Graph colouring is the system of assigning a colour to each vertex of a *** is done in such a way that adjacent vertices do not have equal *** is fundamental in graph *** is often used to solve real-world problems lik...
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Graph colouring is the system of assigning a colour to each vertex of a *** is done in such a way that adjacent vertices do not have equal *** is fundamental in graph *** is often used to solve real-world problems like traffic light signalling,map colouring,scheduling,***,social networks are prevalent systems in our ***,the users are considered as vertices,and their connections/interactions are taken as *** users follow other popular users’profiles in these networks,and some don’t,but those non-followers are connected directly to the popular *** means,along with traditional relationship(information flowing),there is another relation among *** depends on the domination of the relationship between the *** type of situation can be modelled as a directed fuzzy *** the colouring of fuzzy graph theory,edge membership plays a vital *** membership is a representation of flowing information between end nodes of the *** from the communication relationship,there may be some other factors like domination in *** influence of power is captured *** this article,the colouring of directed fuzzy graphs is defined based on the influence of *** with this,the chromatic number and strong chromatic number are provided,and related properties are *** application regarding COVID-19 infection is presented using the colouring of directed fuzzy graphs.
We introduce notions of ordinary and standard products of a-finite measures and prove their existence. This approach allows us to construct invariant extensions of ordinary and standard products of Haar measures. In p...
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We introduce notions of ordinary and standard products of a-finite measures and prove their existence. This approach allows us to construct invariant extensions of ordinary and standard products of Haar measures. In particular, we construct translation-invariant extensions of ordinary and standard Lebesgue measures on R∞ and Rogers-Fremlin measures on l∞, respectively, such that topological weights of quasi-metric spaces associated with these measures are maximal （i.e., 2c）. We also solve some Fremlin problems concerned with an existence of uniform measures in Banach spaces.
We present rational approximations of the Bessel functions J v ( x ), v =0,1,…,10, which can be used to simplify the computation of the Hankel transform to the computation of two Fourier transforms.
We present rational approximations of the Bessel functions J v ( x ), v =0,1,…,10, which can be used to simplify the computation of the Hankel transform to the computation of two Fourier transforms.
This paper presents an algorithm for fitting a bivariate spline function to a set of scattered data. The number of knots and their position are determined automatically. However, the user has to provide a non-negative...
This paper presents an algorithm for fitting a bivariate spline function to a set of scattered data. The number of knots and their position are determined automatically. However, the user has to provide a non-negative constant to control the tradeoff between closeness of fit and smoothness of fit.
In this paper an algorithm is presented for fitting a cubic spline satisfying certain local concavity and convexity constraints, to a given set of data points. When using theL2 norm, this problem results in a quadrati...
In this paper an algorithm is presented for fitting a cubic spline satisfying certain local concavity and convexity constraints, to a given set of data points. When using theL
2 norm, this problem results in a quadratic programming problem which is solved by means of the Theil-Van de Panne procedure. The algorithm makes use of the well-conditioned B-splines to represent the cubic splines. The knots are located automatically, as a function of a given upper limit for the sum of squared residuals. A Fortran IV implementation is given.
The definition of rational Runge-Kutta methods for systems of equations is given. The equations associated with those methods are solved for the second, third and fourth order. The many free parameters in the solution...
Some nonlinear methods for solving single ordinary differiential equations are generalized to solve systems of equations. To perform this, a new vector product, compatible with the Samelson inverse of a vector, is def...
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Some nonlinear methods for solving single ordinary differiential equations are generalized to solve systems of equations. To perform this, a new vector product, compatible with the Samelson inverse of a vector, is defined. Conditions for a given order are derived.
Formulas are given for the calculation of the finite Fourier transform of a B-spline. These formulas are useful for the computation of Fourier coefficients of a function which is given at a discrete set of arbitrary p...
In this paper a method is presented for fitting, in the least-squares sense, a bivariate cubic spline function to values of a dependent variable, specified at points on a rectangular grid in the plane of the independe...
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