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Given a positive real number ε, an ε-isometry or almost isometry (also called a Hausdorff approximation) is a map : between metric spaces such that for x , x ′ ∈ X {\displaystyle x,x'\in X} one has | d Y ( f ( x ) , f ( x ′ ) ) − d X ( x , x ′ ) | < ε , {\displaystyle |d_{Y}(f(x),f(x'))-d_{X}(x,x')|<\varepsilon ,} and
25 wrz 2019 · The study of allometry can be classified into three categories: (1) ontogenetic allometry, which refers to the study of relative growth of body parts over time, and studies the changing size relationships among organs and appendages within organisms during their growth phase; (2) static allometry, which refers to differences in the relative size...
11 cze 2021 · This is an essay about the conceptual foundations of modern biology and the role that mathematics can play for biology. Traditionally, two aspects have been considered as fundamental for or constitutive of life, reproduction and metabolism.
Introduction. This is an essay about the conceptual foundations of modern biology and the role that mathematics can play for biology. Traditionally, two aspects have been considered as funda-mental for or constitutive of life, reproduction and metabo-lism. The concept of evolution puts the emphasis on the first of them, reproduction.
11 gru 2023 · Allometry – scaling in biology. For body size-dependent design constraints to be recognized, a mathematical tool is required. Expressing variables in the form of a simple power law equation, Y =a Mb, provides a quantitative and statistically testable means to identify body size-dependent patterns in biology.
29 paź 2021 · An isometry maps a segment to a segment equal to it, a line to a line, a circle to a circle of the same radius, and a triangle to a triangle congruent to it. An isometry also preserves angles. Proof. We only discuss the case f(z) = rz + s for some \(r,s\in {\mathbb C}\) with |r| = 1; the case \(f(z)=r\overline {z}+s\) is left to the reader.
When an organ grows at the same rate as the rest of the body, α = 1, a condition called isometry. Such an organ maintains a constant proportionate size (but not absolute size) throughout...
