Throughout this paper, let G be a finite group and let all characters be complex characters. Also, let l(G) be the largest irreducible **character** degree of G, s(G) be the second largest irreducible **character** degree of G and t(G) be the third largest irreducible **character** degree of G. The set of all irreducible characters of G is shown by Irr(G) and the set of all irreducible **character** **degrees** of G is shown by cd(G). In [4], B. Huppert conjectured that if G is a finite group and S is a finite non-abelian simple group such that cd(G) = cd(S), then G ∼ = S × A, where A is an abelian group. In [7], [11] and [12], it is shown that L 2 (p), simple K 3 -groups and Mathieu simple groups are determined uniquely by their

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First suppose that n ≥ 4. This implies that nonlinear irreducible **character** **degrees** of the solvable group G are not all equal. We claim that there exists a normal subgroup K > 1 of G such that K G is nonabelian. If G ′ is not a minimal normal subgroup of G, then G has a nontrivial normal subgroup N such that N G is nonabelian. Otherwise, if G ′ is a minimal normal subgroup of G, then it cannot be unique since nonlinear irreducible **character** **degrees** of the solvable group G are not all equal, [5, Lemma 12.3]. So we can see that G has a nontrivial normal subgroup N such that N G is nonabelian. Let K be maximal with respect to the property that K G is nonabelian. It is clear that ( K G ) ′ is the unique minimal normal subgroup of K G . Thus K G satisfies the hypothesis of [5, Lemma 12.3]. So all nonlinear irreducible characters of K G have equal degree f and we have the following cases:

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Abstract. The concept of the bipartite divisor graph for integer subsets has been considered in [M. A. Iranmanesh and C. E. Praeger, Bipartite divisor graphs for integer subsets, Graphs Combin., 26 (2010) 95–105.]. In this paper, we will consider this graph for the set of **character** **degrees** of a finite group G and obtain some properties of this graph. We show that if G is a solvable group, then the number of connected components of this graph is at most 2 and if G is a non-solvable group, then it has at most 3 connected components. We also show that the diameter of a connected bipartite divisor graph is bounded by 7 and obtain some properties of groups whose graphs are complete bipartite graphs.

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Abstract. In a previous paper, the second author established that, given finite fields F < E and certain subgroups C ≤ E × , there is a Galois connection between the intermediate field lattice { L | F ≤ L ≤ E} and C’s subgroup lattice. Based on the Galois connection, the paper then calculated the irreducible, complex **character** **degrees** of the semi-direct product C ⋊ Gal(E/F ). However, the analysis when |F | is a Mersenne prime is more complicated, so certain cases were omitted from that paper.

The study of the structure of a finite group G by imposing conditions on the set cd(G) of the **degrees** of its complex irreducible characters has been considered in many research papers. For example, it has been shown that groups having just two different **character** **degrees** are solvable and these groups have been thoroughly investigated by Isaacs and Passman in [8, 9] and [7, Chapter 12].

π(G) = π(H). Not only its vertex set π(G), but also the prime graph Γ(G) itself can be recognized by a subgroup H generated by few elements: indeed every finite group G contains a three-generated subgroup H such that Γ(H) = Γ(G) (see [8, Theorem C]). A natural question, arising from Theorem 1, is whether a similar result can be proved for the **character** degree graph.

To conclude this section, we briefly report on the natural dual problem to conjugacy classes: the irreducible complex **character** **degrees**. Recently, in [13, 14], it has been handled the case that the irreducible **character** **degrees** of a group G are not divisible by p 2 , and some information about the orders of the Sylow p-subgroups of G/ O p (G) is gained. Observe that there are non-soluble groups

the conjecture. In this paper, we manage to characterize the ﬁnite simple groups by less **character** quantity. Let G be a ﬁnite group; L(G) denotes the largest irreducible **character** degree of G and S(G) denotes the second largest irreducible **character** degree of G. We characterize the ﬁve Mathieu groups G by the order of G and its largest and second largest irreducible **character** **degrees**. Our main results are the following theorems.

confidence, how things will turn out—I may want to say that I believe “probably p”. In other cases, I may be not inclined to claim to believe p, not because I think that not-p, but because I’m not sure whether or not p. All such cases, among others, have been dealt with using a framework of **degrees** of belief, or credences. **Degrees** of belief—or credences—range from 0 to 1, with a degree of belief of 1 amounting to certainty and 0 to certainty of the negation. In cases where I’m generally happy to assert p, but, if pushed, will acknowledge that I’m not certain that p, I can be described as having a degree of belief less than, if relatively close to, 1. Cases where I want to say I’m not sure whether or not p, can amount to different **degrees** of belief that p according to the extent to which I, loosely speaking, am confident that p. We can think of someone’s set of beliefs as an assignment of such values to propositions. There are, then, rational constraints on the relations between the degree of belief in a compound and in their components. For example, your degree of belief in a conjunction should (and, if you are rational, will) be no greater than the degree of belief in each of the conjuncts. The standard framework for modelling these relations is a probabilistic one.

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on the **character** level. On the word level, we go through the hypothesis and compare the cur- rent word with each word in the reference. If a matched word is found at a different position in the reference, the succeeding words of the current word will be iteratively compared, in order to dis- cover the longest matched phrases. This proce- dure becomes expensive on **character** level. The much higher matching probability of characters compared to words will result in many computa- tions. For instance, for the example sentence in Figure 1, the computational time of the C ER is 44

We attempt to further Elsner’s line of work by leveraging text structure (as Mutton and Elson did) and knowlege-based SA to track the emotional tra- jectories of interpersonal relationships rather than of a whole text or an isolated **character**. To ex- tract these relationships, we mined for **character**- to-**character** sentiment by summing the valence values (provided by the AFINN sentiment lexicon (Nielsen, 2011)) over each instance of continuous speech and then assumed that sentiment was di- rected towards the **character** that spoke immedi- ately before the current speaker. This assumption doesn’t always hold; it is not uncommon to find a scene in which two characters are expressing feel- ings about someone offstage. Yet our initial results on Shakespeare’s plays show that the instances of face-to-face dialogue produce a strong enough sig- nal to generate sentiment rankings that match our expectations.

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disciplinary characters, namely the absence of modules, so there is a need for modules as learning media for scout members. While the results of interviews with students, students have not clearly understood the raiser scout material in accordance with the **character** development discipline, due to the lack of examples of activities and images that can clarify the material. In accordance with the results of observations and interviews with teachers and students, the process of fostering disciplinary **character** in Elementary School of 12 Air Kumbang requires a media that is able to explain the material completely and clearly. The media is a module, because the module has more complete material starting from describing the **character** of discipline through the activities of the crowd as well as explanations and sample images as well as the application of making fashion designs in accordance with the scouting activities of the scouts. If the module is packaged attractively, students are more motivated to learn it. In addition, modules can also be used as learning resources that can be used to learn independently. After analyzing and collecting data, draft preparation was then carried out to facilitate the development of multiple media. In drafting, guidelines are needed in the form of books on making learning modules. The results of the developer are in the form of learning modules that contain cover pages, words of introduction, table of contents, introduction, learning, notes and bibliography. Modules are made with pictures so they can attract the attention of students to be motivated to learn modules and students can learn independently using Scout **character** education learning module based on scouting. The development of scout-based **character** education learning

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Horoskopos in Aries, in the house of [N.N., x degrees]; Sun in Cancer, in the House of the Moon, 7 degrees; Moon in Leo, in the House of Mercury, 4 degrees; Mars in Scorpio, in the House[r]

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According to Elias, White, & Stepney (2014) (in Casey, Cort and Kinkopf, Timothy 2016) connecting morality with social and emotional learning. Social and emotional learning is "the ability to recognize and manage emotions, solve problems effectively, set and achieve positive goals, appreciate the perspectives of others, build and maintain positive relationships, make responsible decisions, and constructively handling interpersonal situations." Turning to a negative alternative, some teachers decide to focus on positive learning in changing their students' mindset through teaching and modeling positive behaviors rather than simply punishing students for misbehaving. Teachers handle this issue every day. They often note that students who have behavioral problems in the classroom lack empathy and sympathy for other students. Many teachers watch selfish students. Often, this causes delinquency in the classroom and forces administrators or teachers to punish this behavioral problem. This pattern has a direct impact on the level of detention, suspension, and expulsion and ultimately undermines the school culture itself. What exactly is the difficulty in building **character** education in the classroom?

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For 56 species with ten or more spatially distinct occurrence records (Fig. 5.1b), we used generalised additive modelling to investigate the relative importance of temperature, seasonality and moisture in determining range limits. For each species, performance- weighted multi-models were obtained using stepwise selection (Chapter 3). Highly correlated variables (annual rainfall vs. moisture index, Pearson’s r = 0.92) were separated prior to selection based on univariate model performance. Where possible, statistical normality was improved using power transforms (Appendix 5A). Each predictor was allowed between one and four effective **degrees** of freedom, optimised according to a cross- validation of the sum of squared residuals (Yee and Mitchell, 1991). Linear fits were preferred where smooth terms did not improve predictive performance under cross- validation. Background data were distributed within the same mountain blocs as the presence data (prevalence = 0.2), and specifically at locations where other endemic plant species have been recorded. Thus, absences exhibited similar spatial, environmental and taxonomic bias as presences (Phillips et al., 2009; Ahrends et al., 2011 in Appendix I). Each regression model was iterated ten times using different realisations of background data. The final model for a given grid square was the median prediction across these ten runs. Post- model analysis was restricted to those species for which robust predictive fits were achieved (five-fold cross-validation of the area under the ROC curve, AUC CV ≥ 0.7). We recorded

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The policy texts emanating from the collaborative working of the DfES, Department of Trade and Industry, the Treasury and the Government Office for the Regions all attempt to combine issues of globalisation and the knowledge economy with issues of social justice and equity. Foundation **degrees** themselves display aspects of these differing policy strands, since they focus on associate professional and technical skills gaps and are also aimed at people already in employment. This emphasis on knowledge and skills, as both an economic imperative, related to the global economy, and as a way of effecting a more socially just society can be traced to the work of the Commission for Social Justice 4 established by John Smith. The final report set out the groundwork for a national policy strategy to tackle the problems of economic under- performance, social division and malaise. This national strategy was added to by the influence of Hutton (1995) 5 and Giddens, in terms of the Third Way (1998), and his appointment as Director of LSE. 6

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Abstract: The article deals with the change of costs and its effect upon the change of profit in the monitored firm. The first part is devoted to the theoretical framework of the area. The formula needed for calculating indicators used are stated and described here and economic effects of the **degrees** of effectivness are explained by the means of graphs and formulas. The second part gives the definition of the **degrees** of effectiveness. Each of them is characterised by five items where monitored indicators are evaluated and described on the basis of observed data.

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Case 1: G/N is an r-group for some prime r. Then there exists ψ ∈ Irr(G/N ) such that ψ(1) = r b > 1. As 2 24 is the only nontrivial prime power degree of H, we deduce that ψ(1) = 2 24 and so r = 2. By [3], G has a nonlinear **character** χ ∈ Irr(G) such that χ(1) = 7 2 · 17 is odd. As (χ(1), |G : N |) = 1, by Lemma 2.1, we have χ N ∈ Irr(N ) and hence by Gallagher’s Theorem, we obtain that χτ ∈ Irr(G)

There are some phases of a process risk analysis, that the actual situation is often not sharp and deterministic due to the number of uncertainties. These uncertainties can be classified into two groups: as "objective uncertainties", which arise from a random **character** of the evaluation process (variability) and "subjective uncertainties", arising from limited and partial knowledge and information (imprecision). In such a situation, fuzzy logic can be used. According to Zadeh, fuzzy logic or fuzzy set theory can work with uncertainty and precision and can solve problems where there are no precise boundaries and precise values [5]. The concept of a fuzzy set provides mathematical formulations that can characterize the uncertain parameters involved in the method of risk analysis. According to CHAMOVITZ and COSENZA (2010), the use of fuzzy logic in will be indicated whenever one wishes to approach the constructed model of reality [6] [14]. This assertion is based on the principle of incompatibility established by ZADEH (1973): "As the

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