New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type

We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained.     

Ab initio simulations of liquid electrolytes for energy conversion and storage

Understanding physicochemical properties of liquid electrolytes is essential for predicting and optimizing device performance for a wide variety of emerging energy technologies, including photoelectrochemical water splitting, supercapacitors, and batteries. In this work, we review recent progress and open challenges in predicting structural, dynamical, and electronic properties of the liquids using first-principles approaches. We briefly summarize the basic concepts of first-principles molecular dynamics (FPMD), and we discuss how FPMD methods have enriched our understanding of a number of liquids, including aqueous solutions, organic electrolytes and ionic liquids. We also discuss technical challenges in extending FPMD simulations to the study of liquid electrolytes in more complex environments, including the interface between electrolytes and electrodes, which is a key component in many energy storage and conversion systems.     

Yolk‐Shell Porous Microspheres of Calcium Phosphate Prepared by Using Calcium L‐Lactate and Adenosine 5′‐Triphosphate Disodium Salt: Application in Protein/Drug Delivery

A facile and environmentally friendly approach has been developed to prepare yolk‐shell porous microspheres of calcium phosphate by using calcium L ‐lactate pentahydrate (CL) as the calcium source and adenosine 5′‐triphosphate disodium salt (ATP) as the phosphate source through the microwave‐assisted hydrothermal method. The effects of the concentration of CL, the microwave hydrothermal temperature, and the time on the morphology and crystal phase of the product are investigated. The possible formation mechanism of yolk‐shell porous microspheres of calcium phosphate is proposed. Hemoglobin from bovine red cells (Hb) and ibuprofen (IBU) are used to explore the application potential of yolk‐shell porous microspheres of calcium phosphate in protein/drug loading and delivery. The experimental results indicate that the as‐prepared yolk‐shell porous microspheres of calcium phosphate have relatively high protein/drug loading capacity, sustained protein/drug release, favorable pH‐responsive release behavior, and a high biocompatibility in the cytotoxicity test. Therefore, the yolk‐shell porous microspheres of calcium phosphate have promising applications in various biomedical fields such as protein/drug delivery.     

A nanocomposite prepared from FeOOH and N-doped carbon nanosheets as a peroxidase mimic,and its application to enzymatic sensing of glucose in human urine

A method is described for the synthesis of a nanocomposite containing FeOOH and N-doped carbon nanosheets. The nanocomposite was synthesized by a hydrothermal method using a Fe₃O₄/chitosan nanocomposite as the precursor. The nanocomposite displays peroxidase-like activity and catalyzes the oxidation of 3,3′,5,5′-tetramethylbenzidine (TMB) by H₂O₂. This results in the formation of a blue colored product with an absorption maximum at 652 nm in the UV-vis spectra. Based on these findings, colorimetric assays were worked out for both hydrogen peroxide and glucose. The H₂O₂ assay works in the 5 to 19 μM concentration range, and the limit of detection is 5 nM. The glucose assay works in the 8 μM to 0.8 mM concentration range and has a 0.2 μM detection limit. The method was successfully applied to the determination of glucose in human urine.

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Graphical abstract Schematic of the hydrothermal synthesis of a FeOOH/N-doped carbon nanocomposite. It was used to replace peroxidase enzyme for the catalytic oxidation of 3,3′,5,5′-tetramethylbenzidine (TMB) in a visual colorimetric test for glucose in human urine.

     

Frequency modules and nonexistence of quasi-periodic solutions of nonlinear evolution equations

This paper gives lower estimates for the frequency modules of almost periodic solutions to equations of the form , where A generates a strongly continuous semigroup in a Banach space , F(t,x) is 2π-periodic in t and continuous in (t,x), and f is almost periodic. We show that the frequency module ℳ(u) of any almost periodic mild solution u of (*) and the frequency module ℳ(f) of f satisfy the estimate e ^{2π iℳ(f)}⊂e ^{2π iℳ(u)}. If F is independent of t, then the estimate can be improved: ℳ(f)⊂ℳ(u). Applications to the nonexistence of quasi-periodic solutions are also given.     

A concise synthesis of chilenine via a sequential reaction process

A new short synthesis of chilenine has been achieved in two steps. The precursor amide was readily prepared by the condensation of the corresponding amine and acid. Treatment of the amide with oxalyl chloride in the presence of AlCl₃ at room temperature afforded the desired product chilenine through sequential Friedel-Crafts acylation, amide cyclization to imide, and intramolecular Friedel-Crafts type reaction. The synthesis suggests a new potential of oxalyl chloride for a two-carbon synthon.     

Nanosensing at the single cell level

This article presents an overview of the development, operation, and applications of optical nanobiosensors for use in in vivo detection of biotargets in individual living cells. The nanobiosensors are equipped with immobilized bioreceptor probes (e.g., antibodies, enzyme substrate) selective to specific molecular targets. Laser excitation is transmitted into the fiber producing an evanescent field at the tip of the fiber in order to excite target molecules bound to the bioreceptors immobilized at the fiber tips. A photometric system detects the optical signal (e.g., fluorescence) originated from the analyte molecules or from the analyte–bioreceptor reaction. Examples of detection of biospecies and molecular signaling pathways of apoptosis in a living cell are discussed to illustrate the potential of the nanobiosensor technology for single cell analysis.