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For two rapid-intensification typhoons — Mujigae (2015) and Vicente (2012) — the atmospheric circulation conditions and potential vorticity (PV) anomaly are compared. Although similar in their rapid-intensification (RI) rate, their atmospheric circulation conditions differ considerably, with the absence or presence of an upper-tropospheric inverted trough (IT) being their main difference. The IT provides useful clues for the onset of RI, by estimating the interaction between the environmental upper-tropospheric IT and the typhoon based on eddy momentum flux convergence calculation. The trough–typhoon interaction is examined by comparing the PV transport process for the two cases. An isolated positive PV column develops vertically near Mujigae’s onset of RI, which is not influenced by synoptic-scale PV advection. However, for Vicente, another source — advection from a high-latitude PV reservoir along the upper-tropospheric IT — joins the built-up high-PV anomaly in favor of RI.

This paper presents an innovative calorimetric method for measurements of AC losses of high-temperature superconducting (HTS) tapes by using effect of optical fiber Bragg grating (FBG) wavelength shift resulting from temperature change caused by AC losses, where it is adopted as temperature sensor. The HTS specimen on which the FBG are attached on are adiabatically processed before measuring. Comparing with conventional electric and calorimetric methods, FBG temperature sensor has advantage of rapid response and anti-electromagnetic interference due to its thin geometrical sizes and optical characteristics, it is thus very suitable to AC loss measurement of HTS applications in much more complicated electromagnetic circumstance. By measuring the effect of temperature on wavelength shift in low temperature range, it is indicated that FBG has good enough repeatability of dependence of wavelength shift on temperature measurement around liquid nitrogen temperature of 77 K. After calibration, AC loss of BSCCO HTS tape in self-field is measured by the FBG sensor, and the measured loss is also measured by conventional electric method using lock-in amplifier (LIA). It is shown that the measured AC loss is agreement with the results measured by electric method and those based on Norris theory, so that the presented calorimetric method is available for measuring the AC loss of superconductors and expected to be generalized to AC loss or thermal measurements of other bulk superconductors.

We construct a class of homogeneous vertex representations of C (1) , l ≥ 2, and deduce a series of product-sum identities. These identities have fine interpretation in the number theory.

Let $G$ be a finite cyclic group. Every sequence $S$ over $G$ can be written in the form $S=(n_1g)\cdot...\cdot(n_lg)$ where $g\in G$ and $n_1,\cdots,n_l\in[1,{\hbox{\rm ord}}(g)]$, and the index $\ind S$ of $S$ is defined to be the minimum of $(n_1+\cdots+n_l)/\hbox{\rm ord}(g)$ over all possible $g\in G$ such that $\langle g\rangle=G$. A conjecture says that if $G$ is finite such that $\gcd(|G|,6)=1$, then $\ind(S)=1$ for every minimal zero-sum sequence $S$. In this paper, we prove that the conjecture holds if $S$ is reduced and the (A1) condition is satisfied(see [19])., arXiv admin note: text overlap with arXiv:1303.1682, arXiv:1303.1676 by other authors

Let G be a finite cyclic group. Every sequence S over G can be written in the form S = ( n 1 g ) ⋅ ⋯ ⋅ ( n k g ) where g ∈ G and n 1 , … , n k ∈ [ 1 , ord ( g ) ] , and the index ind S of S is defined to be the minimum of ( n 1 + ⋯ + n k ) / ord ( g ) over all possible g ∈ G such that 〈 g 〉 = G . A conjecture says that if G is finite such that gcd ( | G | , 6 ) = 1 , then ind ( S ) = 1 for every minimal zero-sum sequence S. In this paper, we prove that the conjecture holds if | G | has two prime factors.

Let G be a finite cyclic group. Every sequence S over G can be written in the form S = (n1g)⋅…⋅(nlg) where g ∈ G and n1,…,nl ∈ [1, ord (g)], and the index ind (S) of S is defined to be the minimum of (n1 +⋯+ nl)/ ord (g) over all possible g ∈ G such that 〈g〉 = G. A conjecture says that if G is finite such that gcd (|G|, 6) = 1, then ind (S) = 1 for every minimal zero-sum sequence S. In this paper, we prove that the conjecture holds if S is reduced and at least one ni coprime to |G|.

We define parameterized-Euler-constant function z ↦ γ α ( z ) : = ∑ n = 1 ∞ z n − 1 ( α n − log n + α n ) with parameter α > − 1 , defined on the closed unit disk. The function γ α ( z ) is an extension of the function z ↦ γ ( z ) : = γ 1 ( z ) studied recently and having the property that γ 1 ( 1 ) = C , C being the Euler–Mascheroni constant. Integrals for γ α ( z ) provide its analytic continuation to C ∖ [ 1 , + ∞ ) .

For any Virasoro-toroidal Lie algebra of type X l (1) ( X = A , B , C , D , E , F , G ), we give some explicit irreducible representations from the vertex operators and some oscillator representations of Virasoro algebra.

In present work, we find a class of Lie algebras, which are defined from the symmetrizable generalized intersection matrices. However, such algebras are different from generalized intersection matrix algebras and intersection matrix algebras. Moreover, such Lie algebras generated by semi-positive definite matrices can be classified by the modified Dynkin diagrams., 14 pages. arXiv admin note: text overlap with arXiv:0904.2432 by other authors