We use well-known limit theorems in probability theory to derive a Wallis-type product formula for the gamma function. Our result immediately provides a probabilistic proof of Wallis's product formula for $π$, as well as the duplication formula for...
I think/hope that when Wally does go through his door he would be reincarnated or somehow brought back to life. Like idk if any of y'all have seen ghost whisperer but in that show the husband of the ...
We discuss the mass of the (physical component of the) Higgs boson in one-loop and top-quark mass approximation. For this the minimal Standard Model is regarded as a specific (parameterized) gauge theory of Dirac type. It is shown that the latter f...
We have proposed a fully quantum approach to non-perturbatively calculate the spin-split Landau levels and g-factor of various spin-orbit coupled solids, based on the k.p theory in the matrix mechanics representation. The new method considers the det...
Boij-Söderberg Theory views the Betti diagrams of graded modules over polynomial rings as vectors in a rational vector space, and studies the cone that these vectors generate (called a 'Betti Cone'). The objects of study in this paper are the Betti...
We develop by example a type of index theory for non-Fredholm operators. A general framework using cyclic homology for this notion of index was introduced in a separate article [CaKa13] where it may be seen to generalise earlier ideas of Carey-Pincus...
R. W. Carey and J. Pincus in [CaPi86] proposed and index theory for non-Fredholm bounded operators T on a separable Hilbert space H such that TT* - T*T is in the trace class. We showed in [CGK13] using Dirac-type operators acting on sections of bundl...
We study the Nordström-Vlasov system which describes the dynamics of a self-gravitating ensemble of collisionless particles in the framework of the Nordström scalar theory of gravitation. If the speed of light $c$ is considered as a parameter, it...
This paper motivates and develops a framework for understanding how the socio-technical systems surrounding AI development interact with social welfare. It introduces the concept of ``signaling'' from evolutionary game theory and demonstrates how it...
The Anna Karenina principle is named after the opening sentence in the eponymous novel: Happy families are all alike; every unhappy family is unhappy in its own way. The Two Envelopes Problem (TEP) is a much-studied paradox in probability theory, mat...
We discuss the projectivity of the moduli space of semistable vector bundles on a curve of genus $g\geq 2$. This is a classical result from the 1960s, obtained using geometric invariant theory. We outline a modern approach that combines the recent ma...
The Faddeev model is a classical field theory that models heavy elementary particles by knotted topological solitons. It is a generalization of the well-known classical nonlinear sigma model of Gell-Mann and Levy, and is also related closely to the c...
A fundamental construction in formal language theory is the Myhill-Nerode congruence on words, whose finitedness characterizes regular language. This construction was generalized to functions from $Σ^*$ to $\mathbb{Z}$ by Colcombet, Douéneau-Tabot,...
Katz and Sarnak conjectured that the statistics of low-lying zeros of various family of $L$-functions matched with the scaling limit of eigenvalues from the random matrix theory. In this paper we confirm this statistic for a family of primitive Diric...
We discuss the analytic computation of autocorrelation functions for the generalized Hybrid Monte Carlo algorithm applied to free field theory and compare the results with numerical results for the $O(4)$ spin model in two dimensions. We explain ho...
Generalizing the geometry of the gauge covariant variables in Yang-Mills theory proposed by Johnson and Haagensen, the 4-d geometry associated with a monopole is defined for SU(2). There are three relevant geometries: AdS$_2\times S^2$, $R^2\times...
In this expository article, we study the relation between the boolean functions and the hypercontractivity theorems of Aline Bonami. We focus on the social choice theory, and present some of the most important results in the area, such as the Friedgu...
Digital Engineering, the digital transformation of engineering to leverage digital technologies, is coming globally. This paper explores digital systems engineering, which aims at developing theory, methods, models, and tools to support the emerging...
The biggest indication that a widely publicized event is a false flag is when you ask "who benefits from this" and it just doesn't make sense for the blamed country to have committed the act. I'm of c...
Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. While ordinary teleportation is simple and efficient, port-based teleportation (PBT) enables applications such as universal programmable quantum processors, in...