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This paper investigates a scheduling model with certain co-existing features of serial-batching, dynamic job arrival, multi-types of job, and setup time. In this proposed model, the jobs of all types are first partitioned into serial batches, which are then processed on a single serial-batching machine with an independent constant setup time for each new batch. In order to solve this scheduling problem, we divide it into two phases based on job arrival times, and we also derive and prove certain constructive properties for these two phases. Relying on these properties, we develop a two-phase hybrid algorithm (TPHA). In addition, a valid lower bound of the problem is also derived. This is used to validate the quality of the proposed algorithm. Computational experiments, both with small- and large-scale problems, are performed in order to evaluate the performance of TPHA. The computational results indicate that TPHA outperforms seven other heuristic algorithms. For all test problems of different job sizes, the average gap percentage between the makespan, obtained using TPHA, and the lower bound does not exceed 5.41 %.

Solving partial differential equations using neural networks is mostly a proof of concept approach. In the case of direct function approximation, a single neural network is constructed to be the solution of a particular boundary value problem. Independent variables are fed into the input layer, and a single output is considered as the solution’s value. The network is substituted into the equation, and the residual is then minimized with respect to the weights of the network using a gradient-based method. Our previous work showed that by minimizing all derivatives of the residual up to the third order one can obtain a machine precise solution for 2D boundary value problem using very sparse grids. The goal of this paper is to use this grid complexity advantage in order to obtain a solution faster than finite differences. However, the number of all possible high-order derivatives (and therefore the training time) increases with the number of dimensions and it was unclear whether this goal can be achieved. Here, we demonstrate that this increase can be compensated by using random directional derivatives instead. In 2D case neural networks are slower than finite differences, but for each additional dimension the complexity increases approximately 4 times for neural networks and 125 times for finite differences. This allows neural networks to catch up in 3D case for memory complexity and in 5D case for time complexity. For the first time a machine precise solution was obtained with neural network faster than with finite differences method.

The effects of the aspect ratio on unsteady solutions through the curved duct flow are studied numerically by a spectral based computational procedure with a temperature gradient between the vertical sidewalls for the Grashof number 100 ⩽ Gr ⩽ 2 000. The outer wall of the duct is heated while the inner wall is cooled and the top and bottom walls are adiabatic. In this paper, unsteady solutions are calculated by the time history analysis of the Nusselt number for the Dean numbers Dn = 100 and Dn = 500 and the aspect ratios 1 ⩽ γ ⩽ 3. Water is taken as a working fluid (Pr = 7.0). It is found that at Dn = 100, there appears a steady-state solution for small or large Gr. For moderate Gr, however, the steady-state solution turns into the periodic solution if γ is increased. For Dn = 500, on the other hand, it is analyzed that the steady-state solution turns into the chaotic solution for small and large Gr for any γ lying in the range. For moderate Gr at Dn = 500, however, the steady-state flow turns into the chaotic flow through the periodic oscillating flow if the aspect ratio is increased.

HAVING observed a letter in NATURE, vol. xvii. p. 401, in which extracts from a paper of mine are commented upon by the Rev. F. Bashforth, I trust you will let me make a few remarks by way of explanation.

hQ(x) of bounded one-dimensional sectional curvature. In this paper, such metrics are referred to as supporting functions of a convex set Q. If Q is a finite convex polyhedron in the Lobachevsky space, then the following formula holds: hQ(x) = mini{h i(x)}, where h i(x) are supporting functions of the (n − 1)-dimensional faces of the polyhedron Q. The process of computing h i(x) is recurrent and is reduced to the case where i are kdimensional simplexes in Hn κ (k < n). Such functions, called conformal splines, are computed by the procedure “MatLab.”

BY reference to the last number of the Electrical Review (vol. xxi. p. 262), wherein is printed a short abstract of our paper on “A Null Method of Electro-calorimetry” read before the British Association on September 1, Mr. Huntly will find that the method of measuring specific heats suggested by him is in principle similar to that described by Mr. Gee and myself. The method has been employed for determining specific heats during the last two years, but we have delayed publication till the best working details of the method have been elaborated.

In this paper, a comprehensive investigation of the capacitive active ripple compensation (ARC) techniques is made to conclude which one is optimal to be used in on-board chargers of electric vehicles. Crucial aspects in such an application are: lifetime, volumetric and specific power density (including components’ size and the needed cooling solution), and overall efficiency of the charger. As presented in this paper, all capacitive ARC topologies (buck, boost, and buck–boost) have successfully diverted the low-frequency ripple from the dc side with a maximized power density. The ARC circuit consists of two additional switches, a smoothing auxiliary inductor, and a storage auxiliary capacitor. Finally, the buck capacitive ARC topology proves to be the optimal ARC technique for on-board chargers because of its maximal power density, minimal loss behavior and voltage stress, and long lifetime capability as it requires a downsized capacitance to the extent, where film capacitors or ceramic capacitors can replace the normally used bulky electrolytic capacitors. The performance of the three capacitive ARC techniques is proved by simulation results.

This paper investigates the dynamical behaviors for a four-dimensional energy resource system with time delay, especially in terms of equilibria analyses and Hopf bifurcation analysis. By setting the time delay as a bifurcation parameter, it is shown that Hopf bifurcation would occur when the time delay exceeds a sequence of critical values. Furthermore, the stability and direction of the Hopf bifurcation are determined via the normal form theory and the center manifold reduction theorem. Numerical examples are given in the end of the paper to verify the theoretical results.

Existing techniques for solving nonconvex programming problems often rely on the availability of lower and upper bounds on the problem variables. This paper develops a method for obtaining these bounds when not all of them are availablea priori. The method is a generalization of the method of Fourier which finds bounds on variables satisfying linear inequality constraints. First, nonlinear inequality constraints are converted to equivalent sets of separable constraints. Generalized variable elimination techniques are used to reduce these to constraints in one variable. Bounds on that variable are obtained and an inductive process yields bounds on the others.

The purpose of this paper is to introduce a new three step iteration scheme for approximation of fixed points of the nonexpansive mappings. We show that our iteration process is faster than all of the Picard, the Mann, the Agarwal et al., and the Abbas et al. iteration processes. We support our analytic proof by a numerical example in which we approximate the fixed point by a computer using Matlab program. We also prove some weak convergence and strong convergence theorems for the nonexpansive mappings. MSC:47H09, 47H10.

The problem of obtaining a realistic guaranteeda posteriori bound on the accumulated error in a computed solution to the initial value problem in ordinary differential equations is difficult, because of the “wrapping” effect. This difficulty can sometimes, but not always, be avoided by making use of coordinate transformations. In this paper we propose that the wrapping effect be reduced by enclosing the accumulated error in a convex polygon of a certain form, and we describe one possible way of choosing the faces of such a polygon. The method is computationally expensive, but provides, in cases where other methods are unable to do so, a bound which does not grow exponentially too fast.

The global regularity problem concerning the inviscid SQG and the 3D Euler equations remains an outstanding open question. This paper presents several geometric observations on solutions of these equations. One observation stems from a relation between what we call Eulerian and Lagrangian deformations and reflects the alignment of the stretching directions of these deformations and the tangent direction of the level curves for the SQG equation. Various spatial symmetries in solutions to the 3D Euler equations are exploited. In addition, two observations on the curvature of the level curves of the SQG equation are also included.

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In this paper, we consider the generalized Motzkin paths whose step set consists of $$E = (1, 0), N= (0,1), U = (1,1)$$ and $$D = (1,-1)$$ . In the general case, for the number of such paths running from (0, 0) to $$(k,n-2k)$$ , we define a number triangle, which turns out to be a common extension of Pascal triangle and Delannoy triangle. Under the restriction of above or below the x-axis, these paths can be seen as an unified generalization of the well-known Dyck paths, Motzkin paths, and Schroder paths. We also consider the counting of such paths above the main diagonal. In every condition, we treat with two classes of paths, which are restricted and unrestricted paths. For each class of paths, the corresponding counting array is a Riordan array. Numerous Combinatorial matrices such as the Catalan matrix, Motzkin matrix, and Schroder matrix are special cases of these Riordan arrays.

Porous media have been a significant subject of research for a long time due to their applicability in various sciences. This paper investigates the heat transfer phenomenon in the porous media. A convergent solution is obtained for a two-dimensional time-fractional equation arising in a porous soil heat transfer. He's polynomial and He's variational iteration method are used to accomplish the required goals. The fractional derivative used in the article is described by He’s definition. He's fractional complex transform is used to convert the fractional differential equation into its traditional partner differential equation, which can be solved iteratively. Graphical representations of the results are provided to demonstrate the efficacy of the methods used.

This paper presents a successful implementation of the virtual crack closure integral method to calculate the stress intensity factors of an interfacial crack. The present method would compute the mixed-mode stress intensity factors from the mixed-mode energy release rates of the interfacial crack, which are easily obtained from the crack opening displacements and the nodal forces at and ahead of the crack tip, in a finite element model. The simple formulae which relate the stress intensity factors to the energy release rates are given in three separate categories: an isotropic bimaterial continuum, an orthotropic bimaterial continuum, and an anisotropic bimaterial continuum. In the example of a central crack in a bimaterial block under the plane strain condition, comparisons are made with the exact solution to determine the accuracy and efficiency of the numerical method. It was found that the virtual crack closure integral method does lead to very accurate results with a relatively coarse finite element mesh. It has also been shown that for an anisotropic interfacial crack under the generalized plane strain condition, the computed stress intensity factors using the virtual crack closure method compared favorably with the results using the J integral method applied to two interacting crack tip solutions. In order for the stress intensity factors to be used as physical variables, the characteristic length for the stress intensity factors must be properly defined. A study was carried out to determine the effects of the characteristic length on the fracture criterion based the mixed-mode stress intensity factors. It was found that the fracture criterion based on the quadratic mixture of the normalized stress intensity factors is less sensitive to the changes in characteristic length than the fracture criterion based on the total energy release rate along with the phase angle.

Pattern mining from graph transactional data (GTD) is an active area of research with applications in the domains of bioinformatics, chemical informatics and social networks. Existing works address the problem of mining frequent subgraphs from GTD. However, the knowledge concerning the coverage aspect of a set of subgraphs is also valuable for improving the performance of several applications. In this regard, we introduce the notion of subgraph coverage patterns (SCPs). Given a GTD, a subgraph coverage pattern is a set of subgraphs subject to relative frequency, coverage and overlap constraints provided by the user. We propose the Subgraph ID-based Flat Transactional (SIFT) framework for the efficient extraction of SCPs from a given GTD. Our performance evaluation using three real datasets demonstrates that our proposed SIFT framework is indeed capable of efficiently extracting SCPs from GTD. Furthermore, we demonstrate the effectiveness of SIFT through a case study in computer-aided drug design.

REFERRING to Prof. H. C. Plummer's letter on “An Approximation to the Probability Integral,” published in NATURE of October 25, the following alternative way of representing the normal error function by simple approximation may be of interest. The original demonstration of this has been given by me in Physical Department Paper No. 8, “A Method of Curve Fitting.”

In this paper, an adaptive fuzzy output feedback control approach is developed for a class of SISO uncertain nonlinear strict-feedback systems. The considered nonlinear systems contain unknown nonlinear functions, unknown time-varying delays and unmeasured states. The fuzzy logic systems are first used to approximate the unknown nonlinear functions, and then a high-gain filter is designed to estimate the unmeasured states. Combining the backstepping recursive design technique and adaptive fuzzy control design, an adaptive fuzzy output feedback backstepping control method is developed. It is proved that the proposed adaptive fuzzy control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and both the observer error and tracking error converge to a small neighborhood of the origin. Two key advantages of our scheme are that (i) the high-gain filter is designed to estimate unmeasured states of time-delay nonlinear system, and (ii) the virtual control gains are functions. A simulation is included to illustrate the effectiveness of the proposed approach.

FOR all work in which an error up to 10 per cent in the final result is admissible, the following rough logarithm-table provides a means of multiplying and dividing which is appreciably more rapid than direct calculation, and in simple cases does not require pencil and paper.

MR. C. N. HINSHELWOOD suggests in NATURE of Oct. 18, p. 604, that the English equivalents of eigenfunktion and eigenwert should be proper function and proper value. Having shown how to develop the functions used by Schrodinger (see, for example, my paper in the Phil. Mag., vol. 6, July 1928), may I again suggest from the nature of the Heaviside operator method disclosed that the terms to employ are parametrals and parametral functions.

This paper extends the concept of a normal pair from commutative ring theory to the context of a pair of (associative unital) rings. This is done by using the notion of integrality introduced by Atterton. It is shown that if $$R \subseteq S$$ are rings and $$D=(d_{ij})$$ is an $$n\times n$$ matrix with entries in S, then D is integral (in the sense of Atterton) over the full ring of $$n\times n$$ matrices with entries in R if and only if each $$d_{ij}$$ is integral over R. If $$R \subseteq S$$ are rings with corresponding full rings of $$n\times n$$ matrices $$R_n$$ and $$S_n$$, then $$(R_n,S_n)$$ is a normal pair if and only if (R, S) is a normal pair. Examples are given of a pair $$(\Lambda , \Gamma )$$ of noncommutative (in fact, full matrix) rings such that $$\Lambda \subset \Gamma $$ is (resp., is not) a minimal ring extension; it can be further arranged that $$(\Lambda , \Gamma )$$ is a normal pair or that $$\Lambda \subset \Gamma $$ is an integral extension.

Part I of this paper is concerned with the theory of differential invariants of a symmetric affine connection and a general linear connection of theKonig type. Part II deals with a geometry in which the components of the affine connection areChristoffel symbols, and the general linear connection is of a special sort. This section can be considered in part as an extension of theEinstein-Mayer (5) geometry

This paper tries to trace the different evolutional stages the egg of primitive chordates had to pass through to reach the complex state of the bird egg (Needhams “cleidoic egg”). It tries to ascribe to the evolutional stages the successive appearance of transitional particularities which characterise the egg and the ontogeny of birds. The different forms of individual development in birds are classified in 7 groups, proceeding from primitive to more advanced types. The type of Galliformes, especially of the Megapodidae, is shown to be very probably the most primitive one, while the Passeriformes show the highest degree of advanced specialisation. Proceeding from the primitive stages of chordates to the more advanced stages of brids a steadily growing participation of the maternal organism (and of the parents in general) in the development of the young animal is stated (table 4). Corresponding to this participation we find the young in a more and more intimate dependance of the mother — a dependance that unites the young and his parents in a “system” just as complicated as that built up by the young mammal and its mother. The comparative study allows us to trace the progressive evolution of such a system in avian phylogeny. Ce travail essaie d'etablir les stades de l'evolution par lesquels l'oeuf des cordes primitifs a du successivement passer pour atteindre l'etat complexe realise dans l'oeuf des oiseaux (Needham: „cleidoic egg”). Nous essayons ici d'attribuer aux stades evolutifs l'apparition successive de particularites transitoires qui, dans leur totalite, caracterisent l'oeuf et l'ontogenese des oiseaux. Les differentes formes de l'ontogenese des oiseaux sont groupees en 7 categories, allant d'un mode reconnu primitif a un autre mode evolue. Les Gallinaces, en particulier les Megapodides, nous paraissent se rapprocher le plus du stade primitif; les Passereaux semblent representer le stade le plus avance. En passant des stades primitifs des cordes aux stades plus evolues des oiseaux, on constate une participation progressive de la mere (et des parents en general) a l'ontogenese de l'espece (tableu 4). De cette participation resulte une dependance de plus en plus etroite du jeune animal — dependance qui unit les parents et leur progeniture en un „systeme” superieur depassant l'individu seul et qui n'est pas moins complexe que celui forme par la mere et l'enfant des mammiferes. L'etude comparative permet actuellement de suivre l'evolution progressive d'un tel systeme dans la phylogenese des oiseaux.

Life as a complicated process is composed of causal phenomena. But even if we know the reasons of all that happens in a living organism, we do not know what life really is. The problem of intercausal relation, of “causal structure” remains. The reason why a process takes place, must be found by analysis, causal structures are found by synthesis of the results of this analysis. Causal structures are characterized by two kinds of equilibrium: energetic and specific equilibrium. A state of physical equilibrium is characterized by a minimum of free energy; a biological energetic equilibrium is an organized one, where the vital factors activate the production of energy by each other and force each other to limit that production to the necessary measure. A specific equilibrium is characterized by the properties of its factors, properties by which those factors act as a cause after having received a specific stimulation. Every factor possesses two (or more) specific properties, in accordance with the properties of two neighbouring factors, as a link between two other links in a chain (“amboceptor-character”: e.g. secretine between hydrochloric acid from stomach and sodium bicarbonate from the pancreas). Both forms of equilibrium authorise us to speak of living systems as a “whole”. In the second part of this paper we treat the dynamic aspect of the functions of living systems as a “whole”. This dynamic aspect manifests itself in growth and probably in cortical functions. Blastomeres represent, when isolated, the “whole” of growing potentialities of a germe. In normal contact with each other they restrict themselves to produce a part of that “whole”, in harmony with that which other blastomeres produce. This harmonious restriction can be explained by interaction between all the blastomeres by which every blastomere suppresses in other blastomeres all that it will produce itself. Blastomeres must therefore act on other blastomees not according to their isolate “being”, but according to the influences which they undergo by all other blastomeres, that means according to their “role”. There must be a causal net of interaction between all the blastomeres and that net “as a whole” determines every step of growth. Such a net of relation determines also human history and sociology. Materialism only took account of isolated causes, vitalism only of the effect of the net of causal relations without understanding that such a net might be analysed. In reality there is neither materialism nor vitalism.

In continuation of a previous paper, some consequences of the fundamental equations established there are studied. For some simple hypothetical cases it is shown how some of the parameters which enter in the equations governing the structure of the social group can be determined by means of those equations from actually observable data. Furthermore some general properties of the variation with respect to time of the fundamental distribution function, which enters in the equations, are derived.

In continuation of a previous paper, a mechanism of delayed reflexes is considered more in detail. Equations governing such a mechanism are established and approximately solved. The formulae thus obtained describe the phenomenon of “concentration” of a conditioned reflex around a definite time interval after stimulation. Applied along the lines discussed in the previous paper to some simple combinations of stimuli and responses the formulae lead to a description of the elimination of errors by trial. They give a relation between the number of repetitions, necessary to eliminate a wrong act, and other constants, describing the situation.

This paper presents three theorems concerning the relation between results with obtained and corrected correlation coefficients in the Thurstone method of multiple factor analysis. (1) The rank of the correlational matrix, and thus the number of factors involved, is unaffected by correcting the obtained coefficients for attenuation. (2) The communality of a variable when the obtained coefficients have been corrected for attenuation is equal to the communality with obtained coefficients divided by the reliability coefficient of the variable. (3) The relationship is shown between the factorial matrix of a correlational matrix of raw correlation coefficients and the factorial matrix of a correlational matrix of corrected correlation coefficients, and a method of obtaining either of these factorial matrices from the other is indicated.

This paper presents the trajectory tracking control of an autonomous underwater vehicle (AUV). To cope with parametric uncertainties owing to the hydrodynamic effect, an adaptive control law is developed for the AUV to track the desired trajectory. This desired state-dependent regressor matrix-based controller provides consistent results under hydrodynamic parametric uncertainties. Stability of the developed controller is verified using the Lyapunov's direct method. Numerical simulations are carried out to study the efficacy of the proposed adaptive controller.

Papers involving factorial methods appearing in current literature often misuse factorial methods. These meaningless results are reached because of neglect of certain conditions basic to factor theory. The conditions are

It is shown that from a somewhat more precise form of the fundamental postulates, used in a previous paper as a starting point for a system of mathematical biophysics of psychological phenomena, a mechanism can be derived, which represents the important features of conditioning.

In general, the methods of factor analysis developed during the past five years are based on the reduction of the correlational matrix by successive steps. The first factor loadings are determined and eliminated from the correlational matrix, giving a residual matrix. This process is continued for successive factor loadings until the elements of the last obtained residual matrix may be regarded as due to chance. The method outlined in this paper assumes the maximum number of factorsm in the correlational matrix. Them factor vectors are solved for simultaneously. Once them factor vectors are found, any vectors having only negligible factor loadings may be discarded.

In previous formulations the assumption has been made that the intensity of excitation or inhibition varies with distance. In this paper the simple case of a series of identical neurones is treated. The development shows five possible relations. In future theoretical formulations it is no longer necessary to postulate arbitrary relations in case any of the derived forms can be used.

This paper presents a new method of determining the minimum rank in factor analysis, appropriate to the principal axes solution. The new method is compared with a former method which, with some adjustment, is more convenient for the centroid approach. Both methods are applied to two familiar examples.

The intercorrelations of thirty-seven variables, including the Minnesota battery of “mechanical ability” tests, the seven MacQuarrie tests of “mechanical ability,” O'Connor's Wiggly blocks, and the Stenquist picture-matching test, were analyzed by Thurstone's centroid method. Five factors, Perceptual, Verbal, Youth, Manual Agility, and Spatial, were taken out. Factors prominent in so-called mechanical ability tests are the Spatial and Perceptual ones with Mac-Quarrie's dotting test significantly high in the Manual Agility factor. Each of the factors can be measured with group pencil-and-paper tests.

This paper shows how to compute multiple correlation coefficients, partial correlation coefficients, and regression coefficients from the factorial matrix. Special emphasis is given to computation technique and to approximation formulas. The method is extremely flexible in application since it may be applied to any subset of the original set of observed variables. It is also extremely useful when many of these coefficients are desired.

The paper deals with many projective properties of the neighbourhoods of the third,4th, 5th order of a point on a non-holonome surfaceV32 inS3. Chiefly two remarkable projective correspondences are studied, between the tangent plane and the bundle of directions, with his contact point as centre. Many generalizations are obtained of geometrical loci (so as lines, planes, quadrics) projectively associated with the neighbourhoods of a point on an ordinary (holonome) surface. The last sections are concerned with the extension to theV32 of the quadric ofMoutard and theSegre's correspondence.

In this paper, projective synchronization of drive-response coupled dynamical network with delayed system nodes and coupling time-varying delay is investigated via impulsive control, where the scaling factors are different from each other. Different controllers are designed to achieve the projective synchronization: only impulsive control is used when the scaling factors need extra limitation, while an extra controller, that is, a simple linear feedback controller, is added when the scaling factors don’t need extra limitation. Based on the stability analysis of the impulsive functional differential equation, the sufficient conditions for achieving projective synchronization of such coupled network are established, and an estimate of the upper bound of impulsive intervals ensuring global exponential synchronization of drive-response coupled dynamical network is also given. Numerical examples on the time-delay Lorenz chaotic systems are presented finally to illustrate the effectiveness and advantage of the proposed synchronization criteria.

This paper attempts to show in a non-mathematical way the influence of grouping on standard deviations and correlations, and advances empirical evidence to illustrate with what accuracy values corrected for grouping by Sheppard's correction approximate to values obtained from ungrouped data when the distributions are continuous. This enquiry gained its initial stimulus from the observation that many standard deviations and correlations reported by students of psychology and education are uncorrected for grouping and that frequently errors attributable to the grouping of data are not small when compared with errors of sampling.

The most commonly used method of factoring a matrix of intercorrelations is the centroid method developed by L. L. Thurstone. It is, however, necessary to transform the centroid matrix of factor loadings into a simple structure matrix in order to facilitate the interpretation of the factor loadings. Current methods for effecting this transformation are chiefly graphical and require considerable experience and personal judgment. This paper presents a new method for transforming an arbitrary factor matrix into a simple structure matrix by methods almost completely objective. The theory underlying the method is developed and approximation procedures are derived. The method is applied to a matrix of factor loadings previously analyzed by Thurstone.

This paper is an attempt to integrate the various methods which have been developed for the numerical solution of simultaneous linear equations. It is demonstrated that many of the common methods, including the Doolittle Method, are variations of the method of “single division.” The most useful variation of this method, in case symmetry is present, appears to be the Abbreviated Doolittle method. The method of multiplication and subtraction likewise can be abbreviated in various ways of which the most satisfactory form appears to be the new Compact method. These methods are then applied to such problems as the solution of related equations, the solution of groups of equations, and the evaluation of the inverse of a matrix.

Items have been studied heretofore for their value as elements of particular tests to the neglect of more fundamental research into the multiple potentiality of items. This article proposes a method of grouping items into “synonymies” comprising all of the items which correlate with a given key item. These synonymies can be used for interpretation of the total meaning of the key item: (1) by inspection of the constituent items and (2) by correlational study of obtained single scores of individual persons. The method is illustrated by four items with inter- and intra-correlations, and characteristics of an ideal background reservoir of items are pointed out.

A special case of a problem discussed in a previous paper is treated in greater detail. An equation in the three variables, errors, trials and number of possible choices, is developed and compared with the results of an experiment performed under conditions closely approximating those required for the development of the equation. The agreement is excellent.

In much research in social psychology it is impractical to get quantitative measure of the degree of effectiveness of certain social behaviors, yet associates can sense that effectiveness sufficiently well to detect those who manifest the behavior in very high or in very low degree. This paper develops a technique of biserial correlation from wide-spread classes to deal statistically with such situations, develops standard error formulas for it, and points to a wide range of usefulness for this type of technique.

A case studied in a previous paper, concerning the changes of the relative number of individuals of different types in a social group, is treated under more general assumptions. It is shown that under those more general conditions periodical fluctuations in the structure of the social group may occur.

This paper discusses the influence of test difficulty on the correlation between test items and between tests. The greater the difference in difficulty between two test items or between two tests the smaller the maximum correlation between them. In general, the greater the number of degrees of difficulty among the items in a test or among the tests in a battery, the higher the rank of the matrix of intercorrelations; that is, differences in difficulty are represented in the factorial configuration as additional factors. The suggestion is made that if all tests included in a battery are roughly homogeneous with respect to difficulty existing hierarchies will be more clearly defined and meaningful psychological interpretation of factors more readily attained.

The paper is concerned with projective differential properties of the plane sections made by the planes which pass through a non-asymptotic tangent, of a non-holonome surfaceV32 inS3. Chiefly by this way some surfaces are determined, which are projectively connected with the generic point on theV32.

This paper questions the oft-repeated statement that clinical psychology is an art by examining the main functions of clinical psychologists, i.e., diagnosis and treatment. In examining the concept of diagnosis, evidence is presented which supports the notion that a diagnostic statement has meaning only when it has a referent in the future—when it provides a prediction. A prediction (probability-statement) is determined empirically and may be stated in terms of a regression equation or in terms of a crude generalization from clinical experience. Treatment likewise is determined by tacit or expressed predictions of behavior under alternative conditions. The various conceptions of art as applied to clinical psychology are examined and the conclusion is drawn that clinical psychology is a scientific as opposed to an artistic or intuitive enterprise.