Triangles in a complete chromatic graph with three colors

AbstractLet KN be the complete graph on N vertices, and assume that each edge is assigned precisly one of three possible colors. An old and difficult problem is to find the minimum number of monochromatic triangles as a function of N. We are not able to solve this problem, but we can give sharp bounds for certain combinations of the number of triangles of various kinds. These sharp bounds are related to the main problem, and may be of indepdendent interest

Efficient Quantum Tensor Product Expanders and k-designs

Quantum expanders are a quantum analogue of expanders, and k-tensor product expanders are a generalisation to graphs that randomise k correlated walkers. Here we give an efficient construction of constant-degree, constant-gap quantum k-tensor product expanders. The key ingredients are an efficient classical tensor product expander and the quantum Fourier transform. Our construction works whenever k=O(n/log n), where n is the number of qubits. An immediate corollary of this result is an efficient construction of an approximate unitary k-design, which is a quantum analogue of an approximate k-wise independent function, on n qubits for any k=O(n/log n). Previously, no efficient constructions were known for k>2, while state designs, of which unitary designs are a generalisation, were constructed efficiently in [Ambainis, Emerson 2007].Comment: 16 pages, typo in references fixe

Liquid-gas phase transition and Coulomb instability of asymmetric nuclear systems

We use a chiral SU(3) quark mean field model to study the properties of nuclear systems at finite temperature. The liquid-gas phase transition of symmetric and asymmetric nuclear matter is discussed. For two formulations of the model the critical temperature, $T_c$, for symmetric nuclear matter is found to be 15.8 MeV and 17.9 MeV. These values are consistent with those derived from recent experiments. The limiting temperatures for finite nuclei are in good agreement with the experimental points.Comment: 14 pages, 6 figure

Liquid-gas phase transition and Coulomb instability of asymmetric nuclear systems

We use a chiral SU(3) quark mean field model to study the properties of nuclear systems at finite temperature. The liquid-gas phase transition of symmetric and asymmetric nuclear matter is discussed. For two formulations of the model the critical temperature, $T_c$, for symmetric nuclear matter is found to be 15.8 MeV and 17.9 MeV. These values are consistent with those derived from recent experiments. The limiting temperatures for finite nuclei are in good agreement with the experimental points.Comment: 14 pages, 6 figure

Certain subclasses of multivalent functions defined by new multiplier transformations

In the present paper the new multiplier transformations \mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l) (\delta ,l\geq 0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )} of multivalent functions is defined. Making use of the operator $\mathrm{{\mathcal{J}}}_{p}^{\delta }(\lambda ,\mu ,l),$ two new subclasses $\mathcal{P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ and $\widetilde{\mathcal{P}}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$\textbf{\ }of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums, some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses $\mathcal{P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ and $\widetilde{\mathcal{P}}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out

Recent developments in planet migration theory

Planetary migration is the process by which a forming planet undergoes a drift of its semi-major axis caused by the tidal interaction with its parent protoplanetary disc. One of the key quantities to assess the migration of embedded planets is the tidal torque between the disc and planet, which has two components: the Lindblad torque and the corotation torque. We review the latest results on both torque components for planets on circular orbits, with a special emphasis on the various processes that give rise to additional, large components of the corotation torque, and those contributing to the saturation of this torque. These additional components of the corotation torque could help address the shortcomings that have recently been exposed by models of planet population syntheses. We also review recent results concerning the migration of giant planets that carve gaps in the disc (type II migration) and the migration of sub-giant planets that open partial gaps in massive discs (type III migration).Comment: 52 pages, 18 figures. Review article to be published in "Tidal effects in Astronomy and Astrophysics", Lecture Notes in Physic

Spatial processing of visual information in the movement-detecting pathway of the fly

1. Spatial processing of visual signals in the fly's movement-detecting pathway was studied by recording the responses of directionally-selective movement-detecting (DSMD) neurons in the lobula plate. The summarized results pertain to a type of neuron which preferentially responds to horizontal movement directed toward the animal's midline. Three kinds of visual stimuli were used: moving gratings, reversing-contrast gratings and reversing-contrast bars.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47087/1/359_2004_Article_BF00613743.pd

A White Paper on keV sterile neutrino Dark Matter

We present a comprehensive review of keV-scale sterile neutrino Dark Matter, collecting views and insights from all disciplines involved—cosmology, astrophysics, nuclear, and particle physics—in each case viewed from both theoretical and experimental/observational perspectives. After reviewing the role of active neutrinos in particle physics, astrophysics, and cosmology, we focus on sterile neutrinos in the context of the Dark Matter puzzle. Here, we first review the physics motivation for sterile neutrino Dark Matter, based on challenges and tensions in purely cold Dark Matter scenarios. We then round out the discussion by critically summarizing all known constraints on sterile neutrino Dark Matter arising from astrophysical observations, laboratory experiments, and theoretical considerations. In this context, we provide a balanced discourse on the possibly positive signal from X-ray observations. Another focus of the paper concerns the construction of particle physics models, aiming to explain how sterile neutrinos of keV-scale masses could arise in concrete settings beyond the Standard Model of elementary particle physics. The paper ends with an extensive review of current and future astrophysical and laboratory searches, highlighting new ideas and their experimental challenges, as well as future perspectives for the discovery of sterile neutrinos