Broadband third-order optical nonlinearities of layered franckeite towards mid-infrared regime

The study of nonlinear optical responses in the mid-infrared(mid-IR)regime is essential for advancing ultrafast mid-IR laser applications.However,nonlinear optical effects under mid-IR excitation are rarely reported due to the lack of suitable nonlinear optical materials.The natural van derWaals heterostructure franckeite,known for its narrow bandgap and stability in air,shows great potential for developing mid-IR nonlinear optical devices.We have experimentally demonstrated that layered franckeite exhibits a broadband wavelength-dependent nonlinear optical response in the mid-IR spectral region.Franckeite nanosheets were prepared using a liquid-phase exfoliation method,and their nonlinear optical response was characterized in the spectral range of 3000 nm to 5000 nm.The franckeite nanosheets exhibit broadband wavelengthdependent third-order nonlinearities,with nonlinear absorption and refraction coefficients estimated to be about 10^(-7)cm/W and 10^(-11)cm^(2)/W,respectively.Additionally,a passively Q-switched fluoride fiber laser operating around a wavelength of 2800 nm was achieved,delivering nanosecond pulses with a signal-to-noise ratio of 43.6 dB,based on the nonlinear response of franckeite.These findings indicate that layered franckeite possesses broadband nonlinear optical characteristics in the mid-IR region,potentially enabling new possibilities for mid-IR photonic devices.

Assessment of large-scale multiple forest disturbance susceptibilities with AutoML framework: an Izmir Regional Forest Directorate case

Disturbances such as forest fires,intense winds,and insect damage exert strong impacts on forest ecosystems by shaping their structure and growth dynamics,with contributions from climate change.Consequently,there is a need for reliable and operational methods to monitor and map these disturbances for the development of suitable management strategies.While susceptibility assessment using machine learning methods has increased,most studies have focused on a single disturbance.Moreover,there has been limited exploration of the use of“Automated Machine Learning(AutoML)”in the literature.In this study,susceptibility assessment for multiple forest disturbances(fires,insect damage,and wind damage)was conducted using the PyCaret AutoML framework in the Izmir Regional Forest Directorate(RFD)in Turkey.The AutoML framework compared 14 machine learning algorithms and ranked the best models based on AUC(area under the curve)values.The extra tree classifier(ET)algorithm was selected for modeling the susceptibility of each disturbance due to its good performance(AUC values>0.98).The study evaluated susceptibilities for both individual and multiple disturbances,creating a total of four susceptibility maps using fifteen driving factors in the assessment.According to the results,82.5%of forested areas in the Izmir RFD are susceptible to multiple disturbances at high and very high levels.Additionally,a potential forest disturbances map was created,revealing that 15.6%of forested areas in the Izmir RFD may experience no damage from the disturbances considered,while 54.2%could face damage from all three disturbances.The SHAP(Shapley Additive exPlanations)methodology was applied to evaluate the importance of features on prediction and the nonlinear relationship between explanatory features and susceptibility to disturbance.

Galerkin-Bernstein Approximations for the System of Third-Order Nonlinear Boundary Value Problems

This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .

Quantum Size-Dependent Third-Order Nonlinear Optical Susceptibility in Semiconductor Quantum Dots

The density matrix approach has been employed to investigate the opticalnonlinear polarization in a single semiconductor quantum dot(QD). Electron states are considered tobe confined within a quantum dot with infinite potential barriers. It is shown, by numericalcalculation, that the third-order nonlinear optical susceptibilities for a typical Si quantum dot isdependent on the quantum size of the quantum dot and the frequency of incident light.

Parameter-Dependent Third-Order Susceptibility of In_xGa_(1-x)N/GaN Parabolic Quantum Dots

The electron states confined in wurtzite InxGa1-xN/GaN strained quantum dots （QDs） have been investigated in the effective -mass approximation by solving the Schrtdinger equation, in which parabolic confined potential and strong built-in electric field effect （due to the piezoelectricity and spontaneous polarization） have been taken into account. The real part Rex^（3）（0,0,ω） and the imaginary part Imx^（3）（0,0,ω） of the third-order susceptibil- ity describe quadratic electro-optic effects and electro-absorption process of the QDs respectively. And both of them have been calculated in directions parallel and vertical to z axis. Furthermore, the study shows Rex^（3）（0,0,ω） and Imx^（3）（0,0,ω） increase under resonant conditions with the QDs＇ radius and height increase, and the same results occur when the content increase. In addition, the resonant position shift to the lower energy region when the parabolic frequencies increase.

Dip2a regulates stress susceptibility in the basolateral amygdala

Dysregulation of neurotransmitter metabolism in the central nervous system contributes to mood disorders such as depression, anxiety, and post–traumatic stress disorder. Monoamines and amino acids are important types of neurotransmitters. Our previous results have shown that disco-interacting protein 2 homolog A(Dip2a) knockout mice exhibit brain development disorders and abnormal amino acid metabolism in serum. This suggests that DIP2A is involved in the metabolism of amino acid–associated neurotransmitters. Therefore, we performed targeted neurotransmitter metabolomics analysis and found that Dip2a deficiency caused abnormal metabolism of tryptophan and thyroxine in the basolateral amygdala and medial prefrontal cortex. In addition, acute restraint stress induced a decrease in 5-hydroxytryptamine in the basolateral amygdala. Additionally, Dip2a was abundantly expressed in excitatory neurons of the basolateral amygdala, and deletion of Dip2a in these neurons resulted in hopelessness-like behavior in the tail suspension test. Altogether, these findings demonstrate that DIP2A in the basolateral amygdala may be involved in the regulation of stress susceptibility. This provides critical evidence implicating a role of DIP2A in affective disorders.

Susceptibilities of Mycoplasma Hominis and Ureaplasma Urealyticum to Fluoroquinolones

Objectives: To determine the susceptibilities of M.hominis and U. urealyticum to fluoroquinolones forthe instruction of reasonable clinical application ofantibiotics.Method: The susceptibilities of M. hominis and U.urealyticum to six fluoroquinolones were determinedby the broth dilution method.Results: Sparfloxacin and gatifloxacin were veryactive with MIC50S of 0.03125 and 0.25 μg/ml againstM. hominis, 0.25 and 0.5 μg/ml against U. urealyticum,respectively. Levofloxacin and ofloxacin had MIC50S of1 μg/ml and 2 μg/ml, respectively against both species.Norfloxacin was less effective against both species at16 and 32 μg/ml. Ciprofloxacin was unusual in thatthe MIC50S varied fourfold between species, with 2 μg/ml against M. hominis and 8 μg/ml against U.urealyticum.Conclusions: The results can provide useful infor-mation for selecting fluoroquinolones for treatmentof urogenital mycoplasma infections.

Comparing the Genotype and Drug Susceptibilities between Mycobacterium avium and Mycobacterium intracellulare in China

Objective Mycobacterium avium （M. avium） and Mycobacterium intracellulare （M. intracellulare） are the major causative agents of nontuberculous mycobacteria （NTM）-related pulmonary infections. However, little is known about the differences in drug susceptibility profiles between these two species. Methods A total of 393 NTM isolates were collected from Shanghai Pulmonary Disease Hospital. Sequencing of partial genes was performed to identify the strains at species level. The minimum inhibitory concentration （MIC） was used to evaluate the drug susceptibility against 20 antimicrobial agents. Variable number of tandem repeat （VNTR） typing was conducted to genotype these two species. Results A total of 173 （44.0%） M. avium complex （MAC） isolates were identified, including 41 （10.4%） M. avium isolates and 132 （33.6%） M. intracellulare isolates. Clarithromycin and amikacin were the two most effective agents against MAC isolates. The Hunter-Gaston Discriminatory Index （HGDI） values for VNTR typing of M. avium and M. intracellulare isolates were 0.993 and 0.995, respectively. Levofloxacin resistance was more common among the unclustered strains than among the clustered strains of M. intracellulare. Conclusion M. intrecellulare was the most common NTM species in China. Clarithromycin and amikacin had high antimicrobial activities against MAC. VNTR typing of MAC isolates revealed a high discriminatory power. Levofloxacin resistance was associated with unclustered strains of M. intracellulare.

MULTIPLE POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.

The Susceptibilities of Oxya chinensis(Orthoptera:Acridoidea) to Malathion and Comparison of the Esterase Properties from Three Collected Populations in Tianjin Area,China

The susceptibilities of Oxya chinensis to malathion were studied in three populations collected from outskirt of Tianjin, China, using bioassays and biochemical analysis. Populations were chosen to represent different exposure to insecticides： BDG （Beidagang; low exposure）, BD （Baodi; high exposure previously but low exposure now）, and JN （Jinnan; high exposure）. The results showed that the LD50 values of BD and JN populations were 3.95- and 12.02-fold and 3.64- and 10.07- fold higher than that of BDG population in females and males, respectively. The LD50 values in females were higher than those in males. The results of biochemical analysis indicated that the esterase （EST） activities in JN population were higher than those in BD and BDG populations. They showed that when α-NA, α-NB, and α-NA were used as substrates, females＇ EST activities of JN population were 1.11-, 1.30-, and 1.14-fold and 1.39-, 1.59-, and 1.54-fold higher than those of BD and BDG populations, respectively. When α-NA, α-NB, and β-NA were used as substrates, males＇ EST activities of JN population were 1.13-, 1.12-, and 1,00-fold and 1.20-, 1.14-, and 1.07-fold higher than those of BD and BDG populations, respectively. The results also showed that the specific activities of the females were higher than those of the males in the BD and JN populations, whereas the specific activities of the males were higher than those of the females in the BDG population. The results of bioassay were consistent with those of biochemical analysis. Thus, it was inferred that the elevated ESTs activities might play an important role in conferring the differences of susceptibility of O. chinensis to malathion in the three collected populations. Enzyme kinetic studies indicated that the Km and Vmax values were different among the three collected populations and between the females and the males. The observed changes in the kinetic parameters might be explained by differential expression patterns of isozymes so that the insect esterases have different affinities and maximum velocities toward the same substrate.

Comparison of Susceptibilities of M. tuberculosis H37Ra and M. chelonei subsp. Abscessus to Disinfectants

Objective To determine the susceptibilities of M. tuberculosis H37Ra and M. chelonei subsp. absecessus to several frequently-used disinfectants and to evaluate the practicability of surrogating M. tuberculosis by the latter. Methods A suspension quantitative bactericidal test was set up in accordance with Chinese Technique Standard for Disinfection to evaluate the susceptibility of each mycobacteria strain to each selected disinfectant. Killing log value was used as criterion in comparing the susceptibility to disinfectants between the two strains. Results M. chelonei subsp. abscessus was more resistant to chlorine disinfectant than M. tuberculosis while the two strains were similarly resistant to iodophor disinfectant, peracetic acid, alcohol and glutaraldehyde disinfectant. Conclusion M. chelonei subsp. abscessus has the potential to surrogate M. tuberculosis in evaluating mycobactericidal efficacies of disinfectants.

Third-order elastic, piezoelectric, and dielectric constants

The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations among the third-order constants are obtained.Furthermore,the relations among the third-order elastic,piezoelectric,and dielectric constants of the seven crystal systems and isotropic materials are listed in detail.These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials.It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups,while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material.The reason is that some of the point groups are centrally symmetric,and the other point groups are high symmetry.These results provide the foundation to measure these constants,to choose material,and to research nonlinear problems.Moreover,these results are helpful not only for the study of nonlinear elastic and piezoelectric problems,but also for the research on flexoelectric effects and size effects.

Accuracy of the half-power bandwidth method with a third-order correction for estimating damping in multi-DOF systems

A third-order correction was recently suggested to improve the accuracy of the half-power bandwidth method in estimating the damping of single DOF systems.This paper analyzes the accuracy of the half-power bandwidth method with the third-order correction in damping estimation for multi-DOF linear systems.Damping ratios in a two-DOF linear system are estimated using its displacement and acceleration frequency response curves,respectively.A wide range of important parameters that characterize the shape of these response curves are taken into account.Results show that the third-order correction may greatly improve the accuracy of the half-power bandwidth method in estimating damping in a two-DOF system.In spite of this,the half-power bandwidth method may significantly overestimate the damping ratios of two-DOF systems in some cases.

Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems

This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non- conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conformal invariance of the system are presented. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition that conformal invaxiance of the system would have Lie symmetry under single-parameter infinitesimal transformations is obtained. The corresponding conserved quantity of conformal invariance is derived with the aid of a structure equation. Lastly, an example is given to illustrate the application of the results.

Oscillation Criteria for Third-order NonlinearNeutral Dynamic Equations on Time Scales

Many practical problems, such as those from electronic engineering, mechanicalengineering, ecological engineering, aerospace engineering and so on, need to bedescribed by dynamic equations on time scales, so it is important in theory andpractical significance to study these equations. In this paper, the oscillation andasymptotic behavior of third-order nonlinear neutral delay dynamic equations ontime scales are studied by using generalized Riccati transformation technique, integralaveraging methods and comparison theorems. The main purpose of this paperis to establish some new oscillation criteria for such dynamic equations. The newKamenev criteria and Philos criteria are given, and an example is considered toillustrate our main results.

Symmetry Reduction of Initial-Value Problems for a Class of Third-order Evolution Equations

Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a Cauchyproblem for a system of ordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry.Complete classification theorems are obtained and some examples are taken to show the main reduction procedure.

On the Existence of Positive Solution for a Nonlinear Third-order Three-point Boundary Value Problem

An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, and is not asymptotic at zero and infinity.

Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.

Triple Positive Solutions for a Third-order Three-point Boundary Value Problem

In this paper,we study the existence of triple positive solutions for the nonlinear third-order three-point boundary value problem ■where η∈[0,1/2) is a constant,by using a fixed-point theorem due to Avery and Peterson,we establish results of triple positive solutions to the boundary value problem,and an example is given to illustrate the importance of result obtained.

Third-Order Stokes Wave Solutions of the Free Surface Capillary- Gravity Wave and the Interfacial Internal Wave

Based on the Stokes wave theory, the capillary-gravity wave and the interfacial internal wave in two-layer constant depth＇s fluid system are investigated. The fluids are assumed to be incompressible, inviscid and irrotational. The third-order Stokes wave solutions are given by using a perturbation method. The results indicate that the third-order solutions depend on the surface tension, the density and the depth of each layer. As expected, the first-order solutions are the linear theoretical results （the small amplitude wave theoretical results）. The second-order and the third-order solutions describe the nonlinear modification and the nonlinear interactions. The nonlinear impact appears not only in the n （n〉~2） times＇ high frequency components, but also in the low frequency components. It is also noted that the wave velocity depends on the wave number, depth, wave amplitude and surface tension.