New soft porous frameworks based on lambda-zirconium phosphate and aliphatic dicarboxylates: Synthesis and structural characterization

New dicarboxylate-functionalized pillared materials with a general formula of λ-ZrPO₄(OH)_1-x(OOC(CH₂)_nCOO)_x/2(dmso) (n=6, 8 and 10) have been prepared by post-synthesis modification of the inorganic layers of λ-zirconium phosphate (λ-ZrP), where the superficial Chloride monovalent anionic ligands of λ-layer are partially exchanged with the divalent anionic ligands of a series of long-chain aliphatic dicarboxylic acids, namely octanedioic acid, decanedioic acid and dodecanedioic acid. The synthesized materials are characterized by X-ray diffractometry, FT-IR spectrophotometry, elemental and thermogravimetric analyses. The X-ray diffraction patterns show that the obtained solid phases are pure. Furthermore, the interlayer distance of λ-ZrP systematically increases from 1.02 to 1.59 nm as a result of the incorporation of the mentioned acids inside the interlayer gallery.     

Infinite family of transmission irregular trees of even order

Distance between two vertices is the number of edges in a shortest path connecting them in a connected graph $G$. The transmission of a vertex $v$ is the sum of distances from $v$ to all the other vertices of $G$. If transmissions of all vertices are mutually distinct, then $G$ is a transmission irregular graph. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees of odd order were presented in Alizadeh and Klav?ar (2018). The following problem was posed in Alizadeh and Klav?ar (2018): do there exist infinite families of transmission irregular trees of even order? In this article, such a family is constructed.     

Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability

We consider concentrated vorticities for the Euler equation on a smooth domain $\mathrm{\Omega }?{\mathbf{R}}^2$ in the form of

$\omega =\sum _{j=1}^N{\omega }_j{\chi }_{{\mathrm{\Omega }}_j},|{\mathrm{\Omega }}_j|=\pi r_j^2,\underset{{\mathrm{\Omega }}_j}{\int }{\omega }_{j}d\mu ={\mu }_j\ne 0,$

supported on well-separated vortical domains ${\mathrm{\Omega }}_j$, $j=1,\dots ,N$, of small diameters $O(r_j)$. A conformal mapping framework is set up to study this free boundary problem with ${\mathrm{\Omega }}_j$ being part of unknowns. For any given vorticities ${\mu }_1,\dots ,{\mu }_N$ and small $r_1,\dots ,r_N\in {\mathbf{R}}^{+}$, through a perturbation approach, we obtain such piecewise constant steady vortex patches as well as piecewise smooth Lipschitz steady vorticities, both concentrated near non-degenerate critical configurations of the Kirchhoff–Routh Hamiltonian function. When vortex patch evolution is considered as the boundary dynamics of $?{\mathrm{\Omega }}_j$, through an invariant subspace decomposition, it is also proved that the spectral/linear stability of such steady vortex patches is largely determined by that of the 2N-dimensional linearized point vortex dynamics, while the motion is highly oscillatory in the 2N-codim directions corresponding to the vortical domain shapes.     

Triacetic acid lactone as a bioprivileged molecule in organic synthesis

1. Download high-res image (148KB)
2. Download full-size image

     

Stability of O3 + N2, O3 + O2 and O3 + CO2 double hydrates: DFT study

1. Download : Download high-res image (151KB)
2. Download : Download full-size image

     

Uniqueness of isometric immersions with the same mean curvature

Motivated by the quasi-local mass problem in general relativity, we study the rigidity of isometric immersions with the same mean curvature into a warped product space. As a corollary of our main result, two star-shaped hypersurfaces in a spatial Schwarzschild or AdS-Schwarzschild manifold with nonzero mass differ only by a rotation if they are isometric and have the same mean curvature. We also prove similar results if the mean curvature condition is replaced by an ${\sigma }_2$-curvature condition.     

Condensation of all-cis-tetraphenylcyclotetrasiloxanetetraol in ammonia: new method for preparation of ladder-like polyphenylsilsesquioxanes

1. Download : Download high-res image (68KB)
2. Download : Download full-size image

     

Synthesis and antimycobacterial activity of purine conjugates with (S)-lysine and (S)-ornithine

1. Download high-res image (115KB)
2. Download full-size image

     

Spectral theory approach for a class of radial indefinite variational problems

Considering the radial nonlinear Schrödinger equation

($P_r$)$?\mathrm{\Delta }u+V(x)u=g(x,u)\text{in}{\mathbb{R}}^N,N\ge 3$

we aim to find a radial nontrivial solution for it, where V changes sign ensuring problem ($P_r$) is indefinite and g is an asymptotically linear nonlinearity. We work with variational methods associating problem ($P_r$) to an indefinite functional in order to apply our Abstract Linking Theorem for Cerami sequences in [8] to get a non-trivial critical point for this functional. Our goal is to make use of spectral properties of operator $A:=\mathrm{\Delta }+V(x)$ restricted to $H_{rad}^1({\mathbb{R}}^N)$, the space of radially symmetric functions in $H^1({\mathbb{R}}^N)$, for obtaining a linking geometry structure to the problem and by means of special properties of radially symmetric functions get the necessary compactness.     

Oxidative dehydrogenation of n-octane over a vanadium–magnesium oxide catalyst: Influence of the gas hourly space velocity

Oxidative dehydrogenation (ODH) of n-octane was carried out over a vanadium–magnesium oxide catalyst in a continuous flow fixed bed reactor. The catalyst was characterized by ICP–OES, powder XRD and SEM. The catalytic tests were carried out at different gas hourly space velocities (GHSVs), viz. 4000, 6000, 8000, and 10,000 h^?1. The best selectivity for octenes was obtained at the GHSV of 8000 h^?1, while that for C8 aromatics was attained at the GHSV of 6000 h^?1 at high temperatures (500 and 550 °C). The catalytic testing at the GHSV of 10,000 h^?1 showed the lowest activity, while that at the GHSV of 4000 h^?1 consistently showed the lowest ODH selectivity. Generally, the best ODH performance was obtained by the catalytic testing at the GHSVs of 6000 and 8000 h^?1. No phasic changes were observed after the catalytic testing.