A paradox in metabolism is that, while the vast majority of complex life on Earth requires oxygen for its existence, oxygen is a highly reactive molecule that damages living organisms by producing reactive oxygen species.

The sole existence of partial derivatives satisfying the Cauchy – Riemann equations is not enough to ensure complex differentiability at that point.

So assume ƒ is differentiable at 0, as a function of two real variables from Ω to C. This is equivalent to the existence of two complex numbers and ( which are the partial derivatives of ƒ ) such that we have the linear approximation

The results on the existence of a solution to the conjugation equation depend on the eigenvalues of J and the degree of smoothness required from h. As J does not need to have any special symmetries, its eigenvalues will typically be complex numbers.

Despite this opinion among researchers, evidence has accumulated that supports the existence of complex biological effects of weaker non-thermal electromagnetic fields, ( including weak ELF magnetic fields, although the latter does not strictly qualify as EM radiation < ref >), and modulated RF and microwave fields.

The existence of this distant branch creates a much more complex picture of humankind during the Late Pleistocene than previously thought.

Because no national economy in existence fully manifests the ideal of a free market as theorized by economists, some critics of the concept consider it to be a fantasy – outside of the bounds of reality in a complex system with opposing interests and different distributions of wealth.

The situation was complex though, as over the two hundred years of their existence, the Templars had become a part of daily life throughout Christendom.

However, modern archaeological and anthropological evidence doesn't support this thesis, pointing to the existence of several non-stratified and politically decentralized complex societies.

As many more individuals of each species are born than can possibly survive ; and as, consequently, there is a frequently recurring struggle for existence, it follows that any being, if it vary however slightly in any manner profitable to itself, under the complex and sometimes varying conditions of life, will have a better chance of surviving, and thus be naturally selected.

The oldest known mention of their existence in the region by the exonym Siamese is in a 12th century A. D. inscription at the Khmer temple complex of Angkor Wat in Cambodia, which refers to syam, or " dark brown " people.

Humans have been looking at nature for answers to both complex and simple problems throughout our existence.

Psychoanalytic theory, in particular the claimed existence of an Oedipus complex which instead of instinctual aversion against incest argues for instinctual desire, has influenced many theorists seeking to explain the incest taboo using sociological theories.

Muslims planners, taking advantage of the course of the river Segura, created a complex network of irrigation channels that made the town's agricultural existence prosperous.

This property is commonly associated with philosophy, aspects of existence, and similar concepts that are inherently " too great ", complex, or abstract to be adequately communicated.

After arguing that evolution is capable of explaining the origin of complexity, near the end of the book Dawkins uses this to argue against the existence of God: " a deity capable of engineering all the organized complexity in the world, either instantaneously or by guiding evolution ... must already have been vastly complex in the first place ..." He calls this " postulating organized complexity without offering an explanation.

The existence of multiple theories seems unnecessarily complex to modern sensibility since ratios are, to a large extent, identified with quotients.

* " Romantic jealousy is here defined as a complex of thoughts, feelings, and actions which follow threats to self-esteem and / or threats to the existence or quality of the relationship, when those threats are generated by the perception of a real or potential attraction between one's partner and a ( perhaps imaginary ) rival.

Given an algebraically closed field A containing K, there is a unique splitting field L of p between K and A, generated by the roots of p. If K is a subfield of the complex numbers, the existence is automatic.

The existence of irreducible polynomials of degree greater than one ( without zeros in the original field ) historically motivated the extension of that original number field so that even these polynomials can be reduced into linear factors: from rational numbers ( ), to the real subset of the algebraic numbers ( ), and finally to the algebraic subset of the complex numbers ( ).

He mapped out a complex esoteric cosmology with matter flowing from different planes of existence all existing in the absolute.

Cowan no longer supports the existence of two tiers but claims the only thing now known about the Yellow and Turquoise systems is that they are more complex versions of Orange and Green.

More complex models that have been proposed describe as many as a dozen class levels ; while still others deny the very existence, in the European sense, of " social class " in American society.

Weil suggested that the conjectures would follow from the existence of a suitable " Weil cohomology theory " for varieties over finite fields, similar to the usual cohomology with rational coefficients for complex varieties.

At about the same time, the nominalist philosopher William of Ockham argued, in Book I of his Summa Totius Logicae ( Treatise on all Logic, written some time before 1327 ), that Categories are not a form of Being in their own right, but derivative on the existence of individuals.

Note also the existence of yank — the derivative of force with respect to time.

The curvature tensor measures noncommutativity of the covariant derivative, and as such is the integrability obstruction for the existence of an isometry with Euclidean space ( called, in this context, flat space ).

The 16th-century Swiss alchemist Paracelsus ( Philippus Aureolus Theophrastus Bombastus von Hohenheim ) believed in the existence of alkahest, which he thought to be an undiscovered element from which all other elements ( earth, fire, water, air ) were simply derivative forms.

This method does not require the computation ( nor the existence ) of a derivative, but the price is slower convergence ( the order is approximately 1. 6 ).

Note that the chain rule assumes the existence of total derivative of the inside function H, while

The most notable of these are the conditions for the existence of multiple roots based on the discriminant, which is the resultant of a polynomial and its " derivative ": his working definition of " derivative " was

In finance, a barrier option is an exotic derivative typically an option on the underlying asset whose price breaching the pre-set barrier level either springs the option into existence or extinguishes an already existing option.

While Kadazan was an official designation for this ethnic group, it is widely believed that the term itself was a political derivative that came into existence in the late 1950s to early 1960s.

In Riemannian geometry, the existence of a metric chooses a unique preferred torsion-free covariant derivative, known as the Levi-Civita connection.

The content is not the same, however: rather than individual security, it is the security and continuing existence of an `` ideological group '' -- those in the `` free world '' -- that is basic.

( Since the time-span of the nation-state coincides roughly with the separate existence of the United States as an independent entity, it is perhaps natural for Americans to think of the nation as representative of the highest form of order, something permanent and unchanging.

This bold self-assertion, after decades of humble subservience, is indeed a twentieth-century phenomenon, an abrupt change in the Southern way of existence.

When Heidegger and Sartre speak of a contrast between being and existence, they may be right, I don't know, but their language is too philosophical for me.

This is the rhetoric of righteousness the beatniks use in defending their way of life, their search for wholeness, though their actual existence fails to reach these `` religious '' heights.

But the highroad, according to the description of its traffic, belongs to life as it is lived in unawareness of death, while the way to the churchyard belongs to some other sort of life: a suffering form, an existence wholly comprised in the awareness of death.

As long as perception is seen as composed only of isolated sense data, most of the quality and interconnectedness of existence loses its objectivity, becomes an invention of consciousness, and the result is a philosophical scepticism.

Whitehead contends that the human way of understanding existence as a unity of interlocking and interdependent processes which constitute each other and which cause each other to be and not to be is possible only because the basic form of such an understanding, for all its vagueness and tendency to mistake the detail, is initially given in the way man feels the world.

As he informs Watson, `` My life is spent in one long effort to escape from the commonplaces of existence.

The monitoring is the highest and most restrictive of any organization in existence.

Thus, it is no mystical intuition, but an analyzable conception to say that man and his tradition can `` fall out of existence ''.

An existentialist is a man who perceives himself only as `` esse '', as existence without substance.

Such a response, of course, misses the point that in crisis order is going out of existence.

But this truth is distorted by its extreme application: the assumption of the separate existence of tradition.

Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

Men seem almost universally to want a sense of function, that is, a feeling that their existence makes a difference to someone, living or unborn, close and immediate or generalized.

My argument is that there was no Saxon Shore prior to that time even though the forts had been in existence since the time of Carausius.

The existence of a community is a state of mind -- a conviction that goals and values are widely shared, that effective communication is possible, that mutual trust is reasonably assured.

This is not to deny the existence of pogroms and ghettos, but only to assert that these horrors have had an effect on the nerves of people who did not experience them, that among the various side effects is the local hysteria of Jewish writers and intellectuals who cry out from confusion, which they call oppression and pain.