In this note we will construct several additive Darboux-like functions f : R → R answering some problems from (an earlier version of) [4]. In particular, in Section 2 we will construct, under different additional set theoretical assumptions, additive almost continuous (in sense of Stallings) functions f : R → R whose graph is either meager or null in the plane. In Section 3 we will construct an...

Very recently, J.F.Dillon, and H.Dobbertin proved that, the image set of function ∆k(x) = (x + 1) + x + 1, (where d = 2 − 2 + 1), is a new cyclic difference set in the additive group of the finite field GF (2). Using Fourier analysis on the additive group, we prove that certain sets, constructed by using Dickson polynomials, form a new cyclic difference sets with Singer parameters.

Non-additive entropy measures are important for many applications. We study Havrda and Charvat entropy for record values and have shown that this characterizes the underlying distribution function uniquely. Also the non-additive entropy of record values has been derived in case of some specific distributions. Further we propose a generalized residual entropy measure for record value.

The pseudo-additive relation that the Tsallis entropy satisfies has nothing whatsoever to do with the super-and sub-additivity properties of the entropy. The latter properties, like concavity and convexity, are couched in geometric inequalities and cannot be reduced to equalities. Rather, the pseudo-additivity relation is a functional equation that determines the functional forms of the random ...

A new method for structural topology optimization is introduced which employs the Isogeometric Analysis (IA) method. In this approach, an implicit function is constructed over the whole domain by Non-Uniform Rational B-Spline (NURBS) basis functions which are also used for creating the geometry and the surface of solution of the elasticity problem. Inspiration of the level set method zero level...

metabolome analysis is used to evaluate the characteristics and interactions of low molecular weight metabolites under a specific set of conditions. in cirrhosis, hepatocellular carcinoma, non-alcoholic fatty liver disease (nafld) and non-alcoholic steatotic hepatitis (nash) the  liver  does not function thoroughly due to long-term damage. unfortunately the early detection of cirrhosis, hcc, na...

The set A = {an}∞n=1 of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer can be represented as the sum of h elements of A. If an ∼ αn for some real number α > 0, then α is called an additive eigenvalue of order h. The additive spectrum of order h is the set N (h) consisting of all additive eigenvalues of order h. It is proved that there is a positive nu...