Recently, Mengestie and Takele characterized the bounded and compact properties of the generalized Volterra-type integral operator on weighted Fock spaces with weight functions growing faster than the Gaussian function defining the classical Fock spaces. Their result shows that the operator exhibits a richer bounded and compact structure when it acts between these spaces than the classical Fock spaces counterpart. A next question to raise is: what will happen to these properties if the weight function grows slower than the Gaussian weight function, specifically in the Fock-Sobolev spaces?So, the aim of this paper is to study the bounded and compact properties of the generalized Volterra-type integral operator on Fock-Sobolev spaces, with the goal of investigating the effects of slower growth of the weight function on these properties. Unlike the fast-growing case, our result shows that the operator has a similar bounded and compact structure as in the classical Fock spaces.

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The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all diagonal elements for a Fock state. We consider the harmonic oscillator with the interacting term, λ1x4/6 + λ2x6/120, where λ1 and λ2 are coupling constants, and x is the position operator. The spectrum shows a quantitative result from the second-order, less than 1 percent error, compared to a numerical solution when turning off the λ2. When we turn on the λ2, more deviation occurs, but the error is still less than 2 percent. We show a quantitative result beyond a weak-coupling region. Our study should provide interest in the holographic principle and strongly coupled boundary theory.

Application of regulators in production of pot plants have been increasing due to lowering growth, improving branching and the number of flowering branches. In order to study the effect of levels and application method of trinexapac-ethyl regulator on height control and morphophysiological characteristics and flowering of Zinnia elegans, a factorial experiment based on completely randomized design with three replications was performed. Zinnias seedlings were planted in polyethylene pots and subjected to trinexapac-ethyl with levels of zero, 2×10-3, 1×10-3, 0.5×10-3 and 4.5×10-4 g when the first bud emerged. Trinexapac-ethyl was applied in both foliar spray and soil application. According to the results, 1×10-3 and 2×10-3g trinexapac-ethyl caused significant reduction in plant height. As trinexapac-ethyl level increased, number of branches and flowers were increased accordingly most of which was under the latter treatment. Branch length and leaf number was not affected. The concentrations 1×10-3 and 2×10-3g increased chlorophyll and shoots sugars, but not on root. Similarly, soil application of Trinexapac-ethyl did not showed positive effects. In light of obtained results, foliar spray application of Trinexapac-ethyl may serve as a suitable way to produce dwarf and pot Zinnia elegans  ‘State fair mix’. Based on the obtained results, application of Trinexapac-ethyl as foliar application can control and reduce the height of the Zinnia elegans ‘State fair mix’.

Calix[8]arenes of conformational rigid were isolated. The NMR parameters of the structure of calix[8]arenes have been compared. The study of organic structures to form nanoporous materials is well-known in chemistry phenomena to find the crystal form of calix[8]arene as supramolecule. Investigated and compared hydrogen bonding, oxygen and nitrogen atoms effect on calix[8]arene and its complexes were reported at Hartree-Fock (HF) theory by Gaussian 2003 of program package. In this work, the complexing properties of azobenzene-bridged calix[8]arene with alkali earth metal cations has studied. The complexation properties of calix[8]arene were studied by HF method. The complex of the calixarenes showed different properties for the different cations, depending on the cations and the position of the substituent grafted on the ligand.

In this article, we considered the effect of uniform acceleration on the quantum binomial state, which consists of a superposition of single-mode Fock states with binomial coefficients. In particular, we studied the nonclassical features of the quantum binomial state under Unruh effect. We obtained analytically various witnesses of nonclassicality such as squeezing, Mandel parameter, and Vogel’s criterion. We found that squeezing could be increased or decreased by the Unruh effect for different observers.  In addition, with the increase of the number of single-mode Fock states in the quantum binomial state, the squeezing increases. Moreover, we found the Mandel parameter and Vogel’s criterion which is a sufficient condition for the nonclassicality of the state and compared the results with the inertial observer.

In this study, we estimated the parameters using the State Space model described in ARIMA form. We’ve also used the Monte Carlo Method for simulating the process in 10000 reputations. Then the estimated parameters and the Monte Carlo simulation method are used to forecast TEPIX index, including 739 observations as an in-sample data from 21th of January 2011 to 19th February 2014 and 59 observations from 20th February 2014 to 21th May 2014 as an out of sample data. Furthermore, For more investigation we’ve considered different horizons of forecasting, short-term (equal to 1 week), mid-term (equal to 1 month) and long term (equal to 3 month). The results showed that Tehran stock market data has enough efficiency to forecast them, and showed that the State Space in Form ARIMA model and the Monte Carlo simulation method can be used as a predictive algorithm for TEPIX index and other indices with similar nature.