On conjectures and problems of Ruzsa concerning difference graphs of S-units

Given a finite nonempty set of primes S, we build a graph $\mathcal{G}$ with vertex set $\mathbb{Q}$ by connecting x and y if the prime divisors of both the numerator and denominator of x-y are from S. In this paper we resolve two conjectures posed by Ruzsa concerning the possible sizes of induced nondegenerate cycles of $\mathcal{G}$, and also a problem of Ruzsa concerning the existence of subgraphs of $\mathcal{G}$ which are not induced subgraphs.Comment: 15 page

University student perceptions of the current and future role of non-carbon emitting energy sources in the world

This article documents university student perceptions of the role and viability of non-carbon emitting energy sources in the short term (1 to 3 years) and medium term (10 to 30 years) for Earth. Consequently, the perceptions of 7,980 students at the University of Idaho (Moscow, ID, USA) about the future of geothermal energy (G), hydropower energy (H), nuclear power (NP), ocean thermal energy conversion (OTEC), solar energy (S) and wind energy (W) were measured between 1993 and 2016. All students were enrolled in the introductory environmental science class. Two survey instruments were used to gather this data. The first survey instrument evaluated six energy sources in 1994, 1998, 2002, 2006, 2010 and 2014. The second instrument focused on questions about nuclear energy. In the first survey a significant portion of the students considered solar, wind and nuclear power to be viable nonemitting carbon energy sources in the medium-term (10 to 30 years) future. Also, students taking the survey in later years (2006, 2010, 2014) were much more likely to consider non-carbon energy sources viable in the near and mid-term than students taking the survey in 1994, 1998 and 2002. In general, 46.7% of students considered nuclear power a serious problem at the beginning of the course; however, at the end of the term less than 36% of students still held their initial negative opinion. In addition, a significant majority of the students changed from indicating that fossil fuels were preferable to nuclear energy, an opinion they held at the beginning of the course, to favoring or at least saying that nuclear power was no worse than fossil fuels at the conclusion of the term. The significant findings of this study were: (1) students considered both solar and wind energy viable alternatives that have the potential to be significant on a world-wide basis within 30 years; (2) students saw only a limited expansion of hydropower and geothermal energy in the next 30 years; and (3) once students were educated in an unbiased way – including both the pros and cons of using nuclear energy – they were more receptive to view the nuclear power option favorably

Local Versus Global Thermal States: Correlations and the Existence of Local Temperatures

We consider a quantum system consisting of a regular chain of elementary subsystems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature $T$. We analyze under what condition the state factors into a product of canonical density matrices with respect to groups of $n$ subsystems each, and when these groups have the same temperature $T$. While in classical mechanics the validity of this procedure only depends on the size of the groups $n$, in quantum mechanics the minimum group size $n_{min}$ also depends on the temperature $T$! As examples, we apply our analysis to a harmonic chain and different types of Ising spin chains. We discuss various features that show up due to the characteristics of the models considered. For the harmonic chain, which successfully describes thermal properties of insulating solids, our approach gives a first quantitative estimate of the minimal length scale on which temperature can exist: This length scale is found to be constant for temperatures above the Debye temperature and proportional to $T^{-3}$ below.Comment: 12 pages, 5 figures, discussion of results extended, accepted for publication in Phys. Rev.

Public Views on the Importance and Expansion of Renewable Electricity Production over the Last 35 Years in Idaho, USA

Received: 25 August 2023. Revised: 2 September 2023. Accepted: 7 September 2023. Available online: 25 September 2023.In 2022, Idaho stood fourth among U.S. states in renewable electricity share, with 74% generated from renewable sources like hydro, solar, wind, and geothermal. The dominant contributor has historically been hydropower. However, due to population growth and limited potential for new dam sites, reliance on solar and wind energy has increased. This paper aims to document the evolution of Idahoan public opinion regarding renewable energy's role in electricity production over 35 years. Public surveys were conducted every five years from 1987 to 2022, each involving at least 500 respondents. The surveys reveal strong public support for enhancing Idaho's renewable energy share. Over 75% of respondents expressed pride in the state's renewable electricity generation. Support for solar and wind energy has grown from 60% in 1987 to over 80% in 2022. Geographical preferences emerged, with south-western and south-central residents favoring solar, southeastern residents favoring wind, and northern residents divided between hydro, solar, and wind. The surveys disclose that Idahoans: (1) strongly support increased renewable electricity production, (2) endorse solar and wind energy as key contributors, and (3) desire to replace Idaho’s remaining non-renewable energy production with renewable sources within the next decade

Public Views of the Value, Potential, and Sustainability of Energy Sources Over the Last 30 Years in the Pacific Northwest, USA

The use of renewable energy has been an important topic in the four Pacific Northwestern states for the last 30 years. Large, statistically designed public surveys were conducted in the region in 1990, 2000, 2010, and 2020 to determine the perceived sustainability, future viability, and acceptance of the following ten energy sources: biomass, coal, geothermal, hydropower, natural gas, nuclear, oil, solar, tidal, and wind power. The survey questions were identical in all 4 years of the survey. These surveys were delivered by the US Postal Service to over 3500 randomly chosen residents in each survey year. The public response rate exceeded 50% in each survey year. Demographic data about age, gender, education level, community size, and state of residence of survey respondents were also collected. The survey data were statistically analyzed. In general, the public was literate identifying the renewable and nonrenewable energy sources as the majority of survey respondents correctly identified biomass, geothermal, hydropower, solar, and wind as renewable energy sources. Based on survey results, over 75% of Pacific Northwest residents considered it important or very important that their energy resources were renewable in 2020. The findings of this study were important because it shows that the public is in line with the scientific community with the goal of greatly reducing energy reliance on C containing nonrenewable energy sources including oil, coal, and natural gas. In summary, (1) the public strongly supports the transformation to a sustainable energy system using primarily renewable energy sources, (2) the use of traditional nonrenewable energy sources like natural gas should not be discouraged in the present; however, they should be phased out over the short and medium terms, (3) solar and wind energy should be significant sources to meet future energy needs in the region, and (4) the renewables including biomass and geothermal have a place in the future energy mix within the Pacific Northwest

State Measurements with Short Laser Pulses and Lower-Efficiency Photon Detectors

It has been proposed by Cook (Phys. Scr. T 21, 49 (1988)) to use a short probe laser pulse for state measurements of two-level systems. In previous work we have investigated to what extent this proposal fulfills the projection postulate if ideal photon detectors are considered. For detectors with overall efficiency less than 1 complications arise for single systems, and for this case we present a simple criterion for a laser pulse to act as a state measurement and to cause an almost complete state reduction.Comment: 13 pages, LaTeX; submitted to J. mod. Op

Terahertz quantum cascade lasers - first demonstration and novel concepts

Quantum cascade (QC) lasers operating at terahertz frequencies were demonstrated two years ago, and, since then, their development has proceeded at a very rapid pace. The gain medium of the first devices was based on chirped superlattices, and a resonator relying on the surface plasmon concept was employed to achieve a large optical confinement with concomitant low propagation losses. Laser action was obtained at 4.4 THz, in pulsed mode and at temperatures up to 50 K. Improved fabrication allowed continuous-wave (cw) operation and increased the operating temperature to 75 K. Using a similar active region, lasing at 3.5 THz was achieved. More recently, various groups have introduced several new design concepts such as bound-to-continuum transitions and extraction of carriers via resonant phonon scattering, leading to pulsed operation up to 140 K, output powers of up to 50 mW, and cw operation up to 93 K. The lowest emission frequency is now 2.1 THz, tackling the technologically important region of 1.5-2.5 THz. Stable single-mode emission under all operating conditions has also recently become a reality thanks to the adoption of distributed feedback resonators. This rapid and substantial progress underlines the growing potential of QC lasers in THz photonics

Strong Lens Models for 37 Clusters of Galaxies from the SDSS Giant Arcs Survey

We present strong gravitational lensing models for 37 galaxy clusters from the SDSS Giant Arcs Survey. We combine data from multi-band Hubble Space Telescope WFC3imaging, with ground-based imaging and spectroscopy from Magellan, Gemini, APO, and MMT, in order to detect and spectroscopically confirm new multiply-lensed background sources behind the clusters. We report spectroscopic or photometric redshifts of sources in these fields, including cluster galaxies and background sources. Based on all available lensing evidence, we construct and present strong lensing mass models for these galaxy clusters.Comment: 53 pages; submitted to ApJ

Stability, Gain, and Robustness in Quantum Feedback Networks

This paper concerns the problem of stability for quantum feedback networks. We demonstrate in the context of quantum optics how stability of quantum feedback networks can be guaranteed using only simple gain inequalities for network components and algebraic relationships determined by the network. Quantum feedback networks are shown to be stable if the loop gain is less than one-this is an extension of the famous small gain theorem of classical control theory. We illustrate the simplicity and power of the small gain approach with applications to important problems of robust stability and robust stabilization.Comment: 16 page