Low-frequency scattering of acoustic waves by a bounded rough surface in a half-plane

The problem of the scattering of harmonic plane waves by a rough half-plane is studied here. The surface roughness is finite. The slope of the irregularity is taken as arbitrary. Two boundary conditions are considered, those of Dirichlet and Neumann. An asymptotic solution is obtained, when the wavelength lambda of the incident wave is much larger than the characteristic length of the roughness iota, by means of the method of matched asymptotic expansions in terms of the small parameter epsilon= 2piiota/lambda. For the Dirichlet problem, the solution of the near and far fields is obtained up to O(epsilon2). The far field solution is given in terms of a coefficient that have a simple explicit expression, which also appears in the corresponding solution to the Neumann problem, already solved. Also the scattering cross section is given by simple formulas to O(epsilon3). It is noted that, for the Dirichlet problem, the leading term is of order epsilon3 which, by contrast, is different from that of the circular cylinder in full space, that is, of order epsilon(-1) (log epsilon)(-2). Some examples display the simplicity of the general results based on conformal mapping, which involve arcs of circle, polygonal lines, surface cracks and the like.     

Minor cacospongionolide derivatives from the sponge Fasciospongia cavernosa

Together with the known cacospongionolide, three new related sesterterpenes have been isolated from the sponge Fasciospongia cavernosa, collected from the Northern Adriatic Sea. The structures of the new compounds were proposed on the basis of spectroscopic data.     

Switchable Surface Hydrophobicity–Hydrophilicity of a Metal–Organic Framework

Materials with surfaces that can be switched from high/superhydrophobicity to superhydrophilicity are useful for myriad applications. Herein, we report a metal–organic framework (MOF) assembled from Zn^II ions, 1,4‐benzenedicarboxylate, and a hydrophobic carborane‐based linker. The MOF crystal‐surface can be switched between hydrophobic and superhydrophilic through a chemical treatment to remove some of the building blocks.     

Adsorption and inactivation behavior of horseradish peroxidase on cellulosic fiber surfaces

The physical immobilization behavior of horseradish peroxidase (HRP) on cellulosic fiber surfaces was characterized using adsorption and inactivation isotherms measured by the depletion method followed by fitting of Langmuir’s and Freundlich’s models to the experimental data. The adsorption and inactivation behavior of simpler and relatively non-porous high and low crystalline cellulosic substrates (microcrystalline cellulose and regenerated cellulose) as well as more complex and porous cellulosic pulp fibers (bleached kraft softwood fibers) were investigated. The effect of the sorbent surface energy on HRP adsorption was demonstrated by increasing the hydrophobicity of the cellulosic fibers using an internal sizing agent. The influence of the fiber surface charge density on HRP adsorption was studied via modification of the cellulosic fibers using TEMPO (2,2,6,6-tetramethyl-1-piperidiniloxy radical)-mediated oxidation methods. Results showed that hydrophobic interactions had a much larger effect on HRP adsorption than electrostatic interactions. More hydrophobic fiber surfaces (lower polar surface energy) result in larger enzyme-fiber binding affinity constants and higher binding heterogeneity. It was also found that oxidation of the cellulosic fiber substrate reduces enzyme adsorption affinity but significantly increases the loading capacity per unit weight of the surface.     

1D logistic reaction and p-Laplacian diffusion as p goes to one

Ricerche di Matematica - This work discusses the existence of the limit as p goes to 1 of the nontrivial solutions to the one-dimensional problem: $$begin{aligned} {left{ begin{array}{ll}...     

Polymorphism and photoluminescence properties of K3ErSi2O7

Two polymorphs of tripotassium erbium disilicate, K₃ErSi₂O₇, were synthesized by high‐temperature flux crystal growth during the exploration of the flux technique for growing new alkali rare‐earth elements (REE) containing silicates. Their crystal structures were determined by single‐crystal X‐ray diffraction analysis. One of them (denoted 1 ) crystallizes in the space group P6₃/mmc and is isostructural with disilicates K₃LuSi₂O₇, K₃ScSi₂O₇ and K₃YSi₂O₇, while the other (denoted 2 ) crystallizes in the space group P6₃/mcm and is isostructural with disilicates K₃NdSi₂O₇, K₃REESi₂O₇ (REE = Gd–Yb), K₃YSi₂O₇, K₃(Y_0.9Dy_0.1)Si₂O₇ and K₃SmSi₂O₇. In the crystal structure of polymorph 1 , the Er cations are in an almost perfect octahedral coordination, while in the crystal structure of polymorph 2 , part of the Er cations are in a slightly distorted octahedral coordination and the other part are in an ideal trigonal prismatic coordination environment. Sharing six corners, disilicate Si₂O₇ groups in the crystal structure of polymorph 1 link six ErO₆ octahedra, forming a three‐dimensional network and nine‐coordinated potassium cations are located in its holes. In the crystal structure of polymorph 2 , the disilicate Si₂O₇ groups connect four ErO₆ octahedra, as well as one ErO₆ trigonal prism. Three differently coordinated potassium cations are situated between them. Different site symmetries of the erbium cations in the crystal structures of polymorphs 1 and 2 affect their photoluminescence properties. Only polymorph 2 exhibits luminescence. Intense narrow lines in the emission spectrum are a result of the 4f–4f transition. The green emission line at 560 nm is the result of the Er³⁺ transition ⁴S_3/2→⁴I_15/2, and the luminescence line at 690 nm is the result of a ⁴F_9/2→⁴I_15/2 transition. The crystal morphologies of the two polymorphs are similar. Crystals of polymorph 1 are in the form of a hexagonal prism in combination with a hexagonal base, while crystals of polymorph 2 contain a dihexagonal prism in combination with a hexagonal base, although poorly developed faces of the dihexagonal pyramid can also be noticed.     

The Use of Antioxidant Potential of Chokeberry Juice in Creating Pro-Healthy Dried Apples by Hybrid (Convection-Microwave-Vacuum) Method

The visible trend in the development of the snack market focuses on the use of innovative technologies such as low-temperature or hybrid processes that allow the preservation of native ingredients of raw plant materials. In addition, the high antioxidant potential of, for example, chokeberry fruit can be used to support technological processes and create new products. The aim of the study was to evaluate the possibility of using chokeberry juice concentrate as a component of an osmotic solution to enrich apple samples with natural bio-ingredients and obtain dried apples with increased content of ingredients with antioxidant properties; pro-healthy apple chips. The research material consisted of apples that underwent osmotic dehydration in solutions of sucrose or sucrose and chokeberry juice concentrate and then were dried by the freeze-drying or the hybrid method. The freeze-drying was more beneficial for maintaining the vitamin C content, while the use of the hybrid method resulted in the preservation of more polyphenolic compounds. The sensory evaluation indicated the need to modify the composition of the osmoactive solution. Due to the use of chokeberry juice concentrate, the content of vitamin C, polyphenols, and the antioxidant activity of dried apples was increased.     

Development and Characterization of Novel Composite Films Based on Soy Protein Isolate and Oilseed Flours

The possibility of using oilseed flours as a waste source for film-forming materials with a combination of soy protein isolate in preparation of edible films was evaluated. Physical, mechanical and barrier properties were determined as a function of the oilseed type: hemp, evening primrose, flax, pumpkin, sesame and sunflower. It was observed that the addition of oilseed flours increased the refraction and thus the opacity of the obtained films from 1.27 to 9.57 A mm⁻¹. Depending on the type of flours used, the edible films took on various colors. Lightness (L*) was lowest for the evening primrose film (L* = 34.91) and highest for the soy protein film (L* = 91.84). Parameter a* was lowest for the sunflower film (a* = −5.13) and highest for the flax film (a* = 13.62). Edible films made of pumpkin seed flour had the highest value of the b* color parameter (b* = 34.40), while films made of evening primrose flour had the lowest value (b* = 1.35). All analyzed films had relatively low mechanical resistance, with tensile strength from 0.60 to 3.09 MPa. Films made of flour containing the highest amount of protein, pumpkin and sesame, had the highest water vapor permeability, 2.41 and 2.70 × 10⁻⁹ g·m⁻¹ s⁻¹ Pa⁻¹, respectively. All the edible films obtained had high water swelling values from 131.10 to 362.16%, and the microstructure of the films changed after adding the flour, from homogeneous and smooth to rough. All blended soy protein isolate–oilseed flour films showed lower thermal stability which was better observed at the first and second stages of thermogravimetric analysis when degradation occurred at lower temperatures. The oilseed flours blended with soy protein isolate show the possibility of using them in the development of biodegradable films which can find practical application in the food industry.     

An investigation of polyhedral deformation in two mixed‐metal diarsenates: SrZnAs2O7 and BaCuAs2O7

Two isostructural diarsenates, SrZnAs₂O₇ (strontium zinc diarsenate), (I), and BaCuAs₂O₇ [barium copper(II) diarsenate], (II), have been synthesized under hydrothermal conditions and characterized by single‐crystal X‐ray diffraction. The three‐dimensional open‐framework crystal structure consists of corner‐sharing M2O₅ (M2 = Zn or Cu) square pyramids and diarsenate (As₂O₇) groups. Each As₂O₇ group shares its five corners with five different M2O₅ square pyramids. The resulting framework delimits two types of tunnels aligned parallel to the [010] and [100] directions where the large divalent nine‐coordinated M1 (M1 = Sr or Ba) cations are located. The geometrical characteristics of the M1O₉, M2O₅ and As₂O₇ groups of known isostructural diarsenates, adopting the general formula M1^IIM2^IIAs₂O₇ (M1^II = Sr, Ba, Pb; M2^II = Mg, Co, Cu, Zn) and crystallizing in the space group P2₁/n, are presented and discussed.