A Critical Phenomenon in Solitonic Ising Chains

We discuss a phase transition of the second order taking place in non-local 1D Ising chains generated by specific infinite soliton solutions of the KdV and BKP equations.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

On the structure of the top homology group of the Johnson kernel

The Johnson kernel is the subgroup $\mathcal{K}_g$ of the mapping class group ${\rm Mod}(\Sigma_{g})$ of a genus $g$ oriented closed surface $\Sigma_{g}$ generated by all Dehn twists about separating curves. In this paper we study the structure of the top homology group ${\rm H}_{2g-3}(\mathcal{K}_g, \mathbb{Z})$. For any collection of $2g-3$ disjoint separating curves on $\Sigma_{g}$ one can construct the corresponding abelian cycle in the group ${\rm H}_{2g-3}(\mathcal{K}_g, \mathbb{Z})$; such abelian cycles will be called simplest. In this paper we describe the structure of $\mathbb{Z}[{\rm Mod}(\Sigma_{g})/ \mathcal{K}_g]$-module on the subgroup of ${\rm H}_{2g-3}(\mathcal{K}_g, \mathbb{Z})$ generated by all simplest abelian cycles and find all relations between them.Comment: 22 page

The top homology group of the genus 3 Torelli group

The Torelli group of a genus $g$ oriented surface $\Sigma_g$ is the subgroup $\mathcal{I}_g$ of the mapping class group ${\rm Mod}(\Sigma_g)$ consisting of all mapping classes that act trivially on ${\rm H}_1(\Sigma_g, \mathbb{Z})$. The quotient group ${\rm Mod}(\Sigma_g) / \mathcal{I}_g$ is isomorphic to the symplectic group ${\rm Sp}(2g, \mathbb{Z})$. The cohomological dimension of the group $\mathcal{I}_g$ equals to $3g-5$. The main goal of the present paper is to compute the top homology group of the Torelli group in the case $g = 3$ as ${\rm Sp}(6, \mathbb{Z})$-module. We prove an isomorphism $${\rm H}_4(\mathcal{I}_3, \mathbb{Z}) \cong {\rm Ind}^{{\rm Sp}(6, \mathbb{Z})}_{S_3 \ltimes {\rm SL}(2, \mathbb{Z})^{\times 3}} \mathcal{Z},$$ where $\mathcal{Z}$ is the quotient of $\mathbb{Z}^3$ by its diagonal subgroup $\mathbb{Z}$ with the natural action of the permutation group $S_3$ (the action of ${\rm SL}(2, \mathbb{Z})^{\times 3}$ is trivial). We also construct an explicit set of generators and relations for the group ${\rm H}_4(\mathcal{I}_3, \mathbb{Z})$.Comment: 35 pages, minor correction

Maximal Generalized Rank in Graphical Matrix Spaces

In this note we prove two extensions of a recent combinatorial characterization due to Li, Qiao, Wigderson, Wigderson and Zhang (arXiv:2206.04815) of the maximal dimension of bounded rank subspaces of the graphical matrix space associated with a bipartite graph. Our first result shows that the above characterization remains valid for a wide class of generalized rank functions, including e.g. the permanental rank. Our second result extends the characterization to bounded rank subspaces of the graphical alternating matrix space associated with a general graph.Comment: 10 page

Influence of Carbon Black Content on the Properties of Butadiene Elastomer

В работе приведены результаты исследования физико- механических свойств до и после термического старения, степени набухания в гидравлическом масле, а также температурные свойства эластомеров на основе бутадиенового каучука марки СКД-В в зависимости от содержания малоактивного печного технического углерода марки П‑803. С увеличением содержания технического углерода до 110 масс.ч. в эластомерной матрице происходит повышение относительного удлинения и условной прочности на разрыв, с дальнейшим увеличением содержания наблюдается снижение. С увеличением содержания технического углерода в резиновой смеси показатели плотности, твердости, условного напряжения и агрессивостойкости повышаются. После испытания на термическое старение наблюдается повышение плотности, твердости и условного напряжения, а относительное удлинение и предел прочности при разрыве снижаются. При помощи термомеханического анализатора установлено, что увеличение количества содержания технического углерода в резиновой смеси не оказывает существенного влияния на начало сегментальной подвижности эластомеров, но снижает изменение линейных размеров при повышении температуры. Методом дифференциально сканирующей калориметрии установлено, что изменение количества содержания технического углерода не влияет на среднюю температуру стеклования. При оптимальном содержании технического углерода наблюдается наиболее равномерное распределение частиц в объеме эластомерной матрицы без образования большого количества агломератов либо пустотThe paper presents the results of a study of physical and mechanical properties before and after thermal aging, aggressiveness, as well as the temperature properties of elastomers based on butadiene rubber grade SKD-V, depending on the content of low-activity furnace carbon grade P‑803. With an increase in the content of carbon black up to 110 wt.h. in the elastomeric matrix, an increase in relative elongation and conditional tensile strength occurs, with a further increase in the content, a decrease is observed. The results obtained after thermal aging of samples and their soaking in AMG‑10 hydraulic oil are considered. With an increase in the content of carbon black in the rubber compound, the indicators of density, hardness, conditional stress and aggressiveness increase. After the thermal aging test, an increase in density, hardness and nominal stress is observed, and the elongation and tensile strength decrease. Changing the amount of carbon black in the rubber mixture does not affect the beginning of the segmental mobility of the elastomer, but there is a decrease in the linear-temperature expansion of the samples. Using differential scanning calorimetry, it was found that a change in the amount of carbon black does not affect the glass transition temperature. Using electron microscopy, it was shown that at the optimum content of carbon black, the most uniform distribution of particles occurs in the volume of the elastomeric matrix without the formation of a large number of agglomerates or void

Differential cross section measurements for the production of a W boson in association with jets in proton–proton collisions at √s = 7 TeV

Measurements are reported of differential cross sections for the production of a W boson, which decays into a muon and a neutrino, in association with jets, as a function of several variables, including the transverse momenta (pT) and pseudorapidities of the four leading jets, the scalar sum of jet transverse momenta (HT), and the difference in azimuthal angle between the directions of each jet and the muon. The data sample of pp collisions at a centre-of-mass energy of 7 TeV was collected with the CMS detector at the LHC and corresponds to an integrated luminosity of 5.0 fb[superscript −1]. The measured cross sections are compared to predictions from Monte Carlo generators, MadGraph + pythia and sherpa, and to next-to-leading-order calculations from BlackHat + sherpa. The differential cross sections are found to be in agreement with the predictions, apart from the pT distributions of the leading jets at high pT values, the distributions of the HT at high-HT and low jet multiplicity, and the distribution of the difference in azimuthal angle between the leading jet and the muon at low values.United States. Dept. of EnergyNational Science Foundation (U.S.)Alfred P. Sloan Foundatio