great divergence

Examples of great divergence in the following topics:

• Income Distribution

  • Economist Paul Krugman and journalist Timothy Noah have referred to this trend as the "Great Divergence."
  • The Great Divergence differs in some ways from the pre-Depression era inequality observed in the early 1900s (the last period of great inequality).
  • Explain the development of income distribution in the US since the 1970's and what is meant by the "Great Divergence"

• Early Human Evolution

  • Modern humans and chimpanzees evolved from a common hominoid ancestor that diverged approximately 6 million years ago.
  • Evidence from the fossil record and from a comparison of human and chimpanzee DNA suggests that humans and chimpanzees diverged from a common hominoid ancestor approximately 6 million years ago.
  • This chart shows the evolution of modern humans and includes the point of divergence that occurred between modern humans and the other great apes.

• The Divergence Theorem

  • More precisely, the divergence theorem states that the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence over the region inside the surface.
  • In physics and engineering, the divergence theorem is usually applied in three dimensions.
  • We will apply the divergence theorem for a sphere of radius $R$, whose center is also at the origin.
  • Substituting $E$ for $F$ in the relationship of the divergence theorem, the left hand side (LHS) becomes:
  • Apply the divergence theorem to evaluate the outward flux of a vector field through a closed surface

• Molecular Analyses and Modern Phylogenetic Trees

  • Sequences that are similar to each other frequently are considered to have less time to diverge, while less similar sequences have more evolutionary time to diverge.
  • Furthermore, by assigning a constant mutation rate to a sequence and performing a sequence alignment, it is possible to calculate the approximate time when the sequence of interest diverged into monophyletic groups.
  • Woese compared the minuscule differences in the sequences of ribosomes among a great array of bacteria and showed that they were not all related.
  • However, molecular analyses revealed this to be a false relationship and originally suggested that acoels represented living species of some of the earliest divergent bilaterians.

• Tips for Testing Series

  • Convergence tests are methods of testing for the convergence or divergence of an infinite series.
  • Convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence, or divergence of an infinite series.
  • Limit of the Summand: If the limit of the summand is undefined or nonzero, then the series must diverge.
  • Ratio test: For $r = \lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right|$, if $r < 1$, the series converges; if $r > 1$, the series diverges; if $r = 1$, the test is inconclusive.
  • But if the integral diverges, then the series does so as well.

• Comparison Tests

  • Example: We want to determine if the series $\Sigma \frac{n+1}{2n^2}$ converges or diverges.
  • For this we compare it with the series $\Sigma \frac{1}{n}$, which diverges.
  • As $\lim_{n \to \infty} \frac{n+1}{2n^2} \frac{n}{1} = \frac{1}{2}$, we have that the original series also diverges.
  • If the infinite series $\sum b_n$ diverges and $a_n \ge b_n \ge 0$ for all sufficiently large $n$, then the infinite series $\sum a_n$ also diverges.
  • Since the sum of the sequence $\frac{1}{n}$ $\left ( \text{i.e., }\sum {\frac{1}{n}}\right)$ diverges, the limit convergence test tells that the original series (with $\frac{n+1}{2n^2}$) also diverges.

• Shared Features of Archaea and Eukaryotes

  • The leading hypothesis is that the ancestor of the eukaryotes diverged early from the Archaea, and that eukaryotes arose through fusion of an archaean and eubacterium, which became the nucleus and cytoplasm.
  • Archaea exhibit a great variety of chemical reactions in their metabolism and use many sources of energy.

• Great Vessels of the Heart

  • Great vessels are the major vessels which directly carry blood into or out of the heart.
  • The great vessels collect and distribute blood across the body from numerous smaller vessels.
  • The venae cavae, along with the aorta, are the great vessels involved in systemic circulation.
  • The aorta extends around the heart and travels downward, diverging into the iliac arteries.
  • Describe the great vessels that carry blood to and from the heart

• Primates

  • Some primates (including humans, some great apes, and baboons) are primarily terrestrial rather than tree-dwelling, but all species possess adaptations for climbing trees .
  • The skeleton of primates allows great flexibility in moving through varying environments.
  • Molecular evidence suggests that the last common ancestor between humans and chimpanzees diverged five to six years ago.
  • Both chimpanzees and humans diverged from gorillas about eight million years ago.

• Evidence of Evolution

  • Embryology, the study of the development of the anatomy of an organism to its adult form, provides evidence for evolution as embryo formation in widely-divergent groups of organisms tends to be conserved.
  • Great ape embryos, including humans, have a tail structure during their development that is lost by birth.
  • The great diversification of marsupials in Australia and the absence of other mammals reflect Australia's long isolation.
  • Over time, these species diverge evolutionarily into new species that look very different from their ancestors that may exist on the mainland.