Application of the Complex Moments for Selection of an Optimal Sensor

In the first time we apply the statistics of the complex moments for selection of an optimal pressure sensor (from the available set of sensors) based on their statistical/correlation characteristics. The complex moments contain additional source of information and, therefore, they can realize the comparison of random sequences registered for almost identical devices or gadgets. The proposed general algorithm allows to calculate 12 key correlation parameters in the significance space. These correlation parameters allow to realize the desired comparison. New algorithm is rather general and can be applied for a set of other data if they are presented in the form of rectangle matrices. Each matrix contains N data points and M columns that are connected with repetitious cycle of measurements. In addition, we want to underline that the value of correlations evaluated with the help of Pearson correlation coefficient (PCC) has a relative character. One can introduce also external correlations based on the statistics of the fractional/complex moments that form a complete picture of correlations. To the PCC value of internal correlations one can add at least 7 additional external correlators evaluated in the space of fractional and complex moments in order to realize the justified choice. We do suppose that the proposed algorithm (containing an additional source of information in the complex space) can find a wide application in treatment of different data, where it is necessary to select the “best sensors/chips” based on their measured data, presented usually in the form of random rectangle matrices.

Quintilian as a Literary Critic

This chapter is devoted to the study of the Institutio oratoria as a complex space in which Quintilian, in addition to developing an education manual, a rhetorical treatise, and an essay on the orator’s moral duties and obligations, also includes theoretical reflections on literary criticism as well as analysis and assessments of specific literary works. In this sense, this chapter studies Quintilian as a literary critic. From a general and theoretical point of view, it reviews the relations established within the framework of the Institutio oratoria between literary criticism and poetarum enarratio, or exegesis of poetic texts, which should be practised by grammar students before continuing to the study of rhetoric. This review forces us to reconsider the question of the interdependence that exists between grammar and rhetoric as classical sciences of discourse. From an applicative and practical perspective, the chapter stresses the importance of Book 10 for a better knowledge of the literary critical analyses and evaluations that Quintilian makes of the most important works and authors of Greek and Roman literature, always in relation to its usefulness for the orator’s training through the exercise of reading and on the basis of the principle of imitation of literary models, which not only include poetic texts, but also historical, philosophical, and rhetorical texts. Finally, the chapter reviews the theory of Attic, Asianic, and Rhodian styles in Quintilian’s thinking and his defence of the one which, even defined by hybridization, best adapts itself to the pragmatic-communicative requirements of the rhetorical fact.

A certain η-parallelism on real hypersurfaces in a nonflat complex space form

In this paper, we give the complete classification of real hypersurfaces in a nonflat complex space form from the viewpoint of the η-parallelism of the tensor field h(= (1/2)𝓛 ξ ϕ). In addition we investigate real hypersurfaces whose tensor h is either Killing type or transversally Killing tensor. In particular, we shall determine Hopf hypersurfaces whose tensor h is transversally Killing tensor by using an application of the classification of real hypersurfaces admitting η-parallelism with respect to the tensor h.

Double-Scale Gevrey Asymptotics for Logarithmic Type Solutions to Singularly Perturbed Linear Initial Value Problems

We examine a family of linear partial differential equations both singularly perturbed in a complex parameter and singular in complex time at the origin. These equations entail forcing terms which combine polynomial and logarithmic type functions in time and that are bounded holomorphic on horizontal strips in one complex space variable. A set of sectorial holomorphic solutions are built up by means of complete and truncated Laplace transforms w.r.t time and parameter and Fourier inverse integral in space. Asymptotic expansions of these solutions relatively to time and parameter are investigated and two distinguished Gevrey type expansions in monomial and logarithmic scales are exhibited.

Toeplitz Operators with Lagrangian Invariant Symbols Acting on the Poly-Fock Space of ℂ n

We introduce the so-called extended Lagrangian symbols, and we prove that the C ∗ -algebra generated by Toeplitz operators with these kind of symbols acting on the homogeneously poly-Fock space of the complex space ℂ n is isomorphic and isometric to the C ∗ -algebra of matrix-valued functions on a certain compactification of ℝ n obtained by adding a sphere at the infinity; moreover, the matrix values at the infinity points are equal to some scalar multiples of the identity matrix.

Complex-InversE: Improving bilinear knowledge graph embeddings by mapping into complex space

Knowledge graph link prediction uses known fact links to infer the missing link information in the knowledge graph, which is of great significance to the completion of the knowledge graph. Generating low-dimensional embeddings of entities and relations which are used to make inferences is a popular way for such link prediction problems. This paper proposes a knowledge graph link prediction method called Complex-InversE in the complex space, which maps entities and relations into the complex space. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. The Complex-InversE effectively captures the antisymmetric relations and introduces Dropout and Early-Stopping technologies into deal with the problem of small numbers of relationships and entities, thus effectively alleviates the model’s overfitting. The results of comparison experiment on the public knowledge graph datasets show that the Complex-InversE achieves good results on multiple benchmark evaluation indicators and outperforms previous methods. Complex-InversE’s code is available on GitHub at https://github.com/ZeyuMiao97/Complex-InversE.