Lotka's law: A testing procedure

Instead of the commonly accepted inverse square law, Lotka's original formulation was based on a more general inverse power law: xⁿ·y = c. The exponent and the constant must be estimated from the given set of author productivity data. A step-by-step outline is presented for testing the applicability of Lotka's law. Steps include the computation of the values of the exponent and the constant based on Lotka's method, and the test for significance of the observed frequency distribution against the estimated theoretical distribution derived from Lotka's formula.     

Theory of broadband matching and the problem of compatible impedances

It is shown that Youla's theory of broadband matching between a passive load and a resistive generator with a preassigned transducer power gain characteristic is completely equivalent to Wohlers' solution to the problem of compatible impedences, which transforms a given passive impedance by a lossless coupling network into another specified one.     

Discrete analogues of Green's identities through the graph—theoretic field model

In this paper, we derive discrete versions of Green's identities (which appear in the study of potential field theory) as direct consequences of applying Tellegen's Theorem to the Graph—Theoretic Field Model (GTFM) of a field. The procedure herein is in marked contrast to the existing procedures where Green's Identities are derived from the Divergence Theorem by using some strictly mathematical operations. In particular, Green's third identity, which is the starting point formulation for the Boundary Integral Method, is singled out for special attention in terms of its discrete counterpart in the Graph—Theoretic Field Model. The first discrete identity is used to establish certain properties of solutions for the GTFM and a limiting process is applied to the three discrete identities to derive the traditional vector-calculus forms of Green's identities.     

Pole sensitivity in coupling networks

When designing lossless networks, one is faced with the problem of choosing a zero configuration for the reflection coefficient ?(s). Bode showed that if parasitic capacitances are present as well as for power transfer optimization, the best zero configuration is to locate all of them in the left half-plane. Recently, Bode's result was generalized to include parasitic immitances at both ends (source and load) of the quadripole.This work adds a new result to the theory by looking at the overall transfer function poles. It is shown that (a) if the source resistance varies, one should select left half-plane zeros for ?(s); and (b) if the load impedance varies, one should select right half-plane zeros.The pole sensitivity criterion used is the distance between the actual transfer function poles and the poles of the ideal transfer function.     

Asynchronous performance of hysteresis motor

A simplified model of the hysteresis motor is introduced and analyzed; field analysis is undertaken at hand of Maxwell's stress tensor and Poynting's theorem. The suggested approach provides deeper insight into the power interchange process between stator and rotor.     

On the existence and the magnitude of electronic charges

In order to quantize Dirac's classical point electron¹ we supplement Einstein's classical equation (E/c)² ? p² = b2 with a reciprocal classical equation (CΔt)² ? (Δr)² = a² where b = mc and a is Dirac's signal radius. Δt is the time saved by a light signal in various states of motion of the electron, and a/c is the rest time saved. Our former efforts² of obtaining an integral equation for the probability amplitude have been rectified by Born.³ There is no solution of the integral equation, however, unless advanced and retarded phases are introduced simultaneously, along with Dirac's advanced and retarded potentials. We have obtained a transcendental equation for the eigen-value μ = αγ where α is the Sommerfeld fine-structure constant, and γ is the numerical factor in Dirac's signal radius a = γe²/mc². The smallest eigen-value is μ = 0.0299.That is, ab = hγ = h/210.     

On the Salient Properties of the Hysteresis Machine—I. Non-conducting Rotor

The properties of the hysteresis machine are analyzed on the basis of a cylindrical model. The electromagnetic field in the various regions of the motor is derived by field-theoretical methods (such as Maxwell's equations and Poynting's theorem), and the resulting parameters are applied in turn in determining torques and other relevant quantities. Three limiting particular cases of special interest are examined.     

A state space approach to elasticity

The two-dimensional, plane stress problem of linear elasticity is analyzed within a state space framework. The medium considered is homogeneous and isotropic. Vlasov's mixed formulation of elasticity is used throughout. The field equations are derived in closed form, thus avoiding Vlasov's intermediate infinite series solution. Finally, all the properties of the transfer matrix are shown to follow directly from embedding the problem into a state space setting.     

EURELIOS,the world's first thermomechanical helioelectric power plant

Because of the sheer magnitude—ten thousand times greater than the world's present power requirements—solar energy has long seemed an attractive alternative to conventional sources of power. As this appraisal—based on the world's first helioelectric power plant, in Italy—makes clear, however, there are major problems in the generation of solar energy in Europe, especially in northern parts. A more feasible alternative may be for installations to be established in Third World countries—with abundant space and intense sunshine—and the energy exported in the form of an energy-rich fuel such as hydrogen.     

Certain matters concerning scaling in the magnetron with special reference to the relative efficiency of magnetrons of different sizes

The paper concerns the comparison of the behavior of two magnetron systems of different sizes, all apparatus from the input terminals of the magnetron to the final radiation antenna being contemplated in the picture. The mathematical comparison of the two systems assumes a specially simple form when the electrical conductivities of the corresponding parts of the systems in the two cases are adjusted to values in the inverse ratio of the scaling in linear dimensions. A scaling of this kind is therefore studied. The conclusions reached are as follows:For an assigned potential applied to the two models, the power input is the same, the power radiated from the antenna is the same, the power dissipated in Ohm's law heating in all parts is the same, and the power dissipated in back-bombardment or at the anode is the same.As a corollary to the foregoing, it is inferred that if the corresponding parts of the two models have the same electrical conductivity, then in so far as Ohm's law heating is an important factor at all, it is more important in the small model than in the large one.     

Quasi-power functionals for potential fields from the Graph- Theoretic Field Model

Quasi-power functionals have been traditionally derived through the Method of Weighted Residuals (MWR) and used as the starting formulation for the finite element method. In this paper, we derive similar but more complete functionals for potential fields through a novel approach. We first form discrete quasi-power functions by applying Tellegen's theorem to the Graph-Theoretic Field Model (GTFM) and then obtain the continuous model quasi-power functionals by applying a limiting process to the discrete counterpart. The procedure herein is in marked contrast to the MWR whereby quasi-power functionals are derived by applying mathematical operations to the partial differential system. The procedure can be used with fields with anisotropy, non-linearities and coupled processes, although the example fields used within are linear and isotropic. This paper is a sequel to similar derivations for Green's identities and variational formulations.     

The influence of Ministry of Defence funding on semiconductor research and development in the United Kingdom

This paper argues that the United Kingdom Ministry of Defence's (MoD) sponsorship of industrial semiconductor research and development (R&D) has, by its very nature, influenced the type of R&D performed, and the directions it has taken, to the extent of limiting its potential for subsequent commercial utilization. While much of the fault appears to lie with the semiconductor industry's response to MoD funding of its R&D, especially its over-reliance on such external support, the paper also suggests that the structure, modus operandi, and funding mechanisms of the MoD department concerned have significantly affected the industry's R&D activities. With these criticisms in mind, while at the same time noting the advantageous features of this department's activities, such as its relative autonomy, brief suggestions for ensuring more coherent and continuous state support for semiconductor R&D, including, for example, the use of innovation-oriented procurement policies, are offered.     

The DT-Polynomial Approach to Discrete Time-Varying Network Flow Problems

This paper introduces a polynomial operator called the DT-polynomial as a novel approach to network flow problems. The class of networks dealt with is time-varying in the sense that the capacity, cost, and travel-time of each edge may vary in discrete time. The Dt-polynomial is a polynomial in two operators, D (delay) and T (time), which is used for describing the time-varying transmission characteristics. The paper starts with the mathematics involving the DT-polynomials. A new shortest arrival route algorithm is presented, and its computational complexity is found to be favorable in comparison with others such as Dijkstra's method and the potential method derived from Ford-Fulkerson's technique. Furthermore, a dynamic flow problem is formulated and analyzed in terms of DT-polynomials, and a latest-departure earliest-arrival schedule is given. Finally, a modified DT-polynomial is applied to digital filter networks.     

The battle for survival: Innovating firms' strategic signaling behaviors and their impacts on business success during the shakeout period after the standards war

The shakeout period after the emergence of a dominant design is very important to technology followers and niche market producers, who need adjust to significant changes in the competitive landscape. We posit that such innovating firms use strategic signals that address technical-, market-, and standards-uncertainty associated with their innovations to communicate with market participants to reduce participants' perceived uncertainties associated with the innovative products. Studying technology followers and niche market producers in the personal computer industry during its 1982–1989 shakeout period, we found that technology followers and niche market producers differ in their use of technical-, market-, and standards-related signals. Additionally, using event study methodology, we find that technology followers' strategic signals have significant positive impacts on both their own and other followers' stock prices. Meanwhile, niche market producers' strategic signals have significant positive impacts on their own stock prices, but not significant impacts on other niche market producers and technology followers' stock prices.     

Theory of nonlinear systems

This paper gives a general review of the Theory of Nonlinear Systems. In 1960, the author presented a paper “Theory of Nonlinear Control” at the First IFAC Congress at Moscow. Professor Norbert Wiener, who attended this Congress, drew attention to his work on the synthesis and analysis of nonlinear systems in terms of Hermitian polynomials in the Laguerre coefficients of the past of the input.Wiener's original idea was to use white noise as a probe on any nonlinear system. Applying this input to a Laguerre network gives u₁, u₂,…, u_s, and then to a Hermite polynomial generator gives V(α)'s. Applying the same input to the actual nonlinear system gives output c(t). Putting c(t) and V(α)'s through a product averaging device, we get $\text{c(t)V(α)}\text{=}\text{A}{}_{\mathrm{\alpha }}\text{2л}{}^{\mathrm{<mtext>s</mtext><mtext>2</mtext>}}$, where the upper bar denotes time average and A_α's can be considered as characteristic coefficients of the nonlinear system. A desired output z(itt) may replace c(itt) to get a new set of A_α's.The Volterra functional method suggested by Wiener in 1942 has been greatlydeveloped from 1955 to the present. The method involves a multi-dimensional convolution integral with multi- dimensional kernels. The associated multi-dimensional transforms are given by Y.H. Ku and A.A. Wolf (J. Franklin Inst., Vol. 281, pp. 9–26, 1966). Wiener extended the Volterra functionals by forming an orthogonal set of functionals known as G-functionals, using Gaussian white noise as input. Volterra kernels and Wiener kernels can be correlated and form the characteristic functions of nonlinear systems.From an extension of the linear system to the nonlinear system, the input-output crosscorrelation φ_xy can be shown to be equal to the convolution of system impulse response h₁ with the autocorrelation φ_xx. Using the white noise as input, where its power density spectrum is a constant, say, A, the crosscorrelation is given by φ_xy(σ) = Ah₁(σ), while the autocorrelation is φ_xx(τ) = Au(τ). This extension forms the basis of an optimum method for nonlinear system identification. Measurement of kernels can be made through proper circuitry.Parallel to the Volterra series and the Wiener series, another series based on Taylor-Cauchy transforms developed since 1959 are given for comparison. The Taylor-Cauchy transform method can be applied in the analysis of simultaneous nonlinear systems. It is noted that the Volterra functional method and the Taylor-Cauchy transform method give identical final results.A selected Bibliography is appended not only to include other aspects of nonlinear system theory but also to show the wide application of nonlinear system characterization and identification to problems in biology, ecology, physiology, cybernetics, control theory, socio- economic systems, etc.     

A new approach to average consensus problems with multiple time-delays and jointly-connected topologies

This paper investigates average consensus problem in networks of continuous-time agents with delayed information and jointly-connected topologies. A lemma is derived by extending the Barbalat's Lemma to piecewise continuous functions, which provides a new analysis approach for switched systems. Then based on this lemma, a sufficient condition in terms of linear matrix inequalities (LMIs) is given for average consensus of the system by employing a Lyapunov approach, where the communication structures vary over time and the corresponding graphs may not be connected. Finally, simulation results are provided to demonstrate the effectiveness of our theoretical results.     

A Physical Interpretation of Factorization and Factor Modification in Structural Analysis

The physical interpretation of LDL^t factorization and Bennett's method for matrix factor modification applied to structural analysis are studied. The sparsity of the matrix factors and their effect on matrix modification are examined.     

Approaching 18% efficiency of ternary organic photovoltaics with wide bandgap polymer donor and well compatible Y6 : Y6-1O as acceptor

A series of ternary organic photovoltaics (OPVs) are fabricated with one wide bandgap polymer D18-Cl as donor, and well compatible Y6 and Y6-1O as acceptor. The open-circuit-voltage (V_OC) of ternary OPVs is monotonously increased along with the incorporation of Y6-1O, indicating that the alloy state should be formed between Y6 and Y6-1O due to their excellent compatibility. The energy loss can be minimized by incorporating Y6-1O, leading to the V_OC improvement of ternary OPVs. By finely adjusting the Y6-1O content, a power conversion efficiency of 17.91% is achieved in the optimal ternary OPVs with 30 wt% Y6-1O in acceptors, resulting from synchronously improved short-circuit-current density (J_SC) of 25.87 mA cm⁻², fill factor (FF) of 76.92% and V_OC of 0.900 V in comparison with those of D18-Cl : Y6 binary OPVs. The J_SC and FF improvement of ternary OPVs should be ascribed to comprehensively optimal photon harvesting, exciton dissociation and charge transport in ternary active layers. The more efficient charge separation and transport process in ternary active layers can be confirmed by the magneto-photocurrent and impedance spectroscopy experimental results, respectively. This work provides new insight into constructing highly efficient ternary OPVs with well compatible Y6 and its derivative as acceptor.     

An isoperimetric problem for continuous systems: The aeolian vibration of a conductor span

The equations of motion for perfectly mechanical systems which are restricted to satisfy given constraints are derived through the Lagrangian formulation for continuous media. Hamilton's equations for this situation are derived, and the equations for the balance of energy and angular momentum are generated from fundamental principles. These equations are all specialized to the example of a conductor which is vibrating under Aeolian excitation. Various models for the Hamiltonian density and the constraint energy density due to the wind energy input are also discussed.     

A theory for decoupling lossless coupled tapered lines with applications to directional couplers

A simple theory is presented for decoupling a pair of lossless coupled nonuniform transmission lines (CNUTL), with a common return and supporting TEM waves, into two lossless nonuniform transmission lines (NUTL). This theory is independent of the port terminations, symmetry conditions, etc. The method directly relates the line parameters of the lossless CNUTL's to those of the decoupled lines and vice versa; further, the matrix parameters of the CNUTL's as a four-port are explicitly expressed in terms of those of the decoupled lines as two-ports. This theory is then utilized to study the applications of CNUTL's as directional couplers.It is shown that for CNUTL's to behave as a codirectional coupler, each of the decoupled lines should be a proportional line, while for contradirectional coupler action, the two decoupled lines have to be duals of each other. The coupling response of the codirectional coupler is found to be periodic, while the phase shift between coupled and transmitted signals varies linearly with frequency. The coupling response of various contradirectional couplers with smooth transition at one of the ends, for which the decoupled lines are “basic NUTL's with hyperbolic solutions”, are studied in detail. It is shown that all these couplers have a high-pass response and that the CNUTL's with “hyperbolic cosine squared lines” as decoupled lines have the best response of all the CNUTL's considered.