positive degree
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We compute the total Stiefel Whitney class for a real representation [Formula: see text] of [Formula: see text], where [Formula: see text] is odd. The obstruction class of [Formula: see text] is defined to be the Stiefel Whitney class of lowest positive degree that does not vanish. We provide an expression for the obstruction class of [Formula: see text] in terms of its character values if [Formula: see text].

Aim. Determination of the degree and frequency of positive transgressions by the number of ears of the main spike in F2 populations created by crossing varieties of soft winter wheat of different maturity depending on the hydrothermal conditions of the year and selection of economically valuable biotypes for subsequent breeding work. Methods. Field, laboratory, mathematical and statistical. Results. In the majority of F2 populations, created by hybridization of soft winter wheat varieties of different vegetation periods, a significant form-making process took place in terms of the number of spikelets in the main spike. The experimental data obtained indicate a significant effect of matched pairs before hybridization and hydrothermal conditions of the year on the manifestation and formation of the number of spikelet’s in an ear F2. So, under the conditions of 2019, the majority of F2 populations for the number of spikelet’s in the main spike (17.4–21.5 pcs.) Significantly exceeded the parental forms. A positive degree (Td = 5.3–33.3 %) and the frequency of transgression (Tf = 3.3–96.7 %) were found in 85.7 % of the populations. In 2020, the average population number of spikelets in the main spike (15.0–18.6 pcs.) Was significantly less. When used in hybridization of early maturing varieties by the parent form, the decrease in the number of spikelets was 0.5–19.9 %. At the same time, for crossing mid-early, mid-ripening and mid-late varieties, the number of spikelets decreased by 2.8–28.9 %. Thus, it can be argued that populations in which early maturing varieties were the maternal form are less exposed to unfavorable conditions of the year. A positive degree (Td = 5.3–38.9 %) and the frequency of recombinants (Tf = 3.3–46.7 %), under the conditions of 2020, was established in 35 out of 42 F2 populations, which amounted to 83.3 %. Conclusions. The use of winter wheat varieties of different early maturity in hybridization in most cases contributes to the formation of F2 in populations and the selection of positive transgressive biotypes by the number of spikelets in the main spike. Conducted studies have established a significant effect of the parental forms used in hybridization and the hydrothermal conditions of the year on the formation of the number of spikelets in the main spike in F2 populations of soft winter wheat. Populations where the early maturing varieties were the maternal form are characterized by a more stable manifestation of the number of spikelets in the main spike. The decrease in the number of spikelets in 2020 compared to 2019 was 0.5–19.9 % for 2.8–28.9 % in populations obtained by hybridization of mid-early, mid-ripening and mid-late varieties. In years with contrasting hydrothermal conditions, hybrid populations F2 were identified, which formed more than the average F2 number of spikelets in the main spike and had high rates of the degree and frequency of positive transgressions, namely: Mironovskaya early / Kolchuga; Kolchuga / Stolichnaya; Shchedraia niva / Vidrada; Antonovka / Stolichnaya.

This study deals with the decomposition analysis of prefixes in English and Mandailing Natal Language. The purpose is to find out the similarities and differences of prefixes in both languages. The data of this research were obtained by conducting library research and field research. The data were analyzed and compared to find out the similarities and differences. The findings indicated that there are some of them only found in one language. There are types of the prefix in English (e.g., un-, hyper-, under-, in-, mis-, super-, over-, pre-, inter-). In Mandailing Natal Language, there is the prefix (e.g., ma-, pa-, tar-, tarpa-, sa- and sasa-, um-). Both English and Mandailing Natal language can be found prefixes which are used to indicate a positive degree that is not found in English. There are some similarities and differences between prefixes in English and Mandailing Natal language.

Abstract Thirty-two dairy cows receiving a basal diet containing 34.9% NDF, and 18.6 % starch, were randomly assigned to four treatments: supplementation either with 140 g/d of ground corn (Control), 126 g/d of ground corn and 14 g/d of XPC (SCFPa, Diamond V Original XPC Cedar Rapids, IA), 121 g/d of ground corn and 19 g/d of NutriTek (SCFPb-1x, NutriTek, Diamond V), or 102 g/d of ground corn and 38 g/d of NutriTek (SCFPb-2x) from 4 wk before until 12 wk after calving. SARA was induced during wk 5 and wk 8 after calving by replacing 20% of the basal diet with pellets containing 50% barley and 50% wheat. Ruminal fluid samples were collected at 6 h after feeding on the second day of wk 4 to wk 10 after calving. Weeks 4, 7 and 10 were considered to be non-SARA. Microbial DNA was extracted, llumina sequenced at the V1–V2 regions of the 16S rRNA gene, and operational taxonomic units (OUT) were assigned using QIIME2. Correlation network analysis (CoNet) determined connections between the relative abundances of OTU, including co-occurrences, and to identify hub OTUs with over 15 connections with other OTUs. The degree of connectedness of phyla was normalized as the total number of positive and negative correlations observed for each phylum divided by their relative abundance in the community. In the Control treatment, SARA reduced positive degree of connectedness (19.33 vs 11.95). In all SCFP treatments, SARA increased the positive degree of connectedness (SCFPb-2x: 25.73 vs 23.50, SCFPb-1x: 87.47 vs 116.32, SCFPa: 34.01 vs 51.56). The relative abundances of the hub taxa Bacteroidales RF16 group and Lachnospiraceae, Christensenellaceae R-7 group and Ricenellaceae RC9 gut group were stabilized by SCFPb-2x. Hence, SCFP attenuated the negative effect of SARA on the co-occurrence patterns in the rumen fluid microbiota.

Armin Vamberi, pioneer of Chagatai (or ancient Uzbek) studies in Europe, was one of the first Europeans to visit the famous cities of Khiva, Bukhara and Samarkand in the summer and autumn of 1863. In the preface to the English version of his travels, he summarized the motives that prompted him to go on such a dangerous adventure in the following words: “The fact that the Hungarian language belongs to a group called Altai is well known, but whether it should be attributed to the Finnish or Tatar branch is a question that still awaits a solution. This investigation, which is interesting for us Hungarians, both from a scientific and a national point of view, was the main and driving force of my journey to the East. Through the practical study of living languages, I strove to establish a positive degree of kinship, which immediately struck me as existing between the Hungarian and Turkish-Tatar dialects, when I contemplated them in the faint light that theory gave.”

This study aimed to identify the effect of applying the principle of independence on the quality of internal auditing on firms listed at the Amman Stock Exchange. To achieve the objectives of the study, the descriptive analytical approach was followed, and the study sample consist of a sample of (100) of employee in the companies that listed on the Amman Stock Exchange. The most important findings of the study are that there is a strong degree of agreement among the study participants on the extent of applying the principle of independence in the companies listed on the Amman Stock Exchange, and the general mean for its phrases was (3.86). The study also concluded that there is a good and positive degree of agreement on the quality of the internal audit found in the Jordanian firms listed on the Amman Stock Exchange from the viewpoint of workers in companies at a good level, and The general mean for its phrases was (3.35). Finally, the study found that there was a significant effect on applying the principle of independence to the quality of internal audit in the firms listed on the Amman Stock Exchange. And that the application of the principle of independence in the Jordanian companies listed on the Amman Stock Exchange is responsible for enhancing 27.5% of the quality of internal auditing, which is a good and effective percentage.

Algebraic numbers are the roots of integer polynomials. Each algebraic number α is characterized by its minimal polynomial Pα that is a polynomial of minimal positive degree with integer coprime coefficients, α being its root. The degree of α is the degree of this polynomial, and the height of α is the maximum of the absolute values of the coefficients of this polynomial. In this paper we consider the distribution of algebraic numbers α whose degree is fixed and height bounded by a growing parameter Q, and the minimal polynomial Pα is such that the absolute value of its derivative P'α (α) is bounded by a given parameter X. We show that if this bounding parameter X is from a certain range, then as Q → +∞ these algebraic numbers are distributed uniformly in the segment [-1+√2/3.1-√2/3]

Positive degree day (PDD) indicates the accumulated positive temperature in a given time period; it directly relates to the melting of snow and ice, and it is a key parameter between global warming and cryosphere changes. In this study, we calculated the PDD based on the daily mean temperatures from1960 to 2018 at meteorological stations, and we used measured and interpolated data to determine spatial and temporal distribution and changes in PDD in western China (WC). Results show that the mean annual, warm season, and cold season PDD values at 209 meteorological stations were 3652.2, 2832.9, and 819.3 °C, respectively. PDD spatial distribution in WC is similar to that of air temperature. In WC, PDD mainly ranged from 0 to 5000, 1000 to 4000, and 0 to 1000 °C year−1, respectively for annual, warm season, and cold season. From 1960 to 2018, the observed mean initial day of PDD moved forward by 8.3 days, and the final day was delayed by 8.2 days, with the duration expanding to 16.6 days; the trend in PDD reversed in the 1980s and the change rate in PDD for annual, warm season and cold season was 6.6, 3.8, and 2.7 °C year−1 higher, respectively. Regionally, PDD increased in almost all areas; the high PDD advanced from south to north, east to west, desert to mountain, and low to high altitudes. The results also showed that the warming rate of PDD was lower in the cold season and in high-altitude areas, which was opposite to the observed temperature patterns, however, the non-linear relationship between PDD and mean temperature over a period of time is the main reason for this phenomenon. This study adds more details for the understanding of climate change in WC, and suggests that more attention should be paid to PDD in the study of cryosphere changes.

<p>Glacial cycles are driven by cyclical changes in Earth’s three orbital parameters: obliquity, precession, and eccentricity.  A common interpretation of Milankovitch’s orbital theory suggests that June insolation at 65°N is the dominant forcing in driving glacial cycles. This places emphasis on precession which has the greatest effect on June insolation at 65°N. However, there is abundant evidence for the importance of obliquity in driving glacial cycles. We compare the relative strengths of obliquity and precession on climate to further explore the possibility that obliquity could be more important than common interpretations of Milankovitch’s orbital theory would suggest. We use a set of coupled atmosphere-ocean general circulation model simulations to produce time series of key climate variables. Such variables include snowfall and positive degree-days (the sum of mean daily temperature for all days above 0°C), which are proxies for accumulation and ablation, respectively. We focus our analysis on glacial inception in Scandinavia and Baffin Island, the locations where the Scandinavian and Laurentide ice sheets were initiated. We show that obliquity causes changes in positive degree-days of larger magnitude than those of precession in both Scandinavia and Baffin Island. Snowfall is dominated by obliquity in Scandinavia and by precession in Baffin Island. The location dependence of the importance of obliquity and precession may have implications for deglaciation which occurred at lower latitudes than the inception locations. Additionally, our positive degree-day time series were most closely represented by Milankovitch’s caloric summer insolation metric than June insolation at 65°N.</p>

In this article, we present a study aimed to explore the attitude, interest and perception of students learning English language beyond the classroom using a list of activities such as Readers Theatre, Storyboard, Academic Explorace, Spell it right and Melodies of Pilah. A survey was conducted involving 466 students from different faculties who were taking English proficiency courses at diploma and degree levels at a local university. The findings indicate that both male and female students had a positive degree of interest and attitude toward the English activities carried out beyond the classroom. The popular activities were Readers Theatre and Melodies of Pilah (group singing). The study also indicated that students preferred group activities compared to individual activities. Based on the findings, it is recommended that students should be allowed to explore English materials independently beyond classrooms where language learning takes place implicitly.  The study found that the success of English learning activities carried out beyond the confines of the classroom can generate interest among students to learn the language. The success of English activities carried out beyond classrooms can be assessed by students’ ability to complete the task assigned (the end-product) rather than the processes involved in completing the task. Keywords: language learning, beyond-the-classroom, out-of-class