Synthesis of (r)- and (s)-1-formyl-6,7,8,9-tetrahydro- N,N-(dipropyl)-3H-benz[e]indol-8-amines: Potent and orally active 5-ht1a receptor agonists

An efficient synthesis of the potent and orally active 5-HT_1A agonists, (R)-(+)- and (S)-(-)-1-formyl-6,7,8,9-tetrahydro-N,N-dipropyl-3H-benz[e]indol-8-amines 1a and 1b , is described. This synthesis was accomplished in twelve steps from commercially available 1,5,6,7-tetrahydro-4H-indol-4-one ( 5 ). The key step involved a regio-controlled Friedel-Crafts acylation of 1-(p-toluenesulfonyl)indol-4-acetyl chloride with ethylene to yield a versatile synthon, 3-(p-toluenesulfonyl)-6,7,8,9-tetrahydro-3H-benz[e]indol-8-one ( 10 ). Subsequent coupling of this ketone with chiral α-methylbenzylamine under reductive amination conditions yielded a mixture of diastereomers. These diastereomers were efficiently separated by either chromatography or fractional recrystallization of the derived hydrochloride salts. Debenzylation of the pure diastereomers was followed by alkylation and formylation to yield (R)-(+)- and (S)-(-)-enantiomers 1a and 1b with >99% purity.     

Predictive control of uncertain nonlinear parabolic PDE systems using a Galerkin/neural-network-based model

In this paper, a model predictive control (MPC) scheme for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities, arising in the context of transport-reaction processes, is proposed. A spatial operator of a parabolic PDE system is characterized by a spectrum that can be partitioned into a finite slow and an infinite fast complement. In this view, first, Galerkin method is used to derive a set of finite dimensional slow ordinary differential equation (ODE) system that captures the dominant dynamics of the initial PDE system. Then, a Multilayer Neural Network (MNN) is employed to parameterize the unknown nonlinearities in the resulting finite dimensional ODE model. Finally, a Galerkin/neural-network-based ODE model is used to predict future states in the MPC algorithm. The proposed controller is applied to stabilize an unstable steady-state of the temperature profile of a catalytic rod subject to input and state constraints.     

Heck coupling reaction using monomeric ortho‐palladated complex of 4‐methoxy‐ benzoylmethylenetriphenylphosphorane under microwave irradiation

The activity of [Pd(C₆H₄CH₂ NH₂‐κ²‐C‐N)PPh₃MOBPPY]OTf complex, A (MOBPPY = 4‐methoxybenzoylmethylenetriphenyl‐ phosphoraneylide), was investigated in the Heck–Mizoroki C? C cross‐coupling reaction under conventional heating and microwave irradiation conditions. The complex is an active and efficient catalyst for the Heck reaction of aryl halides. The yields were excellent using a catalytic amount of [Pd(C₆H₄CH₂ NH₂‐κ²‐C‐N)PPh₃MOBPPY]OTf complex in N‐methyl‐2‐pyrrolidinone (NMP) at 130 °C and 600 W. In comparison to conventional heating conditions, the reactions under microwave irradiation gave higher yields in shorter reaction times. Copyright © 2010 European Peptide Society and John Wiley & Sons, Ltd.     

Involutions on certain Banach algebras related to locally compact groups

Let \(\mathcal{{A}}\) be a Banach algebra and let \(\mathcal{{X}}\) be an introverted closed subspace of \(\mathcal{{A}}^*\) . Here, we give necessary and sufficient conditions for that the dual algebra \(\mathcal{{X}}^*\) of \(\mathcal{{X}}\) or the topological centers \({\mathfrak {Z}}_t^{(1)}(\mathcal{{X}}^{*})\) and \({\mathfrak {Z}}_t^{(2)}(\mathcal{{X}}^{*})\) of \(\mathcal{{X}}^*\) are Banach \(*\) -algebras. We finally apply these results to the Banach space \(L_0^\infty (G)\) of all equivalence classes of essentially bounded functions vanishing at infinity on a locally compact group \(G\) .     

Periodogram analysis with missing observations

Estimation of the spectral measure, covariance and spectral density functions of a strictly stationaryr- vector valued time series is considered, under the assumption that some of the observations are missed. The modified periodograms are calculated using data window. The asymptotic normality is studied.     

Study of ultrafast dynamics of 2-picoline by time-resolved photoelectron imaging

The dynamics of electronically excited states in 2-picoline is studied using femtosecond time-resolved photoelectron imaging spectroscopy. The internal conversion from the S(2) state to the vibrationally excited S(1) state is observed in real time. The secondarily populated high vibronic S(1) state deactivates further to the S(0) state. Photoelectron energy and angular distributions reveal the feature of ionization from the singlet 3p Rydberg states. In addition, variation of time-dependent anisotropy parameters indicates the rotational coherence of the molecule.     

Quartic Thue equations

We will give upper bounds upon the number of integral solutions to binary quartic Thue equations. We will also study the geometric properties of a specific family of binary quartic Thue equations to establish sharper upper bounds.     

Warm tachyon inflation and swampland criteria

In this study, the scenario of a two-component warm tachyon inflation is considered, where the tachyon field plays the role of the inflaton by driving the inflation. During inflation, the tachyon scalar field interacts with the other component of the Universe, which is assumed to be photon gas, i.e., radiation. The interacting term contains a dissipation coefficient, and the study is modeled based on two different and familiar choices of the coefficient that were studied in the literature. By employing the latest observational data, the acceptable ranges for the free parameters of the model are obtained. For any choice within the estimated ranges, there is an acceptable concordance between the theoretical predictions and observations. Although the model is established based on several assumptions, it is crucial to verify their validity for the obtained values of the free parameters of the model. It is found that the model is not self-consistent for all values of the ranges, and for some cases, the assumptions are violated. Therefore, to achieve both self-consistency and agreement with the data, the parameters of the model must be constrained. Subsequently, we consider the recently proposed swampland conjecture, which imposes two conditions on the inflationary models. These criteria rule out some inflationary models; however, warm inflation is among those that successfully satisfy the swampland criteria. We conduct a precise investigation, which indicates that the proposed warm tachyon inflation cannot satisfy the swampland criteria for some cases. In fact, for the first case of the dissipation coefficient, in which, there is dependency only on the scalar field, the model agrees with observational data. However, it is in direct tension with the swampland criteria. Nevertheless, for the second case, wherein the dissipation coefficient has a dependency on both the scalar field and temperature, the model exhibits acceptable agreement with observational data, and suitably satisfies the swampland criteria.     

On the Littlewood cyclotomic polynomials

In this article, we study the cyclotomic polynomials of degree N−1 with coefficients restricted to the set {+1,−1}. By a cyclotomic polynomial we mean any monic polynomial with integer coefficients and all roots of modulus 1. By a careful analysis of the effect of Graeffe's root squaring algorithm on cyclotomic polynomials, P. Borwein and K.K. Choi gave a complete characterization of all cyclotomic polynomials with odd coefficients. They also proved that a polynomial p(x) with coefficients ±1 of even degree N−1 is cyclotomic if and only if p(x)=±Φp₁(±x)Φp₂(±xp₁)?Φpr(±xp₁p₂?pr−1), where N=p₁p₂?pr and the pi are primes, not necessarily distinct. Here is the pth cyclotomic polynomial. Based on substantial computation, they also conjectured that this characterization also holds for polynomials of odd degree with ±1 coefficients. We consider the conjecture for odd degree here. Using Ramanujan's sums, we solve the problem for some special cases. We prove that the conjecture is true for polynomials of degree α²pβ−1 with odd prime p or separable polynomials of any odd degree.     

Density functional investigation of the interaction of acetone with small gold clusters

The structural evolution of Au(n) (n=2, 3, 5, 7, 9, and 13) clusters and the adsorption of organic molecules such as acetone, acetaldehyde, and diethyl ketone on these clusters are studied using a density functional method. The detailed study of the adsorption of acetone on the Au(n) clusters reveals two main points. (1) The acetone molecule interacts with one gold atom of the gold clusters via the carbonyl oxygen. (2) This interaction is mediated through back donation mainly from the spd-hybridized orbitals of the interacting gold atom to the oxygen atom of the acetone molecule. In addition, a hydrogen bond is observed between a hydrogen atom of the methyl group and another gold atom (not involved in the bonding with carbonyl oxygen). Interestingly, the authors notice that the geometries of Au(9) and Au(13) undergo a significant flattening due to the adsorption of an acetone molecule. They have also investigated the role of the alkyl chain attached to the carbonyl group in the adsorption process by analyzing the interaction of Au(13) with acetaldehyde and diethyl ketone.