Infinitely Many Solutions and a Ground-State Solution for Klein-Gordon Equation Coupled with Born-Infeld Theory

In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.

Ground-state energy of beryllium atom with parameter perturbation method

We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom＇s Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold perturbation scheme,where the spin-spin interaction of electrons from different shells of the atom is also considered. Calculations show that the obtained ground-state energy is in satisfactory agreement with experiment. It is found that the Coulomb repulsion of the inner-shell electrons enhances the effective nuclear charge seen by the outer-shell electrons, and the shielding effect of the outer-shell electrons to the nucleus is also notable compared with that of the inner-shell electrons.

Influence of Rashba SOI and Polaronic Effects on the Ground-State Energy of Electrons in Semiconductor Quantum Rings

The influence of Rashba spin-orbit interaction （SOI） and polaronic effect on the ground-state energy of electrons in semiconductor quantum rings （QRs） are studied by means of the Lee-Low-Pines variational method. Numerical calculations for GaAs QRs are performed and the results show that the ground-state energy of electrons splits into two branches as E（↑） and E（↓） under the Rashba SOI, which correspond to the spin-up state and spin-down state, respectively. The contribution of the Rashba SOI effect to the ground-state energy of electrons is related to the spin state of electrons and is closely linked to the inner and outer radii of a QR. However, it is independent of the height of the QR. The ground-state energy of electrons decreases due to the polaronic effect in QRs. The energy shift ＆#8710;Ee-LO of the ground-state of the electron induced by the polaronic effect decreases monotonically with increase of the height of a QR and fluctuates with the changes of the radii of QRs. The amplitude of the fluctuation is very sensitive and remarkable to the changes of the inner radius R1 and the outer radius R2.

Ground-state cooling based on a three-cavity optomechanical system in the unresolved-sideband regime

In the unresolved sideband regime,we propose a scheme for cooling mechanical resonator close to its ground state in a three-cavity optomechanical system,where the auxiliary cavities are indirectly connected with the mechanical resonator through standard optomechanical subsystem.The standard optomechanical subsystem is driven by a strong pump laser field.With the help of the auxiliary cavities,the heating process is suppressed and the cooling process of the mechanical resonator is enhanced.More importantly,the average phonon number is much less than 1 in a larger range.This means that the mechanical resonator can be cooled down to its ground state.All these interesting features will significantly promote the physical realization of quantum effects in multi-cavity optomechanical systems.

Experimental Observation of the Ground-State Geometric Phase of Three-Spin XY Model

The geometric phase has become a fundamental concept in many fields of physics since it was revealed. Recently, the study of the geometric phase has attracted considerable attention in the context of quantum phase transition, where the ground state properties of the system experience a dramatic change induced by a variation of an external parameter. In this work, we experimentally measure the ground-state geometric phase of the three-spin XY model by utilizing the nuclear magnetic resonance technique. The experimental results indicate that the geometric phase could be used as a fingerprint of the ground-state quantum phase transition of many-body systems.

A New Method for the Atomic Ground-State Energy in the Screened Coulomb Potential

The new method proposed recently by Friedberg,Lee and Zhao is applied to the derivation of the atomic ground-state energy with the inclusion of the screening effect.The present results are compared with those obtained in the pure Coulomb potential and by the variational approach.The overall good results are obtained with this new method.

Ground-State Structure and Physical Properties of NB_2 Predicted from First Principles

Using the newly developed particle swarm optimization algorithm on crystal structural prediction, we predict a new class of boron nitride with stoicMometry of NB2 at ambient pressure, which belongs to the tetragonal 14m2 space group. Then, its structure, elastic properties, electronic structure, and chemical bonding are investigated by first-principles calculations with the density functional theory. The phonon calculation and elastic constants confirm that the predicted NB2 is dynamically and mechanically stable, respectively. The large bulk modulus, large shear modulus, large Young＇s modulus, and small Poisson＇s ratio show that the 14m2 NB2 should be a new superhard material with a calculated theoretical Vickers hardness value of 66 GPa. Further analysis on density of states and electron localization function demonstrate that the strong B B and 13 N covalent bonds are the main reason for its high hardness in 14m2 NB2.

Ground-state structure determination and mechanical properties of palladium seminitride

Combining first-principles calculations with the particle swarm optimization （PSO） algorithm, we have explored the ground-state structure of Pd2N, whose structure is in debate although it is the first synthesized binary platinum group nitride. The ground-state structure is predicted to be tetragonal with space group P^-4m2, which is energetically more favorable than the previously proposed orthorhombic Co2N-type structure. The stability is confirmed by the subsequent calculations on the phonon dispersion curves and elastic constants. Furthermore, the calculated mechanical properties indicate that Pd2N has low incompressibility and is a common hard material.

Modified Atomic Orbital Calculations of Energy of the(2s^(2)^(1)S)Ground-State,the(2p^(2)^(1)D);(3d^(2)^(1)G)and(4f^(2)^(1)I)Doubly Excited States of Helium Isoelectronic Sequence from H-to Ca^(18+)

We report in this paper the ground-state energy 2s^(2)^(1)S and total energies of doubly excited states 2p^(2)^(1)D,3d^(2)^(1)D,4f^(2)^(1)I of the Helium isoelectronic sequence from H-to Ca^(18+).Calculations are performed using the Modified Atomic Orbital Theory(MAOT)in the framework of a variational procedure.The purpose of this study required a mathematical development of the Hamiltonian applied to Slater-type wave function[1]combining with Hylleraas-type wave function[2].The study leads to analytical expressions which are carried out under special MAXIMA computational program.This first proposed MAOT variational procedure,leads to accurate results in good agreement as well as with available other theoretical results than experimental data.In the present work,a new correlated wave function is presented to express analytically the total energies for the 2s21S ground state and each doubly 2p^(2)^(1)D,3d^(2)^(1)D,4f^(2)^(1)I excited states in the He-like systems.The present accurate data may be a useful guideline for future experimental and theoretical studies in the(nI^(2))systems.

Ground-State Energy and Entropy for One-Dimensional Heisenberg Chain with Alternating D-Term

We study the ground-state information of one-dimensional Heisenberg chain with alternating D-term. Given the ground-state phase diagram, the ground-state energy and the entanglement entropy are obtained by tensor-net work algorithm. The phase transition points are shown in the entanglement entropy figure. The results are agreed with the phase diagram.

The effects of the Dzyaloshinskii-Moriya interaction on the ground-state properties of the XY chain in a transverse field

The effects of the Dzyaloshinski-Moriya （DM） interaction on the ground-state properties of the anisotropic XY chain in a transverse field have been studied by means of correlation functions and entanglement. Different from the case without the DM interaction, the excitation spectra ek of this model are not symmetrical in the momentum space and are not always positive. As a result, besides the ferromagnetic （FM） and the paramagnetic （PM） phases, a gapless chiral phase is induced. In the chiral phase, the von Neumann entropy is proportional to log2 L （L is the length of a subchain） with the coefficient A ~ 1/3, which is the same as that of the XY chain in a transverse field without the DM interaction for 7 = 0 and 0 〈 h 〈 1. And in the vicinity of the critical point between the chiral phase and the FM （or PM） phase, the behaviors of the nearest- neighbor concurrence and its derivative are like those for the anisotropy transition.

Modeling time-dependent mechanical behavior of hard rock considering excavation-induced damage and complex 3D stress states

To investigate the long-term stability of deep rocks,a three-dimensional(3D)time-dependent model that accounts for excavation-induced damage and complex stress state is developed.This model comprises three main components:a 3D viscoplastic isotropic constitutive relation that considers excavation damage and complex stress state,a quantitative relationship between critical irreversible deformation and complex stress state,and evolution characteristics of strength parameters.The proposed model is implemented in a self-developed numerical code,i.e.CASRock.The reliability of the model is validated through experiments.It is indicated that the time-dependent fracturing potential index(xTFPI)at a given time during the attenuation creep stage shows a negative correlation with the extent of excavationinduced damage.The time-dependent fracturing process of rock demonstrates a distinct interval effect of the intermediate principal stress,thereby highlighting the 3D stress-dependent characteristic of the model.Finally,the influence of excavation-induced damage and intermediate principal stress on the time-dependent fracturing characteristics of the surrounding rocks around the tunnel is discussed.

Saturation Estimation with Complex Electrical Conductivity for Hydrate-Bearing Clayey Sediments:An Experimental Study

Clays have considerable influence on the electrical properties of hydrate-bearing sediments.It is desirable to understand the electrical properties of hydrate-bearing clayey sediments and to build hydrate saturation(S_(h))models for reservoir evaluation and monitoring.The electrical properties of tetrahydrofuran-hydrate-bearing sediments with montmorillonite are characterized by complex conductivity at frequencies from 0.01 Hz to 1 kHz.The effects of clay and Sh on the complex conductivity were analyzed.A decrease and increase in electrical conductance result from the clay-swelling-induced blockage and ion migration in the electrical double layer(EDL),respectively.The quadrature conductivity increases with the clay content up to 10%because of the increased surface site density of counterions in EDL.Both the in-phase conductivity and quadrature conductivity decrease consistently with increasing Sh from 0.50 to 0.90.Three sets of models for Sh evaluation were developed.The model based on the Simandoux equation outperforms Archie’s formula,with a root-mean-square error(E_(RMS))of 1.8%and 3.9%,respectively,highlighting the clay effects on the in-phase conductivity.The fre-quency effect correlations based on in-phase and quadrature conductivities exhibit inferior performance(E_(RMS)=11.6%and 13.2%,re-spectively)due to the challenge of choosing an appropriate pair of frequencies and intrinsic uncertainties from two measurements.The second-order Cole-Cole formula can be used to fit the complex-conductivity spectra.One pair of inverted Cole-Cole parameters,i.e.,characteristic time and chargeability,is employed to predict S_(h) with an E_(RMS) of 5.05%and 9.05%,respectively.

A novel complex-high-order graph convolutional network paradigm:ChyGCN

In recent years,there has been a growing interest in graph convolutional networks(GCN).However,existing GCN and variants are predominantly based on simple graph or hypergraph structures,which restricts their ability to handle complex data correlations in practical applications.These limitations stem from the difficulty in establishing multiple hierarchies and acquiring adaptive weights for each of them.To address this issue,this paper introduces the latest concept of complex hypergraphs and constructs a versatile high-order multi-level data correlation model.This model is realized by establishing a three-tier structure of complexes-hypergraphs-vertices.Specifically,we start by establishing hyperedge clusters on a foundational network,utilizing a second-order hypergraph structure to depict potential correlations.For this second-order structure,truncation methods are used to assess and generate a three-layer composite structure.During the construction of the composite structure,an adaptive learning strategy is implemented to merge correlations across different levels.We evaluate this model on several popular datasets and compare it with recent state-of-the-art methods.The comprehensive assessment results demonstrate that the proposed model surpasses the existing methods,particularly in modeling implicit data correlations(the classification accuracy of nodes on five public datasets Cora,Citeseer,Pubmed,Github Web ML,and Facebook are 86.1±0.33,79.2±0.35,83.1±0.46,83.8±0.23,and 80.1±0.37,respectively).This indicates that our approach possesses advantages in handling datasets with implicit multi-level structures.

Pressure-Induced Shifts of R, R＇, and B Line-Groups and Ground-State Zero-Field-Splitting of Ruby

By means of improved ligand-field theory, the 'pure electronic'presure-induced shifts (PS's) and the PS's due to electron-phonon interaction (EPI) of the R_1, R_2,B_1, B_2, B_3, and R′_3 lines and the ground-state zero-Geld-splitting of ruby have been uniformlycalculated. The calculation results are in very good agreement with all the experimental data. Atnormal pressure, ruby is a crystal with very strong crystal field. Thus, the admixture of ∣t_2~2(~3T_1)e~4T_2 】 and ∣t_2~(32)E＞ bases in the wavefunction of R_1 level of ruby is small at normalpressure, and it gradually decreases with increasing pressure, which causes the R_1-line PS of rubyto monotonously red shift with approximate linearity. The combined effect of the pure electronic PSof R_1 line and the PS of R_1 line due to EPI gives rise to the total PS of R_1 line. The analysesand comparisons among the features of R_1-line PS's of three laser crystals (ruby, GSGG:Cr~(3+) andGGG:Cr~(3+)) have been made, and the origin of their difference has been revealed.

Discovery of nano organo-clay complex pore-fractures in shale and its scientific significance:A case study of Cretaceous Qingshankou Formation shale,Songliao Basin,NE China

A new pore type,nano-scale organo-clay complex pore-fracture was first discovered based on argon ion polishing-field emission scanning electron microscopy,energy dispersive spectroscopy and three-dimensional reconstruction by focused ion-scanning electron in combination with analysis of TOC,R_(o)values,X-ray diffraction etc.in the Cretaceous Qingshankou Formation shale in the Songliao Basin,NE China.Such pore characteristics and evolution study show that:(1)Organo-clay complex pore-fractures are developed in the shale matrix and in the form of spongy and reticular aggregates.Different from circular or oval organic pores discovered in other shales,a single organo-clay complex pore is square,rectangular,rhombic or slaty,with the pore diameter generally less than 200 nm.(2)With thermal maturity increasing,the elements(C,Si,Al,O,Mg,Fe,etc.)in organo-clay complex change accordingly,showing that organic matter shrinkage due to hydrocarbon generation and clay mineral transformation both affect organo-clay complex pore-fracture formation.(3)At high thermal maturity,the Qingshankou Formation shale is dominated by nano-scale organo-clay complex pore-fractures with the percentage reaching more than 70%of total pore space.The spatial connectivity of organo-clay complex pore-fractures is significantly better than that of organic pores.It is suggested that organo-complex pore-fractures are the main pore space of laminar shale at high thermal maturity and are the main oil and gas accumulation space in the core area of continental shale oil.The discovery of nano-scale organo-clay complex pore-fractures changes the conventional view that inorganic pores are the main reservoir space and has scientific significance for the study of shale oil formation and accumulation laws.

Complexity Considerations in the Heisenberg Uncertainty Principle

This work introduces a modification to the Heisenberg Uncertainty Principle (HUP) by incorporating quantum complexity, including potential nonlinear effects. Our theoretical framework extends the traditional HUP to consider the complexity of quantum states, offering a more nuanced understanding of measurement precision. By adding a complexity term to the uncertainty relation, we explore nonlinear modifications such as polynomial, exponential, and logarithmic functions. Rigorous mathematical derivations demonstrate the consistency of the modified principle with classical quantum mechanics and quantum information theory. We investigate the implications of this modified HUP for various aspects of quantum mechanics, including quantum metrology, quantum algorithms, quantum error correction, and quantum chaos. Additionally, we propose experimental protocols to test the validity of the modified HUP, evaluating their feasibility with current and near-term quantum technologies. This work highlights the importance of quantum complexity in quantum mechanics and provides a refined perspective on the interplay between complexity, entanglement, and uncertainty in quantum systems. The modified HUP has the potential to stimulate interdisciplinary research at the intersection of quantum physics, information theory, and complexity theory, with significant implications for the development of quantum technologies and the understanding of the quantum-to-classical transition.

Three-dimensional magnetic reconnection in complex multiple X-point configurations in an ancient solar-lunar terrestrial system

Magnetic reconnection processes in three-dimensional(3D)complex field configurations have been investigated in different magneto-plasma systems in space,laboratory,and astrophysical systems.Two-dimensional(2D)features of magnetic reconnection have been well developed and applied successfully to systems with symmetrical property,such as toroidal fusion plasmas and laboratory experiments with an axial symmetry.But in asymmetric systems,the 3D features are inevitably different from those in the 2D case.Magnetic reconnection structures in multiple celestial body systems,particularly star-planet-Moon systems,bring fresh insights to the understanding of the 3D geometry of reconnection.Thus,we take magnetic reconnection in an ancient solar-lunar terrestrial magneto-plasma system as an example by using its crucial parameters approximately estimated already and also some specific applications in pathways for energy and matter transports among Earth,ancient Moon,and the interplanetary magnetic field(IMF).Then,magnetic reconnection of the ancient lunar-terrestrial magnetospheres with the IMF is investigated numerically in this work.In a 3D simulation for the Earth-Moon-IMF system,topological features of complex magnetic reconnection configurations and dynamical characteristics of magnetic reconnection processes are studied.It is found that a coupled lunar-terrestrial magnetosphere is formed,and under various IMF orientations,multiple X-points emerge at distinct locations,showing three typical magnetic reconnection structures in such a geometry,i.e.,the X-line,the triple current sheets,and the A-B null pairs.The results can conduce to further understanding of reconnection physics in 3D for plasmas in complex magnetic configurations,and also a possible mechanism for energy and matters transport in evolutions of similar astrophysical systems.

Synthesis and Physico-Chemical Characterizations of Novel Hydrazone Ligands and Their Metal Complexes against Hormone-Dependent and Independent Cancers

This work deals with the synthesis and physicochemical characterizations of a new group of novel retinoidal ligands and their metal complexes. Their in vitro anti-proliferative activities have shown that ligand L1 is effective against human breast cancer BT-20 and MCF-7 cell lines. At the same time, compound L2 exerts its effect on human prostate cancer PC-3 and human breast cancer MDA-MB-231 and MCF-7 cell lines respectively. The retinoid ligands exert their pleiotropic action toward retinoic acid receptors (RARs) than their metal complexes but all compounds exhibit concentration-dependent.

Channel-Feedback-Free Transmission for Downlink FD-RAN:A Radio Map Based Complex-Valued Precoding Network Approach

As the demand for high-quality services proliferates,an innovative network architecture,the fully-decoupled RAN(FD-RAN),has emerged for more flexible spectrum resource utilization and lower network costs.However,with the decoupling of uplink base stations and downlink base stations in FDRAN,the traditional transmission mechanism,which relies on real-time channel feedback,is not suitable as the receiver is not able to feedback accurate and timely channel state information to the transmitter.This paper proposes a novel transmission scheme without relying on physical layer channel feedback.Specifically,we design a radio map based complex-valued precoding network(RMCPNet)model,which outputs the base station precoding based on user location.RMCPNet comprises multiple subnets,with each subnet responsible for extracting unique modal features from diverse input modalities.Furthermore,the multimodal embeddings derived from these distinct subnets are integrated within the information fusion layer,culminating in a unified representation.We also develop a specific RMCPNet training algorithm that employs the negative spectral efficiency as the loss function.We evaluate the performance of the proposed scheme on the public DeepMIMO dataset and show that RMCPNet can achieve 16%and 76%performance improvements over the conventional real-valued neural network and statistical codebook approach,respectively.