Bishop-Phelps-Bolloba's theorem on bounded closed convex sets

This paper deals with the \emph{Bishop-Phelps-Bollob\'as property} (\emph{BPBp} for short) on bounded closed convex subsets of a Banach space $X$, not just on its closed unit ball $B_X$. We firstly prove that the \emph{BPBp} holds for bounded linear functionals on arbitrary bounded closed convex subsets of a real Banach space. We show that for all finite dimensional Banach spaces $X$ and $Y$ the pair $(X,Y)$ has the \emph{BPBp} on every bounded closed convex subset $D$ of $X$, and also that for a Banach space $Y$ with property $(\beta)$ the pair $(X,Y)$ has the \emph{BPBp} on every bounded closed absolutely convex subset $D$ of an arbitrary Banach space $X$. For a bounded closed absorbing convex subset $D$ of $X$ with positive modulus convexity we get that the pair $(X,Y)$ has the \emph{BPBp} on $D$ for every Banach space $Y$. We further obtain that for an Asplund space $X$ and for a locally compact Hausdorff $L$, the pair $(X, C_0(L))$ has the \emph{BPBp} on every bounded closed absolutely convex subset $D$ of $X$. Finally we study the stability of the \emph{BPBp} on a bounded closed convex set for the $\ell_1$-sum or $\ell_{\infty}$-sum of a family of Banach spaces

Large Global Volatility Matrix Analysis Based on Structural Information

In this paper, we develop a novel large volatility matrix estimation procedure for analyzing global financial markets. Practitioners often use lower-frequency data, such as weekly or monthly returns, to address the issue of different trading hours in the international financial market. However, this approach can lead to inefficiency due to information loss. To mitigate this problem, our proposed method, called Structured Principal Orthogonal complEment Thresholding (Structured-POET), incorporates structural information for both global and national factor models. We establish the asymptotic properties of the Structured-POET estimator, and also demonstrate the drawbacks of conventional covariance matrix estimation procedures when using lower-frequency data. Finally, we apply the Structured-POET estimator to an out-of-sample portfolio allocation study using international stock market data

Integrating Vehicle-to-Grid Technologies in Autonomous Electric Vehicle Systems

Electrochemical Vehicle-to-Grid (V2G) technologies in autonomous electric vehicles (EVs) offer immense potential to revolutionize energy management and optimize the utilization of EVs. By enabling bidirectional energy flow between EVs and the electric grid, V2G allows EVs not only to consume electricity but also to contribute power back to the grid when necessary. When combined with autonomous capabilities, V2G can provide even greater benefits and flexibility. This research abstract highlights key points concerning V2G technologies in autonomous EVs. Firstly, autonomous EVs equipped with V2G technology can function as mobile energy storage units, aiding in grid stabilization and balancing high electricity demand. Secondly, V2G-enabled autonomous EVs can participate in demand response programs, optimizing charging schedules to off-peak hours and reducing strain on the grid during peak demand. Moreover, V2G facilitates the integration of renewable energy sources by allowing autonomous EVs to store and inject excess renewable energy into the grid when needed. Furthermore, V2G-enabled autonomous EVs act as backup power sources during emergencies or power outages, ensuring uninterrupted electricity supply to critical infrastructure. By participating in V2G programs, autonomous EV owners can generate revenue by selling stored energy to the grid and providing grid services, offsetting EV ownership costs. Additionally, autonomous EVs with V2G technology can intelligently manage their charging and discharging based on factors like electricity prices, grid demand, and user preferences, thereby optimizing energy usage and reducing charging costs. While the widespread adoption of V2G technologies in autonomous EVs hinges on infrastructure development, standardization, regulatory frameworks, and user acceptance, their integration is poised to play a significant role in future sustainable energy and transportation systems. As autonomous and electric vehicle technologies continue to evolve, V2G capabilities hold tremendous promise in transforming energy management, promoting grid reliability, and maximizing the benefits of EVs for both consumers and the grid

Utilizing ECG Waveform Features as New Biometric Authentication Method

In this study, we are proposing a practical way for human identification based on a new biometric method. The new method is built on the use of the electrocardiogram (ECG) signal waveform features, which are produced from the process of acquiring electrical activities of the heart by using electrodes placed on the body. This process is launched over a period of time by using a recording device to read and store the ECG signal. On the contrary of other biometrics method like voice, fingerprint and iris scan, ECG signal cannot be copied or manipulated. The first operation for our system is to record a portion of 30 seconds out of whole ECG signal of a certain user in order to register it as user template in the system. Then the system will take 7 to 9 seconds in authenticating the template using template matching techniques. 44 subjects‟ raw ECG data were downloaded from Physionet website repository. We used a template matching technique for the authentication process and Linear SVM algorithm for the classification task. The accuracy rate was 97.2% for the authentication process and 98.6% for the classification task; with false acceptance rate 1.21%