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We consider non-linear generalizations of fractal interpolating functions applied to functions of one and two variables. The use of such interpolating functions in resizing images is illustrated.
Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully evaluated (analytically continued) to produce two…
Convolution powers of $1/x$ are transformed into functions $f_n$, which satisfy a simple recurrence relation. Solutions are characterized and analyzed.
We obtain wave functionals of free real and complex scalar fields on a 1+1 dimensional lattice by explicitly calculating the path integral for transition from one field configuration to another. The obtained expressions are useful for…
Recent lattice calculations of hadron structure functions are described.
The Wilson-Fisher fixed point defines a continuous family of interacting conformal field theories in non-integer dimensions. In integer dimensions, it is widely believed to lie in the same universality class as the critical Ising model. In…
We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial…
Generalized Haag's theorem has been proved in S O (1, k) invariant quantum field theory. Apart from the above mentioned k+1 variables there can be arbitrary number of additional coordinates including noncommutative ones in the theory. New…
From any graph $G$ arises a flat space wavefunction, obtained by integrating a product of propagators associated to the vertices and edges of $G$. This function is a key ingredient in the computation of cosmological correlators, and several…
Warped conformal field theories (WCFTs) are a novel class of non-relativistic theories. A simple, yet non-trivial, example of such theory is a massive Weyl fermion in $(1+1)$-dimensions, which we study in detail. We derive general…
In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…
Convolutional Neural Networks (CNNs) have been widely applied. But as the CNNs grow, the number of arithmetic operations and memory footprint also increase. Furthermore, typical non-linear activation functions do not allow associativity of…
This article proposes a process to reconstruct a Riemann surface with boundary equipped with a conductivity tensor from its boundary and its Dirichlet-Neumann operator. When initial data comes from a two dimensional real Riemannian oriented…
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…
We examine the question of which characteristic functions yield Weyl-Heisenberg frames for various values of the parameters. We also give numerous applications of frames of characteristic functions to the general case (g,a,b).
We present a brief review of some recent results on conformal anomalies in four and more dimensions. The discussion is intended for relativists, so some background on the quantum origin of anomalies and of their simple properties in D=2 is…
We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper…
We present some work relating to fractal transformations on masked iterated function systems and demonstrate how well known algorithms for generating fractal transformations can be modifed for these systems. We also demonstrate that these…
In 1+1 dimensions, the equations of motion of the Horowitz-Polchinski (HP) effective string have a re-writing in terms of a first order system. This is attributed to FZZ duality. In this note, we observe that a similar re-writing exists in…
Fractals are self-repeating patterns which have dimensions given by fractions rather than integers. While the dimension of a system unambiguously defines its properties, a fractional dimensional system can exhibit interesting properties.…