Geometry of the Wiman–Edge monodromy

The Wiman–Edge pencil is a pencil of genus 6 curves for which the generic member has automorphism group the alternating group [Formula: see text]. There is a unique smooth member, the Wiman sextic, with automorphism group the symmetric group [Formula: see text]. Farb and Looijenga proved that the monodromy of the Wiman–Edge pencil is commensurable with the Hilbert modular group [Formula: see text]. In this note, we give a complete description of the monodromy by congruence conditions modulo 4 and 5. The congruence condition modulo 4 is new, and this answers a question of Farb–Looijenga. We also show that the smooth resolution of the Baily–Borel compactification of the locally symmetric manifold associated with the monodromy is a projective surface of general type. Lastly, we give new information about the image of the period map for the pencil.

The role of focus marking in disjunctive questions: A QUD-based approach

Disjunctive questions are ambiguous: they can either be interpreted as polar questions (PolQs), as open disjunctive questions (OpenQs), or as closed alternative questions (ClosedQ). The goal of this paper is to show that the difference in interpretation between these questions can be derived via effects of focus marking directly. In doing so, the proposal brings out the striking parallel between the prosody of questions with foci/contrastive topics on the one hand and that of alternative questions on the other. Unlike previous approaches, this proposal does not rely on structural differences between AltQs and PolQs derived via ellipsis or syntactic movement. To show how this works out, an account of focus and contrastive topic marking in questions is put forward in which f-marking in questions determines what constitutes a possible answer by signaling what the speaker's QUD is like. By imposing a congruence condition between f-marked questions and their answers that requires answers to resolve the question itself as well as its signaled QUD, we predict the right answerhood conditions for disjunctive questions.

In and out of tune

This study explores the potential effects of musical congruence and incongruence on translation quality and creativity. An experiment was carried out in which participants translated excerpts from happy and sad narratives while they listened to source-text congruent and incongruent soundtracks. Statistical analyses were performed to compare translation performance under three different sound conditions: musical congruence, musical incongruence, and silence. The results reveal a positive influence of congruent musical stimuli on translation creativity. Correlations are also found between levels of empathy and creativity, suggesting that an increase in translation creativity under the effects of music could be mediated by reported high levels of empathy under the musical congruence condition.

Metric Diophantine approximation with congruence conditions

We prove a version of the Khinchin–Groshev theorem for Diophantine approximation of matrices subject to a congruence condition. The proof relies on an extension of the Dani correspondence to the quotient by a congruence subgroup. This correspondence together with a multiple ergodic theorem are used to study rational approximations in several congruence classes simultaneously. The result in this part holds in the generality of weighted approximation but is restricted to simple approximation functions.

U-Abundant Semigroups with Ehresmann Transversals

A class of weakly U-abundant semigroups satisfying the congruence condition (C) is investigated, which contains both the class of regular semigroups and the class of abundant semigroups as its subclasses. In particular, the class of weakly U-abundant semigroups satisfying the congruence condition (C) with Ehresmann transversals is studied. After giving some properties of U-abundant semigroups with Ehresmann transversals, we establish some characterization theorems for such semigroups. Our results may be regarded as an extension of the work of Blyth, McAlister and McFadden in regular semigroups and that of El-Qallali, Guo and Chen in abundant semigroups.

Are they really persuaded with the brand embedded in the game?

Purpose The purpose of the paper is to examine whether there is any difference in persuasion of brands embedded in the advergame because of the differences in nature of the game (speed), and are there any differences in persuasion in the same context if the brand is prominently placed versus subtly placed and congruent versus incongruent with the game context. Design/methodology/approach A 2 (nature of advergame: fast or slow) × 2 (brand prominence: prominent or subtle) × 2 (game-product congruence: high or low) between-subject measures design is used; 280 graduate students participated in the study. A 2 × 2 × 2 between-subjects ANOVA is used to test the hypotheses. Findings The findings support that slow-paced advergames with prominent brand placements result in high ad-persuasion compared to subtle brand placements. On the other hand, fast-paced advergames show no difference in persuasiveness despite the fact that whether it is a subtle placement or prominent placement. Furthermore, results also indicate that slow-paced games with prominent placement in low game-product congruence condition resulted in high ad-persuasion compared to that in high game-product congruence condition. Research limitations/implications The process of experimentation used in this study to collect responses were susceptible to some limitations. However, findings of the study are very important for advertising practitioners in terms of game design, implementation and for an effective use of brand and product placements in advergames. Originality/value This research contributes to the literature of online advertising, specifically advergaming context by exploring the impact of nature of game and brand prominence on gamers’ ad-persuasion. Also, this study is the first attempt toward understanding the moderating role of game-product congruence on gamers’ ad-persuasion in the context of advergames.

A VARIANT OF THE BARBAN–DAVENPORT– HALBERSTAM THEOREM

Let L/K be a Galois extension of number fields. The problem of counting the number of prime ideals 𝔭 of K with fixed Frobenius class in Gal (L/K) and norm satisfying a congruence condition is considered. We show that the square of the error term arising from the Chebotarëv Density Theorem for this problem is small "on average". The result may be viewed as a variation on the classical Barban–Davenport–Halberstam Theorem.

Judgments of Auditory—Visual Affective Congruence in Adolescents with and without Autism: A Pilot Study of a New Task Using fMRI

One of the most widely reported developmental deficits associated with autism is difficulty perceiving and expressing emotion appropriately. Brain activation associated with performance on a new task, the Emotional Congruence Task, requires judging affective congruence of facial expression and voice, compared with their sex congruence. Participants in this pilot study were adolescents with normal IQ ( n = 5) and autism or without ( n = 4) autism. In the emotional congruence condition, as compared to the sex congruence of voice and face, controls had significantly more activation than the Autism group in the orbitofrontal cortex, the superior temporal, parahippocampal, and posterior cingulate gyri and occipital regions. Unlike controls, the Autism group did not have significantly greater prefrontal activation during the emotional congruence condition, but did during the sex congruence condition. Results indicate the Emotional Congruence Task can be used successfully to assess brain activation and behavior associated with integration of auditory and visual information for emotion. While the numbers in the groups are small, the results suggest that brain activity while performing the Emotional Congruence Task differed between adolescents with and without autism in fronto-limbic areas and in the superior temporal region. These findings must be confirmed using larger samples of participants.