A lower bound in the problem of realization of cycles

We consider the classical Steenrod problem on realization of integral homology classes by continuous images of smooth oriented manifolds. Let $k(n)$ be the smallest positive integer such that any integral $n$-dimensional homology class becomes realizable in the sense of Steenrod after multiplication by $k(n)$. The best known upper bound for $k(n)$ was obtained independently by G. Brumfiel and V. Buchstaber in 1969. All known lower bounds for $k(n)$ were very far from this upper bound. The main result of this paper is a new lower bound for $k(n)$ which is asymptotically equivalent to the Brumfiel-Buchstaber upper bound (in the logarithmic scale). For $n<24$ we prove that our lower bound is exact. Also we obtain analogous results for the case of realization of integral homology classes by continuous images of smooth stably complex manifolds.Comment: 22 pages; v2: referee's comments taken into account, minor changes, to be published in the Journal of Topolog

Elastohydrodynamic Lubrication (EHL) of Piston Rings in the Internal Combustion Engine

AbstractThe paper analyzes the numerical model of elastohydrodynamic lubrication (EHL) of piston rings in the cylinder liner of the internal combustion engine (ICE). Authors take into account reactions of the lubricating layer, the pressure force of the piston rings on the cylinder wall, forces of the gas pressure in the cylinder, the friction force between the upper edge of the piston ring and the piston groove. A simulation model was developed in the Fortran program and authors have analyzed characteristics and forms of piston rings in the ICE

Detailed Dynamic Modeling of Common Rail Piezo Injector

AbstractA mathematical model of Bosch 3rd generation Common Rail fuel injection system with piezoelectric injector has been created. The numerical calculations for third different accumulator pressures (30, 80 and 160MPa) and third energizing times ET (0.5, 1 and 2ms) have been carried out. The results of calculations of total injected mass per cycle have been compared with the experiment with good agreement. The maximum error for ET=0.5ms is 10.4% and for ET≥1ms is less than 5%

Refraction of dispersive shock waves

We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave often referred to as the shock wave refraction. The refraction of a one-dimensional dispersive shock wave (DSW) due to its head-on collision with the centred rarefaction wave (RW) is considered in the framework of defocusing nonlinear Schr\"odinger (NLS) equation. For the integrable cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain main physical parameters of the DSW refraction. The key features of the DSW-RW interaction predicted by our modulation theory analysis are confirmed by direct numerical solutions of the full dispersive problem.Comment: 45 pages, 23 figures, minor revisio

Genome-wide significant association with seven novel multiple sclerosis risk loci

Objective: A recent large-scale study in multiple sclerosis (MS) using the ImmunoChip platform reported on 11 loci that showed suggestive genetic association with MS. Additional data in sufficiently sized and independent data sets are needed to assess whether these loci represent genuine MS risk factors. Methods: The lead SNPs of all 11 loci were genotyped in 10 796 MS cases and 10 793 controls from Germany, Spain, France, the Netherlands, Austria and Russia, that were independent from the previously reported cohorts. Association analyses were performed using logistic regression based on an additive model. Summary effect size estimates were calculated using fixed-effect meta-analysis. Results: Seven of the 11 tested SNPs showed significant association with MS susceptibility in the 21 589 individuals analysed here. Meta-analysis across our and previously published MS case-control data (total sample size n=101 683) revealed novel genome-wide significant association with MS susceptibility (p<5×10−8) for all seven variants. This included SNPs in or near LOC100506457 (rs1534422, p=4.03×10−12), CD28 (rs6435203, p=1.35×10−9), LPP (rs4686953, p=3.35×10−8), ETS1 (rs3809006, p=7.74×10−9), DLEU1 (rs806349, p=8.14×10−12), LPIN3 (rs6072343, p=7.16×10−12) and IFNGR2 (rs9808753, p=4.40×10−10). Cis expression quantitative locus effects were observed in silico for rs6435203 on CD28 and for rs9808753 on several immunologically relevant genes in the IFNGR2 locus. Conclusions: This study adds seven loci to the list of genuine MS genetic risk factors and further extends the list of established loci shared across autoimmune diseases

Genome-wide significant association with seven novel multiple sclerosis risk loci

Objective: A recent large-scale study in multiple sclerosis (MS) using the ImmunoChip platform reported on 11 loci that showed suggestive genetic association with MS. Additional data in sufficiently sized and independent data sets are needed to assess whether these loci represent genuine MS risk factors. Methods: The lead SNPs of all 11 loci were genotyped in 10 796 MS cases and 10 793 controls from Germany, Spain, France, the Netherlands, Austria and Russia, that were independent from the previously reported cohorts. Association analyses were performed using logistic regression based on an additive model. Summary effect size estimates were calculated using fixed-effect meta-analysis. Results: Seven of the 11 tested SNPs showed significant association with MS susceptibility in the 21 589 individuals analysed here. Meta-analysis across our and previously published MS case-control data (total sample size n=101 683) revealed novel genome-wide significant association with MS susceptibility (p<5×10−8) for all seven variants. This included SNPs in or near LOC100506457 (rs1534422, p=4.03×10−12), CD28 (rs6435203, p=1.35×10−9), LPP (rs4686953, p=3.35×10−8), ETS1 (rs3809006, p=7.74×10−9), DLEU1 (rs806349, p=8.14×10−12), LPIN3 (rs6072343, p=7.16×10−12) and IFNGR2 (rs9808753, p=4.40×10−10). Cis expression quantitative locus effects were observed in silico for rs6435203 on CD28 and for rs9808753 on several immunologically relevant genes in the IFNGR2 locus. Conclusions: This study adds seven loci to the list of genuine MS genetic risk factors and further extends the list of established loci shared across autoimmune diseases