The quantum model of a cluster, consisting of A identical particles, coupled by the internal pair interactions and affected by the external field of a target, is considered. A symbolic-numerical algorithm for generating A−1-dimensional oscillator eigenfunctions, symmetric or antisymmetric with respect to permutations of A identical particles in the new symmetrized coordinates, is formulated and...

Andrews’ spt-function can be written as the difference between the second symmetrized crank and rank moment functions. Using the machinery of Bailey pairs a combinatorial interpretation is given for the difference between higher order symmetrized crank and rank moment functions. This implies an inequality between crank and rank moments that was only known previously for sufficiently large n and...

All the 23 Niemeier lattices are constructed by construction A modulo 4. Explicit generator matrices and symmetrized weight enumerators for the relevant codes are given.

Abstract This article discusses triad transfer analysis via quadratic nonlinearity. To avoid fictitious interactions, symmetrization of the is reviewed, including arbitrary orthogonal decomposition and coarse graining. The directional representation symmetrized proposed by minimizing number edges in a network graph interactions with keeping energy consistency. simplifies visualization allows us...

Decomposable Negation Normal Form formulae (DNNFs) form an interesting propositional fragment, both for efficiency and succinctness reasons. A famous subclass of the DNNF fragment is the OBDD fragment which offers many polytime queries and transformations, including quantifier eliminations (under some ordering restrictions). Nevertheless, the decomposable AND nodes at work in OBDDs enable only ...

An additive hereditary graph property is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If P1, . . . ,Pn are graph properties, then a (P1, . . . ,Pn)-decomposition of a graph G is a partition E1, . . . , En of E(G) such that G[Ei], the subgraph of G induced by Ei, is in Pi, for i = 1, . . . , n. The sum of the properties P1, . . . ,Pn is the property P1 ⊕ · ·...

Sequential composition of voting rules, by making use of structural properties of the voters’ preferences, provide computationally economical ways for making a common decision over a Cartesian product of finite local domains. A sequential composition is usually defined on a set of legal profiles following a fixed order. In this paper, we generalize this by order-independent sequential compositi...

The algebraic stability theorem for pointwise finite dimensional (p.f.d.) R-persistence modules is a central result in the theory of stability for persistence modules. We present a stability theorem for n-dimensional rectangle decomposable p.f.d. persistence modules up to a constant (2n− 1) that is a generalization of the algebraic stability theorem. We give an example to show that the bound ca...

We propose a strategy for disclosure risk evaluation and disclosure control of a microdata set based on fitting decomposable models of a multiway contingency table corresponding to the microdata set. By fitting decomposable models, we can evaluate per-record identification (or re-identification) risk of a microdata set. Furthermore we can easily determine swappability of risky records which doe...

The study of decompositions of sets in U, n ^ 1, into disjoint, mutually isometric subsets has a long and distinguished history. In 1928 J. von Neumann [2] proved that an interval in U (with or without endpoints) is decomposable into Ko disjoint sets which are mutually isometric under translations. In 1951 W. Gustin [1] proved that no such decomposition into n, 2 ^ n < No, sets is possible. A b...