Related papers: Generalized numerical-theoretical transformation
Bernstein's theorem (also called Hausdorff--Bernstein--Widder theorem) enables the integral representation of a completely monotonic function. We introduce a finite completely monotonic function, which is a completely monotonic function…
Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical…
Generalization is at the core of machine learning models. However, the definition of generalization is not entirely clear. We employ set theory to introduce the concepts of algorithms, hypotheses, and dataset generalization. We analyze the…
The nerve theorem is a basic result of algebraic topology that plays a central role in computational and applied aspects of the subject. In topological data analysis, one often needs a nerve theorem that is functorial in an appropriate…
Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\hat{x}, \hat{p}] = i f(\hat{p})$. We apply this deformed quantization to free scalar field theory for $f_\pm =1\pm \beta p^2$.…
The equipartition theorem states that inverse temperature equals the log-derivative of the density of states. This relation can be generalized by introducing a proportionality factor involving an increasing positive function phi(x). It is…
Various forms of Mean Value Theorems are available in the literature. If we use Flett's Mean Value Theorem in Extended Generalized Mean Value Theorem then what would the new theorem look like. A sincere effort is done to develop this…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
Iterating Newton's method symbolically for the general quadratic yields a rational function, the numerator and denominator of which are polynomials with highly composite coefficients.
A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for…
This article belongs to a series on geometric complexity theory (GCT), an approach to the P vs. NP and related problems through algebraic geometry and representation theory. The basic principle behind this approach is called the flip. In…
The generalized Euler number E_{n|k} counts the number of permutations of {1,2,...,n} which have a descent in position m if and only if m is divisible by k. The classical Euler numbers are the special case when k=2. In this paper, we study…
Both in quantum theory and in general probabilistic theories, measurements with $n$ outcomes are modelled as $n$-tuples of \emph{effects} summing up to the unit effect. Why is this the case, and can this assumption be meaningfully relaxed?…
Let $f(x)\in \mathbb{Z}[x]$ be an irreducible polynomial of degree $d\ge 1$. Let $k\ge2$ be an integer. The number of integers $n$ such that $f(n)$ is $k$-free is widely studied in the literature. In principle, one expects that $f(n)$ is…
We prove that several results in different areas of number theory such as the divergent series, summation of arithmetic functions, uniform distribution modulo one and summation over prime numbers which are currently considered to be…
In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].
The basic theorem of the Lagrangian formulation for general superfield theory of fields (GSTF) is proved. The gauge transformations of general type (GTGT) and gauge algebra of generators of GTGT (GGTGT) as the consequences of the above…
To make precise the sense in which the operational predictions of quantum theory conflict with a classical worldview, it is necessary to articulate a notion of classicality within an operational framework. A widely applicable notion of…
This article discusses completeness of Boolean Algebra as First Order Theory in Goedel's meaning. If Theory is complete then any possible transformation is equivalent to some transformation using axioms, predicates etc. defined for this…
Inspired by classical ("actual") Quantum Theory over $\mathbb{C}$ and Modal Quantum Theory (MQT), which is a model of Quantum Theory over certain finite fields, we introduce General Quantum Theory as a Quantum Theory -- in the K{\o}benhavn…