usman ali - Academia.edu (original) (raw)

Papers by usman ali

DE GRUYTER, 2020

The quantitative structures activity relationships (QSAR) and quantitative structures property re... more The quantitative structures activity relationships (QSAR) and quantitative structures property relationships (QSPR) between the chemical compounds are studied with the help of topological indices (TI's) which are the fixed real numbers directly linked with the molecular graphs. Gutman and Trinajstic (1972) defined the first degree based TI to measure the total π-electrone energy of a molecular graph. Recently, Ali and Trinajstic (2018) restudied the connection based TI's such as first Zagreb connection index, second Zagreb connection index and modified first Zagreb connection index to find entropy and accentric factor of the octane isomers. In this paper, we study the modified second Zagreb connection index and modified third Zagreb connection index on the T-sum (molecular) graphs obtained by the operations of subdivision and product on two graphs. At the end, as the applications of the obtained results for the modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes are also included. Mainly, a comparision among the Zagreb indices, Zagreb connection indices and modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes is performed with the help of numerical tables, 3D plots and line graphs using the statistical tools.

In many communication standards, several variable length frames generated by some source coder ma... more In many communication standards, several variable length frames generated by some source coder may be aggregated at a given layer of the protocol stack in the same burst to be transmitted. This decreases the signalization overhead and increases the throughput. However, after a transmission over a noisy channel, Frame Synchronization (FS), i.e., recovery of the aggregated frames, may become difficult due to errors affecting the bursts. This paper proposes several robust FS methods making use of the redundancy present in the protocol stack combined with channel soft information. A trellis-based FS algorithm is proposed first. Its efficiency is obtained at the cost of a large delay, since the whole burst must be available before beginning the processing, which might not be possible in some applications. Thus, a low-delay and reduced-complexity Sliding Window-based variant is introduced. Second, an improved version of an on-the-fly three-state automaton for FS is proposed. Bayesian hypothesis testing is performed to retrieve the correct FS. These methods are compared in the context of the WiMAX MAC layer when bursts are transmitted over Rayleigh fading channels.

HINDAWI, COMPLEXITY, 2020

Topological index (numeric number) is a mathematical coding of the molecular graphs that predicts... more Topological index (numeric number) is a mathematical coding of the molecular graphs that predicts the physicochemical, biological, toxicological, and structural properties of the chemical compounds that are directly associated with the molecular graphs. e Zagreb connection indices are one of the TIs of the molecular graphs depending upon the connection number (degree of vertices at distance two) appeared in 1972 to compute the total electron energy of the alternant hydrocarbons. But after that, for a long period, these are not studied by researchers. Recently, Ali and Trinajstic [Mol. Inform. 37(2018), 1 − 7] restudied the Zagreb connection indices and reported that the Zagreb connection indices comparatively to the classical Zagreb indices provide the better absolute value of the correlation coefficient for the thirteen physicochemical properties of the octane isomers (all these tested values have been taken from the website http://www.moleculardescriptors.eu). In this paper, we compute the general results in the form of exact formulae & upper bounds of the second Zagreb connection index and modified first Zagreb connection index for the resultant graphs which are obtained by applying operations of corona, Cartesian, and lexicographic product. At the end, some applications of the obtained results for particular chemical structures such as alkanes, cycloalkanes, linear polynomial chain, carbon nanotubes, fence, and closed fence are presented. In addition, a comparison between exact and computed values of the aforesaid Zagreb indices is also included.

HINDAWI, JOURNAL OF CHEMISTRY, 2019

Representation or coding of the molecular graphs with the help of numerical numbers plays a vital... more Representation or coding of the molecular graphs with the help of numerical numbers plays a vital role in the studies of physicochemical and structural properties of the chemical compounds that are involved in the molecular graphs. For the first time, the modified first Zagreb connection index appeared in the paper by Gutman and Trinajstic (1972) to compute total electron energy of the alternant hydrocarbons, but after that, for a long time, it has not been studied. Recently, Ali and Trinajstic (2018) restudied the first Zagreb connection index (ZC 1), the second Zagreb connection index (ZC 2), and the modified first Zagreb connection index (ZC * 1) to find entropy and acentric factor of the octane isomers. ey also reported that the values provided by the International Academy of Mathematical Chemistry show better chemical capability of the Zagreb connection indices than the ordinary Zagreb indices. Assume that S 1 and S 2 denote the operations of subdivision and semitotal point, respectively. en, the S-sum graphs Q 1 + S Q 2 are obtained by the cartesian product of S(Q 1) and Q 2 , where S ∈ S 1 , S 2 , Q 1 and Q 2 are any connected graphs, and S(Q 1) is a graph obtained after applying the operation S on Q 1. In this paper, we compute the Zagreb connection indices (ZC 1 , ZC 2 , and ZC * 1) of the S-sum graphs in terms of various topological indices of their factor graphs. At the end, as an application of the computed results, the Zagreb connection indices of the S-sum graphs obtained by the particular classes of alkanes are also included.

DE GRUYTER, 2020

The quantitative structures activity relationships (QSAR) and quantitative structures property re... more The quantitative structures activity relationships (QSAR) and quantitative structures property relationships (QSPR) between the chemical compounds are studied with the help of topological indices (TI's) which are the fixed real numbers directly linked with the molecular graphs. Gutman and Trinajstic (1972) defined the first degree based TI to measure the total π-electrone energy of a molecular graph. Recently, Ali and Trinajstic (2018) restudied the connection based TI's such as first Zagreb connection index, second Zagreb connection index and modified first Zagreb connection index to find entropy and accentric factor of the octane isomers. In this paper, we study the modified second Zagreb connection index and modified third Zagreb connection index on the T-sum (molecular) graphs obtained by the operations of subdivision and product on two graphs. At the end, as the applications of the obtained results for the modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes are also included. Mainly, a comparision among the Zagreb indices, Zagreb connection indices and modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes is performed with the help of numerical tables, 3D plots and line graphs using the statistical tools.

In many communication standards, several variable length frames generated by some source coder ma... more In many communication standards, several variable length frames generated by some source coder may be aggregated at a given layer of the protocol stack in the same burst to be transmitted. This decreases the signalization overhead and increases the throughput. However, after a transmission over a noisy channel, Frame Synchronization (FS), i.e., recovery of the aggregated frames, may become difficult due to errors affecting the bursts. This paper proposes several robust FS methods making use of the redundancy present in the protocol stack combined with channel soft information. A trellis-based FS algorithm is proposed first. Its efficiency is obtained at the cost of a large delay, since the whole burst must be available before beginning the processing, which might not be possible in some applications. Thus, a low-delay and reduced-complexity Sliding Window-based variant is introduced. Second, an improved version of an on-the-fly three-state automaton for FS is proposed. Bayesian hypothesis testing is performed to retrieve the correct FS. These methods are compared in the context of the WiMAX MAC layer when bursts are transmitted over Rayleigh fading channels.

HINDAWI, COMPLEXITY, 2020

Topological index (numeric number) is a mathematical coding of the molecular graphs that predicts... more Topological index (numeric number) is a mathematical coding of the molecular graphs that predicts the physicochemical, biological, toxicological, and structural properties of the chemical compounds that are directly associated with the molecular graphs. e Zagreb connection indices are one of the TIs of the molecular graphs depending upon the connection number (degree of vertices at distance two) appeared in 1972 to compute the total electron energy of the alternant hydrocarbons. But after that, for a long period, these are not studied by researchers. Recently, Ali and Trinajstic [Mol. Inform. 37(2018), 1 − 7] restudied the Zagreb connection indices and reported that the Zagreb connection indices comparatively to the classical Zagreb indices provide the better absolute value of the correlation coefficient for the thirteen physicochemical properties of the octane isomers (all these tested values have been taken from the website http://www.moleculardescriptors.eu). In this paper, we compute the general results in the form of exact formulae & upper bounds of the second Zagreb connection index and modified first Zagreb connection index for the resultant graphs which are obtained by applying operations of corona, Cartesian, and lexicographic product. At the end, some applications of the obtained results for particular chemical structures such as alkanes, cycloalkanes, linear polynomial chain, carbon nanotubes, fence, and closed fence are presented. In addition, a comparison between exact and computed values of the aforesaid Zagreb indices is also included.

HINDAWI, JOURNAL OF CHEMISTRY, 2019

Representation or coding of the molecular graphs with the help of numerical numbers plays a vital... more Representation or coding of the molecular graphs with the help of numerical numbers plays a vital role in the studies of physicochemical and structural properties of the chemical compounds that are involved in the molecular graphs. For the first time, the modified first Zagreb connection index appeared in the paper by Gutman and Trinajstic (1972) to compute total electron energy of the alternant hydrocarbons, but after that, for a long time, it has not been studied. Recently, Ali and Trinajstic (2018) restudied the first Zagreb connection index (ZC 1), the second Zagreb connection index (ZC 2), and the modified first Zagreb connection index (ZC * 1) to find entropy and acentric factor of the octane isomers. ey also reported that the values provided by the International Academy of Mathematical Chemistry show better chemical capability of the Zagreb connection indices than the ordinary Zagreb indices. Assume that S 1 and S 2 denote the operations of subdivision and semitotal point, respectively. en, the S-sum graphs Q 1 + S Q 2 are obtained by the cartesian product of S(Q 1) and Q 2 , where S ∈ S 1 , S 2 , Q 1 and Q 2 are any connected graphs, and S(Q 1) is a graph obtained after applying the operation S on Q 1. In this paper, we compute the Zagreb connection indices (ZC 1 , ZC 2 , and ZC * 1) of the S-sum graphs in terms of various topological indices of their factor graphs. At the end, as an application of the computed results, the Zagreb connection indices of the S-sum graphs obtained by the particular classes of alkanes are also included.