Fixed point theorems in homotopically trivial spaces

We introduce a new concept of generalized Knaster–Kuratowski–Mazurkiewicz (KKM) family of sets and related to this we obtain fixed point theorems and sections results in homotopically trivial spaces.     

The electronic origin of unusually large nJFN coupling constants in some fluoroximes

SOPPA(CCSD) calculations show that the FC term is the most important contribution to the through‐space transmission of J_FN coupling constants for the fluoroximes studied in this work. Because of the well‐known behavior of FC term, a new rationalization for the experimental ^TSJ_FN SSCC is presented. It is mainly based on the overlap matrix (S_ij) between fluorine and nitrogen lone pairs obtained from NBO analyses. An expression is proposed to take into account the influence of the electronic density (D_ij) between coupled nuclei as well as the s% character at the site of the coupling nuclei of bonds and non‐bonding electron pairs involved in D_ij. In using this approach, a linear correlation between ^TSJ_FN versus D_ij is obtained. The most important aspect of this rationalization is related to the facility for understanding the behavior of some unusual experimental coupling constants. It is shown that, at least in this case, the electronic origin of the so‐called through‐space coupling is transmitted through to the overlap of orbitals on the coupled atoms, suggesting that, at least for these compounds, instead of through‐space coupling, it should better be dubbed as ‘through overlapping orbital coupling’. Copyright © 2013 John Wiley & Sons, Ltd.     

Common fixed points of almost generalized contractive mappings in ordered metric spaces

The existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved. Some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature.     

Compatible weighting method with rank order centroid: Maximum entropy ordered weighted averaging approach

In a situation where imprecise attribute weights such as a rank order are captured, various approximate weighting methods have been proposed to aid multiattribute decision analysis. Among others, it is well known that the rank order centroid (ROC) weights result in the highest performance in terms of the identification of the best alternative under the ranked attribute weights. In this paper, we aim to reinterpret the meaning of the ROC weights and to develop a compatible weighting method that is based on other well-established academic disciplines. The ordered weighted averaging (OWA) method is a nonlinear aggregation method in that the weights are associated with the objects reordered according to their magnitudes in the aggregation process. Some interesting semantics can be attached to the approximate weights in view of the measure developed in the OWA method. Furthermore, the weights generated by the maximum entropy method show equally compatible performance with the ROC weights under some condition, which is demonstrated by theoretical and simulation analysis.     

Well-posedness of the fractional Ginzburg–Landau equation

In this paper, we investigate the well-posedness of the real fractional Ginzburg–Landau equation in several different function spaces, which have been used to deal with the Burgers’ equation, the semilinear heat equation, the Navier–Stokes equations, etc. The long time asymptotic behavior of the nonnegative global solutions is also studied in details.     

Nonasymptotic analysis of robust regression with modified Huber's loss

To achieve robustness against the outliers or heavy-tailed sampling distribution, we consider an Ivanov regularized empirical risk minimization scheme associated with a modified Huber's loss for nonparametric regression in reproducing kernel Hilbert space. By tuning the scaling and regularization parameters in accordance with the sample size, we develop nonasymptotic concentration results for such an adaptive estimator. Specifically, we establish the best convergence rates for prediction error when the conditional distribution satisfies a weak moment condition.     

Multiple solutions for a nonlinear and non-homogeneous problem in Orlicz-Sobolev spaces

We study a non-homogeneous boundary value problem in a smooth bounded domain in R^N. We prove the existence of at least two non-negative and non-trivial weak solutions. Our approach relies on Orlicz-Sobolev spaces theory combined with adequate variational methods and a variant of Mountain Pass Lemma.     

Influence of slip condition on the peristaltic transport in an asymmetric channel with heat transfer: An exact solution

The mechanism of peristaltic magnetohydrodynamic (MHD) flow based on slip and heat transfer effects is studied in an asymmetric channel. An incompressible viscous fluid fills the porous space inside the channel. Long wavelength and zero Reynolds number approximation are used in the flow modeling. Expressions of stream function, longitudinal pressure gradient, and temperature are developed. Various interesting phenomena associated with peristalsis, such as pumping and trapping, are discussed in detail. Further the effects of various pertinent parameters on temperature field and heat transfer coefficient are explained with the help of graphs and tables. It is found that pressure rise over one wavelength decreases in pumping region for large values of slip parameter. Similar behavior is observed for temperature field by increasing the slip parameter. However, the volume of trapped bolus decreases by increasing the slip parameter. Copyright © 2010 John Wiley & Sons, Ltd.     

Spaces of idempotent measures of compact metric spaces

We investigate certain geometric properties of the spaces of idempotent measures. In particular, we prove that the space of idempotent measures on an infinite compact metric space is homeomorphic to the Hilbert cube.     

关于拓扑对策中的I2(κ)(∈)I(κ)问题

证明了如果空间类K为D-空间类或闭遗传不可约空间类,则I（K）包含K.这一结果对于K为D空间类和闭遗传不可约空间类,肯定地回答了I（K）是否包含I^2（K）问题.