Suppression of low-frequency ultrasound broadband vibration using star-shaped single-phase metamaterials

In order to suppress the low-frequency ultrasound vibration in the broadband range of 20 k Hz—100 k Hz,this paper proposes and discusses an acoustic metamaterial with low-frequency ultrasound vibration attenuation properties,which is configured by hybrid arc and sharp-angle convergent star-shaped lattices.The effect of the dispersion relation and the bandgap characteristic for the scatterers in star-shaped are simulated and analyzed.The target bandgap width is extended by optimizing the geometry parameters of arc and sharp-angle convergent lattices.The proposed metamaterial configured by optimized hybrid lattices exhibits remarkable broad bandgap characteristics by bandgap complementarity,and the simulation results verify a 99%vibration attenuation amplitude can be obtained in the frequency of20 k Hz—100 k Hz.After the fabrication of the proposed hybrid configurational star-shaped metamaterial by 3D printing technique,the transmission loss experiments are performed,and the experimental results indicate that the fabricated metamaterial has the characteristics of broadband vibration attenuation and an amplitude greater than 85%attenuation for the target frequency.These results demonstrate that the hybrid configurational star-shaped metamaterials can effectively widen the bandgap and realize high efficiency attenuation,which has capability for the vibration attenuation in the application of highprecise equipment.

Star-shaped Differentiable Functions and Star-shaped Differentials

Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated.

FIXED POINTS OF NONEXPANSIVE MAPPINGS ON STAR-SHAPED SUBSETS OF A CONVEX METRIC SPACE

In this paper, we give some characteristic properties of star-shaped sets which include a subset of a convex metric space. Using the characteristic properties, we discuss the existence problems of fixed points of nonexpansive type mappings on star-shaped subsets of convex metric spaces, which generalize the recent results obtained by Ding Xie-ping, Beg and Azam. Finally, we give an example which shows that our generalizations are essential.

Synthesis and characterization of novel star-shaped pyridine cored compounds with alternating carbazole and triphenylamine moieties

Amorphous 2,4,6-trissubstituted pyridines containing three peripheral carbazole or two triphenylamine and one carbazole moieties, respectively, have been synthesized and characterized. The properties of the compounds are investigated by UV-vis absorption, photoluminescence spectroscopy, thermal analysis as well as cyclic voltammetry. The results show that the compounds have high thermal stability, emit blue light. Also, the compounds possess the HOMO and LUMO energy levels comparable to those of NPB. The effects of different substituents on the electronic properties of the materials have been discussed.

SYNTHESIS OF HETEROARM STAR-SHAPED POLYMER BY THE USE OF POLYFUNCTIONAL CHAIN-TRANSFER AGENT via CONVENTIONAL FREE RADICAL POLYMERIZATION

Heteroarm star-shaped polymers were synthesized by conventional free radical polymerization in two steps by the use of polyfunctional chain transfer agent.In the first step,free radical polymerization of methyl methacrylate was carried out in the presence of a polyfunctional chain transfer agent,pentaerythritol tetrakis(3-mercaptopropinate).At appropriate monomer conversions,two-arm PMMA having two residual thiol groups at the chain center or three-arm PMMA having one residual thiol group at the core were o...

PREPARATION AND CHARACTERIZATION OF INCLUSION COMPLEXES OF TWO-ARM LINEAR AND FOUR-ARM STAR-SHAPED POLY(ε-CAPROLACTONE)S WITHα-CYCLODEXTRIN

Both four-ann star-shaped poly（ε-caprolactone） （4sPCL） and two-ann linear PCL （2LPCL） were synthesized and their inclusion complexation with α-cyclodextrin （α-CD） were studied. The inclusion complexes （ICs） formed between the PCL polymers and α-CD were characterized by ^1H-NMR, DSC, TGA, WAXD, and FT-1R, respectively. Both branch ann number and molecular weight of the PCL polymers have apparent effect on the stoichiometry （CL：CD, mol：mol） of these ICs. All these analytical results indicate that the branch arms of the PCL polymers are incorporated into the hydrophobic α-CD cavities and their original crystalline properties are completely suppressed. Moreover, the inclusion complexation between two-ann linear or four-ann star-shaped PCL polymers and α-CD not only enhances the thermal stability of the guest PCL polymers but also improves that of α-CD.

Fiber-based joint time and frequency dissemination via star-shaped commercial telecommunication network

A fiber-based, star-shaped joint time and frequency dissemination scheme is demonstrated. By working in cooperation with the existing commercial telecommunication network. Our scheme enables the frequency, time, and digital data networks to be integrated together and could represent an ideal option of interconnection among scientific institutions.The compensation functions of the time and frequency transfer scheme are set at the client nodes. The complexity of the central node is thus reduced, and future expansion by the addition of further branches will be accomplished more easily.During a performance test in which the ambient temperature fluctuation is 30℃/day, timing signal dissemination stability is achieved to be approximately ±50 ps along 25-km-long fiber spools. After calibration, a timing signal synchronization accuracy of 100 ps is also realized. The proposed scheme offers an option of the construction of large-scale fiber-based frequency and time transfer networks.

SYNTHESIS,CHARACTERIZATION AND NANOPARTICLE FORMATION OF STAR-SHAPED POLY(L-LACTIDE)WITH SIX ARMS

Well-defined star-shaped poly(L-lactide)with six arms(sPLLA)was synthesized via the ring-opening polymerization of L-lactide using dipentaerythritol as initiator and stannous octoate as catalyst in bulk at 125~C.The effects of molar ratios of both monomer to initiator and monomer to catalyst on the molecular weights of as-synthesized sPLLA polymers were in detail investigated.The molecular weights of sPLLA polymers linearly increased with the molar ratio of monomer to initiator,and the molecular weight dist...

pH-sensitive micelles self-assembled from star-shaped TPGS copolymers with ortho ester linkages for enhanced MDR reversal and chemotherapy

TPGS approved by FDA can be used as a P-gp inhibitor to effectively reverse multi-drug resistance(MDR)and as an anticancer agent for synergistic antitumor effects.However,the comparatively high critical micelle concentration(CMC),low drug loading(DL)and poor tumor target limit its further clinical application.To overcome these drawbacks,the pH-sensitive star-shaped TPGS copolymers were successfully constructed via using pentaerythritol as the initial materials,ortho esters as the pH-triggered linkages and TPGS active-ester as the terminated MDR material.The amphiphilic star-shaped TPGS copolymers could self-assemble into free and doxorubicin(DOX)-loaded micelles at neutral aqueous solutions.The micelles exhibited the lower CMC(8.2×10^(−5) mg/ml),higher DL(10.8%)and long-term storage and circulation stability,and showed enhanced cellular uptake,apoptosis,cytotoxicity,and growth inhibition for in vitro MCF-7/ADR and/or MCF-7/ADR multicellular spheroids and in vivo MCF-7/ADR tumors via efficiently targeted drug release at tumoral intracellular pH(5.0),MDR reversal of TPGS,and synergistic effect of DOX and TPGS.Therefore,the pH-sensitive micelles self-assembled from star-shaped TPGS copolymers with ortho ester linkages are potentially useful to clinically transform for enhanced MDR cancer treatment.

Synthesis and Physicochemical Characterization of Biodegradable Star-Shaped Poly Lactide-Co-Glycolide-<i>β</i>-Cyclodextrin Copolymer Nanoparticles Containing Albumin

The purposes of this research were to synthesize and characterize star-shaped poly lactide-co-glycolide-β-cyclo-dextrin (PLGA-β-CD) copolymer by reacting L-lactide, glycolide and β-cyclodextrin in the presence of stannous octoate as a catalyst. The structure of PLGA-β-CD copolymer was confirmed with 1H-NMR, 13C-NMR and FT-IR spectra. Albumin as a model peptide drug was encapsulated within nanoparticles made of PLGA-β-CD with a modified double emulsion method. Transmission electron microscopy (TEM) and scanning electron microscopy (SEM) photomicrographs showed that the nanoparticles have the mean diameter within the range of 80 - 210 nm. Also they were almost spherical in shape. Effects of the experimental parameters, such as copolymer composition, copolymer concentration, and reaction temperature, on particular size and encapsulation efficiency were investigated.

Closed characteristics on non-degenerate star-shaped hypersurfaces in R^(2n)

In this paper, firstly we establish the relation theorem between the Maslov-type index and the index defined by C. Viterbo for star-shaped Hamiltonian systems. Then we extend the iteration formula of C. Viterbo for non-degenerate star-shaped Hamiltonian systems to the general case. Finally we prove that there exist at least two geometrically distinct closed characteristics on any non-degenerate star-shaped compact smooth hypersurface on R2n with n ＞ 1. Here we call a hypersurface non-degenerate, if all the closed characteristics on the given hypersurface together with all of their iterations are non-degenerate as periodic solutions of the corresponding Hamiltonian system. We also study the ellipticity of closed characteristics when n=2.

The Existence of Two Closed Characteristics on Every Compact Star-shaped Hypersurface in R^4

Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least two closed characteristics on every compact star-shaped hypersuface in R4. Then Ginzburg, Hein, Hryniewicz, and Macarini gave this result a second proof. In this paper, we give it a third proof by using index iteration theory, resonance identities of closed characteristics and a remarkable theorem of Ginzburg et at.

Non-hyperbolic Closed Characteristics on Non-degenerate Star-shaped Hypersurfaces in R2n

In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface E C R2n, there exist at least n non-hyperbolic closed characteristics with even Maslov- type indices on E when n is even. When n is odd, there exist at least n closed characteristics with odd Maslov-type indices on E and at least （n - 1） of them are non-hyperbolic. Here we call a compact star-shaped hypersurfaee E ∈R2 index perfect if it carries only finitely many geometrically distinct prime closed characteristics, and every prime closed characteristic （T, y） on E possesses positive mean index and whose Maslov-type index i（y, m） of its m-th iterate satisfies i（y, m） ≠-1 when n is even, and i（y, rn） ≠2{-1,0} when n is odd for all rn E N.

One-step synthesis and self-assembly behavior of thermo-responsive star-shaped β-cyclodextrin-（P（M EO2MA-co-PEGMA））21 copolymers

A novel β-cyclodextrin-poly（2-（2-methoxyethoxy）ethyl methacrylate）-co- poly（ethylene glycol） methacrylate （abbreviated as： β-CD-（P（MEO2MA-co-PEGMA））21） was prepared by using the one-step strategy, and then the star-shaped copolymers were used in the atom transfer radical polymerization （ATRP）. The structure of star-shaped β- CD-（P（MEO2MA-co-PEGMA））21 copolymers were studied by FTIR, 1H NMR and gel permeation chromatography （GPC）. The star-shaped copolymers could self-assembled into micelles in aqueous solution owing to the outer amphiphilic β-CD as a core and the hydrophilic P（MEO2MA-co-PEGMA） segments as a shell. These thermo-responsive starshaped copolymers micelles exhibited lower critical solution temperature （LCST） in water, which could be finely tuned by changing the feed ratio of MEO2MA to PEGMA. The LCST of star-shaped β-CD-（P（MEO2MA-co-PEGMA））21 copolymer micelles were increased from 35℃ to 58℃ with the increasing content of PEGMA. The results were investigated by DLS and TEM. When the temperature was higher than corresponding LCSTs, the micelles started to associate and form spherical nanoparticles. Therefore, β- CD-（P（MEO2MA-co-PEGMA））21 star-shaped copolymer micelles could be potentially applied in nano-carrier, nano-reactor, smart materials and biomedical fields.

Controllable hydrothermal synthesis of star-shaped Sr3Fe2（OH）12 assemblies and their thermal decomposition and magnetic properties

Pure phase star-shaped hydrogarnet Sr3Fe2（OH）12 assemblies were synthesized by a mild hydrothermal method （210℃, 12 h）, and the effects of the preparation conditions on the phase composition of the product were investigated. It was found that the impurity phases could be decreased or eliminated by increasing the molar ratio of Sr2＋ to Fe3＋, and that high temperatures favored the formation of Sr3 Fe2（OH）12 and reduced the concentration of CO32- -containing byproducts. The thermal decomposition of the star-shaped Sr3Fe2（OH）12 assemblies was examined, and the results showed that the dehydration process at higher temperatures is accompanied by the formation of SrFeO3-δ. Above 655 ℃, a solid state reaction between the SrFeO3-δ and Sr（OH）2 or SrCO3 results in the formation of Sr4Fe3O10-δ.The mag- netic properties of the as-synthesized Sr3Fe2（OH）12 and of samples calcined at different temperatures were assessed. A sample calcined at 575 ℃ exhibited greatly enhanced ferromagnetic properties, with a remanent magnetization of 1.28 emu/g and a coercivity of 4522.1 Oe at room temperature.

Two star-shaped small molecule donors based on benzodithiophene unit for organic solar cells

Star-shaped small molecules have attracted great attention for organic solar cells(OSCs)because they have three-dimensional charge-transport characteristics,strong light absorption capacities and easily tunable energy levels.Herein,three-and four-armed star-shaped small molecule donors,namely BDT-3 Th and BDT-4 Th,respectively,have been successfully designed and synthesized,which used benzodithiophene(BDT)as the central unit.The two star-shaped intermediates(2 a and 2 b)could be simultaneously obtained by one-step of Suzuki coupling,and 1,2-dimethoxyethane played a key role in the Suzuki coupling.Both of them have excellent thermal stability,good solubility and broad absorption.Four-armed BDT-4 Th shows a slightly higher extinction coefficient,a deeper HOMO energy level and an obviously better phase separation morphology when blended with Y6 than three-armed BDT-3 Th.As a result,increased power conversion efficiency(PCE)of 5.83%is obtained in the BDT-4 Th:Y6-based OSC devices,which is obviously higher than that of the BDT-3 Th:Y6-based devices(PCE=3.78%).To the best of our knowledge,this is the highest PCE among the BDT-based star-shaped donors-based OSCs.This result provides an effective strategy to obtain star-shaped small molecule donor materials for high efficient organic solar cells.

Synthesis, Characterization and Properties of Novel Star-Shaped π-Conjugated Oligomers with Triphenylamine Core

Four new star-shaped π-conjugated oligomers （TPA-CZ3, TPA-TPA3, TPA-PTZ3 and TPA-BT3） with triphenylamine as a core and different electron-donating ability groups, carbazole, triphenylamine, phenothiazine and bithiophene, as peripheral units have been designed and synthesized via the Heck reaction. These oligomers show good solubility in common organic solvents. Their photophysical, electrochemical, electronic structure and charge transfer properties between these star-shaped n-conjugated oligomers and N,N＇-bis（1-ethylpropyl）-3,4：9,10- perylene bis（tetracarboxyl diimide） （EP-PDI） have been investigated by UV-vis absorption spectra, photolumines- cence （PL） spectra, cyclic voltammetry （CV） measurement, theoretical calculations and fluorescence quenching. The results show that the absorptions and fluorescences of TPA-CZ3, TPA-TPA3 and TPA-PTZ3 are red shifted with the electron-donating ability of the peripheral unit increasing from carbazole to triphenylamine and phenothi- azine. In addition, although the bithiophene group has a weaker electron-donating ability than carbazole, triphenylamine and phenothiazine, the absorption and fluorescence of TPA-BT3 have a red shift than those of TPA-CZ3, TPA-TPA3 and TPA-PTZ3 because TPA-BT3 has a longer conjugation length than TPA-CZ3, TPA-TPA3 and TPA-PTZ3. The triphenylamine core and the peripheral units can constitute a large conjugated structure. The fluorescence quenching properties indicate that efficient charge transfer can happen between the star-shaped oligomers and EP-PDI.

The self-assemblies of a newly designed star-shaped molecule end-capped with bromine atoms studied by scanning tunneling microscopy

A new star-shaped molecule StOF-Br_3 containing oligofluorenes and halogen atoms(Bromine) has been synthesized and studied by Scanning Tunneling Microscopy(STM) at the highly oriented pyrolytic graphite(HOPG) surface.We have obtained the high-resolution self-assembled STM images,from which the highly ordered and closely packed non-porous arrangements of the StOF-Br_3 molecular selfassemblies at the heptanoic acid/HOPG surface could be observed.The molecular models and selfassembled StOF-Br_3 architectures have been given in the following text.Besides,we have also figured out the surface free energy by the density functional theory(DFT) calculation,which proved that the halogen...halogen interaction was strong enough to stabilize the ordered molecular self-assemblies.This work verifies the existence of bromine...bromine interactions,and meanwhile provides a kind of effective approach for quickly building ordered molecular nanoarchitectures with large areas and different geometries.

The inverse problem for differential pencils on a star-shaped graph with mixed spectral data

The partial inverse problem for differential pencils on a star-shaped graph is studied from mixed spectral data.More precisely,we show that if the potentials on all edges on the star-shaped graph but one are known a priori then the unknown potential on the remaining edge can be uniquely determined by partial information on the potential and a part of eigenvalues.

SYNTHESIS, PROPERTIES AND ELECTROPOLYMERIZATION OF STAR-SHAPED OLIGOTHIOPHENES WITH HEXAKIS(FLUOREN-2-YL)BENZENE AS CORE

Star-shaped oligothiophenes with hexakis（fluoren-2-yl）benzene （HFB） as cores were designed and synthesized. Grafting thiophene units to HFB results in a bond flattening of the core, and makes the molecules a flipping-twist shape. Their thermal, photophysical and electrochemical properties were studied. Highly cross-linked conjugated polymers can be produced by electropolymerization of T1-T3.