Related papers: The Compositional Integral: The Narrow And The Com…
We develop a theory for describing composite objects in physics. These can be static objects, such as tables, or things that happen in spacetime (such as a region of spacetime with fields on it regarded as being composed of smaller such…
A new integral representation is derived using a definite integral given by Cauchy and used to evaluate a number of integrals containing the finite series of special functions.
In this paper, we study the class of one dimensional singular integrals that converge in the sense of Cauchy principal value. In addition, we present a simple method for approximating such integrals.
In this PhD thesis, we give a new geometric approach to higher Teichm\"uller theory. In particular we construct a geometric structure on surfaces, generalizing the complex structure, and we explore its link to Hitchin components. The…
We prove a general form of Green Formula and Cauchy Integral Theorem for arbitrary closed rectifiable curves in the plane.
Compositionality is believed to be fundamental to intelligence. In humans, it underlies the structure of thought, language, and higher-level reasoning. In AI, compositional representations can enable a powerful form of out-of-distribution…
Compositional generalization is the capacity to recognize and imagine a large amount of novel combinations from known components. It is a key in human intelligence, but current neural networks generally lack such ability. This report…
Treatises about General Topology that emphasize the notion of uniformity and uniform space find, of course, no difficulty in defining the notion of a complete uniform space and in constructing the completion of a metric space, via its…
It is well known that there is an integral theorem for quaternion-valued functions analogous to Cauchys Theorem for complex-valued functions, namely Fueters Theorem. The class of quaternionic functions for which this applies are generally…
A class of bilinear permutation polynomials over a finite field of characteristic 2 was constructed in a recursive manner recently which involved some other constructions as special cases. We determine the compositional inverses of them…
We consider the problem of solving a linear system of equations which involves complex variables and their conjugates. We characterize when it reduces to a complex linear system, that is, a system involving only complex variables (and not…
Compositional generalization is a basic and essential intellective capability of human beings, which allows us to recombine known parts readily. However, existing neural network based models have been proven to be extremely deficient in…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and discuss the general case. In the final sections, some…
This paper forms part of a larger work where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of "global conformal invariants"; these are defined to be conformally invariant integrals of geometric scalars. The…
Iterative Fast Fourier Transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier…
We define a compact version of the Hilbert transform, which we then use to write explicit expressions for the partial sums and remainders of arbitrary Fourier series. The expression for the partial sums reproduces the known result in terms…
In the paper, we improve our earlier results concerning the existence, uniqueness and differentiability of a global implicit function. Some application to a Cauchy problem for an integro-differential Volterra system of nonconvolution type,…
In this paper, we study the bicomplex version of the Paley-Weiner theorem and the Cauchy integral formula in the upper half-plane.
By suitable examples we illustrate an algorithm for composition of inverse problems.