Tailoring Dielectric Properties of Multilayer Composites Using Spark Plasma Sintering

A straightforward and simple way to produce well-densified ferroelectric ceramic composites with a full control of both architecture and properties using spark plasma sintering (SPS) is proposed. SPS main outcome is indeed to obtain high densification at relatively low temperatures and short treatment times thus limiting interdiffusion in multimaterials. Ferroelectric/dielectric (BST64/MgO/BST64) multilayer ceramic densified at 97% was obtained, with unmodified Curie temperature, a stack dielectric constant reaching 600, and dielectric losses dropping down to 0.5%, at room-temperature. This result ascertains SPS as a relevant tool for the design of functional materials with tailored properties

Quantum deformations of associative algebras and integrable systems

Quantum deformations of the structure constants for a class of associative noncommutative algebras are studied. It is shown that these deformations are governed by the quantum central systems which has a geometrical meaning of vanishing Riemann curvature tensor for Christoffel symbols identified with the structure constants. A subclass of isoassociative quantum deformations is described by the oriented associativity equation and, in particular, by the WDVV equation. It is demonstrated that a wider class of weakly (non)associative quantum deformations is connected with the integrable soliton equations too. In particular, such deformations for the three-dimensional and infinite-dimensional algebras are described by the Boussinesq equation and KP hierarchy, respectively.Comment: Numeration of the formulas is correcte

On the Genus Two Free Energies for Semisimple Frobenius Manifolds

We represent the genus two free energy of an arbitrary semisimple Frobenius manifold as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so-called "genus two G-function". Conjecturally the genus two G-function vanishes for a series of important examples of Frobenius manifolds associated with simple singularities as well as for ${\bf P}^1$-orbifolds with positive Euler characteristics. We explain the reasons for such Conjecture and prove it in certain particular cases.Comment: 37 pages, 3 figures, V2: the published versio

Results of the ontology alignment evaluation initiative 2019

The Ontology Alignment Evaluation Initiative (OAEI) aims at comparing ontology matching systems on precisely defined test cases. These test cases can be based on ontologies of different levels of complexity (from simple thesauri to expressive OWL ontologies) and use different evaluation modalities (e.g., blind evaluation, open evaluation, or consensus). The OAEI 2019 campaign offered 11 tracks with 29 test cases, and was attended by 20 participants. This paper is an overall presentation of that campaign

Menelaus relation and Fay's trisecant formula are associativity equations

It is shown that the celebrated Menelaus relation and Fay's trisecant formula similar to the WDVV equation are associativity conditions for structure constants of certain three-dimensional algebra.Comment: Talk given at the Conference " Mathematics and Physics of Solitons and Integrable Systems", Dijon, 28.6-2.7, 2009. Minor misprints correcte

The structure of 2D semi-simple field theories

I classify all cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their effect on the Gromov-Witten potential is described by Givental's Fock space formulae. This leads to the reconstruction of Gromov-Witten invariants from the quantum cup-product at a single semi-simple point and from the first Chern class, confirming Givental's higher-genus reconstruction conjecture. The proof uses the Mumford conjecture proved by Madsen and Weiss.Comment: Small errors corrected in v3. Agrees with published versio

Stability data, irregular connections and tropical curves

We study a class of meromorphic connections nabla(Z) on P^1, parametrised by the central charge Z of a stability condition, with values in a Lie algebra of formal vector fields on a torus. Their definition is motivated by the work of Gaiotto, Moore and Neitzke on wall-crossing and three-dimensional field theories. Our main results concern two limits of the families nabla(Z) as we rescale the central charge Z to RZ. In the R to 0 ``conformal limit'' we recover a version of the connections introduced by Bridgeland and Toledano Laredo (and so the Joyce holomorphic generating functions for enumerative invariants), although with a different construction yielding new explicit formulae. In the R to infty ``large complex structure" limit the connections nabla(Z) make contact with the Gross-Pandharipande-Siebert approach to wall-crossing based on tropical geometry. Their flat sections display tropical behaviour, and also encode certain tropical/relative Gromov-Witten invariants

Spectroscopic Characterization of Galaxy Clusters in RCS-1: Spectroscopic Confirmation, Redshift Accuracy, and Dynamical Mass–Richness Relation

We present follow-up spectroscopic observations of galaxy clusters from the first Red-sequence Cluster Survey (RCS-1). This work focuses on two samples, a lower redshift sample of ∼30 clusters ranging in redshift from z ∼ 0.2–0.6 observed with multiobject spectroscopy (MOS) on 4–6.5-m class telescopes and a z ∼ 1 sample of ∼10 clusters 8-m class telescope observations. We examine the detection efficiency and redshift accuracy of the now widely used red-sequence technique for selecting clusters via overdensities of red-sequence galaxies. Using both these data and extended samples including previously published RCS-1 spectroscopy and spectroscopic redshifts from SDSS, we find that the red-sequence redshift using simple two-filter cluster photometric redshifts is accurate to σz ≈ 0.035(1 + z) in RCS-1. This accuracy can potentially be improved with better survey photometric calibration. For the lower redshift sample, ∼5 per cent of clusters show some (minor) contamination from secondary systems with the same red-sequence intruding into the measurement aperture of the original cluster. At z ∼ 1, the rate rises to ∼20 per cent. Approximately ten  per cent of projections are expected to be serious, where the two components contribute significant numbers of their red-sequence galaxies to another cluster. Finally, we present a preliminary study of the mass–richness calibration using velocity dispersions to probe the dynamical masses of the clusters. We find a relation broadly consistent with that seen in the local universe from the WINGS sample at z ∼ 0.05

Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence

We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan, Jarvis and Ruan following ideas of Witten. Moreover, on both sides, we highlight two remarkable integral local systems arising from the common formalism of Gamma-integral structures applied to the derived category of the hypersurface {W=0} and to the category of graded matrix factorizations of W. In this setup, we prove that the analytic continuation matches Orlov equivalence between the two above categories.Comment: 72pages, v2: Appendix B and references added. Typos corrected, v3: several mistakes corrected, final versio