A study on distributive and modular lattice ordered fuzzy soft group and its duality

Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle.

Additive Maps Preserving the Star Partial Order on B(H)

Let B（H） be the C^＊-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B（H） preserving the star partial order in both directions if and only if one of the following assertions holds. （1） There exist a nonzero complex number a and two unitary operators U and V on H such that φ（X） = a UXV or φ（X） = α UX^＊ V for all X ∈B（H）. （2） There exist a nonzero a and two anti-unitary operators U and V on H such that φ（X） = αUXV or φ（X） = aUX^＊ Vfor all X∈ B（H）.

Effect of Interchain Coupling on Quantum Lattice Fluctuation and Fluctuation Induced Interchain Order Transition in Trans-polyacetylene

Based on the modified Su-Schrieffer-Heeger Harniltonian and by adding the interchain hopping term,we consider the effect of interchain coupling on quantum lattice fluctuation in trans-polyacetylene.It has been found that the interchain coupling does not always weaken quantum lattice fluctuation.After overcoming a barrier of 1 eV or so,the quantum lattice fluctuation can induce a transition of interchain order.The physical meaning of these features is discussed.

A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations （NPDEs） in the form ut ＋αuux ＋βu^nuz ＋γuxx ＋δuzxx ＋ζxxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions.

A Novel Method of Newton Iteration in Complex Field and Lattice Search for Locating Partial Discharges in Transformers

在变压器局部放电特高频定位的多传感器时间差测量中不可避免地存在误差,这往往导致时间差方程组在实数域内无解。为了得到时间差方程组的最优近似解,提出了复数域牛顿迭代网格搜索方法。该方法在复数域内进行迭代;当迭代结果为实数时就将其作为定位结果;当迭代结果为复数时,以其实部为中心点坐标,在该点周围局部区域内采用网格搜索法计算最优近似解。通过在变压器上开展试验检验了该方法的可行性和准确性。研究表明,在一定时间误差下,在实数域采用牛顿迭代法计算时不收敛,而在复数域可以收敛,平均定位误差为0.20 m。复数域牛顿迭代网格搜索方法能够在一定时间误差下求解时间差方程组,给出最优近似解,实现局部放电定位。

Tunneling dynamics of Bose-Einstein condensates with higher-order interactions in optical lattice

The nonlinear Landau Zener tunneling and nonlinear Rabi oscillations of Bose-Einstein condensate （BEC） with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters （i.e., the modulation amplitude and frequency） and the strength of periodic potential.

Effects of anharmonic lattice distortion on orbital and magnetic orderings in KCuF_3

Lattice, magnetic and orbital structures in KCuF3 are self-consistently determined by our cluster self-consistent field approach based on a spin-orbital-lattice Hamiltonian. Two stable structures are obtained and found to be degenerate, which confirms the presence of the coexistent phases observed experimentally. We clearly show that due to the inherent frustration, the ground state of the system only with the superexchange interaction is degenerate; while the Jahn-Teller distortion, especially the anharmonic effect, stabilizes the orbital ordered phase at about 23% in the x2-y2 orbit and at 77% in the 3z2-r2 orbit. Meanwhile the magnetic moment of Cu is considerably reduced to 0.56μB, and magnetic coupling strengths are highly anisotropic, Jx/Jxy ≈ 18. These results are in good agreement with the experiments, implying that the anharmonic Jahn-Teller effect plays an essential role in stabilising the orbital ordered ground state of KCuF3.

A mass-conserved multiphase lattice Boltzmann method based on high-order difference

The Z–S–C multiphase lattice Boltzmann model [Zheng, Shu, and Chew(ZSC), J. Comput. Phys. 218, 353(2006)]is favored due to its good stability, high efficiency, and large density ratio. However, in terms of mass conservation, this model is not satisfactory during the simulation computations. In this paper, a mass correction is introduced into the ZSC model to make up the mass leakage, while a high-order difference is used to calculate the gradient of the order parameter to improve the accuracy. To verify the improved model, several three-dimensional multiphase flow simulations are carried out,including a bubble in a stationary flow, the merging of two bubbles, and the bubble rising under buoyancy. The numerical simulations show that the results from the present model are in good agreement with those from previous experiments and simulations. The present model not only retains the good properties of the original ZSC model, but also achieves the mass conservation and higher accuracy.

Lattice Boltzmann simulations of high-order statistics in isotropic turbulent flows

The lattice Boltzmann method （LBM） is coupled with the multiple-relaxation- time （MRT） collision model and the three-dimensional 19-discrete-velocity （D3Q19） model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high- order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investi- gated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity （ESS） method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This valida~ tion provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.

Orientational Order of C_(60) Molecules in Low-dimensional Lattices

The orientational order is an important concept of the materials composed of large molecules or clusters. Using high-resolution scanning tunneling microscopy, we have studied the orientational order of two kinds of typical low-dimensional C60 lattices: two-dimensional molecules array and C60(111) multi-layer film surface. Due to the change of the crystal field, their orientational orders are distinctly different from those in bulk system, and some unique phenomena appear.

The Lawson Partial Order on Wrpp Semigroups

In this paper,we introduce Lawson partial order ≤ w on wrpp semigroups.After obtaining some properties of ≤ w,we determine when ≤ w is(left;right) compatible with the multiplication.These results extend and enrich the related results of Lawson and GuoLuo on abundant semigroups,of Guo-Shum on rpp semigroups and of Liu-Guo on wrpp semigroups.

Logical Properties of Lattice Filter of Lattice Implication Algebra

Some new properties of lattice filters are presented based on the order-preserving mapping and lattice homomorphism, and two necessary and sufficient conditions for lattice filters under the chain type are given. Then, the relations between lattice filter and lattice implication algebras （LIAs）, i. e., the relations between lattice filter and LIA-filters, and the related properties are investigated. In addition, three necessary and sufficient conditions for LIA-filters are discussed. The obtained results may serve as some theoretical supports to lattice-valued logical system.

The Existence of Coupled Solutions for a Kind of Nonlinear Operator Equations in Partial Ordered Linear Topology Space

The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method. Some new existence results are obtained.

Continuity of Solution Mappings for Parametric Set Optimization Problems under Partial Order Relations

This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.

A New Relationship Between Partial Orders of Normal Matrices and Their Squares

A new relationship between partial orders of normal matrices and their squares is established.

Results of Associated Implication Algebra on a Partial Ordered Set

Some sufficient and necessary conditions that implication algebra on a partial ordered set is associated implication algebra are obtained, and the relation between lattice H implication algebra and associated implication algebra is discussed. Also, the concept of filter is proposed with some basic properties being studied.

Methane Oxidation to Synthesis Gas Using Lattice Oxygen of La_(1-x)Sr_xMO_(3-λ)(M =Fe,Mn) Perovskite Oxides Instead of Molecular Oxygen

In this paper, the partial oxidation of methane to synthesis gas using lattice oxygen of La1- SrxMO3-λ (M=Fe, x Mn) perovskite oxides instead of molecular oxygen was investigated. The redox circulation between 11% O2/Ar flow and 11% CH4/He flow at 900℃ shows that methane can be oxidized to CO and H2 with a selectivity of over 90.7% using the lattice oxygen of La1- SrxFeO3-λ (x≤0.2) perovskite oxides in an appropriate reaction condition, while the lost lattice x oxygen can be supplemented by air re-oxidation. It is viable for the lattice oxygen of La1- SrxFeO3-λ (x≤0.2) perovskite x oxides instead of molecular oxygen to react with methane to synthesis gas in the redox mode.

A New Class of Partial Orders

Let R be a unital*-ring.For any a,w,b∈R,we apply the w-core inverse to define a new class of partial orders in R,called the w-core partial order.Suppose that a,b∈R are w-core invertible.We say that a is below b under the w-core partial order if a_(w)^(#)a=a_(w)^(#)b and a_(w)a_(w)^(#)=bwa_(w)^(#),where a_(w)^(#)denotes the w-core inverse of a.Characterizations of the w-core partial order are given,and its relationships with several types of partial orders are also considered.In particular,we show that the core partial order coincides with the a-core partial order,and the star partial order coincides with the a*-core partial order.

SIMPLE LATTICE BOLTZMANN MODEL FOR TRAFFIC FLOWS

A lattice Boltzmann model with 5-bit lattice for traffic flows is proposed. Using the Chapman-Enskog expansion and multi-scale technique, we obtain the higher-order moments of equilibrium distribution function. A simple traffic light problem is simulated by using the present lattice Boltzmann model, and the result agrees well with analytical solution.