Related papers: Distributive properties of the rationals
Digital System Research has pioneered the mathematics and design for a new class of computing machine using residue numbers. Unlike prior art, the new breakthrough provides methods and apparatus for general purpose computation using several…
A Noetherian reduced ring $A$ is called a birational derived splinter if for all proper birational maps $X\to\operatorname{Spec}(A)$, the canonical map $A\to Rf_*\mathcal{O}_X$ splits. In equal characteristic zero this property…
Currently there is no known efficient formula for primes. Besides that, prime numbers have great importance in e.g., information technology such as public-key cryptography, and their position and possible or impossible functional generation…
The general rational solution of the Yang-Baxter equation with the symmetry algebra sl(2) can be represented as the product of the simpler building blocks denoted as R-operators. The R-operators are constructed explicitly and have simple…
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the…
The partition functions $P(n,m,p)$, the number of integer partitions of $n$ into exactly $m$ parts with each part at most $p$, and $Q(n,m,p)$, the number of integer partitons of $n$ into exactly $m$ distinct parts with each part at most…
We present the first classification of algebraic identities in 3 variables for linear operators on associative structures. We work in the context of associative triple systems, but since any associative algebra with product $xy$ becomes an…
For a PI-algebra R over a field of characteristic 0 let T(R) be the T-ideal of the polynomial identities of R and let c(R,t) be the codimension series of R (i.e., the generating function of the codimension sequence of R). Let A, B and R be…
Consider a commutative monoid $(M,+,0)$ and a biadditive binary operation $\mu \colon M \times M \to M$. We will show that under some additional general assumptions, the operation $\mu$ is automatically both associative and commutative. The…
For each positive integer n greater than or equal to 2, a new approach to expressing real numbers as sequences of nonnegative integers is given. The n=2 case is equivalent to the standard continued fraction algorithm. For n=3, it reduces to…
In quantum information theory, for $a,b$ two positive operators living in $B(\mathcal{H})$, where $\mathcal{H}$ is a separable Hilbert space, the quantum fidelity is denoted by $a*b =(b^{1/2}ab^{1/2})^{1/2}$. One of the aim of this let ter…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Ann likes oranges much more than apples; Bob likes apples much more than oranges. Tomorrow they will receive one fruit that will be an orange or an apple with equal probability. Giving one half to each agent is fair for each realization of…
We show that the distribution function of the first particle in a discrete orthogonal polynomial ensemble can be obtained through a certain recurrence procedure, if the (difference or q-) log-derivative of the weight function is rational.…
Consider many instances of an arbitrary quadripartite pure state of four quantum systems ABCD. Alice holds the AC part of each state, Bob holds B, while D represents all other parties correlated with ABC. Alice is required to redistribute…
Evidential reasoning is now a leading topic in Artificial Intelligence. Evidence is represented by a variety of evidential functions. Evidential reasoning is carried out by certain kinds of fundamental operation on these functions. This…
A simple mechanism for allocating indivisible resources is sequential allocation in which agents take turns to pick items. We focus on possible and necessary allocation problems, checking whether allocations of a given form occur in some or…
A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter…
The paper works out the canonical probability distribution of the occupancy numbers of a bosonic system and shows that canonical typicality applies to the canonical density operator of the occupancy numbers. The result is that, if, as it is…
Let $X$ be a nonempty set and let $i,j \in \{1,2,3,4\}$. We say that a binary operation $F:X^2\to X$ is $(i,j)$-selective if $$ F(F(x_1,x_2),F(x_3,x_4))~=~F(x_i,x_j), $$ for all $x_1,x_2,x_3,x_4\in X$. In this paper we provide…