161 research outputs found
Torus invariant divisors
Using the language of polyhedral divisors and divisorial fans we describe
invariant divisors on normal varieties X which admit an effective codimension
one torus action. In this picture X is given by a divisorial fan on a smooth
projective curve Y. Cartier divisors on X can be described by piecewise affine
functions h on the divisorial fan S whereas Weil divisors correspond to certain
zero and one dimensional faces of it. Furthermore we provide descriptions of
the divisor class group and the canonical divisor. Global sections of line
bundles O(D_h) will be determined by a subset of a weight polytope associated
to h, and global sections of specific line bundles on the underlying curve Y.Comment: 16 pages; 5 pictures; small changes in the layout, further typos
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Anomalous diffusion in the dynamics of complex processes
Anomalous diffusion, process in which the mean-squared displacement of system
states is a non-linear function of time, is usually identified in real
stochastic processes by comparing experimental and theoretical displacements at
relatively small time intervals. This paper proposes an interpolation
expression for the identification of anomalous diffusion in complex signals for
the cases when the dynamics of the system under study reaches a steady state
(large time intervals). This interpolation expression uses the chaotic
difference moment (transient structural function) of the second order as an
average characteristic of displacements. A general procedure for identifying
anomalous diffusion and calculating its parameters in real stochastic signals,
which includes the removal of the regular (low-frequency) components from the
source signal and the fitting of the chaotic part of the experimental
difference moment of the second order to the interpolation expression, is
presented. The procedure was applied to the analysis of the dynamics of
magnetoencephalograms, blinking fluorescence of quantum dots, and X-ray
emission from accreting objects. For all three applications, the interpolation
was able to adequately describe the chaotic part of the experimental difference
moment, which implies that anomalous diffusion manifests itself in these
natural signals. The results of this study make it possible to broaden the
range of complex natural processes in which anomalous diffusion can be
identified. The relation between the interpolation expression and a diffusion
model, which is derived in the paper, allows one to simulate the chaotic
processes in the open complex systems with anomalous diffusion.Comment: 47 pages, 15 figures; Submitted to Physical Review
Minimization of Adverse Effects Associated with Dental Alloys
Metal alloys are one of the most popular materials used in current dental practice. In the oral cavity, metal structures are exposed to various mechanical and chemical factors. Consequently, metal ions are released into the oral fluid, which may negatively affect the surrounding tissues and even internal organs. Adverse effects associated with metallic oral appliances may have various local and systemic manifestations, such as mouth burning, potentially malignant oral lesions, and local or systemic hypersensitivity. However, clear diagnostic criteria and treatment guidelines for adverse effects associated with dental alloys have not been developed yet. The present comprehensive literature review aims (1) to summarize the current information related to possible side effects of metallic oral appliances; (2) to analyze the risk factors aggravating the negative effects of dental alloys; and (3) to develop recommendations for diagnosis, management, and prevention of pathological conditions associated with metallic oral appliances
Normality and smoothness of simple linear group compactifications
If G is a complex semisimple algebraic group, we characterize the normality
and the smoothness of its simple linear compactifications, namely those
equivariant GxG-compactifications which possess a unique closed orbit and which
arise in a projective space of the shape P(End(V)), where V is finite
dimensional rational G-module. Both the characterizations are purely
combinatorial and are expressed in terms of the highest weights of V. In
particular, we show that Sp(2r) (with r > 0) is the unique non-adjoint simple
group which admits a simple smooth compactification.Comment: v2: minor changes, final version. To appear in Math.
Features of Polymeric Structures By Surface—Selective Laser Sintering of Polymer Particles Using Water as Sensitizer
The development of scaffolds with strictly specific properties is a key aspect of functional tissue regeneration, and it still remains one of the greatest challenges for tissue engineering. This study is aimed to determine the possibility of producing three-dimensional polylactide (PLA) scaffolds using the method of surface-selectiv laser sintering (SSLS) for bone tissue regeneration. In this work, the authors also improved PLA scaffold adhesion properties, which are crucial for successful cellular growth and expansion. Thus, SSLS method proved to be effective in designing threedimensional porous scaffolds with differentiated mechanical properties.
Keywords: regenerative medicine, scaffolds, polylactide, surface – selective laser . sintering, tissue engeneering
Classification of Reductive Monoid Spaces Over an Arbitrary Field
In this semi-expository paper we review the notion of a spherical space. In
particular we present some recent results of Wedhorn on the classification of
spherical spaces over arbitrary fields. As an application, we introduce and
classify reductive monoid spaces over an arbitrary field.Comment: This is the final versio
Affine T-varieties of complexity one and locally nilpotent derivations
Let X=spec A be a normal affine variety over an algebraically closed field k
of characteristic 0 endowed with an effective action of a torus T of dimension
n. Let also D be a homogeneous locally nilpotent derivation on the normal
affine Z^n-graded domain A, so that D generates a k_+-action on X that is
normalized by the T-action. We provide a complete classification of pairs (X,D)
in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1.
This generalizes previously known results for surfaces due to Flenner and
Zaidenberg. As an application we compute the homogeneous Makar-Limanov
invariant of such varieties. In particular we exhibit a family of non-rational
varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo
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