The paper deals with stiff systems of differential equations. To solve this sort of system numerically is a diffult task. In spite of the fact that we come across stiff systems quite often in the common practice, a very interesting and promissing numerical method of solving systems of ordinary differential equations (ODE) based on Taylor series has appeared. The question was how to harness the ...

We present an algorithm to determine if the L-series associated to an automorphic representation and the one associated to an elliptic curve over an imaginary quadratic field agree. By the work of Harris-Soudry-Taylor, Taylor, and Berger-Harcos, we can associate to an automorphic representation a family of compatible -adic representations. Our algorithm is based on Faltings-Serre’s method to pr...

The paper deals with stiff systems of differential equations. To solve this sort of system numerically is a diffult task. In spite of the fact that we come across stiff systems quite often in the common practice, a very interesting and promissing numerical method of solving systems of ordinary differential equations (ODE) based on Taylor series has appeared. The question was how to harness the ...

rayleigh-taylor (rt) instability has a growing importance in many fields including aircraft industry and astrophysics. the development and the growth of rt instability were investigated using sinusoidal disturbances with different wavelength at the interface of two fluids. numerical simulations were performed by solving navier-stokes unsteady equations with the vof formulation. results of the 2...

The problem is to calculate an approximate solution of an initial value problem for an autonomous system of N ordinary differential equations. Using fast power series techniques, we exhibit an algorithm for the pth-order Taylor series method reN quiring only 0(p In p) arithmetic operations per step as p —> + °°. (Moreover, we N show that any such algorithm requires at least 0(p ) operations per...

The behaviour of parallel and distributed programs can be modeled as the occurrence of events and their interrelationship. Event data collected according to the event model is stored within a partial-order data structure, where it can be reasoned about, enabling debugging, program steering, and autonomic feedback control of the application. Reasoning over event data, a critical requirement for ...

The IBM Power4 processor uses series approximation to calculate square root. We formally verified the correctness of this algorithm using the ACL2(r) theorem prover. The proof requires the analysis of the approximation error on a Chebyshev series. This is done by proving Taylor’s theorem, and then analyzing the Chebyshev series using Taylor series. Taylor’s theorem is proved by way of non-stand...

Course recommendation is a key for achievement in student’s academic path. However, it challenging to appropriately select course content among numerous online education resources, due the differences users’ knowledge structures. Therefore, this paper develops novel sentiment classification approach recommending courses using Taylor-chimp Optimization Algorithm enabled Random Multimodal Deep Le...