Introduced the notion of symmetric circulant matrix on skew field, an easy method is given to determine the inverse of symmetric circulant matrix on skew field , with this method , we derived the formula of determine inverse about several special type of symmetric circulant matrix. Mathematics Subject Classification: 05A19, 15A15

A computational theory and model of the ontogeny and development of bilateral symmetry in multicellular organisms is presented. Understanding the origin and evolution of bilateral organisms requires an understanding of how bilateral symmetry develops, starting from a single cell. Bilateral symmetric growth of a multicellular organism from a single starter cell is explained as resulting from the...

We show, using exact lattice chirality, that partition functions of lattice gauge theories with vectorlike fermion representations can be split into “light” and “mirror” parts, such that the “light” and “mirror” representations are chiral. The splitting of the full partition function into “light” and “mirror” is well defined only if the two sectors are separately anomaly free. We show that only...

We theoretically investigate the optical activity of three dimensional Dirac semimetals (DSMs) using circular dichroism (CD). show that DSMs in presence a magnetic field any one mirror-symmetric planes materials exhibit notable dichroic behavior. In particular, for different orientations light with respect to plane, CD type-II can detect mirror anomaly by showing sharply distinct patterns at an...

Our main goal in this paper is to investigate stochastic ternary antiderivatives (STAD). First, we will introduce the random antiderivative operator. Then, by introducing aggregation function using special functions such as Mittag-Leffler (MLF), Wright (WF), H-Fox (HFF), Gauss hypergeometric (GHF), and exponential (EXP-F), select optimal control performing necessary calculations. Next, consider...

We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: On-line learning with a simple square loss and finding a symmetric positiv...