Abstract The aim of this article is to investigate two new classes quaternions, namely, balancing and Lucas-balancing quaternions that are based on numbers, respectively. Further, some identities including Binet’s formulas, summation Catalan’s identity, etc. concerning these also established.

This paper gives the classification of the Whittaker unitary dual for affine graded Hecke algebras of type E. By the Iwahori-Matsumoto involution, this is equivalent also to the classification of the spherical unitary dual for type E. Together with [BM3], [Ba1] and [Ci1], this work completes the classification of the Whittaker Iwahori-spherical unitary dual, or equivalently, the spherical unita...

In this work, we define higher-order Jacobsthal–Lucas quaternions with the help of numbers. We examine some identities quaternions. introduce their basic definitions and properties. give Binet’s formula, Cassini’s identity, Catalan’s d’Ocagne generating functions, exponential functions also relations between Jacobsthal

In this paper, with the help of finite operators and Fibonacci numbers, we define a new family quaternions whose components are operator numbers. We also provide some properties these types quaternions. Moreover, derive many identities related to by using matrix representations.

A new dual-Vt static CMOS circuits, the Split-Gate dual-Vt (SGDVT) logic. are devised. Their performance is compared to that of all-low-Vt. all-high-Vt. and other dual-Vt circuits in terms of speed and energy consumption (both static and dynamic). They achieved speeds close to that of the all-low-Vt circuits. lower leakage (both stand-by and active) than other dual-Vt circuits. and lower leakag...

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, closed-form solution to planar feature-based LiDAR (Light Detection and Ranging) proposed in this paper. Based on Plücker coordinate-based representation linear features three-dimensional space, quad tuple-based introduced, which makes it possible directly determine difference betw...

In this study, we define Pauli–Leonardo quaternions by taking the coefficients of Pauli as Leonardo numbers. We give recurrence relation, Binet formula, generating function, exponential some special equalities, and sum properties these novel quaternions. addition, investigate interrelations between Pauli–Fibonacci, Pauli–Lucas Moreover, create algorithms that determine terms Finally, generate m...