The aim of this paper is to study the existence extreme solutions and their properties for a general ‐Hessian equation involving nonlinear operator. By introducing suitable growth condition developing iterative technique, some new results on asymptotic estimates minimum maximum are derived. Moreover, we also establish sequences that converge uniformly solutions.

Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...

By doing calculations on the methane–water van der Waals complex, we demonstrate that highly converged energy levels and wavefunctions can be obtained using Wigner D basis functions Symmetry-Adapted Lanczos (SAL) method. The is a nondirect product and, therefore, efficient when kinetic operator has accessible singularities. SAL method makes it possible to exploit symmetry label reduce cost of c...

using the riemann-liouville fractional differintegral operator, the lie theory is reformulated. the fractional poisson bracket over the fractional phase space as 3n state vector is defined to be the fractional lie derivative. its properties are outlined and proved. a theorem for the canonicity of the transformation using the exponential operator is proved. the conservation of its generator is p...

in this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $m$-hyponormal operator‎. ‎we show that every analytic extension of a $n$th roots of $m$-hyponormal operator is subscalar of order $2k+2n$‎. ‎as a consequence‎, ‎we get that if the spectrum of such operator $t$ has a nonempty interior in $mathbb{c}$‎, ‎then $t$ has a nontrivial invariant subspace‎. ‎finally‎, ‎w...