45 research outputs found
Higher-order corrections to the short-pulse equation
Using renormalization group techniques, we derive an extended short- pulse
equation as approximation to a nonlinear wave equation. We investigate the new
equation numerically and show that the new equation captures efficiently
higher- order effects on pulse propagation in cubic nonlinear media. We
illustrate our findings using one- and two-soliton solutions of the first-order
short-pulse equation as initial conditions in the nonlinear wave equation
The Sasa-Satsuma higher order nonlinear Schrodinger equation and its bilinearization and multi-soliton solutions
Higher order and multicomponent generalizations of the nonlinear Schrodinger
equation are important in various applications, e.g., in optics. One of these
equations, the integrable Sasa-Satsuma equation, has particularly interesting
soliton solutions. Unfortunately the construction of multi-soliton solutions to
this equation presents difficulties due to its complicated bilinearization. We
discuss briefly some previous attempts and then give the correct
bilinearization based on the interpretation of the Sasa-Satsuma equation as a
reduction of the three-component Kadomtsev-Petvishvili hierarchy. In the
process we also get bilinearizations and multi-soliton formulae for a two
component generalization of the Sasa-Satsuma equation (the
Yajima-Oikawa-Tasgal-Potasek model), and for a (2+1)-dimensional
generalization.Comment: 13 pages in RevTex, added reference
Local Isometric immersions of pseudo-spherical surfaces and evolution equations
The class of differential equations describing pseudo-spherical surfaces,
first introduced by Chern and Tenenblat [3], is characterized by the property
that to each solution of a differential equation, within the class, there
corresponds a 2-dimensional Riemannian metric of curvature equal to . The
class of differential equations describing pseudo-spherical surfaces carries
close ties to the property of complete integrability, as manifested by the
existence of infinite hierarchies of conservation laws and associated linear
problems. As such, it contains many important known examples of integrable
equations, like the sine-Gordon, Liouville and KdV equations. It also gives
rise to many new families of integrable equations. The question we address in
this paper concerns the local isometric immersion of pseudo-spherical surfaces
in from the perspective of the differential equations that give
rise to the metrics. Indeed, a classical theorem in the differential geometry
of surfaces states that any pseudo-spherical surface can be locally
isometrically immersed in . In the case of the sine-Gordon
equation, one can derive an expression for the second fundamental form of the
immersion that depends only on a jet of finite order of the solution of the
pde. A natural question is to know if this remarkable property extends to
equations other than the sine-Gordon equation within the class of differential
equations describing pseudo-spherical surfaces. In an earlier paper [11], we
have shown that this property fails to hold for all other second order
equations, except for those belonging to a very special class of evolution
equations. In the present paper, we consider a class of evolution equations for
of order describing pseudo-spherical surfaces. We show that
whenever an isometric immersion in exists, depending on a jet of
finite order of , then the coefficients of the second fundamental forms are
functions of the independent variables and only.Comment: Fields Institute Communications, 2015, Hamiltonian PDEs and
Applications, pp.N
Discrete Integrable Systems and Hodograph Transformations Arising from Motions of Discrete Plane Curves
We consider integrable discretizations of some soliton equations associated
with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam
equation, the complex Dym equation, and the short pulse equation. They are
related to the modified KdV or the sine-Gordon equations by the hodograph
transformations. Based on the observation that the hodograph transformations
are regarded as the Euler-Lagrange transformations of the curve motions, we
construct the discrete analogues of the hodograph transformations, which yield
integrable discretizations of those soliton equations.Comment: 19 page
Morphologic characteristics of the circle of Willis in patients with migraine
Background: An incomplete circle of Willis (CW) and other abnormalities of CW may predispose to cerebral hypoperfusion which can be one of the factors leading to white matter abnormalities in patients with migraine. This study assessed the relationship between the morphologic characteristics of the CW and migraine.Methods: The study included 150 patients with migraine (age 18-56,12 men and 138 women, 21 patients with migraine with aura and 129 without aura) and 119 patients of controls without migraine who had no history of cerebral ischemia or infarcts on MRI (age 1 8 -6 2 ,4 0 men, 79 women). All patients underwent 3-dimensional time of flight magnetic resonance angiography of the CW. According to the vessel size seen on 3D TOF MR angiograms, the component vessels consisting of CW were regarded as normal, hypoplastic, or absent. The anterior part of the CW (APCW) was considered complete when the anterior communicating artery (ACoA) as well as the A1 segments of the anterior cerebral artery (ΠΠ‘Π) were present on visual examination, incomplete when any of these vessels was missing and indeterminate when we observed a hypoplastic A1 segment of ΠΠ‘Π. The posterior part of the circle of Willis (PPCW) was considered complete when both posterior (PCoA) and the P1 segments of the posterior cerebral artery (PCA) were present on visual examination, incomplete when one of these vessels was missing and indeterminate when we observed hypoplastic PCoA or P1 segment of PCA.Results: We found the following morphologic characteristics of the CW in patients with migraine: complete APCW -137, incomplete APCW - 0, indeterminate APCW -13, complete PPCW -101, incomplete PPCW β 4, indeterminate PPCW - 45; hypoplasia (n=36) or aplasia of the vertebral artery (n=6), duplication of ΠΠ‘Π (n=3) or of A1 segment (n=3), hypoplasia of inferior (n=3) or superior cerebellar artery (n=2). Among these characteristics, only indeterminate patterns of posterior CW were significantly more common in migraineurs than in the control group (30% vs 19%; P < .05; odds ratio 1.79; 95% Cl: 1.0-3.1). No difference was found between migraineurs with and without aura.ΠΠ²Π΅Π΄Π΅Π½ΠΈΠ΅. Π Π°Π·ΠΎΠΌΠΊΠ½ΡΡΡΠΉ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π² ΠΊΡΡΠ³ ΠΈ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠ΅ Π°Π½ΠΎΠΌΠ°Π»ΠΈΠΈ ΡΡΡΠΎΠ΅Π½ΠΈΡ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° ΠΌΠΎΠ³ΡΡ ΠΏΡΠ΅Π΄ΡΠ°ΡΠΏΠΎΠ»Π°Π³Π°ΡΡ ΠΊ ΡΠ΅ΡΠ΅Π±ΡΠ°Π»ΡΠ½ΠΎΠΉ Π³ΠΈΠΏΠΎΠΏΠ΅ΡΡΡΠ·ΠΈΠΈ, ΠΊΠΎΡΠΎΡΠ°Ρ ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ ΠΎΠ΄Π½ΠΈΠΌ ΠΈΠ· ΡΠ°ΠΊΡΠΎΡΠΎΠ², ΠΏΡΠΈΠ²ΠΎΠ΄ΡΡΠΈΡ
ΠΊ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π±Π΅Π»ΡΡ
ΠΎΡΠ°Π³ΠΎΠ² Π² Π²Π΅ΡΠ΅ΡΡΠ²Π΅ Π³ΠΎΠ»ΠΎΠ²Π½ΠΎΠ³ΠΎ ΠΌΠΎΠ·Π³Π° Ρ ΠΏΠ°ΡΠΈΠ΅Π½ΡΠΎΠ² Ρ ΠΌΠΈΠ³ΡΠ΅Π½ΡΡ. Π¦Π΅Π»ΡΡ Π΄Π°Π½Π½ΠΎΠ³ΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π±ΡΠ»ΠΎ ΠΈΠ·ΡΡΠΈΡΡ Π²ΡΡΡΠ΅ΡΠ°Π΅ΠΌΠΎΡΡΡ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
Π°Π½ΠΎΠΌΠ°Π»ΠΈΠΉ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° Ρ Π±ΠΎΠ»ΡΠ½ΡΡ
Ρ ΠΌΠΈΠ³ΡΠ΅Π½ΡΡ ΠΈ Π΄Π°ΡΡ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΡ ΠΌΠΎΡΡΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΡΡΠΎΠ΅Π½ΠΈΡ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π°. ΠΠ°ΡΠ΅ΡΠΈΠ°Π»Ρ ΠΈ ΠΌΠ΅ΡΠΎΠ΄Ρ. Π ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ Π²ΠΊΠ»ΡΡΠ΅Π½Ρ 150 ΠΏΠ°ΡΠΈΠ΅Π½ΡΠΎΠ² Ρ ΠΌΠΈΠ³ΡΠ΅Π½ΡΡ (12 ΠΌΡΠΆΡΠΈΠ½ ΠΈ 138 ΠΆΠ΅Π½ΡΠΈΠ½) Π² Π²ΠΎΠ·ΡΠ°ΡΡΠ΅ ΠΎΡ 18 Π΄ΠΎ 56 Π»Π΅Ρ. ΠΠ· Π½ΠΈΡ
21 ΠΏΠ°ΡΠΈΠ΅Π½Ρ Ρ ΠΌΠΈΠ³ΡΠ΅Π½ΡΡ Ρ Π°ΡΡΠΎΠΉ ΠΈ 129 ΠΏΠ°ΡΠΈΠ΅Π½ΡΠΎΠ² Ρ ΠΌΠΈΠ³ΡΠ΅Π½ΡΡ Π±Π΅Π· Π°ΡΡΡ. ΠΠΈΠ³ΡΠ΅Π½Ρ Π±ΡΠ»Π° Π΄ΠΈΠ°Π³Π½ΠΎΡΡΠΈΡΠΎΠ²Π°Π½Π° ΡΠΎΠ³Π»Π°ΡΠ½ΠΎ ΠΌΠ΅ΠΆΠ΄ΡΠ½Π°ΡΠΎΠ΄Π½ΡΠΌ ΠΊΡΠΈΡΠ΅ΡΠΈΡΠΌ International Headache Society criteria. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½ΠΎΠΉ Π³ΡΡΠΏΠΏΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π»ΠΈΡΡ 119 ΠΏΠ°ΡΠΈΠ΅Π½ΡΠΎΠ² Π±Π΅Π· ΠΌΠΈΠ³ΡΠ΅Π½ΠΈ (40 ΠΌΡΠΆΡΠΈΠ½ ΠΈ 79 ΠΆΠ΅Π½ΡΠΈΠ½), Ρ ΠΊΠΎΡΠΎΡΡΡ
Π½Π΅ Π±ΡΠ»ΠΎ ΠΈΠ½ΡΡΠ»ΡΡΠΎΠ² Π² Π°Π½Π°ΠΌΠ½Π΅Π·Π΅ ΠΈ ΠΈΠ½ΡΠ°ΡΠΊΡΠΎΠ² ΠΏΠΎ ΠΠ Π’. ΠΡ
Π²ΠΎΠ·ΡΠ°ΡΡ Π²Π°ΡΡΠΈΡΠΎΠ²Π°Π» ΠΎΡ 18 Π΄ΠΎ 62 Π»Π΅Ρ. ΠΡΠ΅ΠΌ Π±ΠΎΠ»ΡΠ½ΡΠΌ Ρ ΠΌΠΈΠ³ΡΠ΅Π½ΡΠΌΠΈ ΠΈ ΠΏΠ°ΡΠΈΠ΅Π½ΡΠ°ΠΌ ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½ΠΎΠΉ Π³ΡΡΠΏΠΏΡ Π²ΡΠΏΠΎΠ»Π½Π΅Π½Π° ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎ-ΡΠ΅Π·ΠΎΠ½Π°Π½ΡΠ½Π°Ρ ΡΠΎΠΌΠΎΠ³ΡΠ°ΡΠΈΡ (ΠΠ Π’) Π³ΠΎΠ»ΠΎΠ²Π½ΠΎΠ³ΠΎ ΠΌΠΎΠ·Π³Π° ΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎ-ΡΠ΅Π·ΠΎΠ½Π°Π½ΡΠ½Π°Ρ Π°Π½Π³ΠΈΠΎΠ³ΡΠ°ΡΠΈΡ (ΠΠ -ΠΠ) ΡΠΎΡΡΠ΄ΠΎΠ² Π³ΠΎΠ»ΠΎΠ²Π½ΠΎΠ³ΠΎ ΠΌΠΎΠ·Π³Π°. Π‘ΠΎΠ³Π»Π°ΡΠ½ΠΎ ΡΠ°Π·ΠΌΠ΅ΡΠ°ΠΌ ΡΠΎΡΡΠ΄ΠΎΠ² Π½Π° ΠΠ -ΠΠ ΡΠΎΡΡΠ°Π²Π»ΡΡΡΠΈΠ΅ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π² ΠΊΡΡΠ³ ΡΠΎΡΡΠ΄Ρ Π±ΡΠ»ΠΈ ΠΏΠΎΠ΄ΡΠ°Π·Π΄Π΅Π»Π΅Π½Ρ Π½Π° Π½ΠΎΡΠΌΠ°Π»ΡΠ½ΡΠ΅, Π³ΠΈΠΏΠΎΠ»Π°ΡΡΠΈΡΠ½ΡΠ΅ ΠΈ ΠΎΡΡΡΡΡΡΠ²ΡΡΡΠΈΠ΅. ΠΠ΅ΡΠ΅Π΄Π½ΡΡ ΡΠ°ΡΡΡ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° Π±ΡΠ»Π° ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π° ΠΊΠ°ΠΊ Π·Π°ΠΌΠΊΠ½ΡΡΠ°Ρ, Π΅ΡΠ»ΠΈ ΠΎΠ±Π΅ ΠΏΠ΅ΡΠ΅Π΄Π½ΠΈΠ΅ ΡΠΎΠ΅Π΄ΠΈΠ½ΠΈΡΠ΅Π»ΡΠ½ΡΠ΅ Π°ΡΡΠ΅ΡΠΈΠΈ ΠΈ Π1 ΡΠ΅Π³ΠΌΠ΅Π½Ρ ΠΏΠ΅ΡΠ΅Π΄Π½Π΅ΠΉ ΠΌΠΎΠ·Π³ΠΎΠ²ΠΎΠΉ Π°ΡΡΠ΅ΡΠΈΠΈ (ΠΠΠ) ΠΏΡΠΈΡΡΡΡΡΠ²ΠΎΠ²Π°Π»ΠΈ Π½Π° ΠΠ -Π°Π½Π³ΠΈΠΎΠ³ΡΠ°ΠΌΠΌΠ΅; ΠΏΡΠΈ ΠΎΡΡΡΡΡΡΠ²ΠΈΠΈ ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΈΠ· Π·ΡΠΈΡ
ΡΠΎΡΡΠ΄ΠΎΠ² - Π½Π΅Π·Π°ΠΌΠΊΠ½ΡΡΠΎΠΉ ΠΈ ΠΏΡΠΈ Π½Π°Π»ΠΈΡΠΈΠΈ Π³ΠΈΠΏΠΎΠΏΠ»Π°Π·ΠΈΠΈ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ° Π1 ΠΠΠ - ΠΏΡΠΎΠΌΠ΅ΠΆΡΡΠΎΡΠ½ΠΎΠΉ. ΠΠ°Π΄Π½ΡΡ ΡΠ°ΡΡΡ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° Π±ΡΠ»Π° ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π° ΠΊΠ°ΠΊ Π·Π°ΠΌΠΊΠ½ΡΡΠ°Ρ, Π΅ΡΠ»ΠΈ ΠΎΠ±Π΅ Π·Π°Π΄Π½ΠΈΠ΅ ΡΠΎΠ΅Π΄ΠΈΠ½ΠΈΡΠ΅Π»ΡΠ½ΡΠ΅ Π°ΡΡΠ΅ΡΠΈΠΈ (ΠΠ‘Π) ΠΈ Π 1 ΡΠ΅Π³ΠΌΠ΅Π½Ρ Π·Π°Π΄Π½Π΅ΠΉ ΠΌΠΎΠ·Π³ΠΎΠ²ΠΎΠΉ Π°ΡΡΠ΅ΡΠΈΠΈ (ΠΠΠ) ΠΏΡΠΈΡΡΡΡΡΠ²ΠΎΠ²Π°Π»ΠΈ Π½Π° ΠΠ -Π°Π½Π³ΠΈΠΎΠ³ΡΠ°ΠΌΠΌΠ΅; ΠΏΡΠΈ ΠΎΡΡΡΡΡΡΠ²ΠΈΠΈ ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΈΠ· Π·ΡΠΈΡ
ΡΠΎΡΡΠ΄ΠΎΠ² - Π½Π΅Π·Π°ΠΌΠΊΠ½ΡΡΠΎΠΉ ΠΈ ΠΏΡΠΈ Π½Π°Π»ΠΈΡΠΈΠΈ Π³ΠΈΠΏΠΎΠΏΠ»Π°Π·ΠΈΠΈ ΠΠ‘Π ΠΈΠ»ΠΈ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ° Π 1 ΠΠΠ β ΠΏΡΠΎΠΌΠ΅ΠΆΡΡΠΎΡΠ½ΠΎΠΉ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ. ΠΡ Π²ΡΡΠ²ΠΈΠ»ΠΈ ΡΠ»Π΅Π΄ΡΡΡΠΈΠ΅ ΠΌΠΎΡΡΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠ΅ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° Ρ Π±ΠΎΠ»ΡΠ½ΡΡ
Ρ ΠΌΠΈΠ³ΡΠ΅Π½ΡΠΌΠΈ: Π·Π°ΠΌΠΊΠ½ΡΡΠ°Ρ ΠΏΠ΅ΡΠ΅Π΄Π½ΡΡ ΡΠ°ΡΡΡ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° (n=137), ΠΏΡΠΎΠΌΠ΅ΠΆΡΡΠΎΡΠ½ΡΠΉ ΡΠΈΠΏ ΡΡΡΠΎΠ΅Π½ΠΈΡ ΠΏΠ΅ΡΠ΅Π΄Π½Π΅ΠΉ ΡΠ°ΡΡΠΈ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° (n=13), Π·Π°ΠΌΠΊΠ½ΡΡΠ°Ρ Π·Π°Π΄Π½ΡΡ ΡΠ°ΡΡΡ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° (n=101), Π½Π΅Π·Π°ΠΌΠΊΠ½ΡΡΠ°Ρ Π·Π°Π΄Π½ΡΡ ΡΠ°ΡΡΡ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° (n= 4), ΠΏΡΠΎΠΌΠ΅ΠΆΡΡΠΎΡΠ½ΡΠΉ ΡΠΈΠΏ ΡΡΡΠΎΠ΅Π½ΠΈΡ Π·Π°Π΄Π½Π΅ΠΉ ΡΠ°ΡΡΠΈ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° (n=45); Π³ΠΈΠΏΠΎΠΏΠ»Π°Π·ΠΈΡ ΠΏΠΎΠ·Π²ΠΎΠ½ΠΎΡΠ½ΠΎΠΉ Π°ΡΡΠ΅ΡΠΈΠΈ (n=36), Π°ΠΏΠ»Π°Π·ΠΈΡ ΠΏΠΎΠ·Π²ΠΎΠ½ΠΎΡΠ½ΠΎΠΉ Π°ΡΡΠ΅ΡΠΈΠΈ (n=6), ΡΠ΄Π²ΠΎΠ΅Π½ΠΈΠ΅ ΠΠΠ (n=3), ΡΠ΄Π²ΠΎΠ΅Π½ΠΈΠ΅ Π1 ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ° ΠΠΠ (n=3), Π³ΠΈΠΏΠΎΠΏΠ»Π°Π·ΠΈΡ Π½ΠΈΠΆΠ½Π΅ΠΉ ΠΌΠΎΠ·ΠΆΠ΅ΡΠΊΠΎΠ²ΠΎΠΉ Π°ΡΡΠ΅ΡΠΈΠΈ (n=3), Π³ΠΈΠΏΠΎΠΏΠ»Π°Π·ΠΈΡ Π²Π΅ΡΡ
Π½Π΅ΠΉ ΠΌΠΎΠ·ΠΆΠ΅ΡΠΊΠΎΠ²ΠΎΠΉ Π°ΡΡΠ΅ΡΠΈΠΈ (n=2). Π‘ΡΠ΅Π΄ΠΈ Π·ΡΠΈΡ
Π²Π°ΡΠΈΠ°Π½ΡΠΎΠ² ΡΡΡΠΎΠ΅Π½ΠΈΡ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° ΡΠΎΠ»ΡΠΊΠΎ Π½Π΅Π·Π°ΠΌΠΊΠ½ΡΡΠ°Ρ Π·Π°Π΄Π½ΡΡ ΡΠ°ΡΡΡ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° ΠΈ ΠΏΡΠΎΠΌΠ΅ΠΆΡΡΠΎΡΠ½ΡΠΉ ΡΠΈΠΏ ΡΡΡΠΎΠ΅Π½ΠΈΡ Π·Π°Π΄Π½Π΅ΠΉ ΡΠ°ΡΡΠΈ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° Π²ΡΡΡΠ΅ΡΠ°Π»ΠΈΡΡ Π·Π½Π°ΡΠΈΡΠ΅Π»ΡΠ½ΠΎ ΡΠ°ΡΠ΅ Ρ ΠΏΠ°ΡΠΈΠ΅Π½ΡΠΎΠ² Ρ ΠΌΠΈΠ³ΡΠ΅Π½ΡΡ Ρ Π°ΡΡΠΎΠΉ ΠΏΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ Ρ ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½ΠΎΠΉ Π³ΡΡΠΏΠΏΠΎΠΉ (33% ΠΏΡΠΎΡΠΈΠ² 19%; Π < 0,05; ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠ΅ ΡΠ°Π½ΡΠΎΠ²: 2.0; 95% Π΄ΠΎΠ²Π΅ΡΠΈΡΠ΅Π»ΡΠ½ΡΠΉ ΠΈΠ½ΡΠ΅ΡΠ²Π°Π»: 1,1 -3,5). ΠΠ΅ Π±ΡΠ»ΠΎ Π½Π°ΠΉΠ΄Π΅Π½ΠΎ ΡΠ°Π·Π»ΠΈΡΠΈΠΉ Π² ΡΡΡΠΎΠ΅Π½ΠΈΠΈ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° Ρ Π±ΠΎΠ»ΡΠ½ΡΡ
Ρ ΠΌΠΈΠ³ΡΠ΅Π½ΡΡ Ρ Π°ΡΡΠΎΠΉ ΠΈ Π±Π΅Π· Π°ΡΡΡ. ΠΡΠ²ΠΎΠ΄: ΠΠ°ΡΠΈ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΏΠΎΠΊΠ°Π·Π°Π»ΠΈ, ΡΡΠΎ ΠΏΡΠΎΠΌΠ΅ΠΆΡΡΠΎΡΠ½ΡΠΉ ΡΠΈΠΏ ΡΡΡΠΎΠ΅Π½ΠΈΡ Π·Π°Π΄Π½Π΅ΠΉ ΡΠ°ΡΡΠΈ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΠ΅Ρ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠ½ΡΡ ΡΠ΅ΡΡΡ ΡΡΡΠΎΠ΅Π½ΠΈΡ ΠΠΈΠ»Π»ΠΈΠ·ΠΈΠ΅Π²Π° ΠΊΡΡΠ³Π° Ρ ΠΈΡΡΠ»Π΅Π΄ΡΠ΅ΠΌΡΡ
Π±ΠΎΠ»ΡΠ½ΡΡ
Ρ ΠΌΠΈΠ³ΡΠ΅Π½ΡΡ
Large scale analytic calculations in quantum field theories
We present a survey on the mathematical structure of zero- and single scale
quantities and the associated calculation methods and function spaces in higher
order perturbative calculations in relativistic renormalizable quantum field
theories.Comment: 25 pages Latex, 1 style fil
Perturbation theory for nearly integrable multi-component nonlinear PDEs
The Riemann-Hilbert problem associated with the integrable PDE is used as a
nonlinear transformation of the nearly integrable PDE to the spectral space.
The temporal evolution of the spectral data is derived with account for
arbitrary perturbations and is given in the form of exact equations, which
generate the sequence of approximate ODEs in successive orders with respect to
the perturbation. For vector nearly integrable PDEs, embracing the vector NLS
and complex modified KdV equations, the main result is formulated in a theorem.
For a single vector soliton the evolution equations for the soliton parameters
and first-order radiation are given in explicit formComment: Submitted to Journal of Mathematical Physics (References are
corrected
Generalizations of the short pulse equation
We classify integrable scalar polynomial partial differential equations of second order generalizing the short pulse equation
Geographical Distribution, Incidence, Malignancies, and Outcome of 136 Eastern Slavic Patients With Nijmegen Breakage Syndrome and NBN Founder Variant c.657_661del5
Nijmegen breakage syndrome (NBS) is a DNA repair disorder characterized by combined immunodeficiency and a high predisposition to lymphoid malignancies. The majority of NBS patients are identified with a homozygous five base pair deletion in the Nibrin (NBN) gene (c.657_661del5, p.K219fsX19) with a founder effect observed in Caucasian European populations, especially of Slavic origin. We present here an analysis of a cohort of 136 NBS patients of Eastern Slav origin across Belarus, Ukraine, Russia, and Latvia with a focus on understanding the geographic distribution, incidence of malignancy, and treatment outcomes of this cohort. Our analysis shows that Belarus had the highest prevalence of NBS (2.3 per 1,000,000), followed by Ukraine (1.3 per 1,000,000), and Russia (0.7 per 1,000,000). Of note, the highest concentration of NBS cases was observed in the western regions of Belarus and Ukraine, where NBS prevalence exceeds 20 cases per 1,000,000 people, suggesting the presence of an βEastern Slavic NBS hot spot.β The median age at diagnosis of this cohort ranged from 4 to 5 years, and delay in diagnosis was more pervasive in smaller cities and rural regions. A total of 62 (45%) patients developed malignancies, more commonly in males than females (55.2 vs. 34.2%; p=0.017). In 27 patients, NBS was diagnosed following the onset of malignancies (mean age: 8 years). Malignancies were mostly of lymphoid origin and predominantly non-Hodgkin lymphoma (NHL) (n=42, 68%); 38% of patients had diffuse large B-cell lymphoma. The 20-year overall survival rate of patients with malignancy was 24%. However, females with cancer experienced poorer event-free survival rates than males (16.6% vs. 46.8%, p=0.036). Of 136 NBS patients, 13 underwent hematopoietic stem cell transplantation (HSCT) with an overall survival of 3.5 years following treatment (range: 1 to 14 years). Indications for HSCT included malignancy (n=7) and immunodeficiency (n=6). Overall, 9% of patients in this cohort reached adulthood. Adult survivors reported diminished quality of life with significant physical and cognitive impairments. Our study highlights the need to improve timely diagnosis and clinical management of NBS among Eastern Slavs. Genetic counseling and screening should be offered to individuals with a family history of NBS, especially in hot spot regions. Β© Copyright Β© 2021 Sharapova, Pashchenko, Bondarenko, Vakhlyarskaya, Prokofjeva, Fedorova, Savchak, Mareika, Valiev, Popa, Tuzankina, Vlasova, Sakovich, Polyakova, Rumiantseva, Naumchik, Kulyova, Aleshkevich, Golovataya, Minakovskaya, Belevtsev, Latysheva, Latysheva, Beznoshchenko, Akopyan, Makukh, Kozlova, Varabyou, Ballow, Ong, Walter, Kondratenko, Kostyuchenko and Aleinikova.We thank all doctors for clinical help for patients. We also appreciate the support of patient and their parents for agreeing to take part in this study. TP thanks Sergey?Nikulshin, Marika Grutupa, and Zanna Kovalova. We thank Joseph Dasso for editing this manuscript, primarily for proper English