We study the time evolution of R\'enyi entropy in a system two coupled Brownian SYK clusters evolving from an initial product state. The one cluster grows linearly and then saturates to coarse grained entropy. This Page curve is obtained by different methods, path integral saddle point analysis operator dynamics analysis. Using character dynamics, we derive master equation which controls gives ...

the matrix functions appear in several applications in engineering and sciences. the computation of these functions almost involved complicated theory. thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. the aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. more...

would like to thank Mark Watson for correcting a mistake in his summary of Cantor’s argument. 1A note on citations: Mises’s article appeared in German in 1920. An English translation, “Economic Calculation in the Socialist Commonwealth,” appeared in Hayek’s (1990) collection Collectivist Economic Planning in 1935. 2The current paper assumes a basic familiarity with the socialist calculation deb...

In the context of gauge/gravity duals with flavor, we examine heavy-light mesons which involve a heavy and a light quark. For this purpose we embed two D7 brane probes at different positions into the gravity background. We establish the non-Abelian Dirac-Born-Infeld (DBI) action for these probes, in which the U(2) matrix describing the embedding is diagonal. The fluctuations of the brane probes...

This paper presents a bandwidth enhancing technique using a modified ground plane with diagonal edges, L-shaped slot and parasitic patches with main patch for the design of compact antennas. The proposed low-cost, compact-size rectangular patch antenna on 4. 7?cm × 3. 6?cm printed circuit board (FR-4) is designed and validated through simulations and experiments. Results show that the ground pl...

In order to achieve high reliability in disk array systems, two new schemes using dual parity placement, called DH1 (diagonal±horizontal) and DH2 schemes, are presented. Both DH schemes can tolerate up to two disk failures by using two types of parity information placed in the diagonal and the horizontal directions, respectively, in a matrix of disk partitions. DH1 scheme can reduce the occurre...