In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.

‎highest weight modules of the double affine lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎singular vectors of verma modules are‎ ‎determined using a similar condition with horizontal affine lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

We have analyzed kinetic roughening in Fe-Cr superlattices by energy-filtered transmission electron microscopy. The direct access to individual interfaces provides both static and dynamic roughness exponents. We find an anomalous non-self-affine scaling of the interface roughness with a time dependent local roughness at short length scales. While the deposition conditions affect strongly the lo...

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...

‎Let $R$ be a ring‎ ‎with the Jacobson radical $J(R)$ and let $picolon Rto R/J(R)$ be‎ the canonical map‎. ‎Then $pi$ induces an order preserving group homomorphism‎ ‎$K_0picolon K_0(R)to K_0(R/J(R))$ and an‎ ‎affine continuous map $S(K_0pi)$ between the state space $St(R/J(R))$ and the‎ ‎state space $St(R).$‎ ‎In this paper‎, ‎we consider the natural affine map $S(K_0pi).$ We give a condition ...

This paper is devoted to studying boundedness criteria for extended-real-valued functions. The study is done in the framework of dual vector spaces, using new objects such as self-equilibrated sets and functions. We establish two boundedness new major criteria. The first one says that an extended-real-valued function is bounded below provided it is minorized by an affine map on one of its self-...

TiO2 thin films and Ag/TiO2 nanoparticles were prepared by CVD and plasma bombardment method. XRD results showed the presence of Ag nanoparticles in TiO2 matrix. SEM image confirmed formation of Ag nanoparticles. XPS analysis was utilized to study the chemical state of the Ag/TiO2 nanostructure. Statistical surface analysis revealed that since there i...

We achieve on self-affine Sierpinski carpets the multifractal analysis of the Birkhoff averages of potentials satisfying a Dini condition. Given such a potential, the corresponding Hausdorff spectrum cannot be deduced from that of the associated Gibbs measure by a simple transformation. Indeed, these spectra are respectively obtained as the Legendre transform of two distinct concave differentia...

The two main theorems of this paper provide a characterization of hyperbolic affine iterated function systems defined on R. Atsushi Kameyama [Distances on topological self-similar sets, in Fractal Geometry and Applications: A Jubilee of Benǒit Mandelbrot. Proceedings of Symposia in Pure Mathematics, Volume 72, Part 1, 2004, pages 117–129] asked the following fundamental question: Given a topolo...