The aim of this paper is to develop a functional analytic approach towards nonlinear systems. For linear systems this is well known and the resulting class of well-posed and regular linear systems is well studied. Our approach is based on the theory of nonlinear semigroup and we explain it by means of an example, namely equations of quasi-hyperbolic type. 1 Equations of quasi-hyperbolic type Le...

In a recent paper, Pawale [22] investigated quasi-symmetric 2-(v, k, λ) designs with intersection numbers x > 0 and y = x+ 2 with λ > 1 and showed that under these conditions either λ = x + 1 or λ = x + 2, or D is a design with parameters given in the form of an explicit table, or the complement of one of these designs. In this paper, quasi-symmetric designs with y−x = 3 are investigated. It is...

In this paper we define a new concept of quasi-convolution for analytic functions normalized by f (0) = 0 and f ′(0) = 1 in the unit disk E = {z ∈ C: |z| < 1} . We apply this new approach to study the closure properties of a certain class of analytic and univalent functions under some families of (known and new) integral operators.

Quasi three-dimensional (3D) plasmonic nanostructures consisting of Au nanosquares on top of SU-8 nanopillars and Au nanoholes on the bottom were developed and fabricated using nanoimprint lithography with simultaneous thermal and UV exposure. These 3D plasmonic nanostructures were used to detect cell concentration of lung cancer A549 cells, retinal pigment epithelial (RPE) cells, and breast ca...

We review recent results which relate spectral theory of discrete one-dimensional Schrödinger operators over strictly ergodic systems to uniform existence of the Lyapunov exponent. In combination with suitable ergodic theorems this allows one to establish Cantor spectrum of Lebesgue measure zero for a large class of quasicrystal Schrödinger operators. The results can also be used to study non-u...

(t,m, s)-nets are point sets in Euclidean s-space satisfying certain uniformity conditions, for use in numerical integration. They can be equivalently described in terms of ordered orthogonal arrays, a class of finite geometrical structures generalizing orthogonal arrays. This establishes a link between quasi-Monte Carlo methods and coding theory. In the present paper we prove an asymptotic Gil...

A quasi-symmetric design is a (v, k, λ) design with two intersection numbers x, y where 0 ≤ x < y < k. We show that for fixed x, y, λ with x > 1, λ > 1, y = λ and λ (4xy + ((y − x) − 2x− 2y + 1)λ) a perfect square of a positive integer, there exist finitely many quasi-symmetric designs. We rule out the possibilities of quasi-symmetric designs corresponding to y = x + 3 and (λ, x) = (9, 2), (8, ...

Given positive integers n and k, a k-term quasi-progression of diameter n is a sequence (x1, x2, ..., xk) such that d ≤ xj+1−xj ≤ d+n, 1 ≤ j ≤ k−1, for some positive integer d. Thus an arithmetic progression is a quasi-progression of diameter 0. Let Qn(k) denote the least integer for which every coloring of {1, 2, ..., Qn(k)} yields a monochromatic k-term quasi-progression of diameter n. We obt...

in this paper, we investigate the l-fuzzy proximities and the relationships betweenl-fuzzy topologies, l-fuzzy topogenous order and l-fuzzy uniformity. first, we show that the category of-fuzzy topological spaces can be embedded in the category of l-fuzzy quasi-proximity spaces as a coreective full subcategory. second, we show that the category of l -fuzzy proximity spaces is isomorphic to the ...