相关论文: On Stable embeddability of partitions

In a quantum computer, creating superpositions of quantum bits (qubits) in different states can lead to a speed-up over classical computers [1], but quantum mechanics also allows for the superposition of quantum circuits [2]. In fact, it…

A classification of multipartite entanglement in qubit systems is introduced for pure and mixed states. The classification is based on the robustness of the said entanglement against partial trace operation. Then we use current machine…

We pursue the question how integers can be ordered or partitioned according to their divisibility properties. Based on pseudometrics on $\mathbb{Z}$, we investigate induced preorders, associated equivalence relations, and quotient sets. The…

We are concerned with the stability of a coalitional game, i.e., a transferable-utility (TU) cooperative game. First, the concept of core can be weakened so that the blocking of changes is limited to only those with multilateral backings.…

3d quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion and symmetries with respect to dilatation or shift transformations are classified. Twenty-seven such systems are…

In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…

A system of homogeneous linear equations with integer coefficients is partition regular if, whenever the natural numbers are finitely coloured, the system has a monochromatic solution. The Finite Sums theorem provided the first example of…

We introduce the notion of a restricted exchangeable partition of $\mathbb{N}$. We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In…

We provide a problem definition of the stable marriage problem for a general number of parties $p$ under a natural preference scheme in which each person has simple lists for the other parties. We extend the notion of stability in a natural…

The partition problem is a well-known basic NP-complete problem. We mainly consider the optimization version of it in this paper. The problem has been investigated from various perspectives for a long time and can be solved efficiently in…

In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…

A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant…

Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…

This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…

For many applications the presence of a quantum advantage crucially depends on the availability of resourceful states. Although the resource typically depends on the particular task, in the context of multipartite systems entangled quantum…

A cubic partition is an integer partition wherein the even parts can appear in two colors. In this paper, we introduce the notion of generalized cubic partitions and prove a number of new congruences akin to the classical Ramanujan-type. We…

A finite or infinite matrix $A$ is image partition regular provided that whenever $\mathbb{N}$ is finitely colored, there must be some $\overset{\rightarrow}{x}$ with entries from $\mathbb{N}$ such that all entries of $A…

Integrable quantum mechanical systems for neutral particles with spin $\frac12$ and nontrivial dipole momentum are classified. It is demonstrated that such systems give rise to new exactly solvable problems of quantum mechanics with clear…

Clarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state…

We study approximation algorithms for satisfiable and nearly satisfiable instances of ordering constraint satisfaction problems (ordering CSPs). Ordering CSPs arise naturally in ranking and scheduling, yet their approximability remains…