Birational rigidity of orbifold degree 2 del Pezzo fibrations

Del Pezzo fibrations form a class of possible outputs of the minimal model program. It is known that del Pezzo fibrations of degrees $1,2,3$ over the projective line with smooth total space satisfying the $K^2$-condition are birationally rigid: their Mori fibre space structure is unique. This implies that they are not birational to any Fano varieties, conic bundles or other del Pezzo fibrations. In particular, they are irrational. The families of del Pezzo fibrations with smooth total space of degrees $2$ are rather special, as for "most" families a general del Pezzo fibration has the simplest orbifold singularities. We prove that orbifold del Pezzo fibrations of degree $2$ over the projective line satisfying explicit generality conditions as well as a generalised $K^2$-condition are birationally rigid.Comment: Some typos fixed, exposition improve

17 - Stability Analysis of Stochastically Switching Kuramoto Networks

Motivated by real-world networks with evolving connections, we analyze how stochastic switching affects patterns of synchrony and their stability in networks of identical Kuramoto oscillators with inertia. Stochastic dynamical networks are a useful model for many physical, biological, and engineering systems that have evolving topology, but they have proven to be difficult to work with, and the analytical results are rare. These networks have two characteristic time scales, one is associated with intrinsic dynamics of individual oscillators comprising the network, and the other corresponds to switching period of on-off connections. In the limit of fast switching, the relation between the dynamics of the stochastic network and the static network can be obtained by replacing the switching connections with their mean. We use averaging and Lyapunov function methods to elucidate this non-trivial relationship. We prove that clusters of synchrony which stably appear in the averaged static network can also be observed in the original stochastic network and derive bounds on the switching frequency that guarantee, in a probabilistic sense, the convergence to a stable cluster solution. We also demonstrate the emergence and persistence of chimera states in these stochastic networks

Stability of fibrations over one-dimensional bases

We introduce and study a new notion of stability for varieties fibered over curves, motivated by Koll\'ar's stability for homogeneous polynomials with integral coefficients. We develop tools to study geometric properties of stable birational models of fibrations whose fibers are complete intersections in weighted projective spaces. As an application, we prove the existence of standard models of threefold degree one and two del Pezzo fibrations, settling a conjecture of Corti from 1996.Comment: 34 pages, v2: minor typos corrected. A reference to Loginov's paper arXiv:1710.02482 is adde

Influence of the spatial distribution of border traps in the capacitance frequency dispersion of Al2O3/InGaAs

In this paper, the capacitance frequency dispersion in strong accumulation of capacitance voltage curves has been studied for different high-k dielectric layers in MOS stacks. By studying experimental data at low (77 K) and room temperature (300 K), in oxides with different density of defects, it was possible reflect the spatial distribution of the defects in the capacitance frequency dispersion. The experimental data show that while at room temperature, the capacitance dispersion is dominated by the exchange of carriers from the semiconductor into oxide traps far away from the interface, at low temperature the oxide traps near the Al2O3/InGaAs interface are responsible for the frequency dispersion. The results indicate that the capacitance dispersion in strong accumulation reflect the spatial distribution of traps within the oxide, and that dielectric/semiconductor conduction band offset is a critical parameter for determining the capacitance dispersion for Al2O3/InGaAs based gate stacks.Fil: Palumbo, Félix Roberto Mario. Comisión Nacional de Energía Atómica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Tecnológica Nacional; ArgentinaFil: Aguirre, Fernando Leonel. Universidad Tecnológica Nacional; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica; ArgentinaFil: Pazos, Sebastián Matías. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Tecnológica Nacional; Argentina. Comisión Nacional de Energía Atómica; ArgentinaFil: Krylov, Igor. Technion - Israel Institute of Technology; IsraelFil: Winter, Roy. Technion - Israel Institute of Technology; IsraelFil: Eizenberg, Moshe. Technion - Israel Institute of Technology; Israe

K-stability of Casagrande-Druel varieties

We introduce a new subclass of Fano varieties (Casagrande-Druel varieties), that are $n$-dimensional varieties constructed from Fano double covers of dimension $n-1$. We conjecture that a Casagrande-Druel variety is K-polystable if the double cover and its base space are K-polystable. We prove this for smoothable Casagrande-Druel threefolds, and for Casagrande-Druel varieties constructed from double covers of $\mathbb{P}^{n-1}$ ramified over smooth hypersurfaces of degree $2d$ with $n>d>\frac{n}{2}>1$. As an application, we describe the connected components of the K-moduli space parametrizing smoothable K-polystable Fano threefolds in the families 3.9 and 4.2 in the Mori-Mukai classification.Comment: 58 page

STATIC BEARING CAPACITY OF STEEL-PLATE COMPOSITE WALLS

The features of the behavior of steel-plate composite walls for static loads are considered. Based on the analysis of modern technical and regulatory documentation, the rationale for the chosen research topic is given. A review of the literature is performed, and the features of development are noted. A detailed description and features of the experimental structures under study and the materials used are presented. The features of the test are considered, and the test equipment is described. Analytical and numerical calculations of structures for eccentric compression have been performed. The description of the calculation complex and the used models of materials is presented; the description of numerical models, the features of their construction and calculation are given, the results of calculations are presented – stress distributions, deformations, features of cracking. The general types of experimental eccentric compression wall models are presented, the nature of the loss of bearing capacity of experimental structures is described, and a picture of destruction is presented. The analysis of the experimental data obtained and their comparison with analytical and numerical calculations are performed

Ocean-bottom seismographs based on broadband MET sensors: architecture and deployment case study in the Arctic

The Arctic seas are now of particular interest due to their prospects in terms of hydrocarbon extraction, development of marine transport routes, etc. Thus, various geohazards, including those related to seismicity, require detailed studies, especially by instrumental methods. This paper is devoted to the ocean-bottom seismographs (OBS) based on broadband molecular–electronic transfer (MET) sensors and a deployment case study in the Laptev Sea. The purpose of the study is to introduce the architecture of several modifications of OBS and to demonstrate their applicability in solving different tasks in the framework of seismic hazard assessment for the Arctic seas. To do this, we used the first results of several pilot deployments of the OBS developed by Shirshov Institute of Oceanology of the Russian Academy of Sciences (IO RAS) and IP Ilyinskiy A.D. in the Laptev Sea that took place in 2018–2020. We highlighted various seismological applications of OBS based on broadband MET sensors CME-4311 (60 s) and CME-4111 (120 s), including the analysis of ambient seismic noise, registering the signals of large remote earthquakes and weak local microearthquakes, and the instrumental approach of the site response assessment. The main characteristics of the broadband MET sensors and OBS architectures turned out to be suitable for obtaining high-quality OBS records under the Arctic conditions to solve seismological problems. In addition, the obtained case study results showed the prospects in a broader context, such as the possible influence of the seismotectonic factor on the bottom-up thawing of subsea permafrost and massive methane release, probably from decaying hydrates and deep geological sources. The described OBS will be actively used in further Arctic expeditions