Nonexistence of Large Nuclei in the Liquid Drop Model

We give a simplified proof of the nonexistence of large nuclei in the liquid drop model and provide an explicit bound. Our bound is within a factor of 2.3 of the conjectured value and seems to be the first quantitative result.     

Extended Quantum Conditional Entropy and Quantum Uncertainty Inequalities

Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum. Recently these inequalities have been generalized to the tensor product of several Hilbert spaces and we show here how their derivations can be shortened to a few lines and how they can be generalized. Our proofs utilize the technique of the original derivation of strong subadditivity of the von Neumann entropy.     

Possible lattice distortions in the hubbard model for graphene

The Hubbard model on the honeycomb lattice is a well-known model for graphene. Equally well known is the Peierls type of instability of the lattice bond lengths. In the context of these two approximations we ask and answer the question of the possible lattice distortions for graphene in zero magnetic field. The answer is that in the thermodynamic limit only periodic, reflection-symmetric distortions are allowed and these have at most 6 atoms per unit cell as compared to two atoms for the undistorted lattice.     

Depth from structured defocus that is independent of the object reflectivity function

Depth from defocus using structured light is a useful optical metrology technique since the camera and projector can be placed on the same optical axis and it can cope with depth discontinuities. However, the technique can suffer from large errors when used on surfaces with differing reflective properties. This paper demonstrates a method for overcoming this problem.     

Stability Estimates for the Lowest Eigenvalue of a Schrödinger Operator

There is a family of potentials that minimize the lowest eigenvalue of a Schrödinger operator under the constraint of a given L ^p norm of the potential. We give effective estimates for the amount by which the eigenvalue increases when the potential is not one of these optimal potentials. Our results are analogous to those for the isoperimetric problem and the Sobolev inequality. We also prove a stability estimate for Hölder’s inequality, which we believe to be new.     

A Generalized Topological Recursion for Arbitrary Ramification

The Eynard–Orantin topological recursion relies on the geometry of a Riemann surface S and two meromorphic functions x and y on S. To formulate the recursion, one must assume that x has only simple ramification points. In this paper, we propose a generalized topological recursion that is valid for x with arbitrary ramification. We justify our proposal by studying degenerations of Riemann surfaces. We check in various examples that our generalized recursion is compatible with invariance of the free energies under the transformation ${(x, y) \mapsto (y, x)}$ , where either x or y (or both) have higher order ramification, and that it satisfies some of the most important properties of the original recursion. Along the way, we show that invariance under ${(x, y) \mapsto (y, x)}$ is in fact more subtle than expected; we show that there exists a number of counterexamples, already in the case of the original Eynard–Orantin recursion, that deserve further study.     

Simultaneous Quantification of Neomycin and Bacitracin by LC-ELSD

The first simultaneous quantification of neomycin and bacitracin using liquid chromatography evaporative light scattering detection as an alternative to MS detection and pre-/post-column derivatisation, respectively, was the aim of this study. The developed method was validated for two strength of neomycin and one strength of bacitracin in sterile pharmaceutical formulation and is a fast and efficient tool for content uniformity tests in quality control. With this method the separation of neomycin from sulfate and the base line separation of the four major components of bacitracin (bacitracin A, B1, B2 and B3) was achieved. These four components are responsible for 96% of the microbiological activity. A Phenomenex Synergi POLAR analytical column (250 mm × 4.6 mm, 4 μm I.D.) in combination with 0.5% perfluoropropionic acid and acetonitrile in gradient mode, the peaks of interest could be separated with high efficiency within 14 min. The calibration was performed using a second order regression with an R ² = 0.9999 for neomycin (B and C) sulfate and R ² = 0.9996 for bacitracin A, B1, B2 and B3. The results of the accuracy evaluation were 99.2 and 99.7%, respectively, for neomycin and 100.8% for bacitracin. Injection precision results are 0.4–1.5 RSD% recorded for six injections. The established method has a high potential for routine high-throughput analyses in the pharmaceutical industry.

     

Particle diagrams and statistics of many-body random potentials

We present a method using Feynman-like diagrams to calculate the statistical properties of random many-body potentials. This method provides a promising alternative to existing techniques typically applied to this class of problems, such as the method of supersymmetry and the eigenvector expansion technique pioneered in Benet et al. (2001). We use it here to calculate the fourth, sixth and eighth moments of the average level density for systems with m$m$ bosons or fermions that interact through a random k$k$-body Hermitian potential (k≤m$k\le m$); the ensemble of such potentials with a Gaussian weight is known as the embedded Gaussian Unitary Ensemble   (eGUE) (Mon and French, 1975). Our results apply in the limit where the number l$l$ of available single-particle states is taken to infinity. A key advantage of the method is that it provides an efficient way to identify only those expressions which will stay relevant in this limit. It also provides a general argument for why these terms have to be the same for bosons and fermions. The moments are obtained as sums over ratios of binomial expressions, with a transition from moments associated to a semi-circular level density for m<2k$m<2k$ to Gaussian moments in the dilute limit k?m?l$k?m?l$. Regarding the form of this transition, we see that as m$m$ is increased, more and more diagrams become relevant, with new contributions starting from each of the points m=2k,3k,…,nk$m=2k,3k,\dots ,nk$ for the 2n$2n$th moment.