A note on the eight tetrahedron equations
نویسندگان
چکیده
In this paper we derive from arguments of string scattering a set of eight tetrahedron equations, with different index orderings. It is argued that this system of equations is the proper system that represents integrable structures in three dimensions generalising the Yang-Baxter equation. Under additional restrictions this system reduces to the usual tetrahedron equation in the vertex form. Most known solutions fall under this class, but it is by no means necessary. Comparison is made with the work on braided monoidal 2-categories also leading to eight tetrahedron
منابع مشابه
A NOTE ON "A SIXTH ORDER METHOD FOR SOLVING NONLINEAR EQUATIONS"
In this study, we modify an iterative non-optimal without memory method, in such a way that is becomes optimal. Therefore, we obtain convergence order eight with the some functional evaluations. To justify our proposed method, some numerical examples are given.
متن کاملGeneralized volume and geometric structure of 3-manifolds
For several hyperbolic knots, a relation between certain quantum invariants and the volume of their complements are discovered by R. Kashaev in [2]. In [6], it is shown that Kashaev’s invariants are specializations of the colored Jones polynomials. Kashaev used the saddle point method to obtain certain limit of invariants, and Y. Yokota proved that the equations to determine the saddle points c...
متن کاملA NOTE ON THE AVERAGING METHOD FOR DIFFERENTIAL EQUATIONS WITH MAXIMA
Substantiation of the averaging method for differential equations with maxima is presented. Two theorems on substantiates for differential equations with maxima are established.
متن کاملA note on blow-up in parabolic equations with local and localized sources
This note deals with the systems of parabolic equations with local and localized sources involving $n$ components. We obtained the exponent regions, where $kin {1,2,cdots,n}$ components may blow up simultaneously while the other $(n-k)$ ones still remain bounded under suitable initial data. It is proved that different initial data can lead to different blow-up phenomena even in the same ...
متن کاملOn the Performance of Different Empirical Loss Equations for Flow Through Coarse Porous Media (RESEARCH NOTE)
In this paper, the empirical equations that estimate hydraulic parameters for non-linear flow through coarse porous media are evaluated using a series of independent data collected in the laboratory. In this regard, three different relatively uniform soils ranging in size from 8.5 to 27.6 mm have been selected and three random samples drawn from each material. The physical characteristics such ...
متن کامل