Interannual variability of heat waves in South Korea and their connection with large-scale atmospheric circulation patterns

This study investigates the interannual variation of heat wave frequency (HWF) in South Korea during the past 42 years (1973-2014) and examines its connection with large-scale atmospheric circulation changes. Korean heat waves tend to develop most frequently in late summer during July and August. The leading Empirical Orthogonal Function accounting for 50% of the total variance shows a mono-signed pattern over South Korea, suggesting that the dominant mechanisms responsible for the heat wave are linked in a spatial scale much larger than the nation. It also exhibits a regional variation with more occurrences in the southeastern inland area. The regression of the leading principal component (PC) time series of HWF with large-scale atmospheric circulation identifies a north-south dipole pattern between the South China Sea and Northeast Asia. When this large-scale circulation mode facilitates deep convection in South China Sea, it tends to weaken moisture transport from the South China Sea to Northeast Asia. Enhanced deep convection in the South China Sea triggers a source of Rossby wave train along southerly wind that generates positive geopotential height anomalies around Korea. The anomalous high pressure pattern is accompanied by large-scale subsidence in Korea, thereby providing a favourable condition for extreme hot and dry days in Korea. This study highlights that there is a decadal change of the relationship between Korean heat waves and large-scale atmospheric circulation patterns. The tropical forcing tends to be weakened in the recent decade, with more influences from the Arctic variability from the mid-1990s.ope

Which subnormal Toeplitz operators are either normal or analytic?

We study subnormal Toeplitz operators on the vector-valued Hardy space of the unit circle, along with an appropriate reformulation of P.R. Halmos's Problem 5: Which subnormal block Toeplitz operators are either normal or analytic? We extend and prove Abrahamse's Theorem to the case of matrix-valued symbols; that is, we show that every subnormal block Toeplitz operator with bounded type symbol (i.e., a quotient of two analytic functions), whose co-analytic part has a "coprime decomposition," is normal or analytic. We also prove that the coprime decomposition condition is essential. Finally, we examine a well known conjecture, of whether every submormal Toeplitz operator with finite rank self-commutator is normal or analytic.Comment: Final version, accepted for publication in Journal of Functional Analysi

Hyponormality and Subnormality of Block Toeplitz Operators

In this paper we are concerned with hyponormality and subnormality of block Toeplitz operators acting on the vector-valued Hardy space $H^2_{\mathbb{C}^n}$ of the unit circle. Firstly, we establish a tractable and explicit criterion on the hyponormality of block Toeplitz operators having bounded type symbols via the triangularization theorem for compressions of the shift operator. Secondly, we consider the gap between hyponormality and subnormality for block Toeplitz operators. This is closely related to Halmos's Problem 5: Is every subnormal Toeplitz operator either normal or analytic? We show that if $\Phi$ is a matrix-valued rational function whose co-analytic part has a coprime factorization then every hyponormal Toeplitz operator $T_{\Phi}$ whose square is also hyponormal must be either normal or analytic. Thirdly, using the subnormal theory of block Toeplitz operators, we give an answer to the following "Toeplitz completion" problem: Find the unspecified Toeplitz entries of the partial block Toeplitz matrix A:=[U^*& ? ?&U^*] so that $A$ becomes subnormal, where $U$ is the unilateral shift on $H^2$.Comment: Final version, accepted for publication in Advances in Mathematic

Metal-organic framework based on hinged cube tessellation as transformable mechanical metamaterial

Mechanical metamaterials exhibit unusual properties, such as negative Poisson???s ratio, which are difficult to achieve in conventional materials. Rational design of mechanical metamaterials at the microscale is becoming popular partly because of the advance in three-dimensional printing technologies. However, incorporating movable building blocks inside solids, thereby enabling us to manipulate mechanical movement at the molecular scale, has been a difficult task. Here, we report a metal-organic framework, self-assembled from a porphyrin linker and a new type of Zn-based secondary building unit, serving as a joint in a hinged cube tessellation. Detailed structural analysis and theoretical calculation show that this material is a mechanical metamaterial exhibiting auxetic behavior. This work demonstrates that the topology of the framework and flexible hinges inside the structure are intimately related to the mechanical properties of the material, providing a guideline for the rational design of mechanically responsive metal-organic frameworks