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Winding number and density of states are two fundamental physical quantities for non-self-adjoint quasi-periodic Schr\"odinger operators, which reflect the asymptotic distribution of zeros of the characteristic determinants of the truncated operators under Dirichlet boundary condition, with respect to complexified phase and the energy respectively. We will prove that the winding number is in fact Avila's acceleration and it is also closely related to the density of states by a generalized Thouless formula for non-self-adjoint Schr\"odinger operators and Avila's global theory.

A reflective beam splitter is proposed and verified. The unit cell of the beam splitter is composed of a metal pattern, a dielectric substrate, and a metallic ground. Each subarray structure of the device is composed of four unit cells, which are gradually rotated at 45°. The horizontal and vertical subarrays form a 4×4 gradient metasurface supercell. In the operating frequency band, the incident linearly polarized terahertz wave is reflected and divided into four beams of approximately equal power but different propagation directions. The proposed terahertz beam splitter based on metasurface has the advantages of small size, low cost and easy processing, and can be applied to terahertz stealth and imaging.

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For non-self-adjoint almost-periodic Schr\"odinger operators, a criterion is given to guarantee that they have both the same spectrum and same Lyapunov exponents with the discrete free Laplacian. As a byproduct, we show that the Moser-P\"oschel argument for opening gaps may not be valid for non-self-adjoint operators.

In this paper, a transmissive terahertz (THz) quarter wave plate (QWP) has been proposed to realize the linear-to-circular polarization conversion in terahertz range. This quarter wave plate is composed of two dielectric layers and one metallic layer with asymmetric cross slots. In the range of 0.894–1.378 THz, the axis ratio of proposed device is less than 3 dB, and its polarization conversion efficiency is more than 45%. The distributions of surface currents and electromagnetic field density had been proposed to understand the physical mechanism of proposed device. The linear-to-circular polarization conversion can be attributed to the asymmetric transmission along slots. Finally, the simulation results are validated by experiments in terahertz region. The proposed device has simple geometry and good performance, which can be used as a key component in applications of terahertz communications, terahertz imaging and terahertz sensing.

For the quasi-periodic Schr\"{o}dinger operators in the local perturbative regime where the frequency is Diophantine and the potential is $C^k$ sufficiently small depending on the Diophantine constants, we prove that the length of the corresponding spectral gap has a polynomial decay upper bound with respect to its label. This is based on a refined quantitative reducibility theorem for $C^k$ quasi-periodic ${\rm SL}(2,\mathbb{R})$ cocycles, and also based on the Moser-P\"{o}schel argument for the related Schr\"{o}dinger cocycles. As an application, we are able to show the homogeneity of the spectrum., Comment: 27 pages

A tri-layered terahertz metamaterial based on the gratings-polarization converter-gratings (GPCG) structure is proposed, which is composed of a double L structure array sandwiched by two orthogonal metallic sub-wavelength gratings (SWGs). Simulation results show that two cascaded Fabry–Perot-like resonance cavities result in broadband polarization conversion with significant asymmetric transmission (AT) phenomenon. The improved polarization conversion rate (PCR) is over 0.99 from 0.20 THz to 1.97 THz with a relative bandwidth of 163.13%, almost 1.74 times that of other work, and the enhanced AT parameter is beyond 0.8 from 0.37 THz to 1.73 THz with a relative bandwidth of 129.52%. Moreover, in a wide range of incident angles, the proposed metamaterial maintains great AT performance, thus showing great potential applications in circulators, direction-dependent polarization converters and polarization-sensitive sensing and imaging.

CONTEXT: Diet modification is a mainstay of diabetes management. US Hispanics/Latinos are disproportionately affected by diabetes, but few studies have examined dietary intake among US Hispanics/Latinos with diabetes, and little is known regarding the influence of diabetes awareness on dietary intake. OBJECTIVE: We evaluated macronutrient intake and its associations with diabetes awareness and glycemic control among US Hispanics/Latinos with diabetes. PARTICIPANTS: This analysis included 3310 diabetic adults aged 18–74 years from the Hispanic Community Health Study/Study of Latinos (2008–2011). MAIN OUTCOME MEASURES: Diabetes was defined as diagnosed (based on medical history or antihyperglycemic medication use) or undiagnosed diabetes (based on fasting glucose ≥ 126 mg/dL, glycated hemoglobin [HbA1c] ≥ 6.5%, or 2 h glucose ≥ 200 mg/dL in the absence of a physician diagnosis). Dietary intake was assessed using two 24-hour recalls. RESULTS: Among Hispanic/Latino adults with diabetes, 21.2%, 55.7%, and 71.2% met the American Diabetes Association recommendations for fiber (≥14 g per 1000 kcal), saturated fat (

BACKGROUND: Cardiovascular disease (CVD) risk factor control is a cornerstone of diabetes mellitus management. Little is known about relationships of objectively measured sedentary time and physical activity with major CVD risk factor control in individuals with diabetes mellitus. We examined associations of objectively measured sedentary time and moderate-to-vigorous physical activity with reaching major CVD risk factor control goals among US Hispanic/Latino adults with diabetes mellitus. METHODS AND RESULTS: This cross-sectional analysis included 1699 participants with diabetes mellitus from the Hispanic Community Health Study/Study of Latinos (2008-2011). Logistic regression models were used to estimate the odds ratios (ORs) of meeting the following 5 major CVD risk factor control goals: hemoglobin A1c 40/50 mg/dL for men/women. After adjustment for covariates including moderate-to-vigorous physical activity, less sedentary time was associated with increased odds of reaching hemoglobin A1c (OR=1.76 [95% CI: 1.10, 2.82]) and triglyceride control goals (OR=2.16 [1.36, 3.46]), and reaching ≥3 CVD risk factor control goals (OR=2.08 [1.34, 3.23]) (all ORs for comparisons of extreme tertiles of sedentary time). Moderate-to-vigorous physical activity was not associated with reaching any CVD risk factor control goals. Substituting 60-min/day of sedentary time with light-intensity physical activity was associated with increased odds of reaching hemoglobin A1c (OR=1.18 [1.04, 1.35]), high-density lipoprotein cholesterol (OR=1.17 [1.04, 1.32]), and triglyceride (OR=1.20 [1.05, 1.36]) control goals. CONCLUSIONS: Among US Hispanic/Latino adults with diabetes mellitus, less sedentary time, but not moderate-to-vigorous physical activity, was associated with improved CVD risk factor control, specifically in reaching hemoglobin A1c and triglyceride control goals.