In this paper, a numerical method for solving the constrained optimal control of time-varying singular systems with quadratic performance index is presented. Presented method is based on Bernste in polynomials. Operational matrices of integration, differentiation and product are introduced and utilized to reduce the optimal control of time-varying singular problems to the solution of algebraic ...

In this article, we investigate the existence, uniqueness, nonexistence, and regularity of weak solutions to nonlinear fractional elliptic problem type (P) (see below) involving singular nonlinearity weights in smooth bounded domain. We prove existence solution $$W_{loc}^{s,p}(\Omega )$$ via approximation method. Establishing a new comparison principle independent interest, uniqueness for $$0 \...

n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem. 

In this paper, we define X-slant helix in Euclidean 3-space and we obtain helix, slant helix, clad and g-clad helix as special case of the X-slant helix. Then we study Darboux, tangential darboux developable surfaces and their singular points. Especially we show that the striction lines of these surfaces are singular locus of the surfaces.

Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...

in this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by boundary elements. the integrals in boundary integrals equations are inherently singular. for example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

In this paper, a sample estimator of the tangency portfolio (TP) weights is considered. The focus on situation where number observations smaller than assets in and returns are i.i.d. normally distributed. Under these assumptions, covariance matrix follows singular Wishart distribution and, therefore, regular inverse cannot be taken. bounds approximations for first two moments estimated TP deriv...

We propose an improved tensor renormalization-group (TRG) algorithm, the bond-weighted TRG (BTRG). In BTRG, we generalize conventional by introducing bond weights on edges of network. show that BTRG outperforms and higher-order renormalization group with same dimension, whereas its computation time is almost as TRG. Furthermore, can have nontrivial fixed-point tensors at optimal hyperparameter....