Existence of homoclinic solutions for nonlinear second-order coupled systems

This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, $L^1$-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.     

Stochastic sensitivity analysis of coupled acoustic-structural systems under non-stationary random excitations

This paper presents a new sensitivity analysis method for coupled acoustic–structural systems subjected to non-stationary random excitations. The integral of the response power spectrum density (PSD) of the coupled system is taken as the objective function. The thickness of each structural element is used as a design variable. A time-domain algorithm integrating the pseudo excitation method (PEM), direct differentiation method (DDM) and high precision direct (HPD) integration method is proposed for the sensitivity analysis of the objective function with respect to design variables. Firstly, the PEM is adopted to transform the sensitivity analysis under non-stationary random excitations into the sensitivity analysis under pseudo transient excitations. Then, the sensitivity analysis equation of the coupled system under pseudo transient excitations is derived based on the DDM. Moreover, the HPD integration method is used to efficiently solve the sensitivity analysis equation under pseudo transient excitations in a reduced-order modal space. Numerical examples are presented to demonstrate the validity of the proposed method.     

A novel chaotic image encryption scheme using DNA sequence operations

In this paper, we propose a novel image encryption scheme based on DNA (Deoxyribonucleic acid) sequence operations and chaotic system. Firstly, we perform bitwise exclusive OR operation on the pixels of the plain image using the pseudorandom sequences produced by the spatiotemporal chaos system, i.e., CML (coupled map lattice). Secondly, a DNA matrix is obtained by encoding the confused image using a kind of DNA encoding rule. Then we generate the new initial conditions of the CML according to this DNA matrix and the previous initial conditions, which can make the encryption result closely depend on every pixel of the plain image. Thirdly, the rows and columns of the DNA matrix are permuted. Then, the permuted DNA matrix is confused once again. At last, after decoding the confused DNA matrix using a kind of DNA decoding rule, we obtain the ciphered image. Experimental results and theoretical analysis show that the scheme is able to resist various attacks, so it has extraordinarily high security.     

Comment on: “Entanglement in three coupled oscillators” [Phys. Lett. A 384 (2020) 126134]

In this comment we analyze a method for the solution of the eigenvalue equation for three coupled harmonic oscillators proposed recently. We argue that the authors did not obtain the frequencies and coordinates of the normal modes that make the Hamiltonian operator diagonal but merely six transcendental equations for the relevant parameters that they did not attempt to solve. We derive the conditions for the existence of bound states that the authors did not appear to be able to obtain probably because of the complexity exhibited by those equations.     

UPLC-Q/TOF-MS coupled with multivariate analysis for comparative analysis of metabolomic in Dendrobium nobile from different growth altitudes

Dendrobium nobile alkaloids (DNLA) and glycosides are the main active components extracted from Dendrobium nobile Lindl. (D. nobile) used for thousands of years in China. The pharmacological effects of the above chemical components are significantly different. D. nobile is mainly grown at an altitude ranging from 230 to 800 m in Chishui City, Northwest Guizhou Province. However, it is unclear whether the metabolite in D. nobile is influenced by the planting altitude. Hence, to reveal the different metabolite in D. nobile cultivated at the altitude of 336 m, 528 m, and 692 m, ultra-high performance liquid chromatography with Q/TOF-MS couple with multivariate analysis were developed. Using the orthogonal partial least squares-discriminant analysis, 19 different metabolites were discovered and then tentatively assigned their structures as alkaloids and glycosides by comparing mass spectrometry data with in-house database and literature. Moreover, the result of semiquantitative analysis showed the content of dendrobine that was belonged to alkaloids significantly increased at the altitude of 692 m, whereas the content of glycosides demonstrated an accumulation trend at the altitude of 528 m. The results could provide valuable information for the optimal clinical drug therapeutics and provide a reference for quality control.     

偏硼酸锂-四硼酸锂熔融-电感耦合等离子体原子发射光谱(ICP-AES)法测定石膏中多组分含量

石膏在我国储量丰富,应用广泛,快速准确分析其成分含量对石膏资源的综合利用具有重要意义。针对酸溶法无法测定SiO2,碱熔法无法测定K2O、Na2O的问题,本文建立一种偏硼酸锂-四硼酸锂熔融-电感耦合等离子体发射光谱法同时测定石膏中CaO、SO3、Al2O3、Fe2O3、MgO、TiO2、K2O、Na2O、SiO2含量。实验优化了熔剂用量、熔融温度,结果表明采用试样与偏硼酸锂-四硼酸锂混合熔剂质量比例1：5,在铂金坩埚中1000 ℃熔融10 min,在超声条件下,于50 mL 10 %盐酸中浸取熔融物,能够有效分解试样而浸取待测组分。向标准溶液系列中加入偏硼酸锂-四硼酸锂-盐酸基体溶液以消除基体对测试结果的影响。各待测组分的校准曲线的相关性系数均大于0.9990,方法检出限在3~292 μg/g范围内;采用实验方法分别对国家一级标准物质GBW03109a、GBW03110和实际样品进行测定,标准物质的5次平行测试的相对标准偏差在0.14 %~8.86 %之间,测定结果的相对误差在0.03~8.75 %之间,测试结果与标准值无显著性差异;实际样品中各成分测定值的RSD（n=5）为0.24~8.80 %。该方法操作简单、准确度高、精密度好、检出限低,可以同时测定石膏中的多组分含量,能够为石膏资源综合利用调查评价提供一定的技术支撑 。     

The enormity of the zinc deficiency problem and available solutions; an overview

The societal cost of micronutrient deficiency (MND) or the “hidden hunger” is in millions of dollars/year, reducing the GDP of some countries by as much as 11%. Zn is an important micronutrient for both plants and animals. An estimated 17% of the world population, or around 1.1 billion people, are at the risk of zinc (Zn) deficiency. The deficiency has been related to adverse pregnancy outcomes, stunted growth, premature deaths, immune system dysfunctions, neuro-behavioral disorders, and recently with the failure to recover from COVID-19. These health risks associated with Zn deficiency have compelled FAO and WHO to recommend Zn fortification of diet. Correcting Zn deficiency is a challenge due to several reasons. Close to half of the agricultural soils are Zn deficient, and chemical Zn fertilizers are costly and ineffective. Developing Zn-rich crops through plant breeding and genetic engineering is challenging. Zn-dense diet is costly and cannot be implemented in the low-income region most affected by Zn deficiency. Lack of consensus among regulatory bodies on defining and diagnosing Zn deficiency in plants and Humans. Awareness and other sociocultural issues. Among the most important available solutions are zinc biofortification of the cereal crops, use of zinc biofertilizers, development of Zn-efficient crops with reduced phytate content. The use of Zn supplements, dietary modification, and diversification, especially with fish, are proposed as the most accessible and affordable solutions. Awareness programs in areas suffering the most from Zn deficiency are required. Despite the suggestions from FAO and WHO, global efforts to combat Zn deficiency matching those for combating diseases like HIV are not in place. Coordinated efforts of the international community, especially policy-makers, agricultural scientists, dieticians, physicians, and others, are required to address the issue of hidden hunger.     

Existence and concentration of positive solutions for coupled Schrödinger equations

In this paper, we study the existence and concentration of positive solution of a class of coupled Schrödinger equations. We admit that the potentials may not be non-negative and suppose that the intersection of the sets has positive Lebesgue measure. By studying the modified functional of the associated functional carefully, we establish the existence of positive least energy solutions for the coupled Schrödinger system. Moreover, we prove the concentration phenomenon of the positive solution when the parameter goes to infinity.     

Tuning the properties of a black TiO2-Ag visible light photocatalyst produced by a rapid one-pot chemical reduction

A highly efficient black TiO₂-Ag photocatalytic nanocomposite, active under both UV and visible light illumination, was synthesized by decorating the surface of 25 nm TiO₂ particles with Ag nanoparticles. The material was obtained via a rapid, one-pot, simple (surfactant and complexing agent free) chemical reduction method using silver nitrate and formaldehyde as a metal salt and reducing agent, respectively. The nanocomposite shows an increase of over 800% in the rate of photocatalytic methylene blue dye degradation, compared to commercial unmodified TiO_2, under UV-VIS illumination. Unlike pure TiO₂, the nanocomposite exhibits visible light activation, with a corresponding drop in optical reflectance from 100% to less than 10%. The photocatalytic properties were shown to be strongly enhanced by post-reduction annealing heat treatments in air, which were observed to decrease, rather than coarsen, silver particle size, and increase particle distribution. This, accompanied by a variation in the silver surface oxidation states, appear to dramatically affect the photocatalytic efficiency under both UV and visible light. This highly active photocatalyst could have wide ranging applications in water and air pollution remediation and solar fuel production.     

Exact Boundary Synchronization by Groups for a Kind of System of Wave Equations Coupled with Velocities*

This paper deals with the exact boundary controllability and the exact boundary synchronization for a 1-D system of wave equations coupled with velocities. These problems can not be solved directly by the usual HUM method for wave equations, however, by transforming the system into a first order hyperbolic system, the HUM method for 1-D first order hyperbolic systems, established by Li-Lu(2022) and Lu-Li(2022), can be applied to get the corresponding results.