On Duality in Filtered Cohomologies

For a symplectic manifold(M~(2n), ω) without boundary(not necessarily compact), we prove Poincaré type duality in filtered cohomology rings of differential forms on M, and we use this result to obtain duality between(d + d~Λ)-and dd~Λ-cohomologies.     

Interior regularity for fractional systems

We study the regularity of solutions of elliptic fractional systems of order 2s, $s\in (0,1)$, where the right hand side f depends on a nonlocal gradient and has the same scaling properties as the nonlocal operator. Under some structural conditions on the system we prove interior Hölder estimates in the spirit of [1]. Our results are stable in s allowing us to recover the classic results for elliptic systems due to S. Hildebrandt and K. Widman [11] and M. Wiegner [19].     

A Chaotic-Based Encryption/Decryption Framework for Secure Multimedia Communications

Chaos-based encryption has shown an increasingly important and dominant role in modern multimedia cryptography compared with traditional algorithms. This work proposes novel chaotic-based multimedia encryption schemes utilizing 2D alteration models for high secure data transmission. A novel perturbation-based data encryption for both confusion and diffusion rounds is proposed. Our chaotification structure is hybrid, in which multiple maps are combined combines for media encryption. Blended chaotic maps are used to generate the control parameters for the permutation (shuffling) and diffusion (substitution) structures. The proposed schemes not only maintain great encryption quality reproduced by chaotic, but also possess other advantages, including key sensitivity and low residual clarity. Extensive security and differential analyses documented that the proposed schemes are efficient for secure multimedia transmission as well as the encrypted media possesses resistance to attacks. Additionally, statistical evaluations using well-known metrics for specific media types, show that proposed encryption schemes can acquire low residual intelligibility with excessive nice recovered statistics. Finally, the advantages of the proposed schemes have been highlighted by comparing it against different state-of-the-art algorithms from literature. The comparative performance results documented that our schemes are extra efficacious than their data-specific counterpart methods.     

Energetic,Topological and Electric Field Analyses of Cation-Cation Nucleic Acid Interactions in Watson-Crick Disposition

A theoretical study of the effect of the diprotonation on the nucleic acid bases (A : U, A : T and G : C) in Watson-Crick conformation has been carried out by means of DFT computational methods in vacuum. In addition, the corresponding neutral and monoprotonated binary complexes have been considered. Most of the diprotonated species studied are stable, even though the binding energy is positive due to the overall repulsive electrostatic term. Local electrostatic attractive forces in the regions of hydrogen bonds (HBs) are responsible for equilibrium geometries, as shown by the electric field lines connecting the electrophilic and nucleophilic sites involved in the HB interactions. Secondary electrostatic effects also affect the assembling of the nucleic acid complexes in either neutral or cationic form. In particular, the electric field lines flowing from electrophilic sites in one base to nucleophilic sites in the other reinforce the linking between them. Hence, when the nucleophilic site concerns the free lone pair of the heteroatom involved in the HB interaction as acceptor, the HB distance shortens. However, if the free lone pair of the HB acceptor interacts with an electrophilic site in the same molecule, the HB distance elongates, weakening the HB interaction. The topological analysis of the electron density distribution in HB regions indicates that neutral, monoprotonated and diprotonated complexes show no differences in the nature of their HB's.     

Construction of symplectic graphs by using 2-dimensional symplectic non-isotropic subspaces over finite fields

In most extant studies, symplectic graphs are defined by 1-dimensional subspaces and their orthogonality. In this paper, the symplectic graph is defined by 2-dimensional non-isotropic subspaces and their intersection. The symplectic graph is shown to be a 4-Deza graph. While the first subconstituent is shown to be a 4-Deza graph when $\nu ⩾3$ and a 3-Deza graph when $\nu =2$, the second subconstituent is not regular, and the third subconstituent is a 4-Deza graph except in the case $\nu =2$, when it is empty.     

Behaviour of Low Molecular Weight Compounds,Iron and Copper of Wine Spirit Aged with Chestnut Staves under Different Levels of Micro-Oxygenation

Alternative technologies for a more sustainable wine spirits’ ageing have been studied but a lack of knowledge on the effect of oxygenation level remains. This work examined the behaviour of low molecular weight compounds, iron and copper of a wine spirit aged in 50 L demijohns with chestnut wood staves combined with three levels of micro-oxygenation or nitrogen. Compounds and mineral elements were quantified by HPLC and FAAS, respectively, in samples collected at 8, 21, 60, 180, 270 and 365 days of ageing. Results showed that most of the compounds underwent significant changes in their content over time and behave differently depending on the wine spirit’s oxygenation level: higher contents of gallic acid, syringic acid and vanillin were associated with lower micro-oxygenation level while higher contents of ellagic acid, syringaldehyde, coniferaldehyde and sinapaldehyde resulted from higher one; lowest contents of these compounds were found in the nitrogen modality. Weak correlation between copper and the studied compounds was evidenced whereas closer relationship between iron, vanillin, gallic, syringic and ellagic acids at end of ageing was observed. This study provides innovative information on the role of oxygen in wine spirit’s ageing, and on chestnut wood effect on wine spirit’s mineral composition.     

Geometry of the uniform infinite half‐planar quadrangulation

We give a new construction of the uniform infinite half‐planar quadrangulation with a general boundary (or UIHPQ), analogous to the construction of the UIPQ presented by Chassaing and Durhuus, which allows us to perform a detailed study of its geometry. We show that the process of distances to the root vertex read along the boundary contour of the UIHPQ evolves as a particularly simple Markov chain and converges to a pair of independent Bessel processes of dimension 5 in the scaling limit. We study the “pencil” of infinite geodesics issued from the root vertex as reported by Curien, Ménard, and Miermont and prove that it induces a decomposition of the UIHPQ into 3 independent submaps. We are also able to prove that balls of large radius around the root are on average 7/9 times as large as those in the UIPQ, both in the UIHPQ and in the UIHPQ with a simple boundary; this fact we use in a companion paper to study self‐avoiding walks on large quadrangulations.