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Here, < sub > n </ sub > denotes the sample mean of the first n samples ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >), s < sup > 2 </ sup >< sub > n </ sub > their sample variance, and σ < sup > 2 </ sup >< sub > n </ sub > their population variance.

from
Wikipedia

## Some Related Sentences

Here and <

Therefore

**,**given any positive integer**n****,**it produces a string with Kolmogorov complexity at least as great as**n****.**The program itself has a fixed length U**.**The input to**the**program GenerateComplexString is an integer**n****.**__Here__**,****the**size**of****n**is measured by**the**number**of**bits required to represent**n****,**which is log__<__**sub****>****2****</****sub**>(**n**).__Here__K

**denotes**

**the**field

**of**real numbers or complex numbers

**,**I is a closed

**and**bounded interval b

**and**p

**,**q are real numbers with

**1**

__<__p

**,**q

__<__∞ so that

__Here__k is first-order rate constant having dimension

**1**/ time

**,**

**(**t ) is concentration at a time t

**and**

__<__

**sub**

**>**0

**</**

**sub**

**>**is

**the**initial concentration

**.**

__Here__I

__<__

**sub**

**>**

**2**

**</**

**sub**

**>**is reduced to I

__<__

**sup**>–</

**sup**

**>**

**and**S

__<__

**sub**

**>**

**2**

**</**

**sub**

**>**O

__<__

**sub**

**>**3

**</**

**sub**

**><**

**sup**

**>**

**2**–</

**sup**

**>**

**(**thiosulfate anion ) is oxidized to S

__<__

**sub**

**>**4

**</**

**sub**

**>**O

__<__

**sub**

**>**6

**</**

**sub**

**><**

**sup**

**>**

**2**–</

**sup**>.

The simplest

**,****and**original**,**implementation**of****the**protocol uses**the**multiplicative group**of**integers modulo p**,**where p is prime**and**g is primitive root mod p**.**__Here__is an example**of****the**protocol**,**with non-secret values in__<__span style =" color: blue "> blue**</**span**>,****and**secret values in__<__span style =" color: red "> boldface red**</**span >:__Here__is

**the**center

**of**

**the**ellipse

**,**

**and**is

**the**angle between

**the**

__<__math

**>**X

**</**Math >- axis

**and**

**the**major axis

**of**

**the**ellipse

**.**

__Here__C

__<__

**sub**

**>**p

**</**

**sub**

**>**is

**the**heat capacity at constant pressure

**and**α is

**the**coefficient

**of**

**(**cubic ) thermal expansion

__Here__

**(**Z / 2Z ) is

**the**polynomial ring

**of**Z / 2Z

**and**

**(**Z / 2Z )/( T

__<__

**sup**

**>**

**2**

**</**

**sup**>+ T +

**1**) are

**the**equivalence classes

**of**these polynomials modulo T

__<__

**sup**

**>**

**2**

**</**

**sup**>+ T +

**1**

**.**

__Here__

**the**kets

**and**columns are identified with

**the**vectors

**of**V

**and**

**the**bras

**and**rows with

**the**dual vectors or linear functionals

**of**

**the**dual space V

__<__

**sup**>*</

**sup**

**>,**with conjugacy associated with duality

**.**

# If A is a cartesian product

**of**intervals I__<__**sub****>****1****</****sub****>**× I__<__**sub****>****2****</****sub****>**× ... × I__<__**sub****>****n****</****sub****>,**then A is Lebesgue measurable**and**__Here__**,**| I |**denotes****the**length**of****the**interval I**.**

Here and n

__Here__

__n__is

**the**number

**of**electrons / mole product

**,**F is

**the**Faraday constant

**(**coulombs / mole ),

**and**ΔE is cell potential

**.**

As explained above

**,**Gaussian elimination writes a given m ×__n__matrix A uniquely as a product**of**an invertible m × m matrix S**and**a row-echelon matrix T**.**__Here__**,**S is**the**product**of****the**matrices corresponding to**the**row operations performed**.**__Here__

__n__is

**the**refractive index

**of**

**the**medium in which

**the**measurement is made ;

**and**f is

**the**measured frequency

**of**

**the**source

**.**

__Here__

__n__is

**the**number

**of**digits

**of**precision at which

**the**natural logarithm is to be evaluated

**and**M

**(**

__n__) is

**the**computational complexity

**of**multiplying two n-digit numbers

**.**

__Here__

**,**

**the**coefficients χ

**<**

**sup**>(

__n__)</

**sup**

**>**are

**the**n-th order susceptibilities

**of**

**the**medium

**and**

**the**presence

**of**such a term is generally referred to as an n-th order nonlinearity

**.**

The

**first**question was answered in**the**negative when in 1963**,**Eggan gave examples**of**regular languages**of**star height__n__for every__n__**.**__Here__**,****the**star height h**(**L )**of**a regular language L is defined as**the**minimum star height among all regular expressions representing L**.**The**first**few languages found by are described in**the**following**,**by means**of**giving a regular expression for each language:__Here__d is

**the**spacing between diffracting planes

**,**is

**the**incident angle

**,**

__n__is any integer

**,**

**and**λ is

**the**wavelength

**of**

**the**beam

**.**

__Here__Δk is

**the**field-dependent difference between LCP

**and**RCP absorption

**,**α is

**the**electric permeability

**,**

__n__is

**the**index

**of**refraction

**,**H is

**the**applied magnetic field

**,**k is

**the**Boltzmann constant

**and**T is

**the**temperature

**.**

Here and </

__Here__

**the**last product means that a

**first**electron

**,**r

**<**

**sub**

**>**

**1**

__</__

**sub**

**>,**is in an atomic hydrogen-orbital centered at

**the**second nucleus

**,**whereas

**the**second electron runs around

**the**

**first**nucleus

**.**

Here and denotes

__Here__

**the**term yoga

__denotes__a kind

**of**" meta-theory " that can be used heuristically ; Michel Raynaud writes

**the**other terms " Ariadne's thread "

**and**" philosophy " as effective equivalents

**.**

__Here__highbit

**(**S )

__denotes__

**the**most significant bit

**of**S ;

**the**'< tt >*</ tt >' operator

__denotes__unsigned integer multiplication with lost overflow ; '< tt >^</ tt >' is

**the**bitwise exclusive or operation applied to words ;

**and**P is a suitable fixed word

**.**

Let ρ

**,**θ**,****and**φ be spherical coordinates for**the**source point P**.**__Here__θ__denotes__**the**angle with**the**vertical axis**,**which is contrary to**the**usual American mathematical notation**,**but agrees with standard European**and**physical practice**.**__Here__C

**<**

**sub**

**>**b

**</**

**sub**>( X )

__denotes__

**the**C *- algebra

**of**all continuous bounded functions on X with sup-norm

**.**

__Here__y *( w )

__denotes__

**the**value

**of**

**the**linear functional y *

**(**which is an element

**of**

**the**dual space

**of**W ) when evaluated at

**the**element w ∈ W

**.**This scalar in turn is multiplied by

**x**to give as

**the**final result an element

**of**

**the**space V

**.**

__Here__

**,**|| ||<

**sub**

**>**

**2**

**</**

**sup**

**>**is

**the**matrix 2-norm

**,**c

**<**

**sub**

**>**

**n**

**</**

**sub**

**>**is a small constant depending on

**n**

**,**

**and**ε

__denotes__

**the**unit round-off

**.**

__Here__0

__denotes__

**the**trivial abelian group with a single element

**,**

**the**map from Z to Z is multiplication by

**2**

**,**

**and**

**the**map from Z to

**the**factor group Z / 2Z is given by reducing integers modulo

**2**

**.**

__Here__

**,**

__denotes__

**the**radical

**of**J

**and**I

**(**U ) is

**the**ideal

**of**all polynomials which vanish on

**the**set U

**.**

__Here__

**,**" prequel "

__denotes__status as a " franchise-renewing original " that depicts events earlier in

**the**

**(**internally inconsistent ) narrative cycle than those

**of**a previous installment

**.**

__Here__N

**<**

**sub**

**>**m

**</**

**sub**

**>**

__denotes__

**the**number

**of**turns in loop m

**,**Φ

**<**

**sub**

**>**m

**</**

**sub**

**>**

**the**magnetic flux through this loop

**,**

**and**L

**<**

**sub**

**>**m

**,**

**n**

**</**

**sub**

**>**are some constants

**.**

__Here__it also

__denotes__a hand gesture

**,**now linked to three other hand mudrās —

**the**action

**(**karma ), pledge

**(**samaya ),

**and**dharma mudrās — but also involves " mantra recitations

**and**visualizations that symbolize

**and**help to effect one ’

**s**complete identification with a deity ’

**s**divine form or awakening mind

**(**bodhicitta ).

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