相关论文: Applicability of Partial Ternary Full Adder in Ter…

While quantum circuits built from two-particle dual-unitary (maximally entangled) operators serve as minimal models of typically nonintegrable many-body systems, the construction and characterization of dual-unitary operators themselves are…

We prove the result in the title. We infer, that unlike cylindric algebras, there is a first order axiomatization of the class of completely representable polyadic algebras of infinite dimension, though the one we obtain is infinite; in…

Tensors are widely used to represent multiway arrays of data. The recovery of missing entries in a tensor has been extensively studied, generally under the assumption that entries are missing completely at random (MCAR). However, in most…

Total derivative terms play an important role in the integration of conformal anomaly. In four dimensional space $4D$ there is only one such term, namely $\,{\square}R$. In the case of six dimensions $6D$ the structure of surface terms is…

The algebraic expression $3 + 2 + 6$ can be evaluated to $11$, but it can also be partially evaluated to $5 + 6$. In categorical algebra, such partial evaluations can be defined in terms of the $1$-skeleton of the bar construction for…

There is often a significant trade-off between formulation strength and size in mixed integer programming (MIP). When modeling convex disjunctive constraints (e.g. unions of convex sets), adding auxiliary continuous variables can sometimes…

In this paper we investigate some new problems in additive combinatorics. Our problems mainly involve permutations (or circular permutations) $n$ distinct numbers (or elements of an additive abelian group) $a_1,\ldots,a_n$ with adjacent…

Addition theorems have been indispensable tools for the reduction of quantum transition amplitudes. They are normally utilized at the start of the process to move the angular dependence within plane waves and Coulomb potentials, and the…

This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…

Two arrays form a periodic complementary pair if the sum of their periodic autocorrelations is a delta function. Finding such pairs, however, is challenging for large arrays whose entries are constrained to a small alphabet. One such…

We investigate the fundamental task of addition under uncertainty, namely, addends that are represented as intervals of numbers rather than single values. One potential source of such uncertainty can occur when obtaining discrete-valued…

Tensor parameters that are amortized or regularized over large tensor powers, often called "asymptotic" tensor parameters, play a central role in several areas including algebraic complexity theory (constructing fast matrix multiplication…

Commutative hypercomplex algebras offer significant advantages over traditional quaternions due to their compatibility with linear algebra techniques and efficient computational implementation, which is crucial for broad applicability. This…

For a twisted affine Lie superalgebra with nonzero odd part, we study {tight irreducible weight modules} with bounded weight multiplicities and show that if the action of nonzero real vectors of each affine component of the zero part is…

Mathematically, ternary coding is more efficient than binary coding. It is little used in computation because technology for binary processing is already established and the implementation of ternary coding is more complicated, but remains…

Let A denote the ring of arithmetical functions with unitary convolution, and let V be a finite subset of the positive integers having the property that for every v in V, all unitary divisors of v lie in V. We study the truncation A_V, an…

Kaplanski's Zero Divisor Conjecture envisions that for a torsion-free group G and an integral domain R, the group ring R[G] does not contain non-trivial zero divisors. We define the length of an element a in R[G] as the minimal non-negative…

We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…

This paper shows that it is possible to improve the computational cost, the memory requirements and the accuracy of Quick Fourier Transform (QFT) algorithm for power-of-two FFT (Fast Fourier Transform) just introducing a slight modification…

An additive quaternary $[n,k,d]$-code (length $n,$ quaternary dimension $k,$ minimum distance $d$) is a $2k$-dimensional F_2-vector space of $n$-tuples with entries in $Z_2\times Z_2$ (the $2$-dimensional vector space over F_2) with minimum…