Continuous near-complete photocatalytic degradation of toluene by V/N-doped TiO_(2)loade d on honeycomb ceramics under UV irradiation

Photocatalytic degradation of volatile organic compounds(VOCs)is a significant applying aspect of pho-tocatalysis.Both the modulation of photocatalysts and the rational dispersion of them on supports are key for solar-driven VOC degradation.Conventional batch-type photoreactors have low efficiency while continuous-flow photoreactors suffer from the problem of incomplete removal of VOCs.Herein,aiming for continuous and complete degradation of toluene gas as the target contaminant,continuous-flow pho-tocatalytic degradation reactors were made by adhering the vanadium and nitrogen codoped TiO_(2)on honeycomb ceramics(V/N-TiO_(2)@HC)by a simple sol-gel method.In such a reactor,the rich ordered pores in the HC accelerate mass transport of toluene,and the introduction of V/N dopants narrows the bandgap and widens the light absorption range of TiO_(2),together resulting in continuous and nearly-complete pho-tocatalytic degradation of toluene.The unique and stable structure of HC allows the photocatalysts to be reused.The degradation rate of toluene gas can reach 97.8%,and after 24 rounds of photocatalytic degra-dation,there is still a degradation rate of 96.7%.The impacts of loading times and gaseous flow rate on the photocatalytic performance of V/N-TiO_(2)@HC are studied in detail.Our study provides a practical so-lution for the continuous and complete photocatalytic degradation of VOCs and opens a new application field for HC.

Nonlocal controllability for semilinear problems in Banach spaces

If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t） = Au （t） ＋ Bx（ t） ＋ f（ t, u（t） ）, 0≤t ≤ T with nonlocal initial condition u（0） = u0 ＋ g（u） is discussed in Banach space X. The results show that if semigroup S（t） is strongly continuous, the functionsf and g are compact and the control B is bounded, then it is nonlocally controllable. The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S（t） is compact or strongly continuous. For illustration, a partial differential equation is worked out.

The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators

This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint completely continuous operator T.Under the condition that the approximate operator Th converges to T in norm,it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T.(We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements,nonconforming elements and mixed elements of self-adjoint elliptic differential operators eigenvalue problems,and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue.

Weak and strong convergence of an explicit iteration scheme with perturbed mapping for nonexpansive mappings

In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration scheme are established. In particular, necessary and sufficient conditions for strong convergence of this explicit iteration scheme are obtained. At last, some useful corollaries for strong convergence of this explicit iteration scheme are given.

ON A NONLINEAR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION IN TWO VARIABLES

Using a fixed point theorem of Krasnosel＇skii type, this article proves the exis- tence of asymptotically stable solutions for a Volterra-Hammerstein integral equation in two variables.

NEW FIXED POINT THEOREMS FOR P_1-COMPACT MAPPINGS IN BANACH SPACES

E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.

Space of Operators and Property (MB)

In this paper, a new class of Banach spaces, termed as Banach spaces with property (MB), will be introduced. It is stated that a space X has property (MB) if every V -subset of X* is an L-subset of X* . We describe those spaces which have property (MB) . Also, we show that if a Banach space X has property (MB) and Banach space Y does not contain , then every operator is completely continuous.

Hypercontinuous Posets

The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual of P is generalized completely continuous;(3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO A SYSTEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH DELAY

Using a fixed point method, in this paper we discuss the existence and uniqueness of positive solutions to a class system of nonlinear fractional differential equations with delay and obtain some new results.

EXISTENCE OF NON-TRIVIAL SOLUTION FOR SUPERLINEAR SYSTEM OF INTEGRAL EQUATIONS AND ITS APPLICATIONS

In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations.

THE EXISTENCE OF ALMOST PERIODIC SOLUTION TO A CLASS OF ALMOST PERIODIC DIFFERENTIAL SYSTEM

By means of the fixed point theorem and exponential dichotomy, in this paper we investigate the existence of almost periodic solutions to a class of ndimensional almost periodic systems, which is more general than the systems in [1-2]. We generalize and improve some results in [3].

BOUNDARY VALUE PROBLEM TO DYNAMIC EQUATION ON TIME SCALE

In this paper we consider a nonlinear first-order boundary value problem on a time scale. The existence results of three positive solutions are obtained using fixed point theorems. Finally,examples are presented to illustrate the main results.