Related papers: The Rosenberg-Strong Pairing Function
A realistic nuclear mean-field hamiltonian with pairing has been diagonalized using Fock space representation that allows for nearly exact treatment of the problem. Calculations were performed for all the even-even nuclei with Z in (20,…
The Cantor pairing polynomials are extended to larger 2D sub-domains and more complex mapping, of which the most important property is the bijectivity. If corners are involved inside (but not the borders of) domain, more than one connected…
We study the pairing of fermions in a one-dimensional lattice of tunable double-well potentials using radio-frequency spectroscopy. The spectra reveal the coexistence of two types of atom pairs with different symmetries. Our measurements…
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…
In solar physics, especially in exploratory stages of research, it is often necessary to compare the power spectra of two or more time series. One may, for instance, wish to estimate what the power spectrum of the combined data sets might…
Binary relations are an important abstraction arising in many data representation problems. The data structures proposed so far to represent them support just a few basic operations required to fit one particular application. We identify…
We introduce a family of pairings between a bounded divergence-measure vector field and a function $u$ of bounded variation, depending on the choice of the pointwise representative of $u$. We prove that these pairings inherit from the…
The strength of an extension of Kruskal's Theorem to certain pairs of cohabitation trees is calibrated.
In this paper, we study a more general pair correlation function, $F_h(x,T)$, of the zeros of the Riemann zeta function. It provides information on the distribution of larger differences between the zeros.
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
We investigate progressions in the set of pairs of integers $\mathbb{Z}^2$ and define a generalisation of the Jacobsthal function. For this function, we conjecture a specific upper bound and prove that this bound would be a sufficient…
By using the generalized Bernoulli numbers, we deduce new integral representations for the Riemann zeta function at positive odd-integer arguments. The explicit expressions enable us to obtain criteria for the dimension of the vector space…
We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…
This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…
We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasi-coherent modules on schemes,…
I review the proposal of Berenstein-Douglas for a completely general definition of Seiberg duality. To give evidence for their conjecture I present the first example of a physical dual pair and explicitly check that it satisfies the…
In this paper we extend the well-known investigations of Montgomery and Goldston & Montgomery, concerning the pair-correlation function and its relations with the distribution of primes in short intervals, to a more general version of the…
We introduce a monoid structure on the set of binary search trees, by a process very similar to the construction of the plactic monoid, the Robinson-Schensted insertion being replaced by the binary search tree insertion. This leads to a new…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two…