The Image content detectability and Image structure preservation are closely related concepts with undeniable role in Image quality assessment. However, the most attention of Image quality studies has been paid to Image structure evaluation, few of them focused on Image content detectability. Examining the Image structure was firstly introduced and assessed in Structural SIMilarity (SSIM) Measure, in which, the definition of Image structure is constrained to the intensity covariance between the reference and test Images. Indeed, this Measure discerns the luminance changes in the pixels of the reference and test Images, by employing the low-level statistical features. But this minimal definition of Image structure does not cover the issue of Image content detectability. In this study, we found that the status of Image region Smoothness can reflect its structural content. So, we proposed a novel Smoothness Measure based on the maximally stable extremal regions (MSER) descriptor. Subsequently, we proposed a novel Image structural similarity Measure, in which the fidelity of Image region Smoothness is also taken into account. Experimental results on five popular benchmark Image databases, including A57, LIVE, CSIQ, TID2008 and TID2013, are provided, which confirm that the proposed approach has a reasonable prediction performance compared to the state-of-the-art Image quality metrics.

In this paper we will try to introduce a good Smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should have.

The concept of rotundity is not far from differentiability. There are several papers in the literature devoted to the study of relations between rotundity and Smoothness in Banach spaces. In this paper, we study new relations between some kinds of rotundity and Smoothness in Banach spaces. In particular, we investigate relations between one kind of rotundity, which is called strongly very rotund, and very Smoothness, in Banach spaces. A Banach space is rotund if the midpoint of every two distinct points of unit sphere is in the open unit ball of the Banach space. A Banach space X is smooth if its norm is Gateaux differentiable at every non-zero point of the space and it is very smooth if the norm is very Gateaux differentiable, that is, the second dual norm in the second dual of X is Gateaux differentiable at every non zero point of  X.

In this study digital Image correlation (DIC) technique combined with a high speed video system was used to predict movement of particles in a water model. Comparing with Particle-Image velocimetry (PIV) technique, it provides a low cost alternative approach to visualize flow fields and was successfully employed to predict the movement of particles in a water model at different submergence depth using gas injection. As the submergence depth increases, the number of the exposed eye is reduced accordingly. At 26.4 cm submergence depth, an exposed eye was found at 1.3 of the submergence depth, whereas two exposed eyes were observed at 1.2 depth and near the bottom wall at 24 cm submergence depth.

Some criteria for approximative compactness of every weakly* closed convex set of Orlicz function spaces equipped with the Luxemburg norm are given. Although, criteria for approximative compactness of Orlicz function spaces equipped with the Luxemburg norm were known, we can easily deduce them from our main results.

AbstractThe aim of this study was to investigate the validity, reliability and factor structure of the "How I Think" questionnaire to assess cognitive distortions in Iranian students. The present research design is descriptive and psychometric studies. The statistical population of this study included all male high school students in city Dezful in the academic year 1399-1400, from which 316 students were selected by multi-stage random sampling and completed the How I think and Bass and Perry Aggression Questionnaires (for Convergent validity). Factor analysis, Cronbach's alpha and Pearson correlation were used to analyze the data using SPSS and AMOS 20 software. The results of factor analysis showed that the questionnaire consists of six factors and has good fit indices. The convergent validity of this questionnaire indicated a satisfactory correlation between the dimensions of the scale "How I think" with the Aggression Questionnaire (p <0.01). Cronbach's alpha and Split- half coefficients for the whole scale and its dimensions ranged from 0.66 to 0.92.The conclusion is that the Persian version of the "How do I think" questionnaire for measuring cognitive distortions in Iranian students has acceptable psychometric properties and can be used as a valid tool in research, educational and clinical situations.