1,396 research outputs found
Zel'dovich states with very small mass and charge in nonlinear electrodynamics coupled to gravity
It is shown that in non-linear electrodynamics (in particular, Born-Infeld
one) in the framework of general relativity there exist "weakly singular"
configurations such that (i) the proper mass M is finite in spite of
divergences of the energy density, (ii) the electric charge q and Schwarzschild
mass m ~ q can be made as small as one likes, (iv) all field and energy
distributions are concentrated in the core region. This region has an almost
zero surface area but a finite longitudinal size L=2M. Such configurations can
be viewed as a new version of a classical analogue of an elementary particle.Comment: 11 pages. 1 reference added. To appear in Grav. Cosm
Bunch-excited wakefield in dielectric waveguide with hollow plasma channel
Wakefield excitation by a single relativistic electron bunch in a
plasma-dielectric accelerating structure has been studied both analytically and
numerically. The structure represents a dielectric-loaded cylindrical metal
waveguide, which has partially plasma-filled channel (the hollow plasma
channel) to transport charged particles. Assuming the linear regime of
excitation, analytical expressions have been derived for the longitudinal and
radial wakefields generated by a finite-size electron bunch. Axial profiles of
wakefield component amplitudes have been studied, and their mode and spectrum
analyses have been performed. Furthermore, the electron bunch-driven wakefield
excitation has been PIC-simulated numerically for the quasi-linear regime. The
comparative analysis of the data resulting from analytical studies and the ones
obtained by numerical simulation has demonstrated qualitative agreement between
the results
Reversible Logic Circuit Synthesis
Reversible or information-lossless circuits have applications in digital
signal processing, communication, computer graphics and cryptography. They are
also a fundamental requirement in the emerging field of quantum computation. We
investigate the synthesis of reversible circuits that employ a minimum number
of gates and contain no redundant input-output line-pairs (temporary storage
channels). We prove constructively that every even permutation can be
implemented without temporary storage using NOT, CNOT and TOFFOLI gates. We
describe an algorithm for the synthesis of optimal circuits and study the
reversible functions on three wires, reporting distributions of circuit sizes.
We study circuit decompositions of reversible circuits where gates of the same
type are next to each other. Finally, in an application important to quantum
computing, we synthesize oracle circuits for Grover's search algorithm, and
show a significant improvement over a previously proposed synthesis algorithm.Comment: 30 pages, 14 figs+tables. To appear in IEEE Transactions on
Computer-Aided Design of Electronic Circuits. Contains results presented at
the Intl. Conf. on Computer-Aided Design, 2002 and new material on
decompositions of reversible circuits where gates of the same type are next
to each othe
Hadron and Quark Form Factors in the Relativistic Harmonic Oscillator Model
Nucleon, pion and quark form factors are studied within the relativistic
harmonic oscillator model including the quark spin. It is shown that the
nucleon charge, magnetic and axial form factors and the pion charge form factor
can be explained with one oscillator parameter if one accounts for the scaling
rule and the size of the constituent quarks.Comment: 9 pages, Latex, 3 postscript figures, DFTT 8/9
The Boltzmann equation for colourless plasmons in hot QCD plasma. Semiclassical approximation
Within the framework of the semiclassical approximation, we derive the
Boltzmann equation describing the dynamics of colorless plasmons in a hot QCD
plasma. The probability of the plasmon-plasmon scattering at the leading order
in the coupling constant is obtained. This probability is gauge-independent at
least in the class of the covariant and temporal gauges. It is noted that the
structure of the scattering kernel possesses important qualitative difference
from the corresponding one in the Abelian plasma, in spite of the fact that we
focused our study on the colorless soft excitations. It is shown that
four-plasmon decay is suppressed by the power of relative to the process of
nonlinear scattering of plasmons by thermal particles at the soft momentum
scale. It is stated that the former process becomes important in going to the
ultrasoft region of the momentum scale.Comment: 41, LaTeX, minor changes, identical to published versio
Optical extinction, refractive index, and multiple scattering for suspensions of interacting colloidal particles
We provide a general microscopic theory of the scattering cross-section and
of the refractive index for a system of interacting colloidal particles, exact
at second order in the molecular polarizabilities. In particular: a) we show
that the structural features of the suspension are encoded into the forward
scattered field by multiple scattering effects, whose contribution is essential
for the so-called "optical theorem" to hold in the presence of interactions; b)
we investigate the role of radiation reaction on light extinction; c) we
discuss our results in the framework of effective medium theories, presenting a
general result for the effective refractive index valid, whatever the
structural properties of the suspension, in the limit of particles much larger
than the wavelength; d) by discussing strongly-interacting suspensions, we
unravel subtle anomalous dispersion effects for the suspension refractive
index.Comment: Submitted to Journal of Chemical Physics 37 pages, 4 figure
ΠΠ·Π°ΡΠΌΠΎΠ΄ΡΡ 4,5-Π΄ΠΈΡΠΎΡΠΌΡΠ»-2,3,6,7,8,10-Π³Π΅ΠΊΡΠ°Π³ΡΠ΄ΡΠΎΠ°ΠΊΡΠΈΠ΄ΠΈΠ½-8Π°(1Π)-ΠΊΠ°ΡΠ±ΠΎΠ½ΡΡΡΠΈΠ»Ρ Π· N-Π½ΡΠΊΠ»Π΅ΠΎΡΡΠ»Π°ΠΌΠΈ
Schiff bases are of practical interest as initial materials both for the combinatorial synthesis for libraries of compounds, and for preparation of complexes with metals; thus, currently the intensity of research in this direction is increasing. The possibilities of practical use of complex compounds with organic ligands are quite broad varying from effective catalysts of various chemical processes to molecular sensors. While studying formylation of 5,6,7,8-tetrahydro-1H-spiro[cyclohexane-1,2-quinazolin]-4β(3βH)-one a new domino reaction, which makes it possible to obtain tricyclic acridine systems, has been carried out. In spite of the reduced electrophilicity of the aldehyde groups in 4,5-diformyl-2,3,6,7,8,10-hexahydroacridine-8Π°(1H)-carbonitrile the latter is shown to react with various amines in benzene with azeotropic removal of water using p-TsOH as a catalyst, and with hydroxylamine hydrochloride in i-PrOH. New Schiff bases and oxime obtained are of potential interest as ligands for formation of chelate complexes. The reaction of dialdehyde with N2H4ΓH2O instead of the expected hydrazone resulted in obtaining a macrocyclic compound β a derivative of hexaazacyclooctadecine. The structure of the compounds obtained corresponds to the data of 1H NMR-spectroscopy, mass spectrometry and elemental analysis. The preliminary studies have shown that azomethines β 4,5-phenyl(cyclohexcyl)iminomethyl-2,3,6,7,8,10-hexahydroacridine8Π°(1H)-carbonitrile create complexes with copper and nickel ions.ΠΡΠ½ΠΎΠ²Π°Π½ΠΈΡ Π¨ΠΈΡΡΠ° ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΠΈΠ½ΡΠ΅ΡΠ΅Ρ Π² ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΈΡΡ
ΠΎΠ΄Π½ΡΡ
ΠΊΠ°ΠΊ Π΄Π»Ρ ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΎΡΠ½ΠΎΠ³ΠΎ ΡΠΈΠ½ΡΠ΅Π·Π° Π±ΠΈΠ±Π»ΠΈΠΎΡΠ΅ΠΊ Π²Π΅ΡΠ΅ΡΡΠ², ΡΠ°ΠΊ ΠΈ Π΄Π»Ρ ΡΠΎΠ·Π΄Π°Π½ΠΈΡ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠΎΠ² Ρ ΠΌΠ΅ΡΠ°Π»Π»Π°ΠΌΠΈ, ΠΈ Π² ΠΏΠΎΡΠ»Π΅Π΄Π½Π΅Π΅ Π²ΡΠ΅ΠΌΡ ΠΈΠ½ΡΠ΅Π½ΡΠΈΠ²Π½ΠΎΡΡΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ Π² Π΄Π°Π½Π½ΠΎΠΌ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠΈ ΡΠΎΠ»ΡΠΊΠΎ ΡΠ²Π΅Π»ΠΈΡΠΈΠ²Π°Π΅ΡΡΡ. ΠΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½ΡΡ
ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ Ρ ΠΎΡΠ³Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ Π»ΠΈΠ³Π°Π½Π΄Π°ΠΌΠΈ Π²Π΅ΡΡΠΌΠ° ΡΠΈΡΠΎΠΊΠΈ: ΠΎΡ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΡΡ
ΠΊΠ°ΡΠ°Π»ΠΈΠ·Π°ΡΠΎΡΠΎΠ² ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
Ρ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² Π΄ΠΎ ΠΌΠΎΠ»Π΅ΠΊΡΠ»ΡΡΠ½ΡΡ
ΡΠ΅Π½ΡΠΎΡΠΎΠ². Π Ρ
ΠΎΠ΄Π΅ ΠΈΠ·ΡΡΠ΅Π½ΠΈΡ ΡΠΎΡΠΌΠΈΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ 5β,6β,7β,8β-ΡΠ΅ΡΡΠ°Π³ΠΈΠ΄ΡΠΎ-1βΠ-ΡΠΏΠΈΡΠΎ[ΡΠΈΠΊΠ»ΠΎΠ³Π΅ΠΊΡΠ°Π½-1,2β-Ρ
ΠΈΠ½Π°Π·ΠΎΠ»ΠΈΠ½]-4β(3βΠ)-ΠΎΠ½Π° Π½Π°ΠΌΠΈ Π±ΡΠ»Π° Π½Π°ΠΉΠ΄Π΅Π½Π° Π½ΠΎΠ²Π°Ρ Π΄ΠΎΠΌΠΈΠ½ΠΎ-ΡΠ΅Π°ΠΊΡΠΈΡ, ΠΊΠΎΡΠΎΡΠ°Ρ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ Π²ΡΠΉΡΠΈ Π½Π° ΡΡΠΈΡΠΈΠΊΠ»ΠΈΡΠ΅ΡΠΊΠΈΠ΅ Π³ΠΈΠ΄ΡΠΈΡΠΎΠ²Π°Π½Π½ΡΠ΅ Π°ΠΊΡΠΈΠ΄ΠΈΠ½ΠΎΠ²ΡΠ΅ ΡΠΈΡΡΠ΅ΠΌΡ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ Π½Π΅ΡΠΌΠΎΡΡΡ Π½Π° ΡΠ½ΠΈΠΆΠ΅Π½Π½ΡΡ ΡΠ»Π΅ΠΊΡΡΠΎΡΠΈΠ»ΡΠ½ΠΎΡΡΡ Π°Π»ΡΠ΄Π΅Π³ΠΈΠ΄Π½ΡΡ
Π³ΡΡΠΏΠΏ Π² 4,5-Π΄ΠΈΡΠΎΡΠΌΠΈΠ»2,3,6,7,8,10-Π³Π΅ΠΊΡΠ°Π³ΠΈΠ΄ΡΠΎΠ°ΠΊΡΠΈΠ΄ΠΈΠ½-8Π°(1Π)-ΠΊΠ°ΡΠ±ΠΎΠ½ΠΈΡΡΠΈΠ»Π΅, ΠΎΠ½ ΡΠ΅Π°Π³ΠΈΡΡΠ΅Ρ Ρ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠΌΠΈ Π°ΠΌΠΈΠ½Π°ΠΌΠΈ Π² Π±Π΅Π½Π·ΠΎΠ»Π΅ Ρ Π°Π·Π΅ΠΎΡΡΠΎΠΏΠ½ΠΎΠΉ ΠΎΡΠ³ΠΎΠ½ΠΊΠΎΠΉ Π²ΠΎΠ΄Ρ Ρ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ΠΌ Π² ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΊΠ°ΡΠ°Π»ΠΈΠ·Π°ΡΠΎΡΠ° p-TsOH, Π° ΡΠ°ΠΊΠΆΠ΅ Ρ ΡΠΎΠ»ΡΠ½ΠΎΠΊΠΈΡΠ»ΡΠΌ Π³ΠΈΠ΄ΡΠΎΠΊΡΠΈΠ»Π°ΠΌΠΈΠ½ΠΎΠΌ Π² i-PrOH. ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΡ Π¨ΠΈΡΡΠ° ΠΈ ΠΎΠΊΡΠΈΠΌ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΡΡ ΠΏΠΎΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΠΉ ΠΈΠ½ΡΠ΅ΡΠ΅Ρ Π² ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ Π»ΠΈΠ³Π°Π½Π΄ΠΎΠ² Π΄Π»Ρ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ Ρ
Π΅Π»Π°ΡΠ½ΡΡ
ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠΎΠ². Π ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΡΠ΅Π°ΠΊΡΠΈΠΈ Π΄ΠΈΠ°Π»ΡΠ΄Π΅Π³ΠΈΠ΄Π° Ρ N2H4ΓH2O Π²ΠΌΠ΅ΡΡΠΎ ΠΎΠΆΠΈΠ΄Π°Π΅ΠΌΠΎΠ³ΠΎ Π³ΠΈΠ΄ΡΠ°Π·ΠΎΠ½Π° ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΎ ΠΌΠ°ΠΊΡΠΎΡΠΈΠΊΠ»ΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠ΅ β ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΠΎΠ΅ Π³Π΅ΠΊΡΠ°Π°Π·Π°ΡΠΈΠΊΠ»ΠΎΠΎΠΊΡΠ°Π΄Π΅ΡΠΈΠ½Π°. Π‘ΡΡΠΎΠ΅Π½ΠΈΠ΅ Π²ΡΠ΅Ρ
ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ ΡΠΎΠ³Π»Π°ΡΡΠ΅ΡΡΡ Ρ Π΄Π°Π½Π½ΡΠΌΠΈ Π―ΠΠ 1Π-ΡΠΏΠ΅ΠΊΡΡΠΎΡΠΊΠΎΠΏΠΈΠΈ, ΠΌΠ°ΡΡ-ΡΠΏΠ΅ΠΊΡΡΠΎΠΌΠ΅ΡΡΠΈΠΈ ΠΈ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠ½ΠΎΠ³ΠΎ Π°Π½Π°Π»ΠΈΠ·Π°. ΠΡΠ΅Π΄Π²Π°ΡΠΈΡΠ΅Π»ΡΠ½ΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎΠΊΠ°Π·Π°Π»ΠΈ, ΡΡΠΎ Π°Π·ΠΎΠΌΠ΅ΡΠΈΠ½Ρ β 4,5-ΡΠ΅Π½ΠΈΠ»(ΡΠΈΠΊΠ»ΠΎΠ³Π΅ΠΊΡΠΈΠ»)ΠΈΠΌΠΈΠ½ΠΎΠΌΠ΅ΡΠΈΠ»-2,3,6,7,8,10-Π³Π΅ΠΊΡΠ°Π³ΠΈΠ΄ΡΠΎΠ°ΠΊΡΠΈΠ΄ΠΈΠ½-8Π°(1Π)ΠΊΠ°ΡΠ±ΠΎΠ½ΠΈΡΡΠΈΠ»Π° ΠΎΠ±ΡΠ°Π·ΡΡΡ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½ΡΠ΅ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΡ Ρ ΠΈΠΎΠ½Π°ΠΌΠΈ Π½ΠΈΠΊΠ΅Π»Ρ ΠΈ ΠΌΠ΅Π΄ΠΈ.Β ΠΡΠ½ΠΎΠ²ΠΈ Π¨ΠΈΡΡΠ° ΡΡΠ°Π½ΠΎΠ²Π»ΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ½ΠΈΠΉ ΡΠ½ΡΠ΅ΡΠ΅Ρ Π² ΡΠΊΠΎΡΡΡ Π²ΠΈΡ
ΡΠ΄Π½ΠΈΡ
ΡΠΊ Π΄Π»Ρ ΠΊΠΎΠΌΠ±ΡΠ½Π°ΡΠΎΡΠ½ΠΎΠ³ΠΎ ΡΠΈΠ½ΡΠ΅Π·Ρ Π±ΡΠ±Π»ΡΠΎΡΠ΅ΠΊ ΡΠ΅ΡΠΎΠ²ΠΈΠ½, ΡΠ°ΠΊ Ρ Π΄Π»Ρ ΡΡΠ²ΠΎΡΠ΅Π½Π½Ρ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΡΠ² Π· ΠΌΠ΅ΡΠ°Π»Π°ΠΌΠΈ, Ρ ΠΎΡΡΠ°Π½Π½ΡΠΌ ΡΠ°ΡΠΎΠΌ ΡΠ½ΡΠ΅Π½ΡΠΈΠ²Π½ΡΡΡΡ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Ρ Ρ Π΄Π°Π½ΠΎΠΌΡ Π½Π°ΠΏΡΡΠΌΠΊΡ ΡΡΠ»ΡΠΊΠΈ Π·Π±ΡΠ»ΡΡΡΡΡΡΡΡ. ΠΠΎΠΆΠ»ΠΈΠ²ΠΎΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ½ΠΎΠ³ΠΎ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΡΠ² Π· ΠΎΡΠ³Π°Π½ΡΡΠ½ΠΈΠΌΠΈ Π»ΡΠ³Π°Π½Π΄Π°ΠΌΠΈ Π΄ΠΎΡΠΈΡΡ ΡΠΈΡΠΎΠΊΡ: Π²ΡΠ΄ Π΅ΡΠ΅ΠΊΡΠΈΠ²Π½ΠΈΡ
ΠΊΠ°ΡΠ°Π»ΡΠ·Π°ΡΠΎΡΡΠ² Ρ
ΡΠΌΡΡΠ½ΠΈΡ
ΠΏΡΠΎΡΠ΅ΡΡΠ² Π΄ΠΎ ΠΌΠΎΠ»Π΅ΠΊΡΠ»ΡΡΠ½ΠΈΡ
ΡΠ΅Π½ΡΠΎΡΡΠ². Π£ Ρ
ΠΎΠ΄Ρ Π²ΠΈΠ²ΡΠ΅Π½Π½Ρ ΡΠΎΡΠΌΡΠ»ΡΠ²Π°Π½Π½Ρ 5β,6β,7β,8β-ΡΠ΅ΡΡΠ°Π³ΡΠ΄ΡΠΎ-1βΠ-ΡΠΏΡΡΠΎ[ΡΠΈΠΊΠ»ΠΎΠ³Π΅ΠΊΡΠ°Π½-1,2β-Ρ
ΡΠ½Π°Π·ΠΎΠ»ΡΠ½]-4β(3βΠ)-ΠΎΠ½Ρ Π½Π°ΠΌΠΈ Π±ΡΠ»Π° Π²ΡΠ΄ΠΊΡΠΈΡΠ° Π½ΠΎΠ²Π° Π΄ΠΎΠΌΡΠ½ΠΎ-ΡΠ΅Π°ΠΊΡΡΡ, ΡΠΊΠ° Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡ Π²ΠΈΠΉΡΠΈ Π½Π° ΡΡΠΈΡΠΈΠΊΠ»ΡΡΠ½Ρ Π³ΡΠ΄ΡΠΎΠ²Π°Π½Ρ Π°ΠΊΡΠΈΠ΄ΠΈΠ½ΠΎΠ²Ρ ΡΠΈΡΡΠ΅ΠΌΠΈ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΠΎ Π½Π΅Π·Π²Π°ΠΆΠ°ΡΡΠΈ Π½Π° Π·Π½ΠΈΠΆΠ΅Π½Ρ Π΅Π»Π΅ΠΊΡΡΠΎΡΡΠ»ΡΠ½ΡΡΡΡ Π°Π»ΡΠ΄Π΅Π³ΡΠ΄Π½ΠΈΡ
Π³ΡΡΠΏ Ρ 4,5-Π΄ΠΈΡΠΎΡΠΌΡΠ»-2,3,6,7,8,10-Π³Π΅ΠΊΡΠ°Π³ΡΠ΄ΡΠΎΠ°ΠΊΡΠΈΠ΄ΠΈΠ½Ρ-8Π°(1Π)-ΠΊΠ°ΡΠ±ΠΎΠ½ΡΡΡΠΈΠ»Ρ, Π²ΡΠ½ ΡΠ΅Π°Π³ΡΡ Π· ΡΡΠ·Π½ΠΈΠΌΠΈ Π°ΠΌΡΠ½Π°ΠΌΠΈ Ρ Π±Π΅Π½Π·ΠΎΠ»Ρ Π· Π°Π·Π΅ΠΎΡΡΠΎΠΏΠ½ΠΎΡ Π²ΡΠ΄Π³ΠΎΠ½ΠΊΠΎΡ Π²ΠΎΠ΄ΠΈ Π· Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½ΡΠΌ Π² ΡΠΊΠΎΡΡΡ ΠΊΠ°ΡΠ°Π»ΡΠ·Π°ΡΠΎΡΠ° p-TsOH, Π° ΡΠ°ΠΊΠΎΠΆ Π· ΡΠΎΠ»ΡΠ½ΠΎΠΊΠΈΡΠ»ΠΈΠΌ Π³ΡΠ΄ΡΠΎΠΊΡΠΈΠ»Π°ΠΌΡΠ½ΠΎΠΌ Ρ i-PrOH. ΠΡΡΠΈΠΌΠ°Π½Ρ ΠΎΡΠ½ΠΎΠ²ΠΈ Π¨ΠΈΡΡΠ° ΡΠ° ΠΎΠΊΡΠΈΠΌ ΡΡΠ°Π½ΠΎΠ²Π»ΡΡΡ ΠΏΠΎΡΠ΅Π½ΡΡΠΉΠ½ΠΈΠΉ ΡΠ½ΡΠ΅ΡΠ΅Ρ Ρ ΡΠΊΠΎΡΡΡ Π»ΡΠ³Π°Π½Π΄ΡΠ² Π΄Π»Ρ ΡΡΠ²ΠΎΡΠ΅Π½Π½Ρ Ρ
Π΅Π»Π°ΡΠ½ΠΈΡ
ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΡΠ². Π£ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠ΅Π°ΠΊΡΡΡ Π΄ΡΠ°Π»ΡΠ΄Π΅Π³ΡΠ΄Ρ Π· N2H4ΓH2O Π·Π°ΠΌΡΡΡΡ ΠΎΡΡΠΊΡΠ²Π°Π½ΠΎΠ³ΠΎ Π³ΡΠ΄ΡΠ°Π·ΠΎΠ½Ρ ΠΎΡΡΠΈΠΌΠ°Π½ΠΎ ΠΌΠ°ΠΊΡΠΎΡΠΈΠΊΠ»ΡΡΠ½Ρ ΡΠΏΠΎΠ»ΡΠΊΡ β ΠΏΠΎΡ
ΡΠ΄Π½Ρ Π³Π΅ΠΊΡΠ°Π°Π·Π°ΡΠΈΠΊΠ»ΠΎΠΎΠΊΡΠ°Π΄Π΅ΡΠΈΠ½Ρ. ΠΡΠ΄ΠΎΠ²Π° Π²ΡΡΡ
ΠΎΡΡΠΈΠΌΠ°Π½ΠΈΡ
ΡΠΏΠΎΠ»ΡΠΊ ΠΏΡΠ΄ΡΠ²Π΅ΡΠ΄ΠΆΠ΅Π½Π° Π΄Π°Π½ΠΈΠΌΠΈ Π―ΠΠ 1Π-ΡΠΏΠ΅ΠΊΡΡΠΎΡΠΊΠΎΠΏΡΡ, ΠΌΠ°Ρ-ΡΠΏΠ΅ΠΊΡΡΠΎΠΌΠ΅ΡΡΡΡ Ρ Π΅Π»Π΅ΠΌΠ΅Π½ΡΠ½ΠΎΠ³ΠΎ Π°Π½Π°Π»ΡΠ·Ρ. ΠΠΎΠΏΠ΅ΡΠ΅Π΄Π½Ρ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΠΏΡΠΎΠ΄Π΅ΠΌΠΎΠ½ΡΡΡΡΠ²Π°Π»ΠΈ, ΡΠΎ Π°Π·ΠΎΠΌΠ΅ΡΠΈΠ½ΠΈ β 4,5-ΡΠ΅Π½ΡΠ»(ΡΠΈΠΊΠ»ΠΎΠ³Π΅ΠΊΡΠΈΠ»)ΡΠΌΡΠ½ΠΎΠΌΠ΅ΡΠΈΠ»-2, 3,6,7,8,10-Π³Π΅ΠΊΡΠ°Π³ΡΠ΄ΡΠΎΠ°ΠΊΡΠΈΠ΄ΠΈΠ½-8Π°(1Π)-ΠΊΠ°ΡΠ±ΠΎΠ½ΡΡΡΠΈΠ»Ρ ΡΡΠ²ΠΎΡΡΡΡΡ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½Ρ ΡΠΏΠΎΠ»ΡΠΊΠΈ Π· ΡΠΎΠ½Π°ΠΌΠΈ Π½ΡΠΊΠ΅Π»Ρ ΡΠ° ΠΌΡΠ΄Ρ
Singularity-free model of electric charge in physical vacuum: Non-zero spatial extent and mass generation
We propose a model of a spinless electrical charge as a self-consistent field
configuration of the electromagnetic (EM) field interacting with a physical
vacuum effectively described by the logarithmic quantum Bose liquid. We show
that, in contrast to the EM field propagating in a trivial vacuum, a regular
solution does exist, and both its mass and spatial extent emerge naturally from
dynamics. It is demonstrated that the charge and energy density distribution
acquire Gaussian-like form. The solution in the logarithmic model is stable and
energetically favourable, unlike that obtained in a model with a quartic
(Higgs-like) potential.Comment: 10 pages, 9 figures, final/published versio
- β¦