In this study‎, ‎a new polynomial rank transmutation is proposed with the help of‎ ‎ the idea of quadratic rank transmutation mapping (QRTM)‎. ‎This polynomial rank‎ ‎ transmutation is allowed to extend the range of the transmutation parameter from‎ ‎  [-1,1] to [-1,k]‎‎. ‎At this point‎, ‎the generated distributions gain more&lrm...

and Applied Analysis 3 is Cauchy. If each Cauchy sequence is convergent, then the fuzzy norm is said to be complete, and the fuzzy normed space is called a fuzzy Banach space. Let X,N be a fuzzy normed space and Y,N ′ a fuzzy Banach space. For a given mapping f : X → Y , we use the abbreviation Df ( x, y ) : f ( 2x y ) f ( 2x − y 2f x − fx y − fx − y − 2f 2x , 2.1 for all x, y ∈ X. Recall Df ≡ ...

Standard methods for regularizing ill-posed nonlinear equations rely on derivatives of the nonlinear forward mapping. Thereby stronger structural properties of the concrete problem are neglected and the derived algorithms only show mediocre efficiency. We concentrate on nonlinear mappings with quadratic structure and develop a derivative-free regularization method that allows us to apply classi...

In this paper, we extend the concept of control barrier functions, developed initially for continuous time systems, to the discrete-time domain. We demonstrate safety-critical control for nonlinear discrete-time systems with applications to 3D bipedal robot navigation. Particularly, we mathematically analyze two different formulations of control barrier functions, based on their continuous-time...

The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional equation$$fleft(sqrt[3]{ax^{3}+by^{3}}right)+fleft(sqrt[3]{ax^{3}-by^{3}}right)=2a^{2}f(x)+2b^{2}f(y),;; x,yinmathbb{R},$$for a mapping $f$ from $mathbb{R}$ into a vector space. We also investigate some stability and hyperstability results for...

Minimizing a nonlinear functional is presented as a way of obtaining a planar mapping that matches two similar images. A smoothing term is added to the nonlinear functional to penalize discontinuous and irregular solutions. One option for the smoothing term is a quadratic form generated by a linear differential operator. The functional is then minimized using the Fourier representation of the p...

A nonconvex problem of constrained optimization is analyzed in terms of its ordinary Lagrangian function. New sufficient conditions are obtained for the duality gap to vanish. Among them, the main condition is that the objective and constraint functions be the sums of convex functionals and nonconvex quadratic forms with certain specific spectral properties. The proofs are related to extensions...

In this paper, we determine some stability results concerning the 2-dimensional vector variable quadratic functional equation f(x+ y, z + w) + f(x − y, z − w) = 2f(x, z) + 2f(y, w) in intuitionistic fuzzy normed spaces (IFNS). We define the intuitionistic fuzzy continuity of the 2-dimensional vector variable quadratic mappings and prove that the existence of a solution for any approximately 2-d...

(i) Suppose that an " infinite string " has an initial displacement   x + 1, −1 ≤ x ≤ 0  u (x, 0) = f (x) = 1 − 2x, 0 ≤ x ≤ 1/2   0, x < −1 and x > 1/2 and zero initial velocity u t (x, 0) = 0. Write down the solution of the wave equation u tt = u xx with ICs u (x, 0) = f (x) and u t (x, 0) = 0 using D'Alembert's formula. Illustrate the nature of the solution by sketching the ux-profiles y...