Fast Computation of Exact Ranges of Symmetric Convex and Concave Functions under Interval Uncertainty

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

Existence and multiplicity of nontrivial solutions for‎ ‎$p$-Laplacian system with nonlinearities of concave-convex type and‎ ‎sign-changing weight functions

This paper is concerned with the existence of multiple positive‎ ‎solutions for a quasilinear elliptic system involving concave-convex‎ ‎nonlinearities‎ ‎and sign-changing weight functions‎. ‎With the help of the Nehari manifold and Palais-Smale condition‎, ‎we prove that the system has at least two nontrivial positive‎ ‎solutions‎, ‎when the pair of parameters $(lambda,mu)$ belongs to a c...

ABCD matrix for reflection and refraction of laser beam at tilted concave and convex elliptic paraboloid interfaces and studying laser beam reflection from a tilted concave parabola of revolution

Studying Gaussian beam is a method to investigate laser beam propagation and ABCD matrix is a fast and simple method to simulate Gaussian beam propagation in different mediums. Of the ABCD matrices studied so far, reflection and refraction matrices at various surfaces have attracted a lot of researches. However in previous work the incident beam and the principle axis of surface are in parallel...

The Sugeno fuzzy integral of concave functions

The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membershipvalue of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is presenthas been well established. Most of the integral inequalities studied in the fuzzy integration context normally considerconditions such as monotonicity or comonotonicity....

Fast convolution and Fast Fourier Transform under interval and fuzzy uncertainty

Convolution y(t) = ∫ a(t− s) ·x(s) ds is one of the main techniques in digital signal processing. A straightforward computation of the convolution y(t) requires O(n2) steps, where n is the number of observations x(t0), . . . , x(tn−1). It is well known that by using the Fast Fourier Transform (FFT) algorithm, we can compute convolution much faster, with computation time O(n · log(n)). In practi...