**Distance **
Last updated on
2018/2562
8
26,
a
full moon
day;

approx. 3.927 kilo meter; approx. 2.44 mile; Radical197;

amount; degree; distance; extent; formula; Radical625;

to be distant; Radical549;

2018/2561; **PHYSICS**;
(law
twenty seven): every light has its ending
distance
WHICH
obey C Sequence Number (BF1);
Also see: halt; stop;
Radical99;
e.g. leaf, leaves, fruit, ... ;

Approx. 8 distances available to read, and this DOMAIN 's
imaginary hyper dimensional hyperspace crafts' horizontal ACT3 gray scale has
been in 5 columns [still do not know the cause
of WHY gray scale is not even to left and to right],
but still calculating __parallel time__ because __natural time__ slows
down in ACT3 stage ... ;

IFF __3,4 dimensional__
imaginary hyper space measurement,
distance is measured
by
iro Colour Wave Form
(yellowish variation as distance)
... ; this
DOMAIN; we human beings can live on many moons
but
B L I diff because of ... e.g. yellowish variation;

WHILE measuring 2-sided surface based computing, IFF wormhole distance > device constraint (limit), capture begins; also see: PHYSICS;

1st to understand static 2-point distance, and then understand n-point distance; 2nd to understand non-static distance between hyperspace1 and hyperspace2, without weight; 3rd to understand non-static weighted distance among ACT2 stage Fuzzy S V M s in hyperplane1 AND hyperplane2;

distance | ; | ||||||||

ri | Distance | ( | position | ) | ; | ||||

ri | Distance | ( | position | ) | ; | ||||

IFF | 2D | , | ri | distance | = | Sqrt | ( | ||

( | ^ | 2 | ) | + | ( | ^ | 2 | ||

) | ) | ; | |||||||

distance | = | SQRT | (( | x^2) | + | ( | y^2 | )) | ; |

。

__ 2-point distance__
to

Point P1 and point P2 lie on a line L ;

If point P1 is called A, and point P2 is called B, and then mathematical distance notation can be symbolized/written as AB;

n numbers of points lie in Euclidean space in ACT1 stage was with n dimensions;

n numbers of points P_{1}, P_{2}, P_{3},
P_{4}, ... , P_{n}; and those n numbers of points must NOT lie
in the same Euclidean space in ACT1 stage was with n - 1 dimensions;

IFF square root of 2 (i.e. SQRT2), also see: 98;

WHERE in xy
plane, in ACT1 stage, __ 1 is
abscissa for P1 and
2 is ordinate for P1__,

IFF AB characteristic is in
USB bus testing, for example
AB = 10 cm, CD = 14 cm, EF = 24 cm, ... [ testing a port's tolerance by
tapping/splitting/sharing/... ] and then notice that USB
bus's tolerate distance becomes constraint along with time; Almost all testing
boards, bus extenders, modular devices, ... are based on, engineered by __
distance vs. time__, some engineers may say "due to attenuation", some
engineers may say "due to resistance", some engineers may say "due to
interference", ... , [**Time . Space . Action**];

spore, IFF iroColourWaveForm (from GREEN to BLUE) WHICH specific spectrum, WHAT is max distance variation of the specific spectrum, WHAT is min distance of the specific spectrum, UPS (i.e. Universal Positioning System) for each location in our universe ... ;

。

IFF
GPS embedded floating poly plastic devices
exist,

WHILE calculating
triangulation
on
one
surface
in the
285
Internet,

for
each
minute,
measure
(
direction
AND
doko
location)
of
each
object
(i.e. GPS
embedded floating poly plastic device),

IFF
(abnormal
fast)
speed,
also see: worm_{=}hole

669
for preventing tsunami, for protecting
tsunami, for reducing tsunami; using
this DOMAIN,
me,
this DOMAIN,
you, ... ;

。

**ACT3 Distance Calculation**, for this DOMAIN 's
imaginary hyper craft's parallel time

1st to understand
numerical values in numerology; 2nd to understand
syntax vs. semantics logic
so that only 3 is essential; 3rd to understand
homological
2 and 3 solves 4PP + JUN = 6;3*3
ACT3 vectors and their dimensions must be further developed, a new ACT3
dimension must be developed; For ACT3 simulation developers, develop
3*3 ACT3 vectors, therefore this DOMAIN 's imaginary hyper dimensional
hyperspace crafts can be able to do displacement of number at parallel time. And
then, ACT3 distance
calculation to prove gray scales simulation scientifically;

。

**Distance Approximation**, with
√
(square
root 2)
model;

if distance approximation, 1st to understand ((1/1), (3/2), (7/5), (17/12), (41/29), (99/70), (239/169), (577/408), ... ) a.k.a. √2 model; 2nd to understand decimal expansion as sequence (e.g. multiples); 3rd to develop C Sequence Number for each distance;

Also read the book: THE SQUARE ROOT OF 2, DAVID FLANNERY, 2006 Praxis Publishing Ltd., Library of Congress Control Number: 2005923268, ISBN-13: 978-0387-20220-4, page 191, chapter 5 (Odds and Ends);

。

__ ACT3 Heat
Distance Simulation__, for this DOMAIN 's imaginary hyper crafts' parallel
time,

After understanding __4 Planets Prediction, and then JUN
time__, 1st to understand is 1 stick of light, and then sticks as strings must
be thoroughly understood; In this DOMAIN 's imaginary hyper dimensional hyperspace
craft, 44 sticks need 4 holes to engineer 1 gravity symbol, but heat in distance
has not been tested yet, for example: heat in 24 mm natural time might be diff
IFF ACT3 hyper crafts went very very very far away from our universe ... ;
Therefore, __cold and dark room environmental simulation__ is a must to
measure heat in distance, and then ... ; Also read: Oct., 2007 Volume XVII
Number 3 LINEAR TECHNOLOGY; Fuzzy Gray Scale Simulation;

。

__ Damerau & Levenshtein distance,
1964__:

An extension of Levenshtein distance; In addition to Levenshtein distance, additional recurrence has been computed, a.k.a. transposition, and calculated as:

{TRUE}

if ( i > 1 AND j > 1 AND string[ i ] = string [ j - 1 ] AND string[ i - 1 ] = string [ j ] ) then

2d_array [ i, j ] := is going to be assigned min (

2d_array [ i, j ],

2d_array [ i - 2, j - 2 ] + cost

)

Damerau & Levenshtein distance is a.k.a. edit distance. Can be used in natural language processing; Cannot be used in Metric tree;

/****/

Damerau & Levenshtein distance between string and string can be written as:

declare integer 2d_array [ 0 .. length_of_string, 0 .. length_of_string ] /*** 2D table */

declare integer i, j, cost /*** defined variable */

integer Damerau_Levenshtein_distance (character_data_type string [ 1 .. length_of_string ], character_data_type string [ 1 .. length_of_string ] )

/*** WHERE d table contains length_of_string + 1 rows AND length_of_string columns */

For i from 0 to length_of_string

2d_array [ i, 0 ] := is going to be assigned i

For j from 0 to length_of_string

2d_array [ 0, j ] := is going to be assigned j

For i from 1 to length_of_string For j from 1 to length_of_string

If string[ i ] = string[ j ] then

cost := is going to be assigned 0

else

cost := is going to be assigned 1

2d_array [ i, j ] :=
is going to be
assigned min (parameterA, parameterB, parameterC)
/*** 3 parameters
*/ WHERE parameterA is 2d_array [ i - 1, j ] + 1 for **deletion**,
parameterB is 2d_array [ i, j - 1] + 1 for **insertion**, parameterC is
2d_array [ i - 1, j - 1 ] + cost for **substitution**

if ( i > 1 AND j > 1 AND string[ i ] = string [ j - 1 ] AND string[ i - 1 ] = string [ j ] ) then

2d_array [ i, j ] :=
is going to be assigned
min (parameterD, parameterE)
/*** 2 parameters */
WHERE parameterD is 2d_array [ i,
j ] for **transposition**, parameterE is 2d_array [ i - 2, j - 2 ] + cost for **
transposition**

return 2d_array [return_parameterX, return_parameterY] /*** 2 return_integer_parameters after function integer Damerau_Levenshtein_distance () is called */ WHERE return_parameterX is length_of_string, and return_parameterY is length_of_string

/*** also read: invariant correctness, longest common subsequence problem, upper bound and lower bound, ... , for THIS distance; */

{TRUE} ;

。

__Fuzzy ____
distance, Foundations of Soft Case-Based
Reasoning, Pal & Shiu, 2004__:

WHERE corresponding objects "not subjects" in different coordinates, and those objects' locations can be represented as set of real numbers, and those sets are needed to be ordered [also see: Orbit] therefore must be weighted;

FuzzySVMs' traveling journeys
can be collected as {F_{journey}
(journey = 1, 2,
3, 4, 5,
6, ...) and notice that
journey 1, 2,
3, 4, 5, 6, ... n can become
N Euclidean distances;

Therefore N **E**uclidean **d**istances
can be represented as:

distance_without_weight = {
Ed_{1}, Ed_{2}, Ed_{3}, Ed_{4}, ... , Ed_{N }
};

For each Ed
i^{th}
, dimensional vector (n + 1) can be represented as:

Ed_{i} = (xyz_{i1}, xyz_{i2},
xyz_{i3}, xyz_{i4}, ... , xyz_{iN}, θ_{i});

WHERE xyz_{ij}
corresponds to fuzzy member functions of

F_{journey}
( 1 〱= j 〱= n ) AND
θ_{i }
corresponds 〉Dimensional Time.Space.Action's

action ( i = 1, 2, 3, 4, 5, 6, ... , N);

For each F_{journey}
( 1 〱= j 〱= n ),

**W**eight W_{journey} ( W_{journey}
Є [ O, 1] );

**W**eighted **d**istance:

Wd_{AȢ} = Wd (
Ed_{1}_{A},
Ed_{1}_{Ȣ}
) = [ _{journey = 1}Σ^{n} W^{2}_{journey} (X_{Ajourney}
- XȢ_{journey})^{2} ]^{1/2}

a.k.a.
( _{journey = 1}Σ^{n} W^{2}_{journey}
X^{2}_{journey
})^{1/2} ;

WHERE X^{2}_{journey }= (X_{Ajourney}
- XȢ_{journey})^{2;}

**W**eighted **S**imilarity **M**easurement:

WSM_{AȢ}
= 1 / ( 1 + positive constant
カ **
W**eighted
**d**istance Wd_{AȢ} );

Mapping
〱Fuzzy_{journey} X Fuzzy_{journey}
〉[ O, infinity ],

WHERE **p**oint p_{journey}
of distance follows:

**p**oint p_{journey} ( A, Ȣ) = O IFF A = Ȣ;Also
see:
2-point distance

**p**oint p_{journey} ( A, Ȣ ) = **p**oint p_{journey}
( Ȣ, A );

**p**oint p_{journey} ( A, Ȣ )
〱=
less than or equal
to **p**oint p_{journey} ( A, C
) + **p**oint p_{journey}
( C, Ȣ );n-point

IFF A AND Ȣ are real numbers,

**p**oint p_{journey}
( A, Ȣ ) = | A - Ȣ |;

IFF string AND string are intervals,

**p**oint p_{journey} ( string,
string ) =
max_{AЄstring,
ȢЄstring}
| A - Ȣ |;

{ | 1 | if A ≠ Ȣ | ||

IFF A AND Ȣ are symbols, | point p_{journey}
( A, Ȣ ) = |
|||

O | if A = Ȣ |

Thus weighted fuzzy distance:

= カsquare
root of
√ ( _{
journey = 1}Σ^{n} W^{2}_{journey } **p**oint p^{2}_{journey}
(
Ed_{1}_{A},
Ed_{1}_{Ȣ}
) );

。

__ Hamming & Levenshtein distance__:

In data communication, WHEN error detection and error correction are needed, Hamming & Levenshtein distance is used.

Levenshtein distance, a.k.a. Edit distance

。

__ Jaro & Winkler distance,
1999__:

Distance d_{j }= ( m
/ 3a) + (m / 3b) + ((m - t ) / 3m) WHERE **m**atching
characters are m; length_of_string
and length_of_string
are a and b; numbers of transpositions is t; AND
any 2 characters in string1 and string2 must not farther than max (( a, b ) / 2)
- 1;

__Length of common prefixes l__ with __prefix constant
scale factor p__ prompt Jaro & Winkler distance
for string
and string
can be calculated with weighted as:

d_{w} = d_{j }+ ( l * p * (1 - d_{j}
))

。

__ k-NN algorithm & k-Nearest Neighbor calculation__:

...

millibar ( distance) GDC, using artificial intelligence ... ;

** pore-pore
distance**, [Progress in Transmission
Electron Microscopy 2; Applications in Materials Science; Xiao-Feng Zhang;
Ze
Zhang; Tsinghua University Press and Springer-Verlag Berlin Heidelberg; 2001]

In ACT2 stage, distance has
been defined by __time and number__
Eastern Thought must be understood 1st,
WHEN time has been 4 planets
prediction's 2*7, and JUN time 2*5, WHERE
space can be defined by
locations,
WHAT number has been
by depth and structure as [A, B,
C, D, E, ... ] numbers; Surface study in
material engineering in ACT1 stage, by electron microscopes, silicate ions'
circle characteristic in 5nm ~ 6nm, and those circles
seem larger if those circles are near/close to __particle's surface__,
and those circles seem smaller if those circles are longer/farther to particle's
surface, WHERE pore's axis must be parallel to particle's surface;
The285 distance WHICH
initializes "those circles seem larger if those circles
are near/close to __particle's surface__"
is called/defined as __pore-pore distance__ in ACT1 stage;

Before understanding carbon nano wall, pore-pore distance must be understood; Carbon study such as C60 and above number+ i.e. C70, C76, ... are a.k.a. carbon nanotubes, and ACT3 artificial light, ACT2 gravity7water2, ACT2 gravity2water7, ... must be understood thoroughly.

。

**this DOMAIN 's imaginary ACT3 hyper dimensional
distance**

Consider the following table, and then draw/draft a __
fully
connected / fully distributed connection__, and then whether full moon
day, or no moon day, or
up JUN, or
middle JUN, or
down JUN, ... ; For ACT2, ACT3 Monbusho grant awarded developers, develop
D number
for next generation children, ... ;

C number | 2-point | D number | Numerology | U number | |||||||

1to1 | 3 | 3 | 5 | … | |||||||

1to2 | 62 | 8 | … | ||||||||

1to3 | 74 | 2 | … | ||||||||

1to4 | 89 | 7 | … | ||||||||

1to5 | 69 | 6 | … | ||||||||

2to1 | 62 | 8 | 3 | … | |||||||

2to2 | 3 | 3 | … | ||||||||

2to3 | 26 | 8 | … | ||||||||

2to4 | 69 | 6 | … | ||||||||

2to5 | 89 | 8 | … | ||||||||

3to1 | 74 | 2 | 1 | … | |||||||

3to2 | 26 | 8 | … | ||||||||

3to3 | 4 | 4 | … | ||||||||

3to4 | 44 | 8 | … | ||||||||

3to5 | 78 | 6 | … | ||||||||

4to1 | 89 | 8 | 4 | … | |||||||

4to2 | 69 | 6 | … | ||||||||

4to3 | 44 | 8 | … | ||||||||

4to4 | 3 | 3 | … | ||||||||

4to5 | 54 | 9 | … | ||||||||

5to1 | 69 | 6 | 2 | … | |||||||

5to2 | 89 | 8 | … | ||||||||

5to3 | 78 | 6 | … | ||||||||

5to4 | 54 | 9 | … | ||||||||

5to5 | 3 | 3 | … | ||||||||

1to6 | 181 | 1 | 6 | … | |||||||

2to6 | 169 | 7 | … | ||||||||

3to6 | 143 | 8 | … | ||||||||

4to6 | 101 | 2 | … | ||||||||

5to6 | 119 | 2 | … | ||||||||

6to6 | 4 | 4 | … |

Above table's (E3, E3, E3) color, also see: Lo Shu 's any direction IFF ... ;

time time AND 1, 2, 3, 4, 5, 6, ... number = distance; ACT2 and ACT3 stage parallel time calculation is in progress, also see: 2554; Also see: yojana (distance measured in Pali);

WHICH spectrum of66 location in95 distance, to be 3D Display, without eye-glasses ... ;

For Monbusho level developers, also see: AI global characters IQ;

Develop D number, DEE, Water Clock, ... until ACT3 number 31 can be solved scientifically ... ;

IFF WCS, using GPS ( locating) WCS location, 95 ♯ cm distance direction ... ;

Also see: ri distance;

^{_ }IFF
distance in95 time, a.k.a.
Quality; 4PP+JUN=6;

^{_ }IFF
power
at12 distances (♯
c
meter; ♯
m meter; ♯
... )
electromagnetic induction OR
magnetic resonance;
solar tree;

。

...