Exceptional complex structures and the hypermultiplet moduli of 5d Minkowski compactifications of M-theory

We present a detailed study of a new mathematical object in E6(6)ℝ+ generalised geometry called an ‘exceptional complex structure’ (ECS). It is the extension of a conventional complex structure to one that includes all the degrees of freedom of M-theory or type IIB supergravity in six or five dimensions, and as such characterises, in part, the geometry of generic supersymmetric compactifications to five-dimensional Minkowkski space. We define an ECS as an integrable U*(6) × ℝ+ structure and show it is equivalent to a particular form of involutive subbundle of the complexified generalised tangent bundle L1 ⊂ Eℂ. We also define a refinement, an SU*(6) structure, and show that its integrability requires in addition a vanishing moment map on the space of structures. We are able to classify all possible ECSs, showing that they are characterised by two numbers denoted ‘type’ and ‘class’. We then use the deformation theory of ECS to find the moduli of any SU*(6) structure. We relate these structures to the geometry of generic minimally supersymmetric flux backgrounds of M-theory of the form ℝ4,1 × M, where the SU*(6) moduli correspond to the hypermultiplet moduli in the lower-dimensional theory. Such geometries are of class zero or one. The former are equivalent to a choice of (non-metric-compatible) conventional SL(3, ℂ) structure and strikingly have the same space of hypermultiplet moduli as the fluxless Calabi-Yau case.

A characterization of nonhomogeneous wavelet bi-frames for reducing subspaces of Sobolev spaces

For nonhomogeneous wavelet bi-frames in a pair of dual spaces $(H^{s}(\mathbb{R}^{d}), H^{-s}(\mathbb{R}^{d}))$ ( H s ( R d ) , H − s ( R d ) ) with $s\neq 0$ s ≠ 0 , smoothness and vanishing moment requirements are separated from each other, that is, one system is for smoothness and the other one for vanishing moments. This gives us more flexibility to construct nonhomogeneous wavelet bi-frames than in $L^{2}(\mathbb{R}^{d})$ L 2 ( R d ) . In this paper, we introduce the reducing subspaces of Sobolev spaces, and characterize the nonhomogeneous wavelet bi-frames under the setting of a general pair of dual reducing subspaces of Sobolev spaces.

Generalising G2 geometry: involutivity, moment maps and moduli

We analyse the geometry of generic Minkowski $$ \mathcal{N} $$ N = 1, D = 4 flux compactifications in string theory, the default backgrounds for string model building. In M-theory they are the natural string theoretic extensions of G2 holonomy manifolds. In type II theories, they extend the notion of Calabi-Yau geometry and include the class of flux backgrounds based on generalised complex structures first considered by Graña et al. (GMPT). Using E7(7) × ℝ+ generalised geometry we show that these compactifications are characterised by an SU(7) ⊂ E7(7) structure defining an involutive subbundle of the generalised tangent space, and with a vanishing moment map, corresponding to the action of the diffeomorphism and gauge symmetries of the theory. The Kähler potential on the space of structures defines a natural extension of Hitchin’s G2 functional. Using this framework we are able to count, for the first time, the massless scalar moduli of GMPT solutions in terms of generalised geometry cohomology groups. It also provides an intriguing new perspective on the existence of G2 manifolds, suggesting possible connections to Geometrical Invariant Theory and stability.

Enhanced ACFM detection performance by multi-parameter synergy analysis

A procedure for the enhancement of alternating current field measurement (ACFM) detection performance is proposed based on a multi-parameter synergy analysis (MPSA) algorithm. Firstly, to gain the maximised ACFM signal characteristics, wavelet base property matching is adopted to choose the favourable wavelet bases. To this aim, the following six base properties should be considered: orthogonality, compact support, symmetry, discrete wavelet transform (DWT), vanishing moment and regularity. It is found that the applicable wavelet bases are Haar, Daubechies (DbN), Symlets (SymN) and Coiflets (CoifN). Secondly, the MPSA method is applied to select the optimal mother wavelet candidates. The candidate with the largest MPSA index value is regarded as the optimum wavelet base. Finally, the proposed MPSA denoising strategy is demonstrated using an ACFM experiment. The results indicate that wavelets Db4 with decomposition level (DL)9 and Sym7 with DL8 are most appropriate for x- and z-axis ACFM signal denoising, respectively. The enhanced ACFM detection performance is experimentally verified and it is found that the signal-to-noise ratio (SNR) is increased by 33.8 dB and 26.7 dB for the x- and z-axis signal, respectively.

Authorial neologisms and occasionalisms. The phenomenon of the novel “The Little hero” by F.M. Dostoevsky

The purpose of the study is to identify neologisms and occasionalisms as special words and phrases that characterize the author’s idiostyle; to show their origin; to explain their difference and similarity; to clarify the terminology. The aim of the study is to show new words and combinations of words in the General fabric of the author’s text and explain their use and purpose; to trace the dependence of the number of neologisms and occasionalisms on the conditions of creation of the work and the initial idea of the author. The method of linguistic research is the use of electronic and corpus technology in the study of literary text. Standard spelling program allows you to see in the text of neologisms and occasional, which stand out as different from the norm of literary language. Then the linguistic analysis of innovations is carried out and their classification is made on the basis of similar signs on etymology, word formation and morphological, semantic and phraseological modification. Take into account the precedent of the creation of the neologism occasionalism or due to the Cabinet technology. Clarification of terms to describe the language of the writer and his creative manner leads to a unification of understanding neologisms and occasionalisms in context due to the usage of the author, allowing you to create a special vertext in understanding any text. This is expressed in the anticipation of the perception of the text and in a concise and capacious characterization. Quantitative picture of neologisms-occasionalisms in all the works of Dostoevsky and every in the long term makes it possible to compare how different works of the writer and of works of different authors in the synchrony and diachrony of the Russian language. The research initially is the text of the story “Little hero”, which was written during the imprisonment in the Peter and Paul fortress, that is special for a person and writer extreme conditions of stress, and then drawing the material of other works presenting meaningful, chronological and quantitative interest on the use of neologisms and occasionalisms. This fixation of the reader’s attention on the vanishing moment makes it necessary to create a new word or phrase in the event that the main character of the story becomes invisible, small, almost disappearing. Psychologically, this technique can be explained by the revival of the author’s self-consciousness after severe stress. The phenomenon of the “The Little hero” is in the vanishing hero, and therefore in the vanishing author.

Maximum Vanishing Moment of Compactly Supported B-spline Wavelets

Spline function is of very great interest in field of wavelets due to its compactness and smoothness property. As splines have specific formulae in both time and frequency domain, it greatly facilitates their manipulation. We have given a simple procedure to generate compactly supported orthogonal scaling function for higher order B-splines in our previous work. Here we determine the maximum vanishing moments of the formed spline wavelet as established by the new refinable function using sum rule order method.