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In this paper, the new solitary wave solutions of the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation are obtained by Lie group symmetry method and the extended homoclinic test approach. Firstly, the equation can be reduced to (1+1)-dimensional partial differential equation by Lie group symmetry, and corresponding bilinear forms of the equation are given by symmetry functions. Secondly, the extended homoclinic test approach is employed to obtain the new kink type and singular solitary wave solutions. In addition, some new traveling and non-traveling wave solutions with arbitrary functions and oscillating tail are investigated through the special transformations for the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation.

Abstract The noncentrosymmetric ferromagnetic Weyl semimetal CeAlSi with simultaneous space-inversion and time-reversal symmetry breaking provides a unique platform for exploring novel topological states. Here, by employing multiple experimental techniques, we demonstrate that ferromagnetism and pressure can serve as efficient parameters to tune the positions of Weyl nodes in CeAlSi. At ambient pressure, a magnetism-facilitated anomalous Hall/Nernst effect (AHE/ANE) is uncovered. Angle-resolved photoemission spectroscopy (ARPES) measurements demonstrated that the Weyl nodes with opposite chirality are moving away from each other upon entering the ferromagnetic phase. Under pressure, by tracing the pressure evolution of AHE and band structure, we demonstrate that pressure could also serve as a pivotal knob to tune the positions of Weyl nodes. Moreover, multiple pressure-induced phase transitions are also revealed. These findings indicate that CeAlSi provides a unique and tunable platform for exploring exotic topological physics and electron correlations, as well as catering to potential applications, such as spintronics.

Abstract Light engineering of correlated states in topological materials provides a new avenue of achieving exotic topological phases inaccessible by conventional tuning methods. Here we demonstrate a light control of correlation gaps in a model charge-density-wave (CDW) and polaron insulator (TaSe4)2I recently predicted to be an axion insulator. Our ultrafast terahertz photocurrent spectroscopy reveals a two-step, non-thermal melting of polarons and electronic CDW gap via the fluence dependence of a longitudinal circular photogalvanic current. This helicity-dependent photocurrent reveals continuous ultrafast phase switches from the polaronic state to the CDW (axion) phase, and finally to a hidden Weyl phase as the pump fluence increases. Additional distinctive attributes aligning with the light-induced switches include: the mode-selective coupling of coherent phonons to the polaron and CDW modulation, and the emergence of a non-thermal chiral photocurrent above the pump threshold of CDW-related phonons. The demonstrated ultrafast chirality control of correlated topological states here holds large potentials for realizing axion electrodynamics and advancing quantum-computing applications.

Abstract A representative class of kagome materials, AV3Sb5 (A = K, Rb, Cs), hosts several unconventional phases such as superconductivity, $${{\mathbb{Z}}}_{2}$$ Z 2 non-trivial topological states, and electronic nematic states. These can often coexist with intertwined charge-density wave states. Recently, the discovery of the isostructural titanium-based single-crystals, ATi3Bi5 (A = K, Rb, Cs), which exhibit similar multiple exotic states but without the concomitant charge-density wave, has opened an opportunity to disentangle these complex states in kagome lattices. Here, we combine high-resolution angle-resolved photoemission spectroscopy and first-principles calculations to investigate the low-lying electronic structure of RbTi3Bi5. We demonstrate the coexistence of flat bands and several non-trivial states, including type-II Dirac nodal lines and $${{\mathbb{Z}}}_{2}$$ Z 2 non-trivial topological surface states. Our findings also provide evidence for rotational symmetry breaking in RbTi3Bi5, suggesting a directionality to the electronic structure and the possible emergence of pure electronic nematicity in this family of kagome compounds.

Abstract The recently discovered kagome metals AV3Sb5 (A = Cs, Rb, K) exhibit a variety of intriguing phenomena, such as a charge density wave (CDW) with time-reversal symmetry breaking and possible unconventional superconductivity. Here, we report a rare non-monotonic evolution of the CDW temperature (T CDW) with the reduction of flake thickness approaching the atomic limit, and the superconducting transition temperature (T c) features an inverse variation with T CDW. T CDW initially decreases to a minimum value of 72 K at 27 layers and then increases abruptly, reaching a record-high value of 120 K at 5 layers. Raman scattering measurements reveal a weakened electron-phonon coupling with the reduction of sample thickness, suggesting that a crossover from electron-phonon coupling to dominantly electronic interactions could account for the non-monotonic thickness dependence of T CDW. Our work demonstrates the novel effects of dimension reduction and carrier doping on quantum states in thin flakes and provides crucial insights into the complex mechanism of the CDW order in the family of AV3Sb5 kagome metals.

In this paper, the finite-time stability (FTS) of singular switched systems that have time-varying delays and perturbations is investigated. First, the concept of the FTS of time-varying delay singular switched systems is given, and a specific event-triggered mechanism is proposed. Then, a state feedback mechanism is proposed based on the event-triggered mechanism. Second, using the L-K function and state space decomposition, adequate criteria for the FTS of singular switched systems are found. Sufficient requirements are also presented for meeting the finite-time stable $ H_\infty $ performance index $ \gamma $.

Abstract Condensed matter systems in low dimensions exhibit emergent physics that does not exist in three dimensions. When electrons are confined to one dimension (1D), some significant electronic states appear, such as charge density wave, spin-charge separations, and Su-Schrieffer-Heeger (SSH) topological state. However, a clear understanding of how the 1D electronic properties connects with topology is currently lacking. Here we systematically investigated the characteristic 1D Dirac fermion electronic structure originated from the metallic NbTe2 chains on the surface of the composition-tunable layered compound NbSi x Te2 (x = 0.40 and 0.43) using angle-resolved photoemission spectroscopy. We found the Dirac fermion forms a Dirac nodal line structure protected by the combined $$\widetilde {M_y}$$ M y ̃ and time-reversal symmetry T and proves the NbSi x Te2 system as a topological semimetal, in consistent with the ab-initio calculations. As x decreases, the interaction between adjacent NbTe2 chains increases and Dirac fermion goes through a dimension-crossover from 1D to 2D, as evidenced by the variation of its Fermi surface and Fermi velocity across the Brillouin zone in consistence with a Dirac SSH model. Our findings demonstrate a tunable 1D Dirac electron system, which offers a versatile platform for the exploration of intriguing 1D physics and device applications.

BackgroundAs a natural host of Fasciola gigantica, buffalo is widely infected by F. gigantica. Its impact on buffalo production has caused great losses to the husbandry sector, and repeat infection is non-negligible. In buffaloes experimentally infected with F. gigantica, primary and secondary infection have yielded the same rate of fluke recovery, indicating a high susceptibility of buffalo to F. gigantica, which contributes to the high infection rate. Determining the immunological mechanism of susceptibility will deepen the understanding of the interaction between F. gigantica and buffalo. Here, we explored the immune response of buffaloes against primary and secondary F. gigantica infection, with a focus on cytokines’ dynamics explored through serum cytokine detection.MethodsBuffaloes were assigned to three groups: group A (noninfected, n = 4), group B (primary infection, n = 3), and group C (secondary infection, n = 3). Group B was infected via oral gavage with 250 viable F. gigantica metacercariae, and group C was infected twice with 250 metacercariae at an interval of 4 weeks. The second infection of group C was performed simultaneously with that of group B. Whole blood samples were collected pre-infection (0 weeks) and at 1–6, 10, and 12 weeks after that. The serum levels of seven cytokines (IFN-γ, IL-4, IL-5, IL-10, IL-13, TGF-β, and IL-17) were simultaneously determined using ELISA and further analyzed.ResultsIn the present study, no significant changes in Th1-type cytokines production were detected in early infection, both in primary and secondary infections, while the Th2-type response was strongly induced. A comparison of primary and secondary infection showed no significant difference in the cytokine secretion, which may indicate that the re-infection at 4 weeks after primary infection could not induce a robust adaptive immune response. The full extent of interaction between buffalo and F. gigantica in re-infection requires further study.

The recently discovered Kagome family AV_{3}Sb_{5} (A = K, Rb, Cs) exhibits rich physical phenomena, including non-trivial topological electronic structure, giant anomalous Hall effect, charge density waves (CDW) and superconductivity. Notably, CDW in AV_{3}Sb_{5} is evidenced to intertwine with its superconductivity and topology, but its nature remains elusive. Here, we combine x-ray scattering experiments and density-functional theory calculations to investigate the CDWs in CsV_{3}Sb_{5} and demonstrate the coexistence of 2×2×2 and 2×2×4 CDW stacking phases. Competition between these CDW phases is revealed by tracking the temperature evolution of CDW intensities, which also manifests in different transition temperatures during warming- and cooling measurements. We also identify a meta-stable quenched state of CsV_{3}Sb_{5} after fast-cooling process. Our study demonstrates the coexistence of competing CDW stackings in CsV_{3}Sb_{5}, offering insights in understanding the properties of this system.

The relationship between the charge density wave and excitonic correlations in a layered compound 1T-TiSe2 has remained controversial. Here, the authors observe a photo-induced dimensional crossover of the charge density wave and conclude that excitonic correlations are responsible for its out-of-plane phase coherence.

IntroductionWidespread Fasciola gigantica infection in buffaloes has caused great economic losses in buffalo farming. Studies on F. gigantica excretory and secretory products (FgESP) have highlighted their importance in F. gigantica parasitism and their potential in vaccine development. Identifying FgESP components involved in F. gigantica-buffalo interactions during different periods is important for developing effective strategies against fasciolosis.MethodsBuffaloes were assigned to non-infection (n = 3, as control group) and infection (n = 3) groups. The infection group was orally administrated 250 metacercariae. Sera were collected at 3, 10, and 16 weeks post-infection (wpi) for the non-infection group and at 0 (pre-infection), 1, 3, 6, 8, 10, 13, and 16 wpi for the infection group. FgESP components interacting with sera from the non-infection and infection groups assay were pulled down by co-IP and identified using LC–MS/MS. Interacting FgESP components in infection group were subjected to Kyoto Encyclopedia of Genes and Genomes (KEGG) metabolic pathway and gene ontology (GO) functional annotation to infer their potential functions.Results and discussionProteins of FgESP components identified in the non-infection group at 3, 10, and 16 wpi accounted for 80.5%, 84.3%, and 82.1% of all proteins identified in these three time points, respectively, indicating surroundings did not affect buffalo immune response during maintenance. Four hundred and ninety proteins were identified in the infection group, of which 87 were consistently identified at 7 time points. Following GO analysis showed that most of these 87 proteins were in biological processes, while KEGG analysis showed they mainly functioned in metabolism and cellular processing, some of which were thought to functions throughout the infection process. The numbers of specific interactors identified for each week were 1 (n = 12), 3 (n = 5), 6 (n = 8), 8 (n = 15), 10 (n = 23), 13 (n = 22), and 16 (n = 14) wpi, some of which were thought to functions in specific infection process. This study screened the antigenic targets in FgESP during a dense time course over a long period. These findings may enhance the understanding of molecular F. gigantica-buffalo interactions and help identify new potential vaccine and drug target candidates.

Magnetic topological materials have a variety of interesting properties, but very few material realizations exist. Here, the authors report a topological nodal-line semimetal and a topological massive Dirac metal phase in EuAs3 and demonstrate a magnetism-driven transition between these phases.

BackgroundFasciola gigantica, a tropical liver fluke, infects buffalo in Asian and African countries, causing significant economic losses and posing public health threats. The diagnostic of buffalo fascioliasis caused by F. gigantica is vital in fascioliasis control and preventation. The 22nd gel filtration chromatography fraction of F. gigantica Excretory-Secretory Products (FgESP), namely Fasciola 22 (F22), which was used as a diagnostic antigen in indirect ELISA, has demonstrated great potential for fascioliasis diagnosing. In the absence of rapid diagnostic methods, the use of a colloidal gold immunochromatographic strip based on F22 was applied to detect F. gigantica infection in buffalo.MethodsIn the present study, the 22nd gel filtration chromatography fraction of FgESP (F22) was used as an antigen to establish the colloidal gold-based immunochromatographic strip (ICS). The nitrocellulose membrane was incubated with F22 at the test line (T line) and goat anti-mouse secondary antibody at the control line (C line). The mouse anti-buffalo secondary antibody 2G7 conjugated to colloidal gold particles was used as the detection system for line visualization. The strip was assembled and developed by optimizing reaction conditions. The sensitivity, specificity, stability, and early diagnostic value of the strip were evaluated employing buffalo-derived sera.ResultsAn immunochromatographic strip for the rapid detection of antibodies against F. gigantica-FgICS was developed. The strip demonstrated high sensitivity and specificity. Sensitivity tests confirmed positive results even when the positive reference serum was diluted 4,096 times. Except for one Schistosoma japonicum-positive serum that tested positive via FgICS, specificity tests confirmed no cross-reactivity with other positive sera of Schistosoma japonicum and Babesia bovis. The strip remained stable after storage at 4°C for up to 3 months. In infected buffalo, antibodies could be detected as early as 14–21 days post-infection. The detection of 17 positive sera yielded an 82.4% positive rate via FgICS vs. a 100.0% positive rate via ELISA based on FgESP. For FgICS, the 95% confidence interval of sensitivity was 84.8–95.4%, while specificity was 4.2–14.7%.ConclusionThe immunochromatographic strip FgICS developed in this study provides a simple and rapid method of F. gigantica antibody detection and infected buffalo monitoring in the field.

With the rise of the concept of environmental protection and the attention of all sectors of society to the ecological environment, the selection of green suppliers is a hot topic. In this paper, we develop the combinative distance-based assessment (CODAS) method in the probabilistic hesitant fuzzy sets (PHFSs) to cope with the multiple attributes group decision making (MAGDM). A standardized approach that integrates multiple methods is applied to normalize the original data. Moreover, the statistics variance (SV) method is applied under PHFSs to calculate the objective weighting vector of evaluation criteria. In the end, a case for supplier selection and the comparative analysis are used to confirm the feasibility and utility of this new approach. First published online 30 August 2022

In this article, we develop the COPRAS model to solve the multiple attribute group decision making (MAGDM) under single-valued neutrosophic 2-tuple linguistic sets (SVN2TLSs). Firstly, we introduce the relevant knowledge about SVN2TLSs in a nutshell, such as the definition, the operation laws, a few of fused operators and so on. Then, combine the traditional COPRAS model with SVN2TLNs, and structure as well as elucidate the computing steps of the SVN2TLNCOPRAS pattern. Furthermore, in this article, we propose a method for determining attribute weights in different situations relying on the maximizing deviation method with SVN2TLNs. Last but not least, a numerical example about assessing the safety of construction project has been designed. And for further demonstrating the advantage of the new designed method, we also select a number of existed methods to have comparisons. First published online 13 January 2021

Probabilistic uncertain linguistic sets (PULTSs) have widely been used in MADM or MAGDM. The CODAS method, which is a novel MADM or MAGDM tool, aims to acquire the optimal choice which have the largest Euclidean & Hamming distances from the NIS. This paper designs the probabilistic uncertain linguistic CODAS (PUL-CODAS) method with sine entropy weight. Finally, a numerical example for green supplier selection is given and the obtained results are compared with some existing models. First published online 05 February 2021

Choosing the optimal network security service provider (NSSP) is a very important part of enterprise management decision. And the choice of NSSP is a typical multiple attribute group decision making (MAGDM) issue. In order to provide a better decision method for MAGDM problems, this paper integrates the TODIM method and the probabilistic uncertainty linguistic term set (PULTS), so as to propose the probabilistic uncertain linguistic TODIM model based on the prospect theory (PT-PUL-TODIM). The model combines the advantages of the prospect theory and TODIM method. In the end, a case study concerning NSSP selection problem is given to demonstrate the merits of the developed methods. First published online 31 March 2022

Mengwei Zhao, Guiwu Wei, Yanfeng Guo, Xudong Chen, authors of the article "CPT-TODIM method for interval-valued bipolar fuzzy multiple attribute group decision making and application to industrial control security service provider selection", published in Technological and Economic Development of Economy, 27(5), 1186–1206, https://doi.org/10.3846/tede.2021.15044 inform that several errors occurred in page 1199, σ1 and σ3 values, comprehensive predominance matrix β, and page 1202, Table 8. This has now been corrected. The authors regret the errors.

A diffusive predator-prey system with both the additive Allee effect and the fear effect in the prey subject to Neumann boundary conditions is considered in this paper. Firstly, non-negative and non-trivial solution a priori estimations are shown. Furthermore, for specific parameter ranges, the absence of non-constant positive solutions is demonstrated. Secondly, we use the linearized theory to investigate the stability of non-negative constant solutions. The spatially homogeneous and non-homogeneous periodic solutions, as well as non-constant steady state solutions, are next investigated by using Allee effect parameters as the bifurcation parameter. Finally, numerical simulation is used to illustrate some theoretical results.

With the rapid development of 3D printing technology, 3D printers are manufactured based on the principle of 3D printing technology are more and more widely used in the manufacturing industry. Choosing high quality 3D printers for industrial production is of great significance to the economic growth of enterprises. In fact, it is difficult to select the most optimal 3D printers under a single and simple standard. Therefore, this paper establishes the probabilistic double hierarchy linguistic EDAS (PDHL-EDAS) method for the multiple attribute group decision making (MAGDM). Then the CRITIC model is introduced to derive objective weight and the cumulative prospect theory is leaded into obtain the cumulative weight of PDHLTS. In addition, what’s more, the PDHL-EDAS method is built and applied to the choice of high-quality 3D printer. Finally, compared with the available MAGDM methods under PDHLTS, the built method is proved to be scientific and effective. First published online 15 December 2021

RV6Sn6 (R = Sc, Y, or rare earth) is a new family of kagome metals that have a similar vanadium structural motif as AV3Sb5 (A = K, Rb, Cs) compounds. Unlike AV3Sb5, ScV6Sn6 is the only compound among the series of RV6Sn6 that displays a charge density wave (CDW) order at ambient pressure, yet it shows no superconductivity (SC) at low temperatures. Here, we perform a high-pressure transport study on the ScV6Sn6 single crystal to track the evolutions of the CDW transition and to explore possible SC. In contrast to AV3Sb5 compounds, the CDW order of ScV6Sn6 can be suppressed completely by a pressure of about 2.4 GPa, but no SC is detected down to 40 mK at 2.35 GPa and 1.5 K up to 11 GPa. Moreover, we observed that the resistivity anomaly around the CDW transition undergoes an obvious change at ~2.04 GPa before it vanishes completely. The present work highlights a distinct relationship between CDW and SC in ScV6Sn6 in comparison with the well-studied AV3Sb5.

By the extended (G′G) method and the improved tanh function method, the exact solutions of the (2+1) dimensional Boussinesq equation are studied. Firstly, with the help of the solutions of the nonlinear ordinary differential equation, we obtain the new traveling wave exact solutions of the equation by the homogeneous equilibrium principle and the extended (G′G) method. Secondly, by constructing the new ansatz solutions and applying the improved tanh function method, many non-traveling wave exact solutions of the equation are given. The solutions mainly include hyperbolic, trigonometric and rational functions, which reflect different types of solutions for nonlinear waves. Finally, we discuss the effects of these solutions on the formation of rogue waves according to the numerical simulation.

Abstract The finite dimension estimates of Hausdorff dimension and fractal dimension of the attractor of the dissipative quantum Zakharov equations are mainly studied by using the estimates of the Lyapunov exponents. The main results on the attractor are obtained through studying the linear system DS(t) $\operatorname{DS}(t)$, which is the differential system of solution operator S(t) $S(t)$ for the dissipative quantum Zakharov equations at the initial value (m0,n0,E0) $(m_{0},n_{0},E_{0})$.

In this article, we combine some fundamental theories of the Pythagorean 2-tuple linguistic sets (P2TLSs) with EDAS method and design the Pythagorean 2-tuple linguistic number (P2TLN) EDAS (P2TLN-EDAS) method for multiple attribute group decision making (MAGDM) issue. Firstly, the basic concepts of P2TLSs are introduced. Next, two aggregation operators of P2TLN are defined, and then the calculation steps of EDAS method are listed briefly. Furthermore, P2TLN-EDAS method is given for MAGDM problems and computing steps are proposed in detail. Finally, a computational example related to construction safety assessment is used to expound the effectiveness of the designed method. Meanwhile, we also carried out some comparative analysis between P2TLN-EDAS method and P2TLWA/P2TLWG operators and another P2TLN-TODIM method. The results show that P2TLN-EDAS method derives the same best alternative as P2TLWA, P2TLWG operators and P2TLN-TODIM method. First published online 24 September 2020

We studied the effects of multiband electronic structure on the thermoelectric and electrical transport properties in the normal state of kagome superconductors A V _3 Sb _5 ( A = K, Rb, Cs). In all three members, the multiband nature is manifested by sign changes in the temperature dependence of the Seebeck and Hall resistivity, together with sublinear response of the isothermal Nernst and Hall effects to external magnetic fields in the charge ordered state. Moreover, ambipolar transport effects appear ubiquitously in all three systems, giving rise to sizable Nernst signal. Finally, possible origins of the sign reversal in the temperature dependence of the Hall effect are discussed.

Representation of approximation for manifolds of the stochastic Swift-Hohenberg equation with multiplicative noise has been investigated via non-Markovian reduced system. The approximate parameterizations of the small scales for the large scales are given in the process of seeking for stochastic parameterizing manifolds, which are obtained as pullback limits of some backward-forward systems depending on the time-history of the dynamics of the low modes in a mean square sense through the nonlinear terms. When the corresponding pullback limits of some backward-forward systems are efficiently determined, the corresponding non-Markovian reduced systems can be obtained for researching good modeling performances in practice.

Some dynamics behaviors for the nonautonomous stochastic fifth-order Swift–Hohenberg equation with additive white noise are considered. The existence of pullback random attractors for the nonautonomous stochastic fifth-order Swift–Hohenberg equation with some properties is mainly investigated on the bounded domain and unbounded domain, through the Ornstein–Uhlenbeck transformation and tail-term estimates. Furthermore, on the basis of some conditions, the finiteness of fractal dimension of random attractor is proved.

Magnetic Weyl semimetals (WSMs) bearing long-time seeking are still very rare. We have identified herein that EuCd2Sb2, a semimetal belonging to the type IV magnetic space group, hosts a magnetic exchange induced Weyl state via performing high magnetic field magnetotransport measurements and ab initio calculations. In the A-type antiferromagnetic structure, the external field larger than 3.2 T can align all Eu spins to be fully polarized along the c-axis and consequently drive EuCd2Sb2 into a spin polarized state. Magnetotransport measurements up to ∼55–60 T showed striking Shubnikov-de Hass oscillations associated with a nontrivial Berry phase. The ab initio calculations unveiled a phase transition of EuCd2Sb2 from a small gap antiferromagnetic topological insulator to a spin polarized WSM in which the Weyl points emerge along the Γ-Z path. Fermi arcs on (100) and (010) surfaces are also predicted. Meanwhile, the observed large anomalous Hall effect indicates the existence of Weyl points around the Fermi level. The results pave a way toward the realization of various topological states in a single material through the magnetic exchange manipulation.

Triangular lattice of rare-earth ions with interacting effective spin-1/2 local moments is an ideal platform to explore the physics of quantum spin liquids (QSLs) in the presence of strong spin-orbit coupling, crystal electric fields, and geometrical frustration. The Yb delafossites, NaYbCh_{2} (Ch=O, S, Se) with Yb ions forming a perfect triangular lattice, have been suggested to be candidates for QSLs. Previous thermodynamics, nuclear magnetic resonance, and powder-sample neutron scattering measurements on NaYbCh_{2} have supported the suggestion of the QSL ground states. The key signature of a QSL, the spin excitation continuum, arising from the spin quantum number fractionalization, has not been observed. Here we perform both elastic and inelastic neutron scattering measurements as well as detailed thermodynamic measurements on high-quality single-crystal NaYbSe_{2} samples to confirm the absence of long-range magnetic order down to 40 mK, and further reveal a clear signature of magnetic excitation continuum extending from 0.1 to 2.5 meV. The comparison between the structure of the magnetic excitation spectra and the theoretical expectation from the spinon continuum suggests that the ground state of NaYbSe_{2} is a QSL with a spinon Fermi surface.

In this paper, the existence of random attractors for nonautonomous stochastic reversible Selkov system with multiplicative noise has been proved through Ornstein-Uhlenbeck transformation. Furthermore, the upper semicontinuity of random attractors is discussed when the intensity of noise approaches zero. The main difficulty is to prove the asymptotic compactness for establishing the existence of tempered pullback random attractor.

The existence and approximation of manifolds for the Swift-Hohenberg equation with a proper parameter have mainly been studied. Using the backward-forward systems from Swift-Hohenberg equation, the existence and specific representation forms of manifolds for Swift-Hohenberg equation with a parameter have been obtained. Meanwhile, we make use of technique of deposition of lower and higher frequency spaces of solutions and assume the reduced system to obtain the main numeration approximation system of approximation solution for the original system Swift-Hohenberg equation with a proper parameter.

X-PLY corrugated paperboard is a new-type corrugated paperboard with three layers of orthotropic corrugated sandwiches structure, and may be employed to protect products from shock or vibration damage during distribution. This article deals with the characterization of properties of X-PLY corrugated paperboard relevant to its application for protective packaging in distribution, such as dynamic cushioning curves, vibration transmissibility and frequency curves. The main feature of article is the evaluation on the dynamic shock cushioning characteristics and vibration transmissibility of X-PLY corrugated paperboards by a series of experimental studies on the drop shock tester and vibration tester, the establishment of experimental formulas of dynamic cushioning curves, and the analysis of peak frequencies, vibration transmissibility and damping ratios. By using the fitting polynomial of curve and method of the least mean square, the experimental formulas and characteristic coefficients of dynamic cushioning curves have been obtained. From the vibration tests with slow sine sweep, the peak frequencies and vibration transmissibility are measured and used to estimate the damping ratios. These works provide basic data and curves relevant to its application for protective packaging in distribution.

Honeycomb paperboard is a kind of environmental-friendly package cushioning material with honeycomb sandwich structure, and may be employed to protect products from shock or vibration damage during distribution. This paper deals with the characterization of properties of honeycomb paperboard relevant to its application for protective packaging in transportation, such as dynamic cushion curves and vibration transmissibility. The main feature of the paper is the evaluation on the shock absorbing characteristics and vibration transmissibility of honeycomb paperboards with different thickness by a series of experimental studies on the drop shock machine and vibration table. By using the fitting polynomial of the curve, the experiential formulas and characteristic coefficients of dynamic cushion curves of honeycomb paperboards with different thickness have been obtained. From the vibration tests with slow sine sweep, the peak frequencies and vibration transmissibility are measured and used to estimate the damping ratios. All the works provide basic data and curves relevant to its application for protective packaging in transportation.