In this paper, we consider a particular class of integral equations of the fourth kind and show that tractability and differentiability index of the given system are 3. Tractability and dierentiability index are introduced based on the-smoothing property of a Volterra integral operator and index reduction procedure, respectively. Using the notion of index, we give sucient conditions for the exi...

Accurate quantum mechanical reactive scattering calculations were performed for the collinear C1NO→CN1O reaction using a polynomial-modified London Eyring Polanyi Sato ~PQLEPS! potential energy surface ~PES!, which has a 4.26 eV deep well in the strong interaction region, and a reference LEPS PES, which has no well in that region. The reaction probabilities obtained for both PESs show signature...

We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the polynomial equations. Our algorithm works in time polynomial in the number of equations and the logarithm of the size of the field, whenever the degree of the pol...

In this article we consider the 3D Primitive Equations (PEs) of the ocean, without viscosity and linearized around a stratified flow. As recalled in the Introduction, the PEs without viscosity ought to be supplemented with boundary conditions of a totally new type which must be nonlocal. In this article a set of boundary conditions is proposed for which we show that the linearized PEs are well-...

We present a new algorithm to decide whether two rational parametric curves are related by a projective transformation and detect all such projective equivalences. Given two rational curves, we derive a system of polynomial equations whose solutions define linear rational transformations of the parameter domain, such that each transformation corresponds to a projective equivalence between the t...

A worst case bound for the condition number of a generic system of polynomial equations with integer coefficients is given. For fixed degree and number of equations, the condition number is (non-uniformly, generically) pseudo-polynomial in the input size.

In this article, we consider the 3D viscous primitive equations (PEs for brevity) of the ocean under two physically relevant boundary conditions for the H and H smooth initial data, respectively. The H regularity result of the solution for the viscous PEs of the ocean has been unknown since the work by Cao and Titi [3], and Kobelkov [26]. In this article we provide the global H-regularity resul...

We present a novel approach for preprocessing systems of polynomial equations via graph partitioning. The variable-sharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the corresponding system of equations can be split into smaller ones that can be solved individually. This can provide a tremendous speed-up in computing the solution to the system, bu...

We present a novel approach for solving systems of polynomialequations via graph partitioning. The concept of a variable-sharing graph of asystem of polynomial equations is defined. If such graph is disconnected, thenthe system of equations is actually two separate systems that can be solvedindividually. This can provide a significant speed-up in computing the solutionto the...