Abstract:
In the present paper, we shall give an extension of the well known Pecaric-Rajic inequality in a quasi-Banach space, we establish the generalized inequality for an arbitrary number of finitely many nonzero elements of a quasi-Banach space, and obtain the corresponding upper and lower bounds. As a result, we get some more general inequalities.

Abstract:
In this paper, we present an extension of the so-called classical Sherman-Morrison-Woodbury (for short SMW) formula for bounded homogeneous generalized inverse in Banach spaces. Some particular cases and applications will be also considered. Our results generalize the results of many authors for finite dimensional matrices and Hilbert space operators in the literature.

Abstract:
Due to a lack of suitable minerals, the gas/oil emplacement ages have never been accurately obtained before. CH4-CO2-saline-bearing secondary inclusions are found in quartz from the volcanic rocks of the Yingcheng Formation, the container rocks of the deep CO2 gas reservoir in the Songliao Basin. The inclusion fluid was trapped into microcracks in quartz during the gas emplacement and accumulation, providing an optimal target for the 40Ar-39Ar stepwise crushing technique to determine the CO2 gas emplacement age. 40Ar-39Ar dating results of a quartz sample by stepwise crushing yield a highly linear-regression isochron with an age of 78.4±1.3 Ma, indicating that the accumulation of the deep CO2 gas reservoir in the Songliao Basin occurred in the late Cretaceous. This is the first time to report an exact isotopic age for a CO2 gas reservoir, which indicates that the 40Ar-39Ar dating can serve as a new technique to date the oil/gas emplacement ages.

Abstract:
The exact determination of isotopic ages of hydrocarbon accumulation, reconstruction and destruction periods using traditional isotopic dating methods is complex because of the small numbers of minerals that correlate with hydrocarbons. The quantitative and direct study of hydrocarbon geochronology is therefore an important scientific problem for isotope geochronology and petroleum geology. This study obtains two isotopic ages from a quartz vein sample associated with bitumen in a reverse fault located in the Bankeng paleo-reservoir on the southern margin of the middle Yangtze block (the northern margin of the Jiangnan-Xuefeng uplift) by inclusion 40Ar/39Ar stepwise crushing in a vacuum. Two different and good linear inverse isochrons that correspond to two age plateaus were determined. The two ages correspond to primary inclusions of about 228 Ma and secondary inclusions of about 149 Ma. These inclusion groups represent two distinct kinds of fluids. Quartz veins associated with bitumen in faulted paleo-reservoirs, which have a strict response relationship with tectonization and hydrocarbon accumulation, are the unified products of tectonic processes, hydrocarbon accumulation and reconstruction. Therefore, they can be used to constrain the hydrocarbon accumulation, reconstruction and destruction periods that are controlled by multiphase and complicated tectonic actions. The evolutionary processes of hydrocarbon accumulation can be divided into two periods consisting of a primary oil and gas reservoir formation period in the late Indosinian epoch (about 228 Ma) and a period of oil and gas reservoir reconstruction in the early Yanshan epoch (about 149 Ma). This study quantitatively reconstructs the hydrocarbon accumulation and destruction chronological framework of a giant hydrocarbon accumulation belt along the southern margin of the middle Yangtze block (the northern margin of the Jiangnan-Xuefeng uplift) controlled by multiphase and complicated tectonism. The two ages associated with hydrocarbons here correspond to the special controlling actions of continental tectonics in the Jiangnan-Xuefeng uplift that affected the timeline of reconstruction and destruction in this giant marine hydrocarbon accumulation. This study shows the feasibility and usefulness of dating inclusions with the 40Ar/39Ar technique for hydrocarbon geochronology, especially in the marine hydrocarbon accumulation region of southern China within a geological setting of old strata, high thermal evolution hydrocarbons, and complex, multiphase and multicycle tectonization.

Abstract:
The interaction of a weak probe laser with an inverted-Y type four-level atomic system driven by two additional coherent fields is investigated theoretically. Under the influence of the coherent coupling fields, the steady-state linear susceptibility of the probe laser shows that the system can have single or double electromagnetically induced transparency windows depending on the amplitude and the detuning of the coupling lasers. The corresponding index of refraction associated with the group velocity of the probe laser can be controlled at both transparency windows by the coupling fields. The propagation of the probe field can be switched from superluminal near the resonance to subluminal on resonance within the single transparency window when two coupling lasers are on resonance. This provides a potential application in quantum information processing. We propose an atomic $^{87}Rb$ system for experimental observation.

Abstract:
We investigate the spontaneous emission from an inverted Y-type atomic system coupled by three coherent fields. We use the Schr\"{o}dinger equation to calculate the probability amplitudes of the wave function of the system and derive an analytical expression of the spontaneous emission spectrum to trace the origin of the spectral features. Quantum interference effects, such as the spectral line narrowing, spectrum splitting and dark resonance are observed. The number of spectral components, the spectral linewidth, and relative heights can be very different depending on the physical parameters. A variety of spontaneous emission spectral features can be controlled by the amplitudes of the coupling fields and the preparation of the initial quantum state of the atom. We propose an ultracold atomic $^{87}Rb$ system for experimental observation.

Abstract:
To minimize the excessive vibration and prolong the fatigue life of the offshore wind turbine systems, it is of value to control the vibration that is induced within the structure by implementing certain kinds of dampers. In this paper, a ball vibration absorber (BVA) is experimentally investigated through a series of shake table tests on a 1/13 scaled wind turbine model. The reductions in top displacement, top acceleration, bottom stress and platform stress of the wind turbine tower system subjected to earthquakes and equivalent wind-wave loads, respectively, with a ball absorber are examined. Cases of the tower with rotating blades are also investigated to validate the efficacy of this damper in mitigating the vibration of an operating wind turbine. The experimental results indicate that the dynamic performance of the tested wind turbine model with a ball absorber is significantly improved compared with that of the uncontrolled structure in terms of the peak response reduction.

Abstract:
Let and be Banach spaces, and let be a bounded linear operator. In this paper, we first define and characterize the quasi-linear operator (resp., out) generalized inverse (resp., ) for the operator , where and are homogeneous subsets. Then, we further investigate the perturbation problems of the generalized inverses and . The results obtained in this paper extend some well-known results for linear operator generalized inverses with prescribed range and kernel. 1. Introduction and Preliminaries Let and be Banach spaces, let be a mapping, and let be a subset of . Recall from [1, 2] that a subset in is called to be homogeneous if for any and , we have . If for any and , we have , then we call as a homogeneous operator on , where is the domain of ; is called a bounded homogeneous operator if maps every bounded set in into bounded set in . Denote by the set of all bounded homogeneous operators from to . Equipped with the usual linear operations for , and for , the norm is defined by , and then similar to the space of all bounded linear operators from to , we can easily prove that is a Banach space (cf. [2, 3]). Throughout this paper, we denote by , , and the domain, the null space, and the range of a bounded homogeneous operator , respectively. Obviously, we have . For an operator , let and be closed subspaces of and , respectively. Recall that the out inverse with prescribed range and kernel is the unique operator satisfying . It is well known that the important kinds of generalized inverses, the Moore-Penrose inverse, the Drazin inverse, the group inverse, and so on, are all generalized inverse (cf. [4, 5]). Researches on the generalized inverse of operators or matrices have been actively ongoing for many years (see [5–12], e. g.). Let and let and be two homogeneous subsets in and , respectively. Motivated by related work on in the literature mentioned above and by our own recent research papers [13, 14], in this paper, we will establish the definition of the quasi-linear operator outer generalized inverse with prescribed range and kernel . We give the necessary and sufficient conditions for the existence of the generalized inverses , and we will also study the perturbation problems of the generalized inverse . Similar results on the generalized inverse are also given. 2. Definitions and Some Characterizations of and We first give the concepts of quasi-additivity and quasi-linear projectors in Banach spaces, which are important for us to present the main results in this paper. Definition 1. Let be a subset of and let be a mapping. Ones calls as

Abstract:
In this paper, we investigate the various different generalized inverses in a Banach algebra with respect to prescribed two idempotents $p$ and $q$. Some new characterizations and explicit representations for these generalized inverses, such as $a^{(2)}_{p,q}$, $a^{(1,2)}_{p,q}$ and $a^{(2,l)}_{p,q}$ will be presented. The obtained results extend and generalize some well--known results for matrices or operators.