On Mutual Transform Between Number-Difference State and Phase State Corresponding to Operational Phase Operator

In the mutual transform between the number-difference state and the phase state corresponding to the operational phase operator we find that there exists an end-point ambiguousness. This problem can be avoided by Lighthill's method.

SINGULAR INTEGRAL OPERATORS AND SINGULAR QUADRATURE OPERATORS ASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS OF THE FIRST KIND AND THEIR APPLICATIONS

In this paper, we discuss some singulal integral operators, singular quadrature operators and discrethation matrices associated with singular integral equations of the first kind, and obtain some useful Properties for them. Using these operators we give a unified framework for various collocation methods of numerical solutions of singular integral equations of the fine kind, which appears very simple.

L^p CONTINUITY OF HRMANDER SYMBOL OPERATORS OpS_(0,0) ~m AND NUMERICAL ALGORITHM

If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ （0 ≤δ 〈 ρ≤ 1）. In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 （= F 0 , 2 1 ） → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p （= F 0 , 2 p ） → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.

Interval-valued intuitionistic fuzzy aggregation operators

The notion of the interval-valued intuitionistic fuzzy set （IVIFS） is a generalization of that of the Atanassov＇s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVlFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the t.ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.

Bosonic Operator Realization of Hamiltonian for a Superconducting QuantumInterference Device

Based on the appropriate bosonic phase operator diagonalized in the entangled state representation we construct the Hamiltonian operator model for a superconducting quantum interference device. The current operator and voltage operator equations are derived.

EQUIVALENCE THEOREM ON WEIGHTED SIMULTANEOUS L-APPROXIMATION BY MEANS OF SZASZ-KANTOROVICH OPERATORS AND BASKAKOV-KANTOROVICH OPERATORS

The intention of this paper is to give direct and converse results on weighted simultaneous approximation by means of Sz(?)sz-Kantorovich operators and Baskakov-Kantorovich operators in L_p-norms using the weighted Ditzian-Totik modulus of smoothness.

Gazeau–Klauder coherent states examined from the viewpoint of diagonal ordering operation technique

In this paper we investigate the Gazeau–Klauder coherent states using a newly introduced diagonal ordering operation technique, in order to examine some of the properties of these coherent states. The results coincide with those obtained from other purely algebraic methods, but the calculations are greatly simplified. We apply the general theory to two cases of Gazeau–Klauder coherent states： pseudoharmonic as well as the Morse oscillators.

ON CONSERVATIVE APPROXIMATION BY LINEAR POLYNOMIAL OPERATORS AN EXTENSION OF THE BERNSTEIN'S OPERATOR

In this work we slwly linear polynomial operators preserving some consecutive i-convexities and leaving in-verant the polynomtals up to a certain degree. First we study the existence of an incompatibility between the conservation of cenain i-cotivexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DcVore about the Bernstein's operator ts extended. Finally, from these results a genera'ized Bernstein's operator is obtained.

Operative link on gastritis assessment stage is an appropriate predictor of early gastric cancer

AIM: To assess the predictive value of Operative Link on Gastritis Assessment (OLGA) and Operative Link on Gastric Intestinal Metaplasia Assessment (OLGIM) stages in gastric cancer.METHODS: A prospective study was conducted with 71 patients with early gastric cancer (EGC) and 156 patients with non-EGC. All patients underwent endoscopic examination and systematic biopsy. Outcome measures were assessed and compared, including the Japanese endoscopic gastric atrophy (EGA) classification method and the modified OLGA method as well as the modified OLGIM method. Helicobacter pylori (H. pylori) status was determined for all study participants. Stepwise logistic regression modeling was performed to analyze correlations between EGC and the EGA, OLGA and OLGIM methods.RESULTS: For patients with EGC and patients with non-EGC, the proportions of moderate-to-severe EGA cases were 64.8% and 44.9%, respectively (P = 0.005), the proportions of OLGA stages III-IV cases were 52.1% and 22.4%, respectively (P < 0.001), and the proportions of OLGIM stages III-IV cases were 42.3% and 19.9%, respectively (P < 0.001). OLGA stage and OLGIM stage were significantly related to EGA classification; specifically, logistic regression modeling showed significant correlations between EGC and moderate-to-severe EGA (OR = 1.95, 95% CI: 1.06-3.58, P = 0.031) and OLGA stages III-IV (OR = 3.14, 95%CI: 1.71-5.81, P < 0.001), but no significant correlation between EGC and OLGIM stages III-IV (P = 0.781). H. pylori infection rate was significantly higher in patients with moderate-to-severe EGA (75.0% vs 54.1%, P = 0.001) or OLGA/OLGIM stages III-IV (OLGA: 83.6% vs 55.8%, P < 0.001; OLGIM: 83.6% vs 57.8%, P < 0.001).CONCLUSION: OLGA classification is optimal for EGC screening. A surveillance program including OLGA stage and H. pylori infection status may facilitate early detection of gastric cancer.

Some New Fixed Point Theorems in Probabilistic Metric Spaces

In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.

A REAL-VALUED GENETIC ALGORITHM FOR OPTIMIZATION PROBLEM WITH CONTINUOUS VARIABLES

A real valued genetic algorithm(RVGA) for the optimization problem with continuous variables is proposed. It is composed of a simple and general purpose dynamic scaled fitness and selection operator, crossover operator, mutation operators and adaptive probabilities for these operators. The algorithm is tested by two generally used functions and is used in training a neural network for image recognition. Experimental results show that the algorithm is an efficient global optimization algorithm.

TENSOR SUM AND DYNAMICAL SYSTEMS

In this paper we introduce the concept of tensor sum semigroups. Also we have given the examples of tensor sum operators which induce dynamical system on weighted locally convex function spaces.

SOLUTIONS OF THE GENERALn－TH ORDER VARIABLE COEFFICIENTS LINEAR DIFFERENCE EQUATION

In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski’s sequence convergence.After turning ageneral variable coefficient linear difference equation of order n into a set of operatorequations.we can obtain the solutions of the general n-th order variable coefficientlinear difference equation.

The Quantitative Analysis on Leverage and its Effects

Leverage of modem enterprise＇s financial management includes operating leverage and financial leverage. Both of them exist objectively, are not changeable with human＇s minds. They enlarge enterprise＇s benefit and risk, so they have both positive and negative effects. The degrees of them are measured as DOL and DFL. In financial management, the relationship between DOL and operating risk has regularity in quantity, and so does the relationship between DFL and financial risk.

Completeness in the sense of Cauchy principal value of the eigenfunction systems of infinite dimensional Hamiltonian operator

The properties of eigenvalues and eigenfunctions of the infinite dimensional Hamiltonian operators are studied, and the sufficient conditions of the completeness in the sense of Cauchy principal value of the eigenfunction systems of the infinite dimensional Hamiltonian operators are given. In the end, concrete examples are constructed to justify the effectiveness of the criterion.

Weighted Compact Commutator of Bilinear Fourier Multiplier Operator

Let T_σ be the bilinear Fourier multiplier operator with associated multiplier σ satisfying the Sobolev regularity that sup κ∈Z∥σ_κ∥W^s(R^(2n))< ∞ for some s ∈ (n, 2n]. In this paper, it is proved that the commutator generated by T_σ and CMO(R^n) functions is a compact operator from L^(p1)(R^n, w_1) × L^(p2)(R^n, w_2) to L^p(R^n, ν_w) for appropriate indices p_1, p_2, p ∈ (1, ∞) with1 p=1/ p_1 +1/ p_2 and weights w_1, w_2 such that w = (w_1, w_2) ∈ A_(p/t)(R^(2n)).

Normal Operators Similar to Irreducible Operators

A complete characterization of normal operators which are similar to irreducible operators and some related results are given.

Nijenhuis Operators on n-Lie Algebras

In this paper, we study(n-1)-order deformations of an n-Lie algebra and introduce the notion of a Nijenhuis operator on an n-Lie algebra, which could give rise to trivial deformations. We prove that a polynomial of a Nijenhuis operator is still a Nijenhuis operator. Finally, we give various constructions of Nijenhuis operators and some examples.

Algebraic equations and non-integer orders of fractal operators abstracted from biomechanics

The previous study implies that the fractional operator may stem from the motion in fractal space or the motion of fractal structure abstracted from biological systems.This study is devoted to answering another essential question,i.e.,what determines the order of the fractional operator in fractal structure?This paper generalizes the concept of the fractal cell defined in the previous paper,explores the tree-like and net-like fractal structures with higher-order topology,abstracts two classes of higherorder fractal operators,and derives the algebraic equations satisfied by the fractal operators to answer this question.It is proved that the solutions of the algebraic equations for fractal operators are deterministically related to the fractional-time operators that are usually of fractional orders.By the Vieta theorem,the relation between the solutions of algebraic equations for fractal operators and the physical-component operators is clarified,and the duality constraints between them are revealed.The solutions of the fractal operators show that the topological invariants of the fractal cells are one of the essential factors in determining the fractional orders.A conjecture on the specific order of the fractional-time operator in fractal structure is proposed.

Sharp constants for a class of multilinear integral operators and some applications

We investigate a class of multilinear integral operators with the nonnegative kernels, and prove that the norms of the operators can be obtained by integral of the product of the kernel function and finitely many basic functions. Using the integral, we can easily calculate the sharp constants for the multilinear Hilbert inequality, the generalized Hardy-Littlewood-Sobolev inequality and the multilinear Hardy operator.