On Darboux Integrable Semi-Discrete Chains

Differential-difference equation $\frac{d}{dx}t(n+1,x)=f(x,t(n,x),t(n+1,x),\frac{d}{dx}t(n,x))$ with unknown $t(n,x)$ depending on continuous and discrete variables $x$ and $n$ is studied. We call an equation of such kind Darboux integrable, if there exist two functions (called integrals) $F$ and $I$ of a finite number of dynamical variables such that $D_xF=0$ and $DI=I$, where $D_x$ is the operator of total differentiation with respect to $x$, and $D$ is the shift operator: $Dp(n)=p(n+1)$. It is proved that the integrals can be brought to some canonical form. A method of construction of an explicit formula for general solution to Darboux integrable chains is discussed and for a class of chains such solutions are found.Comment: 19 page

On the classification of Darboux integrable chains

Cataloged from PDF version of article.We study differential-difference equation (d/dx) t (n+1,x) =f (t (n,x),t (n+1,x), (d/dx) t (n,x)) with unknown t (n,x) depending on continuous and discrete variables x and n. Equation of such kind is called Darboux integrable, if there exist two functions F and I of a finite number of arguments x, { t (n+k,x) } k=-∞ ∞, {(dk /d xk) t (n,x) } k=1 ∞, such that Dx F=0 and DI=I, where D x is the operator of total differentiation with respect to x and D is the shift operator: Dp (n) =p (n+1). Reformulation of Darboux integrability in terms of finiteness of two characteristic Lie algebras gives an effective tool for classification of integrable equations. The complete list of Darboux integrable equations is given in the case when the function f is of the special form f (u,v,w) =w+g (u,v). © 2009 American Institute of Physics

N -Acetylcarnosine is a prodrug of L-carnosine in ophthalmic application as antioxidant

Abstract The naturally occurring compound N~-acetylcarnosine (NAC) is proposed as the prodrug of L-carnosine (C) resistant to enzymatic hydrolysis by human serum carnosinase. Rabbit eyes were treated with 1% NAC, C or placebo and extracts of the aqueous humor from the anterior eye chamber were analyzed for imidazole content by reverse phase analytical high performance liquid chromatography (HPLC), thin-layer (TLC) and ion-exchange chromatographic techniques. The topical administration of pure C to the rabbit eye did not lead to accumulation of this compound in the aqueous humor over 30 min in concentration exceeding that in the placebo-treated matched eye. NAC showed dose-dependent hydrolysis in its passage from the cornea to the aqueous humor, releasing C after 15-30 min of ocular administration of prodrug in a series of therapeutical modalities: instillation < subconjunctival injection < ultrasound induced phoresis. Different treatment techniques showed excellent toleration of 1% NAC by the eye. Once in the aqueous humor, C might act as an antioxidant and enter the lens tissue when present at effective concentrations (5-15 mmol/I). The advantage of the ophthalmic prodrug NAC and its bioactivated principle C as universal antioxidants relates to their ability to give efficient protection against oxidative stress both in the lipid phase of biological membranes and in an aqueous environment. NAC is proposed to treat ocular disorders which have the component of oxidative stress in their genesis (cataracts, glaucoma, retinal degeneration, corneal disorders, ocular inflammation, complications of diabetes mellitus, systemic diseases)

Антигенное разнообразие вирусов гриппа А и В, выделенных от детей в г. Санкт-Петербурге в период с 2013 по 2015 г.

Purpose of the study: study of the circulation, isolation and antigenic analysis of influenza viruses A and B in St.-Petersburg in the children aged 0–18 in the seasons 2013–2015.Materials: nasal swabs from children-inpatients from Saint-Petersburg.Methods: virus isolation in MDCK cell culture and chicken embryos, antigenic analysis with the hemagglutination inhibition (HAI) test with the set of hyper-immune rat antisera to the epidemic and reference strains, antigenic cartography.Results: The epidemic seasons 2013–2015 were characterized by the co-circulation in children in St.-Petersburg of influenza sub-types А(H1N1)pdm09, A(H3N2), and B of Yamagata lineage (B yam). In the season 2014–2015 the low activity of epidemic process was observed with the predominant sub-type A(H3N2) and in the next season – 2014–2015 with the more pronounced epidemic activity – the pre-dominance of B yam viruses. Antigenic analysis of influenza viruses А(H1N1)pdm09 which circulated in children revealed their antigenic homogeneity and full correspondence with vaccine strain A/California/07/09. As for А(H3N2) viruses, two antigenic groups were established: strains similar to A/St.-Petersburg/80/14 (sub-clade 3C.2a) and strains similar to A/Switzerland/9715293/13 (sub-clade 3C.3a). А(Н3N2) strains of the season 2013-2014 were similar to the vaccine strain. However isolates of the season 2014-2015 did not fit to the vaccine strain because in the children were predominant strains similar to the evolution branch A/St.-Petersburg/80/14 while according the WHO recommendations the influenza vaccine contained the strain A/Texas/50/12. Antigenic analysis of influenza viruses B showed their homogeneity and all they were B/Phuket/3073/13-like. Influenza strains B also incompletely corresponded to the vaccine strain – B/Massachusetts/2/12 belonging to the different genetic sub-clade. That might be the reason of enhanced morbidity of children with influenza B in the last season.Conclusion: The obtained results stress the urgency for the wide coverage of human population with the epidemic studies, virus isolation in different time periods and geographic regions and their etiological studies with the modern techniques. Only in these conditions we can assure high efficiency of flu seasonal vaccines.Цель исследования: особенности циркуляции, выделение и антигенный анализ вирусов гриппа А и В в Санкт-Петербурге в 2013–2015 гг. от детей от 0 до 18 лет.Материалы исследования: назальные мазки от детей из стационаров и закрытых детских учреждений Санкт-Петербурга.Методы: выделение вирусов на культуре клеток MDCK и куриных эмбрионах, антигенный анализ методом реакции торможения гемагглютинации (РТГА) с набором гипериммунных крысиных антисывороток к эталонным и эпидемическим штаммам гриппа, антигенная картография.Результаты: в эпидемические сезоны 2013–2015 гг. в г. Санкт-Петербурге среди детей была выявлена совместная циркуляция вирусов гриппа А(H1N1)pdm09, A(H3N2), B Ямагатской линии (B yam), причем в сезоне 2013–2014 гг. при общей невысокой активности эпидемического процесса преобладали вирусы A(H3N2), а в следующем эпидемическом сезоне – 2014–2015 гг. – при более высокой интенсивности эпидемии – вирусы В yam. Антигенный анализ вирусов А(H1N1)pdm09, циркулировавших среди детей, выявил их антигенную однородность и полное соответствие вакцинному штамму А/Калифорния/07/09. Зафиксирован антигенный дрейф вирусов А(H3N2), выявлены 2 антигенные группы: вирусы, подобные А/Санкт-Петербург/80/14 (генетическая подгруппа 3С.2а) и вирусы, подобные А/Швейцария/9715293/13 (подгруппа 3С.3а). Вирусы А(Н3N2) сезона 2013–2014 гг. были подобны вакцинному штамму. В то же время изоляты сезона 2014–2015 гг. не соответствовали вакцинному штамму, поскольку среди детей в основном выявлены штаммы, подобные эволюционной ветви А/Санкт-Петербург/80/14, а в вакцину по рекомендации ВОЗ был включен штамм А/Техас/50/12. Антигенный анализ вирусов гриппа В yam показал их однородность, они были подобны эталонному вирусу В/Пхукет/3073/13. Вирусы В также антигенно не полностью соответствовали вакцинному компоненту, поскольку данные вирусы были подобны штамму В/Пхукет/3073/13, а в состав вакцины входил штамм В/Массачусетс/2/12, принадлежащий к другой генетической подгруппе, что могло привести к повышению заболеваемости детей гриппом типа В в данном сезоне. Заключение: для своевременного правильного выбора штаммов, входящих в состав сезонных противогриппозных вакцин, по-прежнему актуальной остается задача как можно более широкого охвата населения эпидемиологическими исследованиями, выделения вирусов в разные периоды эпидемического сезона и в разных географических регионах, их антигенный и генетический анализ современными методами

Antigenic variability of influenza viruses A and B isolated from children in Saint-Petersburg in the period 2013–2015

Purpose of the study: study of the circulation, isolation and antigenic analysis of influenza viruses A and B in St.-Petersburg in the children aged 0–18 in the seasons 2013–2015.Materials: nasal swabs from children-inpatients from Saint-Petersburg.Methods: virus isolation in MDCK cell culture and chicken embryos, antigenic analysis with the hemagglutination inhibition (HAI) test with the set of hyper-immune rat antisera to the epidemic and reference strains, antigenic cartography.Results: The epidemic seasons 2013–2015 were characterized by the co-circulation in children in St.-Petersburg of influenza sub-types А(H1N1)pdm09, A(H3N2), and B of Yamagata lineage (B yam). In the season 2014–2015 the low activity of epidemic process was observed with the predominant sub-type A(H3N2) and in the next season – 2014–2015 with the more pronounced epidemic activity – the pre-dominance of B yam viruses. Antigenic analysis of influenza viruses А(H1N1)pdm09 which circulated in children revealed their antigenic homogeneity and full correspondence with vaccine strain A/California/07/09. As for А(H3N2) viruses, two antigenic groups were established: strains similar to A/St.-Petersburg/80/14 (sub-clade 3C.2a) and strains similar to A/Switzerland/9715293/13 (sub-clade 3C.3a). А(Н3N2) strains of the season 2013-2014 were similar to the vaccine strain. However isolates of the season 2014-2015 did not fit to the vaccine strain because in the children were predominant strains similar to the evolution branch A/St.-Petersburg/80/14 while according the WHO recommendations the influenza vaccine contained the strain A/Texas/50/12. Antigenic analysis of influenza viruses B showed their homogeneity and all they were B/Phuket/3073/13-like. Influenza strains B also incompletely corresponded to the vaccine strain – B/Massachusetts/2/12 belonging to the different genetic sub-clade. That might be the reason of enhanced morbidity of children with influenza B in the last season.Conclusion: The obtained results stress the urgency for the wide coverage of human population with the epidemic studies, virus isolation in different time periods and geographic regions and their etiological studies with the modern techniques. Only in these conditions we can assure high efficiency of flu seasonal vaccines