Introduction: Sand and dust storms (SDS) are natural phenomena that commonly occur in semi-arid and arid parts of the world due to wind erosion and atmospheric turbulence near the Earth's surface. SDS can spread large amounts of dust and aerosol particles in the environment. These storms reduce the visibility to less than 1000 meters, which can affect the various activities and infrastructures. These phenomena have also harmful impacts on human health, and the environment. In recent years, the occurrence of the SDS has increased considerably in Iran, northeastern Iraq, Syria, and southern Saudi Arabia in summer and spring. Therefore, it is important to identify the spatial extent of SDS more accurately. With the development of satellite technologies, remote sensing has played an important role to dust detection due to the possibility of providing extensive spatial coverage. MODIS provides appropriate images for studying SDS. Commonly used MODIS-based dust indices, such as Brightness Temperature Difference (BTD) index between band 32 and band 31 (BTD32-31), and band 20 and 31 (BTD20-31), and Normalize Difference Dust Index (NDDI) can’ t monitor SDS more accurately. These indices have some issues with differentiating between SDS and bright surfaces like deserts, dark surfaces like vegetation regions, clouds, and water bodies. So in this paper, a new dust detection algorithm, which is based on Reflective and thermal infrared bands was introduced and used to identify two dust events in Asia that occurred July 15 and 16, 2008. Methodology: The study area is located in southwestern Asia, which includes Iraq, northeastern Syria, and western Iran. In this research, MODIS Level 1B (L1B) data from the Terra satellite (MOD021KM), and Aerosol Optical Depth (AOD) product of MODIS Level 2 aerosol data (MCD19A2) were utilized to identify SDS and validate the results, respectively. The proposed method was performed in five steps. In the first step, data were mapped to the UTM coordinate system using the MODIS Conversion Toolkit (MCTK) of ENVI 5. 3, and then converted to the calibrated reflectance values of bands 1, 3, 4, and 7, and brightness temperature values of bands 20, 31, and 32. In the second step, BTD32-31, BTD20-31, NDDI, and the proposed new algorithm, which consists of a linear combination of blue (0. 459-0. 479 μ m), Shortwave Infrared (SWIR 2. 105-2. 155 μ m), and three Thermal Infrared (TIR 3. 66-3. 84, 10. 78-11. 28, and 11. 77-12. 27 μ m) bands of MODIS, were calculated. In the third step, the appropriate thresholds for separating dusty pixels from dust-free areas were chosen by visually interpreting and comparing the results of the indices with the true color RGB MODIS images. In the fourth step, by applying the threshold of 290 Kelvin to band 31, the cloudy pixels were separated, and finally, the SDS was identified. In the last step, the performance of the algorithms was validated using the SDS extracted by MODIS true-color images, and MODIS AOD product. Discussion and Results: According to the results of the calculated indices, BTD32-31 could not distinguish between SDS and the other regions, such as deserts, vegetation regions, and water bodies, BTD20-31 could not differentiate between SDS and bright surfaces, such as deserts, and NDDI could not separate SDS from dark surfaces, such as vegetated areas. In comparison with the mentioned indices, the proposed algorithm was able to detect SDS with respect to bright surfaces, dark surfaces, and water bodies, such as Tharthar Lake in Iraq, and the Persian Gulf. This indicated that the proposed algorithm can also represent the dust sources more accurately than BTD32-31, BTD20-31, and NDDI. The spectral profile of the North-South and West-East transects of BTD32-31, BTD20-31, NDDI, and the proposed algorithm also demonstrated that the proposed algorithm has been quite successful in separating dusty pixels from dust-free areas, while the other indices had difficulty differentiating between dust and the other regions by applying a proper threshold. The results of the validation of the dust detection indices to SDS extracted by MODIS true-color images showed that the proposed algorithm, BTD20-31, NDDI, and BTD32-31 detected SDS extent with an overall accuracy of 88. 59%, 81. 39%, 73. 56%, and 57. 92% on July 26, and 96. 34%, 94. 15%, 61. 95%, and 68. 89% on July 27, respectively. The results of the validation of the dust detection indices to SDS extracted by MODIS AOD product also demonstrated that the proposed algorithm, BTD20-31, NDDI, and BTD32-31 detected SDS extent with an overall accuracy of 82. 1%, 74. 02%, 77. 62%, and 51. 9%, respectively. Conclusion: The proposed SDS detection algorithm introduced in this study was based on linear combination of Reflective bands blue (band 3), and SWIR (band 7), and thermal infrared bands 20, 31, and 32. The results indicated that this algorithm was able to effectively separate SDS from dark surfaces, bright surfaces, and water bodies with choosing proper threshold value. It was also possible to detect dust sources by this algorithm. According to the results of this algorithm, the SDS originated from the eastern Syria, Iraqi-Syrian border, northwestern, southeastern, and southern Iraq, and northern Saudi Arabia. Results also indicated that BTD32-31, BTD20-31, NDDI had limitations in separating SDS from the other regions, bright surfaces, and dark surfaces, respectively. Validation of these dust detection indices and the proposed algorithm with respect to SDS extracted by MODIS true-color images showed that the proposed algorithm detected SDS extent with an overall accuracy of more than 88%, which was 7%, 15%, and 31% higher than the results derived from BTD20-31, NDDI and BTD32-31, respectively. Also, according to SDS detected by MODIS MCD19A2 Aerosol Optical Depth (AOD) product data, the proposed index identified SDS with an overall accuracy of 82%, which was 5%, 8%, and 31% higher than the results derived from NDDI, BTD20-31, and BTD32-31, respectively. Therefore, our results suggested that the proposed algorithm could effectively capture large-scale SDS and separate dusty pixels from dust-free areas in western Asia.

It is well known that all subvarieties of the variety of all semigroups are not absolutely closed. So, it is worth to find subvarieties of the variety of all semigroups that are closed in itself or closed in the containing varieties of semigroups. We have gone through this open problem and able to determine that the varieties of right~[left] normal bands and left~[right] quasinormal bands are closed in the varieties of semigroups defined by the identities $axy = xa^ny~[axy = ay^nx],~axy = x^nay~[axy = ayx^n]$ $(n>1)$; and $axy=ax^nay$~$[axy=ayx^ny]$~ $(n>1)$, $axy=a^nxa^ry$ $[axy=ay^rxy^n]$ $(n,r\in \mathbb{N})$, respectively.

Reflective practice, in the shape of post-teaching self-evaluations, is a core element of many pre-service English as a Second Language (ESL) teacher training programmes such as CELTA. Most research on Reflective practice has been carried out with pre-service teachers, but more evidence is needed to understand the Reflective practice of in-service ESL teachers. This study employed a Corpus-Linguistics tool called LancsBox to analyse the nature of Reflective discourse found in 44 post-teaching self-evaluations, written by in-service L1-English ESL teachers, in a language school in Colombia. Corpus Linguistics techniques included frequency lists, keywords, ngrams, and concordances. Results suggest that in-service teachers tend to reflect upon the area of Subject Knowledge the most. Other frequent areas of reflection include Lesson Planning and Classroom Management. Areas such as Understanding Learners and Use of Learning Technologies seem far less important. Generally, the most salient Reflective discourse type they produce is Factual, followed by Prudential and Evaluative discourse. The pedagogical implications of this study are threefold. First, both pre-service and in-service ESL teachers need to be taught how to reflect and this needs to be supported by teacher trainers. Second, to guide overall Reflective practices, tools employed by pre- and in-service ESL teachers to reflect on their lessons could be adapted, so they mirror specific areas of reflection such as the teaching skills and Reflective discourse types being evaluated. Third, the current study suggests a self-reflection tool pre- and in-service ESL teachers can use to assess and reflect on their own teaching practices.