The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd number of qubits) achieves the smallest possible orbit dimension, equal to 3n/2 for n even and (3n+ 1)/2 for n odd, where n is the number of qubits. In this pap...

The aim of the present paper is to investigate the use of quantum chemistry calculations to obtain the torsional dependence of various structural and vibrational-force-field-related quantities that could help in estimating the vibration–torsion–rotation interaction terms needed to treat perturbations observed in the spectra of methanol-like molecules. We begin by using the Gaussian suite of pro...

From the subleading contributions to chiral three-nucleon (3N) interaction [published in Phys. Rev. C 77, 064004 (2008) and 84, 054001 (2011)], their first-order energy per particle of isospin-symmetric nuclear matter pure neutron are derived an analytical way. For variety short-range long-range terms that constitute 3N force pertinent closed 3-ring, 2-ring, 1-ring diagrams evaluated. While 3-r...

To reveal the biosynthetic pathway of long-chain polyunsaturated fatty acids (LC-PUFA) in Ruditapes philippinarum , herein, two acid desaturases (Fads, including one Δ5 Fad and Δ6 Fad-like) three elongases very (Elovls, Elovl2/5 Elovl4-like) genes were firstly cloned from this bivalve their tissue distributions examined. Results showed that newly Fads Elovls contained corresponding conserved fu...

In 1974, Harry Ruderman proposed the following problem in the problem section of this MONTHLY: if m > n ≥ 0 are integers such that 2m − 2n divides 3m − 3n , then show that 2m − 2n divides xm − xn for all natural numbers x . This problem is still open. We prove that there are only finitely many pairs of natural numbers m, n such that 2m − 2n divides 3m − 3n . Since the proof involves the Schmidt...

Effects of final state interaction on asymmetries in inclusive scattering of polarized electrons on polarized 3He are investigated using consistent 3He bound state wave function and 3N continuum scattering states. Significant effects are found, which influence the extraction of the magnetic neutron form factor from AT ′ . The enhancement found experimentally for ATL′ near the 3N breakup thresho...

Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the number of alternating sign matrices of order n equals A(n) := 1!4!7! · · · (3n − 2)! n!(n + 1)! · · · (2n − 1)! . Mills, Robbins, and Rumsey also made the stronger conjecture that the number of such matrices whose (unique) ‘1’ of the first row is at the rth column equals A(n) `n+r−2 n−1 ́`2n−1−r n−1 ́ `3n−2 n−1 ́ . Standing on...

Local Tangent Space Alignment (LTSA) algorithm is a classic local nonlinear manifold learning algorithm based on the information about local neighborhood space, i.e., local tangent space with respect to each point in dataset, which aims at finding the low-dimension intrinsic structure lie in high dimensional data space for the purpose of dimensionality reduction. In this paper, we present a nov...

Let t(C) be the number of tangent pairs among a set C of n Jordan regions in the plane. Pach, Suk, and Treml [6] showed that if C consists of convex bodies and its intersection graph is bipartite then t(C) ≤ 4n−Θ(1), and, moreover, there are such sets that admit at least 3n−Θ( √ n) tangencies. We close this gap and generalize their result by proving that the correct bound is 3n−Θ(1), even when ...