The Liouville-type theorem for integrable Hamiltonian systems with incomplete flows

For integrable Hamiltonian systems with two degrees of freedom whose Hamiltonian vector fields have incomplete flows, an analogue of the Liouville theorem is established. A canonical Liouville fibration is defined by means of an "exact" 2-parameter family of flat polygons equipped with certain pairing of sides. For the integrable Hamiltonian systems given by the vector field $v=(-\partial f/\partial w, \partial f/\partial z)$ on ${\mathbb C}^2$ where $f=f(z,w)$ is a complex polynomial in 2 variables, geometric properties of Liouville fibrations are described.Comment: 6 page

Tarski monoids: Matui's spatial realization theorem

We introduce a class of inverse monoids, called Tarski monoids, that can be regarded as non-commutative generalizations of the unique countable, atomless Boolean algebra. These inverse monoids are related to a class of etale topological groupoids under a non-commutative generalization of classical Stone duality and, significantly, they arise naturally in the theory of dynamical systems as developed by Matui. We are thereby able to reinterpret a theorem of Matui on a class of \'etale groupoids as an equivalent theorem about a class of Tarski monoids: two simple Tarski monoids are isomorphic if and only if their groups of units are isomorphic. The inverse monoids in question may also be viewed as countably infinite generalizations of finite symmetric inverse monoids. Their groups of units therefore generalize the finite symmetric groups and include amongst their number the classical Thompson groups.Comment: arXiv admin note: text overlap with arXiv:1407.147

Environmental monitoring of fish in the Paz watercourse

Appendix 7/15 of the publication "State of the environment in the Norwegian, Finnish and Russian border area 2007" (The Finnish Environment 6/2007)

A Possible Periodicity in the Radio Lightcurves of 3C454.3

During the period 1966.5 - 2006.2 the 15GHz and 8GHz lightcurves of 3C454.3 (z=0.859) show a qsasi-periodicity of ~12.8 yr (~6.9 yr in the rest frame of the source) with a double-bump structure. This periodic behaviour is interpreted in terms of a rotating double-jet model in which the two jets are created from the black holes in a binary system and rotate with the period of the orbital motion. The periodic variations in the radio fluxes of 3C454.3 are suggested to be mainly due to the lighthouse effects (or the variation in Doppler boosting) of the precessing jets which are caused by the orbital motion. In addition, variations in the mass-flow rates accreting onto the black holes may be also involved.Comment: 15 pages, 11 figure

The cinnamyl alcohol dehydrogenase gene family is involved in the response to Fusarium oxysporum in resistant and susceptible flax genotypes

Flax (Linum usitatissimum L.) is used for the production of textile, oils, pharmaceuticals, and composite materials. Fusarium wilt, caused by the fungus Fusarium oxysporum f. sp. lini, is a very harmful disease that reduces flax production. Flax cultivars that are resistant to Fusarium wilt have been developed, and the genes that are involved in the host response to F. oxysporum have been identified. However, the mechanisms underlying resistance to this pathogen remain unclear. In the present study, we used transcriptome sequencing data obtained from susceptible and resistant flax genotypes grown under control conditions or F. oxysporum infection. Approximately 250 million reads, generated with an Illumina NextSeq instrument, were analyzed. After filtering to exclude the F. oxysporum transcriptome, the remaining reads were mapped to the L. usitatissimum genome and quantified. Then, the expression levels of cinnamyl alcohol dehydrogenase (CAD) family genes, which are known to be involved in the response to F. oxysporum, were evaluated in resistant and susceptible flax genotypes. Expression alterations in response to the pathogen were detected for all 13 examined CAD genes. The most significant differences in expression between control and infected plants were observed for CAD1B, CAD4A, CAD5A, and CAD5B, with strong upregulation of CAD1B, CAD5A, and CAD5B and strong downregulation of CAD4A. When plants were grown under the same conditions, the expression levels were similar in all studied flax genotypes for most CAD genes, and statistically significant differences in expression between resistant and susceptible genotypes were only observed for CAD1A. Our study indicates the strong involvement of CAD genes in flax response to F. oxysporum but brings no evidence of their role as resistance gene candidates. These findings contribute to the understanding of the mechanisms underlying the response of flax to F. oxysporum infection and the role of CAD genes in stress resistance

State of fish populations in small forest lakes in the Norwegian, Finnish and Russian area

Appendix 9/15 of the publication "State of the environment in the Norwegian, Finnish and Russian border area 2007" (The Finnish Environment 6/2007)

Diagnostic significance of magnetic resonance imaging for myocardial damage of various genesis

Purpose: to evaluate the diagnostic significance of magnetic resonance imaging in the differential diagnosis of ischemic heart damage and non-coronary myocardial diseases. Materials and methods: a retrospective analysis of medical documentation of 60 patients of cardiac departments of the Rostov Regional Clinical Hospital was conducted. Held a comparative analysis of the informativeness of the application of instrumental researchmethods (ECG, echocardiography, coronary angiography with leftventriculography and magnetic resonance imaging of the heart) among the patients with myocardial damage of different origins. Results: in patients with IHD, postinfarction cardiosclerosis, in most cases, the results of instrumental studies were diagnosed as having a diagnostic relationship. Conducted MRI of the heart was of decisive importance in the evaluation of the state of the myocardium after systemic thrombolysis or questionable ECG and EchoCG data and was also significant in the differential diagnosis of acute coronary syndrome and focal myocarditis. The results of MRI played an important role in determining the etiology of myocardial hypertrophy, in particular hypertrophic cardiomyopathy, and also helped in the case of differential diagnosis in the syndrome of cardiomegaly.Сonclusions: shown a high diagnostic value of magnetic resonance imaging with the use of contrast agents in the differential diagnosis of ischemic and noncoronary myocardial diseases

Multi-frequency polarization properties of ten quasars on deca-parsec scales at z > 3

Global VLBI (EVN+VLBA) polarization observations at 5 and 8.4 GHz of ten high redshift (z > 3) quasars are presented. The core and jet brightness temperatures are found through modelling the self-calibrated uv-data with Gaussian components, which provide reliable estimates of the flux density and size of individual components. The observed high core brightness temperatures (median $T_{\rm b,\,core}=4\times10^{11}$ K) are consistent with Doppler boosted emission from a relativistic jet orientated close to the line-of-sight. This can also explain the dramatic jet bends observed for some of our sources since small intrinsic bends can be significantly amplified due to projection effects in a highly beamed relativistic jet. We also model-fit the polarized emission and, by taking the minimum angle separation between the model-fitted polarization angles at 5 and 8.4 GHz, we calculate the minimum inferred Faraday rotation measure (RM$_{\rm min}$) for each component. We also calculate the minimum intrinsic RM in the rest frame of the AGN (RM$_{\rm min}^{\rm intr}$ = RM$_{\rm min} (1+z)^2$), first subtracting the integrated (presumed foreground) RM in those cases where we felt we could do this reliably. The resulting mean core $|$RM$_{\rm min}^{\rm intr}|$ is 5580 rad m$^{-2}$, with a standard deviation of 3390 rad m$^{-2}$, for four high-z quasars for which we believe we could reliably remove the foreground RM. We find relatively steep core and jet spectral index values, with a median core spectral index of -0.3 and a median jet spectral index of -1.0. Comparing our results with RM observations of more nearby Active Galactic Nuclei at similar emitted frequencies does not provide any significant evidence for dependence of the quasar nuclear environment with redshift.Comment: Published in MNRAS. 18 pages, 7 figures, 5 table

Tumor suppressor function of the SEMA3B gene in human lung and renal cancers

The SEMA3B gene is located in the 3p21.3 LUCA region, which is frequently affected in different types of cancer. The objective of our study was to expand our knowledge of the SEMA3B gene as a tumor suppressor and the mechanisms of its inactivation. In this study, several experimental approaches were used: tumor growth analyses and apoptosis assays in vitro and in SCID mice, expression and methylation assays and other. With the use of the small cell lung cancer cell line U2020 we confirmed the function of SEMA3B as a tumor suppressor, and showed that the suppression can be realized through the induction of apoptosis and, possibly, associated with the inhibition of angiogenesis. In addition, for the first time, high methylation frequencies have been observed in both intronic (32-39%) and promoter (44-52%) CpG-islands in 38 non-small cell lung carcinomas, including 16 squamous cell carcinomas (SCC) and 22 adenocarcinomas (ADC), and in 83 clear cell renal cell carcinomas (ccRCC). Correlations between the methylation frequencies of the promoter and the intronic CpG-islands of SEMA3B with tumor stage and grade have been revealed for SCC, ADC and ccRCC. The association between the decrease of the SEMA3B mRNA level and hypermethylation of the promoter and the intronic CpG-islands has been estimated in renal primary tumors (P < 0.01). Using qPCR, we observed on the average 10- and 14-fold decrease of the SEMA3B mRNA level in SCC and ADC, respectively, and a 4-fold decrease in ccRCC. The frequency of this effect was high in both lung (92-95%) and renal (84%) tumor samples. Moreover, we showed a clear difference (P < 0.05) of the SEMA3B relative mRNA levels in ADC with and without lymph node metastases. We conclude that aberrant expression and methylation of SEMA3B could be suggested as markers of lung and renal cancer progression