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• Our proposed method uniquely integrates all-fiber laser SMI with the principles of laser triangulation. This integration not only enhances the precision of angular measurements but also extends the applicability of the measurement system, enabling high-accuracy measurements in a broader range of conditions, including those challenging for traditional methods. • Our approach significantly reduces reliance on complex optical components, streamlining the design of the experimental setup. This reduction not only lowers the cost of the system but also increases its practicality and ease of use, making this high-precision angular measurement technique more accessible for laboratory and industrial applications. • By utilizing an all-fiber laser and FBGs, our method exhibits excellent resistance to environmental interferences such as temperature fluctuations and mechanical vibrations. This enhanced stability and interference resistance make our approach a powerful tool in applications requiring high reliability and precision, such as in precision engineering and scientific research. This study introduces a cutting-edge all-fiber laser self-mixing interferometry (SMI) system, addressing the need for high-precision angular measurements in scientific and industrial applications. Against the backdrop of traditional methods that often grapple with complexity and sensitivity to environmental disturbances, our approach stands out by offering a simplified, robust alternative with enhanced accuracy. Leveraging the coherence and monochromatic properties of laser light, our system employs a linear-cavity all-fiber configuration that minimizes the need for complex optical components. The integration of fiber Bragg gratings (FBGs) within the setup serves as a cornerstone, providing spectral selectivity and intrinsic stability. Through the fringe counting method and the incorporation of laser triangulation principles, the technique achieves remarkable precision in detecting angular displacements. A comprehensive set of experiments validates the proposed system, showcasing its capability to deliver consistent and reliable measurements. The implementation of Wavelet Transform-based denoising further refines the signal quality, ensuring that the extracted data remains true to the actual angular changes. Despite the inherent challenges such as potential systematic errors and environmental influences, our method demonstrates a high degree of repeatability and fidelity, which is crucial for applications demanding stringent accuracy. [ABSTRACT FROM AUTHOR]

In this paper we demonstrate long-lived states involving a pair of chemically equivalent protons, with lifetimes ∼30 times T 1 up to a total lifetime of ∼117 s at high field (8.45 T). This is demonstrated on trans -ethylene- d 2 in solution, where magnetic inequivalence gives access to the long-lived states. It is shown that the remaining J -coupling between the two quadrupolar deuterium spins, J QQ , splits the conditions for optimally generating proton singlet states. Detailed simulations of the spin evolution are performed, shedding light on the coherent evolution during singlet–triplet conversion as well as on the incoherent evolution that causes relaxation. Subsequently, the simulations are compared with experimental results validating the theoretical insights. Possible applications include storage of hyperpolarization in the proton long-lived state. Of particular interest may be utilization of parahydrogen induced polarization to directly induce the examined long-lived states. [ABSTRACT FROM AUTHOR]

• A w-coordinate system on Jacobi quartic curves is introduced for group arithmetic. • Explicit formulas for 2 and odd degree isogenies on those curves are proposed. • Such formulas are further simplified using the w-coordinates. Isogenies between elliptic curves play a very important role in elliptic curve related cryptosystems and cryptanalysis. It is widely known that different models of elliptic curves would induce different computational costs of elliptic curve arithmetic, and several works have been devoted to accelerate the isogeny computation on various curve models. This paper studies the case of the Jacobi quartic model, which is a classic form of elliptic curves. A new w -coordinate system on extended Jacobi quartic curves is introduced for Montgomery-like group arithmetic. Explicit formulas for 2-isogenies and odd ℓ -isogenies on the specific curves are presented, and based on the w -coordinate system, the computation of such isogenies could be further simplified. [ABSTRACT FROM AUTHOR]