Mapping Theory in History: Conceptual Cites and Social Sites in the French Monarchic State

1999 ◽  
pp. 41-65
Author(s):  
Sarah Hanley
Keyword(s):  
Mapping Theory

Using Generalized Cell Mapping to Approximate Invariant Measures on Compact Manifolds

1997 ◽  
Vol 07 (11) ◽  
pp. 2487-2499 ◽  
Author(s):  
Rabbijah Guder ◽  
Edwin Kreuzer
Keyword(s):  
Dynamical Systems ◽  
Invariant Measures ◽  
Nonlinear Dynamical Systems ◽  
Powerful Method ◽  
Cell Mapping ◽  
Generalized Cell Mapping ◽  
Nonlinear Dynamical ◽  
Long Term Behavior ◽  
Mapping Theory

In order to predict the long term behavior of nonlinear dynamical systems the generalized cell mapping is an efficient and powerful method for numerical analysis. For this reason it is of interest to know under what circumstances dynamical quantities of the generalized cell mapping (like persistent groups, stationary densities, …) reflect the dynamics of the system (attractors, invariant measures, …). In this article we develop such connections between the generalized cell mapping theory and the theory of nonlinear dynamical systems. We prove that the generalized cell mapping is a discretization of the Frobenius–Perron operator. By applying the results obtained for the Frobenius–Perron operator to the generalized cell mapping we outline for some classes of transformations that the stationary densities of the generalized cell mapping converges to an invariant measure of the system. Furthermore, we discuss what kind of measures and attractors can be approximated by this method.

On expansion waves generated by the refraction of a plane shock at a gas interface

1967 ◽  
Vol 30 (2) ◽  
pp. 385-402 ◽  
Author(s):  
L. F. Henderson
Keyword(s):  
Expansion Wave ◽  
Plane Shock ◽  
Wave System ◽  
Expansion Waves ◽  
Reflected Wave ◽  
Expansion Fan ◽  
New Type ◽  
Self Similar ◽  
Fixed Boundaries ◽  
Mapping Theory

The paper deals with the regular refraction of a plane shock at a gas interface for the particular case where the reflected wave is an expansion fan. Numerical results are presented for the air–CH4 and air–CO2 gas combinations which are respectively examples of ‘slow–fast’ and ‘fast–slow’ refractions. It is found that a previously unreported condition exists in which the reflected wave solutions may be multi-valued. The hodograph mapping theory predicts a new type of regular–irregular transition for a refraction in this condition. The continuous expansion wave type of irregular refraction is also examined. The existence of this wave system is found to depend on the flow being self-similar. By contrast the expansion wave becomes centred when the flow becomes steady. Transitions within the ordered set of regular solutions are examined and it is shown that they may be either continuous or discontinuous. The continuous types appear to be associated with fixed boundaries and the discontinuous types with movable boundaries. Finally, a number of almost linear relations between the wave strengths are noted.

Analogies in science and science teaching

2010 ◽  
Vol 34 (4) ◽  
pp. 167-169 ◽  
Author(s):  
Simon Brown ◽  
Susan Salter
Keyword(s):  
Science Teaching ◽  
Student Understanding ◽  
Great Care ◽  
Structure Mapping ◽  
Important Place ◽  
Mapping Theory ◽  
Practice Of Science

Analogies are often used in science, but students may not appreciate their significance, and so the analogies can be misunderstood or discounted. For this reason, educationalists often express concern about the use of analogies in teaching. Given the important place of analogies in the discourse of science, it is necessary that students are explicitly shown how they work, perhaps based on the structure-mapping theory we outline here. When using an analogy, the teacher should very clearly specify both its components and its limitations. Great care is required in developing an analogy to ensure that it is understood as intended and that misconceptions are minimized. This approach models the behavior of a scientist, which helps to develop student understanding of the practice of science.

scholarly journals Toward a Unified Grammar of Reference

2005 ◽  
Vol 24 (1) ◽  
Author(s):  
Giuseppe Longobardi
Keyword(s):  
Empirical Science ◽  
Unified Theory ◽  
Present Account ◽  
Syntactic Theory ◽  
Topological Mapping ◽  
Mapping Theory ◽  
Do So

AbstractThe unification of traditionally distinct and apparently unrelated objects of inquiry under common more abstract principles is one of the most welcome results of empirical science. This article proposes to draw together some insights of Longobardi (1994, 1996, 2001) into a unified theory of object- and kind-reference viewed as a single grammatical phenomenon, though crosslinguistically parametrized. The present account aims to improve both in accuracy and explanatory force over those outlined in the articles just cited. To do so, the combined leading intuitions of such works are first spelt out, in section 6, into a deeper generalization about the form/meaning relation in nominals and later deduced from a more principled mapping theory, proposing that a syntactically specified position, traditionally labeled D, is responsible in many languages for one of human fundamental linguistic abilities, reference to individuals (Topological Mapping Theory). After the unification of the syntactic mechanisms available for reference to individuals, virtually all other distinctions simply follow precisely from that between the two varieties of such entities (kinds and objects) previewed in Carlson’s (1977a) ontology, indirectly confirming its continuing heuristic power, and from widely accepted economy conditions of recent syntactic theory.

scholarly journals A Schwarz lemma for hyperbolic harmonic mappings in the unit ball

2021 ◽  
Vol 127 (3) ◽  
Author(s):  
Jiaolong Chen ◽  
David Kalaj
Keyword(s):  
Unit Ball ◽  
Explicit Form ◽  
Smooth Function ◽  
Harmonic Mapping ◽  
Sharp Inequality ◽  
Schwarz Lemma ◽  
Harmonic Mappings ◽  
Manuscripta Math ◽  
Sharp Constant ◽  
Mapping Theory

Assume that $p\in [1,\infty ]$ and $u=P_{h}[\phi ]$, where $\phi \in L^{p}(\mathbb{S}^{n-1},\mathbb{R}^n)$ and $u(0) = 0$. Then we obtain the sharp inequality $\lvert u(x) \rvert \le G_p(\lvert x \rvert )\lVert \phi \rVert_{L^{p}}$ for some smooth function $G_p$ vanishing at $0$. Moreover, we obtain an explicit form of the sharp constant $C_p$ in the inequality $\lVert Du(0)\rVert \le C_p\lVert \phi \rVert \le C_p\lVert \phi \rVert_{L^{p}}$. These two results generalize and extend some known results from the harmonic mapping theory (D. Kalaj, Complex Anal. Oper. Theory 12 (2018), 545–554, Theorem 2.1) and the hyperbolic harmonic theory (B. Burgeth, Manuscripta Math. 77 (1992), 283–291, Theorem 1).

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