A relationship between three analytical approaches to nonlinear problems

In this work, the relationship between three analytical techniques is demonstrated. The direct relationship between the variational approach (VA) and the Hamiltonian approach (HA) is illustrated for a first approximation, and subsequently the relationship between the variational approach and the harmonic balance method (HBM) is concluded. Moreover, the relationship between HA and VA is investigated for higher order solutions.     

Transition‐Metal‐Functionalized DNA Double‐Crossover Tiles: Enhanced Stability and Chirality Transfer to Metal Centers

The double crossover junction (DX) is a fundamental building block for generating complex and varied structures from DNA. However, its implementation in functional devices is limited to the inherent properties of DNA itself. Here, we developed design strategies to generate the first metal–DX DNA tiles (DX_M) by site‐specifically functionalizing the tile crossovers with tetrahedral binding pockets that coordinate Cu^I. These DX junctions bind two Cu^I ions independently at distinct sites, display greater thermal stability than native DX tiles upon metalation, and melt in a cooperative fashion. In addition, the right‐handed helical chirality of DNA is transferred to the metal centers. Our tiles display high metal ion selectivity, such that Cu^II is spontaneously reduced to Cu^I in situ. By modifying our design over three generations of tiles, we elucidated the thermodynamic and geometric requirements for the successful assembly of DX_M tiles, which have direct applicability in developing robust, stable DNA‐based materials with electroactive, photoactive, and catalytic properties.     

A green four-component synthesis of zwitterionic alkyl/benzyl pyrazolyl barbiturates and their photophysical studies

A novel series of unsymmetrically substituted alkyl/benzyl pyrazolyl barbiturates incorporating highly biologically active pyrazolone and barbiturate moieties was synthesized by four-component reactions of a mixture of ethyl acetoacetate, hydrazine hydrate, aldehydes and barbituric acid/thiobarbituric acid in ethanol without using a catalyst. The photophysical properties of the newly designed alkyl/benzyl pyrazolyl barbiturates were studied, and good quantum yield of some products indicated a definitive scope in the field of biochemical applications. Single-crystal X-ray crystallographic studies revealed that the newly synthesized compounds exist in zwitterionic form. The zwitterionic nature of the new chimera makes them interesting candidates for drug delivery as zwitterionic drugs are known to have highly water soluble properties, specific protein absorption, slow recognition by immune system, slow blood clearance from body and can constantly diffuse and deposit throughout the physiological pH.     

Integrated photonic crystal spectrometers for sensing applications

A combination of negative refraction and diffraction compensation in a superprism-based photonic crystal structure is used to demonstrate a compact on-chip photonic crystal spectrometer. This structure provides strong dispersion and signal isolation, which are essential for forming an efficient and compact spectrometer. Performance of these spectrometers as spectral pattern detectors is discussed. The experimental results show that a PC structure with 80 μm × 220 μm dimension can locate a single spectral feature with better than 10 pm accuracy over a bandwidth of 50 nm around 1550 nm center wavelength at an output signal-to-noise ratio of 13 dB.     

Amberlyst A21: A reusable solid catalyst for green synthesis of pyran annulated heterocycles at room temperature

Amberlyst A21, a neutral ion-exchange resin and a solid base, can catalyze the three-component reaction of aldehyde and malononitrile with various active methylene compounds at room temperature to synthesize a range of pharmaceutically important pyran annulated heterocycles. Use of the solid base could generate a highly green protocol by eliminating chromatographic purification that involves hazardous organic solvents, and facilitate easy recovery and reusability of the catalyst.     

Coupled vibration of a partially fluid-filled cylindrical container with a cylindrical internal body

In the present paper a method is proposed to investigate the effects of a rigid internal body on the coupled vibration of a partially fluid-filled cylindrical container. The internal body is a thin-walled and open-ended cylindrical shell. The internal body is concentrically and partially submerged inside a container. The radial and axial distances between the internal body and the container are filled with fluid. Along the contact surface between the container and the fluid, the compatibility requirement for the fluid–structure interactions is applied and the Rayleigh–Ritz method is used to calculate the natural frequencies and modes of a partially fluid-filled cylindrical container. The fluid domain is continuous, simply connected, and non-convex. The fluid is assumed to be incompressible and inviscid. The velocity potential for fluid motion is formulated in terms of eigenfunction expansions for two distinct fluid regions. The resulting equations are solved by using the Galerkin method. The results from the proposed method are in good agreement with experimental and numerical solutions available in the literature for the partially water-filled cylindrical container without internal body. A finite element analysis is also used to check the validity of the present method for the partially water-filled cylindrical container with internal body. The effects of the fluid level, internal body radius, and internal body length on the natural frequencies of the coupled system are also investigated.     

Iron Oxychloride/Bovine Serum Albumin Nanosheets as Chemodynamic Therapy Agents

Iron oxychloride (FeOCl) is known for reactive oxygen species (ROS) generation through Fenton chemistry. The activity of FeOCl is preserved in the slightly acidic pH value of the tumor microenvironment (pH 6.5−6.9). Such property can be advantageous in biobased systems, where ROS generation can be modulated in slightly acidic conditions, which is characteristic of the solid tumor microenvironment. In the present study, BSA-stabilized FeOCl nanosheets (NSs) are synthesized and characterized by transmission electron microscope, Fourier transform infrared spectroscopy, zeta potential analysis, dynamic light scattering, and UV–vis spectroscopy. The morphology of the nanoparticles is flake-like, and their hydrodynamic diameter is around 200 nm. MTT, apoptosis assay, and trypan blue staining evaluate the toxicity of FeOCl NSs toward the 4T1 cell line. It is found that the toxicity of the NSs is higher in physiological conditions of solid tumors (pH 6.5, H₂O₂ 100 × 10⁻⁶ m ) than in the conditions of healthy organs (pH 7.4). Specifically, cancer cells are in their late apoptotic stage by more than eight times higher at pH 6.5 than pH 7.4. The toxicity results are in agreement with the in vitro catalytic assay of the NSs. Therefore, the FeOCl NSs can be the building blocks for constructing chemodynamic therapy agents.     

Kernels of Gramian operators for frames in shift-invariant subspaces

For an invertible n×n matrix B and Φ a finite or countable subset of L²(Rⁿ), consider the collection X={?(·-Bk):?∈Φ,k∈Zⁿ} generating the closed subspace M of L²(Rⁿ). Our main objects of interest in this paper are the kernel of the associated Gramian G(.) and dual Gramian operator-valued functions. We show in particular that the orthogonal complement of M in L²(Rⁿ) can be generated by a Parseval frame obtained from a shift-invariant system having m generators where . Furthermore, this Parseval frame can be taken to be an orthonormal basis exactly when almost everywhere. Analogous results in terms of dim(Ker(G(.))) are also obtained concerning the existence of a collection of m sequences in the orthogonal complement of the range of analysis operator associated with the frame X whose shifts either form a Parseval frame or an orthonormal basis for that orthogonal complement.