Some extensions of the operator entropy type inequalities

In this paper, we define the generalised relative operator entropy and investigate some of its properties such as subadditivity and homogeneity. As application of our result, we obtain the information inequality. In continuation, we establish some reverses of the operator entropy inequalities under certain conditions by using the Mond–Pe?ari? method.     

On Some Properties of $c$-Frames

In this paper we discuss about $c$-frames, namely continuous frames. Since, $c$-frames are generalizations of discrete frames, we generalize some results of discrete frames to continuous version. We explain some results about relations of projections in Hilbert spaces and $c$-frames to characterize these frames. Also, we will specify (precisely) the synthesis and frame operators of Bochner integrable $c$-frames. Finally, we classify Hilbert-Schmidt operators by $c$-frames and express some new identities for Parseval $c$-frames.     

Summability in of a vector measure

We show a picture of the relations among different types of summability of series in the space  of integrable functions with respect to a vector measure m of relatively norm compact range. In order to do that, we study the class of the so‐called m‐1‐summing operators. We give several applications regarding the existence of copies of c ₀ in , as well as on m‐1‐summing operators which are weakly compact, Asplund or weakly precompact.     

Estimating deflection of a simple beam model using fiber optic bragg-grating sensors

In this paper, we develop a method to estimate the bridge deflection using fiber optic Bragg-grating (FBG) strain sensors. For most structural evaluation of bridge integrity, it is very important to measure the geometric profile, which is a major factor representing the global behavior of civil structures, especially bridges. In the past, because of the lack of appropriate methods to measure the deflection curve of bridges on site, the measurement of deflection has been restricted to just a few discrete points along the bridge, and the measuring points have been limited to the locations installed with displacement transducers. However, by applying classical beam theory, a formula is rearranged to estimate the continuously deflected profile by using strains measured directly from several points. In addition, FBG strain sensors, which are electromagnetic, noise-free and multipoint measurable, are employed to obtain flexural strains more accurately and stably. The regression analysis is performed to obtain a strain function from the measured strain data. Finally, the deflection curve can be estimated by applying the strain function to the formula. An experimental test has also been carried out to verify the developed method.     

Lebesgue积分的产生和意义

论述Lebesgue积分产生的背景和思想形成过程，重点介绍直观、想象、类比、猜测等思维形式在Lebesgue积分产生过程中所发挥的作用．     

随机迭代算法的几乎必然T-稳定性及收敛性

目的是在可分Banach空间的框架下,研究某些类型的-弱压缩型的随机算子的Ishikawa-型及Mann-型随机迭代算法的几乎必然T-稳定性及收敛性.在适当的条件下,证明了该类随机算子的随机不动点的Bochner可积性以及这两类随机迭代算法的几乎必然T-稳定性及收敛性.     

Lebesgue积分的另一种定义

用可数分法代替有限分法,可去掉函数有界和定义域测度有限的限制,一次性地作出函数Lebesgue可积的定义并得出可积的充要条件.