was computed from the data, assuming the pressure to be given by the temperature of the crucible T_c. In calculating the heat of dissociation, the equilibrium temperature was taken as that of the slit chamber T_s which was 24° above T_c. The results of these calculations plotted with log₁₀K_p as ordinates against $\text{1}\text{T}{}_{\mathrm{s}}$ give a straight line whose slope yields the value of the heat of dissociation as 77,100±1200 calories. The curves for the distribution of velocities observed and computed on the assumption of a given ratio of Bi atoms to Bi₂ molecules in the beam were compared in an attempt to test the law of distribution of velocities. On the high velocity side agreement in two curves was obtained within the limits of experimental accuracy. On the low velocity side important deviations were noted of such a sort that the observed curves below a velocity $\text{α}\text{2}$, (α is the most probable velocity) gave more molecules than the theory demanded. Other deviations were observed on some of the runs taken with a fourth slit in which a deficiency of molecules was observed between velocities of .75α and $\text{α}\text{2}$. This deviation was probably due to a warping of the fourth slit carriage due to heat. The nature of the variation at velocities less than $\text{α}\text{2}$ indicated the presence of molecules of greater mass than Bi₂ in the beam and at the lower temperatures a distinct peak corresponding to Bi₈ molecules was observed which were present to less than 2 per cent. The vapor pressure curve for Bi was determined by least square reduction of the observed points to be given by $\text{log}{}_{10}\text{P = ? 52.23 ×}\text{195.26}\text{T}\text{+ 8.56}$ between 1100° and 1220° abs. It lies very close to the extrapolated curve given in the International Critical Tables.     

Enhancement of ethanol production efficiency in repeated-batch fermentation from sweet sorghum stem juice: Effect of initial sugar,nitrogen and aeration

BackgroundEthanol concentration (P_E), ethanol productivity (Q_P) and sugar consumption (SC) are important values in industrial ethanol production. In this study, initial sugar and nitrogen (urea) concentrations in sweet sorghum stem juice (SSJ) were optimized for high P_E (≥ 10%, v/v), Q_P, (≥ 2.5 g/L·h) and SC (≥ 90%) by Saccharomyces cerevisiae SSJKKU01. Then, repeated-batch fermentations under normal gravity (NG) and high gravity (HG) conditions were studied.ResultsThe initial sugar at 208 g/L and urea at 2.75 g/L were the optimum values to meet the criteria. At the initial yeast cell concentration of ~ 1 × 10⁸ cells/mL, the P_E, Q_P and SC were 97.06 g/L, 3.24 g/L·h and 95.43%, respectively. Repeated-batch fermentations showed that the ethanol production efficiency of eight successive cycles with and without aeration were not significantly different when the initial sugar of cycles 2 to 8 was under NG conditions (~ 140 g/L). Positive effects of aeration were observed when the initial sugar from cycle 2 was under HG conditions (180–200 g/L). The P_E and Q_P under no aeration were consecutively lower from cycle 1 to cycle 6. Additionally, aeration affected ergosterol formation in yeast cell membrane at high ethanol concentrations, whereas trehalose content under all conditions was not different.ConclusionInitial sugar, sufficient nitrogen and appropriated aeration are necessary for promoting yeast growth and ethanol fermentation. The SSJ was successfully used as an ethanol production medium for a high level of ethanol production. Aeration was not essential for repeated-batch fermentation under NG conditions, but it was beneficial under HG conditions.How to cite: Sriputorn B, Laopaiboon P, Phukoetphim N, et al. Enhancement of ethanol production efficiency in repeated-batch fermentation from sweet sorghum stem juice: Effect of initial sugar, nitrogen and aeration. Electron J Biotechnol 2020;46. https://doi.org/10.1016/j.ejbt.2020.06.001     

Parameter identification of a class of time-varying systems via orthogonal shifted legendre polynomials

A method of using orthogonal shifted Legendre polynomials for identifying the parameters of a process whose behaviour can be modelled by a linear differential equation with time-varying coefficients in the form of finite-order polynomials is presented. It is based on the repeated integration of the differential equation and the representations of $\text{∫}\text{0}\text{t}$s(τ) dτ = Ps(t) and ts(t) = Rs(t), where P and R are constant matrices and s(t) is a shifted Legendre vector whose elements are shifted Legendre polynomials. The differential input-output equation is converted into a set of overdetermined linear algebraic equations for a least squares solution. The results of simulation studies are included to illustrate the applicability of the method.     

The reflection of hydrogen atoms from lithium fluoride

The paper describes the phenomena associated with the reflection of a sharply defined beam of hydrogen atoms from a crystal of LiF. Of primary interest is the fact that the atoms show interference effects in agreement with the wave mechanics theory and plane grating diffraction patterns are photographed. Evidence of the thermal agitation of the surface ions is obtained from the diffuse reflection with surrounds the specular beam.The Schrödinger wave equation for the motion of a free particle of mass m is

$\text{▽}{}^2\text{ψ ?}\text{4πmi}\text{h}\text{?ψ}\text{?t}\text{= 0}\text{(I)}$

. The solution of this equation corresponding to the kinetic energy $\text{mv}{}^2\text{2}$ is

where

$\text{v }\text{mv}{}^2\text{2}\text{and}\text{σ}\text{mv}\text{h}$

. The motion of such a particle should have the characteristics of a plane wave of frequency ν and wave-length $\text{λ =}\text{1}\text{σ}$. The experiments of various investigators¹ have shown the validity of the wave theory of the motion of the free electron and have given values of the wave-length in agreement with the theory.The free motion of atoms, ions and molecules should likewise have wave characteristics. In the case of the hydrogen atom, as the simplest example, the complete wave equation may be written in the form

$\text{I}\text{m}\text{▽}{}^2\text{x,y,zψ +}\text{I}\text{μ}\text{▽}{}^2\text{η,μζψ ?}\text{8π}{}^2\text{μ?ψ}\text{mh}{}^2\text{η}{}^2\text{+ μ}{}^2\text{+ ζ}{}^2$

$\text{?}\text{4πi}\text{h}\text{?ψ}\text{?t}\text{= 0,}\text{(3)}$

where x, y, z, are the coördinates of the center of mass of the atom and ξ, η, ζ the coördinates of the electron with respect to the center of mass. If m_? and m₊ are the masses of electron and proton, m and μ have the significance

$\text{m = m}{}_{\mathrm{?}}\text{+ m}{}_{\mathrm{+}}\text{and}\text{I}\text{μ}\text{=}\text{I}\text{m}{}_{\mathrm{?}}\text{+}\text{I}\text{m}{}_{\mathrm{+}}$

. Equation (3) is solved by

$\text{ψ = U}{}_1\text{(x,y,z) U}{}_2\text{(η, ν ζ) ?}{}^{\mathrm{<mtext>2\pi iEt</mtext><mtext>h</mtext>}}$

, where E may have a continuous set of values and represents the total energy. U₁ and U₂ must satisfy the equations

$\text{▽}{}_1{}^2\text{U}{}_1\text{+}\text{8π}{}^2\text{mβU}{}_1\text{h}{}^2\text{= 0,}\text{(4)}$

and

$\text{▽}{}_2{}^2\text{U}{}_2\text{+}\text{8π}{}^2\text{μ}\text{h}{}^2\text{(α ?}\text{μ?}\text{m}\text{η}{}^2\text{+ ν}{}^2\text{+ ζ}{}^2\text{)}\text{U}{}_2\text{= 0}\text{(5)}$

, where

$\text{α + β + E}$

.     

Numerical modeling of MHD stability in a cylindrical configuration

A numerical modeling of natural convection under the influence of either axial (B_z) or radial (B_r) magnetic field in a cylindrical configuration filled with a low-Prandtl number electrically conducting fluid, is studied. The finite volume method is used to discretize the equations of continuity, Navier Stokes and energy. A computer program based on the SIMPLER algorithm is developed. The flow and temperature fields are presented by stream function and isotherms, respectively. Stability diagrams are established according to the numerical results of this investigation. These diagrams put in evidence the dependence of the critical Grashof number, Gr_cr with the increase of the Hartmann number, Ha. The strongest stabilization of the convective flows occurs when the magnetic field is applied in the radial direction. This study confirms the possibility of stabilization of a liquid metal flow in natural convection by application of a radial magnetic field.     

Mathematical models of information system use

This report presents the results from a study of mathematical models relating to the usage of information systems. For each of four models, the papers developed during the study provide three types of analyses: reviews of the literature relevant to the model, analytical studies, and tests of the models with data drawn from specific operational situations. (1) The Cobb-Douglas model: x₀ = ax₁^bx₂^(1?b).This classic production model, normally interpreted as applying to the relationship between production, labor, and capital, is applied to a number of information related contexts. These include specifically the performance of libraries, both public and academic, and the use of information resources by the nation's industry. The results confirm not only the utility of the Cobb-Douglas model in evaluation of the use of information resources, but demonstrate the extent to which those resources currently are being used at significantly less than optimum levels. (2) Mixture of Poissons:

$\text{χ}{}_0\text{=}\text{∑}\text{i=0}\text{n}\text{i}\text{∑}\text{j=0}\text{p}\text{n}{}_{\mathrm{j}}\text{e}{}^{\mathrm{mj}}\text{(m}{}_{\mathrm{j}}\text{)′/i!}$

where x₀ is the usage and (n_j,m_j),j = 0 to p, are the p + 1 components of the distribution. This model of heterogeneity is applied to the usage of library materials and of thesaurus terms. In each case, both the applicability and the analytical value of the model are demonstrated. (3) Inverse effects of distance: x = a e^?md if c(d) = rdx = ad^?m if c(d) = r log(d).These two models reflect different inverse effects of distance, the choice depending upon the cost of transportation. If the cost,c(d), is linear, the usage is inverse exponential; if logarithmic, the usage is inverse power. The literature that discusses the relationship between usage of facilities and the distance from them is reviewed. The models are tested with data from the usage of the Los Angeles Public Library, both Central Library and branches, based on a survey of 3662 users. (4) Weighted entropy:

$\text{S(x}{}_1\text{,x}{}_2\text{,...,x}{}_{\mathrm{n}}\text{)= -}\text{∑}\text{i=1}\text{n}\text{r(x}{}_{\mathrm{i}}\text{P(x}{}_{\mathrm{i}}\text{)}\text{log}\text{(p(x}{}_{\mathrm{i}}\text{)).}$

This generalization of the “entropy measure of information” is designed to accommodate the effects of “relevancy”, as measured by r(x), upon the performance of information retrieval systems. The relevant literature is reviewed and the application to retrieval systems is considered.     

Accurate approximate solutions to oscillatory problems with perturbing singular damping

In this paper we attempt to obtain approximate solutions of improved accuracy for a class of differential equations of the form

$\text{d}{}^2\text{y}\text{d}\text{x}{}^2\text{+εμ(x)}\text{d}\text{y}\text{d}\text{x}\text{+ω}{}^2{}_{\mathrm{c}}\text{y = 0}$

, where ε is a real parameter less than unity, ω_c is a positive real constant of order unity and μ(x) is a singular function of x in the region of interest. It does not appear to be possible to find a general analytic expression for the error estimate of the approximate solution. For the case μ(x) = x^?2, however, it is shown that the approximate solution is accurate to 0(ε²), as x → 0^? from negative values, by comparing it with the numerically integrated solution. For the same case, the approximate solution is orders of magnitude more accurate than Poincaré's first-order perturbation solution, which is accurate to $\text{0(}\text{ε}{}^2\text{ln}\text{|x|}\text{|x|}\text{)}$ as x → 0^?. This work arose in search of analytic solutions to a linearized form of the restricted three-body problem.     

Improvement of ethanol production from sweet sorghum juice under batch and fed-batch fermentations: Effects of sugar levels,nitrogen supplementation,and feeding regimes

BackgroundFermentation process development has been very important for efficient ethanol production. Improvement of ethanol production efficiency from sweet sorghum juice (SSJ) under normal gravity (NG, 160 g/L of sugar), high gravity (HG, 200 and 240 g/L of sugar) and very high gravity (VHG, 280 and 320 g/L of sugar) conditions by nutrient supplementation and alternative feeding regimes (batch and fed-batch systems) was investigated using a highly ethanol-tolerant strain, Saccharomyces cerevisiae NP01.ResultsIn the batch fermentations without yeast extract, HG fermentation at 200 g/L of sugar showed the highest ethanol concentration (P_E, 90.0 g/L) and ethanol productivity (Q_E, 1.25 g/L·h). With yeast extract supplementation (9 g/L), the ethanol production efficiency increased at all sugar concentrations. The highest P_E (112.5 g/L) and Q_E (1.56 g/L·h) were observed with the VHG fermentation at 280 g/L of sugar. In the fed-batch fermentations, two feeding regimes, i.e., stepwise and continuous feedings, were studied at sugar concentrations of 280 g/L. Continuous feeding gave better results with the highest P_E and Q_E of 112.9 g/L and 2.35 g/L·h, respectively, at a feeding time of 9 h and feeding rate of 40 g sugar/h.ConclusionsIn the batch fermentation, nitrogen supplementation resulted in 4 to 32 g/L increases in ethanol production, depending on the initial sugar level in the SSJ. Under the VHG condition, with sufficient nitrogen, the fed-batch fermentation with continuous feeding resulted in a similar P_E and increased Q_P by 51% compared to those in the batch fermentation.     

A study on two-layered model (Casson-Newtonian) for blood flow through an arterial stenosis: Axially variable slip velocity at the wall

The present paper sheds some light on a mathematical model for blood flow through stenosed arteries with axially variable peripheral layer thickness and variable slip at the wall. The model consists of a core region of suspension of all the erythrocytes assumed to be a Casson fluid and a peripheral layer of plasma as a Newtonian fluid. For such models, in literature, the peripheral layer thickness and slip velocity are assumed a priori based on experimental observations. In the present analysis, new analytic expressions for the thickness of the peripheral layer, slip velocity and core viscosity have been obtained in terms of measurable quantities (flow rate (Q), centerline velocity (U), pressure gradient (−dp/dz), plasma viscosity (μ_p) and yield stress (θ)). Using the experimental values of Q, U, (−dp/dz), μ_p and θ, the values of the peripheral layer thickness, core viscosity, and slip velocity at the wall have been computed. The theoretically obtained peripheral layer thickness has been compared with its experimental value. It is found that the agreement between the two is very good (error<1.4%). Further, a comparison between theoretical and experimental values of core viscosity is made and it is observed that the error between the two becomes 3.7465% in the case of two-layered model (Casson-Newtonian) for tube diameter 40 μm. The analysis developed here could be used to determine the more accurate values of the apparent viscosity of blood, agreeability, rigidity and deformability of red cells. This information of blood could be useful in the development of new diagnosis tools for many diseases.