A new family of set-theoretic solutions of the Yang–Baxter equation

A new family of non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation is constructed. Two subfamilies, consisting of irretractable square-free solutions, are new counterexamples to Gateva-Ivanova’s Strong Conjecture [7 Gateva-Ivanova, T. (2004). A combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation. J. Math. Phys. 45(10):3828–3858.[Crossref], [Web of Science ®] , [Google Scholar]]. They are in addition to those obtained by Vendramin [15 Vendramin, L. (2016). Extensions of set-theoretic solutions of the Yang-Baxter equation and a conjecture of Gateva-Ivanova. J. Pure Appl. Algebra 220:2064–2076.[Crossref], [Web of Science ®] , [Google Scholar]] and [1 Bachiller, D., Cedó, F., Jespers, E., Okniński, J. (2017). A family of irretractable square-free solutions of the Yang-Baxter equation. Forum Math. (to appear). [Google Scholar]].     

宋元海洋知识中的“海”与“洋”

宋元时期随着航海实践的空前发展,海洋地理空间认知中“九州—四海”的“天下”格局的知识框架逐步被航海实践突破和“遗忘”,在海洋地理认知上抽象的“海”向具象的“洋”的转变,海洋被以多种方式划分和命名为不同的“洋”。宋元对“洋”的划分和命名仍表现为区域性知识,但其基于航海实践的知识生成路径奠定了不同朝代、不同国家形成共同海洋知识和海洋观念的逻辑基础。在中国接受和融入世界共同海洋知识和海洋观念的过程中,宋元海洋实践的空前发展开启了具有重要转折意义的新阶段。     

Hahn–Banach extension theorems for multifunctions revisited

Several generalizations of the Hahn–Banach extension theorem to K-convex multifunctions were stated recently in the literature. In this note we provide an easy direct proof for the multifunction version of the Hahn–Banach–Kantorovich theorem and show that in a quite general situation it can be obtained from existing results. Then we derive the Yang extension theorem using a similar proof as well as a stronger version of it using a classical separation theorem. Moreover, we give counterexamples to several extension theorems stated in the literature. Dedicated to Jean-Paul Penot with the occasion of his retirement.     

A Hadamard matrix of order 428

Four Turyn type sequences of lengths 36, 36, 36, 35 are found by a computer search. These sequences give new base sequences of lengths 71, 71, 36, 36 and are used to generate a number of new T‐sequences. The first order of many new Hadamard matrices constructible using these new T‐sequences is 428. © 2004 Wiley Periodicals, Inc.     

A new family of optimal FHS sets with composite lengths

In frequency-hopping spread spectrum systems, frequency-hopping sequences (FHSs) are widely used to alleviate the interferences caused by the hits of frequencies. In this paper, based on the Zeng–Cai–Tang–Yang cyclotomy and the Chinese Remainder Theorem, a family of FHS sets with composite lengths is constructed and the Hamming correlations of the new FHS sets are derived by some basic properties of cyclotomic numbers. The results show that the proposed FHS sets are optimal with respect to the Peng–Fan bound. Furthermore, it generalizes some earlier cyclotomic constructions of optimal FHS sets and produces optimal FHS sets with new parameters which are not covered in the literature.     

Cosmological Parameters from Planck Data in SU(2)CMB,Their Local ΛCDM Values,and the Modified Photon Boltzmann Equation

A review of the spatially flat cosmological model SU(2)_CMB, minimally induced by the postulate that the cosmic microwave background (CMB) is subject to an SU(2) rather than a U(1) gauge principle, is given. Cosmological parameter values, which are determined from the Planck CMB power spectra at small angular scales, are compared to their values in spatially flat ΛCDM from both local and global extractions. As a global model SU(2)_CMB leans toward local ΛCDM cosmology and is in tension with some global ΛCDM parameter values. Spectral antiscreening / screening effects in SU(2)_CMB radiance are presented within the Rayleigh– Jeans regime in dependence on temperature and frequency. Such radiance anomalies can cause CMB large-angle anomalies. Therefore, it is pointed out how SU(2)_CMB modifies the Boltzmann equation  for the perturbations of the photon phase space distribution at low redshift and why this requires to the solve the ℓ-hierarchy on a comoving momentum grid (q-grid) for all z.     

Lee–Yang zeros in the Rydberg atoms

Lee–Yang (LY) zeros play a fundamental role in the formulation of statistical physics in terms of (grand) partition functions, and assume theoretical significance for the phenomenon of phase transitions. In this paper, motivated by recent progress in cold Rydberg atom experiments, we explore the LY zeros in classical Rydberg blockade models. We find that the distribution of zeros of partition functions for these models in one dimension (1d) can be obtained analytically. We prove that all the LY zeros are real and negative for such models with arbitrary blockade radii. Therefore, no phase transitions happen in 1d classical Rydberg chains. We investigate how the zeros redistribute as one interpolates between different blockade radii. We also discuss possible experimental measurements of these zeros.