Inverse nodal problem for differential pencils

An inverse nodal problem is studied for the diffusion operator with real-valued coefficients on a finite interval with Dirichlet boundary conditions. The oscillation of the eigenfunctions corresponding to large modulus eigenvalues is established and an asymptotic of the nodal points is obtained. The uniqueness theorem is proved and a constructive procedure for solving the inverse problem is given.     

Multiple pure tone noise prediction

This paper presents a fully numerical method for predicting multiple pure tones, also known as “Buzzsaw” noise. It consists of three steps that account for noise source generation, nonlinear acoustic propagation with hard as well as lined walls inside the nacelle, and linear acoustic propagation outside the engine. Noise generation is modeled by steady, part-annulus computational fluid dynamics (CFD) simulations. A linear superposition algorithm is used to construct full-annulus shock/pressure pattern just upstream of the fan from part-annulus CFD results. Nonlinear wave propagation is carried out inside the duct using a pseudo-two-dimensional solution of Burgers? equation. Scattering from nacelle lip as well as radiation to farfield is performed using the commercial solver ACTRAN/TM. The proposed prediction process is verified by comparing against full-annulus CFD simulations as well as against static engine test data for a typical high bypass ratio aircraft engine with hardwall as well as lined inlets. Comparisons are drawn against nacelle unsteady pressure transducer measurements at two axial locations as well as against near- and far-field microphone array measurements outside the duct.     

Digital modeling and control of multiple time-delayed distributed power grid

Distributed power grid (DPG) control systems are so highly interconnected that the effects of local disturbances as well as transmission time delays can be amplified as they propagate through a complex network of transmission lines. These effects deteriorate control performance and could possibly destabilize the overall system. In this paper, a new approximated discretization method and digital design for DPG control systems with multiple state, input and output delays as well as a generalized bilinear transformation method are presented. Based on a procedure for the generation of impulse response data, the multiple fractional/integer time-delayed continuous-time system is transformed to a discrete-time model with multiple integer time delays. To implement the digital modeling, the singular value decomposition (SVD) of a Hankel matrix together with an energy loss level is employed to obtain an extended discrete-time state space model. Then, the extended discrete-time state space model of the DPG control system is reformulated as an integer time-delayed discrete-time system by computing its observable canonical form. The proposed method can closely approximate the step response of the original continuous time-delayed DPG control system by choosing various energy loss levels. For completeness, an optimal digital controller design for the DPG control system and a generalized bilinear transformation method with a tunable parameter are also provided, which can re-transform the integer time-delayed discrete-time model to its continuous-time model. Illustrative examples are given to demonstrate the effectiveness of the developed method.     

N-Doped, porous TiO2 with rutile phase and visible light sensitive photocatalytic activity

Nitrogen-doped, porous rutile has been prepared by hydrothermal reaction of TiN in nitric acid, with the nitrogen atoms present in the interstitial sites and in the form of adsorbed nitrate ions. The N-rutile powder exhibits outstanding photocatalytic activity toward degradation of adsorbed methylene blue under visible light irradiation.     

On the second eigenvalue of the Laplace operator on a spherical band

In this paper we prove that the second eigenvalue of the Laplacian for a spherical band on the unit sphere has multiplicity 2. We also show that among all spherical bands of given fixed area less than the second eigenvalue is maximized at the band which is symmetrical with respect to the equator.

     

Vapor‐Phase Reaction of Citronellal over Mesoporous Molecular Sieves MCM‐41 and Zeolites

The vapor‐phase reaction of citronellal (CTN) at 220 °C and atmospheric pressure has been studied using mesoporous molecular sieves and zeolites in a fixed‐bed reactor. The primary products included isopulegol (IPG), menthone, and pulegol with subsequent reactions to form cyclic hydrocarbons. The CTN conversion and the product selectivity depend on the acidity and the textural property of catalysts. Lewis and/or Brönsted acid sites are essential for catalyzing this reaction. An increase of SiO₂/Al₂O₃ mol ratio diminishes the acid amount of all catalysts and enhances both the surface area and the structural order of MCM‐41. The catalytic activity follows the order of MCM‐41 > HZSM‐5 > Hβ > USY, in accordance with the relative total acid amount except that of MCM‐41. Despite its low acidity, Si‐MCM‐41 exhibits the best catalytic performance due to its uniform mesopores, large surface area and good stability; the CTN conversion and the IPG yield attain 91.9% and 58.6%, respectively, after at least 25 h time‐on‐stream.     

Recovering the Sturm-Liouville Operator with Singular Potential Using Nodal Data

The paper deals with the Sturm-Liouville operator with singular potential. We assume that the potential is a sum of an a priori known distribution from a certain class and an unknown sufficiently smooth function. The inverse problem is to recover the operator using zeros of eigenfunctions (nodes) as an input data. For this inverse problem we obtain a procedure for constructing the solution.     

The unusual paramagnetic mixed-metal carbonyl chalcogenide clusters: [E(2)Cr(2)Fe(CO)(10)](2-) (E = Te,Se)

The rare examples of electron-rich mixed-metal carbonyl telluride and selenide clusters [E(2)Cr(2)Fe(CO)(10)](2-) (E = Te, Se) have been demonstrated. These two novel carbonyl complexes exhibit the unusual paramagnetic behavior.     

Polymer nanoparticles with a sensitive CO2‐responsive hydrophilic/hydrophobic surface

Poly(methyl methacrylate) (PMMA) nanoparticles with a sensitive CO₂‐responsive hydrophilic/hydrophobic surface that confers controlled dispersion and aggregation in water were prepared by emulsion polymerization at 50 °C under CO₂ bubbling using amphiphilic diblock copolymers of 2‐dimethylaminoethyl methacrylate (DMAEMA) and N‐isopropyl acrylamide (NIPAAm) as an emulsifier. The amphiphilicity of the hydrophobic–hydrophilic diblock copolymer at 50 °C was triggered by CO₂ bubbling in water and enabled the copolymer to serve as an emulsifier. The resulting PMMA nanoparticles were spherical, approximately 100 nm in diameter and exhibited sensitive CO₂/N₂‐responsive dispersion/aggregation in water. Using copolymers with a longer PNIPAAm block length as an emulsifier resulted in smaller particles. A higher concentration of copolymer emulsifier led to particles with a stickier surface. Given its simple preparation and reversible CO₂‐triggered amphiphilic behavior, this newly developed block copolymer emulsifier offers a highly efficient route toward the fabrication of sensitive CO₂‐stimuli responsive polymeric nanoparticle dispersions. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 2149–2156     

Chalcogen-Containing Manganese Carbonyl Clusters: Synthesis and Structural Transformations

Recently, we have developed several synthetic routes to the new classes of chalcogen-containing manganese carbonyl clusters, and the interesting structural transformations and reactivity of the resultant clusters have been investigated as well. In this short review, the syntheses and bonding modes of the sulfur, selenium, and tellurium-containing manganese carbonyl complexes reported by our laboratory will be presented, and the cluster growth and transformation will be systematically compared and discussed.