Related papers: Further Comments on "Residue-to-Binary Converters …
Let $s,t$ be natural numbers, and fix an $s$-core partition $\sigma$ and a $t$-core partition $\tau$. Put $d=\gcd(s,t)$ and $m= lcm(s,t)$, and write $N_{\sigma, \tau}(k)$ for the number of $m$-core partitions of length no greater than $k$…
We study the use of transformers to reconstruct the compositions of tensor products of two-dimensional rational conformal field theories (RCFTs) based on their low-energy spectra. The task is challenging due to its combinatorial nature. The…
This is an elementary expository article regarding the application of Kleene's Recursion Theorems in making definitions by recursion. Whereas the Second Recursion Theorem (SRT) is applicable in a first-order setting, the First Recursion…
The main goal of this paper is to give a completely elementary proof for the decomposition theorem of Wright convex functions which was discovered by C.\ T.\ Ng in 1987. In the proof, we do not use transfinite tools, i.e., variants of…
In this article we will introduce a central problem in additive combinatorics, which arised from the famous van der Waerden theorem and an early conjecture of Erd\H{o}s and Tur\'{a}n. The first important theorem was due to Roth in 1953.…
A theory of linearly elastic orthotropic shells is presented, with potential application to the continuous modeling of Carbon NanoTubes. Two relevant features are: the selected type of orthotropic response, which should be suitable to…
Our result in cond-mat/0305147 that, instead of the conventional heat fluctuation theorem (FT), a new FT holds for heat fluctuations for a Brownian particle in a moving confining potential[Wang et al. 2002], was claimed to be disproved in a…
A first deception of QM on antiH already appears in one-center integrals for two-center systems (G. Van Hooydonk, physics/0511115). In reality, full QM is a theory for chiral systems but the QM establishment was wrong footed with a…
We argue that the usual notions of thermodynamic and entanglement entropy have novel analogs in the context of higher spin theories. In particular, the Wald and Ryu-Takayanagi formulas have natural higher spin extensions that we work out…
In this expository paper written for physicists and geometers we introduce the notions of TQFT and of orbifold. Then we survey the construction of TQFT's originating from orbifolds such as Chen-Ruan theory and Orbifold String Topology.
Macroscopic fibers of carbon nanotubes (CNT) have emerged as an ideal architecture to exploit the exceptional properties of CNT building blocks in applications ranging from energy storage to reinforcement in structural composites.…
We study a topological generalization of ideal co-maximality in topological rings and present some of its properties, including a generalization of the Chinese remainder theorem. Using the hyperspace uniformity, we prove a stronger version…
We prove a compact $T(1)$ theorem, involving quantitative estimates, analogous to the quantitative classical $T(1)$ theorem due to Stein. We also discuss the $C_c^\infty$-to-$CMO$ mapping properties of non-compact Calder\'on-Zygmund…
The famous partition theorem of Euler states that partitions of $n$ into distinct parts are equinumerous with partitions of $n$ into odd parts. Another famous partition theorem due to MacMahon states that the number of partitions of $n$…
The famous Nash embedding theorem was aimed for in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, as late as 1985 (see \cite{G}) this…
This article provides an overview of the modeling of the effective thermomechanical properties of the multifunctional carbon nanotube (CNT) reinforced hybrid composites for advanced structural applications. The novel constructional feature…
We establish a generalization of Anush Tserunyan and Jenna Zomback's 2024 Backward Ergodic Theorem. We remove the countable-to-one assumption and thus provide a backward ergodic theorem for arbitrary measure-preserving transformations.…
Conventional wisdom suggests that realistic quantum repeaters will require quasi-deterministic sources of entangled photon pairs. In contrast, we here study a quantum repeater architecture that uses simple parametric down-conversion…
We define a new congruence relation on the set of integers, leading to a group similar to the multiplicative group of integers modulo $n$. It makes use of a symmetry almost omnipresent in modular multiplications and halves the number of…
We give an exposition of an iteration theorem for iterating $(<\lambda)$-closed stationary $\lambda^+$-cc forcing with supports of size $<\lambda$ and preserving these two properties. We discuss the relation of this theorem with other…