Search results for "Exponent"
showing 10 items of 896 documents
Degrees of irreducible characters of the symmetric group and exponential growth
2015
We consider sequences of degrees of ordinary irreducible S n S_n - characters. We assume that the corresponding Young diagrams have rows and columns bounded by some linear function of n n with leading coefficient less than one. We show that any such sequence has at least exponential growth and we compute an explicit bound.
Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions
2009
Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasi-one dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained, and give evidence of an interesting dimensional crossover between two and one dimensions.
ChemInform Abstract: Intramolecular Michael Reaction of tert-Butylsulfinyl Ketimines: Asymmetric Synthesis of 3-Substituted Indanones.
2012
The reaction proceeds in the presence of the Ruppert—Prakash reagent (Tms-CF3) with either TBAT or TBAF as a base.
Experimental evidence for fractional time evolution in glass forming materials
2002
The infinitesimal generator of time evolution in the standard equation for exponential (Debye) relaxation is replaced with the infinitesimal generator of composite fractional translations. Composite fractional translations are defined as a combination of translation and the fractional time evolution introduced in [Physica A, 221 (1995) 89]. The fractional differential equation for composite fractional relaxation is solved. The resulting dynamical susceptibility is used to fit broad band dielectric spectroscopy data of glycerol. The composite fractional susceptibility function can exhibit an asymmetric relaxation peak and an excess wing at high frequencies in the imaginary part. Nevertheless…
Non-exponential relaxation in disordered materials: Phenomenological correlations and spectrally selective experiments
1998
Abstract In most glass-forming materials external perturbations are relaxed in a non-exponential fashion. It is shown that the degree of non-exponentiality is phenomenologically correlated with the departure from simple thermally activated behavior as measured by the fragility index m. In model glass formers such as the Ge-As-Se ternary alloy, and to some degree for amorphous materials in general, the correlations with these properties are observed also for other characteristic features. These include the specific heat step and the aging kinetics in the glass transformation range. While phenomenological correlations have proven very useful for rationalizing the properties of many glass form…
ChemInform Abstract: Base-Dependent Stereodivergent Intramolecular Aza-Michael Reaction: Asymmetric Synthesis of 1,3-Disubstituted Isoindolines.
2014
For the reaction of the compounds (I) the careful choice of the base allows the exclusive formation of either cis or trans diastereoisomer with the exception of the trihalogenates (Ie) and (If), which afford the cis-products regardless of the base used.
On differences and similarities in the analysis of Lorenz, Chen, and Lu systems
2015
Currently it is being actively discussed the question of the equivalence of various Lorenzlike systems and the possibility of universal consideration of their behavior (Algaba et al., 2013a,b, 2014b,c; Chen, 2013; Chen and Yang, 2013; Leonov, 2013a), in view of the possibility of reduction of such systems to the same form with the help of various transformations. In the present paper the differences and similarities in the analysis of the Lorenz, the Chen and the Lu systems are discussed. It is shown that the Chen and the Lu systems stimulate the development of new methods for the analysis of chaotic systems. Open problems are discussed. peerReviewed
Stochastic Stability Analysis for Markovian Jump Neutral Nonlinear Systems
2012
In this paper, the stability problem is studied for a class of Markovian jump neutral nonlinear systems with time-varying delay. By Lyapunov-Krasovskii function approach, a novel mean-square exponential stability criterion is derived for the situations that the system's transition rates are completely accessible, partially accessible and non-accessible, respectively. Moreover, the developed stability criterion is extended to the systems with different bounded sector nonlinear constraints. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed methods.
Robust Finite-Time Control of Switched Linear Systems and Application to a Class of Servomechanism Systems
2015
This paper investigates finite-time (FT) stability and stabilization problems for a class of switched linear systems with polytopic uncertainties. Both stable and unstable subsystems are considered to coexist in the system, and a new concept of extended FT stability is proposed as the first attempt. A stability criterion is first established, where the admissible maximum switching number is obtained while ensuring extended FT stability of switched linear systems with time-varying delays under a given maximum ratio between the running time of unstable subsystems and the running time of stable subsystems. Sufficient conditions on the existence of desired memory state-feedback controllers are …
Comparative evaluation of postoperative pain and periapical healing after root canal treatment using three different base endodontic sealers – A rand…
2022
Abstract Backgroundː Endodontic Sealers come in direct contact with periapical tissue through the apical foramen and lateral canals, influencing the postoperative pain and periapical healing. The aim of the present study was to evaluate and compare postoperative pain and periapical healing after root canal treatment using different base endodontic sealers.Methodsː Primary root canal treatment was initiated in 63 patients diagnosed with necrotic pulp and apical periodontitis, followed by which the endodontic sealers used for obturation were selected based on the random allocation of the participants to the following groups; Tubli-Seal, AH Plus and BioRoot RCS. Postoperative pain was recorded…