Distance-based metrics has been practiced to various wide-ranging physicochemical applications, especially in the characterization and modeling of chemical structures. Computational techniques to acquire the precise analytic expressions for a number of distance-based topological indices of inorganic chemical networks and nano-materials are newly growing areas of reticular chemistry. Among these numerical invariants, the eccentricity-based indices are significant for their careful prediction of pharmaceutical properties. In this paper, we work out for the closed formulas of the various eccentricity-based indices, namely the eccentric-connectivity index, the total eccentric-connectivity index, the Zagreb eccentricity indices, the augmented eccentric-connectivity index, the modified eccentric-connectivity index, and the edge version of the eccentric-connectivity index for triazine-and porphyrin-based dendrimers. Furthermore, the expressions for the eccentric-connectivity, total eccentric-connectivity, and modified eccentricconnectivity polynomials are presented for these classes of dendrimers. INDEX TERMSEccentricity-based indices, eccentric-connectivity polynomials, molecular graph, triazinebased dendrimers, porphyrin dendrimers.

Abstract. Let I ⊂ J be monomial ideals of a polynomial algebra S over a field. Then the Stanley depth of J/I is smaller or equal with the Stanley depth of √ J/ √ I. We give also an upper bound for the Stanley depth of the intersection of two primary monomial ideals Q, Q ′ , which is reached if Q, Q ′ are irreducible, ht(Q + Q ′ ) is odd and √ Q, √ Q ′ have no common variable.

It is revealed from the previous studies that there is a strong relation between the chemical characteristic of a chemical compound and its molecular structure. Topological indices defined on the molecular structure of biomolecules can help to gain a better understanding of their physical features and biological activities. Eccentricity connectivity indices are distance-based molecular structure descriptors that have been used for the mathematical modeling of biological activities of diverse nature. As the porphyrin has photofunctional properties, such as a large absorption cross-section, fluorescence emission, and photosensitizing properties, due to these properties, porphyrin dendrimers can be used as photofunctional nanodevices. In this paper, we compute the exact formulae of different versions of eccentric connectivity index and their corresponding polynomials for a class of porphyrin-cored dendrimers. The results obtained can be used in computer-aided molecular design methods applied to pharmaceutical engineering.

Accurate forecasting for the crude oil price is important for government agencies, investors, and researchers. To cope with this issue, in this paper, a new paradigm is designed for the reconstruction of intrinsic mode functions (IMFs) of decomposition and ensemble models to reduce the complexity in computation and to enhance the forecasting accuracy. Decomposition and ensemble methodologies significantly enhance the forecasting accuracy under the framework of “divide and conquer” with the proposed reconstruction of IMFs method. The proposed approach used the autocorrelation at lag 1 of all IMFs for the reconstruction. The ensemble empirical mode decomposition (EEMD) technique is employed to decompose the data into different IMFs. Models that utilized the decomposed data relatively perform well, as compared to its application to the undecomposed data. However, sometimes, the decomposition may produce poor results due to the error accumulation at the end. Thus, in this study, the reconstruction of IMFs is proposed for minimizing the aforementioned error, thereby increasing the forecasting accuracy. The Brent and West Texas Intermediate (WTI) datasets (daily and weekly) are exploited to compare the forecasting performance of autoregressive integrated moving average (ARIMA) along with artificial neural network (ANN) models with the decomposed data. The results have proven that the new paradigm of reconstruction of IMFs through autocorrelation was a better and simple strategy that significantly improved the performance of single models including ARIMA and ANN. Hence, it is concluded that the proposed model takes less computational time and achieved higher forecasting accuracy with the reconstruction of IMFs as opposed to using all IMFs.

In many applications and problems in material engineering and chemistry, it is valuable to know how irregular a given molecular structure is. Furthermore, measures of the irregularity of underlying molecular graphs could be helpful for quantitative structure property relationships and quantitative structure-activity relationships studies, and for determining and expressing chemical and physical properties, such as toxicity, resistance, and melting and boiling points. Here we explore the following three irregularity measures: the irregularity index by Albertson, the total irregularity, and the variance of vertex degrees. Using graph structural analysis and derivation, we compute the above-mentioned irregularity measures of several molecular graphs of nanotubes.