[permalink] [id link]

Formally, for received words, let denote the Hamming distance between and, that is, the number of positions in which and differ.

from
Wikipedia

## Some Related Sentences

Formally and for

__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__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

**.**

*

**,**see On__Formally__Undecidable Propositions**of**Principia Mathematica**and**Related Systems__for__details on English translations**.**__Formally__named " United Press Associations "

__for__incorporation

**and**legal purposes

**,**but publicly known

**and**identified as United Press or UP

**,**it was created by

**the**1907 uniting

**of**three smaller news syndicates by

**the**Midwest newspaper publisher E

**.**W

**.**Scripps

**.**

__Formally__stated

**,**

**the**FFT

**is**a method

__for__computing

**the**discrete Fourier transform

**of**a sampled signal

**.**

__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__it

**is**precisely

**in**allowing quantification over class variables α

**,**β

**,**etc.,

**that**we assume a range

**of**values

__for__these variables to refer to

**.**

__Formally__

**,**a decision problem

**is**P-complete ( complete

__for__

**the**complexity class P ) if it

**is**

**in**P

**and**

**that**every problem

**in**P can be reduced to it by using an appropriate reduction

**.**

If R

**is**a ring**,****let**R**denote****the**ring**of**polynomials**in****the**indeterminate X over R**.**Hilbert proved**that**if R**is**" not too large ",**in****the**sense**that**if R**is**Noetherian**,****the**same must be true__for__R**.**__Formally__**,**__Formally__

**,**

**the**sequence

**of**partial sums

**of**some infinite summation converges if

__for__every fixed power

**of**X

**the**coefficient stabilizes: there

**is**a point beyond

**which**all further partial sums have

**the**same coefficient

**.**

__Formally__

**,**a function ƒ

**is**real analytic on an open set D

**in**

**the**real line if

__for__any x < sub > 0 </ sub >

**in**D one can write

__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

**is**an open subset

**of**

**the**complex plane

**,**a point

**of**

**,**

**and**

**is**a holomorphic function

**,**then

**is**called a removable singularity

__for__if there exists a holomorphic function

**which**coincides with on

**.**

__Formally__

**,**we have

__for__

**the**approximation to

**the**full solution A

**,**a series

**in**

**the**small parameter ( here called ), like

**the**following:

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__

**,**cl ( S ) denotes

**the**smallest subset Y

**of**M

**that**contains S such

**that**

__for__each reaction ( A

**,**B )

__Formally__

**,**it

**is**a coalition

**of**U

**.**S

**.**

**and**European CEOs

**,**largely from transnational corporations

**,**launched at

**the**urging

**of**former United States Secretary

**of**Commerce Ron Brown

**in**Seville ( Spain )

**in**late 1995 at a conference attended by CEOs from more than 100 U

**.**S

**.**

**and**EU companies

**and**by top government representatives led by

**the**Commissioners

__for__Trade

**and**Industry

**and**by

**the**U

**.**S

**.**Secretary

**of**Commerce

**.**

__Formally__

**,**a government would lay out its reasons

__for__going to war

**,**as well as its intentions

**in**prosecuting it

**and**

**the**steps

**that**might be taken to avert it

**.**

__Formally__

**,**

**the**movement

**is**a rondo

**that**acts as

**the**theme

__for__a set

**of**eight variations

**,**capped off by a dramatic coda

**.**

(

__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**motion merely calls on parliament to thank

**the**monarch or viceroy

__for__

**the**speech via an Address

**in**Reply

**.**

; Electronics:

__Formally__a fixture**in**radio shacks**,**now used__for__assembly**and**repair**of**all sorts**of**electronic equipment including communication**,**computer**,****and**home entertainment items**.**
It has been leased from

**the**National Trust since 1974 by**the**Somerset Wildlife Trust (__Formally__Somerset Trust__for__Nature Conservation )**and****is**run as a nature reserve**and**visitor centre**.**

Formally and received

__Formally__nominated on December 11

**,**1851

**,**Curtis was confirmed by

**the**United States Senate on December 20

**,**1851

**,**

**and**

__received__his commission

**the**same day

**.**

__Formally__nominated on January 3

**,**1820

**,**Bland was confirmed by

**the**United States Senate on January 5

**,**1820

**,**

**and**

__received__his commission

**the**same day

**.**

__Formally__trained

**in**music composition

**,**Dargel studied with Oliveros

**,**John Luther Adams

**,**

**and**Lewis Nielson

**,**

**and**

__received__a B

**.**A

**.**

__Formally__nominated on January 5

**,**1950

**,**he was confirmed by

**the**United States Senate on February 8

**,**1950

**,**

**and**

__received__his commission on February 10

**,**1950

**.**

Formally and words

__Formally__

**,**if f

**is**a harmonic function

**,**then f cannot exhibit a true local maximum within

**the**domain

**of**definition

**of**f

**.**In other

__words__

**,**either f

**is**a constant function

**,**or

**,**

**for**any point inside

**the**domain

**of**f

**,**there exist other points arbitrarily close to at

**which**f takes larger values

**.**

Formally and let

__Formally__

**,**

__let__be a stochastic process

**and**

__let__represent

**the**cumulative distribution function

**of**

**the**joint distribution

**of**at times

**.**

__Formally__

**,**

__let__A be a real matrix

**of**

**which**we want to compute

**the**eigenvalues

**,**

**and**

__let__A < sub > 0 </ sub >:= A

**.**

__Formally__

**,**

__let__G be a Coxeter group with reduced root system R

**and**k < sub > v </ sub > a multiplicity function on R ( so k < sub > u </ sub > = k < sub > v </ sub > whenever

**the**reflections σ < sub > u </ sub >

**and**σ < sub > v </ sub > corresponding to

**the**roots u

**and**v are conjugate

**in**G ).

__Formally__

**,**

__let__P be a poset ( partially ordered set ),

**and**

__let__F be a filter on P ;

**that**

**is**

**,**F

**is**a subset

**of**P such

**that**:

__Formally__

**,**

__let__X be any scheme

**and**S be a sheaf

**of**graded-algebras (

**the**definition

**of**

**which**

**is**similar to

**the**definition of-modules on a locally ringed space ):

**that**

**is**

**,**a sheaf with a direct sum decomposition

0.121 seconds.