for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

buprenorphine is a partial mu agonist and kappa antagonist which is used for the treatment of pain and opioid addiction. a mixture of buprenorphine hydrochloride and naloxone hydrochloride has been approved for the treatment of opioid dependence.in this study a third order derivative spectrophotometric method based on zero-crossing technique has been used for the simultaneous determination of b...

Starting from second-order conditions for C scalar unconstrained optimization problems described in terms of the second-order Dini directional derivative, we pose the problem, whether similar conditions for C vector optimization problems can be derived. We define second-order Dini directional derivatives for vector functions and apply them to formulate such conditions as a Conjecture. The proof...

A universal approach by Laplace transform to the variational iteration method for fractional derivatives with the nonsingular kernel is presented; in particular, the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative with the non-singular kernel is considered. The analysis elaborated for both non-singular kernel derivatives is shown the necessity of considering...

We study the C-oriented line simplification problem: Given a polygonal chain P represented by an ordered set of vertices PI , ... , pn in the plane, a set of orientations C, and a constant c, we search for a "C-oriented" polygonal chain Q consisting of the minimum number of line segments that has distance at most c to P in the Frechet metric. A polygonal chain is C-oriented if the line segments...

In 1996, Ricardo Ricardo Mañé discovered that Mather measures are in fact the minimizers of a ”universal” infinite dimensional linear programming problem. This fundamental result has many applications, one of the most important is to the estimates of the generic number of Mather measures. Mañé obtained the first estimation of that sort by using finite dimensional approximations. Recently, we we...

We provide a tractable theory of innovation and diffusion of technologies to explore the role of international trade and foreign direct investment (FDI). We model innovation and diffusion as a process involving the combination of new ideas with insights from other industries or countries. We provide conditions under which each country’s equilibrium frontier of knowledge converges to a Frechet d...

We study a simple model of the world economy where the engine of growth is the flows of ideas. Ideas are assumed to diffuse randomly across pair of goods, where the processes used in the production of the lower cost good is adopted. We assume that producers in a country can learn from all sellers of goods to this country. We analyze how trade in goods, and impediments to it, affect this diffusi...

In this study, a derivative method is applied for the determination of dye concentration in fabrics dyed with tricomponent dye mixtures. The reflectance of spectra of the samples were recorded between 400 and 700 nm. Initially, the obtained (K/S) spectra were divided by the spectrum of a standard sample dyed with two of the components in the ternary mixture and the derivative spectra were calcu...