2,199 research outputs found
An improved Ant Colony System for the Sequential Ordering Problem
It is not rare that the performance of one metaheuristic algorithm can be
improved by incorporating ideas taken from another. In this article we present
how Simulated Annealing (SA) can be used to improve the efficiency of the Ant
Colony System (ACS) and Enhanced ACS when solving the Sequential Ordering
Problem (SOP). Moreover, we show how the very same ideas can be applied to
improve the convergence of a dedicated local search, i.e. the SOP-3-exchange
algorithm. A statistical analysis of the proposed algorithms both in terms of
finding suitable parameter values and the quality of the generated solutions is
presented based on a series of computational experiments conducted on SOP
instances from the well-known TSPLIB and SOPLIB2006 repositories. The proposed
ACS-SA and EACS-SA algorithms often generate solutions of better quality than
the ACS and EACS, respectively. Moreover, the EACS-SA algorithm combined with
the proposed SOP-3-exchange-SA local search was able to find 10 new best
solutions for the SOP instances from the SOPLIB2006 repository, thus improving
the state-of-the-art results as known from the literature. Overall, the best
known or improved solutions were found in 41 out of 48 cases.Comment: 30 pages, 8 tables, 11 figure
Noncommutative sedeons and their application in field theory
We present sixteen-component values "sedeons", generating associative
noncommutative space-time algebra. The generalized second-order and first-order
equations of relativistic quantum mechanics based on sedeonic wave function and
sedeonic space-time operators are proposed. We also discuss the description of
fields with massive quantum on the basis of second-order and first-order
equations for sedeonic potentials.Comment: 18 pages, 2 table
Octonic Electrodynamics
In this paper we present eight-component values "octons", generating
associative noncommutative algebra. It is shown that the electromagnetic field
in a vacuum can be described by a generalized octonic equation, which leads
both to the wave equations for potentials and fields and to the system of
Maxwell's equations. The octonic algebra allows one to perform compact combined
calculations simultaneously with scalars, vectors, pseudoscalars and
pseudovectors. Examples of such calculations are demonstrated by deriving the
relations for energy, momentum and Lorentz invariants of the electromagnetic
field. The generalized octonic equation for electromagnetic field in a matter
is formulated.Comment: 12 pages, 1 figur
Sedeonic relativistic quantum mechanics
We represent sixteen-component values "sedeons", generating associative
noncommutative space-time algebra. We demonstrate a generalization of
relativistic quantum mechanics using sedeonic wave functions and sedeonic
space-time operators. It is shown that the sedeonic second-order equation for
the sedeonic wave function, obtained from the Einstein relation for energy and
momentum, describes particles with spin 1/2. We show that for the special types
of wave functions the sedeonic second-order equation can be reduced to the set
of sedeonic first-order equations analogous to the Dirac equation. At the same
time it is shown that these sedeonic equations differ in space-time properties
and describe several types of massive and corresponding massless particles. In
particular we proposed four different equations, which could describe four
types of neutrinos.Comment: 22 pages, 3 table
Π€ΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΌΠΈΠΊΡΠΎΡΡΡΡΠΊΡΡΡΡ Π² Ρ ΠΎΠ΄Π΅ ΠΊΡΠΈΠΎΠ³Π΅Π½Π½ΠΎΠΉ ΠΏΡΠΎΠΊΠ°ΡΠΊΠΈ ΠΌΠ΅Π΄ΠΈ
ΠΡΠΎΠ²Π΅Π΄Π΅Π½Π° ΡΡΠ°ΡΠ΅Π»ΡΠ½Π°Ρ Π°ΡΡΠ΅ΡΡΠ°ΡΠΈΡ ΠΌΠΈΠΊΡΠΎΡΡΡΡΠΊΡΡΡΡ ΠΈ ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ²ΠΎΠΉΡΡΠ² ΠΌΠ΅Π΄ΠΈ, ΠΏΠΎΠ΄Π²Π΅ΡΠ³Π½ΡΡΠΎΠΉ ΡΠ°Π·Π»ΠΈΡΠ½ΠΎΠΉ ΡΡΠ΅ΠΏΠ΅Π½ΠΈ ΠΊΡΠΈΠΎΠ³Π΅Π½Π½ΠΎΠΉ ΠΏΡΠΎΠΊΠ°ΡΠΊΠΈ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΡΠ²ΠΎΠ»ΡΡΠΈΡ Π·Π΅ΡΠ΅Π½Π½ΠΎΠΉ ΡΡΡΡΠΊΡΡΡΡ, Π² ΠΎΡΠ½ΠΎΠ²Π½ΠΎΠΌ, ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ»Π°ΡΡ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΠΌ ΡΡΡΠ΅ΠΊΡΠΎΠΌ Π΄Π΅ΡΠΎΡΠΌΠ°ΡΠΈΠΈ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π½Π°Π»ΠΈΠ·Π° ΡΠ΅ΠΊΡΡΡΡΠ½ΡΡ
Π΄Π°Π½Π½ΡΡ
Π±ΡΠ» ΡΠ΄Π΅Π»Π°Π½ Π²ΡΠ²ΠΎΠ΄, ΡΡΠΎ ΠΊΡΠΈΠΎΠ³Π΅Π½Π½ΡΠ΅ ΡΡΠ»ΠΎΠ²ΠΈΡ Π΄Π΅ΡΠΎΡΠΌΠ°ΡΠΈΠΈ Π½Π΅ ΠΏΡΠΈΠ²Π΅Π»ΠΈ ΠΊ ΡΡΠ½Π΄Π°ΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎΠΌΡ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠ° ΠΏΠ»Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ΅ΡΠ΅Π½ΠΈΡ, ΠΈ ΠΎΡΠ½ΠΎΠ²Π½ΡΠΌ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠΎΠΌ Π΄Π΅ΡΠΎΡΠΌΠ°ΡΠΈΠΈ Π±ΡΠ»ΠΎ Π΄ΠΈΡΠ»ΠΎΠΊΠ°ΡΠΈΠΎΠ½Π½ΠΎΠ΅ {111} ΡΠΊΠΎΠ»ΡΠΆΠ΅Π½ΠΈΠ΅. Π£ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ ΠΊΡΠΈΠΎΠ³Π΅Π½Π½Π°Ρ ΠΏΡΠΎΠΊΠ°ΡΠΊΠ° ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡ ΠΊ ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠΌΡ ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΡ ΠΏΡΠΎΡΠ½ΠΎΡΡΠΈ ΠΈ Π½Π΅ΠΊΠΎΡΠΎΡΠΎΠΌΡ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΠΏΠ»Π°ΡΡΠΈΡΠ½ΠΎΡΡΠΈ
ΠΠ»ΠΈΡΠ½ΠΈΠ΅ ΠΊΡΠΈΠΎΠ³Π΅Π½Π½ΠΎΠΉ ΠΎΡΠ°Π΄ΠΊΠΈ Π½Π° ΠΌΠΈΠΊΡΠΎΡΡΡΡΠΊΡΡΡΡ ΠΊΠ°ΡΠ°Π½ΠΎΠΉ ΠΌΠ΅Π»ΠΊΠΎΠ·Π΅ΡΠ½ΠΈΡΡΠΎΠΉ ΠΌΠ΅Π΄ΠΈ
ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½Π° Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΠΈΠ·ΠΌΠ΅Π»ΡΡΠ΅Π½ΠΈΡ Π·Π΅ΡΠ΅Π½ Π² ΡΠ΅Ρ
Π½ΠΈΡΠ΅ΡΠΊΠΈ ΡΠΈΡΡΠΎΠΉ ΠΌΠ΅Π΄ΠΈ ΠΏΡΡΠ΅ΠΌ ΠΊΡΠΈΠΎΠ³Π΅Π½Π½ΠΎΠΉ ΠΎΡΠ°Π΄ΠΊΠΈ. Π£ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ ΡΠ²ΠΎΠ»ΡΡΠΈΡ ΡΡΡΡΠΊΡΡΡΡ Π² ΡΠ΅Π»ΠΎΠΌ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ»Π°ΡΡ ΡΠΏΠ»ΡΡΠΈΠ²Π°Π½ΠΈΠ΅ΠΌ ΠΈΡΡ
ΠΎΠ΄Π½ΡΡ
Π·Π΅ΡΠ΅Π½ Π² Ρ
ΠΎΠ΄Π΅ Π΄Π΅ΡΠΎΡΠΌΠ°ΡΠΈΠΈ. ΠΠ½Π°Π»ΠΈΠ· ΡΠ΅ΠΊΡΡΡΡΠ½ΡΡ
Π΄Π°Π½Π½ΡΡ
ΠΈ ΡΠΏΠ΅ΠΊΡΡΠ° ΡΠ°Π·ΠΎΡΠΈΠ΅Π½ΡΠΈΡΠΎΠ²ΠΎΠΊ ΠΏΠΎΠΊΠ°Π·Π°Π», ΡΡΠΎ ΠΎΡΠ½ΠΎΠ²Π½ΡΠΌ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠΎΠΌ ΠΏΠ»Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΡΠ²Π»ΡΠ»ΠΎΡΡ ΠΎΠ±ΡΡΠ½ΠΎΠ΅ {111} Π΄ΠΈΡΠ»ΠΎΠΊΠ°ΡΠΈΠΎΠ½Π½ΠΎΠ΅ ΡΠΊΠΎΠ»ΡΠΆΠ΅Π½ΠΈΠ΅ ΠΏΡΠΈ Π½Π΅ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠΌ Π²ΠΊΠ»Π°Π΄Π΅ ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π΄Π²ΠΎΠΉΠ½ΠΈΠΊΠΎΠ²Π°Π½ΠΈΡ
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