Straight Line Curve Research Articles

NUMERICAL INVESTIGATION OF HVAF-SPRAYED Fe-BASED AMORPHOUS COATINGS

A numerical analysis was performed to predict the effect of the convergent section geometry of a gun nozzle on the high-velocity air-fuel (HVAF) thermal spray Fe-based amorphous coating (AC) process. A computational fluid dynamics model was applied to investigate the gas-flow field and the behavior of in-flight particles at nozzle entrance convergent section length ranging from 28 mm to 56.8 mm and different shapes of the Laval nozzle convergent section (a straight line and Vitosinski convergence curve). On the one hand, the change in the gas-flame flow characteristics for the Vitosinski curve shows a uniform and stable flame compared with the straight-line curve in the convergent section. The straight-line curve shape of the Laval nozzle convergent section has a higher particle temperature compared with the Vitosinski-curve shape of the Laval nozzle convergent section. The particle dwell time for the straight-line curve shape of the Laval nozzle convergent section is longer than that for the Vitosinski curve shape of the Laval nozzle convergent section. On the other hand, the nozzle entrance convergent section length obviously affects the particle temperature, and the particle dwell time increases with the increasing nozzle entrance convergent section length. By analyzing both the melt status of the particles and particle velocity, the optimal gun configuration (0.7 V) producing low-porosity coatings was predicted. These calculations were experimentally verified by producing a low-porosity (1.37 %) Fe-based AC, fabricated with HVAF using the predicted optimal gun configuration.

Magneto-nanofluid numerical modelling of chemically reactive Eyring-Powell fluid flow towards both flat and cylindrical an inclined surfaces: A comparative study

An article is made to report the combined effects of both chemical reaction and dual stratification on boundary layer magneto-hydrodynamic Eyring Powell nanofluid flow towards both flat and cylindrical an inclined stretching surfaces under the region of stagnation point along with heat and mass transfer characteristics. The flow situation is carried out by considering physical effects namely, thermal radiation and heat generation. To be more specific, the fluid flow is entertained through no slip condition i-e the velocity of particles is directly related to velocity of surface due to stretching. The physical situation within the real concerned constraints is translated in terms of differential equations as a boundary value problem. To make implementation of computational algorithm possible, firstly the intricate PDE’s are transformed into ODE’s by using suitable transformation, secondly resulting boundary value problem is converted into an initial value problem. These constructed ordinary differential equations are solved computationally by shooting technique charted with Runge-Kutta scheme. The effect logs of involved physical flow parameters are explored with the aid of graphical outcomes and tabular values. A straight line curve fitting way of communication is executed to inspect the impact of both thermophoresis parameter and Brownian motion parameter on heat and mass transfer rates. It is found that heat transfer normal to the cylindrical surface shows decline attitude towards both thermophoresis and Brownian motion parameters.

J M Keynes's Differential Calculus, D-Z Model of Chapters 3, 20, 21 and the Appendix to Chapter 19 of the General Theory Is a Full Blown Mathematical Model Like that in Pigou's 1933 the Theory of Unemployment and Is Not a Framework for Verbal Discussion

J M Keynes's mathematical approach in all three of his major works, A Treatise on Probability, A Treatise on Money, and The General Theory of Employment, Interest and Money, was to provide his readers with the major, mathematical results of his formal, technical analysis. However, he expected his readers to have had the necessary training and knowledge of the required mathematical techniques, which he was using in order to be able to support his conclusions to fill in the missing initial and intermediate mathematical steps that he would not provide. This, of course, means that readers of these books, who are mathematically confused, illiterate, inept or innumerate, will not be able to follow what Keynes is doing technically in the General Theory or his other works. These readers will conclude that Keynes is only providing very general functional relationships that are not technically developed. This sort of reader of the General Theory usually adds on the following two claims. The first claim is that Keynes was a strict Marshallian, who would only provide a verbal summary of his privately, worked out, technical analysis in his published works. The second claim is to interpret Keynes's critique of pseudo mathematics on pp. 297-298 and p. 305 of the GT as an attack on the use of any mathematical and formal analysis whatsoever. The latest author to take this approach is Roger Backhouse (2010), who argues that Keynes used the word only to describe the classical and neoclassical special, mathematical analysis that was being used to support their claims while using the word function only to describe his own general analysis, which could not be formally developed. It is a straightforward matter to demonstrate that there is no support for any of Backhouse's claims, who demonstrates repeatedly that he does not know the difference between algebra and differential calculus, which makes use of algebra. Keynes used the terms and function to describe his own work in the GT. He also used these terms to describe the 'classical' school which he demonstrated was a special case of his own GT. Keynes's framework actually reaches back, like the work of Adam Smith, to Aristotle's general theory of money, ethics, economics, politics, and civics. Keynes did not use the word function to only describe his own analysis in the General Theory. Keynes did not use the word to only describe the classical analysis. The words and function have been completely misapplied, misconstrued, misused, and misinterpreted by Backhouse, Carabelli and Cedrini, and by Wray. Keynes's Aggregate Supply Function, is a linear, straight line curve. Keynes's Aggregate Demand Function, D, is a concave curve. Keynes's Aggregate Supply Curve, a locus of the set of all possible Z and D intersections, is a convex curve by design. Keynes's Liquidity Preference Demand for Money function, L, when combined with M, the supply of money, is a curve that is identical to the Figure 2 curve in Hicks's 1937 article in Econometrica. There is nothing original, new, novel, innovative, or creative in Hick's 1937 article on IS-LM except for one thing. He actually drew the IS-LM curves as exactly described by Keynes in the GT on p. 207 of the General Theory. Hicks's exposition is inferior to Champernowne’s model and exposition. It is quite disconcerting to realize that Keynes's GT still has not been read carefully and methodically some 81 years after its publication.

Thermal Conductivity of Food Products using: A Correlation Analysis Based on Artificial Neural Networks (ANNs)

This paper presents the correlation between the predicted and desired/targeted thermal conductivity of food products as a function of moisture content, temperature and apparent density. The food products considered in this work are the bakery products which include bread, bread dough, cake, and whole-wheat dough. Statistical data of results from previous work in existing literatures were used in this work for a wide range of moisture contents, temperatures and apparent densities resulting from baking conditions. The results of this work showed straight line curves when the predicted values of thermal conductivity were plotted against the targeted values of thermal conductivity. This demonstrates correlation between the predicted and targeted thermal conductivities when the points are joined together (best fit-points), hence, a very good agreement between the predicted and the desired values of thermal conductivity. The two ANN models that were finally selected, after several configurations had been considered and evaluated, are the optimal ANN model that was found to be a network with two hidden layers and eight neurons and the simplest ANN model was equally found to be a network with one hidden layer and ten neurons. The estimated errors between the predicted and desired (or targeted) thermal conductivity values of the bakery products for both the optimal ANN and simplest ANN models are the MRE, MAE and SE. Moreover, the results also showed that the optimal ANN model had an MRE of 0.04878%, an MAE of 0.0054W/mK and an SE of 0.0015W/mK while the simplest ANN model was estimated to have an MRE of 0.03388%, an MAE of 0.0034W/mK and an SE of 0.0011W/mK. These errors are approximately equal to zero (i.e., 0 W/mK) and could, therefore, be regarded as a good result for the prediction. Since the simplest ANN model had the least values of all three errors (MRE, MAE and SE) when compared with other configurations, including the optimal ANN model, it is, however, regarded as the best ANN model and is, thus, recommended.

Nucleobindin 1 Is a Calcium-regulated Guanine Nucleotide Dissociation Inhibitor of Gαi1

Nucleobindin 1 (NUCB1) is a widely expressed multidomain calcium-binding protein whose precise physiological and biochemical functions are not well understood. We engineered and heterologously expressed a soluble form of NUCB1 (sNUCB1) and characterized its biophysical and biochemical properties. We show that sNUCB1 exists as a dimer in solution and that each monomer binds two divalent calcium cations. Calcium binding causes conformational changes in sNUCB1 as judged by circular dichroism and fluorescence spectroscopy experiments. Earlier reports suggested that NUCB1 might interact with heterotrimeric G protein α subunits. We show that dimeric calcium-free sNUCB1 binds to expressed Gα(i1) and that calcium binding inhibits the interaction. The binding of sNUCB1 to Gα(i1) inhibits its basal rate of GDP release and slows its rate and extent of GTPγS uptake. Additionally, our tissue culture experiments show that sNUCB1 prevents receptor-mediated Gα(i)-dependent inhibition of adenylyl cyclase. Thus, we conclude that sNUCB1 is a calcium-dependent guanine nucleotide dissociation inhibitor (GDI) for Gα(i1). To our knowledge, sNUCB1 is the first example of a calcium-dependent GDI for heterotrimeric G proteins. We also show that the mechanism of GDI activity of sNUCB1 is unique and does not arise from the consensus GoLoco motif found in RGS proteins. We propose that cytoplasmic NUCB1 might function to regulate heterotrimeric G protein trafficking and G protein-coupled receptor-mediated signal transduction pathways.

Effect of buffers and ionic strength on the stability constant of complexes of iron(III) with salicylic acid and its derivatives

The 1: 1 complex formed by iron(III) with salicylic add and Its seven derivatives were studied by spectrophotometry and the effect of phthalate-HCl and KCl-HCl buffers on the value of stability constants of 1: 1 complex determined by spectrophotometry, was evaluated. The thermodynamic value of stability constant of each system was determined by obtaining the values at different ionic strength and extrapolating them to zero ionic strength. For extrapolation, a new approach was made which gives a straight line curve making it easier to extrapolate at zero ionic strength to get the thermodynamic value thus reducing the uncertainty in extrapolation.

Ultraviolet inactivation of feline calicivirus, human enteric viruses and coliphages.

Norwalk and Norwalk-like viruses (NLV) are major causes of food- and water-related disease in the United States. There is no host cell line in which the NLV can be tested for infectivity. Feline calicivirus (FCV) and NLV both belong to the family Caliciviridae. FCV can be assayed for infectivity in the Crandell Reese feline kidney cell line, so FCV serves as a surrogate for NLV. This study is the first report of UV inactivation of FCV and also of using the plaque technique, in contrast to the 50% tissue culture infectious dose end point technique, to determine the FCV infectivity titer. The infectivity titers (log10 plaque-forming units/mL) of UV-inactivated FCV, hepatitis A virus (HAV), poliovirus type 1 (PV1) and two small, round coliphages were plotted as a function of UV dose and analyzed by regression analysis and analysis of variance. These fitted straight-line curves represent exponential inactivation, so UV inactivation can be said to show "one-hit kinetics." The decimal inactivation doses of UV for FCV, HAV, PV1, MS2 and phiX174 were 47.85, 36.50, 24.10, 23.04 and 15.48 mW s/cm2, respectively. FCV appears to be the most UV resistant among the tested viruses.

Inverter harmonic reduction using Walsh function harmonic elimination method

A pulse-width-modulated (PWM) inverter using the Walsh function harmonic elimination method is proposed in this paper. By using the Walsh domain waveform analytic technique, the harmonic amplitudes of the inverter output voltage can be expressed as functions of switching angles. Thus, the switching angles are optimized by solving linear algebraic equations instead of solving nonlinear transcendental equations. The local piecewise linear relations between the switching angles and the fundamental amplitude can be obtained under an appropriate initial condition. By searching all feasible initial conditions, the global solutions are obtained. The relations between switching angles and fundamental amplitude can be approximated by straight-line curve fitting. Thus, on-line control of fundamental amplitude and frequency is possible for the microcomputer-based implementation. The developed algorithm can be applied to both bipolar and unipolar switching schemes. The theoretical predictions are confirmed by computer simulations and DSP-based hardware implementation.

Effect of frequency on the fatigue behavior of [�45]4s laminate of carbon fiber reinforced polyetheretherketone (PEEK) composites under tension-tension loading

Fatigue behavior of carbon fiber reinforced poly etheretherketone (PEEK) laminated composite was investigated. The [±45]4s AS-4/PEEK laminated composites under static tensile measurement at various test temperatures were conducted. Three tension-tension fatigue loading frequencies, 1 Hz, 5 Hz and 10 Hz, were selected to study the effect of frequency on the fatigue behavior of [±45]4s AS-4/PEEK laminate. The survival probability of experimental fatigue life data under different stress amplitude tests were estimated and analyzed by the median rank order-statistic cumulative-distribution function and the Weibull distribution function. The S-N curves at different fatigue loading frequencies exhibited a trend of two-segment straight line curves. The increase in surface temperature of specimens was found and the thermal stress history was also investigated by thermo-image techniques during fatigue life testing. The fatigue failure mechanism was investigated by X-ray radiography.

A Model to Establish the Limit of Decision and the Limit of Detection for Straight-Line Curves in a Case of Heteroscedasticity

Abstract A problem arises when determining the decision and detection limits in a series of results where the variance of the error distribution of the analytical signals around their expectation is not a constant when applying a method proposed by Hubaux and Vos6. In this paper an approach is proposed to overcome this difficulty, that involves the use of a transform method to convert heteroscedastic data to homoscedastic data so that the limit of detection can be obtained by projection of the confidence band about the linear regression. This approach is applied to the case of a gravimetric determination of sulphate ion in the 1 – 5 mgL−1 SO4 2- range. The results obtained from this approach are compared from others obtained previously.

Fractals and the analysis of growth paths.

A simple practical method exists for classifying and comparing planar curves composed of connected line segments. This method assigns, a single numberD, the fractal dimension, to each curve.D=log(n)/[log(n)+log(d/L)], where:n is the number of line segments,L is the total length of the line segments, andd is the planar diameter of the curve (the greatest distance between any two endpoints). At one end of the spectrum, for straight line curves,D=1; at the other end of the spectrum, for random walk curves,D→2. Standard statistics are done on the logarithms of the fractal dimension [log(D)]. With this measure, trails of biological movement, such as the growth paths of the cells and the paths of wandering organisms, can be analyzed to determine the likelihood that these trails are random walks and also to compare the straightness of the trails before and after experimental interventions.

Fractals and the analysis of growth paths

A simple practical method exists for classifying and comparing planar curves composed of connected line segments. This method assigns a single number D, the fractal dimension, to each curve. D =log( n)/[log( n) + log( d/L)],where: n is the number of line segments, L is the total length of the line segments, and d is the planar diameter of the curve (the greatest distance between any two endpoints). At one end of the spectrum, for straight line curves, D = 1; at the other end of the spectrum, for random walk curves, D→2. Standard statistics are done on the logarithms of the fractal dimension [log( D)]. With this measure, trails of biological movement, such as the growth paths of cells and the paths of wandering organisms, can be analyzed to determine the likelihood that these trails are random walks and also to compare the straightness of the trails before and after experimental interventions.

Crosslink density and solvent swelling of filled and unfilled stocks

The network segment density (γg) by solvent-swollen compression modulus of gum stocks and of stocks containing nonreinforcing fillers was calculated to be 6.6093 × 10−9h0Sf/ϕBd2 in mmole/m3 of gel at 25°C, where h0 is the height of the unswollen sample in cm, S is the slope of the height versus applied weight curve in g per mil (0.001 in.), ϕB is the volume fraction of binder, d is the diameter of the initial sample in cm, and f is a factor equal to (1− ϕs/ϕB)1/3/(1− ϕS)2/3, where ϕS is the volume fraction of extract. The volume fraction of crosslinked polymer containing nonreinforcing fillers at equilibrium in a solvent (V2) was determined for the cases where the filler is insoluble and partially adheres to the binder, where the filler is partially solube and there is no binder–filler adhesion, and where the filler is completely soluble in the swelling solvent. The relations were tested and found to hold for polyester–polyurethane stocks containing plasticizer and soluble and insoluble fillers. Log V2 fell on single straight-line curves with respect to log γg for gum stocks and filled stocks both when V2 was measured in solvents which dissolved none or dissolved part of the fillers.

On the fire resistance of structural steel elements derived from standard fire tests or by calculation

Due to high costs, a fire resistance test of a load-bearing structural element is usually limited to one test specimen — in a few countries, to two test specimens. Accordingly, there are no possibilities of evaluating the test results statistically. For a single test specimen, the actual quality of the structural material represents a random sample from a wide variety. This applies also to the initial imperfections of the structural elements. In consequence of this, a standard fire resistance test is generally carried out on a test specimen with a load-bearing capacity which is greater — most often significantly greater — than the load-bearing capacity related to the characteristic values of the mechanical material strength and of the imperfections of the structural member. In current practice, no corrections of the test results with respect to this are made. In a conventional analytical design, a determination of the load-bearing capacity of a structure at room temperature conditions is based on the characteristics values of the strength and imperfections. Extended to a structural fire engineering design, this procedure will give an analytically determined fire resistance of a load-bearing structural element which is lower — normally essentially lower — than the corresponding value derived from a standard fire resistance test. Available methods for a simplified calculation of the temperature of fire exposed steel structures are, as a rule, based on the assumption of a uniformly distributed temperature structure at each time of fire exposure. The ECCS Recommendations for an analytical design of steel structures exposed to a standard fire follow this kind of approach. For certain types of steel structures, for example, beams with a slab on the upper flange, a considerable temperature variation arises over the cross section as well as in the longitudinal direction during a fire resistance test. A simplified, analytical method, which neglects this influence, gives a further underestimation of the fire resistance in relation to the corresponding result obtained in a standard fire resistance test. The described discrepancies between an analytical and an experimental determination of the fire resistance are further discussed and analysed in Sections 2 and 3, with particular reference to different types of steel structures. The discussion is focussed on the loading and restraint conditions, the scatter of material properties and geometrical imperfections, and the temperature variation over the structure or structural element. The discussion is summarized in Section 4 and alternative methods of correction are outlined briefly for obtaining an improved consistency between the analytical and the experimental approaches. In Section 5, one of these methods is further developed to a design basis which can be applied easily in practice. Principally, the method is characterized by a correction of the analytically determined load-bearing capacity, based on the characteristic value of the structural material properties, the characteristic value of the imperfections of the structure, and a uniformly distributed steel temperature across and along the structure. Two different sequences of the design procedure are dealt with, defined according to Figs. 10 and 11. The resultant correction factors, ƒ and κ, belonging to the respective sequences, are given by Figs. 8 and 12 for columns, isostatic beams, and hyperstatic beams. The straight line curves in Figs. 9 and 13 show corresponding, simplified relationships for the ƒ and κ factors. The derived method of correction must be characterized as an approximate approach. This is in consequence of the present state of knowledge, which does not allow a solution of high accuracy. The task to develop a correction procedure which leads to improved consistency between an analytically and an experimentally determined fire resistance, should also be seen in the context of the inadequate reproducibility of the standard fire resistance test.

Regulation of Adenylate Cyclase in Two Rat Liver Cell Lines, 3C4 and 62

Adenylate cyclase (EC 4.6.1.1) activities were examined in membrane preparations from two rat liver cell lines (62 and 3C4) which were grown in monolayer cultures. The cells were epithelial-like in growth character. Adenylate cyclase from the line 62 was stimulated by epinephrine, Gpp(NH)p, and prostaglandins A1,A2,E1,E2, and F2alpha, but not by glucagon. Arrhenius plots of adenylate cylase activity from line 62 gave straight lines, except when epinephrine was present in the assay; epinephrine-stimulated activity gave a distinct break at 20 degrees C. Adenylate cyclase activity in line 3C4 was stimulated by glucagon ten times greater than by epinephrine. It was responsive to Gpp(NH)p and all the prostaglandins. Arrhenius plots of adenylate cyclase activity of line 3C4 always gave straight line curves. Prostaglandins flattened the straight line curves (allowed temperature independence) of adenylate cyclase activity in membranes from both cell lines.

Studies of gas→liquid (non-Newtonian) slug flow: void fraction meter, void fraction and slug characteristics

Measurements are reported of the void fraction, slug velocity and slug frequency for the cocurrent slug flow of highly viscous non-Newtonian fluids and air. The experimental work was performed in a horizontal tubular test section 2.54 cm in internal diameter and 10.67 m long. Three different polymer solutions were used over wide concentration ranges. The void fraction and slug characterization measurements were carried out with a specially constructed coil void fraction meter operating in a capacitive mode. This system allowed not only the measurement of the instantaneous void fraction but also a recording of the slug voidage trace. Correlations are presented for void fraction, slug velocity and slug frequency, noting in all cases the effects of fluid rheology and apparent viscosity. (1) An investigation of the effects of non-Newtonian liquids on the behaviour of cocurrent gas-liquid slug flow has been undertaken. (2) To allow experimentation with viscous fluids, a new electrically resonating void fraction meter was devised which worked satisfactorily for a wide variety of polymer solutions when it was carefully tuned. (3) Empirical rheological constants were obtained for a wide range of polymer solutions. (4) Slug frequencies, velocities and average void fractions were measured. (5) Liquid slugs travel at approximately the maximum gas velocity even when the liquid becomes quite viscous. (6) The method of Gregory and Scott 16 correlates slug frequency data for each individual polymer system. No generalized correlation has been obtained. (7) The void fraction data can be expressed according to the method of Zuber and Findlay. However, the straight line curves are peculiar to each individual polymer system. (8) Most importantly, the void fraction data are correlated according to the method of Lockhart and Martinelli provided that the liquid phase pressure drop in the parameter X is calculated by allowing for the non-Newtonian characteristics of the liquid phase. This is the most general and useful result of the work.

Electron–Nuclear Double Resonance of 53Cr3+ in Aluminum Alums

Electron–nuclear double resonance (ENDOR) studies are reported for the isotope 53Cr3+ enriched to 96% in the aluminum alums RbAl(SO4)2∙12H2O and CsAl(SO4)2∙12H2O. The measurements were made at 4.2 K and X-band microwave frequencies (~9.4 GHz). The values of the spin Hamiltonian hyperfine parameters A, B, and Q′ are found to be quite similar to those obtained previously in the corresponding gallium alums even though the zero field splitting parameter D is significantly different. A plot of A − B vs. Q′ indicates that the amount of distortion existing at a chromium site can be related to the type of monovalent ion present, i.e. Rb or Cs. It is possible to draw straight line curves relating the parameters Q′ vs. D, A − B vs. D, and Vzz vs. D which account quite well for all the ENDOR data obtained so far in the alums and GAISH and which could be generally true for chromium magnetic complexes in crystals with D values not too close to zero.

Thermal Conductivity in the Two-Band Model of Superconducting Transition Metals Containing Nonmagnetic Impurities

Using the Green's-function formulation, an expression has been derived for the thermal conductivity of transition-metal superconductors containing nonmagnetic impurities in the two-band model of Suhl, Matthias, and Walker (SMW). The calculations have been carried out neglecting the interband electron-phonon coupling and taking the interband-scattering collision time ${\ensuremath{\tau}}_{\mathrm{sd}}\ensuremath{\approx}{10}^{\ensuremath{-}12}$ sec. The thermal conductivity $K$ is found to be the sum of two terms ${K}_{1}$ and ${K}_{2}$. ${K}_{1}$ is the dominating term and depends in a complicated manner on both energy gap parameters ${\overline{\ensuremath{\Delta}}}_{s}$ and ${\overline{\ensuremath{\Delta}}}_{d}$, due to $s$ and $d$ bands, respectively. On the other hand, ${K}_{2}$ depends only on ${\overline{\ensuremath{\Delta}}}_{d}$ and is smaller by a factor of \ensuremath{\sim}${10}^{\ensuremath{-}7}$. A log-log plot of thermal conductivity vs temperature turns out to be a straight-line curve with a slight change in its slope at a temperature which depends upon the impurity concentration. Furthermore, $K$ is found to decrease with increase in impurity concentration. These qualitative features of the present study are in very good agreement with the recent experimental investigations of Anderson et al. on niobium and lend support to the validity of the SMW two-band-model theory.

Reversible electrode reactions: Reduction of Cd-oxalate-succinate complex at D.M.E.

The reduction of Cd-oxalate-succinate system has been studied at D.M.E. It has been found to be reversible and diffusion-controlled involving two electrons as indicated by slope of straight line curve of E de vs. log ( i i d − i ) and direct proportionality of diffusion current to the effective height of mercury column. The stability constants β 12 β 11 and β 21 for complexes Cd(ox.)(succ.) 2, Cd(ox.)(succ.) and Cd(ox.) 2(succ.) have been evaluated by Schaap and McMasters' method; log β 12 = 4017, log β 21 = 4·982 ± 0·020 and a negative value for β 11. Cd(ox.)(succ.) probably does not exist in solution.

Threshold exposure duration as a function of luminance for visual recognition

Threshold exposure duration was measured at set luminances for recognition at successively higher criteria of 1, 2, 3, 4, and 5 correct letters in nonsense words. Two sizes of letters were used and triads of Landolt “Cs” were compared with letters. Tachistoscopic procedures were the typical ascending seriesin the method of limits and pre- and postexposure light adaptation. Obtained log t vs log I functions were two-part straight line curves both describable by the equation, log t + log Ik = log C, but with k and C abruptly changing at a certain I. Reciprocity (k = 1) held only for low Is and the low criterion; as criterion was raised at low Is k became less negative (about −.60 at five correct) for both sizesand for “Cs.” At higher Is, k shifted from −.25 to −.40 with increasing criterion for large letters, but variedaround −.45 at all criteria for small. The lower the criterion, the lower the / and t at which k and C abruptly changed for large letters, but only t was lower for small. Changes in t with acuity requirement change, and from one criterion level to the next, were not uniform over all Is. Results may reflect obscuring procedural factors or basic properties of visual recognition processes. Some interpretations in terms of procedural variables are offered. It appears more likely that visual recognition involves central processes for which time is needed in excess of that for summation of luminances for mere detection by sensory processes, as expressed in Bloch s’ reciprocity law.