A Two-Layer Encoding Learning Swarm Optimizer Based on Frequent Itemsets for Sparse Large-Scale Multi-Objective Optimization

Traditional large-scale multi-objective optimization algorithms(LSMOEAs)encounter difficulties when dealing with sparse large-scale multi-objective optimization problems(SLM-OPs)where most decision variables are zero.As a result,many algorithms use a two-layer encoding approach to optimize binary variable Mask and real variable Dec separately.Nevertheless,existing optimizers often focus on locating non-zero variable posi-tions to optimize the binary variables Mask.However,approxi-mating the sparse distribution of real Pareto optimal solutions does not necessarily mean that the objective function is optimized.In data mining,it is common to mine frequent itemsets appear-ing together in a dataset to reveal the correlation between data.Inspired by this,we propose a novel two-layer encoding learning swarm optimizer based on frequent itemsets(TELSO)to address these SLMOPs.TELSO mined the frequent terms of multiple particles with better target values to find mask combinations that can obtain better objective values for fast convergence.Experi-mental results on five real-world problems and eight benchmark sets demonstrate that TELSO outperforms existing state-of-the-art sparse large-scale multi-objective evolutionary algorithms(SLMOEAs)in terms of performance and convergence speed.

Transient responses of double-curved sandwich two-layer shells resting on Kerr's foundations with laminated three-phase polymer/GNP/fiber surface and auxetic honeycomb core subjected to the blast load

This work uses refined first-order shear theory to analyze the free vibration and transient responses of double-curved sandwich two-layer shells made of auxetic honeycomb core and laminated three-phase polymer/GNP/fiber surface subjected to the blast load.Each of the two layers that make up the double-curved shell structure is made up of an auxetic honeycomb core and two laminated sheets of three-phase polymer/GNP/fiber.The exterior is supported by a Kerr elastic foundation with three characteristics.The key innovation of the proposed theory is that the transverse shear stresses are zero at two free surfaces of each layer.In contrast to previous first-order shear deformation theories,no shear correction factor is required.Navier's exact solution was used to treat the double-curved shell problem with a single title boundary,while the finite element technique and an eight-node quadrilateral were used to address the other boundary requirements.To ensure the accuracy of these results,a thorough comparison technique is employed in conjunction with credible statements.The problem model's edge cases allow for this kind of analysis.The study's findings may be used in the post-construction evaluation of military and civil works structures for their ability to sustain explosive loads.In addition,this is also an important basis for the calculation and design of shell structures made of smart materials when subjected to shock waves or explosive loads.

Two-Layer Attention Feature Pyramid Network for Small Object Detection

Effective small object detection is crucial in various applications including urban intelligent transportation and pedestrian detection.However,small objects are difficult to detect accurately because they contain less information.Many current methods,particularly those based on Feature Pyramid Network(FPN),address this challenge by leveraging multi-scale feature fusion.However,existing FPN-based methods often suffer from inadequate feature fusion due to varying resolutions across different layers,leading to suboptimal small object detection.To address this problem,we propose the Two-layerAttention Feature Pyramid Network(TA-FPN),featuring two key modules:the Two-layer Attention Module(TAM)and the Small Object Detail Enhancement Module(SODEM).TAM uses the attention module to make the network more focused on the semantic information of the object and fuse it to the lower layer,so that each layer contains similar semantic information,to alleviate the problem of small object information being submerged due to semantic gaps between different layers.At the same time,SODEM is introduced to strengthen the local features of the object,suppress background noise,enhance the information details of the small object,and fuse the enhanced features to other feature layers to ensure that each layer is rich in small object information,to improve small object detection accuracy.Our extensive experiments on challenging datasets such as Microsoft Common Objects inContext(MSCOCO)and Pattern Analysis Statistical Modelling and Computational Learning,Visual Object Classes(PASCAL VOC)demonstrate the validity of the proposedmethod.Experimental results show a significant improvement in small object detection accuracy compared to state-of-theart detectors.

Two-layer formation-containment fault-tolerant control of fixed-wing UAV swarm for dynamic target tracking

This paper tackles the formation-containment control problem of fixed-wing unmanned aerial vehicle(UAV)swarm with model uncertainties for dynamic target tracking in three-dimensional space in the faulty case of UAVs’actuator and sensor.The fixed-wing UAV swarm under consideration is organized as a“multi-leader-multi-follower”structure,in which only several leaders can obtain the dynamic target information while others only receive the neighbors’information through the communication network.To simultaneously realize the formation,containment,and dynamic target tracking,a two-layer control framework is adopted to decouple the problem into two subproblems:reference trajectory generation and trajectory tracking.In the upper layer,a distributed finite-time estimator(DFTE)is proposed to generate each UAV’s reference trajectory in accordance with the control objective.Subsequently,a distributed composite robust fault-tolerant trajectory tracking controller is developed in the lower layer,where a novel adaptive extended super-twisting(AESTW)algorithm with a finite-time extended state observer(FTESO)is involved in solving the robust trajectory tracking control problem under model uncertainties,actuator,and sensor faults.The proposed controller simultaneously guarantees rapidness and enhances the system’s robustness with fewer chattering effects.Finally,corresponding simulations are carried out to demonstrate the effectiveness and competitiveness of the proposed two-layer fault-tolerant cooperative control scheme.

A Two-Layer Fuzzy Control Strategy for the Participation of Energy Storage Battery Systems in Grid Frequency Regulation

To address the frequency fluctuation problem caused by the power dynamic imbalance between the power system and the loadwhen a large number of newenergy sources are connected to the grid,a two-layer fuzzy control strategy is proposed for the participation of the energy storage battery system in FM.Firstly,considering the coordination of FM units responding to automatic power generation control commands,a comprehensive allocation strategy of two signals under automatic power generation control commands is proposed to give full play to the advantages of two FM signals while enabling better coordination of two FM units responding to FM commands;secondly,based on the grid FM demand and battery FM capability,a double-layer fuzzy control strategy is proposed for FM units responding to automatic power generation control commands in a coordinated manner under dual-signal allocation mode to precisely allocate the power output depth of FM units,which can control the fluctuation of frequency deviation within a smaller range at a faster speed while maintaining the battery charge state;finally,the proposed Finally,the proposed control strategy is simulated and verified inMatlab/Simulink.The results show that the proposed control strategy can control the frequency deviation within a smaller range in a shorter time,better stabilize the fluctuation of the battery charge level,and improve the utilization of the FM unit.

Conditioned medium from human dental pulp stem cells treats spinal cord injury by inhibiting microglial pyroptosis

Human dental pulp stem cell transplantation has been shown to be an effective therapeutic strategy for spinal cord injury.However,whether the human dental pulp stem cell secretome can contribute to functional recovery after spinal cord injury remains unclear.In the present study,we established a rat model of spinal cord injury based on impact injury from a dropped weight and then intraperitoneally injected the rats with conditioned medium from human dental pulp stem cells.We found that the conditioned medium effectively promoted the recovery of sensory and motor functions in rats with spinal cord injury,decreased expression of the microglial pyroptosis markers NLRP3,GSDMD,caspase-1,and interleukin-1β,promoted axonal and myelin regeneration,and inhibited the formation of glial scars.In addition,in a lipopolysaccharide-induced BV2 microglia model,conditioned medium from human dental pulp stem cells protected cells from pyroptosis by inhibiting the NLRP3/caspase-1/interleukin-1βpathway.These results indicate that conditioned medium from human dental pulp stem cells can reduce microglial pyroptosis by inhibiting the NLRP3/caspase-1/interleukin-1βpathway,thereby promoting the recovery of neurological function after spinal cord injury.Therefore,conditioned medium from human dental pulp stem cells may become an alternative therapy for spinal cord injury.

Characteristic analysis of scattering field in two-layer media by Green's function

The problem of three-dimensional(3D) acoustic scattering in a complex medium has aroused considerable interest of researchers for many years. An ultrasonic scattered field calculating technique is proposed to study the scattering echo from strongly scattered materials in a two-layer medium in this work. Firstly, with the high frequency stationary phase method,the Green's function of two-layer fluid media is derived. And then based on the idea of integral equation discretization,the Green's function method is extended to two-layer fluid media to derive the scattering field expression of defects in a complex medium. With this method, the scattering field of 3D defect in a two-layer medium is calculated and the characteristics of received echoes are studied. The results show that this method is able to solve the scattering P wave field of 3D defect with arbitrary shape at any scattering intensity in two-layer media. Considering the circumstance of waterimmersion ultrasonic non-destructive test(NDT), the scattering sound field characteristics of different types of defects are analyzed by simulation, which will help to optimize the detection scheme and corresponding imaging method in practice so as to improve the detection quality.

Cooperative Caching Strategy Based on Two-Layer Caching Model for Remote Sensing Satellite Networks

In Information Centric Networking(ICN)where content is the object of exchange,in-network caching is a unique functional feature with the ability to handle data storage and distribution in remote sensing satellite networks.Setting up cache space at any node enables users to access data nearby,thus relieving the processing pressure on the servers.However,the existing caching strategies still suffer from the lack of global planning of cache contents and low utilization of cache resources due to the lack of fine-grained division of cache contents.To address the issues mentioned,a cooperative caching strategy(CSTL)for remote sensing satellite networks based on a two-layer caching model is proposed.The two-layer caching model is constructed by setting up separate cache spaces in the satellite network and the ground station.Probabilistic caching of popular contents in the region at the ground station to reduce the access delay of users.A content classification method based on hierarchical division is proposed in the satellite network,and differential probabilistic caching is employed for different levels of content.The cached content is also dynamically adjusted by analyzing the subsequent changes in the popularity of the cached content.In the two-layer caching model,ground stations and satellite networks collaboratively cache to achieve global planning of cache contents,rationalize the utilization of cache resources,and reduce the propagation delay of remote sensing data.Simulation results show that the CSTL strategy not only has a high cache hit ratio compared with other caching strategies but also effectively reduces user request delay and server load,which satisfies the timeliness requirement of remote sensing data transmission.

Vibration of a Two-Layer“Metal+PZT”Plate Contacting with Viscous Fluid

The present work investigates the mechanically forced vibration of the hydro-elasto-piezoelectric system consisting of a two-layer plate“elastic+PZT”,a compressible viscous fluid,and a rigid wall.It is assumed that the PZT(piezoelectric)layer of the plate is in contact with the fluid and time-harmonic linear forces act on the free surface of the elastic-metallic layer.This study is valuable because it considers for the first time the mechanical vibration of the metal+piezoelectric bilayer plate in contact with a fluid.It is also the first time that the influence of the volumetric concentration of the constituents on the vibration of the hydro-elasto-piezoelectric system is studied.Another value of the present work is the use of the exact equations and relations of elasto-electrodynamics for elastic and piezoelectric materials to describe the motion of the plate layers within the framework of the piecewise homogeneous body model and the use of the linearized Navier-Stokes equations to describe the flow of the compressible viscous fluid.The plane-strain state in the plate and the plane flow in the fluid take place.For the solution of the corresponding boundary-value problem,the Fourier transform is used with respect to the spatial coordinate on the axis along the laying direction of the plate.The analytical expressions of the Fourier transform of all the sought values of each component of the system are determined.The origins of the searched values are determined numerically,after which numerical results on the stress on the fluid and plate interface planes are presented and discussed.These results are obtained for the case where PZT-2 is chosen as the piezoelectric material,steel and aluminum as the elastic metal materials,and Glycerin as the fluid.Analysis of these results allows conclusions to be drawn about the character of the problem parameters on the frequency response of the interfacial stress.In particular,it was found that after a certain value of the vibration frequency,the presence of the metal layer in the two-layer plate led to an increase in the absolute values of the above interfacial stress.

Preparation of FeCoNi medium entropy alloy from Fe^(3+)-Co^(2+)-Ni^(2+)solution system

In recent years,medium entropy alloys have become a research hotspot due to their excellent physical and chemical performances.By controlling reasonable elemental composition and processing parameters,the medium entropy alloys can exhibit similar properties to high entropy alloys and have lower costs.In this paper,a FeCoNi medium entropy alloy precursor was prepared via sol-gel and coprecipitation methods,respectively,and FeCoNi medium entropy alloys were prepared by carbothermal and hydrogen reduction.The phases and magnetic properties of FeCoNi medium entropy alloy were investigated.Results showed that FeCoNi medium entropy alloy was produced by carbothermal and hydrogen reduction at 1500℃.Some carbon was detected in the FeCoNi medium entropy alloy prepared by carbothermal reduction.The alloy prepared by hydrogen reduction was uniform and showed a relatively high purity.Moreover,the hydrogen reduction product exhibited better saturation magnetization and lower coercivity.

A Formulation of the Porous Medium Equation with Time-Dependent Porosity: A Priori Estimates and Regularity Results

We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to depend very little of) the time variable t. In this work, we want to study the case where it does depend on t(and xas well). For this purpose, we make a change of unknown function V=ϕSin order to obtain a saturation-like (advection-diffusion) equation. A priori estimates and regularity results are established for the new equation based in part on what is known from the saturation equation, when ϕis independent of the time t. These results are then extended to the full saturation equation with time-dependent porosity ϕ=ϕ(x,t). In this analysis, we make explicitly the dependence of the various constants in the estimates on the porosity ϕby the introduced transport vector w, through the change of unknown function. Also we do not assume zero-flux boundary, but we carry the analysis for the case Q≡0.

Enhancing Erectile Function and Alleviating Andropause Symptoms: Clinical Efficacy of a Human Stem Cell Conditioned Medium Cream

Erectile dysfunction (ED) is increasingly prevalent in Japan, exceeding 30%, and increasing with age. Unhealthy lifestyle habits, obesity, insufficient exercise, and smoking have been implicated in its pathogenesis, along with endothelial dysfunction of the corpora cavernosa and impaired blood flow to the penis considered underlying factors. However, the current treatments are limited to Phosphodiesterase-5 (PDE5) inhibitors. ED is the primary symptom of andropathy. This study reports the clinical efficacy of human stem cell-conditioned medium cream for ED treatment. Ten men without underlying diseases suspected of andropause with ED (mean age 43.2 ± 4.4 y, Hb 15.2 ± 0.6 gm/dL, AST/ALT 30.2/37.9 ± 12.4/14.0, eGFR 82.7 ± 12.4 mL/min/1.73 m2) were targeted. The cream was applied twice daily to the genital and scrotal areas. The erectile hardness score (EHS), International Index of Erectile Function-5 (IIEF-5), and Aging Male Symptoms (AMS) scale were used to evaluate the participants before and 30 days after use, and the results were compared using paired t-tests. The post-use qualitative opinions were collected through interviews. Significant improvements were observed compared to baseline in the IIEF-5 (11.8 ± 4.6→17.2 ± 5.1, P < 0.001), and AMS (46.3 ± 6.7→37.6 ± 5.3, P < 0.001) scores post cream use. EHS did not show a statistically significant difference, but a trend towards improvement was observed. Qualitative feedback included increased morning erection, improved maintenance of erection during intercourse, and reduced post work fatigue. Human stem cell-conditioned medium contains endothelial growth factors that potentially contribute to the improvement of ED and andropause by enhancing corporal endothelial function. Future studies should include control groups to further investigate the efficacy of these treatments.

Review on the plastic instability of medium -Mn steels for identifying the formation mechanisms of Lüders and Portevin -Le Chatelier bands

Plastic instability,including both the discontinuous yielding and stress serrations,has been frequently observed during the tensile deformation of medium-Mn steels(MMnS)and has been intensively studied in recent years.Unfortunately,research results are controversial,and no consensus has been achieved regarding the topic.Here,we first summarize all the possible factors that affect the yielding and flow stress serrations in MMnS,including the morphology and stability of austenite,the feature of the phase interface,and the deformation parameters.Then,we propose a universal mechanism to explain the conflicting experimental results.We conclude that the discontinuous yielding can be attributed to the lack of mobile dislocation before deformation and the rapid dislocation multiplication at the beginning of plastic deformation.Meanwhile,the results show that the stress serrations are formed due to the pinning and depinning between dislocations and interstitial atoms in austenite.Strain-induced martensitic transformation,influenced by the mechanical stability of austenite grain and deformation parameters,should not be the intrinsic cause of plastic instability.However,it can intensify or weaken the discontinuous yielding and the stress serrations by affecting the mobility and density of dislocations,as well as the interaction between the interstitial atoms and dislocations in austenite grains.

A Dual-Cluster-Head Based Medium Access Control for Large-Scale UAV Ad-Hoc Networks

Unmanned Aerial Vehicle(UAV)ad hoc network has achieved significant growth for its flexibility,extensibility,and high deployability in recent years.The application of clustering scheme for UAV ad hoc network is imperative to enhance the performance of throughput and energy efficiency.In conventional clustering scheme,a single cluster head(CH)is always assigned in each cluster.However,this method has some weaknesses such as overload and premature death of CH when the number of UAVs increased.In order to solve this problem,we propose a dual-cluster-head based medium access control(DCHMAC)scheme for large-scale UAV networks.In DCHMAC,two CHs are elected to manage resource allocation and data forwarding cooperatively.Specifically,two CHs work on different channels.One of CH is used for intra-cluster communication and the other one is for inter-cluster communication.A Markov chain model is developed to analyse the throughput of the network.Simulation result shows that compared with FM-MAC(flying ad hoc networks multi-channel MAC,FM-MAC),DCHMAC improves the throughput by approximately 20%~50%and prolongs the network lifetime by approximately 40%.

Heat-Generating Effects Involving Multiple Nanofluids in a Hybrid Convective Boundary Layer Flow on the Sloping Plate in a Porous Medium

The hybrid convective boundary layer circulation involving multiple nanofluids via a medium with pores is approaching a sloping plate. An investigation regarding the heat-generating effects upon the examined nanofluid flows has been carried out through computational analysis. A mathematical framework employing governing differential equations that are partial has been implemented to produce an ensemble of ordinary differential equations, which happen to be nonlinear that incorporate nanofluid flows by utilizing acceptable transformations. Through the combination of the Nachtsheim-Swigert shooting method and the Runge-Kutta method, the group of resulting non-dimensionalized equations is solved computationally. In a few special, confined cases, the corresponding numeric output is thereafter satisfactorily matched with the existing available research. The consequences of heat generation regarding local skin friction coefficient and rate of heat in conjunction with mass transfer have been investigated, evaluated, and reported on the basis of multiple nanofluid flows.

Micromechanism and mathematical model of stress sensitivity in tight reservoirs of binary granular medium

Research on reservoir rock stress sensitivity has traditionally focused on unary granular structures,neglecting the binary nature of real reservoirs,especially tight reservoirs.Understanding the stresssensitive behavior and mathematical characterization of binary granular media remains a challenging task.In this study,we conducted online-NMR experiments to investigate the permeability and porosity evolution as well as stress-sensitive control mechanisms in tight sandy conglomerate samples.The results revealed stress sensitivity coefficients between 0.042 and 0.098 and permeability damage rates ranging from 65.6%to 90.9%,with an average pore compression coefficient of 0.0168—0.0208 MPa 1.Pore-scale compression occurred in three stages:filling,compression,and compaction,with matrix pores playing a dominant role in pore compression.The stress sensitivity of binary granular media was found to be influenced by the support structure and particle properties.High stress sensitivity was associated with small fine particle size,high fines content,high uniformity coefficient of particle size,high plastic deformation,and low Young's modulus.Matrix-supported samples exhibited a high irreversible permeability damage rate(average=74.2%)and stress sensitivity coefficients(average=0.089),with pore spaces more slit-like.In contrast,grain-supported samples showed low stress sensitivity coefficients(average=0.021)at high stress stages.Based on the experiments,we developed a mathematical model for stress sensitivity in binary granular media,considering binary granular properties and nested interactions using Hertz contact deformation and Poiseuille theory.By describing the change in activity content of fines under stress,we characterized the non-stationary state of compressive deformation in the binary granular structure and classified the reservoir into three categories.The model was applied for production prediction using actual data from the Mahu reservoir in China,showing that the energy retention rates of support-dominated,fill-dominated,and matrix-controlled reservoirs should be higher than 70.1%,88%,and 90.2%,respectively.

Assessing Factors Influencing Solar Energy Adoption among Small and Medium Enterprises in Mzuzu City, Malawi

One of the many renewable energy sources that offer advantages is solar energy, which also lowers energy prices and promotes environmental sustainability and energy security. Despite these advantages, various barriers, such as installation costs, have prevented small and medium-sized enterprises from investigating this invention. Malawi has a significant energy shortfall such that most businesses have been hindered from their profit maximization goals. The “Photovoltaic systems” (PV) that transform sunlight into electricity are the subject of this study. This type of solar energy system is situated on the building’s roof and generally produces electricity for businesses and even homes. Solar energy offers a great impact to small and medium enterprises in Mzuzu city with a cost-effective and dependable alternative to energy that has the potential to change the game. Therefore the aim of the study was to identify factors that encourage the adoption of solar energy among small medium enterprises in the city of Mzuzu city. And to identify some of barriers faced when adopting solar energy among small and medium enterprises in the city of Mzuzu. The research approach employed in the study was a survey. A survey is a type of research methodology in which primary data is gathered from a sample using a questionnaire. When information is to be gathered from a wider sample, a survey is employed. A bigger sample size was needed in this study in order to facilitate hypothesis testing. It is advised to apply a logical approach while using the survey. The survey utilized a five-point Likert scale. The study used convenience sampling to select study participants. The sample size in this study was determined using Cochran’s sample size formula. Statistical Package for Social Sciences (SPSS) and Microsoft Excel were used for statistical analysis. About 97.2% of the participants were aware of solar as a source of energy compared to 2.8 % who were unaware. The majority of participants use solar energy for lighting only, seconded by those who use electricity. The least number of participants use solar energy for cooling only. The majority of participants 21.5% indicated partnership and collaboration as the most motivating factor for the adoption of solar energy. This was followed by technical expertise 19.1 % the least number of participants 10.8% expressed that policy and regulatory frameworks were associated with the adoption of solar energy. This study found that there are no statistically significant factors influencing barriers to the adoption of solar energy. The price of solar energy adoption was identified as the least factor associated with the acceptance or rejection of solar energy. Nonetheless, the reasons given by the homes that had embraced solar technology aligned with the findings of other studies. This survey also found that although the public was aware of solar energy, and technology, there were still a number of factors that mattered, especially for non-adopters.

Effect of dietary supplementation with discardednutrient medium of Cordyceps militaris on layingperformance and diversity of intestinal flora in laying hens

The aim of the experiment was to explore the feasibility of discarded nutrient medium of Cordyceps militaris as feed in the production of laying hens. 100 g/kg, 200 g/kg, 300 g/kg of discarded nutrient medium of Cordyceps militaris were added to the basal diet of laying hens. The results showed that the optimal addition of discarded nutrient medium of Cordyceps militaris in the diet of laying hens was 10%. According to the results of measuring the conventional indicators of eggs, the weight of eggs produced by laying hens fed with discarded nutrient medium of Cordyceps militaris was higher than that of laying hens fed with ordinary laying hens. The content of interleukin-1(IL-1) in the experimental group was significantly higher than that in the control group, and the concentration of IL-1 increased by 141.5 pg/mL, which indicated that the application of discarded nutrient medium of Cordyceps militaris effectively improved the immunity of laying hens. The high-throughput analysis of the intestinal contents of the two groups of laying hens showed that the microbial population abundance of the intestinal tract of the experimental group was greater than that of control group, and the application of discarded nutrient medium of Cordyceps militaris increased the diversity of bacteria in the intestinal tract of laying hens. In addition, the sensitivity of some pathogenic bacteria in the intestinal tract of chickens to drugs was also increased, thereby reducing the use of antibiotics. The secondary utilization of discarded nutrient medium of Cordyceps militaris has great development and utilization prospects, which provided a scientific reference and basic theoretical basis for the development of discarded nutrient medium of Cordyceps militaris as feed in the production of laying hens.

Electromagnetic Scattering in a Two-layered Medium

The object of this paper is to investigate the three-dimensional electro- magnetic scattering problems in a two-layered background medium. These problems have an important application in today＇s technology, such as to detect objects that are buried in soil. Here, we model both the exterior impedance problem and the inhomogeneous medium problem in R3. We establish uniqueness and existence for the solution of the two scattering problems, respectively.

THE INTERIOR TRANSMISSION EIGENVALUE PROBLEM FOR AN ANISOTROPIC MEDIUM BY A PARTIALLY COATED BOUNDARY

We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and possesses different transmission conditions.Using the variational method,we obtain the well posedness of the interior transmission problem,which plays an important role in the proof of the discreteness of eigenvalues.Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n≡1,where a fourth order differential operator is applied.In the case of n■1,we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.