Nanoscale coordination polymers for platinum-based anticancer drug delivery

Pt-containing nanoscale coordination polymer (NCP) particles with the formula of Tb2(DSCP)3(H2O)12 (where DSCP represents disuccinatocisplatin), NCP-1, were precipitated from an aqueous solution of Tb3+ ions and DSCP bridging ligands via the addition of a poor solvent. SEM and TEM images showed that as-synthesized NCP-1 exhibited a spherical morphology with a DLS diameter of 58.3 +/- 11.3 nm. NCP-1 particles were stabilized against rapid dissolution in water by encapsulation in shells of amorphous silica. The resulting silica-coated particles NCP-1' exhibited significantly longer half-lives for DSCP release from the particles (a t1/2 of 9 h for NCP-1' with 7 nm silica coating vs t1/2 of 1 h for as-synthesized NCP-1). In vitro cancer cell cytotoxicity assays with the human colon carcinoma cell line (HT-29) showed that internalized NCP-1' particles readily released the DSCP moieties which were presumably reduced to cytotoxic Pt(II) species to give the Pt-containing NCPs anticancer efficacy superior to the cisplatin standard. The generality of this degradable nanoparticle formulation should allow for the design of NCPs as effective delivery vehicles for a variety of biologically and medically important cargoes such as therapeutic and imaging agents.     

Constructions of primitive formally dual pairs having subsets with unequal sizes

The concept of formal duality was proposed by Cohn, Kumar and Schürmann, which reflects a remarkable symmetry among energy‐minimizing periodic configurations. This formal duality was later translated into a purely combinatorial property by Cohn, Kumar, Reiher and Schürmann, where the corresponding combinatorial objects were called formally dual pairs. Motivated by this surprising application on the energy minimization problem, we focus on the algebraic constructions of primitive formally dual pairs. It is worth noting that almost all known examples of primitive formally dual pairs satisfy that the two subsets have the same size. Indeed, prior to this work, there was only one known example derived from computer search, which had subsets with unequal sizes in ${\mathbb{Z}}_2\times {\mathbb{Z}}_4^2$. Inspired by this example, we propose a lifting construction framework and a recursive construction framework, which generate new primitive formally dual pairs from known ones. As an application, for $m\ge 2$, we obtain $m+1$ pairwise inequivalent primitive formally dual pairs in ${\mathbb{Z}}_2\times {\mathbb{Z}}_4^{2m}$, which have subsets with unequal sizes.     

Skew Hadamard Difference Sets from Dickson Polynomials of Order 7

Skew Hadamard difference sets have been an interesting topic of study for over 70 years. For a long time, it had been conjectured the classical Paley difference sets (the set of nonzero quadratic residues in where ) were the only example in Abelian groups. In 2006, the first author and Yuan disproved this conjecture by showing that the image set of is a new skew Hadamard difference set in with m odd, where denotes the first kind of Dickson polynomials of order n and . The key observation in the proof is that is a planar function from to for m odd. Since then a few families of new skew Hadamard difference sets have been discovered. In this paper, we prove that for all , the set is a skew Hadamard difference set in , where m is odd and . The proof is more complicated and different than that of Ding‐Yuan skew Hadamard difference sets since is not planar in . Furthermore, we show that such skew Hadamard difference sets are inequivalent to all existing ones for by comparing the triple intersection numbers.     

Tangential Interpolation in Weighted Vector-valued H p Spaces, with Applications

In this paper, norm estimates are obtained for the problem of minimal-norm tangential interpolation by vector-valued analytic functions in weighted H^p spaces, expressed in terms of the Carleson constants of related scalar measures. Applications are given to the notion of p-controllability properties of linear semigroup systems and controllability by functions in certain Sobolev spaces.     

Conditions for Admissibility of Observation Operators and Boundedness of Hankel Operators

We derive new necessary and sufficient conditions for admissibility of observation operators for certain C ₀-semigroups. We also prove a new sufficient criterion for admissibility for observation operators with infinite-dimensional output space on contraction semigroups. If the contraction semigroup is completely non-unitary and its co-generator has finite defect indices, then this criterion is also necessary. In the case of the right shift semigroup on L ²(0,), these conditions translate into conditions for the boundedness of Hankel operators.     

On projective planes admitting elations and homologies

We consider projective planes Π of ordern with abelian collineation group Γ of ordern(n?1) which is generated by (A, m)-elations and (B, l)-homologies wherem =AB andA εl. We prove

1. Ifn is even thenn=2^e and the Sylow 2-subgroup of Γ is elementary abelian.
2. Ifn is odd then the Sylow 2-subgroup of Γ is cyclic.
3. Ifn is a prime then Π is Desarguesian.
4. Ifn is not a square thenn is a prime power.

     

Studies on Gas Purification by a Pulsed Microwave Discharge at 2.46 GHz in Mixtures of N2/NO/O2 at Atmospheric Pressure

Pulsed microwave discharges operated at atmospheric pressure in gas mixtures containing N₂, O₂, and NO are investigated experimentally and theoretically for various gas mixture constituents and operating conditions with respect to the ability of exhaust gas purification. The rotational gas temperature and the vibrational temperature of N₂ are derived from CARS measurements. The composition of the exhaust gas after treatment is monitored using FTIR spectroscopy. The processes of the chemical, electronic, and vibrational kinetics are described by a model that has been developed to calculate the species densities. The results obtained show that in N₂/NO gas mixtures an overall reduction of NO_x takes place. In the case of N₂/O₂/NO gas mixtures, no net reduction of NO_x is achieved for a pulsed microwave power below 3600 W, a pulse length of 50 s, and a typical repetition frequency of 2 kHz.     

The luminescence of Fe3+ and Cr3+ IN α-gallia

The photoluminescence of Fe³⁺ in octahedral oxygen co-ordination has been observed in Fe³⁺- doped α-gallia. The energy of the emission is in good agreement with that predicted from measured spectral data for Cr³⁺ in α-gallia and the literature data for Cr³⁺ and Fe³⁺ in α-alumina.