We derive a new algorithm for computing the action f(A)V of the cosine, sine, hyperbolic cosine, and hyperbolic sine of a matrix A on a matrix V , without first computing f(A). The algorithm can compute cos(A)V and sin(A)V simultaneously, and likewise for cosh(A)V and sinh(A)V , and it uses only real arithmetic when A is real. The algorithm exploits an existing algorithm expmv of Al-Mohy and Hi...

The manner in which sma.ll perturbations in the data give rise to a perturbation in the solution of a two point. boundary value problem will determine how effectively the solution can be approximated nmnerically. However ·this 'conditioning' also has a number of other implications that are less obvious. 'rhese include the effec·t on the stability of numerical schemes, the condi·tioning of shoot...

A new risk analysis system for estimating the risk factors in tunneling is suggested in consideration of the complex effect in tunnel construction. It is verified that various risk factors can be expressed by stability and environment index using numerical and statistical analysis. Stability index includes the factors of safety of ground condition, the amount of ground settlement, condition of ...

‎ in this paper, we investigate stability analysis of fractional differential systems equipped with the conformable fractional derivatives. some stability conditions of fractional differential systems are proposed by applying the fractional exponential function and the fractional laplace transform. moreover, we check the stability of conformable fractional lotka-volterra system with the multi-st...

The concept of cluster stability is introduced to assess the validity of data partitionings found by clustering algorithms. It allows us to explicitly quantify the quality of a clustering solution, without being dependent on external information. The principle of maximizing the cluster stability can be interpreted as choosing the most self-consistent data partitioning. We present an empirical e...

This paper gives an overview of recent achievements of the multiwavelet theory. The construction of multiwavelets is based on a multiresolution analysis with higher multiplicity generated by a scaling vector. The basic properties of scaling vectors such as L-stability, approximation order and regularity are studied. Most of the proofs are sketched.

ab initio calculations at hf/6-31g* level of theory for geometry optimization and mp2/6-31g*//hf/6-31g* for a single point total energy calculation are reported for the importantenergy-minimum conformations and transition-state geometries of 1, 3-diazacyclohepta-1, 2-diene (2) and 1, 3-diazacycloocta-1, 2-diene (3). the c2 symmetric twist-chair (2-tc)conformation of 2 is calculated to be 7.4 kj...

a novel method to compute the stability region in power system transient stability analysis is presented. this method is based on the set analysis. the key to this method is to construct the hamilton-jacobi-isaacs (hji) partial differential equation (pde) of a nonlinear system, using which we can compute the backward reachable set by applying the level set methods. the backward reachable set of...