On some class of reductions for Itoh-Narita-Bogoyavlenskii lattice

We show a broad class of constraints compatible with Itoh-Narita-Bogoyavlenskii lattice hierarchy. All these constraints can be written in the form of discrete conservation law $I_{i+1}=I_i$ with appropriate homogeneous polynomial discrete function $I=I[a]$.Comment: 15 page

On some integrable lattice related by the Miura-type transformation to the Itoh-Narita-Bogoyavlenskii lattice

We show that by Miura-type transformation the Itoh-Narita-Bogoyavlenskii lattice, for any $n\geq 1$, is related to some differential-difference (modified) equation. We present corresponding integrable hierarchies in its explicit form. We study the elementary Darboux transformation for modified equations.Comment: Latex, 9 page

A class of integrable lattices and KP hierarchy

We introduce a class of integrable $l$-field first-order lattices together with corresponding Lax equations. These lattices may be represented as consistency condition for auxiliary linear systems defined on sequences of formal dressing operators. This construction provides simple way to build lattice Miura transformations between one-field lattice and $l$-field ($l\ge 2$) ones. We show that the lattices pertained to above class is in some sense compatible with KP flows and define the chains of constrained KP Lax operators.Comment: LaTeX, 13 pages, accepted for publication in J. Phys. A: Math. Ge

Differential constraints for the Kaup -- Broer system as a reduction of the 1D Toda lattice

It is shown that some special reduction of infinite 1D Toda lattice gives differential constraints compatible with the Kaup -- Broer system. A family of the travelling wave solutions of the Kaup -- Broer system and its higher version is constructed.Comment: LaTeX, uses IOP styl

Reductions of integrable lattices

Based on the notion of Darboux-KP chain hierarchy and its invariant submanifolds we construct some class of constraints compatible with integrable lattices. Some simple examples are given.Comment: 17 page

THE OCCURRENCE OF MORPHOLOGICAL ANOMALIES IN GREEN FROGS POPULATION SYSTEMS (PELOPHYLAX FITZINGER, 1843) FROM THE NORTH-EASTERN PART OF THE AREAS

In 2007–2013, a total of 754 specimens were investigatedfrom 15 localities situated in Mari El Republic and southern part of Kirovskaya Province (north-eastern part of the Pelophylax areas). We observed 4 types of morphological anomalies among specimensof marsh frog (polyphalangy, asymmetric and symmetric cases ofpolydactyly, brachidactyly), and 4 types of morphological anomaliesamong specimens of pool frog (polyphalangy, asymmetric andsymmetric cases of polydactyly and depigmentation of iris). Abnormal specimens weren’t found among hybrids. The occurrence of abnormal adult specimens in population systems was 1,75–7,7%. Morphological anomalies were found in population systems of 3 types (R-, L- and REL-) from 5 localities.В 2007–2013 гг. Было исследовано 754 особи из 15 локалитетов Республики Марий Эл и южной части Кировской области (северо-восточная часть ареалов Pelophylax). Нами отмечены 4 варианта морфологических аномалий у особей озерной лягушки (полифалангия, асимметричные и симметричные случаи полидактилия, брахидактилия) и 4 варианта морфологических аномалий у особей прудовой лягушки (полифалангия, асимметричные и симметричные случаи полидактилия и депигментация радужной оболочки). Аномальные особи не были отмечены среди гибридов. Встречаемость аномальных взрослых особей в популяционных системах составила 1,75–7,7%. Морфологические аномалии были обнаружены в популяционных системах 3 типов (R-, L- и REL-) из 5 населенных пунктов.Выражаю искреннюю благодарность С. Н. Литвинчуку и Ю. М. Розанову (Санкт-Петербург) за идентификацию лягушек методом проточной ДНК-цитометрии, а также С. Н. Литвинчуку, В. И. Казакову и П. А. Селезневу за помощь в сборе материала

Minimal coupling method and the dissipative scalar field theory

Quantum field theory of a damped vibrating string as the simplest dissipative scalar field investigated by its coupling with an infinit number of Klein-Gordon fields as the environment by introducing a minimal coupling method. Heisenberg equation containing a dissipative term proportional to velocity obtained for a special choice of coupling function and quantum dynamics for such a dissipative system investigated. Some kinematical relations calculated by tracing out the environment degrees of freedom. The rate of energy flowing between the system and it's environment obtained.Comment: 15 pages, no figur

Morphological Deformities in Anuran Amphibians from the Khoper River Valley in the “Privolzhskaya Lesostep’” Nature Reserve and Adjacent Territories

In summer 2016, we investigated Ostrovtsovskaya Lesostep’ (Penza region, Russia) and caught more than 130 specimens belonging to 4 species of anuran amphibians. We found a symmetric case of “hyperxanthism” of the eyes (a new type of anomaly among amphibians) in one Rana arvalis specimen, one asymmetric amely in Bombina bombina, and 21 specimens of Pelophylax ridibundus (19% of total sample) with deformed fore and hind limbs. We define some anomalies as “Rostand’s anomaly P” (in its extreme manifestations). The potential reasons of the morphological anomalies were discussed

The incidence of the anomaly P syndrome in water frogs (Anura, Ranidae, Pelophylax) from the Middle Volga River (Russia)

The anomaly P is a widespread morphological anomaly, which occurs in some groups of amphibians, caused by the trematode parasite Strigea robusta (Digenea: Strigeidae). This anomaly has been previously recorded in water frogs of the genus Pelophylax and toads of the genera Bufo and Bufotes. The anomaly P includes symmetrical polydactyly cases as a mild attenuated form of the complex syndrome, which in severe cases includes strong deformations of hindlimbs and forelimbs. Strigea robusta has a complex 3-host life cycle using planorbid mollusks as the first intermediate hosts, amphibian larvae as the second intermediate hosts, and anatid birds as the definitive hosts. Herein, we described new records of the anomaly P syndrome in water frogs of the genus Pelophylax from the northeastern parts of their ranges. Symmetrical polydactyly (as a mild form of the anomaly P syndrome) was found in 30 individuals of three species of water frogs from seven localities: in 25 individuals of P. lessonae from four waterbodies, in four individuals of P. ridibundus from three waterbodies, and one individual of P. esculentus. In Gusevo pond, three individuals of P. lessonae with severe cases of the syndrome were found. This is the first record of the anomaly P in reliably identified hybridogenetic edible frogs (P. esculentus) that have been identified in nature. Additionally, we provided new data about the occurrence of the anomaly P and the prevalence of the trematode S. robusta in mollusks taken from two water bodies where anomalous water frogs were found

Morphological Deformities in Anuran Amphibians from the Khoper River Valley in the “Privolzhskaya Lesostep’” Nature Reserve and Adjacent Territories

In summer 2016, we investigated Ostrovtsovskaya Lesostep’ (Penza region, Russia) and caught more than 130 specimens belonging to 4 species of anuran amphibians. We found a symmetric case of “hyperxanthism” of the eyes (a new type of anomaly among amphibians) in one Rana arvalis specimen, one asymmetric amely in Bombina bombina, and 21 specimens of Pelophylax ridibundus (19% of total sample) with deformed fore and hind limbs. We define some anomalies as “Rostand’s anomaly P” (in its extreme manifestations). The potential reasons of the morphological anomalies were discussed.We would like to replace old acknowledgements with: “Authors are grateful to A. Dubois, S.N. Litvinchuk and V.L. Vershinin for valuable advices about classification of anomalies. We are thankful to A.N. Dobrolyubov for opportunity to work on the territory of nature reserve «Privolzhskaya Lesostep’».The work was supported by the RFBR (№ 18-04-00640 А, №16-34-00119 and № 15-29-02550) and by the grant of Mari State University (№ 2017-06b from 11.01.2017).