A frog is any member of a diverse and carnivorous group of short-bodied, tailless amphibians composing the order Anura. The oldest fossil "proto-frog" appeared in the early Triassic of Madagascar, but molecular clock dating suggests their origins may extend further back to the Permian, 265 million years ago. Frogs are distributed, ranging from the tropics to subarctic regions, but the greatest concentration of species diversity is in tropical rainforests. There are accounting for around 88 % of extant amphibian species, they are one of the five most diverse vertebrate orders. Warty frog species tend to be called toads, but the distinction between frogs and toads is informal, not from taxonomy or evolutionary history. An adult frog has a stout body, protruding eyes, anteriorly-attached tongue, limbs folded underneath, no tail. Frogs have glandular skin, with secretions ranging from distasteful to toxic, their skin varies in colour from well-camouflaged dappled brown and green to vivid patterns of bright red or yellow and black to show toxicity and ward off predators.

Adult frogs live on dry land. Frogs lay their eggs in water; the eggs hatch into aquatic larvae called tadpoles that have internal gills. They have specialized rasping mouth parts suitable for herbivorous, omnivorous or planktivorous diets; the life cycle is completed. A few species bypass the tadpole stage. Adult frogs have a carnivorous diet consisting of small invertebrates, but omnivorous species exist and a few feed on plant matter. Frog skin has a rich microbiome, important to their health. Frogs are efficient at converting what they eat into body mass, they are an important food source for predators and part of the food web dynamics of many of the world's ecosystems. The skin is semi-permeable, making them susceptible to dehydration, so they either live in moist places or have special adaptations to deal with dry habitats. Frogs produce a wide range of vocalizations in their breeding season, exhibit many different kinds of complex behaviours to attract mates, to fend off predators and to survive.

Frogs are valued as food by humans and have many cultural roles in literature and religion. They are seen as environmental bellwethers, with declines in frog populations viewed as early warning signs of environmental damage. Frog populations have declined since the 1950s. More than one third of species are considered to be threatened with extinction and over 120 are believed to have become extinct since the 1980s; the number of malformations among frogs is on the rise and an emerging fungal disease, has spread around the world. Conservation biologists are working to resolve them; the use of the common names "frog" and "toad" has no taxonomic justification. From a classification perspective, all members of the order Anura are frogs, but only members of the family Bufonidae are considered "true toads"; the use of the term "frog" in common names refers to species that are aquatic or semi-aquatic and have smooth, moist skins. There are numerous exceptions to this rule; the European fire-bellied toad has a warty skin and prefers a watery habitat whereas the Panamanian golden frog is in the toad family Bufonidae and has a smooth skin.

The origin of the order name Anura — and its original spelling Anoures — is the Ancient Greek "alpha privative" prefix ἀν- "without", οὐρά, meaning "animal tail". It refers to the tailless character of these amphibians; the origins of the word frog are debated. The word is first attested in Old English as frogga, but the usual Old English word for the frog was frosc, it is agreed that the word frog is somehow related to this. Old English frosc remained in dialectal use in English as frosh and frosk into the nineteenth century, is paralleled in other Germanic languages, with examples in the modern languages including German Frosch, Icelandic froskur, Dutch vors; these words allow us to reconstruct a Common Germanic ancestor *froskaz. The third edition of the Oxford English Dictionary finds that the etymology of *froskaz is uncertain, but agrees with arguments that it could plausibly derive from a Proto-Indo-European base along the lines of *preu = "jump". How Old English frosc gave rise to frogga is, uncertain, as the development does not involve a regular sound-change.

Instead, it seems that there was a trend in Old English to coin nicknames for animals ending in -g, with examples—themselves all of uncertain etymology—including dog, pig and wig. Frog appears to have been adapted from frosc as part of this trend. Meanwhile, the word toad, first attested as Old English tādige, is unique to English and is of uncertain etymology, it is the basis for the word tadpole, first attested as Middle English taddepol meaning'toad-head'. About 88% of amphibian species are classified in the order Anura; these include over 7,100 species in 55 families, of which the Craugastoridae, Hylidae and Bufonidae are the richest in species. The Anura include any fossil species that fit within the anuran definition; the characteristics of anuran adults include: 9 or fewer presacral vertebrae, the presence of a urostyle formed of fu

Adolph Hausrath, a German theologian, was born at Karlsruhe. He was educated at Jena, Göttingen and Heidelberg, where he became Privatdozent in 1861, professor extraordinary in 1867 and ordinary professor in 1872, he was a disciple of a strong Protestant. His scholarship was sound and his style vigorous. Hausrath died on 2 August 1909 in Heidelberg. Among other works he wrote Der Apostel Paulus, Neutestamentliche Zeitgeschichte, D. F. Strauss und die Theologie seiner Zeit, lives of Richard Rothe, Luther. Under the pseudonym George Taylor he wrote several historical romances Antinous, which ran through five editions, is the story of a soul "which courted death because the objective restraints of faith had been lost." Klytia was a 16th-century story, Jetta a tale of the great immigrations, Elfriede "a romance of the Rhine". This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed.. "Hausrath, Adolph". Encyclopædia Britannica. 13. Cambridge University Press. P. 71.

Media related to Adolf Hausrath at Wikimedia Commons Works by Adolf Hausrath at Project Gutenberg

Fermi liquid theory is a theoretical model of interacting fermions that describes the normal state of most metals at sufficiently low temperatures. The interactions among the particles of the many-body system do not need to be small; the phenomenological theory of Fermi liquids was introduced by the Soviet physicist Lev Davidovich Landau in 1956, developed by Alexei Abrikosov and Isaak Khalatnikov using diagrammatic perturbation theory. The theory explains why some of the properties of an interacting fermion system are similar to those of the ideal Fermi gas, why other properties differ. Important examples of where Fermi liquid theory has been applied are most notably electrons in most metals and liquid helium-3. Liquid helium-3 is a Fermi liquid at low temperatures. Helium-3 is an isotope of helium, with 1 neutron and 2 electrons per atom; because there is an odd number of fermions inside the nucleus, the atom itself is a fermion. The electrons in a normal metal form a Fermi liquid, as do the nucleons in an atomic nucleus.

Strontium ruthenate displays some key properties of Fermi liquids, despite being a correlated material, is compared with high temperature superconductors like cuprates. The key ideas behind Landau's theory are the notion of adiabaticity and the Pauli exclusion principle. Consider a non-interacting fermion system, suppose we "turn on" the interaction slowly. Landau argued that in this situation, the ground state of the Fermi gas would adiabatically transform into the ground state of the interacting system. By Pauli's exclusion principle, the ground state Ψ 0 of a Fermi gas consists of fermions occupying all momentum states corresponding to momentum p < p F with all higher momentum states unoccupied. As interaction is turned on, the spin and momentum of the fermions corresponding to the occupied states remain unchanged, while their dynamical properties, such as their mass, magnetic moment etc. are renormalized to new values. Thus, there is a one-to-one correspondence between the elementary excitations of a Fermi gas system and a Fermi liquid system.

In the context of Fermi liquids, these excitations are called "quasi-particles". Landau quasiparticles are long-lived excitations with a lifetime τ that satisfies ℏ τ ≪ ϵ p where ϵ p is the quasiparticle energy. At finite temperature, ϵ p is on the order of the thermal energy k B T, the condition for Landau quasiparticles can be reformulated as ℏ τ ≪ k B T. For this system, the Green's function can be written in the form G ≈ Z ω + μ − ϵ where μ is the chemical potential and ϵ is the energy corresponding to the given momentum state; the value Z is called the quasiparticle residue and is characteristic of Fermi liquid theory. The spectral function for the system can be directly observed via angle-resolved photoemission spectroscopy, can be written in the form: A = Z δ where v F is the Fermi velocity. Physically, we can say that a propagating fermion interacts with its surrounding in such a way that the net effect of the interactions is to make the fermion behave as a "dressed" fermion, altering its effective mass and other dynamical properties.

These "dressed" fermions are what we think of as "quasiparticles". Another important property of Fermi liquids is related to the scattering cross section for electrons. Suppose we have an electron with energy ϵ 1 above the Fermi surface, suppose it scatters with a particle in the Fermi sea with energy ϵ 2. By Pauli's exclusion principle, both the particles after scattering have to lie above the Fermi surface, with energies ϵ 3, ϵ 4 > ϵ F. Now, suppose the initial electron has energy close to the Fermi surface ϵ ≈ ϵ F Then, we have that ϵ 2, ϵ 3, ϵ 4 {\displaystyle \epsilon _,\epsilon _,\epsilon _