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We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…
In the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner,…
Representation learning, and interpreting learned representations, are key areas of focus in machine learning and neuroscience. Both fields generally use representations as a means to understand or improve a system's computations. In this…
This paper defines a linear representation for nonlinear maps $F:\mathbb{F}^n\rightarrow\mathbb{F}^n$ where $\mathbb{F}$ is a finite field, in terms of matrices over $\mathbb{F}$. This linear representation of the map $F$ associates a…
Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a…
The problem of representation of elements of weighted space of infinitely differentiable functions on real line by exponential series is considered.
A representation invariant is a property that holds of all values of abstract type produced by a module. Representation invariants play important roles in software engineering and program verification. In this paper, we develop a…
An integer sequence that is defined by initial values and a linear recurrence with constant integer coefficients, can be represented by the difference of two arithmetic terms containing exponentiation. All constants occuring in the term are…
Cognitive Architectures are the forefront of the research into developing an artificial cognition. However, they approach the problem from a separated memory and program model of computation. This model of computation poses a fundamental…
We study isometric representations of the semigroup $\mathbb{Z}_+\backslash \{1\}$. Notion of an inverse representation is introduced and a complete description (up to unitary equivalence) of such representations is given. Also, we study a…
In this paper we examine the existence of bicomplexified inverse Fourier transform as an extension of its complexified inverse version within the region of convergence of bicomplex Fourier transform. In this paper we use the idempotent…
For a fixed integer $k \ge 0$, consider representations of positive integers as sums of binomial coefficients of the form $\binom{n}{k}$. While exact minimal bounds for the number of required summands are known only in a few low-dimensional…
The inverse problem of X-tray transforms considers reconstructing functions from some data that are easier to measure, which is typically the integral of that function along geodesics. We prove that if the domain has a foliation structure,…
By the theory of elliptic curves, we study the integers representable as the product of the sum of four integers with the sum of their reciprocals and give a sufficient condition for the integers with a positive representation.
Let $\mathcal{B} = (B_1,\ldots, B_h)$ be an $h$-tuple of sets of positive integers. Let $g_{\mathcal{B} }(n)$ count the number of representations of $n$ in the form $n = b_1\cdots b_h$, where $b_i \in B_i$ for all $i \in \{1,\ldots, h\}$.…
Let f(x_1,x_2,...,x_m) = u_1x_1+u_2 x_2+... + u_mx_m be a linear form with positive integer coefficients, and let N_f(k) = min{|f(A)| : A \subseteq Z and |A|=k}. A minimizing k-set for f is a set A such that |A|=k and |f(A)| = N_f(k). A…
Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…