A new modular indole synthesis. Construction of the highly strained CDEF parent tetracycle of nodulisporic acids A and B

[reaction: see text] Construction of the highly strained CDEF parent tetracycle, a structural motif found only in the potent ectoparasiticidal agents (+)-nodulisporic acids A and B and related congeners, has been achieved via a new modular indole synthesis, exploiting a sequential Stille cross-coupling/Buchwald-Hartwig union/cyclization tactic. The new indole synthesis holds the promise of rapid assembly of diverse, highly substituted indoles possessing uncommon substitution patterns.     

Indole diterpenoid synthetic studies. Construction of the heptacyclic core of (-)-nodulisporic acid D

[structure: see text] Construction of the heptacyclic core of (-)-nodulisporic acid D, a representative member of a recently discovered class of architecturally complex, ectoparasiticidal indole alkaloids, has been achieved. The modular synthetic strategy comprises an expedient, stereocontrolled synthesis of a tricyclic western hemisphere, in conjunction with union of an eastern hemisphere, exploiting the 2-substituted indole synthetic protocol introduced and developed in our laboratory.     

On exact solutions to epidemic dynamic models

In this study, we address an SIR (susceptible-infected-recovered) model that is given as a system of first order differential equations and propose the SIR model on time scales which unifies and extends continuous and discrete models. More precisely, we derive the exact solution to the SIR model and discuss the asymptotic behavior of the number of susceptibles and infectives. Next, we introduce an SIS (susceptible-infected-susceptible) model on time scales and find the exact solution. We solve the models by using the Bernoulli equation on time scales which provides an alternative method to the existing methods. Having the models on time scales also leads to new discrete models. We illustrate our results with examples where the number of infectives in the population is obtained on different time scales.     

Invariant Measures for Set-Valued Dynamical Systems

A continuous map on a compact metric space, regarded as a dynamical system by iteration, admits invariant measures. For a closed relation on such a space, or, equivalently, an upper semicontinuous set-valued map, there are several concepts which extend this idea of invariance for a measure. We prove that four such are equivalent. In particular, such relation invariant measures arise as projections from shift invariant measures on the space of sample paths. There is a similarly close relationship between the ideas of chain recurrence for the set-valued system and for the shift on the sample path space.

     

Fractionation of cigarette smoke condensate for chemical and biological testing

Large-scale fractionation of cigarette smoke condensate (CSC) was carried out by gel filtration and silicic acid column chromatography, and selected fractions and their subfractions were tested for tumorigenicity by mouse-skin bioassay. The weak-acid fraction was separated into four subfractions, the polynuclear aromatic hydrocarbon (PAH) fraction into two subfractions, and the polar neutral lipid fraction into three subfractions. Also, combinations of subfractions were examined for synergic effects and portions of all active material were subjected to chemical analyses by gel filtration, column, thinlayer and gas chromatography, and ultraviolet and mass spectrometry. A weak-acid subfraction (F-63) in which catechol was concentrated, and which comprized 3.27% CSC was shown to be tumorigenic, as were combinations of this sub fraction with the active PAH (F-67) sub fraction and a polar, neutral lipid (F-70) sub fraction, representing 0.01 and 0.05% CSC, respectively. The results indicated that catechol may be a potent cocarcinogen and that the PAH in CSC interact with other components to exert a tumorigenic effect.     

Incorporation of an Allene Unit into α‐Pinene via β‐Elimination

The two double‐bond isomers 3‐iodo‐2,6,6‐trimethylbicyclo[3.1.1]hept‐2‐ene ( 6b ) and 3‐iodo‐4,6,6‐trimethylbicyclo[3.1.1]hept‐2‐ene ( 11 ) were synthesized by reacting 2,6,6‐trimethylbicyclo[3.1.1]heptan‐3‐one ( 9 ) with hydrazine, followed by treatment with I₂ in the presence of Et₃N. Treatment of 11 with t‐BuOK as base in diglyme at 220° resulted in the formation of 9 and 6,6‐dimethyl‐4‐methylidenebicyclo[3.1.1]hept‐2‐ene ( 12 ). For the formation of 9 , the cyclic allene 7 is proposed as an intermediate. Treatment of the second isomer, 6b , with t‐BuOK at 170° gave rise to the diene 12 and the dimerization product 17 . The underlying mechanism of this transformation is discussed. On the basis of density‐functional‐theory (DFT) calculations on the allene 7 and the alkyne 15 , the formation of the latter as the intermediate was excluded.     

Synthesis,Structure and Chemistry of a Twisted Olefinic Bis-didentate Proligand: 5,5′-Bi-5H-cyclopenta[2,1-b : 3,4-b′]dipyridinylidene

The elusive chiral twisted alkene, 5,5′-bi-5H-cyclopenta[2,1-b : 3,4-b′]dipyridinylidene, known also as 9,9′-bi-4,5-diazafluorenylidene (BDAF), has been prepared in racemic form from 9-bromo-4,5-diazafluorene and from 9,9′-bi-4,5-diazafluorenyl and fully characterised. X-Ray measurements show that there is a twist of 37.8° about the double bond between the 4,5-diazafluorenylidene units. A 1 : 1 charge-transfer compound with 7,7,8,8-tetracyanoquinodimethane (TCNQ) contains an unusual packing arrangement which is centred around the formation of spiral stacks. Each BDAF molecule contributes one 4,5-diazofluorenylidene unit to the backbone of the stack, while the second half is involved in hydrogen-bonding interactions and additional stacking with TCNQ. Examples of complexes containing the axially symmetric tetradentate ligand binding to one and to two metal ions, [M(bdaf)Cl₂] and [(MCl₂)₂(bdaf)] (M=Co, Ni, Zn), are reported.     

Training Multilayer Perceptron with Genetic Algorithms and Particle Swarm Optimization for Modeling Stock Price Index Prediction

Predicting stock market (SM) trends is an issue of great interest among researchers, investors and traders since the successful prediction of SMs’ direction may promise various benefits. Because of the fairly nonlinear nature of the historical data, accurate estimation of the SM direction is a rather challenging issue. The aim of this study is to present a novel machine learning (ML) model to forecast the movement of the Borsa Istanbul (BIST) 100 index. Modeling was performed by multilayer perceptron–genetic algorithms (MLP–GA) and multilayer perceptron–particle swarm optimization (MLP–PSO) in two scenarios considering Tanh (x) and the default Gaussian function as the output function. The historical financial time series data utilized in this research is from 1996 to 2020, consisting of nine technical indicators. Results are assessed using Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE) and correlation coefficient values to compare the accuracy and performance of the developed models. Based on the results, the involvement of the Tanh (x) as the output function, improved the accuracy of models compared with the default Gaussian function, significantly. MLP–PSO with population size 125, followed by MLP–GA with population size 50, provided higher accuracy for testing, reporting RMSE of 0.732583 and 0.733063, MAPE of 28.16%, 29.09% and correlation coefficient of 0.694 and 0.695, respectively. According to the results, using the hybrid ML method could successfully improve the prediction accuracy.     

New sequence spaces in multiple normed spaces

In this work, using lacunary sequences and the notion of ideal convergence we define and examine new sequence spaces with respect to a sequence of modulus functions in n-normed linear spaces. Further, the definition of I_θ-convergence in n-normed linear spaces and some related results are given.