The deductive organization of Euclid’s Elements serves as a model for mathematical and scientific texts in a variety of subjects from antiquity through the early modern period, not only in the West but also in the Islamic world and beyond. The study of this tradition demands formal methods that will explicitly and unambiguously represent the deductive structures of given texts. This paper explo...

Explicit Runge–Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge–Kutta schemes available in literature. Furthermore, they have a small principal error n...

In the first part of this article we introduce the notion of a backwardforward conditioning (BFC) system that generalises the notion of zero-class admissibiliy introduced in [21]. We can show that unless the spectum contains a halfplane, the BFC property occurs only in siutations where the underlying semigroup extends to a group. In a second part we present a sufficient condition for exact obse...

we then write sn → s(A), where A is the A method of summability. Appropriate choices of A= [an,k] for n,k ≥ 0 give the classical methods [2]. In this paper, we present various summability analogs of the strong law of large numbers (SLLN) and their rates of convergence in an unified setting, beyond the class of random-walk methods. A convolution summability method introduced in the next section ...

depth estimation of the top of the bedrock in the sedimentary basins is the main goal in geomagnetic explorations. the depth estimation of this kind of anomalies can be done using different methods, in the cases where the bedrock is magnetized. in this article, we use the standard euler deconvolution method and its results to interpret the magnetic data from the reshm region in semnan province ...

This paper introduces a three and a four order explicit time stepping method. These methods have high stage order and favorable monotonicity properties. The proposed methods are based on multistagemultistep (MM) schemes that belong to the broader class of general linear methods, which are generalizations of both Runge-Kutta and linear multistep methods. Methods with high stage order alleviate t...

In this paper, we investigate the nonlinear stability of contact waves to Cauchy problem compressible Euler-Fourier system with a reacting mixture in one dimension under non-zero mass condition. If corresponding Riemann for Euler admits discontinuity solution, it is shown that wave nonlinearly stable, while strength and initial perturbation are suitably small. Especially, obtain decay rate by u...

We consider quasi-neutral limits in two-fluid isentropic Euler-Poisson equations arising in the modeling of unmagnetized plasmas and semiconductors. For periodic smooth solutions, we justify an asymptotic expansion in a time interval independent of the Debye length. This implies the convergence of the equations to compressible Euler equations. The proof is based on energy estimates for symmetri...