Formally reported from November 1944 onwards, witnesses often assumed that the foo fighters were secret weapons employed by the enemy, but they remained unidentified post-war and were reported by both Allied and Axis forces.

Formally divided into lower and upper Ullern in 1740, both farms were bought by Herman Severin Løvenskiold, in 1878 and 1866 respectively.

Formally, the algorithm's performance will be a random variable determined by the random bits ; thus either the running time, or the output ( or both ) are random variables.

Formally, given two partially ordered sets ( S, ≤) and ( T, ≤), a function f: S → T is an order-embedding if f is both order-preserving and order-reflecting, i. e. for all x and y in S, one has

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

Several significant events in 2001 persuaded BNFL to upgrade the fuel routes of both Calder Hall and Chapelcross to near modern standards at a cost of tens of millions of pounds to guarantee that a License Instrument would be granted by the NII to permission final defuelling: the engineering work is being carried out by BNS Nuclear Services ( Formally Alstec ).

Formally, the problem of supervised pattern recognition can be stated as follows: Given an unknown function ( the ground truth ) that maps input instances to output labels, along with training data assumed to represent accurate examples of the mapping, produce a function that approximates as closely as possible the correct mapping.

Formally speaking, the strategy pattern defines a family of algorithms, encapsulates each one, and makes them interchangeable.

Formally, a graph rewriting system usually consists of a set of graph rewrite rules of the form, with being called pattern graph ( or left-hand side ) and being called replacement graph ( or right-hand side of the rule ).

Formally, the novel is notable because of its lack of paragraphing, a digressive style, the blending of fact and fiction, very long and complex sentences ( one sentence is about 9 pages long ) as well as the inclusion of a set of mysterious and evocative photographs, scattered throughout the book, which enhance the melancholy message of the text.

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.

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, starting with a linearly independent set of vectors

Formally, a system is said to be observable if, for any possible sequence of state and control vectors, the current state can be determined in finite time using only the outputs ( this definition is slanted towards the state space representation ).

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 unique factorization domain is defined to be an integral domain R in which every non-zero and non-unit x of R can be written as a product ( including an empty product ) of irreducible elements p < sub > i </ sub > of R and a unit u:

Formally, a hypergraph is a pair where is a set of elements called nodes or vertices, and is a set of non-empty subsets of called hyperedges or edges.

Formally described, it alternates slow sections in a modal F with faster sections, " Neue Kraft fühlend " ( with renewed strength ), in D. The slow sections each have two elements, ( 1 ) a passage reminiscent of the opening of the first movement in which the instruments overlap each other with a brief motive ; ( 2 ) a chorale, the actual song.

Formally, start with a set Ω and consider the sigma algebra Σ on Ω consisting of all subsets of Ω.

Formally, a deterministic Büchi automaton is a tuple A = ( Q, Σ, δ, q < sub > 0 </ sub >, F ) that consists of the following components:

Formally, a signed graph Σ is a pair ( G, σ ) that consists of a graph G = ( V, E ) and a sign mapping or signature σ from E to the sign group