Quadratic Nature Research Articles

On the quadratic nature of the singularity curves of planar three-degree-of-freedom parallel manipulators

In this paper, the singularity loci of general three-degree-of-freedom planar parallel manipulators are studied and a graphical representation of these loci in the manipulator's workspace is obtained. The algorithm used here is based on the determination of the roots of the determinant of the manipulator's Jacobian matrix. As mentioned elsewhere, two different types of singularities can occur when parallel manipulators are actuated. Both types are considered here and it is shown that one of the two types leads to a trivial description while the second one is more challenging. On the other hand, architectural singularities are not considered since they are assumed to be eliminated from the outset by a proper choice of the kinematic parameters. Indeed, for the type of manipulator studied here, architectural singularities are very easy to predict and were studied in detail elsewhere. Analytical expressions describing the singularity locus of a planar parallel manipulator are obtained here. Moreover, it is shown that, for a given orientation of the platform, the singularity locus in the plane of motion is a quadratic form, i.e., either a hyperbola, a parabola or an ellipse. Examples illustrating these results are given. For each of these examples, the corresponding singularity locus is graphically superimposed on the manipulator's workspace. This feature has been included in a package developed for the CAD of parallel manipulators. Cases of manipulators for which the singularity locus is located outside of the workspace for certain orientations of the platform are presented. Additionally, three-dimensional representions of the singularity loci are given. The graphical representation of the singularity loci is a very powerful design tool which can be of great help, especially in the context of parallel manipulators.

Disseminating active map information to mobile hosts

The article describes an active map service (AMS) that supports context-aware computing by providing clients with information about located-objects and how those objects change over time. The authors focus on the communication issues of disseminating information from an active map server to its clients, and in particular, address how to deal with various overload situations that can occur. Simple unicast callbacks to interested clients work well enough if only a few located-objects are moving at any given time and only a few clients wish to know about any given move. However, if many people are moving about in the same region and many clients are interested in their motion, then the AMS may experience overload due to the quadratic nature of the communications involved. This overload affects both the server as well as any slow communications links being used. Mobile distributed computing enables users to interact with many different mobile and stationary computers over the course of the day. Navigating a mobile environment can be aided by active maps that describe the location and characteristics of objects within some region as they change over time.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Simple electrical biasing for minimizing the nonlinearities of quantum-well Mach-Zehnder modulators

The quadratic nature of the electro-optic effect in semiconductor Mach-Zehnder modulators based on the quantum-confined Stark effect allows simple electrical biasing to eliminate either the second-order or the third-order distortions in the optical output, improving the device linearity for single-octave bandwidth multicarrier analog modulation applications.

Graphic analysis of isobiological effectiveness for twice‐a‐day radiotherapy regimens and its application

AbstractThe effectiveness of twice‐a‐day (BID) hyperfractionated radiotherapy (RT) schedules has been demonstrated for carcinomas of the head and neck, the lung, and advanced stage breast cancers. Fractionation choices include identical or different doses of the two daily treatments referred to as equally split or unequally split BID doses, respectively. The choices of equally split, unequally split, or a mixture of both are based on the consideration of maximal tumor control or minimal late tissue effect. The comparison of biological effectiveness of different regimens is commonly done by computing the individual biological effective doses (BED) to tumor and late tissue. For this purpose, a different theoretical approach which adopts the concept of isobiological effectiveness may be more general and analytic than point dose computation. Taking advantage of the quadratic nature, a graphic analysis of isobiological effectiveness (GAIBE) was developed to analyze how to optimize the regimens for tumor killing effect and late tissue sparing effect. In this analysis, a Cartesian plot of two dose axes representing the two daily doses is used. The loci of isobiological effective dose (isoBED) regimens are circular on this plot. Thus, the effects of many regimens on tumor and late reacting tissue may be observed simultaneously by comparing the isoBED loci. Graphically, with GAIBE analysis and, mathematically, for a given isoBED to tumor, we have demonstrated that equally split hyperfractionation schedules will deliver the lowest biological effectiveness to late reacting tissues among all isoBED regimens to tumor. Situations when unequally split regimens are beneficial are also discussed. Another variable of clinical importance is the repopulation phenomenon which may counteract the biological effectiveness with increasing length of treatment course. The additive nature of BED from daily treatments allows GAIBE analysis to compensate for the repopulation phenomenon and aid the determination of the course length. Our analysis can also be used for the design of concomitant boost BID regimens. A subroutine in BASIC language has been developed and is available upon request. As a corollary of GAIBE analysis, for a chosen total dose, once‐daily treatment (QD) will result in the most tumor killing and the BID half‐dose exposures will have the least tumor killing. Other combinations of BID exposures with the sum of doses equal to QD exposure will have varying degrees of tumor killing which fall in between these two extremes. This concept from GAIBE analysis may be applied to determine α/β values for tumor cell lines using equally split exposures. © 1994 Wiley‐Liss, Inc.

The weak coupling limit for quadratic interaction

The weak coupling limit of a ‘‘system+reservoir’’ model with nonlinear (quadratic) interaction is discussed. In a previous paper [Accardi and Lu, Stoch. Process. Phys. Geom., 1–26], it has been shown that, if the matrix elements of the van Hove rescaled evolution are taken with respect to the same collective vectors used for linear interactions, then the limiting evolution is not unitary. In the present paper, we choose a new type of collective vectors and obtain, in the weak coupling limit, a unitary evolution satisfying a quantum stochastic differential equation. A remarkable feature of the limiting process is that the quadratic nature of the interaction shows up in a nontrivial choice of the Hilbert space where the limiting quantum noise takes its values, which is qualitatively new with respect to all the models considered up to now.

Effect of prostaglandins on luteal function during early pregnancy in pigs.

Luteal cells were obtained by digestion of luteal tissue of cyclic (day 12) and early pregnant (days 12, 20 and 30) pigs. Suspensions of the dispersed luteal cells (5 x 10(4) cells ml-1) were incubated for 2 h in minimum essential medium (MEM) alone (control) and MEM with different concentrations of prostaglandin F2 alpha (PGF2 alpha) and PGE2 (0.01, 0.1, 1, 10, 100 and 1000 ng ml-1) and luteinizing hormone (LH) 100 and 1000 ng ml-1, or with combinations of LH + PGF2 alpha and LH + PGE2. Net progesterone production was measured in the incubation media by direct radioimmunoassay. The overall response pattern of the luteal cells to exogenous hormones on day 12 of the oestrous cycle and pregnancy differed (P < 0.05) from treatment on day 20 and 30 of pregnancy. In general progesterone production was higher (P < 0.05) and the response to PGF2 alpha and PGE2 treatment was most obvious on day 12 of the oestrous cycle and pregnancy. Overall, PGF2 alpha stimulated progesterone production in a dose-dependent manner (P < 0.05). The response to PGE2 was of a quadratic nature (P < 0.05) in which the lowest and the highest doses of PGE2 were associated with a greater production of progesterone than were the intermediate doses. Treatment of luteal cells with PGF2 alpha + LH or PGE2 + LH caused overall inhibition (P < 0.05) of progesterone production compared with treatment with each hormone alone. This interaction was not affected by the dose of LH used. These findings indicate that PGF2 alpha and PGE2 are involved in the autocrine control of corpus luteum function.

The relationship between stream or river discharge and thyroid hormone levels in wild adult Atlantic salmon (Salmo salar L.)

Thyroxine and tri-iodothyronine levels were determined in groups of adult Atlantic salmon (Salmo salar L.) of both sexes at river entry in summer or as they entered a spawning tributary in late autumn. Hormone levels were considered in relation to river or stream discharge rate at capture. For tri-iodothyronine, there was a quadratic or linear relationship with discharge rate for each sex at both sites. For thyroxine, there was a quadratic relationship with discharge rate at tributary entry but no relationship with discharge rate at river entry. It is argued that raised hormone levels at higher discharge rates are a probable consequence of increased motor activity associated with greater water velocity. The quadratic nature of most of the models is attributed to physiological or behavioural limitation of the response.

Sliding observers for robot manipulators

High precision measurements of the joint displacements are available on robot manipulators. By contrast, the velocity measurements obtained through tachometers are in many cases contaminated by noise. It is therefore economically and technically interesting to investigate the possibility of accurately estimating the speed from available measurements. This paper presents a new approach for estimating the state vector of a robot manipulator, using nonlinear sliding mode observers. Robot models with and without friction are analysed. In both cases, convergence conditions for the observed state vector are given. The results are strongly based on the physical properties of the robot, such as energy conservation and the quadratic nature of the Coriolis and centripetal forces.

Electrophysiological evidence of nonlinear distortion products to two-tone stimuli

Spectral analysis of auditory-evoked potential recordings from ten normal-hearing subjects to two-tone signals revealed energy at difference tone (DT = f2-f1) and cubic difference (CDT = 2f1-f2) frequencies that was not present in the acoustic signal. Control experiments and calibrations provided substantial evidence supportive of the biological nature of these auditory nonlinearities, suggesting that they are not the result of electromagnetic, acoustic, or analytic artifact. Amplitudes of DT- and CDT-evoked responses were evaluated for rarefaction and condensation signals with f1 = 510 and 800 Hz across frequency ratios (f2/f1) of 1.16, 1.26, 1.36, and 1.46. Additionally, time-domain summation and subtraction of separately collected evoked responses to rarefaction and condensation signals were performed to demonstrate that these electrophysiological DT and CDT responses reflect their expected quadratic and cubic nature. Suggestions for development of clinical applications of assessing auditory nonlinearities using this methodology are provided.

Investigations of the Nature of Critical Line Very Close to a Double Critical Point

AbstractThe curvature of the line of critical points in a reentrant ternary mixture is determined by approaching the double critical point (DCP) extremely closely. The results establish the continuous and quadratic nature of this line. Out study encompasses as small a loop size (ΔT) as 663 mK. The DCP is realized when ΔT becomes zero.

Designer invariants for large phylogenies.

The Cavender-Felsenstein edge-length invariants for binary characters on 4-trees provide the starting point for the development of "customized" invariants for evaluating and comparing phylogenetic hypotheses. The binary character invariants may be generalized to k-valued characters without losing the quadratic nature of the invariants as functions of the theoretical frequencies f(UVXY) of observable character configurations (U at organism 1, V at 2, etc.). The key to the approach is that certain sets of these configurations constitute events which are probabilistically independent from other such sets, under the symmetric Markov change models studied. By introducing more complex sets of configurations, we find the quadratic invariants for 5-trees in the binary model and for individual edges in 6-trees or, indeed, in any size tree. The same technique allows us to formulate invariants for entire trees, but these are cubic functions for 6-trees and are higher-degree polynomials for larger trees. With k-valued characters and, especially, with large trees, the types of configuration sets (events) used in the simpler examples are too rare (i.e., their predicted frequencies are too low) to be useful, and the construction of meaningful pairs of independent events becomes an important and nontrivial task in designing invariants suited to testing specific hypotheses. In a very natural way, this approach fits in with well-known statistical methodology for contingency tables. We explore use of events such as "only transitions occur for character i (i.e., position i in a nucleic acid sequence) in subtree a" in analyzing a set of data on ribosomal RNA in the context of the controversy over the origins of archaebacteria, eubacteria, and eukaryotes.

Sliding Observers for Robot Manipulators

High precision measurements of the joint displacements are available on robot manipulators. By contrast, the velocity measurements obtained through tachometers are in many cases contaminated of noise. Its is therefore economically and technically interesting to investigate the possibility of accurately estimating the speed from indirect available measurements. This paper presents a new approach for estimating the state vector of a robot manipulator, using nonlinear sliding mode observers. Robot models with and without friction are analyzed. In both cases, convergence conditions for the observed state vector are given. The results are strongly based on the physical properties of the robot, such as energy conservation and the quadratic nature of the Coriolis and centripetal forces. These facts are also used to simplify the observer design.

Nonlinear instability in long time calculations of a partial difference equation

The stability of long time ( t → ∞) calculations of nonlinear partial difference equations is examined. The model chosen is a discretisection in space and time of the Korteweg de Vries equation. The standard linearized von Neumann stability analysis, although necessary, is not sufficient, since it ignores the quadratic nature of the nonlinearity in the problem. Nonlinear stability is analysed by perturbing a constant solution with a period 3 Fourier mode. This leads to a nonlinear system of ordinary differential equations, the stability of which is examined by phase plane analysis. The results obtained contrast strongly with those obtained from the linear analysis. A numerical illustration shows how a single Fourier mode initial condition through side band growth, eventually causes blow-up in a long time calculation.

On the revised theory of the thermoelastic effect

In an earlier paper, a revised theory of the thermoelastic effect was presented which offers an explanation of the mean stress dependence of the thermoelastic “constant”. Further experimental results are presented here to validate this theory, and to demonstrate that the predicted higher harmonic thermal response of a body under a single frequency excitation is indeed observable. The presence of this higher harmonic response is due to the weak quadratic nature of the stress-temperature relationship. It is suggested that the ability to accurately measure this component may be the key to making practical residual stress measurements using this theory.

Water production function of sorghum for Northeast Brazil

The results of an experiment to determine the water production function of sorghum for Northeast Brazilian conditions are reported. The experiment was designed in two random blocks consisting of four growth stages for irrigation deficit and four levels of nitrogen. The crop response to water was found to be of quadratic nature. Regression coefficients were developed for each nitrogen and growth stage treatment between water use and grain yields. The most critical stage was found to be the vegetative stage followed by flowering and grain formation stages. The yield response factors as according to Doorenbos and Kassam were found to vary drastically not only with different nitrogen levels and crop growth stages but also with different irrigation levels. A modified linear equation has been suggested. The coefficients of this modified equation have been determined for all four stages and for the four nitrogen levels for sorghum. The highest average water use efficiency of 109.3 kg ha −1 cm −1 of water and highest obtainable grain yield of 4.92 t/ha was found to be at 425 mm of water use and 45 kg/ha of nitrogen. The crop coefficients ( K c) to compute crop water use from pan evaporation vary between 0.4 and 0.81 with an average for the whole growing period of 0.75.

A nine-noded quadratic control-volume-based finite element for heat conduction

A control-volume -based finite element formulation is presented for the nine-noded, quadratic, quadrilateral finite element for application to conduction heat transfer. The formulation is presented with the nine-noded element being used rather than the eight-noded element for reasons of convenience of control volume definition. The quadratic nature of the element in itself offers greater geometric flexibility and the potential for significantly higher accuracy than does the previous linear control volume element. It was observed that for steady-state conduction, the central control volume 'numerical molecule' is the optimal, fourth order operator on a uniform grid; however, due to the large connectivity for the corner control volume, such a 'molecule' interpretation is not readily facilitated. Performance of the element was evaluated through application to two test problems. It was observed that on the predominantly flux prescribed problem the performance is comparable to that of the Galerkin formulation. However, for the Dirichlet problem, a reduction of error by two orders of magnitude over the Galerkin formulation was observed.

Signal transmission in the catfish retina. III. Transmission to type-C cell.

Current injected into horizontal-cell somas and axons produced transient (on-off) depolarizations from type-C cells (commonly known as transient amacrine cells) similar to those produced by light. Both the light- and current-induced responses had very small linear components and nonlinear components as represented by the second-order kernels, which reproduced the cell's response with a reasonable degree of accuracy. The second-order kernels were well defined and stereotyped. The quadratic nature of the nonlinear component is reflected in the frequency doubling response as well as the very steep input-output relationship of the cell. Type-C cell's responses evoked by light and current differed in a subtle but distinct fashion, and this difference appeared in the signature of the second-order kernels. The light-produced kernels had two diagonal positive peaks and off-diagonal valleys ("four-eye" structure), whereas the current-produced kernels had a single on-diagonal positive peak with off-diagonal negative valleys ("three-eye" structure). The difference in the kernel configuration was reflected in the cell's step-evoked response. Some type-C cells produced faster responses whereas others produced slower responses, whether evoked by light or by current. Our past and present results show that type-C cells produce a very nonlinear response that is not necessarily complex.

Vertical dispersion of spherical, heavy particles in turbulent open channel flow

The results of an experimental study on the motion of heavy particles (heavierthan water) in an open channel flow over a smooth bed are presented in the paper. Some aspects of the diffusion and dispersion of the particles are analysed and especially the effects of lift force and the quadratic nature of drag forces when present. The results show that for a given fall velocity in still water, the vertical dispersion increases with increase in particle diameter. Measured mean particle downward velocities are lower than the settling velocities in still water.

Enhancement of susceptibility and the electrical resistivity of organic metals with a small mean free path

The electronic mean free path of organic metals at ambient temperature is small, approximately one lattice constant.This small mean free path requires a reformulation of transport theory, and also gives rise to new physical effects. The gain susceptibility is enhanced over the Pauli value by approximately a factor of two, and the resistivity continues to follow a T 2-law and does not saturate even when the mean free path becomes smaller than a lattice constant. A theory is described which accounts for these unusual effects. The theory is somewhat analogous to polaron theory and makes use of the quadratic nature of the electron-phonon coupling. The electrons are localized by ‘phonon traps’ accounting for the transition to a Curie-like behavior. Tunneling between these non-degenerate molecular sites gives rise to a T 2-law with a coefficient close to that of the low-temperature state where the conductivity is metallic.

Enhancement of susceptibility and the electrical resistivity of organic metals with a small mean free path

Abstract The spin susceptibility of organic metals is enhanced over the Pauli value at ambient temperature, where the mean free path is close to one lattice constant. The resistivity continues to follow the T 2 law in this regime. A theory is described which accounts for these unusual effects. The theory is somewhat analogous to polaron theory and makes use of the quadratic nature of the electron-phonon coupling. The electrons are localized by short-lived “phonon traps”, accounting for the transition to a Curie-like behaviour. Tunnelling between these nun-degenerate molecular sites gives rise to a T 2 law with a coefficient close to that of the low-temperature state, where the conductivity is metallic.