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 $L$-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