Related papers: Central differences, Euler numbers and symbolic me…
An expression in the form of an easily computed integral is given for the determinant of the scalar GJMS operator on an odd--dimensional sphere. Manipulation yields a sum formula for the logdet in terms of the logdets of the ordinary…
This paper investigates quenching solutions of an one-dimensional, two-sided Riemann-Liouville fractional order convection-diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in…
The current paper focuses on fundamental groups and Euler characteristics of various digital models of the 2-dimensional sphere. For all models that we consider, we show that the fundamental groups are trivial, and compute the Euler…
A heuristic formula for 5-point approximation of the first derivative of an unknown function whose values are measured with an error at unequally spaced points is proposed. The derivative at a given point is calculated using the effective…
Motivated by problems from statistical analysis for discretely sampled SPDEs, first we derive central limit theorems for higher order finite differences applied to stochastic process with arbitrary finitely regular paths. These results are…
In this paper the classical Euler-Bernoulli beam (CEBB) theory is reformulated utilising fractional calculus. Such generalisation is called fractional Euler-Bernoulli beams (FEBB) and results in non-local spatial description. The parameters…
Results providing conditions on a family of integro-differential operators to determine a formal automorphism are established. Equivalently, the problem can be read in terms of existence and uniqueness of formal solutions of Cauchy problems…
In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…
We characterize bifurcation values of polynomial functions by using the theory of perverse sheaves and their vanishing cycles. In particular, by introducing a method to compute the jumps of the Euler characteristics with compact support of…
The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier-integrals. The double exponential transformation is not only useful for numerical computations but it is…
In this paper we obtain some explicit expressions for the Euler characteristic of a rank n coherent sheaf F on P^N and of its twists F(t) as polynomials in the Chern classes c_i(F), also giving algorithms for the computation. The employed…
Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two…
We consider the construction of the fundamental function and Abelian differentials of the third kind on a plane algebraic curve over the field of complex numbers that has no singular points. The algorithm for constructing differentials of…
We present several sequences involving harmonic numbers and the central binomial coefficients. The calculational technique is consists of a special summation method that allows, based on proper two-valued integer functions, to calculate…
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…
A quantitative definition of numerical stiffness for initial value problems is proposed. Exponential integrators can effectively integrate linearly stiff systems, but they become expensive when the linear coefficient is a matrix, especially…
One familiar with the Euler zeta function, which established the remarkable relationship between the prime and composite numbers, might naturally ponder the results of the application of this special function in cases where there is no…
For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR…
We present a unified algebraic framework utilizing the formal Bell transform to bridge the Dirichlet convolution of arithmetic functions with the combinatorial structure of infinite Euler-type products. By analyzing the logarithmic…
The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a…