THE FEKETE-SZEG?INEQUALITY AND SUCCESSIVE COEFFICIENTS DIFFERENCE FOR A SUBCLASS OF CLOSE-TO-STARLIKE MAPPINGS IN COMPLEX BANACH SPACES

Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.

Early ABA-stimulated maintenance of Cl^(−) homeostasis by mepiquat chloride priming confers salt tolerance in cotton seeds

Mepiquat chloride(MC)priming alleviates the effects of salt stress during seed germination in cotton(Gossypium hirsutum L.),but the mechanisms underlying its effects are unknown.We found that MC priming increases salt tolerance,as evidenced by marked increases in seed vigor and germination rates,and alleviated salt toxicity by reducing Cl^(−)accumulation in germinating seeds.Consistently,electrophysiological experiments revealed that the seeds with MC priming displayed superior Cl^(−)exclusion ability in the root apex.These beneficial effects of MC priming were abolished by the abscisic acid(ABA)-synthesis blocker fluridone under salt stress.MC priming induced an early response to acclimatization and stress,as indicated by rapidly increasing ABA content during initial exposure to salt stress.Transcriptome analyses revealed that MC priming induced an array of differentially expressed genes(DEGs)in germinating seeds.The most noticeable changes in germinating seeds were MC priming-induced increases in the expression of DEGs encoding components of ABA biosynthesis,ABA catabolism,and ABA signaling pathways under salt stress.MC priming also increased the expression of some DEGs encoding Cl^(−)ion transporters(e.g.CCC,SLAC1/SLAH1/SLAH3,CLC,and ALMT9)in germinating seeds.These results indicate that MC priming-induced ABA contributes to Cl^(−)homeostasis in tissues and acts as a positive regulator of salt tolerance via regulation of Cl^(−)transporters(particularly CCC and SLAC1/SLAH1/SLAH3).Taken together,these findings shed light on the molecular mechanism underlying MC-mediated tolerance to salt stress during seed germination.

ON REFINEMENT OF THE COEFFICIENT INEQUALITIES FOR A SUBCLASS OF QUASI-CONVEX MAPPINGS IN SEVERAL COMPLEX VARIABLES

Let K be the familiar class of normalized convex functions in the unit disk.In[14],Keogh and Merkes proved that for a function f(z)=z+∑k=2∞a k z k in the class K,|a 3−λa 22|≤max{13,|λ−1|},λ∈C.The above estimate is sharp for eachλ.In this article,we establish the corresponding inequality for a normalized convex function f on U such that z=0 is a zero of order k+1 of f(z)−z,and then we extend this result to higher dimensions.These results generalize some known results.

Reducing the carbon emissions from Qianxi tomato fruits preservation by cold atmospheric plasma

China has pledged to reach its dual-carbon goals(i.e.,carbon peak and carbon neutrality)at the end of 2060.To reduce carbon emission in food preservation industry,the preservation effects of cold atmospheric plasma intermittent treatment(1 min/6 h each day,PL4)combined with 15℃ and 4℃ only on Qianxi tomato fruits during 7 d storage were investigated.Results indicated that the firmness,L*,sensory taste,glutathione(GSH)content,mineral(Fe,P,K)content,polyphenol oxidase activity of PL4 tomatoes were significantly increased than that in Control during earlier period storage,with worse weight loss,titratable acid,a*,b*,lycopene content,·OH radical scavenging capacity and same moisture content,total soluble solids,polysaccharide content,total phenolics content,total flavonoid content,ascorbic acid content,1,1-diphenyl-2-picrylhydrazyl radical scavenging capacity,pectin methylesterase activity.Moreover,the power and R134a consumption of PL4 were highly decreased by around 56.4 kW·h and 0.3 g respectively during whole storage as compared to Control,and reduced more than 99.8%carbon emission based on equipment using stage.All in all,this study illustrated that PL4 treatment can be applied as an ecofriendly,low carbon and sustainable preservation strategy for short-term storage of fruits under 4℃ or higher temperature.

Fekete and Szego problem for a subclass of quasi-convex mappings in several complex variables

Let K be the familiar class of normalized convex functions in the unit disk. Keogh and Merkes proved the well-known result that maxf∈A ｜a3 - λa22｜ ≤ max{1/3, ｜λ - 1}, ,λ ∈ C, and the estimate is sharp for each ∈. We investigate the corresponding problem for a subclass of quasi-convex mappings of type B defined on the unit ball in a complex Banach space or on the unit polydisk in Cn. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.

Highly sensitive and selective two-photon sensing of cartap using Au@Ag core-shell nanoparticles

A highly sensitive and selective two-photon sensing scheme for detection of cartap was developed by using Au@Ag bimetallic core-shell nanoparticles.Cartap was found to induce the aggregation of Au@Ag nanoparticles and up to 700-fold enhancement in two-photon photoluminescence.Huge enhancement in two-photon photoluminescence allows achieving a detection limit of as low as 0.0062 mg/kg,which is better than the conventional colorimetric methods.This two-photon sensing scheme has a broad dynamic range and displays excellent selectivity in detection of cartap against over other ten kinds of commonly used insecticides.

Fekete and Szeg problem in one and higher dimensions

In this paper, we establish the Fekete and Szeg inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in C^n.

Study of Linear and Nonlinear Optical Properties of Four Derivatives of Substituted Aryl Hydrazones of 1,8-Naphthalimide

Four 1,8-naphthalimide hydrazone molecules with different electron-donating groups have been applied in the study of linear and nonlinear optical(NLO)properties.These compounds showed strong green emission in solution.Their NLO properties such as two-photon absorption(TPA)behavior with femtosecond laser pulses ca.800 nm and excited-state absorption(ESA)behavior with nanosecond laser pulses at 532 nm were investigated.Compound 4 presented the largest two-photon cross section(550 GM)among them due to two factors:the conjugated length of compound 4 is the longest and the electron-donating ability of compound 4 is the strongest.Different from TPA behavior,compound 2 showed the best nonlinear absorption properties at 532 nm and its nonlinear absorption coef-ficient and third-order nonlinear optical susceptibilitiesχ^(3)were up to 1.41×10^(−10) MKS and 4.65×10^(−12) esu,re-spectively.Through the modification of the structure,the nonlinear optical properties of these compounds at differ-ent wavelengths(532 and 800 nm)were well tuned.The great broad-band nonlinear optical properties indicate hy-drazones are good candidates for organic nonlinear optical absorption materials.

Recent results on nucleon spin structure study at RHIC

Both the PHENIX and STAR experiments at the Relativistic Heavy Ion Collider （RHIC） at Brookhaven National Laboratory are running polarized proton-proton collisions at √s = 200 and 500 GeV. The main goal of the RHIC spin physics program is to gain deeper insight into the spin structure of the nucleon. We will give an overview of recent spin results from RHIC, particularly the study of gluon polarization via jet/hadron production and sea quark polarization via W boson production in longitudinally polarized proton-proton collisions.

The Coefficient Inequalities for a Class of Holomorphic Mappings in Several Complex Variables

The authors establish the coefficient inequalities for a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in C^n,which are natural extensions to higher dimensions of some Fekete and Szego inequalities for subclasses of the normalized univalent functions in the unit disk.

Sharp distortion theorems for a subclass of close-to-convex mappings

We introduce the class of strongly close-to-convex mappings of order c~ in the unit ball of a complex Banach space, and then, we give the sharp distortion theorems for this class of mappings in the unit ball of a complex Hilbert space X or the unit polydisc in Cn. As an application, a sharp growth theorem for strongly close-to-convex mappings of order α is obtained.