Numerical Treatments of Functional Fredholm Integral Equation in 2D with Discontinuous Kernels

This work proposes a new definition of the functional Fredholm integral equation in 2D of the second kind with discontinuous kernels (FT-DFIE). Furthermore, the work is concerned to study this new equation numerically. The existence of a unique solution of the equation is proved. In addition, the approximate solutions are obtained by two powerful methods Toeplitz Matrix Method (TMM) and Product Nystr?m Methods (PNM). The given numerical examples showed the efficiency and accuracy of the introduced methods.

Functional Integrals and Collective Excitations in Boson-Fermion Model

In this paper, collective excitations in the boson-fermion model are investigated by means of functional integration method. The equations of energy gap and excitation spectrum are derived. Moreover, the Bose energy spectrum of zero wave vector Fermi fields is also calculated.

Functional Integrals and Free Energy in sine-Gordon-Thirring Model with Impurity Coupling

The free energy at low temperature in 1D sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon-Thirring model, free energy is obtained from perturbation expansion of functional determinant. Moreover, the free energy of massive model is calculated by use of an auxiliary Bose field method.

Functional Integrals and Quantum Fluctuations on Two-Dimensional Noncommutative Space-Time

The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.

Functional Integrals and Excitation Energy in Three-Band Hubbard Model

The normal and anomalous Green＇s functions of antiferromagnetie state in three-band Hubbard model are studied by using functional integrals and temperature Green＇s function method. The equations of energy spectrum are derived. In addition, excitation energy of Fermi fields are calculated under long wave approximation.

Functional Integrals and Variational-Cumulant Expansion in sine-Gordon-Thirring Model

The free energy in 1D sine-Gordon- Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strongcoupling range of fcrmion systems.

ON THE DISTRIBUTION OF VALUES AND DEFICIENT FUNCTION OF A GENERAL RANDOM INTEGRAL FUNCTION

Under suitable conditions on {X-n}, the author obtains the important results: it is almost sure that the random integral function f(w) = Sigma (infinity)(n=0) X(n)z(n) (of finite positive order) has no deficient function, and any direction is a Borel direction (without finite exceptional value) of f(w).

Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints

A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with uncertain and continuous functions in the process of backstepping design.The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint,but also mixes the states and errors to directly constrain the state,reducing the conservativeness of the constraint satisfaction condition.Considering that the states in most nonlinear systems are immeasurable,a fuzzy adaptive states observer is constructed to estimate the unknown states.Combined with adaptive backstepping technique,an adaptive fuzzy output feedback control method is proposed.The proposed control method ensures that all signals in the closed-loop system are bounded,and that the tracking error converges to a bounded tight set without violating the full state constraint.The simulation results prove the effectiveness of the proposed control scheme.

AREA INTEGRAL FUNCTIONS FOR SECTORIAL OPERATORS ON L^p SPACES

Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.

Understanding biological functions through molecular networks

The completion of genome sequences and subsequent high-throughput mapping of molecular networks have allowed us to study biology from the network perspective. Experimental, statistical and mathematical modeling approaches have been employed to study the structure, function and dynamics of molecular networks, and begin to reveal important links of various network properties to the functions of the biological systems. In agreement with these functional links, evolutionary selection of a network is apparently based on the function, rather than directly on the structure of the network. Dynamic modularity is one of the prominent features of molecular networks. Taking advantage of such a feature may simplify network-based biological studies through construction of process-specific modular networks and provide functional and mechanistic insights linking genotypic variations to complex traits or diseases, which is likely to be a key approach in the next wave of understanding complex human diseases. With the development of ready-to-use network analysis and modeling tools the networks approaches will be infused into everyday biological research in the near future.

Engrafted newborn neurons could functionally integrate into the host neuronal network

The limited capability to regenerate new neurons following injuries of the central neural system（CNS）still remains a major challenge for basic and clinical neuroscience.Neural stem cells（NSCs）could nearly have the potential to differentiate into all kinds of neural cells in vitro.

α-times Integrated Cosine Operator Functions with Growth ω

For a continuous,increasing functionω:[0,∞)→C of finite exponential type,we establish a Hille-Yosida type theorem for strongly continuous α-times(α>0)integrated cosine operator functions with O(ω).It includes the corresponding results for n-times integrated cosine operator functions that are polynomially bounded and exponentially bounded.

On the generalized Cauchy function and new Conjecture on its exterior singularities

This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x ＋ iy plane consisted of the simply connected open domain D ＋ bounded by C and the open domain D outside C. （1） With f （z） assumed to be C n （n ∞-times continuously differentiable） z ∈ D ＋ and in a neighborhood of C, f （z） and its derivatives f （n） （z） are proved uniformly continuous in the closed domain D ＋ = [D ＋ ＋ C]. （2） Cauchy’s integral formulas and their derivatives z ∈ D ＋ （or z ∈ D ） are proved to converge uniformly in D ＋ （or in D = [D ＋C]）, respectively, thereby rendering the integral formulas valid over the entire z-plane. （3） The same claims （as for f （z） and J[ f （z）]） are shown extended to hold for the complement function F（z）, defined to be C n z ∈ D and about C. （4） The uniform convergence theorems for f （z） and F（z） shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle ｜z｜ = 1 such that the four general- ized Hilbert-type integral transforms are proved. （5） Further, the singularity distribution of f （z） in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . （6） A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. （7） Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. （8） Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f （z） in domain D , based on the continuous numerical value of f （z） z ∈ D ＋ = [D ＋ ＋ C], is presented for resolution as a conjecture.

AREA INTEGRAL FUNCTIONS AND H∞ FUNCTIONAL CALCULUS FOR SECTORIAL OPERATORS ON HILBERT SPACES

Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s results on H∞ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.

THE REGULARITY OF QUASI-MINIMA AND ω-MINIMA OF INTEGRAL FUNCTIONALS

In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf（x, u, Du）dx, （1） where Ω is an open subset of Euclidean N-space （N ≥ 3）, u：Ω → R,the Carath′eodory function f satisfies the critical Sobolev exponent growth condition ｜Du｜^p＊ ｜u｜^p＊-a（x） ≤ f（x,u,Du） ≤ L（｜Du｜^p＋｜u｜^p＊ ＋ a（x））, （2） where L≥1, 1pN,p^＊ = Np/N-p , and a（x） is a nonnegative function that lies in a suitable Lp space. In the second part, we study the locally Hlder continuity of ω-minima of （1）. Our method is to compare the ω-minima of （1） with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland’s variational principal.

THE INTEGRATION OF ALGEBROIDAL FUNCTIONS

In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the defi- nition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.

Functional Integral Approach to Transition Temperature of a Homogeneous ImperfectBose Gas

A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresponding ideal gas. We obtain the expression of the transition temperature shift as , where n is the density of particle number and a is the scattering length. The result has never been reported in the literature.

An integrated approach to evaluation on ecological service functions for urban green space and its application

This methodological investigation deals with measurement and valuation of ecological service functions for urban green space. Social, economic and ecological dimensions for such types of function were analyzed and a concept “integrated ecological service functions” (IESF) was put forward for evaluation. Based upon this conceptual approach, an index system for measuring IESF for urban green space was established. With a methodological integration of fuzzy mathematics, decision making analysis and Delphi method, an AHP fuzzy evaluation techniques for IESF for urban green space, called AFIFUG method, was developed. Such a method has been directly applied to the land use strategic planning of Tianjin out ring green belt(TOGB), and its analysis results have been successfully put into operation.

ON THE EXISTENCE OF INFINITELY MANY CRITICAL POINTS OF THE EVEN FUNCTIONAL integral from n=Q to (F(x,u,Du))+integral from n=■Q to (G(x,u))

In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.

THE CAUCHY TYPE INTEGRAL FOR M-ANALYTIC FUNCTION AND ITS APPLICATION

In this paper, the Cauchy type integral for M-analytic function is investigated which is by definition the regular solution of the elliptic system f_x+Mf_y=0, where M is a constant m×m matrix without any real eigenvalues and f is an m×q matrix.