Certain sufficient conditions for a subclass of analytic functions involving Hohlov operator

Making use of the Hohlov operator, the authors obtain inclusion relations between the classes of certain normalized analytic functions. Relevant connections of our work with the earlier works are pointed out.     

On the properties of OWA operator weights functions with constant level of orness

The result of aggregation performed by the ordered weighted averaging (OWA) operator heavily depends upon the weighting vector used. A number of methods have been presented for obtaining the associated weights. In this paper, we present analytic forms of OWA operator weighting functions, each of which has properties of rank-based weights and a constant level of orness, irrespective of the number of objectives considered. These analytic forms provide significant advantages for generating the OWA weights over previously reported methods. First, the OWA weights can be efficiently generated by using proposed weighting functions without solving a complicated mathematical program. Moreover, convex combinations of these specific OWA operators can be used to generate the OWA operators with any predefined values of orness once specific values of orness are a priori stated by the decision maker. Those weights have a property of constant level of orness as well. Finally, the OWA weights generated at a predefined value of orness make almost no numerical difference with maximum entropy OWA weights in terms of dispersion.     

Interpolation with function space representation of membership functions

This paper generalizes a previous Cartesian approach for interpolating fuzzy rules comprised of membership functions with finite number of characteristic points. Instead of representing membership functions as points in Cartesian spaces, they now become elements in the space of square, integrable function. Interpolation is thus conducted between the antecedent and consequent function spaces. The generalized representation allows an extended class of membership functions satisfying two monotonicity conditions to be accommodated in the interpolation process. They include the popular bell-shaped membership functions, which were not possible before with the Cartesian representation. The work also extends the similarity triangle-based interpolation technique from the previous Cartesian representation to the new representation. Ensuing issues on computational complexity and nonunique conclusion are discussed. Other concepts such as spanning set and extensibility functions are also presented under the generalized framework. Examples to illustrate the extended approach and to compare with the Cartesian approach are given.     

Modeling the space of camera response functions

Many vision applications require precise measurement of scene radiance. The function relating scene radiance to image intensity of an imaging system is called the camera response. We analyze the properties that all camera responses share. This allows us to find the constraints that any response function must satisfy. These constraints determine the theoretical space of all possible camera responses. We have collected a diverse database of real-world camera response functions (DoRF). Using this database, we show that real-world responses occupy a small part of the theoretical space of all possible responses. We combine the constraints from our theoretical space with the data from DoRF to create a low-parameter empirical model of response (EMoR). This response model allows us to accurately interpolate the complete response function of a camera from a small number of measurements obtained using a standard chart. We also show that the model can be used to accurately estimate the camera response from images of an arbitrary scene taken using different exposures. The DoRF database and the EMoR model can be downloaded at http://www.cs.columbia.edu/CAVE.     

Subordination and superordination of a certain integral operator on meromorphic functions

Using the methods of differential subordination and superordination, sufficient conditions on the integral operator of meromorphic functions in the punctured unit disk for obtaining, respectively, the best dominant and the best subordinant are determined. New Sandwich-type results are also obtained.     

Finding better weight functions for generalized Shepard's operator on infinite intervals

In this paper, we investigate the difference of Shepard's generalized operators S _σ from the approximated set of data for various weight functions σ. Bounds are given for the sizes of the ‘bumps’ shown on the graph of S _σ for σ(d)=1/d in dimension N=1, and the best weight function σ for practical use is proposed.     

Superpositions of continuous functions defined on a Baire space

We consider uniformly continuous functions on a Baire space and introduce the notion of a continuity modulus of a function. We formulate a condition on the growth of the continuity modulus φ guaranteeing that superpositions of n-ary functions with continuity modulus φ do not exhaust all (n + 1)-ary functions with continuity modulus φ for any n. Moreover, negating this property leads to the inverse effect.     

Inverse spectral problems for impulsive Dirac operators with spectral parameters contained in the boundary and discontinuity conditions polynomially

An inverse spectral problem is studied for Dirac operators with discontinuities in the case when an spectral parameter appears not only in the differential equation but also in the one of boundary condition and jump conditions, polynomially.     

The Sturm-Liouville Eigenvalue Problem and NP-Complete Problems in the Quantum Setting with Queries

We show how a number of NP-complete as well as NP-hard problems can be reduced to the Sturm-Liouville eigenvalue problem in the quantum setting with queries. We consider power queries which are derived from the propagator of a system evolving with a Hamiltonian obtained from the discretization of the Sturm-Liouville operator. We use results of our earlier paper concering the complexity of the Sturm-Liouville eigenvalue problem. We show that the number of power queries as well the number of qubits needed to solve the problems studied in this paper is a low degree polynomial. The implementation of power queries by a polynomial number of elementary quantum gates is an open issue. If this problem is solved positively for the power queries used for the Sturm-Liouville eigenvalue problem then a quantum computer would be a very powerful computation device allowing us to solve NP-complete problems in polynomial time.      

A class of meromorphic multivalent functions with negative coefficients defined by a differential operator

For 0≤μ≤λ, 0<α≤1, 1/(p+1)<τ≤1, m∈N₀=N∪{0} and p∈N, a new class of meromorphic p-valent functions defined by means of the differential operator is introduced and systematically studied. Membership in this class is characterized through coefficient estimates. Distortion, radii of starlikeness and convexity of order , Hadamard convolution product, an integral operator, convex combinations and neighborhoods are also investigated.     

On the location of straight discontinuity intervals of arbitrary sectionally analytic functions by using complex path-independent integrals

The classical method of locating zeros and poles of analytic and meromorphic functions in the complex plane via the evaluation of complex path-independent integrals on closed contours surrounding the sought zeros and poles is generalized to become applicable (for the first time) to the location of straight discontinuity intervals of completely general sectionally analytic functions possessing such an interval. Such is the case e.g. in crack problems in plane elasticity or in airfoils in plane fluid dynamics. This generalization makes use of appropriate or arbitrary quadrature rules and, in this way, it leads to a completely numerical method. The method is illustrated in the case of a simple sectionally analytic function, where the classical Chebyshev and Legendre polynomials are used and numerical results are presented. Possible generalizations of the present results are also reported in brief and are strongly expected in future.     

Some preserving subordination and superordination of analytic functions involving the Liu-Owa integral operator

In this paper, we obtain some subordination and superordination-preserving results of analytic functions involving the Liu-Owa integral operator. Sandwich-type result is also obtained.     

Necessary conditions for exact controllability with a finite-dimensional input space

We derive necessary conditions for exact controllability of infinite-dimensional systems described by , where the generator A has a Riesz basis of eigenvectors and the input space is finite-dimensional. These conditions are in terms of the eigenvalues of A and the degree of unboundedness of B, but no further information about B is needed. Our results easily imply lack of exact controllability for a wide range of distributed parameter systems. It is known from partial differential equation (PDE) examples that the addition of damping into an exactly controllable second order system can destroy exact controllability. We discuss the effect of damping on such systems using our general conditions. We also give simple new proofs for results about the lack of exact controllability of hyperbolic systems in more than one space dimension.     

Approximation of functions by means of a new generalized Bernstein operator

In this paper we first use a probabilistic method to construct a linear positive polynomial operatorL _{m, r} ^α,β Bernstein type, depending on a non-negative integer parameterr and on two real parameters α and β, such that 0≤α≤β. Then we investigate the approximation properties of this operator mapping into itself the Banach spaceC[0,1] of real-valued continuous functions on [0,1]. A special attention is accorded to the case of the operatorL _m,r=L _m,r ^0,0 . We prove that the remainder of the approximation formula of a functionfεC[0,1] byL _m,r f can be represented either by means of divided differences, or in an integral form, obtained by using a classical theorem of Peano. We give also an asymptotic estimate for this remainder. The operatorL _m,r enjoys the variation diminishing property—in the sense of I. J. Schoenberg [15]. By extending the known inequalities of T. Popoviciu [12] and G. G. Lorentz [7], we evaluate the orders of approximation in terms of the modulus of continuity of the functionf or of its derivative. In the last section of this paper we determine the point spectrum of the operatorL _m,r and , finally, we present a quadrature formula which can be constructed by means of this operator. Dedicated to Professor Aldo Ghizzetti on his 75th birthday     

Stability of discrete-time systems joined with a saturation operator on the state–space: Generalized form of Liu-Michel’s criterion

A novel criterion for the global asymptotic stability of discrete-time systems in a state–space realization using saturation arithmetic was previously given by Liu and Michel. In their approach, as in most (or probably all) existing approaches, the matrix is assumed to be symmetric. In this communique, it is shown that their approach is such as to be extended to allow the use of an unsymmetric matrix . Taking note of this, a more general form of their criterion is presented. A modified form of the criterion is also presented. Examples show the effectiveness of the generalized approach. To the best of author’s knowledge, this communique is the first report of exploiting an unsymmetric to obtain a stability condition with reduced conservatism.     

Solving the forced Duffing equation with integral boundary conditions in the reproducing kernel space

In this paper, we propose a new method to solve the forced Duffing equation with integral boundary conditions. Its exact solution is represented in the form of a series in the reproducing kernel space. The n-term approximation u _n (x) of the exact solution u(x) is proved to converge to the exact solution. Some numerical examples are displayed to demonstrate the accuracy of the present method.