Kashif Nazar | Comsats University Islamabad (original) (raw)

Papers by Kashif Nazar

Fractals

Artificial Neural Network (ANN) is a supervised learning nonlinear complex model. This characteri... more Artificial Neural Network (ANN) is a supervised learning nonlinear complex model. This characteristic enables ANN to be used in nonlinear system modeling and classification applications. This research work proposed a technique called Wavelet Neural Network (WNN), and in the hidden layers of WNN, Morlet and Mexican are used as an activation function. During the processing, the WNN gets stuck in the local minimum causing slow convergence. For evaluating such kinds of problems, numerous algorithms have been tried and used. Consequently, this proposed research work used a novel meta-heuristic search technique called Accelerated Particle Swarm Optimization (APSO) algorithm combined with the WNN. Due to the effective convergence and fast searching toward an optimal solution, the APSO algorithm is used. In the proposed APSOWNN algorithm, APSO searches for the best sub-search solution. In conclusion, this model is assessed on the basis of total of three different datasets like the 4-bit OR,...

In this work, by applying the symbolic computation with ansatz functions approach and logarithmic... more In this work, by applying the symbolic computation with ansatz functions approach and logarithmic transformation, we investigate the analytical rational solitons of the mixed Chen-Lee-Liu derivative nonlinear Schrödinger (MCLLNLS)-equation. We acquire two categories of M-shaped rational solutions and their dynamics are revealed in figures by choosing the proper vales of concerned parameters. Moreover two types of interaction of M-shaped rational solutions with kink wave are computed. Furthermore we evaluate multiwaves solutions, Homoclinic breather, kink cross-rational solutions and periodic cross-rational solutions for governing model. We also investigate the stability property of attained solutions and present in the form of table.

IEEE Access

For having an in-depth study and analysis of various network's structural properties such as inte... more For having an in-depth study and analysis of various network's structural properties such as interconnection, extensibility, availability, centralization, vulnerability and reliability, we require distance based graph theoretic parameters. Numerous parameters like distance based dimensions help in designing queuing models in restaurants, public health and service facilities and production lines. Likewise, allocations of robots in several production units are indebted to these. Moreover, chemists and druggists use these parameters in finding out new drug type and structural formula of a chemical compound. In this article, we are finding out the extremal values of local fractional metric dimension of a class of network bearing convex as well as symmetric properties known by the name of convex polytopes. Also we have related the significance of our findings towards the end of the manuscript in the form of fire exit plan. The same will serve as a guide for future architects in planning a floor with a conducive fire exit plan. 11 INDEX TERMS Metric dimension, fractional metric dimension, convex polytopes, resolving sets. I. INTRODUCTION 12 A network G comprises of two sets that are V (G) set of ver-13 tices and E(G) the set of objects that forms connection among 14 the nodes/vertices called edges where E(G) ⊆ V (G) × V (G).

Computer Modeling in Engineering & Sciences, 2022

The Ahlfors map of an n-connected region is a n-to-one map from the region onto the unit disk. Th... more The Ahlfors map of an n-connected region is a n-to-one map from the region onto the unit disk. The Ahlfors map being n-to-one map has n zeros. Previously, the exact zeros of the Ahlfors map are known only for the annulus region and a particular triply connected region. The zeros of the Ahlfors map for general bounded multiply connected regions has been unknown for many years. The purpose of this research is to find the zeros of the Ahlfors map for general bounded multiply connected regions using integral equation method. This work develops six new boundary integral equations for Ahlfors map of bounded multiply connected regions. The kernels of these integral equations are the generalized Neumann kernel, adjoint Neumann kernel, Neumann-type kernel and Kerzman-Stein type kernel. These integral equations are constructed from a non-homogeneous boundary relationship satisfied by an analytic function on a multiply connected region. The first four integral equations have kernels containing...

Coatings, 2020

This study presents the theoretical investigation of a roll-over thin layer formation under the l... more This study presents the theoretical investigation of a roll-over thin layer formation under the lubrication approximation theory. The set of differential equations derived by lubrication approximation is solved by the optimal homotopy asymptotic method (OHAM) to obtain precise expressions for pressure and velocity gradients. Critical quantities such as velocity, pressure gradient, and coating layer depth are numerically estimated. The impact of parameters affecting the coating and layer formation is revealed in detail. Results indicate that the transport properties of the higher-grade fluid play an essential role in regulating velocity, pressure, and the final coated region. Moreover, couple stress effects on the properties of fluid particles to be coated on roller-surface have also been studied.

Journal of Chemistry, 2020

Silicon carbide (SiC), also called carborundum, is a semiconductor containing silicon and carbon.... more Silicon carbide (SiC), also called carborundum, is a semiconductor containing silicon and carbon. Dendrimers are repetitively branched molecules that are typically symmetric around the core and often adopt a spherical three-dimensional morphology. Bismuth(III) iodide is an inorganic compound with the formula BiI3. This gray-black solid is the product of the reaction between bismuth and iodine, which once was of interest in qualitative inorganic analysis. In chemical graph theory, we associate a graph to a compound and compute topological indices that help us in guessing properties of the understudy compound. A topological index is the graph invariant number, calculated from a graph representing a molecule. Most of the proposed topological indices are related either to a vertex adjacency relationship (atom-atom connectivity) in the graph or to topological distances in the graph. In this paper, we aim to compute the first and second Gourava indices and hyper-Gourava indices for silico...

Journal of Chemistry, 2019

There is extremely a great deal of mathematics associated with electrical and electronic engineer... more There is extremely a great deal of mathematics associated with electrical and electronic engineering. It relies upon what zone of electrical and electronic engineering; for instance, there is much increasingly theoretical mathematics in communication theory, signal processing and networking, and so forth. Systems include hubs speaking with one another. A great deal of PCs connected together structure a system. Mobile phone clients structure a network. Networking includes the investigation of the most ideal method for executing a system. Graph theory has discovered a significant use in this zone of research. In this paper, we stretch out this examination to interconnection systems. Hierarchical interconnection systems (HINs) give a system to planning systems with diminished connection cost by exploiting the area of correspondence that exists in parallel applications. HINs utilize numerous levels. Lower-level systems give nearby correspondence, while more significant level systems enc...

Coatings, 2019

In present learning, surface protection layer progression of a third-grade fluid (TGF) is examine... more In present learning, surface protection layer progression of a third-grade fluid (TGF) is examined. Fluid transport within the micro passage made by the firm bladehas beenpresented. Main system of equations of fluidity have been narrated and streamlined by means of lubrication approximation theory (LAT). Here, approximate solutions of velocity, pressure gradient, and coating depth have been presented. Results of coating and layer forming have been tabulated and discussed as well. It is observed that the transport properties of third-order fluid delivers an instrument to regulate flow velocity, pressure, and affect the final coated region.

Journal of Optics, 2018

Surface electromagnetic waves are the solution of Maxwell's frequency domain equations at the... more Surface electromagnetic waves are the solution of Maxwell's frequency domain equations at the interface of two dissimilar materials. In this article, two canonical boundary-value problems have been formulated to analyze the multiplicity of electromagnetic surface waves at the interface between two dissimilar materials in the visible region of light. In the first problem, the interface between two semi-infinite rugate filters having symmetric refractive index profiles is considered and in the second problem, to enhance the multiplicity of surface electromagnetic waves, a homogeneous dielectric slab of 400 nm is included between two semi-infinite symmetric rugate filters. Numerical results show that multiple Bloch surface waves of different phase speeds, different polarization states, different degrees of localization and different field profiles are propagated at the interface between two semi-infinite rugate filters. Having two interfaces when a homogeneous dielectric layer is placed between two semi-infinite rugate filters has increased the multiplicity of electromagnetic surface waves.

Symmetry, 2019

Linguistic variables play a vital role in several qualitative decision environments, in which dec... more Linguistic variables play a vital role in several qualitative decision environments, in which decision-makers assume several feasible linguistic values or criteria instead of a single term for an alternative or variable. The motivation for the use of words or sentences instead of numbers is that linguistic classification and characterizations are generally less precise than numerical ones. In this research article, we encourage the fuzzy linguistic approach and introduce the novel concept known as m-polar fuzzy linguistic variable (mFLV) to increase the affluence of linguistic variables based on m-polar fuzzy (mF) approach. An mF set is an effective concept for interpreting uncertainty and fuzziness. The concept of mFLV is more versatile and sensible for dealing with real-life problems, when data comes from qualitative and multipolar information. We also introduce an mF linguistic ELECTRE-I approach to solve multiple-criteria decision-making (MCDM) and multiple-criteria group decisi...

Indian Journal of Science and Technology, 2015

The Ahlfors map of an n-connected region is a n-to-one map from the region onto the unit disk. Th... more The Ahlfors map of an n-connected region is a n-to-one map from the region onto the unit disk. The Ahlfors map being n-toone map has n zeros. Previously, the exact zeros of the Ahlfors map are known only for the annulus region. The zeros of the Ahlfors map for general bounded doubly connected regions has been unknown for many years. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded doubly connected region. The method depends on the values of Szego kernel, its derivative and the derivative of boundary correspondence function of the Ahlfors map. The Ahlfors map and Szego kernel are both classically related to each other. Ahlfors map can be computed using Szego kernel without relying on the zeros of Ahlfors map. The Szego kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The numerical examples presented here prove the effectiveness of the proposed method.

AIP Conference Proceedings, 2016

The relation between the Ahlfors map and Szegö kernel S(z, a) is classical. The Szegö kernel is a... more The relation between the Ahlfors map and Szegö kernel S(z, a) is classical. The Szegö kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The exact zeros of the Ahlfors map are unknown except for the annulus region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded doubly connected region. The method depends on the values of S(z(t), a), S (z(t), a) and θ (t) where θ(t) is the boundary correspondence function of Ahlfors map. A formula is derived for computing S (z(t), a). An integral equation is constructed for solving θ (t). The numerical examples presented here prove the effectiveness of the proposed method.

AIP Conference Proceedings, 2015

The Ahlfors map of an n–connected region is a branched n–to–one map from the region onto the unit... more The Ahlfors map of an n–connected region is a branched n–to–one map from the region onto the unit disk. In this paper we derived new boundary integral equations for Ahlfors map of bounded multiply connected regions. One of them has the potential to be useful in computing the zeros of Ahlfors map. The kernels of these boundary integral equations are the generalized Neumann kernel, adjoint Neumann kernel, Neumann-type kernel and Kerzman-Stein kernel. These integral equations are constructed from a non-homogeneous boundary relationship satisfied by an analytic function on multiply connected regions.

Jurnal Teknologi, 2015

This paper presents a new boundary integral equation with the adjoint Neumann kernel associated w... more This paper presents a new boundary integral equation with the adjoint Neumann kernel associated with where is the boundary correspondence function of Ahlfors map of a bounded multiply connected region onto a unit disk. The proposed boundary integral equation is constructed from a boundary relationship satisfied by the Ahlfors map of a multiply connected region. The integral equation is solved numerically for using combination of Nystrom method, GMRES method, and fast multiple method. From the computed values of we solve for the boundary correspondence function which then gives the Ahlfors map. The numerical examples presented here prove the effectiveness of the proposed method.

The relation between the Ahlfors map and Szegö kernel S (z, a) is classical. The Szegö kernel is ... more The relation between the Ahlfors map and Szegö kernel S (z, a) is classical. The Szegö kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The exact zeros of the Ahlfors map are known for a particular family of doubly connected regions and a particular triply connected region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded multiply connected regions with smooth boundaries. The method depends on the values of S (z(t), a), S (z(t), a) and θ (t), where θ(t) is the boundary correspondence function of Ahlfors map. A formula is derived for computing S (z(t), a). An integral equation for θ (t) is used for finding the zeros of Ahlfors map. The numerical examples presented here demonstrate the method.

Fractals

Artificial Neural Network (ANN) is a supervised learning nonlinear complex model. This characteri... more Artificial Neural Network (ANN) is a supervised learning nonlinear complex model. This characteristic enables ANN to be used in nonlinear system modeling and classification applications. This research work proposed a technique called Wavelet Neural Network (WNN), and in the hidden layers of WNN, Morlet and Mexican are used as an activation function. During the processing, the WNN gets stuck in the local minimum causing slow convergence. For evaluating such kinds of problems, numerous algorithms have been tried and used. Consequently, this proposed research work used a novel meta-heuristic search technique called Accelerated Particle Swarm Optimization (APSO) algorithm combined with the WNN. Due to the effective convergence and fast searching toward an optimal solution, the APSO algorithm is used. In the proposed APSOWNN algorithm, APSO searches for the best sub-search solution. In conclusion, this model is assessed on the basis of total of three different datasets like the 4-bit OR,...

In this work, by applying the symbolic computation with ansatz functions approach and logarithmic... more In this work, by applying the symbolic computation with ansatz functions approach and logarithmic transformation, we investigate the analytical rational solitons of the mixed Chen-Lee-Liu derivative nonlinear Schrödinger (MCLLNLS)-equation. We acquire two categories of M-shaped rational solutions and their dynamics are revealed in figures by choosing the proper vales of concerned parameters. Moreover two types of interaction of M-shaped rational solutions with kink wave are computed. Furthermore we evaluate multiwaves solutions, Homoclinic breather, kink cross-rational solutions and periodic cross-rational solutions for governing model. We also investigate the stability property of attained solutions and present in the form of table.

IEEE Access

For having an in-depth study and analysis of various network's structural properties such as inte... more For having an in-depth study and analysis of various network's structural properties such as interconnection, extensibility, availability, centralization, vulnerability and reliability, we require distance based graph theoretic parameters. Numerous parameters like distance based dimensions help in designing queuing models in restaurants, public health and service facilities and production lines. Likewise, allocations of robots in several production units are indebted to these. Moreover, chemists and druggists use these parameters in finding out new drug type and structural formula of a chemical compound. In this article, we are finding out the extremal values of local fractional metric dimension of a class of network bearing convex as well as symmetric properties known by the name of convex polytopes. Also we have related the significance of our findings towards the end of the manuscript in the form of fire exit plan. The same will serve as a guide for future architects in planning a floor with a conducive fire exit plan. 11 INDEX TERMS Metric dimension, fractional metric dimension, convex polytopes, resolving sets. I. INTRODUCTION 12 A network G comprises of two sets that are V (G) set of ver-13 tices and E(G) the set of objects that forms connection among 14 the nodes/vertices called edges where E(G) ⊆ V (G) × V (G).

Computer Modeling in Engineering & Sciences, 2022

The Ahlfors map of an n-connected region is a n-to-one map from the region onto the unit disk. Th... more The Ahlfors map of an n-connected region is a n-to-one map from the region onto the unit disk. The Ahlfors map being n-to-one map has n zeros. Previously, the exact zeros of the Ahlfors map are known only for the annulus region and a particular triply connected region. The zeros of the Ahlfors map for general bounded multiply connected regions has been unknown for many years. The purpose of this research is to find the zeros of the Ahlfors map for general bounded multiply connected regions using integral equation method. This work develops six new boundary integral equations for Ahlfors map of bounded multiply connected regions. The kernels of these integral equations are the generalized Neumann kernel, adjoint Neumann kernel, Neumann-type kernel and Kerzman-Stein type kernel. These integral equations are constructed from a non-homogeneous boundary relationship satisfied by an analytic function on a multiply connected region. The first four integral equations have kernels containing...

Coatings, 2020

This study presents the theoretical investigation of a roll-over thin layer formation under the l... more This study presents the theoretical investigation of a roll-over thin layer formation under the lubrication approximation theory. The set of differential equations derived by lubrication approximation is solved by the optimal homotopy asymptotic method (OHAM) to obtain precise expressions for pressure and velocity gradients. Critical quantities such as velocity, pressure gradient, and coating layer depth are numerically estimated. The impact of parameters affecting the coating and layer formation is revealed in detail. Results indicate that the transport properties of the higher-grade fluid play an essential role in regulating velocity, pressure, and the final coated region. Moreover, couple stress effects on the properties of fluid particles to be coated on roller-surface have also been studied.

Journal of Chemistry, 2020

Silicon carbide (SiC), also called carborundum, is a semiconductor containing silicon and carbon.... more Silicon carbide (SiC), also called carborundum, is a semiconductor containing silicon and carbon. Dendrimers are repetitively branched molecules that are typically symmetric around the core and often adopt a spherical three-dimensional morphology. Bismuth(III) iodide is an inorganic compound with the formula BiI3. This gray-black solid is the product of the reaction between bismuth and iodine, which once was of interest in qualitative inorganic analysis. In chemical graph theory, we associate a graph to a compound and compute topological indices that help us in guessing properties of the understudy compound. A topological index is the graph invariant number, calculated from a graph representing a molecule. Most of the proposed topological indices are related either to a vertex adjacency relationship (atom-atom connectivity) in the graph or to topological distances in the graph. In this paper, we aim to compute the first and second Gourava indices and hyper-Gourava indices for silico...

Journal of Chemistry, 2019

There is extremely a great deal of mathematics associated with electrical and electronic engineer... more There is extremely a great deal of mathematics associated with electrical and electronic engineering. It relies upon what zone of electrical and electronic engineering; for instance, there is much increasingly theoretical mathematics in communication theory, signal processing and networking, and so forth. Systems include hubs speaking with one another. A great deal of PCs connected together structure a system. Mobile phone clients structure a network. Networking includes the investigation of the most ideal method for executing a system. Graph theory has discovered a significant use in this zone of research. In this paper, we stretch out this examination to interconnection systems. Hierarchical interconnection systems (HINs) give a system to planning systems with diminished connection cost by exploiting the area of correspondence that exists in parallel applications. HINs utilize numerous levels. Lower-level systems give nearby correspondence, while more significant level systems enc...

Coatings, 2019

In present learning, surface protection layer progression of a third-grade fluid (TGF) is examine... more In present learning, surface protection layer progression of a third-grade fluid (TGF) is examined. Fluid transport within the micro passage made by the firm bladehas beenpresented. Main system of equations of fluidity have been narrated and streamlined by means of lubrication approximation theory (LAT). Here, approximate solutions of velocity, pressure gradient, and coating depth have been presented. Results of coating and layer forming have been tabulated and discussed as well. It is observed that the transport properties of third-order fluid delivers an instrument to regulate flow velocity, pressure, and affect the final coated region.

Journal of Optics, 2018

Surface electromagnetic waves are the solution of Maxwell's frequency domain equations at the... more Surface electromagnetic waves are the solution of Maxwell's frequency domain equations at the interface of two dissimilar materials. In this article, two canonical boundary-value problems have been formulated to analyze the multiplicity of electromagnetic surface waves at the interface between two dissimilar materials in the visible region of light. In the first problem, the interface between two semi-infinite rugate filters having symmetric refractive index profiles is considered and in the second problem, to enhance the multiplicity of surface electromagnetic waves, a homogeneous dielectric slab of 400 nm is included between two semi-infinite symmetric rugate filters. Numerical results show that multiple Bloch surface waves of different phase speeds, different polarization states, different degrees of localization and different field profiles are propagated at the interface between two semi-infinite rugate filters. Having two interfaces when a homogeneous dielectric layer is placed between two semi-infinite rugate filters has increased the multiplicity of electromagnetic surface waves.

Symmetry, 2019

Linguistic variables play a vital role in several qualitative decision environments, in which dec... more Linguistic variables play a vital role in several qualitative decision environments, in which decision-makers assume several feasible linguistic values or criteria instead of a single term for an alternative or variable. The motivation for the use of words or sentences instead of numbers is that linguistic classification and characterizations are generally less precise than numerical ones. In this research article, we encourage the fuzzy linguistic approach and introduce the novel concept known as m-polar fuzzy linguistic variable (mFLV) to increase the affluence of linguistic variables based on m-polar fuzzy (mF) approach. An mF set is an effective concept for interpreting uncertainty and fuzziness. The concept of mFLV is more versatile and sensible for dealing with real-life problems, when data comes from qualitative and multipolar information. We also introduce an mF linguistic ELECTRE-I approach to solve multiple-criteria decision-making (MCDM) and multiple-criteria group decisi...

Indian Journal of Science and Technology, 2015

The Ahlfors map of an n-connected region is a n-to-one map from the region onto the unit disk. Th... more The Ahlfors map of an n-connected region is a n-to-one map from the region onto the unit disk. The Ahlfors map being n-toone map has n zeros. Previously, the exact zeros of the Ahlfors map are known only for the annulus region. The zeros of the Ahlfors map for general bounded doubly connected regions has been unknown for many years. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded doubly connected region. The method depends on the values of Szego kernel, its derivative and the derivative of boundary correspondence function of the Ahlfors map. The Ahlfors map and Szego kernel are both classically related to each other. Ahlfors map can be computed using Szego kernel without relying on the zeros of Ahlfors map. The Szego kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The numerical examples presented here prove the effectiveness of the proposed method.

AIP Conference Proceedings, 2016

The relation between the Ahlfors map and Szegö kernel S(z, a) is classical. The Szegö kernel is a... more The relation between the Ahlfors map and Szegö kernel S(z, a) is classical. The Szegö kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The exact zeros of the Ahlfors map are unknown except for the annulus region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded doubly connected region. The method depends on the values of S(z(t), a), S (z(t), a) and θ (t) where θ(t) is the boundary correspondence function of Ahlfors map. A formula is derived for computing S (z(t), a). An integral equation is constructed for solving θ (t). The numerical examples presented here prove the effectiveness of the proposed method.

AIP Conference Proceedings, 2015

The Ahlfors map of an n–connected region is a branched n–to–one map from the region onto the unit... more The Ahlfors map of an n–connected region is a branched n–to–one map from the region onto the unit disk. In this paper we derived new boundary integral equations for Ahlfors map of bounded multiply connected regions. One of them has the potential to be useful in computing the zeros of Ahlfors map. The kernels of these boundary integral equations are the generalized Neumann kernel, adjoint Neumann kernel, Neumann-type kernel and Kerzman-Stein kernel. These integral equations are constructed from a non-homogeneous boundary relationship satisfied by an analytic function on multiply connected regions.

Jurnal Teknologi, 2015

This paper presents a new boundary integral equation with the adjoint Neumann kernel associated w... more This paper presents a new boundary integral equation with the adjoint Neumann kernel associated with where is the boundary correspondence function of Ahlfors map of a bounded multiply connected region onto a unit disk. The proposed boundary integral equation is constructed from a boundary relationship satisfied by the Ahlfors map of a multiply connected region. The integral equation is solved numerically for using combination of Nystrom method, GMRES method, and fast multiple method. From the computed values of we solve for the boundary correspondence function which then gives the Ahlfors map. The numerical examples presented here prove the effectiveness of the proposed method.

The relation between the Ahlfors map and Szegö kernel S (z, a) is classical. The Szegö kernel is ... more The relation between the Ahlfors map and Szegö kernel S (z, a) is classical. The Szegö kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The exact zeros of the Ahlfors map are known for a particular family of doubly connected regions and a particular triply connected region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded multiply connected regions with smooth boundaries. The method depends on the values of S (z(t), a), S (z(t), a) and θ (t), where θ(t) is the boundary correspondence function of Ahlfors map. A formula is derived for computing S (z(t), a). An integral equation for θ (t) is used for finding the zeros of Ahlfors map. The numerical examples presented here demonstrate the method.