The one-particle density matrix $$\gamma(x, y)$$ is one of the key objects in quantum-mechanical approximation schemes. self-adjoint operator $$\Gamma$$ with kernel trace class, but no sharp results on decay its eigenvalues were previously known. note presents asymptotic formula $$\lambda_k \sim (Ak)^{-8/3}$$ , $$A \ge 0$$ as $$k\to\infty$$ for $$\lambda_k$$ and describes main ideas proof.

The Ohno relation for multiple zeta values can be formulated as saying that a certain operator, defined indices, is invariant under taking duals. In this paper, we generalize the to regularized by showing that, although suitably generalized operator not duals, between its at an index and dual written explicitly in terms of gamma function.

In this paper, we present a new type of set called $\Psi_{\Gamma}-C$ by using the operator $\Psi_{\Gamma}$. We investigate relationships these sets with some special which were studied in literature. For instance $\theta$-open set, semi $\theta$-semiopen regular $\theta$-closed set. particular, show that is weaker than Furthermore, prove collection closed under arbitrary union. Finally, obtain ...

The goal of this paper is to present a Dunkl-Gamma type operator with the help generalization two-variable Hermite polynomials and derive its approximating properties via classical modulus continuity, second continuity Peetre’s K-functional.

For an infinite system of particles arriving in and departing from a habitat $X$ -- locally compact Polish space with positive Radon measure $\chi$ Markov process is constructed explicit way. Along its location $x\in X$, each particle characterized by age $\alpha\geq 0$ time since arriving. As the state one takes set marked configurations $\widehat{\Gamma}$, equipped metric that makes it comple...

Methods and apparatuses for reducing the oscillatory motion of rotary crane payloads during operator-commanded or computer-controlled maneuvers. An Input-shaping filter receives input signals from multiple operator input devices and converts them into output signals readable by the crane controller to dampen the payload tangential and radial sway associated with rotation of the jib. The input s...