Underwater Cable Localization Method Based on Beetle Swarm Optimization Algorithm

Dear Editor,This letter concerns the localization of three-core underwater cables which are widely deployed for offshore energy transmission.It is a non-trivial problem,since the external magnetic field of threecore underwater cables is variable which reduces the accuracy of localization.To solve this problem,in this letter,an approximate equation is firstly derived to formulate the external magnetic field of a three-core armored underwater cable by considering the seafloor environments and the structure of three-core cables.

Zero Distribution of a Class of Real Polynomial Systems

设P:IR^(2n)→IR~?(2n)是(q_1,…,q_(2n))次实多项式映射,满足q_(2j-1)-q_(2j),j=1,2,…,n。本文讨论这类多项式映射的实零点分布,并给出计算一批实零点的方法。

Extensions of strongly π-regular general rings

The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.

The Fundamentals Underlying the Computations of Acceleration for General Dynamic Applications:Issues and Noteworthy Perspectives

To-date,with the exception of the Newmark method and the midpoint rule,most computational algorithms under the umbrella of LMS methods,which are predominantly employed in research and commercial software fail to properly evaluate acceleration computations accurately for conducting the numerical dynamic simulations.Indeed,this is not trivial and a sound theoretical basis of the fundamental underlying issues is described in detail.In this paper,we provide a resolution and point-out several noteworthy perspectives to address the proper evaluation of acceleration computations for structural dynamics applications with focus on the class of LMS methods as an illustration.

Multi-soliton Solutions of the Konopelchenko-Dubrovsky Equation

By using the standard truncated Painlevé analysis, a Backlund transformation is used to obtain some new types of multi-soliton solutions of the (2+ 1)-dimensional integrable Konopelchenko-Dubrovsky equation from the trivial vacuum solution.

NONLINEAR MODULATION OF THE SHORT INTERNAL WAVES IN THE WEAKLY STRATIFIED OCEAN

A nonlinear evolution equation of 2 - D short internal waves under condition of weak stratification-cubic Schrodinger equation- is derived by using the reductive perturbation method. Because aB【0 in the Schrodinger equation, in the linear system the sideband perturbation for the harmonic wave modulation is neutrally stable. At the same time, there is also a sort of wave pack -et-KdV envelope soliton. In the nonlinear system the dark soliton is obtained under condition of weak stratification. It is shown that the vertical perturbation of the Brunt-Vaisala frequency plays a role in forming the KdV envelope soliton and dark soliton.

Nonlocality Distillation and Trivial Communication Complexity for High-Dimensional Systems

A nonlocality distillation protocol for arbitrary high-dimensional systems is proposed. We study the nonlocality distillation in the 2-input d-output bi-partite case. Firstly, we give the one-parameter nonlocal boxes and their correlated distilling protocol. Then, we generalize the one-parameter nonlocality distillation protocol to the twoparameter case. Furthermore, we introduce a contracting protocol testifying that the 2-input d-output nonlocal boxes make communication complexity trivial.

THE FREDHOLM THEOREM FOR SYSTEMS OF INTEGRO-FUNCTIONAL EQUATIONS

Some problems of hyperbolic systems of partial differential equations can be turned into systems of in-tegro-functional equations of the following form[1]here F（x） = （f1（x）,…,fm（x））T and H（x）=（h1（x）,…,tm（x））T both belong to （C∞[-R,R]）m, are theunknown and know vector functions respectively; λis a parameter, 0【R≤+∞, T is an integral func-tional operator, such thathere s is a positive integer, A; and B1 are square matrices of order m, αi and βi are constants satisfying |αi|【1, |βi|≤1.

SOLUTIONS FOR SUPERLINEAR(n-1,1)CONJUGATE BOUNDARY VALUE PROBLEMS

The author investigates the existence of positive and nontrivial solutions for superlinear (n - 1, 1) conjugate boundary value problems by means of topological degree theory and cone theory. The main theorems improve some results published recently.

Nonlocal Effects of Low-Energy Excitations in Quantum-Spin-Liquid Candidate Cu_(3)Zn(OH)_(6)FBr

We systematically study the low-temperature specific heats for the two-dimensional kagome antiferromagnet,Cu_(3)Zn(OH)_(6)FBr.The specific heat exhibits a T1.7 dependence at low temperatures and a shoulder-like feature above it.We construct a microscopic lattice model of Z_(2) quantum spin liquid and perform large-scale quantum Monte Carlo simulations to show that the above behaviors come from the contributions from gapped anyons and magnetic impurities.Surprisingly,we find the entropy associated with the shoulder decreases quickly with grain size d,although the system is paramagnetic to the lowest temperature.While this can be simply explained by a core-shell picture in that the contribution from the interior state disappears near the surface,the 5.9-nm shell width precludes any trivial explanations.Such a large length scale signifies the coherence length of the nonlocality of the quantum entangled excitations in quantum spin liquid candidate,similar to Pippard’s coherence length in superconductors.Our approach therefore offers a new experimental probe of the intangible quantum state of matter with topological order.

Nonlocal Symmetry of the Lax Equation Related to Riccati-Type Pseudopotential

We investigate the Lax equation that can be employed to describe motions of long waves in shallow water under gravity.A nonlocal symmetry of this equation is given and used to find exact solutions and derive lower integrable models from higher ones.It is interesting that this nonlocal symmetry links with its corresponding Riccati-type pseudopotential.By introducing suitable and simple auxiliary dependent variables,the nonlocal symmetry is localized and used to generate new solutions from trivial solutions.Meanwhile,this equation is reduced to an ordinary differential equation by means of this nonlocal symmetry and some local symmetries.

From Nothing to Something: Discrete Integrable Systems

Chinese ancient sage Laozi said that everything comes from'nothing'.Einstein believes the principle of nature is simple.Quantum physics proves that the world is discrete.And computer science takes continuous systems as discrete ones.This report is devoted to deriving a number of discrete models,including well-known integrable systems such as the KdV,KP,Toda,BKP,CKP,and special Viallet equations,from'nothing'via simple principles.It is conjectured that the discrete models generated from nothing may be integrable because they are identities of simple algebra,model-independent nonlinear superpositions of a trivial integrable system(Riccati equation),index homogeneous decompositions of the simplest geometric theorem(the angle bisector theorem),as well as the Möbious transformation invariants.

Dynamics of the Entanglement Spectrum of the Haldane Model under a Sudden Quench

One of the appealing features of topological systems is the presence of robust edge modes.Under a sudden quantum quench,the edge modes survive for a characteristic time that scales with the system size,during which the nontrivial topology continues to manifest in entanglement properties,even though the post-quench Hamiltonian belongs to a trivial phase.We exemplify this in the quench dynamics of a two-dimensional Haldane model with the help of one-particle entanglement spectrum and the probability density of its mid-states.We find that,beyond our knowledge in one-dimensional models,the momentum dependence of the transverse velocity plays a crucial role in the out-of-equilibrium evolution of the entanglement properties.

Statistics of Leaders in Index-Driven Networks

We study the statistical properties of leaders in growing networks with age.A leader of a network is defined as the node with the largest degree and the age of the node is trivially labeled by its index,i.e.,the time it joins the network.As networks evolve with the addition of new nodes connecting to old ones with the possibility that is proportional to the index of the target,we investigate both the average number and index of leaders as well as the degree distribution of nodes.The average number of leaders first increases quickly with time and then saturates to a finite value and the average index of leaders increases algebraically with time.Both features result from the degree distribution with an exponential tail.Analytical calculations based on the rate equation are verified by numerical simulations.

Size Dependency of Income Distribution and Its Implications

We systematically study the size dependency of income distributions,i.e.income distribution versus the population of a country.Using the generalized Lotka--Uolterra model to fit the empirical income data for 1996-2007 in the U.S.A,we find an important parameter A that can scale with aβpower of the size(population)of the U.S.A.in that year.We point out that the size dependency of income distributions,which is a very important property but seldom addressed in previous studies,has two non-trivial implications:(1)the allometric growth pattern,i.e.the power-law relationship between population and GDP in different years,can be mathematically derived from the size-dependent income distributions and also supported by the empirical data;(2)the connection with the anomalous scaling for the probability density function in critical phenomena,since the re-scaled form of the income distributions has asymptotically exactly the same mathematical expression for the limit distribution of the sum of many correlated random variables.

Experimental and Theoretical Studies on Velocity Field of Buoyancy Convection in KNbO_(3) Melt

The Schlieren technique coupling with a differential interference microscope was applied to visualize the KNbO_(3) melt motion in a loop-shaped Pt wire heater.The natural convection in KNbO_(3) melt was traced by observing the movement of the tiny KNbO_(3) crystals(~10μm)and the stream velocities of these tracer crystals were measured.In theoretical analysis,the Navier--Stokes equation was solved as a stable field.The general solution for this system of the differential equation was expressed by an approximate power series of azimuth and radius vector.The expression was substituted in the differential equation;a non-trivial solution was obtained exactly.The velocity distribution in the vertical section was obtained which is in qualitative agreement with the experimental result.

Topological Distillation by Principal Component Analysis in Disordered Fractional Quantum Hall States

We study the behavior of two-dimensional electron gas in the fractional quantum Hall(FQH)regime in the presence of disorder potential.The principal component analysis is applied to a set of disordered Laughlin ground state model wave function to enable us to distill the model wave function of the pure Laughlin state.With increasing the disorder strength,the ground state wave function is expected to deviate from the Laughlin state and eventually leave the FQH phase.We investigate the phase transition from the Laughlin state to a topologically trivial state by analyzing the overlap between the random sample wave functions and the distilled ground state wave function.It is proposed that the cross point of the principal component amplitude and its counterpart is the critical disorder strength,which marks the collapse of the FQH regime.

Modified Chaplygin Gas with Variable G and Λ

We consider a modified Chaplygin gas with the gravitational constant G and the cosmological constantΛ.The trivial solution describes decelerating phase to accelerating phase of the universe.The non-static with constant equation of state describes the inflationary solution.For static universe,GandΛmust be formed arbitrarily,and for static universe with constant equation of state,GandΛshould be constant.

Exact Solution for Perk-Schultz Model with Boundary Impurities

The Perk-Schultz model with SUq(m\n)spin boundary impurities is constructed by dressing the c-number reflecting K matrix with local L-matrix which acts non-trivially on an impurity Hilbert space.The eigenvalue of the transfer matrix and the corresponding Bethe ansatz equations with different c-number reflecting K-matrices are obtained by using the nested Bethe ansatz method(m≠n).When m=1,n=2,our results come back to that of super-symmetric t-J model with SU_(q)(1\2)spin boundary impurities.

Knotted pictures of the Bell bases on the surface of a trivial torus

By means of the method of torus knot theory, this paper gives the complete processes of obtaining the knotted pictures of four Bell b^es from the knotted pictures of four basic two qubit states.