An engineering system approach of 2-D cylindrical model of transient mass balance calculations of ozone and other concerned chemicals along with fourteen photolysis, ozone-generating and ozone-depleting chemical react...An engineering system approach of 2-D cylindrical model of transient mass balance calculations of ozone and other concerned chemicals along with fourteen photolysis, ozone-generating and ozone-depleting chemical reaction equations was developed, validated, and used for studying the ozone concentrations, distribution and peak of the layer, ozone depletion and total ozone abundance in the stratosphere. The calculated ozone concentrations and profile at both the Equator and a 60˚N location were found to follow closely with the measured data. The calculated average ozone concentration was within 1% of the measured average, and the deviation of ozone profiles was within 14%. The monthly evolution of stratospheric ozone concentrations and distribution above the Equator was studied with results discussed in details. The influences of slow air movement in both altitudinal and radial directions on ozone concentrations and profile in the stratosphere were explored and discussed. Parametric studies of the influences of gas diffusivities of ozone D<sub>O3</sub> and active atomic oxygen D<sub>O</sub> on ozone concentrations and distributions were also studied and delineated. Having both influences through physical diffusion and chemical reactions, the diffusivity (and diffusion) of atomic oxygen D<sub>O</sub> was found to be more sensitive and important than that of ozone D<sub>O3</sub> on ozone concentrations and distribution. The 2-D ozone model present in this paper for stratospheric ozone and its layer and depletion is shown to be robust, convenient, efficient, and executable for analyzing the complex ozone phenomena in the stratosphere. .展开更多
Robust stability test algorithms of interval 2\|D polynomials and rank\|one polytope of 2\|D polynomials have been developed. To simplify the robust stability test procedure of interval 2\|D polynomials and rank on po...Robust stability test algorithms of interval 2\|D polynomials and rank\|one polytope of 2\|D polynomials have been developed. To simplify the robust stability test procedure of interval 2\|D polynomials and rank on polytope of 2\|D polynomials, we introduce the definition of perturbation radius of 2\|D uncertain polynomials. Based on the perturbation radius of 2\|D polynomials, we establish sufficient conditions of robust Schur stability for the two kinds of uncertain 2\|D polynomials. Examples are given to illustrate the applicaton of our test theorems.展开更多
In this paper,we introduce type 2 degenerate poly-Fubini polynomials and derive several interesting characteristics and properties.In addition,we define type 2 degenerate unipoly-Fubini polynomials and establish some ...In this paper,we introduce type 2 degenerate poly-Fubini polynomials and derive several interesting characteristics and properties.In addition,we define type 2 degenerate unipoly-Fubini polynomials and establish some certain identities.Furthermore,we give some relationships between degenerate unipoly polynomials and special numbers and polynomials.In the last section,certain beautiful zeros and graphical representations of type 2 degenerate poly-Fubini polynomials are shown.展开更多
We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind.In this paper,we investigate some identities and properties for them in connection with central factorial numbers of the second...We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind.In this paper,we investigate some identities and properties for them in connection with central factorial numbers of the second kind and the higher-order type 2 Bernoulli polynomials.We give some relations between the higher-order type 2 Bernoulli numbers of the second kind and their conjugates.展开更多
This article studies distributed pose(orientation and position)estimation of leader–follower multi-agent systems over𝜅-layer graphs in 2-D plane.Only the leaders have access to their orientations and position...This article studies distributed pose(orientation and position)estimation of leader–follower multi-agent systems over𝜅-layer graphs in 2-D plane.Only the leaders have access to their orientations and positions,while the followers can measure the relative bearings or(angular and linear)velocities in their unknown local coordinate frames.For the orientation estimation,the local relative bearings are used to obtain the relative orientations among the agents,based on which a distributed orientation estimation algorithm is proposed for each follower to estimate its orientation.For the position estimation,the local relative bearings are used to obtain the position constraints among the agents,and a distributed position estimation algorithm is proposed for each follower to estimate its position by solving its position constraints.Both the orientation and position estimation errors converge to zero asymptotically.A simulation example is given to verify the theoretical results.展开更多
In this article, the 2-variable general polynomials are taken as base with Peters polynomials to introduce a family of 2-variable Peters mixed type polynomials.These polynomials are framed within the context of monomi...In this article, the 2-variable general polynomials are taken as base with Peters polynomials to introduce a family of 2-variable Peters mixed type polynomials.These polynomials are framed within the context of monomiality principle and their properties are established. Certain summation formulae for these polynomials are also derived. Examples of some members belonging to this family are considered and numbers related to some mixed special polynomials are also explored.展开更多
The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polyn...The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials. Furthermore, the generating function for mixed products of Laguerre 2D and Hermite 2D polynomials and for products of two Hermite 2D polynomials is calculated. A set of infinite sums over products of two Laguerre 2D polynomials as intermediate step to the generating function for products of Laguerre 2D polynomials is evaluated but these sums possess also proper importance for calculations with Laguerre polynomials. With the technique of operator disentanglement some operator identities are derived in an appendix. They allow calculating convolutions of Gaussian functions combined with polynomials in one- and two-dimensional case and are applied to evaluate the discussed generating functions.展开更多
Let G = (V;E) be a simple connected graph. The Wiener index is the sum of distances between all pairs of vertices of a connected graph. The Schultz topological index is equal to and the Modified Schultz topological in...Let G = (V;E) be a simple connected graph. The Wiener index is the sum of distances between all pairs of vertices of a connected graph. The Schultz topological index is equal to and the Modified Schultz topological index is . In this paper, the Schultz, Modified Schultz polynomials and their topological indices of Jahangir graphs J<sub>2,m</sub> for all integer number m ≥ 3 are calculated.展开更多
文摘An engineering system approach of 2-D cylindrical model of transient mass balance calculations of ozone and other concerned chemicals along with fourteen photolysis, ozone-generating and ozone-depleting chemical reaction equations was developed, validated, and used for studying the ozone concentrations, distribution and peak of the layer, ozone depletion and total ozone abundance in the stratosphere. The calculated ozone concentrations and profile at both the Equator and a 60˚N location were found to follow closely with the measured data. The calculated average ozone concentration was within 1% of the measured average, and the deviation of ozone profiles was within 14%. The monthly evolution of stratospheric ozone concentrations and distribution above the Equator was studied with results discussed in details. The influences of slow air movement in both altitudinal and radial directions on ozone concentrations and profile in the stratosphere were explored and discussed. Parametric studies of the influences of gas diffusivities of ozone D<sub>O3</sub> and active atomic oxygen D<sub>O</sub> on ozone concentrations and distributions were also studied and delineated. Having both influences through physical diffusion and chemical reactions, the diffusivity (and diffusion) of atomic oxygen D<sub>O</sub> was found to be more sensitive and important than that of ozone D<sub>O3</sub> on ozone concentrations and distribution. The 2-D ozone model present in this paper for stratospheric ozone and its layer and depletion is shown to be robust, convenient, efficient, and executable for analyzing the complex ozone phenomena in the stratosphere. .
基金This w ork is supported by N S F C of P. R. China and D F G of Germ any.
文摘Robust stability test algorithms of interval 2\|D polynomials and rank\|one polytope of 2\|D polynomials have been developed. To simplify the robust stability test procedure of interval 2\|D polynomials and rank on polytope of 2\|D polynomials, we introduce the definition of perturbation radius of 2\|D uncertain polynomials. Based on the perturbation radius of 2\|D polynomials, we establish sufficient conditions of robust Schur stability for the two kinds of uncertain 2\|D polynomials. Examples are given to illustrate the applicaton of our test theorems.
基金This work was supported by the Taif University Researchers Supporting Project(TURSP-2020/246)“Taif University,Taif,Saudi Arabia”.
文摘In this paper,we introduce type 2 degenerate poly-Fubini polynomials and derive several interesting characteristics and properties.In addition,we define type 2 degenerate unipoly-Fubini polynomials and establish some certain identities.Furthermore,we give some relationships between degenerate unipoly polynomials and special numbers and polynomials.In the last section,certain beautiful zeros and graphical representations of type 2 degenerate poly-Fubini polynomials are shown.
基金This work was supported by the National Research Foundation of Korea(NRF)Grant Funded by the Korea Government(No.2020R1F1A1A01071564).
文摘We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind.In this paper,we investigate some identities and properties for them in connection with central factorial numbers of the second kind and the higher-order type 2 Bernoulli polynomials.We give some relations between the higher-order type 2 Bernoulli numbers of the second kind and their conjugates.
基金supported by Nanyang Technological University,Singapore under the Wallenberg-NTU Presidential Postdoctoral Fellowship and the Natural Science Foundation in Heilongjiang Province,China(YQ2022F003).
文摘This article studies distributed pose(orientation and position)estimation of leader–follower multi-agent systems over𝜅-layer graphs in 2-D plane.Only the leaders have access to their orientations and positions,while the followers can measure the relative bearings or(angular and linear)velocities in their unknown local coordinate frames.For the orientation estimation,the local relative bearings are used to obtain the relative orientations among the agents,based on which a distributed orientation estimation algorithm is proposed for each follower to estimate its orientation.For the position estimation,the local relative bearings are used to obtain the position constraints among the agents,and a distributed position estimation algorithm is proposed for each follower to estimate its position by solving its position constraints.Both the orientation and position estimation errors converge to zero asymptotically.A simulation example is given to verify the theoretical results.
基金UGC-BSR Reaserch Start-Up-Grant (Office Memo No. 30-90/2015(BSR)) awarded to the author by the University Grants Commission (UGC), Government of India, New Delhi
文摘In this article, the 2-variable general polynomials are taken as base with Peters polynomials to introduce a family of 2-variable Peters mixed type polynomials.These polynomials are framed within the context of monomiality principle and their properties are established. Certain summation formulae for these polynomials are also derived. Examples of some members belonging to this family are considered and numbers related to some mixed special polynomials are also explored.
文摘The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials. Furthermore, the generating function for mixed products of Laguerre 2D and Hermite 2D polynomials and for products of two Hermite 2D polynomials is calculated. A set of infinite sums over products of two Laguerre 2D polynomials as intermediate step to the generating function for products of Laguerre 2D polynomials is evaluated but these sums possess also proper importance for calculations with Laguerre polynomials. With the technique of operator disentanglement some operator identities are derived in an appendix. They allow calculating convolutions of Gaussian functions combined with polynomials in one- and two-dimensional case and are applied to evaluate the discussed generating functions.
文摘Let G = (V;E) be a simple connected graph. The Wiener index is the sum of distances between all pairs of vertices of a connected graph. The Schultz topological index is equal to and the Modified Schultz topological index is . In this paper, the Schultz, Modified Schultz polynomials and their topological indices of Jahangir graphs J<sub>2,m</sub> for all integer number m ≥ 3 are calculated.