Fraïssé’s Construction from a Topos-Theoretic Perspective

We present a topos-theoretic interpretation of (a categorical generalization of) Fraïssé’s construction in Model Theory, with applications to homogeneous models and countably categorical theories.     

A General Method for Building Reflections

We establish a general method for generating reflections between categories. We then apply our technique to generate adjunctions starting from geometric morphisms between Grothendieck toposes; as particular cases, we recover various well-known Stone-type adjunctions and establish several new ones.     

Structure,Biosynthesis, and Occurrence of Bacterial Pyrrolizidine Alkaloids

Pyrrolizidine alkaloids (PAs) are widespread plant natural products with potent toxicity and bioactivity. Herein, the identification of bacterial PAs from entomopathogenic bacteria using differential analysis by 2D NMR spectroscopy (DANS) and mass spectrometry is described. Their biosynthesis was elucidated to involve a non‐ribosomal peptide synthetase. The occurrence of these biosynthesis gene clusters in Gram‐negative and Gram‐positive bacteria indicates an important biological function in bacteria.     

Newman’s identity and infinite families of congruences modulo 7 for broken 3-diamond partitions

In 2007, Andrews and Paule introduced the notion of broken k-diamond partitions. Let \(\Delta _k(n)\) denote the number of broken k-diamond partitions of n for a fixed positive integer k. Recently, Paule and Radu presented some conjectures on congruences modulo 7 for \(\Delta _3(n)\) which were proved by Jameson and Xiong based on the theory of modular forms. Very recently, Xia proved several infinite families of congruences modulo 7 for \(\Delta _3(n)\) using theta function identities. In this paper, many new infinite families of congruences modulo 7 for \(\Delta _3(n)\) are derived based on an identity of Newman and the (p; k)-parametrization of theta functions due to Alaca, Alaca and Williams. In particular, some non-standard congruences modulo 7 for \(\Delta _3(n)\) are deduced. For example, we prove that for \(\alpha \ge 0\), \(\Delta _3\left( \frac{14\times 757^{\alpha }+1}{3}\right) \equiv 6 -\alpha \ (\mathrm{mod}\ 7)\).     

An inequality concerning the growth bound of an evolution family and the norm of a convolution operator

Let \(\mathcal {U}=\{U(t,s)\}_{t\ge s\ge 0}\) be a strongly continuous and exponentially bounded evolution family acting on a complex Banach space X and let \(\mathcal {X}\) be a certain Banach function space of X-valued functions. We prove that the growth bound of the family \(\mathcal {U}\) is less than or equal to \(-\frac{1}{c(\mathcal {U}, \mathcal {X})}\) provided that the convolution operator \(f\mapsto \mathcal {U}*f\) acts on \(\mathcal {X}.\) It is well known that under the latter assumption, the convolution operator is bounded and then \(c(\mathcal {U}, \mathcal {X})\) denotes (ad-hoc) its norm in \(\mathcal {L}(\mathcal {X}).\) As a consequence, we prove that if \(\sup \nolimits _{s\ge 0}\int \nolimits _{s}^\infty \Vert U(t,s)\Vert dt=u_1(\mathcal {U})<\infty ,\) then \(\omega _0(\mathcal {U})u_1(\mathcal {U})\le -1.\) Finally, we give an example showing that the accuracy of the estimates may be quite accurate.     

Facile synthesis of silver core - silica shell composite nanoparticles

Combining metal nanoparticles and dielectrics (e.g. silica) to produce composite materials with high dielectric constant is motivated by application in energy storage. Control over dielectric properties and their uniformity throughout the composite material is best accomplished if the composite is comprised of metal core - dielectric shell structured nanoparticles with tunable dimensions. We have synthesized silver nanoparticles in the range of 40-100nm average size using low concentration of saccharide simultaneously as the reducing agent and electrostatic stabilizer. Coating these silver particles with silica from tetraalkoxysilanes has different outcomes depending on the alcoholic solvent and the silver particle concentration. A common issue in solution-based synthesis of core-shell particles is heterogeneous nucleation whereupon two populations are formed: the desired core-shell particles and undesired coreless particles of the shell material. We report the formation of Ag@SiO(2) core-shell particles without coreless silica particles as the byproduct in 2-propanol. In ethanol, it depends on the silver surface area available whether homogeneous nucleation of silica on silver is achieved. In methanol and 1-butanol, core-shell particles did not form. This demonstrates the significance of controlling the tetraalkoxysilane hydrolysis rate when growing silica shells on silver nanoparticles.     

Effect of pH on H2O2 production in the radiolysis of water

The yields of hydrogen peroxide have been measured in the radiolysis of aqueous solutions of acrylamide, bromide, nitrate, and air in the pH range of 1-13. Hydrogen peroxide is the main stable oxidizing species formed in the radiolysis of water, and its long-term yield is found to be very sensitive to the system used in the measurements. Experiments with γ-irradiation combined with model calculations show that the primary yields of hydrogen peroxide are nearly independent of pH in the range of 2-12. Slightly higher primary yields are suggested at very low pH in particular when O(2) is present, while the yields seem to decrease at very high pH. Irradiations were performed with 5 MeV H ions, 5 MeV He ions, and 10 MeV C ions to evaluate the intratrack and homogeneous kinetic contributions to H(2)O(2) formation with different ions. Many of the trends in hydrogen peroxide yields with pH observed with γ-irradiations are observed with irradiation by the heavy ions. The lower yields of radicals in the homogeneous phase with the heavier ions tend to minimize the effects of radicals on the hydrogen peroxide yields at long times.     

The strong perfect graph conjecture holds for diamonded odd cycle-free graphs

In this paper, we show that the strong perfect graph conjecture holds for a new class of graphs which we call diamonded odd cycle-free graphs. The class of diamonded odd cycle-free graphs contains the classes of threshold graphs and K₄\e-free graphs.