Superposition formulas of multi-solution to a reduced(3+1)-dimensional nonlinear evolution equation

We gave the localized solutions,the interaction solutions and the mixed solutions to a reduced(3+1)-dimensional nonlinear evolution equation.These solutions were characterized by superposition formulas of positive quadratic functions,the exponential and hyperbolic functions.According to the known lump solution in the outset,we obtained the superposition formulas of positive quadratic functions by plausible reasoning.Next,we constructed the interaction solutions between the localized solutions and the exponential function solutions with the similar theory.These two kinds of solutions contained superposition formulas of positive quadratic functions,which were turned into general ternary quadratic functions,the coefficients of which were all rational operation of vector inner product.Then we obtained linear superposition formulas of exponential and hyperbolic function solutions.Finally,for aforementioned various solutions,their dynamic properties were showed by choosing specific values for parameters.From concrete plots,we observed wave characteristics of three kinds of solutions.Especially,we could observe distinct generation and separation situations when the localized wave and the stripe wave interacted at different time points.

A New HARQ Scheme for 5G Systems via Interleaved Superposition Retransmission

Within the framework of the 5G new radio(NR),we propose a new hybrid automatic repeat request(HARQ)scheme to improve the throughput performance.The difference between the proposed scheme and the conventional one lies in the first retransmission,where the erroneous coded block group is interleaved and superimposed(XORed)onto a fresh coded block group.At the receiver,an iterative message-passing decoding algorithm can be employed to recover the target erroneous code block group(CBG).Only when the superposed retransmission fails,the conventional incremental redundancy(IR)or repetition redundancy(RR)retransmission is initiated.In any case,since the first retransmission is along with but has negligible effect on the fresh CBG,it costs neither transmitted power nor bandwidth.Monte-Carlo simulation results reveal that the presented HARQ schemes can achieve throughput improvements up to 10%over block fading channels and up to 50%over fast fading channels in comparison with the original 5G CBG-level HARQ scheme but without excessively increasing the implementation complexity.

Extension of sound field reconstruction based on element radiation superposition method in a sparsity framework

Nearfield acoustic holography(NAH)is a powerful tool for realizing source identification and sound field reconstruction.The wave superposition(WS)-based NAH is appropriate for the spatially extended sources and does not require the complex numerical integrals.Equivalent source method(ESM),as a classical WS approach,is widely used due to its simplicity and efficiency.In the ESM,a virtual source surface is introduced,on which the virtual point sources are taken as the assumed sources,and an optimal retreat distance needs to be considered.A newly proposed WS-based approach,the element radiation superposition method(ERSM),uses piston surface source as the assumed source with no need to choose a virtual source surface.To satisfy the application conditions of piston pressure formula,the sizes of pistons are assumed to be as small as possible,which results in a large number of pistons and sampling points.In this paper,transfer matrix modes(TMMs),which are composed of the singular vectors of the vibro-acoustic transfer matrix,are used as the sparse basis of piston normal velocities.Then,the compressive ERSM based on TMMs is proposed.Compared with the conventional ERSM,the proposed method maintains a good pressure reconstruction when the number of sampling points and pistons are both reduced.Besides,the proposed method is compared with the compressive ESM in a mathematical sense.Both simulations and experiments for a rectangular plate demonstrate the advantage of the proposed method over the existing methods.

Building color and Psychological Evaluation Based on Superposition Analysis:A case study of Pingguoyuan Street in Beijing City

China’s construction has entered the high-quality development stage,and the building color landscape as the constituent element of the quality of urban artificial landscape has attracted more and more attention.In the process of building the building color evaluation system with the appeal of“public participation”,it is necessary to absorb and adopt public opinions,and the color planning practice cannot completely match the public opinions.In this paper,Pingguoyuan Street in Beijing City was taken as an example,and factor grading was constructed based on the relevant principle of“sensitivity grading”by analyzing the coupling relationship between color and urban artificial landscape structure.GIS technology was used to integrate and analyze residents’color sensitivity data obtained by investigation and interview and form the psychological evaluation of residents’color perception of artificial landscape,so as to provide scientific basis for the color planning of Pingguoyuan Street in Beijing City from the perspective of“space justice”.

On the Proof of the Contradiction of Set Theory

The article is devoted to proving the inconsistency of set theory arising from the existence of strange trees. All steps of the proof rely on common informal set-theoretic reasoning, but they take into account the prohibitions that were introduced into axiomatic set theories in order to overcome the difficulties encountered by the naive Cantor set theory. Therefore, in fact, the article is about proving the inconsistency of existing axiomatic set theories, in particular, the ZFC theory.

Origin and Superposition Metallogenic Model of the Sandstone-type Uranium Deposit in the Northeastern Ordos Basin,China

This paper deals with the metallogenic model of the sandstone type uranium deposit in the northeastern Ordos Basin from aspects of uranium source, migration and deposition. A superposition metallogenic model has been established due to complex uranium mineralization processes with superposition of oil-gas reduction and thermal reformation.

The entropic squeezing of superposition of two arbitrary coherent states

In this paper the superpositions of two arbitrary coherent states ｜ψ〉 = α ｜β｜ ＋ be^iψ ｜mβe^iδ〉 are constructed by using the superposition principle of quantum mechanics. The entropic squeezing effects of the quantum states are studied. The numerical results indicate that the amplitudes, the ratio between the amplitudes of two coherent states, the phase difference between the two components and the relative phase of the two coefficients play important roles in the squeezing effects of the position entropy and momentum entropy.

The classification of travelling wave solutions and superposition of multi-solutions to Camassa-Holm equation with dispersion

Under the travelling wave transformation, the Camassa-Holm equation with dispersion is reduced to an integrable ordinary differential equation （ODE）, whose general solution can be obtained using the trick of one-parameter group. Furthermore, by using a complete discrimination system for polynomial, the classification of all single travelling wave solutions to the Camassa-Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More generally, an implicit linear structure in the Camassa-Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa-Holm equation with dispersion.

Propagation of the off-axis superposition of partially coherent beams through atmospheric turbulence

The propagation properties of the off-axis superposition of partially coherent beams through atmospheric turbulence and their beam quality in terms of the mean-squared beam width w（z） and the power in the bucket （PIB） are studied in detail, where the effects of partial coherence, off-axis beam superposition and atmospheric turbulence are considered. The analytical expressions for the intensity, the beam width and the PIB are derived, and illustrative examples are given numerically. It is shown that the maximum intensity/max and the PIB decrease and w（z） increases as the refraction index structure constant Cn^2 increases. Therefore, the turbulence results in a degradation of the beam quality. However, the resulting partially coherent beam with a smaller value of spatial correlation parameter γ and larger values of separate distance Xd and beam number M is less affected by the turbulence than that with a larger value of y and smaller values of Xd and M. The main results obtained in this paper are explained physically.

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave is established under some smallness conditions. To do this, we first construct a new viscous contact wave such that the momentum equation is satisfied exactly and then determine the shift of the viscous shock wave. By using them together with an inequality concerning the heat kernel in the half space, we obtain the desired a priori estimates. The proof is based on the elementary energy method by the anti-derivative argument.

WAVE SUPERPOSITION METHOD BASED ON VIRTUAL SOURCE BOUNDARY WITH COMPLEX RADIUS VECTOR FOR SOLVING ACOUSTIC RADIATION PROBLEMS

By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.

Vibration Superposition in Tunnel Blasting with Millisecond Delay

According to explosion dynamics and elastic wave theory, the models of particle vibration velocity for simultaneous blasting and milliseeond blasting are built. In the models, influential factors such as delay interval and charge quantity, are considered. The calculated vibration velocity is compared with the field test results, which shows that the theoretical values are close to the experimental ones. Meanwhile, the particle vibration velocity decreases quickly with time due to the damping of rock mass and has a harmonic motion, and the particle vibration velocity of millisecond blasting has short interval. The superposition of particle vibration velocities may reduce vibration because of wave interference, or magnify the surrounding rock response to the blastinginduced vibration.

Wigner Frequency Point Slice Analysis of Superposition Data for Phased-Array Ground Penetrating Radar

According to the frequency property of Phasedarray ground penetrating radar (PGPR), this paper gives a frequency point slice method based on Wigner time-frequency analysis. This method solves the problem of analysis for the PGPR's superposition data and makes detecting outcome simpler and detecting target more recognizable. At last, the analytical results of road test data of the Three Gorges prove the analytical method efficient. Key words phased-array ground penetrating radar - wigner time-frequency analysis - superposition data - object identification CLC number TN 715.7 Foundation item: Supported by the National Nature Science Foundation of China (50099620) and 863 Program Foundation of China (2001AA132050-03)Biography: ZOU Lian (1975-), male, Ph. D candidate, research direction: signal processing.

DEGREE OF APPROXIMATION BY SUPERPOSITIONS OF A SIGMOIDAL FUNCTION

In this paper we study the degree of approximation by superpositions of a sigmoidal function.We mainly consider the univariate case.If f is a continuous function,we prove that for any bounded sigmoidal function σ,d_(n,σ)(f)≤‖σ‖ω(f,1/(n+1)).For the Heaviside function H(x),we prove that d_(n,H)(f)≤ω(f,1/(2(n+1))). If f is a continuous funnction of bounded variation,we prove that d_(n,σ)(f)≤‖σ‖/(n+1)V(f)and d_(n,H)(f)≤ 1/(2(n+1))V(f).For he Heaviside function,the coefficient 1 and the approximation orders are the best possible.We compare these results with the classical Jackson and Bernstein theorems,and make some conjec- tures for further study.

SUPERPOSITION ABOUT THE 3D VORTEX SOLUTIONS OF THE FLUID DYNAMIC EQUATION

A class of exact general solutions of an axisymmetric flow of the fluid dynamic equations is given. Then some examples are discussed. Some vortex solutions can be superposed to give other exact solutions. It can be used to analyse the generation and evolution of the vortex ring.

On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge

A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge.The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied.The solution procedure incorporates separation of variables,symplectic eigen solution and superposition.The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems.The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use.The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.

Dynamic Superposition and Levitation Capability of Two Confronting Ultrasonic Waves

The superposition dynamics of two confronting ultrasonic waves and their levitation capability for centimeter-sized thin disks are investigated by numerical analyses and validated by experiments. The sound pressure simulation reveals that two opposite ultrasonic waves provide a more effective standing-wave field than a single ultrasonic wave when the diameter of disk-shaped object approaches the wavelength scale. The dynamic superposition of two confronting beams facilitates the acoustic levitation of the clay disk and aluminum disk with diameters of 0.97 and 0.90. The acoustic radiation forces exerting on these thin disks are measured experimentally, which exhibit a better levitation stability for the centimeter-sized thin disks. The equilibrium levitation positions of the two disks are located near the sound pressure node, and the maximum acoustic radiation pressure on their surfaces is less than one percent of the maximum sound pressure.

Amplitude-squared squeezing of superposition of coherent states

This paper discusses the amplitude-squared squeezing for the superposition of two coherent states with their phase differences being separately π/2, 3π/2, and π1, as well as for the superposition state of two pseudoclassical states. According to the analysis, it is found that the superposition state of two coherent states with their phase differences π/2 and 3π/2, and the superposition state of two pseudoclassical states both do exhibit the amplitude-squared squeezing. Also, some specific states are found to exhibit even stronger squeezing effects when relative phase of the superposition is equal to the average photon number. Amplitude-squared squeezing is dependent on the difference in phase between two coherent states.

Spatial-Modulated Physical-Layer Network Coding Based on Block Markov Superposition Transmission for Maritime Relay Communications

As an alternative to satellite communications,multi-hop relay networks can be deployed for maritime long-distance communications.Distinct from terrestrial environment,marine radio signals are affected by many factors,e.g.,weather conditions,evaporation ducting,and ship rocking caused by waves.To ensure the data transmission reliability,the block Markov superposition transmission(BMST)codes,which are easily configurable and have predictable performance,are applied in this study.Meanwhile,the physical-layer network coding(PNC)scheme with spatial modulation(SM)is adopted to improve the spectrum utilization.For the BMST-SMPNC system,we propose an iterative algorithm,which utilizes the channel observations and the a priori information from BMST decoder,to compute the soft information corresponding to the XORed bits constructed by the relay node.The results indicate that the proposed scheme outperforms the convolutional coded SM-PNC over fast-fading Rician channels.Especially,the performance can be easily improved in high spatial correlation maritime channel by increasing the memory m.

DIVERSITY-AND-MULTIPLEXING TRADEOFF AND THROUGHPUT OF SUPERPOSITION CODING RELAYING STRATEGY

While the Network Coding cooperative relaying (NC-relaying) has the merit of high spectral efficiency,Superposition Coding relaying (SC-relaying) has the merit of high throughput. In this paper,a novel concept,coded cooperative relaying,is presented,which is a unified scheme of the NC-relaying and SC-relaying. For the SC-relaying strategy which can be considered one-way coded relaying scheme with multi-access channel,the close-form solution of the outage probabilities of the basic signal and additional signal are obtained firstly. Secondly,the Diversity-and-Multiplexing Tradeoff (DMT) characteristics of basic signal and additional signal are investigated entirely as well as the optimal close-form solutions. The compared numerical analysis shows the evaluation error of throughput based on the close-form solution is about 0.15 nats,which is within the acceptable error range. Due to the mutual effect between the both source signals,the available maximal values of the two multiplexing gains are less than 1.