Discrete Cartesian Coordinate Transformations: Using Algebraic Extension Methods
Applied Sciences,
Год журнала:
2025,
Номер
15(3), С. 1464 - 1464
Опубликована: Янв. 31, 2025
It
is
shown
that
it
reasonable
to
use
Galois
fields,
including
those
obtained
by
algebraic
extensions,
describe
the
position
of
a
point
in
discrete
Cartesian
coordinate
system
many
cases.
This
approach
applicable
any
problem
which
number
elements
(e.g.,
pixels)
into
considered
fragment
plane
dissected
finite.
In
particular,
obviously
processing
vast
majority
digital
images
actually
encountered
practice.
The
representation
coordinates
using
fields
form
GF(p2)
analog
through
complex
variable.
two
different
types
extensions
can
be
used
simultaneously
represent
transformations
described
fields.
One
corresponds
classical
scheme,
uses
irreducible
equations.
second
type
proposed
this
report
involves
formal
additional
solution
some
equation,
has
usual
solution.
correctness
justified
expansion
matrices
defined
over
basic
field.
basis
for
development
new
methods
information
protection,
designed
control
groups
UAVs
zone
direct
radio
visibility.
such
systems
equations
written
terms
finite
structures.
Язык: Английский
Prospects for the Use of Quasi-Mersen Numbers in the Design of Parallel-Serial Processors
Applied Sciences,
Год журнала:
2025,
Номер
15(2), С. 741 - 741
Опубликована: Янв. 13, 2025
It
is
shown
that
a
serial-parallel
processor,
comparable
in
bit
capacity
to
16-bit
binary
can
be
implemented
based
on
an
algorithm
built
the
residue
number
system,
distinctive
feature
of
which
use
first
four
quasi-Mersenne
numbers,
i.e.,
prime
numbers
representable
as
pk=2k+1,
k=1,2,3,4.
Such
set
satisfies
criterion
2p1p2p3p4+1=P,
where
P
also
number.
Fulfillment
this
ensures
possibility
convenient
considered
RNS
for
calculating
partial
convolutions
developed
convenience
using
convolutional
neural
networks.
processor
proposed
type
adders
modulo
number,
each
operates
independently.
A
circuit
2k+1
adder
proposed,
called
trigger
circuit,
since
its
peculiarity
existence
(at
certain
values
summed
quantities)
two
stable
states.
The
advantage
such
compared
known
analogs,
simplicity
design.
Possibilities
further
development
approach
related
digital
logarithm
operation,
allows
reducing
operations
multiplication
addition
operations,
are
discussed.
Язык: Английский
Hydrogel-based THz wave absorber
Results in Optics,
Год журнала:
2025,
Номер
unknown, С. 100810 - 100810
Опубликована: Март 1, 2025
Язык: Английский
Neural network properties of hydrophilic polymers as a key for development of the general theory of evolution
Royal Society Open Science,
Год журнала:
2025,
Номер
12(4)
Опубликована: Апрель 1, 2025
The
analysis
of
the
existing
literature
demonstrates
that
in
order
to
address
fundamental
challenges
associated
with
origin
life,
it
is
essential
consider
this
problem
from
a
comprehensive
perspective,
specifically
vantage
point
general
theory
evolution
complex
systems.
From
these
positions,
life
should
be
regarded
as
distinctive
instance
an
information
storage
and
processing
system
emerges
naturally.
Evolutionary
processes
examined
coevolution
material
informational
components,
which
has
not
been
sufficiently
emphasized
hitherto.
It
shown
specific
example
respect
analogues
neural
networks
spontaneously
formed
solutions
some
hydrophilic
polymers.
Such
systems
lead
formation
non-trivial
objects.
A
wide
range
other
examples
considered,
proving
occurring
participation
polymers
interpreted,
among
things,
view
objects,
which,
under
certain
conditions,
influence
at
molecular
supramolecular
level.
reasonable
use
tools
classical
dialectics
solve
such
problems
life.
Язык: Английский