28 research outputs found
Strong wavefront lemma and counting lattice points in sectors
We compute the asymptotics of the number of integral quadratic forms with
prescribed orthogonal decompositions and, more generally, the asymptotics of
the number of lattice points lying in sectors of affine symmetric spaces. A new
key ingredient in this article is the strong wavefront lemma, which shows that
the generalized Cartan decomposition associated to a symmetric space is
uniformly Lipschitz
Khinchin theorem for integral points on quadratic varieties
We prove an analogue the Khinchin theorem for the Diophantine approximation
by integer vectors lying on a quadratic variety. The proof is based on the
study of a dynamical system on a homogeneous space of the orthogonal group. We
show that in this system, generic trajectories visit a family of shrinking
subsets infinitely often.Comment: 19 page
The main directions for pharmacological correction (combinations of drugs for general anesthesia) of neurological and cognitive disorders in patients with neoplasms of the central nervous system
The aim of the study was to develop a goal-oriented combination of drugs for general anesthesia, based on a retrospective assessment of the baseline level of neurological and cognitive disorders in adults and children at the stage of preparation for surgery for neoplasms of the central nervous system (sub- and supratentorial neoplasms - SubTNN and SupraTNN), and a prospective evaluation of complications in the postoperative perio
Evaluation of the influence of combinations of drugs for general anesthesia on change of activity of stress-limiting and stress-realizing links on the clinical model of acute stress damage
When a person is in a state of anesthesia - sedation, the realization of the stress reaction is carried out through the mesocortical - limbic system, while performing intensive therapy outside sedation - through the amygdala and the hippocampus. In this regard, the response of the stress system under anesthesia and outside it will be different and, consequently, the evaluation of reactions during anesthesia is extremely interesting and necessary for targeted (individual) choice of combinations of drugs for anesthesia, depending on their effect on the links of the stress system. The more interesting is the response of the stress system in the conditions of the existing pathology, which in itself is accompanied by a stressful respons
Pharmacological correction of intercept hemodynamics in acute kidney damage (part 1)
Development of vasoconstriction of kidney arterioles and reduction of renal blood flow is one of the main mechanism of acute kidney injury (AKI) formation. Methods for evaluation of intrarenal hemodynamics status are rather limited. Evident interest for the clinician is the possibility of rapid and non-invasive assessment of renal hemodynamics using the dopplerography method. The method makes it possible to visualize the kidney vessels and conduct a qualitative and quantitative evaluation of renal blood flow. Peculiarities of disturbed blood flow in the kidneys can determine the individuality of pharmacological correction and intensive care in patients with AK
The Asymptotic distribution of circles in the orbits of Kleinian groups
Let P be a locally finite circle packing in the plane invariant under a
non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When
Gamma is geometrically finite, we construct an explicit Borel measure on the
plane which describes the asymptotic distribution of small circles in P,
assuming that either the critical exponent of Gamma is strictly bigger than 1
or P does not contain an infinite bouquet of tangent circles glued at a
parabolic fixed point of Gamma. Our construction also works for P invariant
under a geometrically infinite group Gamma, provided Gamma admits a finite
Bowen-Margulis-Sullivan measure and the Gamma-skinning size of P is finite.
Some concrete circle packings to which our result applies include Apollonian
circle packings, Sierpinski curves,
Schottky dances, etc.Comment: 31 pages, 8 figures. Final version. To appear in Inventiones Mat
Campana points of bounded height on vector group compactifications
We initiate a systematic quantitative study of subsets of rational points
that are integral with respect to a weighted boundary divisor on Fano
orbifolds. We call the points in these sets Campana points. Earlier work of
Campana and subsequently Abramovich shows that there are several reasonable
competing definitions for Campana points. We use a version that delineates well
different types of behaviour of points as the weights on the boundary divisor
vary. This prompts a Manin-type conjecture on Fano orbifolds for sets of
Campana points that satisfy a klt (Kawamata log terminal) condition. By
importing work of Chambert-Loir and Tschinkel to our set-up, we prove a log
version of Manin's conjecture for klt Campana points on equivariant
compactifications of vector groups.Comment: 52 pages; minor revision, changes in the definition of Campana point
The subconvexity problem for \GL_{2}
Generalizing and unifying prior results, we solve the subconvexity problem
for the -functions of \GL_{1} and \GL_{2} automorphic representations
over a fixed number field, uniformly in all aspects. A novel feature of the
present method is the softness of our arguments; this is largely due to a
consistent use of canonically normalized period relations, such as those
supplied by the work of Waldspurger and Ichino--Ikeda.Comment: Almost final version to appear in Publ. Math IHES. References
updated
Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors
We consider two dimensional maps preserving a foliation which is uniformly
contracting and a one dimensional associated quotient map having exponential
convergence to equilibrium (iterates of Lebesgue measure converge exponentially
fast to physical measure). We prove that these maps have exponential decay of
correlations over a large class of observables. We use this result to deduce
exponential decay of correlations for the Poincare maps of a large class of
singular hyperbolic flows. From this we deduce logarithm laws for these flows.Comment: 39 pages; 03 figures; proof of Theorem 1 corrected; many typos
corrected; improvements on the statements and comments suggested by a
referee. Keywords: singular flows, singular-hyperbolic attractor, exponential
decay of correlations, exact dimensionality, logarithm la
Evaluation of the influence of combinations of drugs for general anesthesia on change of activity of stress-limiting and stress-realizing links on the clinical model of acute stress damage
When a person is in a state of anesthesia - sedation, the realization of the stress reaction is carried out through the mesocortical - limbic system, while performing intensive therapy outside sedation - through the amygdala and the hippocampus. In this regard, the response of the stress system under anesthesia and outside it will be different and, consequently, the evaluation of reactions during anesthesia is extremely interesting and necessary for targeted (individual) choice of combinations of drugs for anesthesia, depending on their effect on the links of the stress system. The more interesting is the response of the stress system in the conditions of the existing pathology, which in itself is accompanied by a stressful respons