SUMMARY
Many different control schemes have been proposed in the technical literature to control the special class of underactuated systems, the- so-called brachiation robots. However, most of these schemes are limited with regard to the method by which the robot executes the brachiation movement. Moreover, many of these control strategies do not take into account the energy of the system as a decision variable. To observe the behavior of the system’s, energy is very important for a better understanding of the robot dynamics while performing the motion. This paper discusses a variety of energy-based strategies to better understand how the system’s energy may influence the type of motion (under-swing or overhand) the robot should perform.
Abstract
Even though for generic $$ \mathcal{N} $$
N
= 1 theories it is not possible to separate distinct branches of supersymmetric vacua, in this paper we study a special class of $$ \mathcal{N} $$
N
= 1 SCFTs, these of Class $$ {\mathcal{S}}_k $$
S
k
for which it is possible to define Coulomb and Higgs branches precisely as for the $$ \mathcal{N} $$
N
= 2 theories of Class $$ \mathcal{S} $$
S
from which they descend. We study the BPS operators that parameterise these branches of vacua using the different limits of the superconformal index as well as the Coulomb and Higgs branch Hilbert Series. Finally, with the tools we have developed, we provide a check that six dimensional (1, 1) Little String theory can be deconstructed from a toroidal quiver in Class $$ {\mathcal{S}}_k $$
S
k
.
Abstract
Recently, Kim and Kim (Russ. J. Math. Phys. 27(2):227–235, 2020) have studied new type degenerate Bernoulli numbers and polynomials by making use of degenerate logarithm. Motivated by (Kim and Kim in Russ. J. Math. Phys. 27(2):227–235, 2020), we consider a special class of polynomials, which we call a new type of degenerate Daehee numbers and polynomials of the second kind. By using their generating function, we derive some new relations including the degenerate Stirling numbers of the first and second kinds. Moreover, we introduce a new type of higher-order degenerate Daehee polynomials of the second kind. We also derive some new identities and properties of this type of polynomials.
We study the value distribution of a special class difference polynomial about finite order meromorphic function. Our methods of the proof are also different from ones in the previous results by Chen (2011), Liu and Laine (2010), and Liu and Yang (2009).
Norm inequalities involving a special class of functions for sector matrices