Formally, the Cisalpine Republic was an independent state allied with France, but the treaty of alliance established the effective subalternity of the new republic to France.

Formally established in 1927, the Walker Art Center began as the first public art gallery in the Upper Midwest.

Formally established in 1475, though in fact much older, it has 75, 000 codices from throughout history.

Formally established during the Han Dynasty, zhou continued to exist until the establishment of the Republic of China — a period of over 2000 years.

Formally established in Los Angeles in 1922, the largest and most active Woodcraft organization is Los Angeles ' Woodcraft Rangers, which has a proud 87-year history of providing innovative and creative programs for children in the under-served areas of greater Los Angeles.

Formally established on October 21st, 1969, it includes 18 departments providing 31 different undergraduate courses, as well as a number of graduate programs.

Formally established in 1922, over the decades Woodcraft Rangers has modified Seton ’ s original emphasis on outdoor life to incorporate activities that meet the needs of an increasingly urban population, but the goal of changing behavior and encouraging positive outcomes through interaction and education remains central to its mission today.

Formally established in 1920 as the Aviation Ministry, the ROCAF was active during the tenure of the ROC on Mainland China.

Formally, the WOA was established during a meeting held in the Olympic Museum on 21 November 1995 by 25 founder members.

Formally, Training Group ceased to exist and No 22 Group was established.

Formally established in 1921, the Profintern was intended to act as a counterweight to the influence of the so-called " Amsterdam International ," the Social Democratic International Federation of Trade Unions, an organization branded as class collaborationist and an impediment to revolution by the Comintern.

However, shortly after this positive result, Kurt Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems ( 1931 ), showing that in any sufficiently strong axiomatic system there are true statements which cannot be proved in the system.

Formally, as per the 2002 Memorandum of Understanding between the BSI and the United Kingdom Government, British Standards are defined as:

Formally speaking, a collation method typically defines a total order on a set of possible identifiers, called sort keys, which consequently produces a total preorder on the set of items of information ( items with the same identifier are not placed in any defined order ).

Formally, this sharing of dynamics is referred to as universality, and systems with precisely the same critical exponents are said to belong to the same universality class.

Formally, both the pattern and searched text are vectors of elements of Σ.

Limits and colimits in a category C are defined by means of diagrams in C. Formally, a diagram of type J in C is a functor from J to C:

Formally, Gaussian integers are the set

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, we are given a set of hypotheses and a set of manifestations ; they are related by the domain knowledge, represented by a function that takes as an argument a set of hypotheses and gives as a result the corresponding set of manifestations.

Formally, two variables are inversely proportional ( or varying inversely, or in inverse variation, or in inverse proportion or in reciprocal proportion ) if one of the variables is directly proportional with the multiplicative inverse ( reciprocal ) of the other, or equivalently if their product is a constant.

Formally, they are partial derivatives of the option price with respect to the independent variables ( technically, one Greek, gamma, is a partial derivative of another Greek, called delta ).

Formally, the two parts are given by the following expression, where is the number being encoded:

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, they are known as Ridunians, from the Latin Riduna.

( Formally speaking, this then satisfies the premises of an axiom of well-founded induction, which asserts that these two conditions are sufficient for the proposition to hold for all x.

Formally, the outcomes Y < sub > i </ sub > are described as being Bernoulli-distributed data, where each outcome is determined by an unobserved probability p < sub > i </ sub > that is specific to the outcome at hand, but related to the explanatory variables.

Formally unnamed icefields are not listed

Formally this approximation is founded on the variational principle, valid for Hamiltonians that are bounded from below.

Formally, an analytic function ƒ ( z ) of the real or complex variables z < sub > 1 </ sub >,…, z < sub > n </ sub > is transcendental if z < sub > 1 </ sub >, …, z < sub > n </ sub >, ƒ ( z ) are algebraically independent, i. e., if ƒ is transcendental over the field C ( z < sub > 1 </ sub >, …, z < sub > n </ sub >).

These are manufactured by Amphenol ( Formally Alcatel Components and ITT Cannon Australia ).

Formally most of these approaches are similar to an artificial neural network, as inputs to a node are summed up and the result serves as input to a sigmoid function, e. g., but proteins do often control gene expression in a synergistic, i. e. non-linear, way.

Formally, the sets of free and bound names of a process in π – calculus are defined inductively as follows.

Formally, one inserts under the trace for each degree of freedom

Formally, let p and q be two nonzero polynomials, respectively of degree m and n. Thus:

“ Formally stated, interactivity is an expression of the extent that in a given series of communication exchanges, any third ( or later ) transmission ( or message ) is related to the degree to which previous exchanges referred to even earlier transmissions ” ( Sheizaf Rafaeli, “ Interactivity, From New Media to Communication ,” pages 110-34 in Advanced Communicational Science: Merging Mass and Interpersonal Processes, ed.

Formally organized vocational programs supported by federal funds allow high school students to gain experience in a field of work which is likely to lead to a full-time job on graduation.

Formally, arbitrage transactions have negative skew – prices can get a small amount closer ( but often no closer than 0 ), while they can get very far apart.

Formally, their designation is the letter Ž and the number.

Formally, a topological space X is called compact if each of its open covers has a finite subcover.

Formally, they were part of the non-resident sections, but in fact constituted a separate division, largely autonomous in their activities.

Formally, the Congress serves two functions: to approve changes to the Party constitution regarding policy and to elect a Central Committee, about 300 strong.

More rigorously, the divergence of a vector field F at a point p is defined as the limit of the net flow of F across the smooth boundary of a three dimensional region V divided by the volume of V as V shrinks to p. Formally,

Formally, there is a clear distinction: " DFT " refers to a mathematical transformation or function, regardless of how it is computed, whereas " FFT " refers to a specific family of algorithms for computing DFTs.

Formally, one has an implication, not an equivalence, so the solution set may get larger.

Formally, oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100 % ionic.

Formally, a bifunctor is a functor whose domain is a product category.

Formally inaugurated in March 2004, the Global Leadership Foundation works to " promote good governance – democratic institutions, open markets, human rights and the rule of law – and to contribute to the prevention and resolution of conflict through mediation.

Formally given to bishop Philip of Senj, the permission to use the Glagolitic liturgy ( the Roman Rite conducted in Slavic language instead of Latin, not the Byzantine rite ), actually extended to all Croatian lands, mostly along the Adriatic coast.

Formally, the system is said to have memory.

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, an inner product space is a vector space V over the field together with an inner product, i. e., with a map

Formally neutral and reluctant to become involved with the great powers except as a last resort, Kuwait turned to the United States, the Soviet Union and Britain for naval protection of its tanker fleet after twenty-one ships were attacked in the gulf since late 1986.

* 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.

Massiah: Formally Charged + Deliberate Elicitation.

*, see On Formally Undecidable Propositions of Principia Mathematica and Related Systems for details on English translations.

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.

Formally introduced in September 1979, Initial samples were released in February 1980, with production chips available over the counter in November.

* Nuclear bunker buster: Formally known as the Robust Nuclear Earth Penetrator ( RNEP ), this program aimed to modify an existing gravity bomb to penetrate into soil and rock in order to destroy underground targets.

Formally, a profinite group is a Hausdorff, compact, and totally disconnected topological group: that is, a topological group that is also a Stone space.