Use Of Zero Research Articles

Structural Optimization under Topological Constraint Represented by Homology Groups. 2nd Report. Topological Constraint on One-Dimensional Complex by Use of Zero- and One-Dimensional Homology Groups.

Topology of any one-dimensional complex can be represented by zero and one-dimensional homology groups which are isomorphic to the direct sum of additive groups. In this paper, a method of constraint on the topology of a frame treated as a one-dimensional complex is proposed using homology groups. As a numerical example, the total strain energy of the frame is minimized under the constraint of topology and constant weight. Useless members are eliminated from a ground structure by use of genetic algorithm. Any number of additive groups can be freely set up as a topological constraint because of the generalized inverse matrices, and a rule of code in the genetic algorithm is designed so that all strings generated in the process of optimization could satisfy the topological constraint. As a result, it is found that loops in the topology of the optimum structure adjoin each other. The proposed method is also applied to the topological optimization of a square board fixed on a rigid wall and loaded vertically on points distant from the wall.

An investigation into the use of zeros in some scattering processes

The authors investigate the reliability of the use of zeros of differential cross sections in the complex cos theta plane as a method of locating resonances and identifying their spin. The inherent uncertainty in locating such zeros tends to invalidate such methods.

Detecting nonrandom associations between proportions by tests of remaining-space variables

Descriptive and inferential applications of the “remaining-space” transformation Zj = Yj/(1 — Yi),where the Ys are members of the same set of proportions, are briefly reviewed in connection with petrographic variation diagrams. The sign reversal of the Al2O3-SiO2correlations in the Taupo complex, first noted by Darroch and Ratcliff, is probably the rule rather than the exception in subalkaline basalt-rhyolite or gabbro-granite associations. Darroch argues that the Snow test of Yj/(1 — Yj)versus Yi/(1 — Yj)would be in general more conservative than combined tests of Yjversus Yi/(1 — Yj)and Yiversus Yj/(1 — Yi).At Taupo, however, the two procedures give identical results for all pairings of six major compositional variables. To first-order approximation, the use of zero as null value in the testing of correlations involving remaining-space variables is valid only if, as postulated both by Connor and Mosimann and by Darroch and Ratcliff, variances are proportional to means in the initial open array. It is argued here that the perfect rank correlation of means and variances thus postulated would survive closure. In Taupo, as in most Harker arrays, the contribution of alumina to the total variance is very small. In the Taupo suite, in addition, the contribution of combined alkalies to the total variance is anomalously large; the result is that at Taupo the rank correlation of means and variances is very weak.

The use of zeros and zero-directions in model reduction

The concept of zeros and zero-directions of a linear time-invariant multivariable system is applied to the problem of shifting eigenvectors into the kernel of the information extraction map C. By making the maximum number of the closed system modes unobservable, a lower-order transfer-function matrix is obtained. The state feedback structure reducing the model to one of lower dimensions does not exploit all of the degrees of freedom. A part of them are used for pole allocation of the remaining observable poles using a dyadic feedback technique. The suggested technique is applied to reduce a broad class of multivariable systems into first-order multivariable systems. Finally, a dynamical structure realizing the same objectives is introduced.

Use of Zero Counting for Estimating the Zero-Frequency Spectral Density of Radar Glint for Known Target Types

Some simple formulas of Blachman giving the zero-frequency spectral density of phase rate for narrowband Gaussian random noise in terms of the latter's spectral radius of gyration are used to derive the zero-frequency spectral density of radar glint for a complex target in terms of the radius of gyration of the collection of radar scatterers and the rate of zero crossings of the target echo.

Closure to “Discussions of ‘The Use of Zeros and Poles for Frequency Response or Transient Response’” (1954, Trans. ASME, 76, pp. 1339–1343)

Closure to “Discussions of ‘The Use of Zeros and Poles for Frequency Response or Transient Response’” (1954, Trans. ASME, 76, pp. 1339–1343)

The Use of Zeros and Poles for Frequency Response or Transient Response

Abstract The characteristic equation of a control system is often of the form 1/KG(s) + 1 = 0, in which G(s) is (s − q1) (s − q2)… /(s − p1) (s − p2)… Each factor of G(s), such as (s − p1), is a complex variable which can be plotted as a vector in the s-plane from the pole p1 to the point s. The complex product G(s) is itself a vector whose magnitude is the product of magnitudes and whose angle is the sum of the angles of its factors. Frequency response is computed directly for s points along the jω-axis. In order to find the roots of 1/KG(s) = −1, the locus of s is sketched, where for each point on this locus the total angle of G(s) is equal to 180 deg; a point on this locus is then a root if K = 1/|G(s)|. For given initial conditions the Laplace transform permits the transient response of the system to be written directly.

Still More Ado about Zero

Previous articleNext article No AccessStill More Ado about ZeroFoster E. GrossnickleFoster E. Grossnickle Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Elementary School Journal Volume 33, Number 5Jan., 1933 Article DOIhttps://doi.org/10.1086/456886 Views: 1Total views on this site PDF download Crossref reports no articles citing this article.

ON THE USE OF ZERO AND TWENTY IN THE MAYA TIME SYSTEM

American AnthropologistVolume 4, Issue 2 p. 237-275 Free Access ON THE USE OF ZERO AND TWENTY IN THE MAYA TIME SYSTEM GEORGE BYRON GORDON, GEORGE BYRON GORDONSearch for more papers by this author GEORGE BYRON GORDON, GEORGE BYRON GORDONSearch for more papers by this author First published: April‐June 1902 https://doi.org/10.1525/aa.1902.4.2.02a00050Citations: 2AboutPDF ToolsExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume4, Issue2April‐June 1902Pages 237-275 RelatedInformation