Real eigenvalues determined by recursion of eigenstates

Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the system is not Hermitian,the eigenvalues can still be purely real under specific symmetry.Hence,great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian systems.In this work,from a distinct perspective,we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of eigenstates.Consequently,our findings provide another path to extract the real energy spectrum of non-Hermitian systems,which guarantees the conservation of probability and stimulates future experimental observations.

Efficient method to calculate the eigenvalues of the Zakharov–Shabat system

A numerical method is proposed to calculate the eigenvalues of the Zakharov–Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential function for the Zakharov–Shabat eigenvalue problem. The mapping can distribute Chebyshev nodes very well considering the gradient for the potential function. Using Chebyshev polynomials, tanh(ax) mapping, and Chebyshev nodes, the Zakharov–Shabat eigenvalue problem is transformed into a matrix eigenvalue problem. This method has good convergence for the Satsuma–Yajima potential and the convergence rate is faster than the Fourier collocation method. This method is not only suitable for simple potential functions but also converges quickly for a complex Y-shape potential. It can also be further extended to other linear eigenvalue problems.

On the eigenvalues and eigendisplacement of the critical mode in horizontally layered media

Wave propagation in horizontally layered media is a classical problem in seismic-wave theory.In semi-infinite space,a nondispersive Rayleigh wave mode exists,and the eigendisplacement decays exponentially with depth.In a layered model with increasing layer velocity,the phase velocity of the Rayleigh wave varies between the S-wave velocity of the bottom half-space and that of the classical Rayleigh wave propagated in a supposed half-space formed by the parameters of the top layer.If the phase velocity is the same as the P-or S-wave velocity of the layer,which is called the critical mode or critical phase velocity of surface waves,the general solution of the wave equation is not a homogeneous(expressed by trigonometric functions)or inhomogeneous(expressed by exponential functions)plane wave,but one whose amplitude changes linearly with depth(expressed by a linear function).Theories based on a general solution containing only trigonometric or exponential functions do not apply to the critical mode,owing to the singularity at the critical phase velocity.In this study,based on the classical framework of generalized reflection and transmission coefficients,the propagation of surface waves in horizontally layered media was studied by introducing a solution for the linear function at the critical phase velocity.Therefore,the eigenvalues and eigenfunctions of the critical mode can be calculated by solving a singular problem.The eigendisplacement characteristics associated with the critical phase velocity were investigated for different layered models.In contrast to the normal mode,the eigendisplacement associated with the critical phase velocity exhibits different characteristics.If the phase velocity is equal to the S-wave velocity in the bottom half-space,the eigendisplacement remains constant with increasing depth.

Comparative Study on the Policy of Multiplicity Issues in Clinical Trials at Home and Abroad

Objective To study the content of China’s guiding principles on multiplicity issues in clinical trials,and to provide reference for the revision of China’s relevant guiding principles.Methods Based on ICH E9,the similarities and differences of the guiding principles of US Food and Drug Administration(FDA),European Medicines Agency(EMA),and National Medical Products Administration(NMPA)on the multiplicity issues in clinical trials were compared one by one.Results and Conclusion In general,NMPA guidelines are based on ICH E9,but in detail,the guidelines of FDA and EMA focus differently on the multiplicity issues.Therefore,NMPA guidelines need to be detailed and comprehensive.NMPA guidelines can be refined by referring to foreign guidelines to improve the practical guiding significance for clinical research and promote the level of domestic clinical trials in line with international standards.

Petrochemical eigenvalues and diagrams for the identification of metamorphic rocks'protolith,taking the host rocks of Dashuigou tellurium deposit in China as an example

The Dashuigou tellurium deposit is the world’s only known independent tellurium deposit.By restoring metamorphic rocks’protolith,we seek to understand not only the development and evolution trajectory of the region but also the origin of the relevant deposits.While there are many ways to restore metamorphic rocks’protolith,we take the host metamorphic rocks of Dashuigou tellurium deposit and leverage various petrochemical eigenvalues and related diagrams previously proposed to reveal the deposit’s host metamorphic rocks’protolith.The petrochemical eigenvalues include molecular number,Niggli’s value,REE parity ratio,CaO/Al_(2)O_(3)ratio,Fe^(3+) /(Fe^(3+) -+Fe^(2+) )ratio,chondrite-normalized REE value,logarithmic REE value,various REE eigenvalues including scandium,Eu/Sm ratio,total REE amount,light and heavy REEs,δEu,Eu anomaly,Sm/Nd ratio,and silicon isotope δ^(30) SiNBS-29‰,etc.The petrochemical plots include ACMs,100 mg-c-(al+alk),SiO_(2)-(Na_(2)O+K_(2)O),(al+fm)-(c+alk)versus Si,FeO+Fe_(2)O^(3+) TiO)-Al_(2)O_(3)-MgO,c-mg,Al_(2)O_(3)-(Na_(2)O+K_(2)O),chondrite-normalized REE model,La/Yb-REE,and Sm/Nd ratio,etc.On the basis of these comprehensive analyses,the following conclusions are drawn,starting from the many mantle-derived types of basalt developed in the study area of different geological ages,combined with the previously published research results on the deposit s fluid inclusions and sulfur and lead isotopes.The deposit is formed by mantle degassing in the form of a mantle plume in the late Yanshanian orogeny.The degassed fluids are rich in nano-sc ale substances including Fe,Te,S,As,Bi,Au,Se,H_(2),CO_(2),N_(2),H_(2)O,and CH_(4),which are enriched by nano-effect,and then rise to a certain part of the crust in the form of mantle plume along the lithospheric fault to form the deposit.The ultimate power for tellurium mineralization was from H_(2)flow with high energy,which was produced through radiation from the melted iron of the Earth’s outer core.The H,flow results in the Earth’s degassing,as well as the mantle and crust’s uplift.

GDS-MIMO-OFDM雷达通信一体化波形设计

针对正交频分复用(OFDM)雷达通信一体化波形存在的通信速率较低、自相关旁瓣较高的问题,提出了一种基于Gold码扩频的多输入多输出-正交频分复用(MIMO-OFDM)雷达通信一体化波形。将MIMO-OFDM与扩频序列相结合,利用相关性较好的Gold码对通信信息进行扩频,再与OFDM脉冲符号进行调制,进而设计出一种既能提高通信速率又能改善雷达性能的一体化波形。仿真实验证明,较相同仿真条件下的Gold-OFDM、脉冲压缩-正交频分复用(PC-OFDM)一体化波形而言,所设计的一体化波形的通信速率能够倍数提高且可以在不影响通信性能的前提下降低信号模糊函数的旁瓣,从而改善一体化系统的雷达性能。

基于NOMA-OFDM的雷达通信一体化波形设计

针对基于正交频分复用的雷达通信一体化波形设计中,通信信息的随机性会影响雷达性能以及过高峰均包络比(PAPR)可能导致信号在射频端出现严重失真的问题,文中提出了利用非正交多址将雷达信号与通信信号在功率域中分开,以降低通信信息随机性对雷达性能的影响,并利用主动星座图扩展(ACE)对叠加信号进行PAPR抑制的波形设计方法。首先,分析了传统功率分配原则导致叠加星座出现混叠的原因,并给出在不同调制阶数的最佳功率分配;其次,从理论上分析了ACE技术对叠加信号进行PAPR抑制的可行性;最后,仿真结果表明,在不同调制方式和不同信噪比下,当功率分配最佳时能同时达成雷达信号高检测率和通信符号最低误码率。ACE技术的使用同时保证了优良的雷达性能和通信端的低误码率,对叠加信号的PAPR有较好的抑制效果。

A Review on Vibration Control of Multiple Cylinders Subjected to FlowInduced Vibrations

The fatigue damage caused by flow-induced vibration(FIV)is one of the major concerns for multiple cylindrical structures in many engineering applications.The FIV suppression is of great importance for the security of many cylindrical structures.Many active and passive control methods have been employed for the vibration suppression of an isolated cylinder undergoing vortex-induced vibrations(VIV).The FIV suppression methods are mainly extended to the multiple cylinders from the vibration control of the isolated cylinder.Due to the mutual interference between the multiple cylinders,the FIV mechanism is more complex than the VIV mechanism,which makes a great challenge for the FIV suppression.Some efforts have been devoted to vibration suppression of multiple cylinder systems undergoing FIV over the past two decades.The control methods,such as helical strakes,splitter plates,control rods and flexible sheets,are not always effective,depending on many influence factors,such as the spacing ratio,the arrangement geometrical shape,the flow velocity and the parameters of the vibration control devices.The FIV response,hydrodynamic features and wake patterns of the multiple cylinders equipped with vibration control devices are reviewed and summarized.The FIV suppression efficiency of the vibration control methods are analyzed and compared considering different influence factors.Further research on the FIV suppression of multiple cylinders is suggested to provide insight for the development of FIV control methods and promote engineering applications of FIV control methods.

LARGE DEVIATIONS FOR TOP EIGENVALUES OFβ-JACOBI ENSEMBLES AT SCALING TEMPERATURES

Letλ=(λ_(1),…,λ_(n))beβ-Jacobi ensembles with parameters p_(1),p_(2),n andβ,withβvarying with n.Set■.Suppose that■and 0≤σγ<1.We offer the large deviation for p_(1)+p_(2)/p_(1)■λ_(i)whenγ>0 via the large deviation of the corresponding empirical measure and via a direct estimate,respectively,whenγ=0.

Estimates on the eigenvalues of complex nonlocal Sturm-Liouville problems

The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems.The bounds of the real and imaginary parts of eigenvalues for the nonlocal Sturm-Liouville differential equation involving complex nonlocal potential terms associated with nonlocal boundary conditions are obtained in terms of the integrable conditions of coefficients and the real part of the eigenvalues.

Cycle Multiplicity of Total Graph of Complete Bipartite Graph

Cycle multiplicity of a graph G is the maximum number of edge disjoint cycles in G. In this paper, we determine the cycle multiplicity of and then obtain the formula of cycle multiplicity of total graph of complete bipartite graph, this generalizes the result for, which is given by M.M. Akbar Ali in [1].

High Permeability in Broadband of Co-sputtered [Fe-Fe_(20)Ni_(80)/Cr]_(n) Multilayer Films

To achieve high microwave permeability in wide-band for the micron-thick magnetic films,[Fe-Fe_(20)Ni_(80)/Cr]_(n) multilayer structure was proposed by co-sputtering Fe and FeNi to form the magnetic layers and Cr to form the interlayers.The multilayer structure contributes to the high permeability by reducing the coercivity and diminishing out-of-plane magnetization.The maximum imaginary permeability of[Fe-Fe_(20)Ni_(80)/Cr]_(n) multilayer film reaches a large value of 800 at 0.52 GHz even though its overall thickness exceeds 1μm.Besides,the magnetic resonance frequency of the multilayer film can be modulated from 0.52 to 1.35 GHz by adjusting the sputtering power of Fe from 0 to 86 W,and its bandwidth for μ’’>200(Δf) is as large as 2.0 GHz.The desirable broad Δf of magnetic permeability,which can be well fitted by the Landau-Lifshitz-Gilbert equations,is due to dual magnetic resonances originated from double magnetic phases of Fe and FeNi that are of different saturation magnetization.The micron-thick multilayer films with high permeability in extended waveband are promising candidate for electromagnetic noise suppression application.

Biomarkers for neuromyelitis optica:a visual analysis of emerging research trends

Neuromyelitis optica is an inflammatory demyelinating disease of the central nervous system that differs from multiple sclerosis.Over the past 20 years,the search for biomarke rs for neuromyelitis optica has been ongoing.Here,we used a bibliometric approach to analyze the main research focus in the field of biomarkers for neuromyelitis optica.Research in this area is consistently increasing,with China and the United States leading the way on the number of studies conducted.The Mayo Clinic is a highly reputable institution in the United States,and was identified as the most authoritative institution in this field.Furthermore,Professor Wingerchuk from the Mayo Clinic was the most authoritative expe rt in this field.Keyword analysis revealed that the terms "neuro myelitis optica"(261 times), "multiple sclerosis"(220 times), "neuromyelitis optica spectrum disorder"(132 times), "aquaporin4"(99 times),and "optical neuritis"(87 times) were the most frequently used keywords in literature related to this field.Comprehensive analysis of the classical literature showed that the majority of publications provide conclusive research evidence supporting the use of aquaporin-4-IgG and neuromyelitis optica-IgG to effectively diagnose and differentiate neuromyelitis optica from multiple sclerosis.Furthermore,aquaporin-4-IgG has emerged as a highly specific diagnostic biomarker for neuromyelitis optica spectrum disorder.Myelin oligodendrocyte glycoprotein-IgG is a diagnostic biomarke r for myelin oligodendrocyte glycoprotein antibody-associated disease.Recent biomarkers for neuromyelitis optica in clude cerebrospinal fluid immunological biomarkers such as glial fibrillary acidic protein,serum astrocyte damage biomarkers like FAM19A5,serum albumin,and gammaaminobutyric acid.The latest prospective clinical trials are exploring the potential of these biomarkers.Preliminary results indicate that glial fibrillary acidic protein is emerging as a promising candidate biomarker for neuromyelitis optica spectrum disorder.The ultimate goal of future research is to identify non-invasive biomarkers with high sensitivity,specificity,and safety for the accurate diagnosis of neuro myelitis optica.

THE EXISTENCE AND MULTIPLICITY OF k-CONVEX SOLUTIONS FOR A COUPLED k-HESSIAN SYSTEM

In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are continuous and nonnegative functions.By introducing some new growth conditions on the nonlinearities f_(1) and f_(2),which are more flexible than the existing conditions for the k-Hessian systems(equations),several new existence and multiplicity results for k-convex solutions for this kind of problem are obtained.

混合NOMA/OFDMA可见光通信系统资源分配算法

为了进一步降低混合非正交多址/正交频分复用多址(NOMA/OFDMA)技术的多用户多小区可见光通信系统的误码率,提出了一种功率和子载波的联合分配算法。该算法以最小化系统误符号率为优化目标,实现了子小区间载波和用户功率的联合最优分配。首先,理论推导出系统的误符号率表达式;然后,使用Matlab软件进行仿真,模拟可见光通信系统模型,并借助遗传算法得到最优的分配结果;最后,将该算法与现有的算法进行了对比。仿真结果表明,所提算法的误符号率性能更优。

Promising use of metformin in treating neurological disorders:biomarker-guided therapies

Neurological disorders are a diverse group of conditions that affect the nervous system and include neurodegenerative diseases(Alzheimer’s disease,multiple sclerosis,Parkinson’s disease,Huntington’s disease),cerebrovascular conditions(stroke),and neurodevelopmental disorders(autism spectrum disorder).Although they affect millions of individuals around the world,only a limited number of effective treatment options are available today.Since most neurological disorders express mitochondria-related metabolic perturbations,metformin,a biguanide type II antidiabetic drug,has attracted a lot of attention to be repurposed to treat neurological disorders by correcting their perturbed energy metabolism.However,controversial research emerges regarding the beneficial/detrimental effects of metformin on these neurological disorders.Given that most neurological disorders have complex etiology in their pathophysiology and are influenced by various risk factors such as aging,lifestyle,genetics,and environment,it is important to identify perturbed molecular functions that can be targeted by metformin in these neurological disorders.These molecules can then be used as biomarkers to stratify subpopulations of patients who show distinct molecular/pathological properties and can respond to metformin treatment,ultimately developing targeted therapy.In this review,we will discuss mitochondria-related metabolic perturbations and impaired molecular pathways in these neurological disorders and how these can be used as biomarkers to guide metformin-responsive treatment for the targeted therapy to treat neurological disorders.

In situ formation of multiple catalysts for enhancing the hydrogen storage of MgH_(2) by adding porous Ni_(3)ZnC_(0.7)/Ni loaded carbon nanotubes microspheres

MgH_(2) is considered one of the most promising hydrogen storage materials because of its safety,high efficiency,high hydrogen storage quantity and low cost characteristics.But some shortcomings are still existed:high operating temperature and poor hydrogen absorption dynamics,which limit its application.Porous Ni_(3)ZnC_(0.7)/Ni loaded carbon nanotubes microspheres(NZC/Ni@CNT)is prepared by facile filtration and calcination method.Then the different amount of NZC/Ni@CNT(2.5,5.0 and 7.5 wt%)is added to the MgH_(2) by ball milling.Among the three samples with different amount of NZC/Ni@CNT(2.5,5.0 and 7.5 wt%),the MgH_(2)-5 wt%NZC/Ni@CNT composite exhibits the best hydrogen storage performances.After testing,the MgH_(2)-5 wt%NZC/Ni@CNT begins to release hydrogen at around 110℃ and hydrogen absorption capacity reaches 2.34 wt%H_(2) at 80℃ within 60 min.Moreover,the composite can release about 5.36 wt%H_(2) at 300℃.In addition,hydrogen absorption and desorption activation energies of the MgH_(2)-5 wt%NZC/Ni@CNT composite are reduced to 37.28 and 84.22 KJ/mol H_(2),respectively.The in situ generated Mg_(2)NiH_(4)/Mg_(2)Ni can serve as a"hydrogen pump"that plays the main role in providing more activation sites and hydrogen diffusion channels which promotes H_(2) dissociation during hydrogen absorption process.In addition,the evenly dispersed Zn and MgZn2 in Mg and MgH_(2) could provide sites for Mg/MgH_(2) nucleation and hydrogen diffusion channel.This attempt clearly proved that the bimetallic carbide Ni_(3)ZnC_(0.7) is a effective additive for the hydrogen storage performances modification of MgH_(2),and the facile synthesis of the Ni_(3)ZnC_(0.7)/Ni@CNT can provide directions of better designing high performance carbide catalysts for improving MgH_(2).

Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems

This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.

Trace formula of the integro-differential operator on a quantum graph

In this paper we study the eigenvalue problem for integro-differential operators on a lasso graph.The trace formula of the operator is established by applying the residual technique in complex analysis.

Modified multiple-component scattering power decomposition for PolSAR data based on eigenspace of coherency matrix

A modified multiple-component scattering power decomposition for analyzing polarimetric synthetic aperture radar(PolSAR)data is proposed.The modified decomposition involves two distinct steps.Firstly,ei⁃genvectors of the coherency matrix are used to modify the scattering models.Secondly,the entropy and anisotro⁃py of targets are used to improve the volume scattering power.With the guarantee of high double-bounce scatter⁃ing power in the urban areas,the proposed algorithm effectively improves the volume scattering power of vegeta⁃tion areas.The efficacy of the modified multiple-component scattering power decomposition is validated using ac⁃tual AIRSAR PolSAR data.The scattering power obtained through decomposing the original coherency matrix and the coherency matrix after orientation angle compensation is compared with three algorithms.Results from the experiment demonstrate that the proposed decomposition yields more effective scattering power for different PolSAR data sets.