Algebraic Means Research Articles

Polynomial iterations for root extraction

This paper discusses polynomial iterations, of built-in second and third order, for efficient extraction of kth roots. The iterative formulas are constructed by a-priori design, using only elementary algebraic means, suitable as an instructive subject for a mathematical-educational laboratory. A full error-decay analysis accompanies the microcomputer runs, which are at the heart of the computational assignments. The learning process in a mathematical laboratory environment is given a major consideration throughout.

SL(n+1, C) strata and orbits in the solution space of Euclidean CP n models

We further study the action of SL(n+1, C) on the space of finite action solutions of the bidimensional Euclidean CPn models. We decompose the space of k-instantons into strata. Each stratum in characterized by an integer m with 0≤m≤min(k, n) which can be calculated from the instanton by purely algebraic means. The k-instantons with m=n are called generic. Their stratum is shown to be dense in the space of k-instantons when k≥n. The isotropy subgroups for each stratum are identified.

Internal symmetry algebra of exactly integrable dynamical systems in the quantum domain

For the example of the generalized Toda chain in two-dimensional space it is shown that in the quantum domain the semisimple algebras of the classical problem go over into the associative Hopf algebras described by Drinfel'd as quantum algebras. In terms of the quantum algebras, the Heisenberg operators of the interacting field can be expressed as functions of the in fields by means of the formulas of the classical theory, and the expressions obtained earlier for them acquire a simple algebraic meaning.

Pure Lie algebraic approach to the modified Korteweg–de Vries equation

It is explained, using only Lie algebraic means, how the modified-KdV-like equations arise. As an example, the modified-KdV equation is treated.

Time-Budget Estimates of Avian Energy Expenditure: Physiological and Meteorological Considerations

Daily energy expenditures ($H_{td}$) of aviary-housed budgerygahs (Melopsittacus undulatus) were estimated simultaneously using doubly labeled-water (DLW) and timebudget (TB) methods under summer and winter conditions. Laboratory validation of the DLW technique displayed excellent agreement with concomitant gravimetric measures of CO₂ production (algebraic mean difference = -0.04%; range = -5.2%-6.2%). The aviary studies combined continuous 24-h recording of each bird's daily activities with quantification of its thermal environment (wind speed and air and operative temperatures). Activity and thermoregulatory costs of birds used for TB studies were measured in the laboratory. Comparison of $H_{td}'s$ predicted by DLW to values predicted by the TB method indicate that measurement of activity costs at the time of the study and their subsequent evaluation through existing heat-transfer models are equally important to determining reliable energy budgets. Avian TB studies that fail to address these concerns a...

Relational algebraic semantics of deterministic and nondeterministic programs

Abstract relational algebra is proposed as a practical means to describe the denotational semantics of programming languages. We apply this method of semantics description to a functional language and demonstrate the usefulness of this approach by some examples. In particular, we prove the correctness of a program transformation rule within our calculus. Then, the deterministic language DFP is extended to a nondeterministic functional language NFP in order to investigate three kinds of nondeterminism, viz. erratic, angelic, and demonic nondeterminism. We provide a relational algebraic semantics for each kind of nondeterminism. These three different semantics are not obtained by using three different orderings on certain domains, but by using three different interpretations on the same ordered domain. The alternative kinds of nondeterminism are then compared and an illustrative example is given. Finally, we characterize the natural numbers with relational algebraic means. The uniform description of domains and programs makes it possible to prove the termination of ‘concrete’ deterministic and nondeterministic programs by induction.

Supercuspidal Duality for the Two-Fold Cover of SL 2 and the Split O 3

Introduction. As first introduced the Shimura-Shintani-Niwa correspondence was a correspondence between homomorphic cusp forms of half-integral weight and certain modular forms of integral weight. Various authors have studied this correspondence in a representation-theoretic framework. Gelbart's seminal work [G1] provides some tools for translation and miscellaneous results. Using Whittaker models and L-functions, Gelbart and Piatetski-Shapiro [GPS1], [GPS2], obtained a generalized correspondence between automorphic cuspidal representations of GL2, the metaplectic group, and automorphic representations of GL2. Flicker [F] used a variation on the Selberg trace formula to extend the work of Gelbart and Piatetski-Shapiro. Finally, Waldspurger [W] returned to Whittaker models andL-functions to obtain a correspondence between automorphic cuspidal representations of SL2, the nontrivial two-fold cover of SL2, and automorphic representations of PGL2. Our more modest results complement the above and are obtained by purely algebraic means. We now attempt a brief summary.

The anharmonic oscillator problem: a new algebraic solution

The second-order (one-dimensional or radial) differential Schrodinger equation with the potential V(r)= mu r2+ nu r4 may be re-interpreted as a difference equation of the fourth order (indeed, the Hamiltonian is a pentadiagonal matrix in the standard harmonic oscillator basis mod n), n=0, 1, . . .). Thus, the authors construct its four independent general solutions by purely algebraic means, via expansions in powers of (n+1)-14/. Next, preserving the analogy between difference and differential equations, the physical wavefunctions (n mod psi ) and their energies are determined by the matching of the 'Jost' and 'regular' solutions. Finally, using the simplest matching conditions 'at the origin', the resulting numerical algorithm is demonstrated to be both stable and quickly convergent.

Evaluation of thermal efficiency for heat regenerators in periodic operation by approximate methods

Thermal efficiency of heat regenerators in periodic operation is one of the most important quantities to the designer and plant engineer. The current procedures for calculation of efficiency are model dependent numerical algorithms which require considerable computational time. In this work approximate formulae, applicable to all model types, have been developed for quick calculation, by algebraic means, of the regenerator efficiency in single pass, cocurrent or countercurrent operation. The formulae require only the knowledge of the variance of the impulse response of a model based on the assumed heat transfer mechanisms in the regenerator. A method is introduced for utilizing the representation of the regenerator thermal impulse response by a gamma probability density function in obtaining the solution and efficiency for cocurrent periodic operation. An analogy to countercurrent heat recuperators and the intergral of the impulse response are used to develop a formula for efficiency for the countercurrent case. The accuracy of the developed approximations is discussed and shown to be well within the accuracy of the parameters of the system.

Alternative statistical approach to evaluating interlaboratory performance.

We report a new technique for realistic assessment of laboratory performance as measured by proficiency testing. Interlaboratory results accumulated from 129 participants during 18 months provide the baseline data from which we established "state-of-the-art" performance criteria for three ranges of pH, pCO2, and pO2. By concurrent use of two statistical measurement techniques, the cumulative percentile rank and the algebraic and absolute mean error, laboratories can accurately evaluate their performance in terms of acceptable state-of-the-art criteria, total error, or medical usefulness. The approach facilitates assessment of the nature of the errors that have led to inferior performance and identification of probable areas where improvement is possible. If criteria based on regulatory standards or medical usefulness goals are included, the system can provide a basis for licensure or professional quality improvement.

Motion perception during dichoptic viewing of moving random-dot stereograms

The relation between binocular and monocular motion perception was investigated. A random-dot stereogram (30 × 30 deg arc), containing a central figure seen in front of the background in stereoscopic vision, was viewed dichoptically by human subjects without a fixed visual frame of reference. The images seen by the right and left eye were moved laterally according to a triangular wave form, in counterphase, but with variable amplitude ratios. Under this condition only purely lateral movement and no motion in depth of the stereogram as a whole was perceived, while stereoscopic vision of the figure-background relation was maintained. The magnitude of the binocularly perceived lateral motion, signalled by manual tracking of the perceived displacement, equalled the algebraic mean of the monocular motion percepts. As a special case, when the two images forming the stereogram were moved with equal velocities but in opposite directions they were perceived as a completely stationary, fused image in stereoscopic depth. Only the addition of a stationary reference (a bar or grating seen by both eyes) resulted in the perception of motion in depth. We conclude that a visual frame of reference is essential for perception of motion in depth but not for perception of lateral movements. Moreover, it seems likely that not absolute binocular disparity (retinal locus differences) but relative binocular disparity (differences in angular distance between two or more corresponding features in the two retinal images) is a cue for perception of depth.

Simulation of diffusions with boundary conditions

We propose a simulation scheme for diffusions, based on the construction of a sequence of weakly convergent jump Markov processes. This involves a discretization in space, rather than time, in the generator. Weak convergence gives a very precise control of the scheme and the Markov properly allows the computation of such quantities as invariant measures or asymptotic decay rates by algebraic means.

Multiple-word correcting convolutional codes

Two classes of multiple-word correcting convolutional encoders are defined and analyzed. We obtain some conditions for these encoders to be noncatastrophic, and we describe ways to check the (word) minimum distance of the generated codes. The first class can easily be analyzed by algebraic means, but the redundancy of the corresponding codes is not arbitrarily iow. The codes generated by the second class of encoders may have a lower redundancy, but their analysis requires the use of a computer program.

The relationship between the self-dualized classification of boolean functions and spectral coefficient classification

Abstract The most compact algebraic means of classification of boolean functions is the self-dualized (SD) classification, which subsumes the weaker NP and NPN algebraic procedures. However, an alternative non-algebraic means of function classification is the use of spectral coefficient data assembled in positive, canonic form. Here we show that invariance operations performed in the spectral domain are equivalent to the operations involved in the algebraic SD classification procedure.

Lie Algebras for Potential Scattering

We consider a new Lie-algebraic framework for the P\"oschl-Teller potential, in which a single [$\mathrm{sp}(2,R)$ Casimir] operator has both bound and scattering states. This approach allows the determination of the $S$ matrix by purely algebraic means.

A generalized Dunkerley-Graeffe procedure for complex vibrating systems

The combined use of the principle underlying Dunkerley's rule for the approximate determination of the gravest eigenfrequency of a multi-degree-of-freedom elastic system and of the root-squaring process suggested by Graeffe provide a generalized procedure for the approximate solution of complex frequency equations, i.e., for the determination of any number of eigenvalues at the desired accuracy level, provided that the eigenfunctions involved can be expressed in series expansion. By simple algebraic means, the method yields solutions in cases for which sophisticated computing facilities would otherwise be necessary and provides the means for checking complicated computer outputs as well as approximate results for preliminary design purposes.

Détermination rapide de l'extrait sec des fromages à l'aide d'un four à micro-ondes

RAPID MICROWAVE OVEN DETERMINATION OF THE DRY MATTER CONTENT IN CHEESE An experiment was carried out todetermine the repeatability and accuracy of the dry matter determination of cheese with the microwave aven instrument TMS Checker K 375 A (Anritsu Co. Japon). Sixt Y one samples of various type of cheeses (fresh lactic cheese, soft cheese semi-harâ and hard cheese) ranging from 19.9 % ta 62.8 % dry matter, were analysed with the microwave oven (4 replicates) and with the reference drying aven method (2 replicates). The coefficient of variation of repeatability is on an average 0.26 % for the microwave and varies [rom. 0.28 % for high moisture content cheese ta 0.10 % for low moisture content cheese, for the reference method. The standard deviation of accuracy of the microwave aven, calculated [rom. the algebraic mean differences between the two methods is 0.27 % dry matter content, indicating a 95 % confidence interval of ± 0.54 % for the estimated true value. In a field experiment, it has been demonstrated that the TMS Checker is a useful tool for checking rapidly the variation of soft

General solutions to inverse transport problems

A new approach is developed for solving time-independent inverse problems for particle or radiation transport described by the monoenergetic linear Boltzmann equation. For a homogeneous plane geometry medium, the approach leads to a set of inverse solutions which can be obtained by purely algebraic means; previously derived methods appear as special cases. All these solutions require only measurements of the angular intensities at the surface. The analysis is extended to time-dependent and energy-dependent problems.

Derivation of universal logic modules, for n ≥ 3, by algebraic means

Universal logic modules (ULMs) are digital circuit configurations which, by appropriate connection to their input terminals, can be made to realise all possible combinational logic functions of a given number of independent binary input variables. The paper describes a method for deriving ULM circuits in general, and in particular considers circuits with three input variables. These are known to need at least five input terminals, and several circuit configurations with this minimum number exist in the literature. The paper discloses five more; four of the five involve negation of the output, but the fifth does not.

The Laws of Anchoring When There are Two Anchors

A study was conducted to explore the phenomenon of anchoring in situations where two anchors are presented. It was hypothesized that subjects will use the subjective reliability perceived for each source of information as a weight. Three types of anchoring behaviours were founds 1) The algebraic mean of the two potential anchors was used as an anchor. 2) The most reliable source of information was used as an anchor. 3) None of the information sources were used as an anchor.