A rector is a senior official in an educational institution, can refer to an official in either a university or a secondary school. Outside the English-speaking world the rector is the most senior official in a university, whilst in the United States the most senior official is referred to as President and in the United Kingdom and Commonwealth of Nations the most senior official is the Chancellor, whose office is ceremonial and titular; the term and office of a rector can be referred to as a rectorate. The title is used in universities in Europe, and is common in Latin American countries. It is used in Brunei, Russia, the Philippines, Indonesia and the Middle East. In the ancient universities of Scotland the office is sometimes referred to as Lord Rector, is the third most senior official, is responsible for chairing the University Court; the head of a university in Germany is called a president, rector magnificus or rectrix magnifica, as in some Belgian universities. In Dutch universities, the rector magnificus is the most publicly prominent member of the board, responsible for the scientific agenda of the university.

In the Netherlands, the rector is, not the chair of the university board. The chair has, in the most influence over the management of the University. In some countries, including Germany, the position of head teacher in secondary schools is designated as rector. In the Netherlands, the terms "rector" and "conrector" are used for high school directors; this is the case in some Maltese secondary schools. In the Scandinavian countries, the head of a university or a gymnasium is called a rektor. In Sweden and Norway, this term is used for the heads of primary schools. In Finland, the head of a primary school or secondary schools is called a rector provided the school is of sufficient size in terms of faculty and students, otherwise the title is headmaster; the head of some Finnish universities is called chancellor. In the Iberian Peninsula, Portugal's and Spain's university heads or presidents have the title; those universities whose foundation has been approved by the Pope, as e.g. the rector of the University of Coimbra, the oldest Portuguese university, is referred to as Magnífico Reitor.

The others are referred to as Excelentíssimo Senhor Reitor. In Spain, all Rectors must be addressed as Señor Rector Magnífico according to the law, but the Rector of the University of Salamanca, the oldest on the Iberian Peninsula, is styled according to academic protocol as Excelentísimo y Ilustrísimo Señor Profesor Doctor Don, Rector Magnífico de la Universidad de Salamanca. In a few "Crown lands" of the Austrian Empire, one seat in the Landtag was reserved for the rector of the capital's university, notably: Graz in Steiermark, Innsbruck in Tirol, Wien in Nieder-Österreich. Today Austrian universities are headed by a Rectorate consisting of one Rector and 3-5 additional Vizerectors; the Rector is the CEO of the university. The heads of Czech universities are called the rektor; the rector acts in the name of the university and decides the university's affairs unless prohibited by law. The rector is nominated by the University Academic Senate and appointed by the President of the Czech Republic.

The nomination must be agreed by a simple majority of all senators, while a dismissal must be agreed by at least three fifths of all senators. The vote to elect or repeal a rector is secret; the term of office is four years and a person may hold it for at most two consecutive terms. The rector appoints vice-rectors. Rectors' salaries are determined directly by the Minister of Education. Among the most important rectors of Czech universities were reformer Jan Hus, physician Jan Jesenius, theologian Rodrigo de Arriaga and representative of Enlightenment Josef Vratislav Monse. Jiřina Popelová became the first female Rector in 1950; the rectors are addressed "Your Magnificence Rector". In Danish, rektor is the title used in referring to the heads of universities, schools of commerce and construction, etc. Rektor may be used for the head of any educational institution above the primary school level, where the head is referred to as a'skoleinspektør'. In universities, the second-ranked official of governance is known as prorektor.

Most English universities are formally headed by "chancellors". In a few colleges, the equivalent person is called a "president", "provost", or "warden". At two Oxford colleges, Lincoln College and Exeter College, the head is called "rector". At Oxford and Cambridge, the university's overall head is called "chancellor", but this is chiefly a ceremonial position while the academic head of each university is the "vice-chancellor". At St Chad's College, one of the two so-called "recognised colleges" of the University of Durham, there is a "rector" as titular head while the academic head is the "principal"; the Universit

In computer science, denotational semantics is an approach of formalizing the meanings of programming languages by constructing mathematical objects that describe the meanings of expressions from the languages. Other approaches provide formal semantics of programming languages including axiomatic semantics and operational semantics. Broadly speaking, denotational semantics is concerned with finding mathematical objects called domains that represent what programs do. For example, programs might be represented by partial functions or by games between the environment and the system. An important tenet of denotational semantics is that semantics should be compositional: the denotation of a program phrase should be built out of the denotations of its subphrases. Denotational semantics originated in the work of Christopher Strachey and Dana Scott published in the early 1970s; as developed by Strachey and Scott, denotational semantics provided the meaning of a computer program as a function that mapped input into output.

To give meanings to recursively defined programs, Scott proposed working with continuous functions between domains complete partial orders. As described below, work has continued in investigating appropriate denotational semantics for aspects of programming languages such as sequentiality, non-determinism and local state. Denotational semantics have been developed for modern programming languages that use capabilities like concurrency and exceptions, e.g. Concurrent ML, CSP, Haskell; the semantics of these languages is compositional in that the meaning of a phrase depends on the meanings of its subphrases. For example, the meaning of the applicative expression f is defined in terms of semantics of its subphrases f, E1 and E2. In a modern programming language, E1 and E2 can be evaluated concurrently and the execution of one of them might affect the other by interacting through shared objects causing their meanings to be defined in terms of each other. E1 or E2 might throw an exception which could terminate the execution of the other one.

The sections below describe special cases of the semantics of these modern programming languages. Denotational semantics are given to a program phrase as a function from an environment to its denotation. For example, the phrase n*m produces a denotation when provided with an environment that has binding for its two free variables: n and m. If in the environment n has the value 3 and m has the value 5 the denotation is 15. A function can be modeled as a set of ordered pairs of argument and corresponding result values. For example, the set denotes a function with result 1 for argument 0, result 3 for the argument 4, undefined otherwise; the problem to be solved is to provide meanings for recursive programs that are defined in terms of themselves such as the definition of the factorial function as A solution is to build up the meanings by approximation. The factorial function is a total function from ℕ to ℕ. At the beginning, we start with the empty function. Next, we add the ordered pair to the function to result in another partial function that better approximates the factorial function.

Afterwards, we add yet another ordered pair to create an better approximation. It is instructive to think of this chain of iteration as F0, F1, F2... where Fi indicates i-many applications of F. F0 is the undefined partial function; this iterative process builds a sequence of partial functions from ℕ to ℕ. Partial functions form a chain-complete partial order using ⊆ as the ordering. Furthermore, this iterative process of better approximations of the factorial function forms an expansive mapping because each F i ≤ F i + 1 using ⊆ as the ordering. So by a fixed-point theorem, there exists a fixed point for this iterative process. In this case, the fixed point is the least upper bound of this chain, the full factorial function, which can be expressed as the direct limit ⨆ i ∈ N F i. Here, the symbol "⊔" is the directed join, meaning "least upper bound"; the directed join is the join of directed sets. The concept of power domains has been developed to give a denotational semantics to non-deterministic sequential programs.

Writing P for a power-domain constructor, the domain P is the domain of non-deterministic computations of type denoted by D. There are difficulties with fairness and unboundedness in domain-theoretic models of non-determinism. Many researchers have argued that the domain-theoretic models given above do not suffice for the more general case of concurrent computation. For this reason various new models have been introduced. In the early 1980s, people began using the style of denotational semantics to give semantics for concurrent languages. Examples include Will Clinger's work with the actor model. All these lines of inquiry remain under investigation (see e.g. the various denotational models fo

Chloryl fluoride is the chemical compound with the formula ClO2F. It is encountered as side-product in reactions of chlorine fluorides with oxygen sources, it is the acyl fluoride of chloric acid. ClO2F was first reported by Schmitz and Schumacher in 1942, who prepared it by the fluorination of ClO2; the compound is more conveniently prepared by treatment of sodium chlorate and chlorine trifluoride and purified by vacuum fractionation, i.e. selectively condensing this species separately from other products. This species is a gas boiling at −6 °C: 6 NaClO3 + 4 ClF3 → 6 ClO2F + 2 Cl2 + 3 O2 + 6 NaF In contrast to O2F2, ClO2F is a pyramidal molecule; this structure is predicted by VSEPR. The differing structures reflects the greater tendency of chlorine to exist in positive oxidation states with oxygen and fluorine ligands; the related Cl-O-F compound perchloryl fluoride, ClO3F, is tetrahedral. The related bromine compound bromyl fluoride adopts the same structure as ClO2F, whereas iodyl fluoride forms a polymeric substance under standard conditions.

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