Cyclic Solution and Optimal Approximation of the Quaternion Stein Equation

In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation AXB - X = F . Firstly, the matrix equation equivalent to the target structure matrix is constructed by using the complex decomposition of the quaternion matrix, to obtain the necessary and sufficient conditions for the existence of the cyclic solution of the equation and the expression of the general solution. Secondly, the Stein equation is converted into the Sylvester equation by adding the necessary parameters, and the condition for the existence of a cyclic solution and the expression of the equation’s solution are then obtained by using the real decomposition of the quaternion matrix and the Kronecker product of the matrix. At the same time, under the condition that the solution set is non-empty, the optimal approximation solution to the given quaternion circulant matrix is obtained by using the property of Frobenius norm property. Numerical examples are given to verify the correctness of the theoretical results and the feasibility of the proposed method. .

Hermite Positive Definite Solution of the Quaternion Matrix Equation Xm + B*XB = C

This paper discusses the necessary and sufficient conditions for the existence of Hermite positive definite solutions of the quaternion matrix equation Xm+ B*XB = C (m > 0) and its iterative solution method. According to the characteristics of the coefficient matrix, a corresponding algebraic equation system is ingeniously constructed, and by discussing the equation system’s solvability, the matrix equation’s existence interval is obtained. Based on the characteristics of the coefficient matrix, some necessary and sufficient conditions for the existence of Hermitian positive definite solutions of the matrix equation are derived. Then, the upper and lower bounds of the positive actual solutions are estimated by using matrix inequalities. Four iteration formats are constructed according to the given conditions and existence intervals, and their convergence is proven. The selection method for the initial matrix is also provided. Finally, using the complexification operator of quaternion matrices, an equivalent iteration on the complex field is established to solve the equation in the Matlab environment. Two numerical examples are used to test the effectiveness and feasibility of the given method. .

钛酸钡/硅橡胶与多壁碳纳米管/硅橡胶交替多层复合材料的设计及电机转换性能

分别以钛酸钡(BT)和多壁碳纳米管(MWCNT)作为硅橡胶(SR)的填料,采用多次涂覆法,设计并制备了BT/SR和MWCNT/SR交替多层结构的复合介电弹性体B/SR-M/SR,研究了B/SR-M/SR复合材料的电机转换性能及交替多层结构对其性能的影响。结果表明,B/SR-M/SR复合材料的杨氏模量略高于纯SR,且表现出高介电常数、低介电损耗的特点。在1 kHz下,B/SR-M/SR的介电常数最大为5.6,为纯SR(3.2)的1.77倍,而相应的介电损耗为0.003,与纯SR(0.001)接近。MWCNT含量对复合材料的电导特性无显著影响,但会降低其击穿场强。B/SR-M/SR的最大电致应变为7.37%,远高于纯SR(1.43%)。此外,对比填充相同含量填料的三相复合材料,B/SR-M/SR复合材料的电机转换性能更佳。

Synthesis, characteristics of hierarchical EU-1 zeolite for xylene isomerization probe reaction

Introduced a method of synthesizing hierarchical EU-1 zeolite with organosilanes as additive, and studied the influences of following different kinds of organosilanes on the synthesis of hierarchical EU-1 zeolite: γ-glycidoxy propyl trimethoxy silane(GPTMS), N-β-(aminoethyl)-γ-aminopropyl methyl dimethoxyl silane(APAEDMS),and N-(β-aminoethyl)-γ-aminopropyl dimethoxyl(ethyoxyl) silane(TMPED). The hierarchical EU-1 samples were characterized by XRD, SEM, N_2 adsorption, FT-IR and NH_3-TPD to analyze the crystallinity, morphology, surface area, pore size distribution and acidity. The results showed that hierarchical EU-1 zeolites were successfully synthesized; organosilanes have great influence on crystal morphology of EU-1 zeolites; the exterior surface area of hierarchical EU-1 zeolite, which synthesized with organosilanes(APAEDMS) adding into synthesis system, increased by 62.1% and mesopore volume increased by 129.1% compared with conventional EU-1 zeolites, thus can reduce the diffusional restriction markedly in catalytic reaction. The catalytic performance of hierarchical EU-1zeolites were evaluated in m-xylene isomerization on fixed bed reactor. The catalytic data showed that the isomerization activity PX/X of the hierarchical EU-1 zeolites reached around 24.09% in theoretical thermodynamic equilibrium from 23.83%, and the selectivity of C_8 aromatic hydrocarbon increased from 75.16% to 84.87%. The conversion of p-xylene increased from 16.30% to 18.41%.

Modification and sequential treatment of EU-1 zeolite in mild alkali and alkaline-acid conditions

EU-1 zeolites were sequentially treated with low-concentration sodium carbonate(Na_2CO_3) and hydrochloric acid(HCl) solutions.The obtained samples were characterized by X-ray diffraction(XRD),scanning electron microscopy(SEM),N_2 adsorption/desorption,temperature programmed desorption of NH_3(NH_3-TPD),solid state^(27)A1 nuclear magnetic resonance(^(27)A1 NMR),and the catalytic performances of the treated samples were tested in the xylene isomerization reaction.The results showed that the external surface area and mesoporous volume of the sample sequentially treated with 0.05 mol·L^(-1) Na_2CO_3 and 0.1 mol·L^(-1) HCl solutions reached73.9 m^2·g^(-1) and 0.162 cm^3·g^(-1),respectively.The catalytic performances of EU-1 zeolites were significantly improved,that the activity of the probe reaction increased from 23.03%to 23.61%and the selectivity increased from85.09%to 87.14%compared with those of parent sample.Furthermore,it was found that only amorphous silica and alumina species was dissolved during the post-treatment process,but the framework structure and the acidic properties of EU-1 zeolite remained intact.

Simultaneously Effi cient Solar Light Harvesting and Charge Transfer of Hollow Octahedral Cu_(2)S/CdS p-n Heterostructures for Remarkable Photocatalytic Hydrogen Generation

Solar-driven water splitting is a promising alternative to industrial hydrogen production.This study reports an elaborate design and synthesis of the integration of cadmium sulfi de(CdS)quantum dots and cuprous sulfi de(Cu_(2)S)nanosheets as three-dimensional(3D)hollow octahedral Cu_(2)S/CdS p-n heterostructured architectures by a versatile template and one-pot sulfi dation strategy.3D hierarchical hollow nanostructures can strengthen multiple refl ections of solar light and provide a large specifi c surface area and abundant reaction sites for photocatalytic water splitting.Owing to the construction of the p-n heterostructure as an ideal catalytic model with highly matched band alignment at Cu_(2)S/CdS interfaces,the emerging internal electric fi eld can facilitate the space separation and transfer of photoexcited charges between CdS and Cu_(2)S and also enhance charge dynamics and prolong charge lifetimes.Notably,the unique hollow Cu_(2)S/CdS architectures deliver a largely enhanced visible-light-driven hydrogen generation rate of 4.76 mmol/(g·h),which is nearly 8.5 and 476 times larger than that of pristine CdS and Cu_(2)S catalysts,respectively.This work not only paves the way for the rational design and fabrication of hollow photocatalysts but also clarifi es the crucial role of unique heterostructure in photocatalysis for solar energy conversion.

Calcium-dependent protein kinases CPK21 and CPK23 phosphorylate and activate the iron-regulated transporter IRT1 to regulate iron deficiency in Arabidopsis

Iron(Fe)is an essential micronutrient for all organisms.Fe availability in the soil is usually much lower than that required for plant growth,and Fe deficiencies seriously restrict crop growth and yield.Calcium(Ca2+)is a second messenger in all eukaryotes;however,it remains largely unknown how Ca2+regulates Fe deficiency.In this study,mutations in CPK21 and CPK23,which are two highly homologous calcium-dependent protein kinases,conferredimpaired growth and rootdevelopment under Fe-deficient conditions,whereas constitutively active CPK21 and CPK23 enhanced plant tolerance to Fe-deficient conditions.Furthermore,we found that CPK21 and CPK23 interacted with and phosphorylated the Fe transporter IRONREGULATED TRANSPORTER1(IRT1)at the Ser149 residue.Biochemical analyses and complementation of Fe transport in yeast and plants indicated that IRT1 Ser149 is critical for IRT1 transport activity.Taken together,these findings suggest that the CPK21/23-IRT1 signaling pathway is critical for Fe homeostasis in plants and provides targets for improving Fe-deficient environments and breeding crops resistant to Fe-deficient conditions.

An epipolythiodioxopiperazine alkaloid and diversified aromatic polyketides with cytotoxicity from the Beibu Gulf coral-derived fungus Emericella nidulans GXIMD 02509

Marine microorganisms,especially marine fungi,have historically proven their value as a prolific source for structurally novel and pharmacologically active secondary metabolites(Deshmukh et al.,2018;Carroll et al.,2022).The corals constitute a dominant part of reefs with the highest biodiversity,and harbor highly diverse and abundant microbial symbionts in their tissue,skeleton,and mucus layer,with species-specific core members that are spatially partitioned across coral microhabitats(Wang WQ et al.,2022).The coral-associated fungi were very recently found to be vital producers of structurally diverse compounds,terpenes,alkaloids,peptides,aromatics,lactones,and steroids.

Compact wideband FSS-absorber-based low-RCS reflectarray antenna

This paper presents a method to realize compact broadband low-RCS ReflectArray(RA)antenna based on a Frequency Selective Surface(FSS)absorber and a reflective metasurface.Such an FSS absorber consists of a resistance-loaded lossy layer and an FSS layer,which is utilized to reach an absorption-transmission response.The bottom reflective metasurface works as a phase array,reshaping the quasi-sphere wave from the feeding antenna into the quasi-plane wave.As a demonstration,the low-RCS RA antenna is simulated,fabricated,and measured.The simulated and measured results show that the developed low-RCS RA antenna has an aperture efficiency of 42.7%and a gain of 25.4 dBi in the X band.In the meantime,it simultaneously reaches the 10 dB RCS reduction for the orthogonal polarizations at the S and C bands,corresponding to a fractal bandwidth of 120%.Specifically,the adopted patch-feeding antenna makes the RA antenna more compact than the horn-feed conventional ones.Furthermore,the proposed RA antenna uses a few layers of substrates,making it lower in cost and easier for fabrication.The proposed design may have potential application in integrated stealth communication systems.

GTPase ROP6 negatively modulates phosphate deficiency through inhibition of PHT1;1 and PHT1;4 in Arabidopsis thaliana

Phosphorus,an essential macroelement for plant growth and development,is a major limiting factor for sustainable crop yield.The Rho of plant(ROP)GTPase is involved in regulating multiple signal transduction processes in plants,but potentially including the phosphate deficiency signaling pathway remains unknown.Here,we identified that the rop6 mutant exhibited a dramatic tolerant phenotype under Pi-deficient conditions,with higher phosphate accumulation and lower anthocyanin content.In contrast,the rop6 mutant was more sensitive to arsenate(As(V))toxicity,the analog of Pi.Immunoblot analysis displayed that the ROP6 protein was rapidly degraded through ubiquitin/26S proteasome pathway under Pi-deficient conditions.In addition,pull-down assay using GST-RIC1 demonstrated that the ROP6 activity was decreased obviously under Pi-deficient conditions.Strikingly,protein-protein interaction and two-voltage clamping assays demonstrated that ROP6 physically interacted with and inhibited the key phosphate uptake transporters PHT1;1 and PHT1;4 in vitro and in vivo.Moreover,genetic analysis showed that ROP6 functioned upstream of PHT1;1 and PHT1;4.Thus,we conclude that GTPase ROP6 modulates the uptake of phosphate by inhibiting the activities of PHT1;1 and PHT1;4 in Arabidopsis.