I present here a brief resume, without proofs, of the print \Monodromy of certain Painlev e VI transcendents and reeection groups", written by Prof. Boris Dubrovin and myself (SISSA preprint n. 149=97=FM). In this paper, we study the global analytic properties of the solutions of a particular family of Painlev e VI equations with the parameters = = 0, = 1 2 and arbitrary. We introduce a class o...

We discuss in this paper various aspects of the off-critical O(n) model in two dimensions. We find the ground-state energy conjectured by Zamolodchikov for the unitary minimal models, and extend the result to some non-unitary minimal cases. We apply our results to the discussion of scaling functions for polymers on a cylinder. We show, using the underlying N =2 supersymmetry, that the scaling f...

in this article, we study the analytical solutions of different parabolic heat equations with different boundaryconditions in the form of multi-term fractional differential equations. then we compare these analytical solutions with numerical finite difference methods. this comparison demonstrates the accuracy of the analytical and numerical methods presented here.

this paper presents a class of theoretical and iterative method for linear partial differential equations. an algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. in this technique, the solution is calculated in the form of a series with easily computable components. there test modeling problems from mathematical mechanic, physi...

the index of matrix a in cn.n is equivalent to the dimension of largest jor-dan block corresponding to the zero eigenvalue of a. in this paper, indicialequations and normal equations for solving inconsistent singular linear systemof equations are investigated.

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

In this paper we suggest generalizations of elliptic integrable tops to matrix-valued variables. Our consideration is based on R-matrix description which provides Lax pairs in terms of quantum and classical R-matrices. First, we prove that for relativistic (and non-relativistic) tops such Lax pairs with spectral parameter follow from the associative Yang-Baxter equation and its degenerations. T...

Acceleration–force setups for multi-rigid-body dynamics are known to be inconsistent for some configurations and sufficiently large friction coefficients (a Painleve paradox). This difficulty is circumvented by time-stepping methods using impulse-velocity approaches, which solve complementarity problems with possibly nonconvex solution sets. We show that very simple configurations involving two...