In this paper, a new statistical averaging technique is proposed for finding an optimal solution to a multi-objective linear fractional programming problem (MOLFPP) and multi-objective linear programming problem (MOLP...In this paper, a new statistical averaging technique is proposed for finding an optimal solution to a multi-objective linear fractional programming problem (MOLFPP) and multi-objective linear programming problem (MOLPP) by using new arithmetic averaging method and new geometric averaging method. It is significantly noticeable same characteristics among all the technique while taking maximum or minimum among all optimized values for multi-objective functions using simplex algorithm. The characteristics provided from the problems are verified by the numerical examples.展开更多
The fractional-order Boussinesq equations(FBSQe)are investigated in this work to see if they can effectively improve the situation where the shallow water equation cannot directly handle the dispersion wave.The fuzzy ...The fractional-order Boussinesq equations(FBSQe)are investigated in this work to see if they can effectively improve the situation where the shallow water equation cannot directly handle the dispersion wave.The fuzzy forms of analytical FBSQe solutions are first derived using the Adomian decomposition method.It also occurs on the sea floor as opposed to at the functionality.A set of dynamical partial differential equations(PDEs)in this article exemplify an unconfined aquifer flow implication.Thismethodology can accurately simulate climatological intrinsic waves,so the ripples are spread across a large demographic zone.The Aboodh transform merged with the mechanism of Adomian decomposition is implemented to obtain the fuzzified FBSQe in R,R^(n) and(2nth)-order involving generalized Hukuhara differentiability.According to the system parameter,we classify the qualitative features of the Aboodh transform in the fuzzified Caputo and Atangana-Baleanu-Caputo fractional derivative formulations,which are addressed in detail.The illustrations depict a comparison analysis between the both fractional operators under gH-differentiability,as well as the appropriate attributes for the fractional-order and unpredictability factorsσ∈[0,1].A statistical experiment is conducted between the findings of both fractional derivatives to prevent changing the hypothesis after the results are known.Based on the suggested analyses,hydrodynamic technicians,as irrigation or aquifer quality experts,may be capable of obtaining an appropriate storage intensity amount,including an unpredictability threshold.展开更多
The goal of this research is to develop a new,simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential e...The goal of this research is to develop a new,simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential equations(PDEs)with variable coefficient.ARA-transform is a robust and highly flexible generalization that unifies several existing transforms.The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s expansion.The process of finding approximations for dynamical fractional-order PDEs is challenging,but the ARA-residual power series technique magnifies this challenge by articulating the solution in a series pattern and then determining the series coefficients by employing the residual component and the limit at infinity concepts.This approach is effective and useful for solving a massive class of fractional-order PDEs.Five appealing implementations are taken into consideration to demonstrate the effectiveness of the projected technique in creating solitary series findings for the governing equations with variable coefficients.Additionally,several visualizations are drawn for different fractional-order values.Besides that,the estimated findings by the proposed technique are in close agreement with the exact outcomes.Finally,statistical analyses further validate the efficacy,dependability and steady interconnectivity of the suggested ARA-residue power series approach.展开更多
Under certain conditions, ultrafast pulsed laser interaction with matter leads to the formation of self-organized conical as well as periodic surface structures(commonly reffered to as, laser induced periodic surface ...Under certain conditions, ultrafast pulsed laser interaction with matter leads to the formation of self-organized conical as well as periodic surface structures(commonly reffered to as, laser induced periodic surface structures, LIPSS). The purpose of the present investigations is to explore the effect of fsec laser fluence and ambient environments(Vacuum &O_2) on the formation of LIPSS and conical structures on the Ti surface. The surface morphology was investigated by scanning electron microscope(SEM). The ablation threshold with single and multiple(N = 100) shots and the existence of an incubation effect was demonstrated by SEM investigations for both the vacuum and the O_2 environment. The phase analysis and chemical composition of the exposed targets were performed by x-ray diffraction(XRD) and energy dispersive x-ray spectroscopy(EDS), respectively. SEM investigations reveal the formation of LIPSS(nano & micro). FFT d-spacing calculations illustrate the dependence of periodicity on the fluence and ambient environment. The periodicity of nano-scale LIPSS is higher in the case of irradiation under vacuum conditions as compared to O_2. Furthermore, the O2 environment reduces the ablation threshold. XRD data reveal that for the O_2 environment, new phases(oxides of Ti) are formed. EDS analysis exhibits that after irradiation under vacuum conditions, the percentage of impurity element(Al) is reduced. The irradiation in the O_2 environment results in 15% atomic diffusion of oxygen.展开更多
We propose a theoretical study investigating the spread of the novel coronavirus(COVID-19)reported inWuhan City of China in 2019.We develop a mathematical model based on the novel corona virus’s characteristics and t...We propose a theoretical study investigating the spread of the novel coronavirus(COVID-19)reported inWuhan City of China in 2019.We develop a mathematical model based on the novel corona virus’s characteristics and then use fractional calculus to fractionalize it.Various fractional order epidemicmodels have been formulated and analyzed using a number of iterative and numerical approacheswhile the complications arise due to singular kernel.We use the well-known Caputo-Fabrizio operator for the purposes of fictionalization because this operator is based on the non-singular kernel.Moreover,to analyze the existence and uniqueness,we will use the well-known fixed point theory.We also prove that the considered model has positive and bounded solutions.We also draw some numerical simulations to verify the theoretical work via graphical representations.We believe that the proposed epidemic model will be helpful for health officials to take some positive steps to control contagious diseases.展开更多
There has been lots of interest in exploring the thermodynamic properties at the horizon of a black hole spacetime.It has been shown earlier that for different spacetimes,the Einstein field equations at the horizon ca...There has been lots of interest in exploring the thermodynamic properties at the horizon of a black hole spacetime.It has been shown earlier that for different spacetimes,the Einstein field equations at the horizon can be expressed as the first law of black hole thermodynamics.Using the idea of foliation,we develop a simpler procedure toobtain such results.We considerγ=constant slices,for the Schwarzschild and Reissner-Nordstrom black hole spacetimes.The Einstein field equations for the induced 3-dimensional metrics of the hypersurfaces are expressed in thermodynamic quantities under the virtual displacements of the hypersurfaces.As expected,it is found that the field equations of the induced metric corresponding to the horizon can be written as afirst law of black hole thermodynamics.It is to be mentioned here that our procedure is much easier,to obtain such results,as here one has to essentially deal with(n-1)-dimensional induced metric for an n-dimensional spacetime.展开更多
Most of the earthquake faults in North-East India, China, mid Atlantic-ridge, the Pacific seismic belt and Japan are found to be predominantly dip-slip in nature. In the present paper a dip-slip fault is taken situate...Most of the earthquake faults in North-East India, China, mid Atlantic-ridge, the Pacific seismic belt and Japan are found to be predominantly dip-slip in nature. In the present paper a dip-slip fault is taken situated in an elastic layer over a viscoelastic half space representing the lithosphere-asthenosphere system. A movement of the dip-slip nature across the fault occurs when the accumulated stress due to various tectonic reasons e.g. mantle convection etc., exceeds the local friction and cohesive forces across the fault. The movement is assumed to be slipping in nature, expressions for displacements, stresses and strains are obtained by solving associated boundary value problem with the help of integral transformation and Green’s function method and a suitable numerical methods is used for computation. A detailed study of these expressions may give some ideas about the nature of stress accumulation in the system, which in turn will be helpful in formulating an earthquake prediction programme.展开更多
In the last few years, Graphene oxide material and biomolecules studies have increased. The various synthesis methods of graphene oxide are constantly pursued to improve and provide safer and more effective alternativ...In the last few years, Graphene oxide material and biomolecules studies have increased. The various synthesis methods of graphene oxide are constantly pursued to improve and provide safer and more effective alternatives. Though the preparation of graphene oxide from Graphite powder or Graphite flake through Hummers method is one of the oldest techniques but still now it is one of the most suitable methods. Here, Graphene Oxide has been prepared from a tunable material Hydrogenated diamond like carbon (HDLC) which is an atomically smooth surface that can be deposited on high-surface area Silicon (100) wafer plate. The HDLC film was heated at a fixed temperature of 900<span style="white-space:nowrap;">°</span>C for 30 min in high vacuum ~1 × 10<sup><span style="white-space:nowrap;">−</span>6</sup> torr and oxygenated at room temperature. A synthetic sequence is described involving Oxidation of annealed HDLC (A-HDLC). Raman measurements confirm the G and D peak by Oxidation of A-HDLC and FTIR confirms functional groups. Atomic force microscopy (AFM) images describe the surface of A-HDLC, Oxidized Graphene and BSA immobilized GO. This GO onto Silicon substrate offers many technical advantages than as oxidized graphene Synthesis from other Chemical methods.展开更多
In Kronecker products works, matrices are sometimes regarded as vectors and vectors are sometimes made in to matrices. To be precise about these reshaping we use the vector and diagonal extraction operators. In the pr...In Kronecker products works, matrices are sometimes regarded as vectors and vectors are sometimes made in to matrices. To be precise about these reshaping we use the vector and diagonal extraction operators. In the present paper, the results are organized in the following ways. First, we formulate the coupled matrix linear least-squares problem and present the efficient solutions of this problem that arises in multistatic antenna array processing problem. Second, we extend the use of connection between the Hadamard (Kronecker) product and diagonal extraction (vector) operator in order to construct a computationally-efficient solution of non-homogeneous coupled matrix differential equations that useful in various applications. Finally, the analysis indicates that the Kronecker (Khatri-Rao) structure method can achieve good efficient while the Hadamard structure method achieve more efficient when the unknown matrices are diagonal.展开更多
Slow evaporation method was used to grow pure and KCl (10 mol%) doped KAP single crystal. The solubility and metastable zone width of aqueous solutions of pure and KCl (10 mol%) doped KAP crystal were evaluated to ana...Slow evaporation method was used to grow pure and KCl (10 mol%) doped KAP single crystal. The solubility and metastable zone width of aqueous solutions of pure and KCl (10 mol%) doped KAP crystal were evaluated to analyze the crystallization process. Measuring the induction period τ, the critical nucleation parameters like interfacial energy (σ), energy of formation of the critical nucleus (ΔG*) were determined using the classical theory of nucleation. The structural properties and optical constants of the grown crystals have been put to test and observed that the addition of KCl results in an enhancement of properties of the crystal. Grown crystals were characterized by powder X-ray diffraction. FTIR spectra confirmed the presence of KCl in pure KAP crystal. UV- Visible spectroscopic studies revealed that addition of KCl in pure KAP crystal increased transparency from 75% to 80%. The analysis of the optical absorption data revealed the presence of both indirect and direct transitions and both of these band gaps increased with the addition of KCl. The transmittance data was analyzed to calculate the refractive index, oscillator energy, dispersion energy, electric susceptibility, zero-frequency dielectric constant and both the real and imaginary parts of the dielectric permittivity as a function of photon energy. The moments of ε(E) were also determined. The dispersion i.e. spectral dependence of the refractive index was discussed according to the single-effective oscillator model proposed by Wemple and DiDomenico.展开更多
In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study diffusion-type traffic flow model based on exponential velocity density relation, which prov...In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study diffusion-type traffic flow model based on exponential velocity density relation, which provides a non-linear second-order parabolic partial differential equation. The analytical solution of the diffusion-type traffic flow model is very complicated to approximate the initial density of the Cauchy problem as a function of x from given data and it may cause a huge error. For the complexity of the analytical solution, the numerical solution is performed by implementing an explicit upwind, explicitly centered, and second-order Lax-Wendroff scheme for the numerical solution. From the comparison of relative error among these three schemes, it is observed that Lax-Wendroff scheme gives less error than the explicit upwind and explicit centered difference scheme. The numerical, analytical analysis and comparative result discussion bring out the fact that the Lax-Wendroff scheme with exponential velocity-density relation of diffusion type traffic flow model is suitable for the congested area and shows a better fit in traffic-congested regions.展开更多
A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming probl...A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.展开更多
This study investigates the cilia transport phenomenon from the perspectives of the heat transfer and variable viscosity in a bending channel. The rightward wall is maintained at a temperature of T0, and the leftward ...This study investigates the cilia transport phenomenon from the perspectives of the heat transfer and variable viscosity in a bending channel. The rightward wall is maintained at a temperature of T0, and the leftward wall has a temperature of T1. Each wall has a metachronal wave that travels along its wall. The structures of the ciliary assemblies are calculated by the well-known simplifying suppositions of the large wavelength and the small Reynolds number approximation. The flow phenomenon for the Newtonian fluid is described as a function of cilia and a metachronal wave velocity. The pressure rise is calculated with MATHEMATICA. The theme of the cilia beating flow is inspected with scheming plots, and its features are discussed at the end of the article.展开更多
Let q be a prime power.By PL(F_q)the authors mean a projective line over the finite field F_q with the additional point∞.In this article,the authors parametrize the conjugacy classes of nondegenerate homomorphisms wh...Let q be a prime power.By PL(F_q)the authors mean a projective line over the finite field F_q with the additional point∞.In this article,the authors parametrize the conjugacy classes of nondegenerate homomorphisms which represent actions ofΔ(3,3,k) =〈u,v:u^3=v^3=(uv)~k=1〉on PL(F_q),where q≡±1(modk).Also,for various values of k,they find the conditions for the existence of coset diagrams depicting the permutation actions ofΔ(3,3,k)on PL(F_q).The conditions are polynomials with integer coefficients and the diagrams are such that every vertex in them is fixed by(■)~k.In this way,they getΔ(3,3,k)as permutation groups on PL(F_q).展开更多
The surface, structural, and mechanical properties of zirconium after irradiation with Ti: sapphire laser(800 nm, 30 fs,1 k Hz) have been investigated. The zirconium targets were exposed for a varying number of laser ...The surface, structural, and mechanical properties of zirconium after irradiation with Ti: sapphire laser(800 nm, 30 fs,1 k Hz) have been investigated. The zirconium targets were exposed for a varying number of laser pulses ranging from 500 to 2000 at a fixed fluence of 3.6 J/cm^2 corresponding to an intensity of 1.2×10^(14)W/cm^2 in ambient environments of deionized water and propanol. A scanning electron microscope(SEM) was employed to investigate the surface morphology of the irradiated zirconium. The SEM analysis shows the formation of various kinds of features including nanoscale laser induced periodic surface structures(LIPSS), sponge like surface structure, flakes, conical structures, droplets, pores, and cavities. The energy dispersive x-ray spectroscopy(EDS) analysis exhibits the variation in chemical composition along with an enhanced diffusion of oxygen under both ambient conditions. The crystal structure and phase analyses of the exposed targets were explored by x-ray diffraction(XRD) and Raman spectroscopy techniques, respectively. The XRD analysis confirms the presence of various phases of zirconium hydride and zirconia after ablation in both de-ionized water and propanol. However, excessive hydrides are formed in the case of propanol. The Raman analysis supports the EDS and XRD results. It also reveals the presence of oxides(zirconia) after irradiation in both de-ionized water and propanol environments.The chemical reactivity of zirconium was significantly improved in the presence of liquids which were accountable for the growth of novel phases and modification in the chemical composition of the irradiated Zr. A nanohardness tester was employed to measure the nanohardness of the laser treated targets. The initial increase and then decrease in nanohardness was observed with an increase in the number of laser pulses in the de-ionized water environment. In the case of propanol,a continuous decrease in hardness was observed.展开更多
Let be a polynomial of degree n and for a complex number , let ?denote the polar derivative of the polynomial ?with respect to . In this paper, first we extend as well as generalize the result proved by Dewan and Mir ...Let be a polynomial of degree n and for a complex number , let ?denote the polar derivative of the polynomial ?with respect to . In this paper, first we extend as well as generalize the result proved by Dewan and Mir [Inter. Jour. Math. and Math. Sci., 16 (2005), 2641-2645] to polar derivative. Besides, another result due to Dewan et al. [J. Math. Anal. Appl. 269 (2002), 489-499] is also extended to polar derivative.展开更多
Let , , be a polynomial of degree n having no zero in , , then Qazi [Proc. Amer. Math. Soc., 115 (1992), 337-343] proved . In this paper, we first extend the above inequality to polar derivative of a polynomial. Furth...Let , , be a polynomial of degree n having no zero in , , then Qazi [Proc. Amer. Math. Soc., 115 (1992), 337-343] proved . In this paper, we first extend the above inequality to polar derivative of a polynomial. Further, as an application of our result, we extend a result due to Dewan et al. [Southeast Asian Bull. Math., 27 (2003), 591-597] to polar derivative.展开更多
In present work chitosan functionalized magnetic nanoparticles (CMNPs) were successfully prepared and investigated for the removal of Reactive Orange 107 dye (RO 107) from water. The chitosan was extracted from shrimp...In present work chitosan functionalized magnetic nanoparticles (CMNPs) were successfully prepared and investigated for the removal of Reactive Orange 107 dye (RO 107) from water. The chitosan was extracted from shrimp shells (Penaeus merguiensis) and was characterized by solubility test and fourier transform infrared spectroscopy (FTIR). Degree of deacetylation of chitosan was examined by 1H-NMR and potentiometric titration method. Thereafter, the chitosan was used for synthesis of CMNPs. The synthesized CMNPs were characterized by FTIR, scanning electron microscopy-energy dispersive spectroscopy (SEM-EDS), thermal gravimetric analysis (TGA) and atomic force microscopy (AFM). Effects of various variables such as contact time, pH, stirring speed, adsorbent dosage, temperature, and concentration of electrolyte on extraction efficiency were evaluated. Freundlich isotherm model fits better that shows the removal of RO 107 with CMNPs by multilayer adsorption behaviour. Furthermore, kinetic study showed that adsorption process followed pseudo-second order kinetic model regulated by chemisorption. Thermodynamic analysis explained that adsorption of RO 107 onto CMNPs was endothermic as well as spontaneous. The developed CNMPs were applied to environmental remediation of spiked RO 107 treated waste water samples with 96.20% removal potential, hence, offered an effective sorbent for removal of RO 107 contaminated water samples.展开更多
In this paper, we present the general exact solutions of such coupled system of matrix fractional differential equations for diagonal unknown matrices in Caputo sense by using vector extraction operators and Hadamard ...In this paper, we present the general exact solutions of such coupled system of matrix fractional differential equations for diagonal unknown matrices in Caputo sense by using vector extraction operators and Hadamard product. Some illustrated examples are also given to show our new approach.展开更多
文摘In this paper, a new statistical averaging technique is proposed for finding an optimal solution to a multi-objective linear fractional programming problem (MOLFPP) and multi-objective linear programming problem (MOLPP) by using new arithmetic averaging method and new geometric averaging method. It is significantly noticeable same characteristics among all the technique while taking maximum or minimum among all optimized values for multi-objective functions using simplex algorithm. The characteristics provided from the problems are verified by the numerical examples.
文摘The fractional-order Boussinesq equations(FBSQe)are investigated in this work to see if they can effectively improve the situation where the shallow water equation cannot directly handle the dispersion wave.The fuzzy forms of analytical FBSQe solutions are first derived using the Adomian decomposition method.It also occurs on the sea floor as opposed to at the functionality.A set of dynamical partial differential equations(PDEs)in this article exemplify an unconfined aquifer flow implication.Thismethodology can accurately simulate climatological intrinsic waves,so the ripples are spread across a large demographic zone.The Aboodh transform merged with the mechanism of Adomian decomposition is implemented to obtain the fuzzified FBSQe in R,R^(n) and(2nth)-order involving generalized Hukuhara differentiability.According to the system parameter,we classify the qualitative features of the Aboodh transform in the fuzzified Caputo and Atangana-Baleanu-Caputo fractional derivative formulations,which are addressed in detail.The illustrations depict a comparison analysis between the both fractional operators under gH-differentiability,as well as the appropriate attributes for the fractional-order and unpredictability factorsσ∈[0,1].A statistical experiment is conducted between the findings of both fractional derivatives to prevent changing the hypothesis after the results are known.Based on the suggested analyses,hydrodynamic technicians,as irrigation or aquifer quality experts,may be capable of obtaining an appropriate storage intensity amount,including an unpredictability threshold.
文摘The goal of this research is to develop a new,simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential equations(PDEs)with variable coefficient.ARA-transform is a robust and highly flexible generalization that unifies several existing transforms.The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s expansion.The process of finding approximations for dynamical fractional-order PDEs is challenging,but the ARA-residual power series technique magnifies this challenge by articulating the solution in a series pattern and then determining the series coefficients by employing the residual component and the limit at infinity concepts.This approach is effective and useful for solving a massive class of fractional-order PDEs.Five appealing implementations are taken into consideration to demonstrate the effectiveness of the projected technique in creating solitary series findings for the governing equations with variable coefficients.Additionally,several visualizations are drawn for different fractional-order values.Besides that,the estimated findings by the proposed technique are in close agreement with the exact outcomes.Finally,statistical analyses further validate the efficacy,dependability and steady interconnectivity of the suggested ARA-residue power series approach.
文摘Under certain conditions, ultrafast pulsed laser interaction with matter leads to the formation of self-organized conical as well as periodic surface structures(commonly reffered to as, laser induced periodic surface structures, LIPSS). The purpose of the present investigations is to explore the effect of fsec laser fluence and ambient environments(Vacuum &O_2) on the formation of LIPSS and conical structures on the Ti surface. The surface morphology was investigated by scanning electron microscope(SEM). The ablation threshold with single and multiple(N = 100) shots and the existence of an incubation effect was demonstrated by SEM investigations for both the vacuum and the O_2 environment. The phase analysis and chemical composition of the exposed targets were performed by x-ray diffraction(XRD) and energy dispersive x-ray spectroscopy(EDS), respectively. SEM investigations reveal the formation of LIPSS(nano & micro). FFT d-spacing calculations illustrate the dependence of periodicity on the fluence and ambient environment. The periodicity of nano-scale LIPSS is higher in the case of irradiation under vacuum conditions as compared to O_2. Furthermore, the O2 environment reduces the ablation threshold. XRD data reveal that for the O_2 environment, new phases(oxides of Ti) are formed. EDS analysis exhibits that after irradiation under vacuum conditions, the percentage of impurity element(Al) is reduced. The irradiation in the O_2 environment results in 15% atomic diffusion of oxygen.
基金supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project No. (PNURSP2022R14),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia。
文摘We propose a theoretical study investigating the spread of the novel coronavirus(COVID-19)reported inWuhan City of China in 2019.We develop a mathematical model based on the novel corona virus’s characteristics and then use fractional calculus to fractionalize it.Various fractional order epidemicmodels have been formulated and analyzed using a number of iterative and numerical approacheswhile the complications arise due to singular kernel.We use the well-known Caputo-Fabrizio operator for the purposes of fictionalization because this operator is based on the non-singular kernel.Moreover,to analyze the existence and uniqueness,we will use the well-known fixed point theory.We also prove that the considered model has positive and bounded solutions.We also draw some numerical simulations to verify the theoretical work via graphical representations.We believe that the proposed epidemic model will be helpful for health officials to take some positive steps to control contagious diseases.
文摘There has been lots of interest in exploring the thermodynamic properties at the horizon of a black hole spacetime.It has been shown earlier that for different spacetimes,the Einstein field equations at the horizon can be expressed as the first law of black hole thermodynamics.Using the idea of foliation,we develop a simpler procedure toobtain such results.We considerγ=constant slices,for the Schwarzschild and Reissner-Nordstrom black hole spacetimes.The Einstein field equations for the induced 3-dimensional metrics of the hypersurfaces are expressed in thermodynamic quantities under the virtual displacements of the hypersurfaces.As expected,it is found that the field equations of the induced metric corresponding to the horizon can be written as afirst law of black hole thermodynamics.It is to be mentioned here that our procedure is much easier,to obtain such results,as here one has to essentially deal with(n-1)-dimensional induced metric for an n-dimensional spacetime.
文摘Most of the earthquake faults in North-East India, China, mid Atlantic-ridge, the Pacific seismic belt and Japan are found to be predominantly dip-slip in nature. In the present paper a dip-slip fault is taken situated in an elastic layer over a viscoelastic half space representing the lithosphere-asthenosphere system. A movement of the dip-slip nature across the fault occurs when the accumulated stress due to various tectonic reasons e.g. mantle convection etc., exceeds the local friction and cohesive forces across the fault. The movement is assumed to be slipping in nature, expressions for displacements, stresses and strains are obtained by solving associated boundary value problem with the help of integral transformation and Green’s function method and a suitable numerical methods is used for computation. A detailed study of these expressions may give some ideas about the nature of stress accumulation in the system, which in turn will be helpful in formulating an earthquake prediction programme.
文摘In the last few years, Graphene oxide material and biomolecules studies have increased. The various synthesis methods of graphene oxide are constantly pursued to improve and provide safer and more effective alternatives. Though the preparation of graphene oxide from Graphite powder or Graphite flake through Hummers method is one of the oldest techniques but still now it is one of the most suitable methods. Here, Graphene Oxide has been prepared from a tunable material Hydrogenated diamond like carbon (HDLC) which is an atomically smooth surface that can be deposited on high-surface area Silicon (100) wafer plate. The HDLC film was heated at a fixed temperature of 900<span style="white-space:nowrap;">°</span>C for 30 min in high vacuum ~1 × 10<sup><span style="white-space:nowrap;">−</span>6</sup> torr and oxygenated at room temperature. A synthetic sequence is described involving Oxidation of annealed HDLC (A-HDLC). Raman measurements confirm the G and D peak by Oxidation of A-HDLC and FTIR confirms functional groups. Atomic force microscopy (AFM) images describe the surface of A-HDLC, Oxidized Graphene and BSA immobilized GO. This GO onto Silicon substrate offers many technical advantages than as oxidized graphene Synthesis from other Chemical methods.
文摘In Kronecker products works, matrices are sometimes regarded as vectors and vectors are sometimes made in to matrices. To be precise about these reshaping we use the vector and diagonal extraction operators. In the present paper, the results are organized in the following ways. First, we formulate the coupled matrix linear least-squares problem and present the efficient solutions of this problem that arises in multistatic antenna array processing problem. Second, we extend the use of connection between the Hadamard (Kronecker) product and diagonal extraction (vector) operator in order to construct a computationally-efficient solution of non-homogeneous coupled matrix differential equations that useful in various applications. Finally, the analysis indicates that the Kronecker (Khatri-Rao) structure method can achieve good efficient while the Hadamard structure method achieve more efficient when the unknown matrices are diagonal.
文摘Slow evaporation method was used to grow pure and KCl (10 mol%) doped KAP single crystal. The solubility and metastable zone width of aqueous solutions of pure and KCl (10 mol%) doped KAP crystal were evaluated to analyze the crystallization process. Measuring the induction period τ, the critical nucleation parameters like interfacial energy (σ), energy of formation of the critical nucleus (ΔG*) were determined using the classical theory of nucleation. The structural properties and optical constants of the grown crystals have been put to test and observed that the addition of KCl results in an enhancement of properties of the crystal. Grown crystals were characterized by powder X-ray diffraction. FTIR spectra confirmed the presence of KCl in pure KAP crystal. UV- Visible spectroscopic studies revealed that addition of KCl in pure KAP crystal increased transparency from 75% to 80%. The analysis of the optical absorption data revealed the presence of both indirect and direct transitions and both of these band gaps increased with the addition of KCl. The transmittance data was analyzed to calculate the refractive index, oscillator energy, dispersion energy, electric susceptibility, zero-frequency dielectric constant and both the real and imaginary parts of the dielectric permittivity as a function of photon energy. The moments of ε(E) were also determined. The dispersion i.e. spectral dependence of the refractive index was discussed according to the single-effective oscillator model proposed by Wemple and DiDomenico.
文摘In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study diffusion-type traffic flow model based on exponential velocity density relation, which provides a non-linear second-order parabolic partial differential equation. The analytical solution of the diffusion-type traffic flow model is very complicated to approximate the initial density of the Cauchy problem as a function of x from given data and it may cause a huge error. For the complexity of the analytical solution, the numerical solution is performed by implementing an explicit upwind, explicitly centered, and second-order Lax-Wendroff scheme for the numerical solution. From the comparison of relative error among these three schemes, it is observed that Lax-Wendroff scheme gives less error than the explicit upwind and explicit centered difference scheme. The numerical, analytical analysis and comparative result discussion bring out the fact that the Lax-Wendroff scheme with exponential velocity-density relation of diffusion type traffic flow model is suitable for the congested area and shows a better fit in traffic-congested regions.
文摘A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.
文摘This study investigates the cilia transport phenomenon from the perspectives of the heat transfer and variable viscosity in a bending channel. The rightward wall is maintained at a temperature of T0, and the leftward wall has a temperature of T1. Each wall has a metachronal wave that travels along its wall. The structures of the ciliary assemblies are calculated by the well-known simplifying suppositions of the large wavelength and the small Reynolds number approximation. The flow phenomenon for the Newtonian fluid is described as a function of cilia and a metachronal wave velocity. The pressure rise is calculated with MATHEMATICA. The theme of the cilia beating flow is inspected with scheming plots, and its features are discussed at the end of the article.
文摘Let q be a prime power.By PL(F_q)the authors mean a projective line over the finite field F_q with the additional point∞.In this article,the authors parametrize the conjugacy classes of nondegenerate homomorphisms which represent actions ofΔ(3,3,k) =〈u,v:u^3=v^3=(uv)~k=1〉on PL(F_q),where q≡±1(modk).Also,for various values of k,they find the conditions for the existence of coset diagrams depicting the permutation actions ofΔ(3,3,k)on PL(F_q).The conditions are polynomials with integer coefficients and the diagrams are such that every vertex in them is fixed by(■)~k.In this way,they getΔ(3,3,k)as permutation groups on PL(F_q).
基金the Higher Education Commission (HEC)the support from Osterreichische Forschungsfodergesellschaft (FFG) (Project 834325)
文摘The surface, structural, and mechanical properties of zirconium after irradiation with Ti: sapphire laser(800 nm, 30 fs,1 k Hz) have been investigated. The zirconium targets were exposed for a varying number of laser pulses ranging from 500 to 2000 at a fixed fluence of 3.6 J/cm^2 corresponding to an intensity of 1.2×10^(14)W/cm^2 in ambient environments of deionized water and propanol. A scanning electron microscope(SEM) was employed to investigate the surface morphology of the irradiated zirconium. The SEM analysis shows the formation of various kinds of features including nanoscale laser induced periodic surface structures(LIPSS), sponge like surface structure, flakes, conical structures, droplets, pores, and cavities. The energy dispersive x-ray spectroscopy(EDS) analysis exhibits the variation in chemical composition along with an enhanced diffusion of oxygen under both ambient conditions. The crystal structure and phase analyses of the exposed targets were explored by x-ray diffraction(XRD) and Raman spectroscopy techniques, respectively. The XRD analysis confirms the presence of various phases of zirconium hydride and zirconia after ablation in both de-ionized water and propanol. However, excessive hydrides are formed in the case of propanol. The Raman analysis supports the EDS and XRD results. It also reveals the presence of oxides(zirconia) after irradiation in both de-ionized water and propanol environments.The chemical reactivity of zirconium was significantly improved in the presence of liquids which were accountable for the growth of novel phases and modification in the chemical composition of the irradiated Zr. A nanohardness tester was employed to measure the nanohardness of the laser treated targets. The initial increase and then decrease in nanohardness was observed with an increase in the number of laser pulses in the de-ionized water environment. In the case of propanol,a continuous decrease in hardness was observed.
文摘Let be a polynomial of degree n and for a complex number , let ?denote the polar derivative of the polynomial ?with respect to . In this paper, first we extend as well as generalize the result proved by Dewan and Mir [Inter. Jour. Math. and Math. Sci., 16 (2005), 2641-2645] to polar derivative. Besides, another result due to Dewan et al. [J. Math. Anal. Appl. 269 (2002), 489-499] is also extended to polar derivative.
文摘Let , , be a polynomial of degree n having no zero in , , then Qazi [Proc. Amer. Math. Soc., 115 (1992), 337-343] proved . In this paper, we first extend the above inequality to polar derivative of a polynomial. Further, as an application of our result, we extend a result due to Dewan et al. [Southeast Asian Bull. Math., 27 (2003), 591-597] to polar derivative.
文摘In present work chitosan functionalized magnetic nanoparticles (CMNPs) were successfully prepared and investigated for the removal of Reactive Orange 107 dye (RO 107) from water. The chitosan was extracted from shrimp shells (Penaeus merguiensis) and was characterized by solubility test and fourier transform infrared spectroscopy (FTIR). Degree of deacetylation of chitosan was examined by 1H-NMR and potentiometric titration method. Thereafter, the chitosan was used for synthesis of CMNPs. The synthesized CMNPs were characterized by FTIR, scanning electron microscopy-energy dispersive spectroscopy (SEM-EDS), thermal gravimetric analysis (TGA) and atomic force microscopy (AFM). Effects of various variables such as contact time, pH, stirring speed, adsorbent dosage, temperature, and concentration of electrolyte on extraction efficiency were evaluated. Freundlich isotherm model fits better that shows the removal of RO 107 with CMNPs by multilayer adsorption behaviour. Furthermore, kinetic study showed that adsorption process followed pseudo-second order kinetic model regulated by chemisorption. Thermodynamic analysis explained that adsorption of RO 107 onto CMNPs was endothermic as well as spontaneous. The developed CNMPs were applied to environmental remediation of spiked RO 107 treated waste water samples with 96.20% removal potential, hence, offered an effective sorbent for removal of RO 107 contaminated water samples.
文摘In this paper, we present the general exact solutions of such coupled system of matrix fractional differential equations for diagonal unknown matrices in Caputo sense by using vector extraction operators and Hadamard product. Some illustrated examples are also given to show our new approach.
