Synthesis of water soluble metalloporphyrin-cored amphiphilic star block copolymer photocatalysts for an environmental application

Two series of water-soluble metalloporphyrin-cored amphiphilic star block copolymers were synthesized by controlled radical polymerizations such as atom transfer radical polymerization (ATRP) and reversible addition fragmentation chain transfer (RAFT), which gave eight amphiphilic block copolymer arm chains consisting of poly(n-butyl acrylate-b-poly(ethylene glycol) methyl ether methacylate) (PnBA-b-PEGMEMA, M_n,GPC = 78,000, M_w/M_n = 1.2, 70 wt% of PPEGMEMA) and poly(styrene-b-2-dimethylamino ethyl acrylate) (PS-b-PDMAEA, M_n,GPC = 83,000, M_w/M_n = 1.2, 67 wt% of PDMAEA), yielding porphyrin(Pd)-(PnBA-b-PPEGMEMA)₈ and porphyrin(Pd)-(PS-b-PDMAEA)₈, respectively. Obtained metalloporphyrin polymer photocatalysts were homogeneously solubilized in water to apply to the removal of chlorophenols in water, and was distinguished from conventional water-insoluble small molecular metalloporphyrin photocatalysts. Notably, we found that the water-soluble star block copolymers with hydrophobic–hydrophilic core–shell structures more effectively decomposed the chlorophenol, 2,4,6-trichlorophenol (2,4,6-TCP), in water under visible light irradiation (k = 1.39 h^?1, t_1/2 = 0.5 h) in comparison to the corresponding water-soluble star homopolymer, because the hydrophobic core near the metalloporphyrin effectively captured and decomposed the hydrophobic chlorophenols in water.     

Structural Analysis of Unsaturated Glycosphingolipids Using Shotgun Ozone-Induced Dissociation Mass Spectrometry

Glycosphingolipids are essential biomolecules widely distributed across biological kingdoms yet remain relatively underexplored owing to both compositional and structural complexity. While the glycan head group has been the subject of most studies, there is paucity of reports on the lipid moiety, particularly the location of unsaturation. In this paper, ozone-induced dissociation mass spectrometry (OzID-MS) implemented in a traveling wave-based quadrupole time-of-flight (Q-ToF) mass spectrometer was applied to study unsaturated glycosphingolipids using shotgun approach. Resulting high resolution mass spectra facilitated the unambiguous identification of diagnostic OzID product ions. Using [M+Na]⁺ adducts of authentic standards, we observed that the long chain base and fatty acyl unsaturation had distinct reactivity with ozone. The reactivity of unsaturation in the fatty acyl chain was about 8-fold higher than that in the long chain base, which enables their straightforward differentiation. Influence of the head group, fatty acyl hydroxylation, and length of fatty acyl chain on the oxidative cleavage of double bonds was also observed. Application of this technique to bovine brain galactocerebrosides revealed co-isolated isobaric and regioisomeric species, which otherwise would be incompletely identified using contemporary collision-induced dissociation (CID) alone. These results highlight the potential of OzID-MS in glycosphingolipids research, which not only provides complementary structural information to existing CID technique but also facilitates de novo structural determination of these complex biomolecules.

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Simulation of Atomic Force Microscopy for investigating BaTiO3 and LiMn2O4 nanostructures based on Phase Field Approach

Atomic Force Microscopy (AFM) probes the surface features of specimens using an extremely sharp tip scanning the sample surface while the force is applied. AFM is also widely used for investigating the electrically non-conductive materials by applying an electric potential on the tip. Piezoresponse Force Microscopy (PFM) and Electrochemical Strain Microscopy (ESM) are variants of AFM for different materials. Both PFM and ESM signals are obtained by observing the displacement of the tip when applying electric fields during the scanning process. The PFM technique is based on converse piezoelectric effect of ferroelectrics and the ESM technique is based on electrochemical coupling in solid ionic conductors. In this work, two continuum-mechanical formulations for simulation of PFM and ESM are discussed. In the first model, for PFM simulation, a phase field approach based on the Allen-Cahn equation for non-conserved order parameters is employed for ferroelectrics. Here, the polarization vector is chosen as order parameter. Since ferroelectrics have highly anisotropic properties, this model accounts for transversely isotropic symmetry using an invariant formulation. The polarization switching behavior under the electric field will be discussed with some numerical examples. In the simulation of ESM, we employ a constitutive model based on the work of Bohn et al. [8] for the modeling of lithium manganese dioxide LiMn₂O₄ (LMO). It simulates the deformation of the LMO particle according to an applied voltage and the evolution of lithium concentration after removing a DC pulse. The modeling results are compared to experimental data. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem

We study a stochastic optimal control problem for a partially observed diffusion. By using the control randomization method in Bandini et al. (2018), we prove a corresponding randomized dynamic programming principle (DPP) for the value function, which is obtained from a flow property of an associated filter process. This DPP is the key step towards our main result: a characterization of the value function of the partial observation control problem as the unique viscosity solution to the corresponding dynamic programming Hamilton–Jacobi–Bellman (HJB) equation. The latter is formulated as a new, fully non linear partial differential equation on the Wasserstein space of probability measures. An important feature of our approach is that it does not require any non-degeneracy condition on the diffusion coefficient, and no condition is imposed to guarantee existence of a density for the filter process solution to the controlled Zakai equation. Finally, we give an explicit solution to our HJB equation in the case of a partially observed non Gaussian linear–quadratic model.     

LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS

This paper is devoted to the quasilinear equation ■where p 2,Ω is a(bounded or unbounded) domain of R~N,w_1,w_2 are nonnegative continuous functions and f is an increasing function. We establish a Liouville type theorem for nontrivial stable solutions of the equation under some mild assumptions on Ω,w_1, w_2 and f, which extends and unifies several results on this topic.     

Dynamic Picone's identity and its applications

We prove some Picone-type identities and inequalities for a class of first-order nonlinear dynamic systems and derive various weighted inequalities of Wirtinger type and Hardy type on time scales. As applications we study oscillatory and related properties of these systems including Reid's roundabout theorem on disconjugacy, Sturm's separation and comparison theorems, as well as a variational method in the oscillation theory.     

The Obstacle Version of the Geometric Dynamic Programming Principle: Application to the Pricing of American Options Under Constraints

We provide an obstacle version of the Geometric Dynamic Programming Principle of Soner and Touzi (J. Eur. Math. Soc. 4:201–236, 2002) for stochastic target problems. This opens the doors to a wide range of applications, particularly in risk control in finance and insurance, in which a controlled stochastic process has to be maintained in a given set on a time interval [0,T]. As an example of application, we show how it can be used to provide a viscosity characterization of the super-hedging cost of American options under portfolio constraints, without appealing to the standard dual formulation from mathematical finance. In particular, we allow for a degenerate volatility, a case which does not seem to have been studied so far in this context.     

Uniform Regularity in a Wedge and Regularity of Traces of CR Functions

We discuss in Sect. 1 the property of regularity at the boundary of separately holomorphic functions along families of discs and apply, in Sect. 2, to two situations. First, let W\mathcal{W} be a wedge of ℂ ⁿ with C ^ω , generic edge ℰ: a holomorphic function f on W\mathcal{W} has always a generalized (hyperfunction) boundary value bv(f) on ℰ, and this coincides with the collection of the boundary values along the discs which have C ^ω transversal intersection with ℰ. Thus Sect. 1 can be applied and yields the uniform continuity at ℰ of f when bv(f) is (separately) continuous. When W\mathcal{W} is only smooth, an additional property, the temperateness of f at ℰ, characterizes the existence of boundary value bv(f) as a distribution on ℰ. If bv(f) is continuous, this operation is consistent with taking limits along discs (Theorem 2.8). By Sect. 1, this yields again the uniform continuity at ℰ of tempered holomorphic functions with continuous bv. This is the theorem by Rosay (Trans. Am. Math. Soc. 297(1):63–72, 1986), in whose original proof the method of “slicing” by discs is not used.     

An Initial-Boundary Value Problem for the Korteweg–de Vries Equation with Dominant Surface Tension

We consider the initial-boundary value problem (IBVP) for the Korteweg–de Vries equation with zero boundary conditions at x=0 and arbitrary smooth decreasing initial data. We prove that the solution of this IBVP can be found by solving two linear inverse scattering problems (SPs) on two different spectral planes. The first SP is associated with the KdV equation. The second SP is self-conjugate and its scattering function is found in terms of entries of the scattering matrix s(k) for the first SP. Knowing the scattering function, we solve the second inverse SP for finding the potential self-conjugate matrix. Consequently, the unknown object entering coefficients in the system of evolution equations for s(k,t) is found. Then, the time-dependent scattering matrix s(k,t) is expressed in terms of s(k)=s(k,0) and of solutions of the self-conjugate SP. Knowing s(k,t), we find the solution of the IBVP in terms of the solution of the Gelfand–Levitan–Marchenko equation in the first inverse SP.