Discontinuity of the Lempert function of the spectral ball

We give some further criteria for continuity or discontinuity of the Lempert funtion of the spectral ball $\Omega_n$, with respect to one or both of its arguments, in terms of cyclicity the matrices involved.Comment: 12 pages; the converse to theorem 1.3, mistakenly claimed in v1 & 2, excised from v3, is now proved in some case

Disks extremal with respect to interpolation constants

We define a function µ from the set of sequences in the unit ball to R*+ by taking the greatest lower bound of the reciprocal of the interpolating constant of the sequences of the disk which get mapped to the given sequence by a holomorphic mapping from the disk to the ball. Its properties are studied in the spirit of the work of Amar and Thomas

Pluricomplex Green and Lempert functions for equally weighted poles

For $\Omega$ a domain in $\mathbb C^n$, the pluricomplex Green function with poles $a_1, ...,a_N \in \Omega$ is defined as $G(z):=\sup \{u(z): u\in PSH_-(\Omega), u(x)\le \log \|x-a_j\|+C_j \text{when} x \to a_j, j=1,...,N \}$. When there is only one pole, or two poles in the unit ball, it turns out to be equal to the Lempert function defined from analytic disks into $\Omega$ by $L_S (z) :=\inf \{\sum^N_{j=1}\nu_j\log|\zeta_j|: \exists \phi\in \mathcal {O}(\mathbb D,\Omega), \phi(0)=z, \phi(\zeta_j)=a_j, j=1,...,N \}$. It is known that we always have $L_S (z) \ge G_S(z)$. In the more general case where we allow weighted poles, there is a counterexample to equality due to Carlehed and Wiegerinck, with $\Omega$ equal to the bidisk. Here we exhibit a counterexample using only four distinct equally weighted poles in the bidisk. In order to do so, we first define a more general notion of Lempert function "with multiplicities", analogous to the generalized Green functions of Lelong and Rashkovskii, then we show how in some examples this can be realized as a limit of regular Lempert functions when the poles tend to each other. Finally, from an example where $L_S (z) > G_S(z)$ in the case of multiple poles, we deduce that distinct (but close enough) equally weighted poles will provide an example of the same inequality. Open questions are pointed out about the limits of Green and Lempert functions when poles tend to each other.Comment: 25 page

Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

Astrochemical Properties of Planck Cold Clumps

We observed 13 Planck cold clumps with the James Clerk Maxwell Telescope/SCUBA-2 and with the Nobeyama 45 m radio telescope. The N2H+ distribution obtained with the Nobeyama telescope is quite similar to SCUBA-2 dust distribution. The 82 GHz HC3N, 82 GHz CCS, and 94 GHz CCS emission are often distributed differently with respect to the N2H+ emission. The CCS emission, which is known to be abundant in starless molecular cloud cores, is often very clumpy in the observed targets. We made deep single-pointing observations in DNC, (HNC)-C-13, N2D+, and cyclic-C3H2 toward nine clumps. The detection rate of N2D+ is 50%. Furthermore, we observed the NH3 emission toward 15 Planck cold clumps to estimate the kinetic temperature, and confirmed that most targets are cold (less than or similar to 20 K). In two of the starless clumps we observed, the CCS emission is distributed as it surrounds the N2H+ core (chemically evolved gas), which resembles the case of L1544, a prestellar core showing collapse. In addition, we detected both DNC and N2D+. These two clumps are most likely on the verge of star formation. We introduce the chemical evolution factor (CEF) for starless cores to describe the chemical evolutionary stage, and analyze the observed Planck cold clumps.Peer reviewe

Disks extremal with respect to interpolation constants

We define a function µ from the set of sequences in the unit ball to R*+ by taking the greatest lower bound of the reciprocal of the interpolating constant of the sequences of the disk which get mapped to the given sequence by a holomorphic mapping from the disk to the ball. Its properties are studied in the spirit of the work of Amar and Thomas

Emotion Expressing Idioms in English and Vietnamese: A Contrastive Analysis

Abstract Language is a repertoire of culture and a powerful and versatile medium in communication. Idioms mirror human wisdom in the process of conceptualization of the world. Idioms have interlocked and grown into records of a community’s past culture. Idioms therefore constitute a rich, but at the same time elusive, area of cross-cultural exchanges. Idioms reflect the colour and variety of human social activities, and so play an important role in the linguistic ontologization of emotions. The vocabulary of emotions has been the object of intensive investigations in many languages, but bibliographical exploration reveals that idioms as a component of the lexicon are not yet part of the main field of theoretical interest. In particular, while there have been studies of idioms of emotion in English, there have been few on emotion idioms in Vietnamese, and very few systematic investigations of emotion idioms (EIs) across English and Vietnamese. Hence, our linguistic study of the conceptualization of emotions in English and Vietnamese will significantly contribute to the development of this research domain with data from a language other than English. The study undertakes a contrastive investigation of idioms that express the seven basic emotional concepts of HAPPINESS, SADNESS, ANGER, DISGUST, LOVE, FEAR, and DESIRE in English and Vietnamese. There are three foci: (1) similarities and differences in formal structure between the EIs in English and Vietnamese; (2) similarities and differences in semantics between such idioms; and (3) an investigation of the patterning and regularities of the established similarities and differences between the EIs in the two languages. To the end, we have conducted a hand search approach of the dictionaries in both languages, which has enabled the establishing of a corpus of 1065 entries (603 for English and 462 for Vietnamese). As regards the formal structure, the study sets up the lexicogrammatical frames for the canonical forms and variation patterns of the idioms, and interrelates quantitatively and quantitatively the relationship of the idioms’ variant form vis-à-vis the canonical form. In light of the findings, the study has shown that a high level of canonicity is observed in the idioms in both English and Vietnamese. In general, they conform to a restricted number of construction types: verbal, nominal, adjectival, prepositional, and sentential. Nevertheless, many other idioms permit variable flexibility in their composition: the substitutability of their component parts, insertion of lexical items, and some variation in syntactic patterning. For the idioms which are logged as canonical and variant, we have suggested rules to cover the patterns. As regards the semantic features of the idioms, the study is substantially reliant on the theory of conceptual metaphor (CMT) and metonymy, as first developed by Lakoff & Johnson (1980), to analyze the data. The data analysis leads to the discovery of conceptual mappings/correspondences from the various source domains on to the target domains of emotions, which are very productive of idioms. An in-depth analysis of cross-linguistic and cross-cultural aspects in the idioms is provided to determine similarities and differences in terms of conceptualization of the emotions between the two languages. The contrastive analysis of idioms reported in the traditional literature is usually the comparison of idioms with body-part terms: e.g., mát mặt (‘cool face’) ‘HAPPINESS’ in Vietnamese; lose one’s head in English, animals: e.g., gầm như hổ đói (‘roar like tiger hungry’); go ape ‘ANGER’, and colours: e.g., đỏ mặt tía tai (‘red face purple ear’); blue in the face ‘ANGER’. The present analysis seeks greater explanatory depth and theoretical grounding in the framework of cognitive linguistics. We present the semantic patterning of the idioms, and the patterning in turn reveals how English and Vietnamese people talk about and structure the abstract conceptual domains (i.e., emotions) (Gibbs & Wilson, 2002). In light of the findings, this research has revealed both commonalities and differences in the conceptualization of the emotions in English and Vietnamese. The affinities are grounded in common bodily experiences. On the other hand, cross-cultural variations are also obvious. The most important conclusion that can be drawn for the study is that metaphors and metonymies involved in emotion-expressing idioms are not only heavily subject to physiological basis (Solomon, 1984), but also to cultural influences on the basis of the cultural image schemas (Dobrovol'skij & Piirainen, 2006; Emanatian, 1995; Geeraerts & Grondelaers, 1995; Ungerer, 1993). The thesis also presents implications concerning the linguistic ontologization of emotions, and their application to second language learning and the translation of idioms