Reciprocity Relation between Alternative Gravity Formulas

We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.

Magnetic Nonreciprocity in a Hybrid Device of Asymmetric Artificial Spin-Ice-Superconductors

Controlling the size and distribution of potential barriers within a medium of interacting particles can unveil unique collective behaviors and innovative functionalities.We introduce a unique superconducting hybrid device using a novel artificial spin ice structure composed of asymmetric nanomagnets.This structure forms a distinctive superconducting pinning potential that steers unconventional motion of superconducting vortices,thereby inducing a magnetic nonreciprocal effect,in contrast to the electric nonreciprocal effect commonly observed in superconducting diodes.Furthermore,the polarity of the magnetic nonreciprocity is in situ reversible through the tunable magnetic patterns of artificial spin ice.Our findings demonstrate that artificial spin ice not only precisely modulates superconducting characteristics but also opens the door to novel functionalities,offering a groundbreaking paradigm for superconducting electronics.

Rayleigh reciprocity relations： Applications

Classical reciprocity relations have wide applications in acoustics, from field representation to generalized optical theorem. In this paper we introduce our recent results on the applications and generalization of classical Rayleigh reciprocity relation： higher derivative reciprocity relations as a generalization of the classical one and a theoretical proof on the Green＇s function retrieval from volume noises.

Solution of scattering from rough surface with a 2D target above it by a hybrid method based on the reciprocity theorem and the forward-backward method

This paper proposes a hybrid method based on the forward-backward method （FBM） and the reciprocity theorem （RT） for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, the equivalent electric/magnetic current densities on the rough surface as well as the scattering field from it are numerically calculated by FBM, and the scattered field from the isolated target is obtained utilizing the method of moments （MOM）. Meanwhile, the rescattered coupling interactions between the target and the surface are evaluated employing the combination of FBM and RT. Our hybrid method is first validated by available MOM results. Then, the functional dependences of bistatic and monostatic scattering from the target above rough surface upon the target altitude, incident and scattering angles are numerically simulated and discussed. This study presents a numerical description for the scattering mechanism associated with rescattered coupling interactions between a target and an underlying randomly rough surface.

Uniqueness,reciprocity theorem,and plane waves in thermoelastic diffusion with a fractional order derivative

In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.

DUAL RECIPROCITY HYBRID BOUNDARY NODE METHOD FOR THREE-DIMENSIONAL ELASTICITY WITH BODY FORCE

Combining Dual Reciprocity Method （DRM） with Hybrid Boundary Node Method （HBNM）, the Dual Reciprocity Hybrid Boundary Node Method （DRHBNM） is developed for three-dimensional linear elasticity problems with body force. This method can be used to solve the elasticity problems with body force without domain integral, which is inevitable by HBNM. To demonstrate the versatility and the fast convergence of this method, some numerical examples of 3-D elasticity problems with body forces are examined. The computational results show that the present method is effective and can be widely applied in solving practical engineering problems.

Improved Channel Reciprocity for Secure Communication in Next Generation Wireless Systems

To secure the wireless connection between devices with low computational power has been a challenging problem due to heterogeneity in operating devices,device to device communication in Internet of Things(IoTs)and 5G wireless systems.Physical layer key generation(PLKG)tackles this secrecy problem by introducing private keys among two connecting devices through wireless medium.In this paper,relative calibration is used as a method to enhance channel reciprocity which in turn increases the performance of the key generation process.Channel reciprocity based key generation is emerged as better PLKG methodology to obtain secure wireless connection in IoTs and 5G systems.Circulant deconvolution is proposed as a promising technique for relative calibration to ensure channel reciprocity in comparison to existing techniques Total Least Square(TLS)and Structured Total Least Square(STLS).The proposed deconvolution technique replicates the performance of the STLS by exploiting the possibility of higher information reuse and its lesser computational complexity leads to less processing time in comparison to the STLS.The presented idea is validated by observing the relation between signalto-noise ratio(SNR)and the correlation coefficient of the corresponding channel measurements between communicating parties.

Generation method of GPS L1C codes based on quadratic reciprocity law

A new code concept is used for the L1 civil（L1C） signal of the global positioning system（GPS）.The generation of L1C codes is quite different from the generation of traditional ranging codes.Thus,it is necessary to find a method for the correct generation to pave the way for future research.L1C codes are based on only one Legendre sequence which consists of Legendre symbols.To calculate these Legendre symbols,the Euler criterion is always used to evaluate quadratic residues.However,due to the great length of L1C codes,this procedure causes overflow problems.Therefore,the quadratic reciprocity law,some related theorems and properties are introduced to solve the problems.Moreover,if the quadratic reciprocity law,some related theorems and properties are used to calculate different Legendre symbols,the combination modes may vary,which causes a complex generation process.The proposed generation method deals with this complex generation process effectively.In addition,through simulations,it is found that the autocorrelation features of obtained Legendre sequences and L1C codes are in accordance with theoretical results,which proves the correctness of the proposed method.

Reciprocity as an Ever-Present Dual Property of Everything

Reciprocity may be understood as relation of action and reaction in the sense of Hegel’s philosophical definition. Quoting Kant, freedom and ethical necessities are reciprocally limited. In this contribution, a more mathematical than philosophical reflection about reciprocity as an ever-present dual property of everything was given. As a crystallographer, the author is familiar with the action of Fourier transforms and the relation between a crystal lattice and its reciprocal lattice, already pointing to the duality between particles and waves. A generalization of the reciprocity term was stimulated by results of the famous Information Relativity (IR) theory of Suleiman with its proven physical manifestation of matter-wave duality, compared to the set-theoretical E-Infinity theory developed by El Naschie, where the zero set represents the pre-quantum particle, and the pre-quantum wave is assigned to the empty set boundary surrounding the pre-particle. Expectedly, the most irrational number of the golden mean is involved in these thoughts, because this number is intimately connected with its inverse. An important role plays further Hardy’s maximum quantum entanglement probability as the fifth power of φand its connection to the dark matter. Remembering, the eleven dimensions in Witten’s M-theory may be decomposed into the Lucas number L5 = 11 = φ−5 – φ5. Reciprocity is indeed omnipresent in our world as piloting waves that accompany all observable earthen and cosmic matter. As a side effect of the IR theory some fundamental constants such as the gyromagnetic factor of the electron, Sommerfeld’s fine-structure constant as well as the charge of the electron must be marginally changed caused by altered relativistic corrections. Consequences also arise for our vision about the evolution of life and consciousness.

Reciprocity Relation between the Mass Constituents of the Universe and Hardy’s Quantum Entanglement Probability

In this short contribution, a reciprocity relation between mass constituents of the universe was explained governed by Hardy’s maximum entanglement probability of φ5 = 0.09017. While well explainable through a set-theoretical argumentation, the relation may also be a consequence of a coupling factor attributed to the normed dimensions of the universe. Also, very simple expressions for the mass amounts were obtained, when replacing the Golden Mean φ by the Archimedes’ constant π. A brief statement was devoted to the similarity between the E-Infinity Theory of El Naschie and the Information Relativity Theory of Suleiman. In addition, superconductivity was also linked with Hardy’s entanglement probability.

A Sound Field Separation and Reconstruction Technique Based on Reciprocity Theorem and Fourier Transform

We show a method to separate the sound field radiated by a signal source from the sound field radiated by noise sources and to reconstruct the sound field radiated by the signal source. The proposed method is based on reciprocity theorem and the Fourier transform. Both the sound field and its gradient on a measurement surface are needed in the method. Evanescent waves are considered in the method, which ensures a high resolution reconstruction in the near field region of the signal source when evanescent waves can be measured. A simulation is given to verify the method and the influence of measurement noise on the method is discussed.

Reciprocity Effect between Silicate Bacteria and Wollastonite

This paper studied the reciprocity effect between wollastonite and a strain silicate bacterium from purple soil. We analyzed the changes of pH value, glucose (GLU) residual concentration, electrolyte and Mn, Si, Fe etc. in the culture liquid with wollastonite after 48 h. The results show that the GLU wastage of silicate bacteria with wollastonite is 2.5 times of the bacterial contrast. It showed wollastonite could obviously accelerate silicate bacteria growth, but bacterial cell broken and distorted badly have been found by SEM analysis. The solubilization of silicate bacteria to Si element of wollastonite reached above 10 times. At the same time, three apices in FTIR of wollastonite (898 cm-1, 925 cm-1, 962 cm-1) descended obviously after the action of silicate bacteria, which shows that a great deal of Si has dissolved out. So we can get that wollastonite has remarkable effect to the growth of silicate bacteria and silicate bacteria has obvious solubilization to Si of wollastonite.

MULTIPLE RECIPROCITY METHOD WITH TWO SERIES OF SEQUENCES OF HIGH-ORDER FUNDAMENTAL SOLUTION FOR THIN PLATE BENDING

The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi_harmonic operator and Laplace operator, applying the multiple reciprocity method(MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high_order fundamental solution sequences.

APPLICATION OF THE DUAL RECIPROCITY BOUNDARY ELEMENT METHOD TO SOLUTION OF NONLINEAR DIFFERENTIAL EQUATION

In this paper the dual reciprocity boundary element method is employed to solve nonlinear differential equation del(2) u + u + epsilon u(3) = b. Results obtained in an example have a good agreement with those by FEM and show the applicability and simplicity of dual reciprocity method (DRM) in solving nonlinear differential equations.

Interrogating the Contending Issues in Nigeria-Ghana Relations: Reciprocity of Consequences or Constructive Engagement

The objective of this paper is to offer theoretical,analytical,and methodological investigations into the character of Nigeria’s relations and reactions towards Ghana on how it has been able to get to the level of reciprocity over trade disputes,political differences/relevance and superiority of influence in West Africa,Africa,and the world.In recent times,the counter measurers over demolition of Nigeria’s High Commission building in Accra and here conducts against the Ghana’s moves while it opted for constructive engagement and downplay the call for retaliatory or regulatory steps on Ghana.It also investigated how Nigeria has been able to use its constructive dialogue skills/diplomacy over reasons of reciprocity on other matters of national interest in relation to Ghana as citizens of both states have been deeply affected while businesses shutdown in both capitals at critical stages.The paper posits to examine the point of departure and seek ways for diplomatic intervention,and calls for leadership political will,factoring in the case of African Continental Free Trade Area Agreements,National and Strategic interests of both states,and the establishment of a compensation fund to Nigeria and Nigerians in Ghana.The paper makes use of secondary data while it adopts theories of interdependence and reciprocity as theoretical frameworks for the study.

‘Disciplining Oneself’and‘Disciplining Others’in Social Life:On the Contemporary Significance of Confucius’s Principle of Loyalty and Reciprocity

In a moral sense,there is an essential di erence between“disciplining oneself”and“disciplining others”in that the former means one setting rules for and giving orders to oneself in regard to one’s own conduct,which are unconditionally compulsory,while the latter is exible in the sense that one’s rules and orders for oneself are not compulsory to others and cannot prohibit others from doing something.In principle,Confucius’s sayings,“do not impose upon others that which you would not wish for yourself”and“establish others in seeking to establish yourself and promote others in s eeking to promote yourself”have epitomized the line of demarcation between them.His doctrine of“not imposing upon others that which you would not wish for yourself,”though based on self-preservation and self-interest,represents a standard of conduct of highly universal value.If the overwhelming majority of a society follows it as their standard of conduct,refraining from harming others in order to protect oneself from harm,then the whole society will endure little,if not no,strife and struggle.

Uniqueness theorem,theorem of reciprocity,and eigenvalue problems in linear theory of porous piezoelectricity

The uniqueness theorem and the theorem of reciprocity in the linearized porous piezoelectricity are established under the assumption of positive definiteness of elastic and electric fields. General theorems in the linear theory of porous piezoelectric materials are proved for the quasi-static electric field approximation. The uniqueness theorem is also proved without using the positive definiteness of the elastic field. An eigenvalue problem associated with free vibrations of a porous piezoelectric body is stud- ied using the abstract formulation. Some properties of operators are also proved. The problem of frequency shift due to small disturbances, based on an abstract formulation, is studied using a variational and operator approach. A perturbation analysis of a special ease is also given.

Dynamic Nonreciprocity with a Kerr Nonlinear Resonator

On-chip optical nonreciprocal devices are vital components for integrated photonic systems and scalable quantum information processing.Nonlinear optical isolators and circulators have attracted considerable attention because of their fundamental interest and their important advantages in integrated photonic circuits.However,optical nonreciprocal devices based on Kerr or Kerr-like nonlinearity are subject to dynamical reciprocity when the forward and backward signals coexist simultaneously in a nonlinear system.Here,we theoretically propose a method for realizing on-chip nonlinear isolators and circulators with dynamic nonreciprocity.Dynamic nonreciprocity is achieved via the chiral modulation on the resonance frequency due to coexisting self-and cross-Kerr nonlinearities in an optical ring resonator.This work showing dynamic nonreciprocity with a Kerr nonlinear resonator can be an essential step toward integrated optical isolation.

A bilateral heterogeneous graph model for interpretable job recommendation considering both reciprocity and competition

Amidst the inefficiencies of traditional job-seeking approaches in the recruitment ecosystem, the importance of automated job recommendation systems has been magnified. However, existing models optimized to maximize user clicks for general product recommendations prove inept in addressing the unique challenges of job recommendation, namely reciprocity and competition. Moreover, sparse data on online recruitment platforms can further negatively impact the performance of existing job recommendation algorithms. To counteract these limitations, we propose a bilateral heterogeneous graph-based competition iteration model. This model comprises three integral components: 1) two bilateral heterogeneous graphs for capturing multi-source information from people and jobs and alleviating data sparsity, 2) fusion strategies for synthesizing attributes and preferences to produce mutually beneficial job matches, and 3) a competition-enhancing strategy for dispersing competition realized through a two-stage optimization algorithm. Augmented by granular attention mechanisms for enhanced interpretability, the model’s efficacy, competition dispersion, and interpretability are validated through rigorous empirical evaluations on a real-world recruitment platform.

Reciprocity evaluation based adaptive CCM reconstruction in FDD multi-antenna systems

In view of the difficulty of obtaining downlink channel state information,partial reciprocity based channel covariance matrix(CCM)reconstruction has attracted a lot of attention in frequency division duplex(FDD)multi-antenna systems.Taking both the impact of CCM reconstruction on system performance and design complexity,we investigate an adaptive CCM reconstruction in this paper.Specifically,to effectively evaluate the validity of the reciprocity,we firstly analyze the characteristics of the partial reciprocity and define a reciprocity evaluation criterion.Then,we propose a partial antenna based angular power spectrum(APS)estimating algorithm to further reduce the complexity of the CCM reconstruction.Finally,simulation results demonstrate the superiority of our proposed schemes.