Formally the " head of state " can also personally be the " head of government " ( ex officio or by ad hoc cumulation such as an absolute monarch nominating himself ) but otherwise has formal precedence over the Head of Government and other ministers, whether he is their actual political superior ( absolute monarch, executive president ) or rather theoretical or ceremonial in character.

Formally, the theorem is stated as follows: There exist unique integers q and r such that a = qd + r and 0 ≤ r < | d |, where | d | denotes the absolute value of d.

Formally, collective noun forms such as “ a group of people ” are represented by second-order variables, or by first-order variables standing for sets ( which are well-defined objects in mathematics and logic ).

Formally, an elliptic function is a function meromorphic on for which there exist two non-zero complex numbers and with ( in other words, not parallel ), such that and for all.

Formally, if there exists some B ≥ 0 such that

Formally, cl ( S ) denotes the smallest subset Y of M that contains S such that for each reaction ( A, B )

Formally, the word is applied to persons who are publicly accepted in a recognised capacity, such as professional employment, graduation from a course of study, etc., to give critical commentaries in one or any of a number of specific fields of public or private achievement or endeavour.

Formally, the case where only a subset of parameters is defined is still a composite hypothesis ; nonetheless, the term point hypothesis is often applied in such cases, particularly where the hypothesis test can be structured in such a way that the distribution of the test statistic ( the distribution under the null hypothesis ) does not depend on the parameters whose values have not been specified under the point null hypothesis.

Formally, a measurable cardinal is an uncountable cardinal number κ such that there exists a κ-additive, non-trivial, 0-1-valued measure on the power set of κ.

Formally, a ring is an Abelian group ( R, +), together with a second binary operation * such that for all a, b and c in R,

Formally, a coalgebra over a field K is a vector space C over K together with K-linear maps Δ: C → C ⊗ C and ε: C → K such that

Formally, a Hopf algebra is a ( associative and coassociative ) bialgebra H over a field K together with a K-linear map S: H → H ( called the antipode ) such that the following diagram commutes:

Formally, given such that, the corresponding characteristic number is:

Formally, assuming the axiom of choice, cardinality of a set X is the least ordinal α such that there is a bijection between X and α.

Formally a congruence subgroup is one that contains Γ ( N ) for some N, and the least such N is the level or Stufe of the subgroup.

Formally, given a vector field v, a vector potential is a vector field A such that

Formally, knowing the step response of a dynamical system gives information on the stability of such a system, and on its ability to reach one stationary state when starting from another.

Formally, a vertex cover of a graph G is a set C of vertices such that each edge of G is incident to at least one vertex in C. The set C is said to cover the edges of G. The following figure shows examples of vertex covers in two graphs ( and the set C is marked with red ).

Formally, choose such that

Formally, a string is a finite sequence of symbols such as letters or digits.

Formally, a cardinal number κ is λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus-power set such that κ is in M and M contains all its sequences of length less than κ, there is a non-trivial elementary embedding j of M into a transitive model with the critical point of j being κ and j ( κ ) ≥ λ.

Formally, given a finite set X, a collection C of subsets of X, all of size n, has Property B if we can partition X into two disjoint subsets Y and Z such that every set in C meets both Y and Z.

Formally, we define a bad field as a structure of the form ( K, T ), where K is an algebraically closed field and T is an infinite, proper, distinguished subgroup of K, such that ( K, T ) is of finite Morley rank in its full language.

Formally, the principle of subsidiarity applies to those areas where the Community does not have exclusive competence, the principle delineating those areas where the Community should and should not act.

Formally, assuming our intuition from the finite dimensional case carries over into the infinite dimensional setting, the measure should then be equal to

Formally, this follows from the convolution theorem in mathematics, which relates the Fourier transform of the power spectrum ( the intensity of each frequency ) to its autocorrelation.

Formally the Prince-Electors elected a King of the Romans, who was elected in Germany but became Holy Roman Emperor only when crowned by the Pope.

* Formally, when working over the reals, as here, this is accomplished by considering the limit as ε → 0 ; but the " infinitesimal " language generalizes directly to Lie groups over general rings.

Formally, these failed when they were rejected by the Church of England's General Synod in 1972 ; conversations and co-operation continued, however, leading in 2003 to the signing of a covenant between the two churches.

In late 1900s the day that of the City was founded is Jakin School is a Private School is Formally Part of Jakin School Board was Grades One through Twelve there is no Football field on this school. In 1966 When Jakin School was Closed were Sent to Blakely-Union Elementary, Junior High, and High School ( which later Became Early County High, Middle, and Elementary School ). while Carver school was built for African-American students grades One through Twelve. although late 1960s when Carver school was closed along with Kestler School was based in Damascus were sent to Washington High & Elementary at Blakely. In addition to small farm agriculture, Jakin's early economic growth resulted from turpentine.

Formally, it is anything which when offered in payment extinguishes the debt.

Formally since 19 June 1971 when Lövenich ( now part of Cologne ) was an independent town.

Formally, a composite number n = d · 2 < sup > s </ sup > + 1 with d being odd is called a strong pseudoprime to a relatively prime base a when one of the following conditions hold:

Formally, a graph is symmetric with respect to the origin if it is unchanged when reflected across both the x-axis and y-axis.

Formally, a natural number n is called superabundant precisely when, for any m < n,

Formally, these failed when they were rejected by the Church of England's General Synod in 1972, however conversations and co-operation continued leading in 2003 to the signing of a covenant between the two churches.

MAC, also called " Mitochondrial Outer Membrane Permeabilization Pore " is regulated by various proteins, such as those encoded by the mammalian Bcl-2 family of anti-apoptopic genes, the homologs of the ced-9 gene found in C. elegans.

As a result, the malignant cells experience an abnormal response to apoptosis induction: cycle regulating genes ( such as p53, ras or c-myc ) are mutated or inactivated in diseased cells, and further genes ( such as bcl-2 ) also modify their expression in tumors.

Active NF-κB induces the expression of anti-apoptotic genes such as Bcl-2, resulting in inhibition of apoptosis.

Most current genome annotation systems work similarly, but the programs available for analysis of genomic DNA, such as the GeneMark program trained and used to find protein-coding genes in Haemophilus influenzae, are constantly changing and improving.

Because such strains transfer chromosomal genes very efficiently they are called Hfr ( high frequency of recombination ).

Gene therapy may be used for treating, or even curing, genetic and acquired diseases like cancer and AIDS by using normal genes to supplement or replace defective genes or to bolster a normal function such as immunity.

Worse, it is not known exactly whether genes have more than one function, which creates uncertainty as to whether replacing such genes is indeed desirable.

In the area of language acquisition, for example, some ( such as Steven Pinker ) have argued that specific information containing universal grammatical rules must be contained in the genes, whereas others ( such as Jeffrey Elman and colleagues in Rethinking Innateness ) have argued that Pinker's claims are biologically unrealistic.

As Hox genes code for transcription factors, this causes different activated combinations of both Hox and other genes in discrete anteroposterior transverse segments of the neural tube ( neuromeres ) and related patterns in surrounding tissues, such as branchial arches, lateral mesoderm, neural crest, skin and endoderm, in the head to tail direction.

The production of Dolly showed that genes in the nucleus of such a mature differentiated somatic cell are still capable of reverting back to an embryonic totipotent state, creating a cell that can then go on to develop into any part of an animal.

Researchers in molecular and evolutionary biology no longer question this theory, although some of the details, such as the mechanisms for loss of genes from organelles to host nuclear genomes, are still being worked out.

Genetics deals with the molecular structure and function of genes, gene behavior in context of a cell or organism ( e. g. dominance and epigenetics ), patterns of inheritance from parent to offspring, and gene distribution, variation and change in populations, such as through Genome-Wide Association Studies.

However, other methods exploit natural forms of gene transfer, such as the ability of Agrobacterium to transfer genetic material to plants, or the ability of lentiviruses to transfer genes to animal cells.

Other forms of genetic engineering include gene targeting and knocking out specific genes via engineered nucleases such as zinc finger nucleases or engineered homing endonucleases.

In such circumstances then, " genome " describes all of the genes and information on non-coding DNA that have the potential to be present.

Scientists have taken the logical step of trying to introduce genes directly into human cells, focusing on diseases caused by single-gene defects, such as cystic fibrosis, haemophilia, muscular dystrophy and sickle cell anemia.

Other forms of genetic engineering include gene targeting and knocking out specific genes via engineered nucleases such as zinc finger nucleases, engineered I-CreI homing endonucleases, or nucleases generated from TAL effectors.

Unfortunately, some of the most commonly occurring disorders, such as heart disease, high blood pressure, Alzheimer's disease, arthritis, and diabetes, are caused by the combined effects of variations in many genes.