On the Regularity Property of Differential Polynomials Modulo Regular Differential Chains

International audienceThis paper provides an algorithm which computes the normal form of a rational differential fraction modulo a regular differential chain if, and only if, this normal form exists. A regularity test for polynomials modulo regular chains is revisited in the nondifferential setting and lifted to differential algebra. A new characterization of regular chains is provided

Extrapolation of power series by self-similar factor and root approximants

The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of extrapolation is developed based on self-similar factor and root approximants, suggested earlier by the authors. It is shown that these approximants and their combinations can effectively extrapolate power series to the region of large variables, even up to infinity. Several examples from quantum and statistical mechanics are analysed, illustrating the approach.Comment: 21 pages, Latex fil

A Linear Algebra Approach for Detecting Binomiality of Steady State Ideals of Reversible Chemical Reaction Networks

Motivated by problems from Chemical Reaction Network Theory, we investigate whether steady state ideals of reversible reaction networks are generated by binomials. We take an algebraic approach considering, besides concentrations of species, also rate constants as indeterminates. This leads us to the concept of unconditional binomiality, meaning binomiality for all values of the rate constants. This concept is different from conditional binomiality that applies when rate constant values or relations among rate constants are given. We start by representing the generators of a steady state ideal as sums of binomials, which yields a corresponding coefficient matrix. On these grounds we propose an efficient algorithm for detecting unconditional binomiality. That algorithm uses exclusively elementary column and row operations on the coefficient matrix. We prove asymptotic worst case upper bounds on the time complexity of our algorithm. Furthermore, we experimentally compare its performance with other existing methods

Infiltration in soils with a saturated surface

Key Points Analytic description of infiltration in soils Comparison of constant flux and saturated surface infiltration Linking infiltration to soil/water properties An earlier infiltration equation relied on curve fitting of infiltration data for the determination of one of the parameters, which limits its usefulness in practice. This handicap is removed here, and the parameter is now evaluated by linking it directly to soil-water properties. The new predictions of infiltration using this evaluation are quite accurate. Positions and shapes of soil-water profiles are also examined in detail and found to be predicted analytically with great precision

Lagrangian Curves in a 4-dimensional affine symplectic space

Lagrangian curves in R4 entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify La- grangrian curves with constant symplectic curvatures, to construct a class of Lagrangian tori in R4 and determine Lagrangian geodesic