let $gamma(s_n)$ be the minimum number of proper subgroups‎ ‎$h_i, i=1‎, ‎dots‎, ‎l $ of the symmetric group $s_n$ such that each element in $s_n$‎ ‎lies in some conjugate of one of the $h_i.$ in this paper we‎ ‎conjecture that $$gamma(s_n)=frac{n}{2}left(1-frac{1}{p_1}right)‎ ‎left(1-frac{1}{p_2}right)+2,$$ where $p_1,p_2$ are the two smallest primes‎ ‎in the factorization of $ninmathbb{n}$ an...

In this paper, we introduce some classes of univalent harmonic functions with respect to the symmetric conjugate points by means subordination, analytic parts which are reciprocal starlike (or convex) functions. Further, discuss geometric properties classes, such as integral expression, coefficient estimation, distortion theorem, Jacobian growth estimates, and covering theorem.

The present study proposes novel micro-jet impingement heat sink with effusion holes for flow extraction. The design consists of impingement nozzles surrounded by multiple effusion holes to take away the spent fluid. A three-dimensional numerical model is used for steady, incompressible, laminar flow and conjugate heat transfer for the performance analysis of the proposed design. The computatio...

We resolve two open problems on Kronecker coefficients g(λ,μ,ν) of the symmetric group. First, we prove that for partitions λ,μ,ν with fixed Durfee square size, grow at most polynomially. Second, show maximal g(λ,λ,λ) self-conjugate λ superexponentially. also give applications to explicit special cases.

A weak Brønsted acid-catalyzed asymmetric guanidine aza-conjugate addition reaction has been developed. C2-symmetric, dual hydrogen-bond donating bistriflamides are shown to be highly effective in activating α,β-unsaturated esters toward the intramolecular addition of a pendant guanidinyl nucleophile. Preliminary mechanistic investigation, including density functional theory calculations and ki...

We investigate several classes of state-dependent quantum cloners for three-level systems. These cloners optimally duplicate some of the four maximally-conjugate bases with an equal fidelity, thereby extending the phase-covariant qubit cloner to qutrits. Three distinct classes of qutrit cloners can be distinguished, depending on two, three, or four maximally-conjugate bases are cloned as well (...