Related papers: Singular Brascamp-Lieb inequalities with cubical s…
We improve on the spectral large sieve inequality for symmetric-squares. We also prove a lower bound showing that the most optimistic upper bound is not true for this family.
In this paper we establish Minkowski inequality and Brunn--Minkowski inequality for $p$-quermassintegral differences of convex bodies. Further, we give Minkowski inequality and Brunn--Minkowski inequality for quermassintegral differences of…
We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg-Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we…
Let $x=a+ib$ be a complex number, so we have the following inequality $$(1/\sqrt{2})|a+b|\leq |x|\leq |a|+|b|$$ We give an operator version of above inequality. Also we obtain some results for normal operators.
Infinitesimal symmetries of $S^1$-bundle gerbes are modelled with multiplicative vector fields on Lie groupoids. It is shown that a connective structure on a bundle gerbe gives rise to a natural horizontal lift of multiplicative vector…
The purpose of this paper is to introduce the notion of isoclinism and cover in a multiplicative Lie algebra which may be helpful to describe all multiplicative Lie algebra structures on a group. Consequently, we give the existence of the…
We prove Marchenko-type uniqueness theorems for inverse Sturm-Liouville problems. Moreover, we prove a generalization of Ambarzumyans theorem.
We derive necessary and sufficient inseparability conditions imposed on the variance matrix of symmetric qubits. These constraints are identified by examining a structural parallelism between continuous variable states and two qubit states.…
In the paper two important theorems about complete affine spheres are generalized to the case of statistical structures on abstract manifolds. The assumption about constant sectional curvature is replaced by the assumption that the…
In 2012, Nazarov used Bergman kernels and Hormander's $L^2$ estimates for the $\bar\partial$-equation to give a new proof of the Bourgain--Milman theorem for symmetric convex bodies and made some suggestions on how his proof should extend…
We discuss general Bell inequalities for bipartite and multipartite systems, emphasizing the connection with convex geometry on the mathematical side, and the communication aspects on the physical side. Known results on families of…
We show that constructible models of arbitrary complete continuous first-order theories are unique up to isomorphism.
We present a set of Bell inequalities for multiqubit quantum systems. These Bell inequalities are shown to be able to detect multiqubit entanglement better than previous Bell inequalities such as Werner-Wolf-Zukowski- Brukner ones.…
We exhibit a computational type theory which combines the higher-dimensional structure of cartesian cubical type theory with the internal parametricity primitives of parametric type theory, drawing out the similarities and distinctions…
Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…
Recent progress in understanding the structure of cosmological singularities is reviewed. The well-known picture due to Belinskii, Khalatnikov and Lifschitz (BKL) is summarized briefly and it is discussed what existing analytical and…
We prove Ptolemaean Inequality and Ptolemaeus' Theorem in the closure complex hyperbolic plane endowed with the Cygan metric.
Through the question of singular topologies in the Boulatov model, we illustrate and summarize some of the recent advances in Group Field Theory.
In this paper, we construct the additional symmetries of the supersymmetric BKP(SBKP) hierarchy. These additional flows constitute a B type $SW_{1+\infty}$ Lie algebra because of the B type reduction of the supersymmetric BKP hierarchy.…
We prove the Levin-Ste\v{c}kin inequality using Chebyshev's inequality and symmetrization. Symmetry and slightly modified Chebyshev's inequality are also the key to an elementary proof of Clausing's inequality .