Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces

In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.

Acoustic characteristics of pulse detonation engine sound propagating in enclosed space

Acoustic characteristics of pulse detonation engine(PDE)sound propagating in enclosed space are numerically and experimentally investigated.The finite element software LS-DYNA is utilized to numerically simulate the PDE sound propagating in enclosed space.Acoustic measurement systems are established for testing the PDE sound in enclosed space,and the time-frequency characteristics of PDE sound in enclosed space are reported in detail.The experimental results show that the sound waveform of PDE sound in enclosed space are quite different from those in open space,and the reflection and superposition of PDE sound on the walls of enclosed space results in the sound pressure oscillating obviously.It is found that the peak sound pressure level(PSPL)and overall sound pressure level(OASPL)of PDE sound in enclosed space are higher than those in open space and their difference increases with the rise of propagation distance.The results of the duration of PDE sound indicate that the A duration of PDE sound in enclosed space is higher than that in open space except at measuring points located at 2-m and 5-m while the B duration is higher at each of all measuring points.Results show that the enclosed space has a great influence on the acoustic characteristic of PDE sound.This research is helpful in performing PDE experiments in enclosed laboratories to prevent the PDE sound from affecting the safety of laboratory environment,equipment,and staffs.

Numerical Simulation of Residual Circulation due to Bottom Roughness Variability Under Tidal Flows in A Semi-Enclosed Bay

Nowadays there are some chronic serious environmental problems, such as eutrophication, blue tide and so on, in a complicated coastal zone or a semi-enclosed bay, because the water exchanges between an inner bay and an outer sea is weak compared with the supply of contaminant. Under this situation, a method to improve the water quality by 3-dimensional small unsymmetrical structures has been proposed by Komatsu et al. In this paper, several numerical simulations of the tidal current and concentration for various arrangements of bottom roughness in a semi-enclosed model bay are carfled out with a depth-averaged 2-D numerical model. The model is solved by the hybrid finite analytic method with nonstaggered grid. And the SIMPLES algorithm with Rhie and Chow＇ s momentum interpolation technique is used for the simulation. The effect of Komatsu＇ s method for water purification is examined by numerical simulation. The result of numerical experiment indicates that it is possible to generate a new tidal residual current and to activate a tidal exchange by bottom roughness arrangement only.

Influence of Reclamation Works on the Marine Environment in a Semi-Enclosed Bay

The flow and seawater exchange rates have been predicted using a two-dimensional numerical model and a Lagrangian method for a semi-enclosed shallow bay where reclaiming and dredging works are scheduled. The wind effect on the flow and material transport has been emphasized, and a thirty-year mean value of wind has been considered in the numerical simulation. As a whole, even after the reclaiming and dredging are conducted, the flow pattern looks similar to the original state. However, velocity variations up to 20% to 100% appear in the vicinity of the construction area. In the case of summer wind forcing, the seawater exchange rate increases from 71.6% to 82.9% after the reclaiming and dredging, as indicated by a particle-tracking method. On the contrary, in the case of winter wind forcing, the seawater exchange rate appears to be 97.2% under natural conditions but decreases slightly to 93.2% after the reclaiming and dredging. Thus, the wind forcing plays an important role in controlling the seawater exchange rates. The seawater exchange rate is further improved by 15% if the dredging is simultaneously carried out with the reclaiming. This suggests that the dredging can be an effective means to mitigate the variation of flow.

Strong convergence theorems for nonexpansive semi-groups in Banach spaces

Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.

Investigation of wave characteristics in a semi-enclosed bay based on SWAN model validated with buoys and ADP-observed currents

In this study, the simulating waves nearshore (SWAN) model with a locally refined curvilinear grid system was constructed to simulate waves in Jervis Bay and the neighbouring ocean of Australia, with the aim of examining the wave characteristics in an area with special topography and practical importance. This model was verified by field observations from buoys and acoustic Doppler profilers (ADPs). The model precisions were validated for both wind-generated waves and open-ocean swells. We present an approach with which to convert ADP-observed current data from near the bottom into the significant wave height. Our approach is deduced from the Fourier transform technique and the linear wave theory. The results illustrate that the location of the bay entrance is important because it allows the swells in the dominant direction to propagate into the bay despite the narrowness of the bay entrance. The wave period T p is also strongly related to the wave direction in the semi-enclosed bay. The Tp is great enough along the entire propagating direction from the bay entrance to the top of the bay, and the largest Tp appears along the north-west coast, which is the end tip of the swells’ propagation.

Radial tidal current field in a semi-enclosed rectangular basin: formation and evolution

The radial tidal current field accounts for the formation of the radial sand ridges in the South Yellow Sea. Understanding the formation and evolution of this radial tidal current field is vital to assessing the morphodynamic features in the area. A semi-enclosed rectangular basin with and without a coastal barrier was schematized from the topography of the Bohai Sea and Yellow Sea. The 2D tidal current field in this basin was simulated using the DELFT3D-FLOW model. The concept of tidal wave refraction, which highlights the effect of the sloped or stepped submarine topography on the propagation of the tidal waves, was introduced to explain the formation of the radial tidal current field. Under the effect of tidal wave refraction, co-phase lines of the counterclockwise rotating tidal wave and incident tidal wave are transformed into clockwise and counterclockwise deflections, respectively, leading to the convergence and divergence of the flow field. Regardless of whether a coastal barrier exists or not, the outer radial tidal current field might emerge over certain topography. The responses of the radial tidal current field in this basin to the environmental variations such as coastline changes and bottom erosions were discussed. Results show that local protrusion near the focal point of the radial tidal current field will have limited effects on the location of the tidal system. However, a remarkable shift of the amphidromic point toward the entrance and central axis of this basin and a movement of the focal point of the radial tidal current field toward the entrance could be caused by the significant seaward coastline advance and submarine slope erosion.

More Properties of Semi-Linear Uniform Spaces

In this paper we shall generalize the definition given in [1] for Lipschitz condition and contractions for functions on a non-metrizable space, besides we shall give more properties of semi-linear uniform spaces.

NONLINEAR SEMIGROUPS AND DIFFERENTIAL INCLUSIONSIN PROBABILISTIC NORMED SPACES

The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.

COMMON FIXED POINT OF GENERALIZED WEAKLY CONTRACTIVE MAPS IN PARTIAL METRIC SPACES

In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized （ψ, Ф）-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.

CONTINUITY OF GENERALIZED INVERSES OF LINEAR OPERATORS IN BANACH SPACES AND ITS APPLICATIONS

The perturbation problem of generalized inverse is studied. And some new stability characteristics of generalized inverses were presented. It was also proved that the stability characteristics of generalized inverses were independent of the choice of the generalized inverse. Based on this result, two sufficient and necessary conditions for the lower semi-continuity of generalized inverses as the set-valued mappings are given.

On Irresolute Topological Vector Spaces

In this paper, our focus is to investigate the notion of irresolute topological vector spaces. Irresolute topological vector spaces are defined by using semi open sets and irresolute mappings. The notion of irresolute topological vector spaces is analog to the notion of topological vector spaces, but mathematically it behaves differently. An example is given to show that an irresolute topological vector space is not a topological vector space. It is proved that: 1) Irresolute topological vector spaces possess open hereditary property;2) A homomorphism of irresolute topological vector spaces is irresolute if and only if it is irresolute at identity element;3) In irresolute topological vector spaces, the scalar multiple of semi compact set is semi compact;4) In irresolute topological vector spaces, every semi open set is translationally invariant.

Constant modulus semi-blind space-time equalizer based on structure risk minimum criterion

A new adaptive filtering principle based on capability control and semi-blind method is presented. A new semi-blind space-time equalizer based on constant modulus characteristic and structure risk minimum （SRM） criterion is also proposed. The equalizer sufficiently exploits the learning information of communication signals by using the structure information of filter itself through capability control technique. Namely, it maximizes the amount of learning information to im- prove filter tracking performance. Simulations are carried out and the result is compared with that of typical recursive least squares space-time equalizer （RLS-STE） and constant modulus semi-blind space-time equalizer （ CM-SB-STE ）. The results show that, even if with insufficient training data, the SRM constant modulus semi-blind space-time equalizer （SCM-SB-STE） keeps good tracking per- formance, showing promises in mobile wireless communications.

AN EXTREMUM THEORY OF THE RESIDUAL FUNCTIONAL IN SOBOLEV SPACES W^(m,p)t(Ω)

In the present paper the concept and properties of the residual functional in Sobolev space are investigated. The weak compactness, force condition, lower semi-continuity and convex of the residual functional are proved. In Sobolev space, the minimum principle of the residual functional is proposed. The minimum existence theoreomfor J(u) =0 is given by the modern critical point theory. And the equivalence theorem or five equivalence forms for the residual functional equation are also proved.

COVERING PROPERTIES ON H-SPACES AND APPLICATIONS

Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.

Chen’s Inequalities for Submanifolds in (<i>&kgreen;, &#181</i>)-Contact Space Form with a Semi-Symmetric Non-Metric Connection

In this paper, we obtain Chen’s inequalities in (k,?μ)-contact space form with a semi-symmetric non-metric connection. Also we obtain the inequalites for Ricci and K-Ricci curvatures.