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Equations of motion for the light-like QCD Wilson loops are studied in the generalized loop space (GLS) setting. To this end, the classically conformal-invariant non-local variations of the cusped Wilson exponentials lying (partially) on…
A generalization $\mathfrak{Gal}_{\ell}(p,q)$ of the conformal Galilei algebra $\mathfrak{g}_{\ell}(d)$ with Levi subalgebra isomorphic to $\mathfrak{sl}(2,\mathbb{R})\oplus\mathfrak{so}(p,q)$ is introduced and a virtual copy of the latter…
We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.
Letting tau denote the inverse transpose automorphism of GL(n,q), a formula is obtained for the number of g in GL(n,q) so that gg^{tau} is equal to a given element h. This generalizes a result of Gow and Macdonald for the special case that…
General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…
This paper studies linear generalised complex structures over vector bundles, as a generalised geometry version of holomorphic vector bundles. In an adapted linear splitting, a linear generalised complex structure on a vector bundle $E\to…
We extend expansion formulas of Liu given in 2013 to the context of multiple series over root systems. Liu and others have shown the usefulness of these formulas in Special Functions and number-theoretic contexts. We extend Wang and Ma's…
Discrete transforms, such as the discrete Fourier transform, are widely used in machine learning to improve model performance by extracting meaningful features. However, with numerous transforms available, selecting an appropriate one often…
In this paper, we give a new discovery of conversion of generalized singular values. New formulation is proposed.
We classify translatively exponential and GL(2,Z) covariant valuations on lattice polygons valued at measurable real functions. A typical example of such valuations is induced by the Laplace transform, but as it turns out there are many…
We reconsider the perturbative expansion of the Wilson loop in 2d noncommutative gauge theories, using an improved integration method. For the class of maximally crossed diagrams in the $\theta \to \infty$ limit we find an intriguing…
A GGC (Generalized Gamma Convolution) representation of Riemann's Xi-function is constructed.
The two-parametric quantum superalgebra $U_{p,q}[gl(2/2)]$ and its induced representations are considered. A method for constructing all finite-dimensional irreducible representations of this quantum superalgebra is also described in…
We present the second-order expression for the observed redshift, accounting for all the relativistic effects from the light propagation and from the frame change at the observer and the source positions. We derive the generic…
Transseries in the sense of \'Ecalle are constructed using a topological approach. A general contractive mapping principle is formulated and proved, showing the closure of transseries under a wide class of operations. In the second part we…
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…
We derive a generalized Rogers generating function and corresponding definite integral, for the continuous $q$-ultraspherical polynomials by applying its connection relation and utilizing orthogonality. Using a recent generalization of the…
We propose a relativistic gravitational theory leading to modified Newtonian dynamics, a paradigm that explains the observed universal galactic acceleration scale and related phenomenology. We discuss phenomenological requirements leading…
In this paper, we study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed complementarity problem on the non-negative orthant. We…