On endomorphisms of degree two

LetR be a commutative ring, Δ∈R and letRΔ be the set of conjugacy classes ofR-module endomorphismsf satisfyingf ∘ f = Δ·id. Using a certain subspace of the tensor product of two endomorphisms a commutative and associative product on Rx0394; can be defined. ForR = ℤ a generalization of the composition of quadratic forms arises as a special case.     

Thermal Effects on Hydrothermal Biomass Liquefaction

Batch pressure vessels commonly used for hydrothermal liquefaction have typical heating times in the range of 30 to 60 min. Thermodynamically, the complex set of reactions are path dependent, so that the heating rate can possibly affect yields and the composition of the resultant liquid products. It is postulated that the mode of heat transfer becomes an uncontrolled variable in kinetic studies and can seriously impact scale-up. To confirm this hypothesis and minimize these heat-transfer-related artifacts, we designed a batch pressure vessel equipped with an induction heating system, which allows the reduction of heat-up times by about two orders of magnitude to several seconds, compared to tens of minutes with standard pressure reactors. This system was used to study the direct liquefaction of corn stover and aspen wood with a pretreatment. The heating rate was found to have no significant effect on the composition of the liquid products. However, the liquid yields are dependent on the heating rate. Varying the cooling rate does not show obvious effects. The results confirm that the heating rate, as governed by the mode of heat transfer, is an important factor that needs to be considered during scale-up.     

Spectra and essential spectral radii of composition operators on weighted Banach spaces of analytic functions

We determine the spectra of composition operators acting on weighted Banach spaces of analytic functions on the unit disc defined for a radial weight v, when the symbol of the operator has a fixed point in the open unit disc. We also investigate in this case the growth rate of the Koenigs eigenfunction and its relation with the essential spectral radius of the composition operator.     

Bounded universal functions in one and several complex variables

We show how to obtain functions that are universal for the ball of , where . The existence of our functions will follow from universality criteria, but we also show how to construct them. Then we study the connection between certain interpolating sequences, runaway automorphisms, and the existence of universal functions on domains in .      

Design of Multicomponent Peptide Fibrils with Ordered and Programmable Compositional Patterns

Advanced applications of biomacromolecular assemblies require a stringent degree of control over molecular arrangement, which is a challenge to current synthetic methods. Here we used a neighbor-controlled patterning strategy to build multicomponent peptide fibrils with an unprecedented capacity to manipulate local composition and peptide positions. Eight peptides were designed to have regulable nearest neighbors upon co-assembly, which, by simulation, afforded 412 different patterns within fibrils, with varied compositions and/or peptide positions. The fibrils with six prescribed patterns were experimentally constructed with high accuracy. The controlled patterning also applies to functionalities appended to the peptides, as exemplified by arranging carbohydrate ligands at nanoscale precision for protein recognition. This study offers a route to molecular editing of inner structures of peptide assemblies, prefiguring the uniqueness and richness of patterning-based material design.     

Hollow STW-Type Zeolite Single Crystals with Aluminum Gradient for Highly Selective Production of p-Xylene from Methanol-Toluene Alkylation

Zeolites with uniform micropores are important shape-selective catalysts. However, the external acid sites of zeolites have a negative impact on shape-selective catalysis, and the microporosity may lead to serious diffusion limitation. Herein, we report on the direct synthesis of hierarchical hollow STW-type zeolite single crystals with a siliceous exterior. In an alkalinous fluoride medium, the nucleation of highly siliceous STW zeolites takes place first, and the nanocrystals are preferentially aligned on the outer surface of the gel agglomerates to grow into single crystalline shells upon crystallization. The lagged crystallization of the internal Al-rich amorphous gels onto the inner surface of nanocrystalline zeolite shells leads to the formation of hollow cavities in the core of the zeolite crystals. The hollow zeolite single crystals possess a low-to-high aluminum gradient from the surface to the core, resulting in an intrinsic inert external surface, and exhibit superior catalytic performance in toluene methylation reactions.     

Phase relations in the K2W2O7-K2WO4-KPO3-Bi2O3 system and structure of K6.5Bi2.5W4P6O34

The phase relations in the cross-section of the K₂W₂O₇-K₂WO₄-KPO₃ containing 15 mol% Bi₂O₃ were undertaken using flux method. Crystallization fields of K_6.5Bi_2.5W₄P₆O₃₄, K₂Bi(PO₄)(WO₄), Bi₂WO₆, KBi(WO₄)₂ and their cocrystallization areas were identified. Novel phase K_6.5Bi_2.5W₄P₆O₃₄ was characterized by single-crystal X-ray diffraction: sp. gr. P−1, a=9.4170(5), b=9.7166(4), c=17.6050(7) Å, α=90.052(5)°, β=103.880(5)° and γ=90.125(5)°. It has a layered structure, which contains {K₇Bi₅W₈P₁₂O₆₈}_∞ layers stacked parallel to ab plane and sheets composed by potassium atoms separating these layers. Sandwich-like {K₇Bi₅W₈P₁₂O₆₈}_∞ layers are assembled from [W₂P₂O₁₃]_∞ and [BiPO₄]_∞ building units, and are penetrated by tunnels with K/Bi atoms inside. FTIR-spectra of K₂Bi(PO₄)(WO₄) and K_6.5Bi_2.5W₄P₆O₃₄ were discussed on the basis of factor group theory.     

Approximation numbers for composition operators on spaces of entire functions

We study the degree of compactness of composition operators $C_{\phi }$ acting on weighted Hilbert spaces of entire functions, which include (i) the space of entire Dirichlet series, (ii) the space of entire power series, and (iii) the Fock space (we must have $\phi \left(z\right)=az+b$, and it is known that $C_{\phi }$ is compact if and only if $\left|a\right|<1$). More precisely, the sequence $\left(a_n\right)$ of approximation numbers of $C_{\phi }$ is investigated: for (i), we give the exact formula for $\left(a_n\right)$, while for (ii) and (iii) we give upper and lower estimates for $a_n$, showing that $a_n$ behaves like ${\left|a\right|}^n$ up to a subexponential factor. In particular, $C_{\phi }$ belongs to all Schatten classes $S_p,p>0$ as soon as it is compact.     

Separating classes of composition operators via subnormal condition

Several classes have been considered to study the weak subnormalities of Hilbert space operators. One of them is -hypnormality, which comes from the Bram-Halmos criterion for subnormal operators. In this note we consider -hyponormality, which is the parallel version corresponding to the Embry characterization for subnormal operators. We characterize -hyponormality of composition operators via -th Radon-Nikodym derivatives and present some examples to distinguish the classes.

     

On analytic perturbations of a family of Feigenbaum-like equations

We prove existence of solutions (?,λ) of a family of Feigenbaum-like equations

(0.1)