506 research outputs found
Representations of reductive normal algebraic monoids
The rational representation theory of a reductive normal algebraic monoid
(with one-dimensional center) forms a highest weight category, in the sense of
Cline, Parshall, and Scott. This is a fundamental fact about the representation
theory of reductive normal algebraic monoids. We survey how this result was
obtained, and treat some natural examples coming from classical groups.Comment: 10 pages. To appear in a volume of the Fields Communications Series:
"Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics," edited by
Mahir Can, Zhenheng Li, Benjamin Steinberg, and Qiang Wan
The Horizontal Component of Photospheric Plasma Flows During the Emergence of Active Regions on the Sun
The dynamics of horizontal plasma flows during the first hours of the
emergence of active region magnetic flux in the solar photosphere have been
analyzed using SOHO/MDI data. Four active regions emerging near the solar limb
have been considered. It has been found that extended regions of Doppler
velocities with different signs are formed in the first hours of the magnetic
flux emergence in the horizontal velocity field. The flows observed are
directly connected with the emerging magnetic flux; they form at the beginning
of the emergence of active regions and are present for a few hours. The Doppler
velocities of flows observed increase gradually and reach their peak values
4-12 hours after the start of the magnetic flux emergence. The peak values of
the mean (inside the +/-500 m/s isolines) and maximum Doppler velocities are
800-970 m/s and 1410-1700 m/s, respectively. The Doppler velocities observed
substantially exceed the separation velocities of the photospheric magnetic
flux outer boundaries. The asymmetry was detected between velocity structures
of leading and following polarities. Doppler velocity structures located in a
region of leading magnetic polarity are more powerful and exist longer than
those in regions of following polarity. The Doppler velocity asymmetry between
the velocity structures of opposite sign reaches its peak values soon after the
emergence begins and then gradually drops within 7-12 hours. The peak values of
asymmetry for the mean and maximal Doppler velocities reach 240-460 m/s and
710-940 m/s, respectively. An interpretation of the observable flow of
photospheric plasma is given.Comment: 20 pages, 10 figures, 3 tables. The results of article were presented
at the ESPM-13 (12-16 September 2011, Rhodes, Greece, Abstract Book p. 102,
P.4.12,
http://astro.academyofathens.gr/espm13/documents/ESPM13_abstract_programme_book.pdf
Self-similar solution of a nonsteady problem of nonisothermal vapour condensation on a droplet growing in diffusion regime
This paper presents a mathematically exact self-similar solution to the joint
nonsteady problems of vapour diffusion towards a droplet growing in a
vapour-gas medium and of removal of heat released by a droplet into a
vapour-gas medium during vapour condensation. An equation for the temperature
of the droplet is obtained; and it is only at that temperature that the
self-similar solution exists. This equation requires the constancy of the
droplet temperature and even defines it unambiguously throughout the whole
period of the droplet growth. In the case of strong display of heat effects,
when the droplet growth rate decreases significantly, the equation for the
temperature of the droplet is solved analytically. It is shown that the
obtained temperature fully coincides with the one that settles in the droplet
simultaneously with the settlement of its diffusion regime of growth. At the
obtained temperature of the droplet the interrelated nonsteady vapour
concentration and temperature profiles of the vapour-gas medium around the
droplet are expressed in terms of initial (prior to the nucleation of the
droplet) parameters of the vapour-gas medium. The same parameters are used to
formulate the law in accordance with which the droplet is growing in diffusion
regime, and also to define the time that passes after the nucleation of the
droplet till the settlement of diffusion regime of droplet growth, when the
squared radius of the droplet becomes proportionate to time. For the sake of
completeness the case of weak display of heat effects is been studied.Comment: 12 pages, 4 figure
A Survey of Satisfiability Modulo Theory
Satisfiability modulo theory (SMT) consists in testing the satisfiability of
first-order formulas over linear integer or real arithmetic, or other theories.
In this survey, we explain the combination of propositional satisfiability and
decision procedures for conjunctions known as DPLL(T), and the alternative
"natural domain" approaches. We also cover quantifiers, Craig interpolants,
polynomial arithmetic, and how SMT solvers are used in automated software
analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest,
Romania. 201
A glassy contribution to the heat capacity of hcp He solids
We model the low-temperature specific heat of solid He in the hexagonal
closed packed structure by invoking two-level tunneling states in addition to
the usual phonon contribution of a Debye crystal for temperatures far below the
Debye temperature, . By introducing a cutoff energy in the
two-level tunneling density of states, we can describe the excess specific heat
observed in solid hcp He, as well as the low-temperature linear term in the
specific heat. Agreement is found with recent measurements of the temperature
behavior of both specific heat and pressure. These results suggest the presence
of a very small fraction, at the parts-per-million (ppm) level, of two-level
tunneling systems in solid He, irrespective of the existence of
supersolidity.Comment: 11 pages, 4 figure
On The Mobile Behavior of Solid He at High Temperatures
We report studies of solid helium contained inside a torsional oscillator, at
temperatures between 1.07K and 1.87K. We grew single crystals inside the
oscillator using commercially pure He and He-He mixtures containing
100 ppm He. Crystals were grown at constant temperature and pressure on the
melting curve. At the end of the growth, the crystals were disordered,
following which they partially decoupled from the oscillator. The fraction of
the decoupled He mass was temperature and velocity dependent. Around 1K, the
decoupled mass fraction for crystals grown from the mixture reached a limiting
value of around 35%. In the case of crystals grown using commercially pure
He at temperatures below 1.3K, this fraction was much smaller. This
difference could possibly be associated with the roughening transition at the
solid-liquid interface.Comment: 15 pages, 6 figure
The Role of Certain Species of Small Mammals in the Persistence of Natural Focality in the Territory of Forest-Steppe Zone of the Natural Tularemia Focus of the Stavropol Region
Epizootiological monitoring of the forest-steppe area of the natural tularemia focus in the Stavropol region has revealed that the role of particular species of small mammals in the persistence of natural tularemia focality is unequal. Epizootic activity of the focus in 1959-1970 was determined by the numerous species of rodents: Microtus arvalis , mice of Syvaemus genus and Mus musculus . In 1972-2010 there occurred significant changes in the grouping of the main tularemia agent carriers under the influence of strong anthropogenic pressure. Nowadays the leading role is played by the widely-spread and subsistent mice of Sylvaemus genus and C. suaveolens , the latter ones being responsible for 31.2 % of overall, isolated from small mammals, tularemia agent strains. In addition to this, epizootic significance of M. arvalis has greatly changed. Index of strains isolated from field vole has lowered from 55.3 up to 28.4. Numbers of M. arvalis and Mus musculus are continuously on the low level, which is due to the absence of favorable breeding conditions. It reduces their impact on the persistence of natural focality in the territory under surveillance significantly
NMR Study of Disordered Inclusions in the Quenched Solid Helium
Phase structure of rapidly quenched solid helium samples is studied by the
NMR technique. The pulse NMR method is used for measurements of spin-lattice
and spin-spin relaxation times and spin diffusion coefficient
for all coexisting phases. It was found that quenched samples are two-phase
systems consisting of the hcp matrix and some inclusions which are
characterized by and values close to those in liquid phase. Such
liquid-like inclusions undergo a spontaneous transition to a new state with
anomalously short times. It is found that inclusions observed in both the
states disappear on careful annealing near the melting curve. It is assumed
that the liquid-like inclusions transform into a new state - a glass or a
crystal with a large number of dislocations. These disordered inclusions may be
responsible for the anomalous phenomena observed in supersolid region.Comment: 10 pages, 3 figure
Defects and glassy dynamics in solid He-4: Perspectives and current status
We review the anomalous behavior of solid He-4 at low temperatures with
particular attention to the role of structural defects present in solid. The
discussion centers around the possible role of two level systems and structural
glassy components for inducing the observed anomalies. We propose that the
origin of glassy behavior is due to the dynamics of defects like dislocations
formed in He-4. Within the developed framework of glassy components in a solid,
we give a summary of the results and predictions for the effects that cover the
mechanical, thermodynamic, viscoelastic, and electro-elastic contributions of
the glassy response of solid He-4. Our proposed glass model for solid He-4 has
several implications: (1) The anomalous properties of He-4 can be accounted for
by allowing defects to freeze out at lowest temperatures. The dynamics of solid
He-4 is governed by glasslike (glassy) relaxation processes and the
distribution of relaxation times varies significantly between different
torsional oscillator, shear modulus, and dielectric function experiments. (2)
Any defect freeze-out will be accompanied by thermodynamic signatures
consistent with entropy contributions from defects. It follows that such
entropy contribution is much smaller than the required superfluid fraction, yet
it is sufficient to account for excess entropy at lowest temperatures. (3) We
predict a Cole-Cole type relation between the real and imaginary part of the
response functions for rotational and planar shear that is occurring due to the
dynamics of defects. Similar results apply for other response functions. (4)
Using the framework of glassy dynamics, we predict low-frequency yet to be
measured electro-elastic features in defect rich He-4 crystals. These
predictions allow one to directly test the ideas and very presence of glassy
contributions in He-4.Comment: 33 pages, 13 figure
Test of exotic scalar and tensor interactions in K_e3 decay using stopped positive kaons
The form factors of the decay K+ --> pi0 e+ nu (K_e3) have been determined
from the comparison of the experimental and Monte Carlo Dalitz distributions
containing about 10^5 K_e3 events. The following values of the parameters were
obtained: lambda_+ = 0.0278 +- 0.0017(stat) +- 0.0015(syst), f_S/f_+(0) =
0.0040 +- 0.0160(stat) +- 0.0067(syst) and f_T/f_+(0) = 0.019 +- 0.080(stat) +-
0.038(syst). Both scalar f_S and tensor f_T form factors are consistent with
the Standard Model predictions of zero values.Comment: 10 pages, 5 figures, contributed to the proceedings of NANP
Conference, Dubna, June 19-23, 200
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