The Harary-Hill Conjecture states that the number of crossings in any drawing of the complete graph Kn in the plane is at least Z(n) := 1 4 ⌊ n 2 ⌋ ⌊ n−1 2 ⌋ ⌊ n−2 2 ⌋ ⌊ n−3 2 ⌋ . In this paper, we settle the Harary-Hill conjecture for shellable drawings. We say that a drawing D of Kn is s-shellable if there exist a subset S = {v1, v2, . . . , vs} of the vertices and a region R of D with the fo...

We generate space-time coupled attosecond pulse trains with a 1.8 μm wavelength laser pulse using the ‘attosecond lighthouse’ technique. We show low divergence, spatially well-separated beamlets from low ionization potential gas media. We also find that there is little long trajectory contribution—only the short trajectory contribution is clearly visible for any beamlet. These results open a ne...

This work describes a cryogenic, electro-optically -switched Yb:YAG laser that generates 114-W average TEM power with 47% optical-to-optical efficiency. Pulse repetition frequency is 5 kHz, pulse duration is 16 ns full-width at half-maximum, and is less than 1.05.

This work describes a cryogenic, electro-optically -switched Yb:YAG laser that generates 114-W average TEM power with 47% optical-to-optical efficiency. Pulse repetition frequency is 5 kHz, pulse duration is 16 ns full-width at half-maximum, and is less than 1.05.

This work describes a cryogenic, electro-optically -switched Yb:YAG laser that generates 114-W average TEM power with 47% optical-to-optical efficiency. Pulse repetition frequency is 5 kHz, pulse duration is 16 ns full-width at half-maximum, and is less than 1.05.

We propose a new method for creating an optimal coherence in a two-level system (TLS) based on adiabatic following. Optimal coherence is achieved by choosing the time-dependent phase of the pulse that provides vanishing field-TLS detuning dðtÞ at central time when the pulse amplitude reaches maximum. For example, dðtÞ 1⁄4 d0ð1 expððt t0Þ=s0ÞÞ for t 6 t0 and d 1⁄4 0 for t > t0. The pulse envelop...

There are various types of lasers available for hair reduction, but the choice of an ideal laser for ethnic skin has its own limitations. The choice of the right laser for the right skin type is very important. Before starting with the laser therapy, it is important to assess the skin type, the fluence, the pulse duration and the type of laser to be used.

In the past lecture, we investigated the preferential attachment model for the generation of power law degree distributions. While “rich-get-richer” models may be considered close to the truth for WWW-like graphs, they do not seem appropriate for graphs such as the Internet, as there appears no natural reason why nodes would choose to attach to high-degree nodes (or be more likely to find out a...

The creation of a surface breaks the translational symmetry of the bulk with the electrons redistributing to lower their energy, resulting in a new lattice structure. Surface relaxation and reconstruction have been studied for years, and it is generally assumed that theory and experiment are in fairly good agreement for the ground state properties at a metal surface. There is a conceptual pictu...