Abstract In this paper we investigate certain fusion relations associated to an integrable vertex model on the square lattice which is invariant under Sp (4) symmetry. We establish a set of functional include transfer matrix inversion identity. The solution these in thermodynamic limit allows us compute partition function per site fundamental representation model. As byproduct also obtain mixin...

We prove a certain type of inequalities concerning the integral of the Fourier transform of a function integrable on the real line.

This brief review deals with prepotentials inspired by N = 1 SUSY considerations due to Cachazo, Intrilligator, Vafa. These prepotentials associated with matrix models following Dijkgraaf and Vafa should be considered as given on an enlarged moduli space that includes Whitham times (couplings of the superpotential). This moduli space is nothing but the whole moduli space of (decorated) hyperell...

We give a sufficient condition on the Monge-Ampère mass of a plurisubharmonic function u for exp(−2u) to be locally integrable.

Let ( Z , ? ) be a Walsh Brownian motion with spinning measure . Suppose ? is probability on R n We first provide necessary and sufficient condition for to stopping distribution of Then if the stopped process required uniformly integrable, we show that such time exists only balanced Next, under assumption being balanced, identify minimal times those ? integrable. Finally, generalize Vallois’ em...

Two discretizations, linear and nonlinear, of basic notions of the complex analysis are considered. The underlying lattice is an arbitrary quasicrystallic rhombic tiling of a plane. The linear theory is based on the discrete Cauchy-Riemann equations, the nonlinear one is based on the notion of circle patterns. We clarify the role of the rhombic condition in both theories: under this condition t...

In this paper we introduce an abstract integral which includes both product integrals and additive integrals. Thus our theory of Riemann integration embraces both the product integrals of Volterra [l, 2, 3](2), Birkhoff [3], and Masani [l] and the classical additive integrals of Riemann [l] and Stieltjes [l]. Similarly our theory of Lebesgue integration includes the Lebesgue product integrals o...