The paper investigates vanishing conditions on the first cohomology module of a normalized rank 2 vector bundle F on P which force F to split. The present vanishing conditions improve other conditions known in the literature and are obtained with simple computations on the Euler characteristic function, avoiding the speciality lemma and other heavy tools.

Let Γ denote a Q-polynomial distance-regular graph with diameter at least three and standard module V . We introduce two direct sum decompositions of V . We call these the displacement decomposition for Γ and the split decomposition for Γ. We describe how these decompositions are related.

Let F be a non-Archimedean locally compact field, let G be a split connected reductive group over F . For a parabolic subgroup Q ⊂ G and a ring L we consider the G-representation on the L-module (∗) C∞(G/Q, L)/ ∑

In this work we investigate, by means of direct numerical hyperviscous simulations, how rotation affects the bidimensionalization of a turbulent flow. We study a thin layer of fluid, forced by a two-dimensional forcing, within the framework of the "split cascade" in which the injected energy flows both to small scales (generating the direct cascade) and to large scale (to form the inverse casca...

Some necessary and sufficient conditions are given for the existence of a G-positive (G-repositive) solution to adjointable operator equations $AX=C,AXA^{left( astright) }=C$ and $AXB=C$ over Hilbert $C^{ast}$-modules, respectively. Moreover, the expressions of these general G-positive (G-repositive) solutions are also derived. Some of the findings of this paper extend some known results in the...

Abstract Established face-to-face surveys encounter increasing pressures to move online. Such a mode switch is accompanied with methodological challenges, including the need shorten questionnaire that each respondent receives. Split Questionnaire Designs (SQDs) randomly assign respondents different fractions of full (modules) and, subsequently, impute data are missing by design. Thereby, SQDs r...

The Video Compressor/Decompressor (CODEC) performs compression and decompression of video data by combining a Motion estimation and compensation module, Transformation module, and Entropy encoding module. Among these three modules, the spatial redundancy can be eliminated by the transformation module which exists in the spatial domain of video sequence. Discrete Cosine Transformation (DCT) is t...

In this paper, we investigate the split variational inequality problem in Hilbert spaces, which an operator is ?-inverse strongly ?-monotone and another pseudomonotone. We construct iterative algorithm for solving problem. show strong convergence of suggested algorithm.

The paper presents a hybrid regresseion model with the main emphasis put on the regression tree unit. It discusses input and output variable transformation, determining the final decision of hybrid models and node split optimization of regression trees. Because of the ability to generate logical rules, a regression tree maybe the preferred module if it produces comparable results to other modul...