Association of UCP3, APN,and TNF-a Gene Polymorphisms with Type 2 Diabetes in a Population of Northern Chinese Han Patients

We observed the polymorphism distribution and coaction of uncoupling protein 3(UCP3)-55C/T,adiponectin(APN)+45T/G and tumor necrosis factor(TNF)-a-308G/A on the onset and development of T2DM in a North...     

Partitioning of Selected Anisole and Veratrole Derivatives between Water and Anionic Surfactant Micelles

The UV absorption spectra of six structurally related derivatives of anisole and veratrole, i.e., anisaldehyde, (E)-anethole, estragole, veratraldehyde, methyleugenol and (E)-methylisoeugenol, were recorded at various concentrations of the anionic surfactants, either sodium lauryl sulfate (SLS) or sodium lauryl ether sulfate (SLES) at T = 298 K. In addition, conductivity and density measurements were made for the SLS and SLES solutions to determine the volumetric properties of the studied surfactants. Next, using the W. Al-Soufi, L. Pińeiro and M. Novo model (APN model) including the pseudo-phase model for micellar solubilization, the values of micelle-water partition coefficients for each perfume-surfactant system were determined. In addition, the relations between the molecular structures of the solute and the head group of the surfactant and the value of the micelle-water partition coefficient as well as the octanol-water one were discussed.     

APN permutations on and Costas arrays

We study PN and APN functions over the integers modulo n. We give some construction techniques based on Costas arrays, which allow us to construct APN permutations on where p is a prime. Although PN permutations do not exist, one set of our functions is very close to being a set of PN permutations.     

The crooked property

Crooked permutations were introduced twenty years ago to construct interesting objects in graph theory. These functions, over ${\mathbb{F}}_{2^n}$ with odd n, are such that their derivatives have as image set a complement of a hyperplane. The field of applications was extended later, in particular to cryptography. However binary crooked functions are rare. It is still unknown if non quadratic crooked functions do exist. We extend the concept and propose to study the crooked property for any characteristic. A function F, from ${\mathbb{F}}_{p^n}$ to itself, satisfies this property if all its derivatives have as image set an affine subspace. We show that the partially-bent vectorial functions and the functions satisfying the crooked property are strongly related. We later focus on the components of these functions, establishing that the existence of linear structures is here decisive. We then propose a symbolic approach to identify the linear structures. We claim that this problem consists in solving a system of linear equations, and can often be seen as a combinatorial problem.     

On equivalence between known polynomial APN functions and power APN functions

Constructions and equivalence of APN functions play a significant role in the research of cryptographic functions. On finite fields of characteristic 2, 6 families of power APN functions and 14 families of polynomial APN functions have been constructed in the literature. However, the study on the equivalence among the aforementioned APN functions is rather limited to the equivalence in the power APN functions. Meanwhile, the theoretical analysis on the equivalence between the polynomial APN functions and the power APN functions, as well as the equivalence in the polynomial APN functions themselves, is far less studied. In this paper, we give the theoretical analysis on the inequivalence in 8 known families of polynomial APN functions and power APN functions.