Entire Maps Research Articles

Assessment of the Cold Formability of Ferritic Steels Using Parameters Determined in Uniaxial Tensile Testing

Possibilities and limits of the uniaxial tensile testing in the assessment of cold formability of ferritic low alloy steels are evaluated in the paper. Cold formability covering both sheet and massive forming, including entire formability maps, strain hardening etc., can be estimated from six material parameters determined in a uniaxial tensile test. A master stress strain curve to explain multiple n behavior is proposed. Effects of alloying, especially chromium, and other metallurgical parameters on cold formability are discussed.

On entire rational maps in real algebraic geometry.

On entire rational maps in real algebraic geometry.

Dynamics of entire maps

Dynamics of entire maps

Convex Affine Maximal Surfaces

We consider a smooth surface in 3-space that is locally representable in suitable cartesian coordinates (x,y,z) as the graph of a strongly convex function $$\rm z=u(x,y)$$ sucn a surface is an extremal for the interior variation of tne affinely invariant area $$\rm\int\int w(x,y)dxdy \,w = (u_{xx}u_{yy}-u_{xy} ^2)^{1\over4},$$ if and only if it satisfies the following Euler-Lagrange equation $${\rm \partial\over\partial x}\rm \Biggl({u_{yy}w_{x}-u_{xy}w_{y}\over w^4}\Biggr)+{\rm \partial\over\partial y}\rm \Biggl({-u_{xy}w_{x}+u_{xx}w_{y}\over w^4}\Biggr)=0$$ We prove that, under various types of technical assumptions concerning the asymptotic behavior of u(x,y), the only solutions of this equation describe paraboloids. The problem is equivalent to a problem concerning the global behavior of entire holomorphic maps with a type of constraint not studied previously.

A mathematical structure for analyzing maps

The growing use of computers in environmental management is profoundly changing data collection procedures, analytic processes, and even the decision-making environment itself. The emerging technology of geographic information systems (GIS) is expanding this revolution to integrate spatial information fully into research, planning, and management of land. In one sense, this technology is similar to conventional map processing involving traditional maps and drafting aids, such as pens, rub-on shading, rulers, planimeters, dot grids, and acetate sheets for light-table overlays. In another sense, these systems provide advanced analytic capabilities, enabling managers to address complex issues in entirely new ways. This report discusses a fundamental approach to computer-assisted map analysis that treats entire maps as variables. The set of analytic procedures for processing mapped data forms a mathematical structure analogous to traditional statistics and algebra. All of the procedures discussed are available for personal computer environments.

Dynamics of entire functions near the essential singularity

AbstractWe show that entire functions which are critically finite and which meet certain growth conditions admit ‘Cantor bouquets’ in their Julia sets. These are invariant subsets of the Julia set which are homeomorphic to the product of a Cantor set and the line [0, ∞). All of the curves in the bouquet tend to ∞ in the same direction, and the map behaves like the shift automorphism on the Cantor set. Hence the dynamics near ∞ for these types of maps may be analyzed completely. Among the entire maps to which our methods apply are exp (z), sin (z), and cos (z).

Designs On Signs / Myth And Meaning In Maps

Every map is at once a synthesis of signs and a sign in itself: an instrument of depiction – of objects, events, places – and an instrument of persuasion – about these, its makers and itself. Like any other sign, it is the product of codes: conventions that prescribe relations of content and expression in a given semiotic circumstance. The codes that underwrite the map are as numerous as its motives, and as thoroughly naturalized within the culture that generates and exploits them. Intrasignificant codes govern the formation of the cartographic icon, the deployment of visible language, and the scheme of their joint presentation. These operate across several levels of integration, activating a repertoire of representational conventions and syntactical procedures extending from the symbolic principles of individual marks to elaborate frameworks of cartographic discourse. Extrasignificant codes govern the appropriation of entire maps as sign vehicles for social and political expression – of values, goals, aesthetics and status – as the means of modern myth. Map signs, and maps as signs, depend fundamentally on conventions, signify only in relation to other signs, and are never free of their cultural context or the motives of their makers.

Structural Instability of exp(z)

The entire function exp(z) has a Julia set eqval to the whole plane. We show that there are complex X's near 1 such that \e: has an attracting periodic orbit. Hence e~ is not structurally stable. The study of the dynamics of complex analytic maps goes back to Fatou and Julia in the 1920s. Recently, there has been a rebirth of interest in this subject, due mainly to the interesting new results of Mandelbrot (Ma), Douady-Hubbard (DH), and Sullivan (S). Most of this recent work has dealt with polynomials or rational maps, rather than with entire maps. The reason for this is that rational maps may be regarded as smooth maps of the Riemann sphere, whereas, because of the essential singularity at infinity, entire maps cannot. Thus, compactness is lost and, with it, many of the global theorems in the subject. Nevertheless, entire maps like ez share many of the dynamical features of rational maps. However, as was shown in (DK), the exponential map has several additional features that are not found in the polynomial case. For example, Misiurewicz (M) has shown that the Julia set of ez is the entire plane, something that cannot occur for polynomials. Recall that the Julia set of a map is the set of points at which the family of iterates of the map fails to be a normal family of functions, and that periodic points are dense in the Julia set (F). In particular, periodic points for ez are dense in the plane. This raises the question of the structural stability of ez. One may check easily that if an entire function is topologically conjugate to ez, then it is affinely equivalent to Xez for some X g C. Hence, structural stability here means within the class of maps Xez. In this limited class of maps, it would seem that there is a good chance for stability. Nevertheless, our main result is that this is not so. Theorem. ez is not structurally stable. We remark that this result is a crucial step in the recent proof of Ghys, Goldberg, and Sullivan (GGS) that ez is recurrent (in the sense that there are no positive measure cross sections to the grand orbits of ez). The natural question of the ergodicity of ez remains open.

A simple formalism for the study of transformed aeromagnetic profiles and source location problems

Up to now, magnetic interpretation through processing of aeromagnetic maps has been based on two classes of methods, Fourier transform and direct convolution techniques; the first class requires transformation of entire maps and does not easily allow local studies, whereas the other gives only numerical values of filter coefficients. In the present paper a suitable continuation function is determined and used to obtain simple analytical expressions for all classical filters (upward and downward continuation, vertical gradient and derivatives up to any order, and reduction to the pole). This formalism allows local studies to be performed and gives both physical and mathematical insight into transformed aeromagnetic profiles; at the same time it leads to simple formulas and cheap digital computations and should be handled easily by nonspecialists. Tests on analytical and numerical models show the quality of the continuation function and of the various transformed profiles. It is also shown that study of the behavior of the continuation function can yield valuable information to locate sources of magnetic anomalies with good precision.