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This essay aims to propose construction theory, a new domain of theoretical research on machine construction, and use it to shed light on a fundamental relationship between living and computational systems. Specifically, we argue that…
A fresh look on carbon-based transistor channel materials like single-walled carbon nanotubes (CNT) and graphene nanoribbons (GNR) in future electronic applications is given. Although theoretical predictions initially promised that GNR…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
Recently, a method was described for deriving Holographic RG equation in $AdS_{D+1}$ space starting from an Exact RG equation of a $D$-dimensional boundary CFT (Sathiapalan, Sonoda, 2017). The evolution operator corresponding to the Exact…
Recent results of several authors have led to constructions of parallelotopes which are bounded remainder sets for totally irrational toral rotations. In this brief note we explain, in retrospect, how some of these results can easily be…
We discuss some applications of fusion rules and intertwining operators in the representation theory of cyclic orbifolds of the triplet vertex operator algebra. We prove that the classification of irreducible modules for the orbifold vertex…
Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in…
In recent decades, a growing number of discoveries in fields of mathematics have been assisted by computer algorithms, primarily for exploring large parameter spaces that humans would take too long to investigate. As computers and…
Hua's fundamental theorem of geometry of hermitian matrices characterizes all bijective maps on the space of all hermitian matrices, which preserve adjacency in both directions. In this and subsequent paper we characterize maps on the set…
The level-k U(1) Chern-Simons theory is a spin topological quantum field theory for k odd. Its dynamics is captured by the 2d CFT of a compact boson with a certain radius. Recently it was recognized that a dependence on the 2d spin…
Multisets are like sets, except that they can contain multiple copies of their elements. If there are $n_i$ copies of $i$, $1\leq i\leq t$, in multiset $M_t$, then there are $\binom{n_1+\cdots+n_t}{n_1,\ldots, n_t}$ possible permutations of…
This paper gives some further details of proofs of some theorems related to the quantum dynamical Yang-Baxter equation. This mainly expands proofs given in "Lectures on the dynamical Yang-Baxter equation" by P. Etingof and O. Schiffmann,…
We construct a finite convergent semi-quadratic presentation for the Chinese monoid by adding column generators and using combinatorial properties of insertion algorithms on Chinese staircases. We extend this presentation into a coherent…
The ratio of central charges in four-dimensional CFTs has been suggested by Hofman and Maldacena to lie within an interval whose boundaries are fixed by the number of supersymmetries. We compute this ratio for a set of interacting N=1…
In this paper, we give a new proof of an arithmetic analogue of the Riemann-Roch Theorem, due originally to Serge Lang. Lang's result was first proved using the lattice point geometry of Minkowski. By contrast, our proof is completely…
We present a space-efficient algorithm to compute the Hilbert class polynomial H_D(X) modulo a positive integer P, based on an explicit form of the Chinese Remainder Theorem. Under the Generalized Riemann Hypothesis, the algorithm uses…
Bidirectional Encoder Representations from Transformers (BERT) have shown to be a promising way to dramatically improve the performance across various Natural Language Processing tasks [Devlin et al., 2019]. Meanwhile, progress made over…
Recently, a new notion of quantum R\'enyi divergences has been introduced by M\"uller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J.Math.Phys. 54:122203, (2013), and Wilde, Winter, Yang, Commun.Math.Phys. 331:593--622, (2014), that has…
An old theorem of Ad\'amek constructs initial algebras for sufficiently cocontinuous endofunctors via transfinite iteration over ordinals in classical set theory. We prove a new version that works in constructive logic, using "inflationary"…
Carbon nanotube (CNT) is expected for much more important and broader applications in the future, because of its amazing electrical and mechanical properties. However, today, the prospect is detained by the fact that the growth of CNTs…