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61.
In this paper, we prove that, if the product A=A1?An is a Fredholm operator where the ascent and descent of A are finite, then Aj is a Fredholm operator of index zero for all j, 1?j?n, where A1,…,An be a symmetric family of bounded operators. Next, we investigate a useful stability result for the Rako?evi?/Schmoeger essential spectra. Moreover, we show that some components of the Fredholm domains of bounded linear operators on a Banach space remain invariant under additive perturbations belonging to broad classes of operators A such as γ(Am)<1 where γ(⋅) is a measure of noncompactness. We also discuss the impact of these results on the behavior of the Rako?evi?/Schmoeger essential spectra. Further, we apply these latter results to investigate the Rako?evi?/Schmoeger essential spectra for singular neutron transport equations in bounded geometries. 相似文献
62.
In this paper we study spectral properties of a 3 × 3 block operator matrix with unbounded entries and with domain consisting
of vectors which satisfy certain relations between their components. It is shown that, under certain conditions, this block
operator matrix defines a closed operator, and the essential spectra of this operator are determined. These results are applied
to a three-group transport equation. 相似文献
63.
Diagana (Handbook on operator theory. Springer, Basel, pp 875–880, 2015) studied some sufficient conditions such that if S, T and K are three unbounded linear operators with S being a closed operator, then their algebraic sum \(S+T+K\) is also a closed operator. The main focus of this paper is to extend these results to the closable operator by adding a new concept of the gap and the \(\gamma \)-relative boundedness inspired by the work of Jeribi et al. (Linear Multilinear Algebra 64:1654–1668, 2015). After that, we apply the obtained results to study the specific properties of some block operator matrices. 相似文献
64.
I. Ya. Aref’eva 《Physics of Particles and Nuclei》2010,41(6):835-843
The current paradigm suggests that BH/WH formation in particles collisions will happen when a center-mass energy of colliding
particles is sufficiently above the Planck scale (the transplanckian region). We confirm the classical geometrical cross section
of the BH production reconsidering the process of two transplanckian particles collision in the rest frame of one of incident
particles. This consideration permits to use the standard Thorne’s hoop conjecture for a matter compressed into a region to prove a variant of the conjecture dealing with a total amount of compressed energy in the case of colliding particles. We briefly mention that the process of BH formation is catalyzed by the negative cosmological
constant and by a particular scalar matter, namely dilaton, while it is relaxed by the positive cosmological constant and
at a critical value just turns off. 相似文献
65.
66.
Experimental Mechanics - There has recently been a rising interest in the nonlinear wave transmission behavior of phononic crystals. However, experimental studies focusing on the nonlinear wave... 相似文献
67.
Emilie S. Vosegaard Dr. Maja K. Thomsen Dr. Lennard Krause Thomas B. E. Grønbech Dr. Aref Mamakhel Seiya Takahashi Prof. Dr. Eiji Nishibori Prof. Dr. Bo B. Iversen 《Chemistry (Weinheim an der Bergstrasse, Germany)》2022,28(54):e202201295
Melamine is a precursor and building block for graphitic carbon nitride (g-CN) materials, a group of layered materials showing great promise for catalytic applications. The synthetic pathway to g-CN includes a polycondensation reaction of melamine by evaporation of ammonia. Melamine molecules in the crystal organize into wave-like planes with an interlayer distance of 3.3 Å similar to that of g-CN. Here we present an extensive investigation of the experimental electron density of melamine obtained from modelling of synchrotron radiation X-ray single-crystal diffraction data measured at 25 K with special focus on the molecular geometry and intermolecular interactions. Both intra- and interlayer structures are dominated by hydrogen bonding and π-interactions. Theoretical gas-phase optimizations of the experimental molecular geometry show that bond lengths and angles for atoms in the same chemical environment (C−N bonds in the ring, amine groups) differ significantly more for the experimental geometry than for the gas-phase-optimized geometries, indicating that intermolecular interactions in the crystal affects the molecular geometry. In the experimental crystal geometry, one amine group has significantly more sp3-like character than the others, hinting at a possible formation mechanism of g-CN. Topological analysis and energy frameworks show that the nitrogen atom in this amine group participates in weak intralayer hydrogen bonding. We hypothesize that melamine condenses to g-CN within the layers and that the unique amine group plays a key role in the condensation process. 相似文献
68.
69.
Faiçal Abdmouleh Salma Charfi Aref Jeribi 《Journal of Mathematical Analysis and Applications》2012,386(1):83-90
In this paper, we consider the sum and the product of two operators acting on a Banach space and we present some new and quite general conditions to investigate their Wolf, Schechter and Browder essential spectra. 相似文献
70.