The reaction dynamics of O(3P) + O2(3Sigma_g-) collisions in the O3(1A') electronic ground state is characterized on a high-level MRCI+Q/aug-cc-pVQZ potential energy surface represented as a reproducing kernel. For the atom exchange reactions involving the ^{16}O and ^{18}O isotopes as the atomic collision partner, associated with rates k6(T) and k8(T), respectively, a negative temperature-dependence of k(T), consistent with experiments was found. The absolute rates typically underestimate measured rates by 50 percent, depending on the experiment considered. For the ratio R(T) = k8(T)/k6(T), the measured T-dependence was found, including a cusp at lower temperatures. The differences between experiments and computations are primarily due to neglect of quantum effects, primarily zero-point effects. For the atomization reaction, leading to 3O(3P), the rates is lower by approximately one order of magnitude compared with experiments, which is a clear improvement over simulations using previous potential energy surfaces computed with smaller basis sets. Non-adiabatic effects are deemed minor for the atom exchange reactions.

This paper establishes a general topological condition under which the semilocal stability of a set-valued mapping can be exactly determined by its local stability properties. Specifically, we investigate the relationship between the Lipschitz upper semicontinuity modulus -- a semilocal measure of variation for the image set -- and the local calmness moduli. While these two quantities coincide for mappings with convex graphs, the relationship generally breaks down in the absence of convexity, making the semilocal modulus exceptionally difficult to compute. We prove that if a mapping is outer semicontinuous in the Painlevé-Kuratowski sense and locally compact around the nominal parameter, the Lipschitz upper semicontinuity modulus is exactly the supremum of the local calmness moduli over the nominal set. In addition to the theoretical advance, this equality enables the precise calculation of semilocal error bounds via point-based formulae. We illustrate the broad applicability of this theorem by setting it up in several non-convex frameworks in parametric optimization, including piecewise convex and semi-algebraic mappings, feasible and optimal set mappings under full data perturbations, generalized equations and linear complementarity problems, semi-infinite inequality systems, and parameterized sub-level sets.

In deep networks, operations such as ReLU and hardware-driven clamping often cause activations to accumulate near the edges of the distribution, leading to biased clustering and suboptimal quantization in existing nonlinear (NL) quantization methods. This paper introduces Boundary Suppressed K-Means Quantization (BS-KMQ), a novel NL quantization approach designed to reduce the resolution requirements of analog-to-digital converters (ADCs) in in-memory computing (IMC) systems. By suppressing boundary outliers before clustering, BS-KMQ achieves more balanced and informative NL quantization levels. The resulting NL references are implemented using a reconfigurable in-memory NL-ADC, achieving a 7x area improvement over prior NL-ADC designs. When evaluated on ResNet-18, VGG-16, Inception-V3, and DistilBERT, BS-KMQ achieves at least 3x lower quantization error compared to linear, Lloyd-Max, cumulative distribution function (CDF), and K-means methods. It also improves post-training quantization accuracy by up to 66.8%, 25.4%, 66.6%, and 67.7%, respectively, compared to linear quantization. After low-bit fine-tuning, BS-KMQ maintains competitive accuracy with significantly fewer NL-ADC levels (3/3/4/4b). System-level simulations on ResNet-18 (6/2/3b) demonstrate up to a 4x speedup and 24x energy efficiency improvement over existing IMC accelerators.

Building on recent work of Krueger and the second author, we prove the consistency of the Guessing Model Principle at $ω_2$ together with the existence of an almost Kurepa Suslin tree. In particular, it is consistent that the Guessing Model Principle holds but is destructible by a ccc forcing of size $ω_1$. We also prove the consistency of the existence of a weak Kurepa tree together with the failure of the Kurepa Hypothesis and a certain guessing model principle that, for example, implies the tree property at $ω_2$.

This paper presents a novel hardware system for high-speed, event-sparse sampling-based electronic skin (e-skin)that integrates sensing and neuromorphic computing. The system is built around a 16x16 piezoresistive tactile array with front end and introduces a event-based binary scan search strategy to classify the digits. This event-driven strategy achieves a 12.8x reduction in scan counts, a 38.2x data compression rate and a 28.4x equivalent dynamic range, a 99% data sparsity, drastically reducing the data acquisition overhead. The resulting sparse data stream is processed by a multi-layer convolutional spiking neural network (Conv-SNN) implemented on an FPGA, which requires only 65% of the computation and 15.6% of the weight storage relative to a CNN. Despite these significant efficiency gains, the system maintains a high classification accuracy of 92.11% for real-time handwritten digit recognition. Furthermore, a real neuromorphic tactile dataset using Address Event Representation (AER) is constructed. This work demonstrates a fully integrated, event-driven pipeline from analog sensing to neuromorphic classification, offering an efficient solution for robotic perception and human-computer interaction.

We aim to investigate the blowout jet-like prominence eruption, which occurred on October 6$^{th}$, 2023, with the help of imaging and spectroscopic observations. Firstly, the prominence rises slowly with a speed of 33 km/s, followed by a fast rise (i.e., 338 km/s). Later, the northern leg breaks completely, and the eruption forms the blowout jet. The jet consists of different plasma threads, which show a range of upflow (i.e., 125 to 593 km/s) and downflow velocities (i.e., 43 to 158 km/s). The jet plasma column exhibits transverse oscillations, and this motion (untwisting motion) propagate at the speed of 267 km/s, are consistent with being Alfev{é}n waves. The transverse motion has the time period, amplitude, and transverse velocity of 1332 s, 26.19 Mm, and 126.18$\pm$7.27 km/s, respectively, and this transverse oscillation decays over time. Interestingly, the different plasma threads within the jet's body exhibit decayless transverse oscillations, and these decayless oscillations are related to the main decaying transverse oscillation. The transverse velocity of these decayless oscillations ranges from 66 to 30 km/s, the amplitudes from 8.52 to 2.74 Mm, and periods from 811 to 406 s. In addition, the spectroscopic analysis reveals Si~{\sc iv} lines are forming in the optically thick conditions in high electron density regions (i.e., near the base of the blowout jet). Lastly, we mention that two weak C-class flares occurred during this event, and further, one CME also occurred, which propagated with the speed of $\sim$250 km/s.

Graphics (e.g., figures and charts) are ubiquitous in scientific papers, yet separating graphics from text increases cognitive load in understanding text-graphic connections. Research has found that word-scale graphics, or visual embellishments at typographic size, can augment original text, making it more expressive and easier to understand. However, whether, if so, how scientific papers adopt word-scale graphics for scholarly communication remains unclear. To address this gap, we conducted a corpus study reviewing 909 word-scale graphics extracted from 126,797 scientific papers. Through analysis, we propose a framework that characterizes where (positioning), why (communicative function), and how (visual representation) authors apply word-scale graphics in scientific papers. Our findings reveal that word-scale graphics are rarely used, that icons dominate visual representation, and that visual representation connects with communicative function (e.g., using quantitative graphs for data annotation). We further discuss opportunities to enhance scholarly communication with word-scale graphics through technical and administrative innovations.

In this work, we develop the discrete solvability analysis for perturbed saddle-point problems in Banach spaces with forcing terms regularised by means of a projector constructed using the adjoint of a weighted Clément quasi-interpolation. We take as driving example the linearised Poisson--Boltzmann (an advection-diffusion-reaction problem) in mixed form. We use perturbation arguments on the continuous and discrete levels and then derive a priori estimates that remain valid when the load that appears on the right-hand side of the "second" equation is in $\mathrm{H}^{-1}$. Further, we show a supercloseness result and {analyse convergence} of an adequate adaptation of Stenberg postprocessing for mixed advection equations with non-regular data. We provide numerical results that illustrate the convergence of the proposed scheme.

We investigate a mathematical model for a bacterial population in a continuously stirred tank reactor with wall attachment. The model couples a free-boundary value problem for substrate diffusion in the one-dimensional biofilm with a system of nonlinear ODEs for biofilm thickness, suspended biomass, and free substrate concentration. We establish global well-posedness and analyze the long-term dynamics. In particular, we characterize the local and global stability of the trivial (washout) equilibrium, prove the existence of a nontrivial equilibrium, and, under additional structural assumptions, establish its uniqueness and derive conditions for its local stability.

Suppose that u is the potential function of a complete Kähler-Einstein metric on a bounded strictly convex domain in $\mathbb{C}^n$. We prove that u itself is strictly convex.

Rate-induced tipping is an instability that occurs in a system when its time-dependent rate parameter becomes larger than a threshold value. We investigate a Pearson diffusion process, a diffusion process having solutions staying in a bounded domain under certain conditions, whose noise-free limit experiences a rate-induced tipping such that solutions escape from the domain in a finite time. We show that the existence of noise leads to faster escapement from the domain.

Airfoil shape optimization presents a challenge where classical solvers frequently struggle with computational efficiency and local minima. In the promising paradigm of quantum computing, the coherent Ising machine (CIM), a specialized physical solver, offers acceleration capabilities. However, its native discrete binary architecture restricts the application in aerodynamic design. To bridge this gap, we propose a comprehensive framework that translates airfoil shape optimization into hardware-compliant quadratic unconstrained binary optimization formulations. We integrate high-order response surface models via the Rosenberg order reduction, enabling the CIM to capture strong nonlinearities in the aerodynamic performance response. Furthermore, we introduce a block-diagonal scalarization strategy that compose trade-off scenarios into a single optimization. Validated on the NACA 4-digit airfoil series using CIM hardware with 615 spins, the framework successfully locates the global optimum with a computational speedup of three orders of magnitude compared to the classical simulated annealing. The parallel embedding capacity allows for the extraction of an entire optimal Pareto front in a single hardware execution. This work demonstrates a viable, quantum-enhanced paradigm for engineering optimization.

We investigate the collective behavior of motile rods immersed in a monolayer of apolar rods confined between vertically vibrating plates using numerical simulations. We uncover an antidiffusive instability whereby motile rods segregate from the apolar medium and form flocks whose size increases with the medium concentration. Remarkably, enhanced segregation leads to a reduction of the global polar order. The flock structure is strongly influenced by the anisotropy of the medium rods. For small aspect ratios, the flocks are elongated perpendicular to the mean direction of motion, whereas for larger aspect ratios, they elongate along the direction of motility. We rationalize the emergence of segregation-induced disorder using a minimal mean-field model.

Intelligent reflecting surfaces (IRSs) are poised to revolutionize next-generation wireless communication systems by enhancing channel quality and spectrum efficiency through advanced wave manipulation. However, extremely large-scale IRS {(XL-IRS)} deployments face significant challenges in channel estimation due to multiplicative path loss and near-field (NF) effects, where spherical wavefronts couple distance and angle parameters. Existing polar-domain codebook-based compressive sensing methods for NF channel estimation suffer from low accuracy and high complexity, caused by the need for high-resolution grids of both distance and angle parameters. To address this, we propose a harmonic processing-inspired channel estimation framework for NF {XL-IRS} systems by leveraging tensor modalization to decouple channel parameters. Drawing an analogy to musical harmonic analysis, our approach decomposes the high-dimensional NF channel tensor into independent factor matrices, modeled as ``chords," representing distance and angle parameters. Through harmonic analysis-inspired distance parameter decoupling, we design a compact, distance-dependent codebook that enables high-resolution NF channel parameter estimation. This approach significantly reduces the codebook size compared to polar-domain methods. {Then, we} derive the Cramér-Rao lower bound (CRLB) to evaluate the estimators. Finally, simulation results show an 8.5 dB improvement in normalized mean square error (NMSE) compared to conventional methods, underscoring its low complexity and high accuracy.

Chebyshev filtered subspace iteration is a well-known algorithm for the solution of (symmetric/Hermitian) algebraic eigenproblems which has been implemented in several application codes~\cite{Kronik:2006ff, abinit:2020} or in stand alone libraries~\cite{ChASE}. An essential part of the algorithm is the QR-factorization of the array of vectors spanning the active subspace that have been filtered by the Chebyshev filter. Typically such an array has an a-priori unknown high condition number that directly influences the choice of QR-factorization algorithm. In this work we show how such condition number can be bound from above with precise and inexpensive estimates. We then proceed to use these estimates to implement a mechanism for the choice of QR-factorization in the ChASE library. We show how such mechanism enhance the performance of the library without compromising on its accuracy.

Firms increasingly use randomized experiments to decide whether to scale up an intervention and, if so, how to re-optimize related operational choices such as inventory, capacity, or pricing. In many settings, experiments are performed on small samples, so the estimated effect of the intervention is uncertain. A common practice is to plug a 'significant' estimate of the effect into both (i) the rollout rule and (ii) the downstream optimization. However, this can lead to avoidable losses because the costs of over- versus under-estimating the effect are often asymmetric. The technically ideal approach is to obtain a data-dependent decision rule that minimizes the Bayes risk, but this lacks transparency and requires more computations. We propose Predict-Adjust-Then-Rollout-Optimize (PATRO), a plug-in approach that keeps the standard estimate, but makes data-independent adjustments, respectively, for the two types of decision. We show that the two adjustments can be substitutes or complements and provide an alternating-iteration method to compute the pair. PATRO performs both in theory and numerically close or equivalent to the Bayes-optimal benchmark, making it a simple, effective way to convert noisy experimental results into better rollout and operational decisions.

Synchrony patterns describe network states in which nodes of a coupled dynamical system are grouped into clusters based on synchronization between nodes. Beyond simple synchrony, synchronized clusters may also exhibit active or inactive states, and the collection of all such clusters constitutes an activity pattern. Although these patterns may arise naturally in networks with permutation symmetries, the requirement of symmetries imposes a restrictive and often unrealistic assumption, as many real-world networks lack such symmetries. In this work, we present synchrony patterns of coexisting active-inactive clusters that cannot be identified through symmetries. Considering dynamical systems in which intrinsic dynamics and coupling functions are odd functions in phase space, we identify all possible patterns a network can exhibit through symmetry breaking of identically synchronized clusters. The symmetry breaking of invariant clusters generates antisynchronized clusters, allowing active-inactive clusters to coexist. We show that while active clusters are external equitable partitions, inactive clusters can be purely dynamics-induced. Starting with a symmetry-broken state, we show that the existence of different invariant patterns is a function of coupling strength and intercluster weights. Finally, by combining synchronization manifolds with the Laplacian eigenvectors, we identify transversal perturbations for these patterns and present a stability analysis.

This study presents an investigation of nearly two dozen candidate Luminous Blue Variables (cLBVs) in the galaxies M31 and M33. Eight stars have been studied in detail, while an additional sixteen objects are briefly mentioned. Multi-epoch spectra of confirmed cLBVs from LAMOST and previous literature show broad hydrogen, He I lines, abundant Fe II and [Fe II] emission lines, and discernible spectral variability, consistent with the characteristics of known LBVs. Low outflow velocities inferred from P Cygni profiles are also incorporated into the classification criteria. Moreover, key stellar properties, including temperature and luminosity, are determined using the Spectral Energy Distribution (SED) fitting and spectral modeling. By comparison with stellar evolutionary tracks on the temperature luminosity diagram, the initial masses are estimated to be in the range of approximately 32 to 60 $M_{\odot}$. Except for J013401 and J013411, other stars locate within the typical LBV region between the S Doradus instability strip and their outburst phase. More importantly, our sample, except for the binary system, are all positioned in the LBVs region rather than that of B[e]SGs in the near-infrared color-color diagram. Based on all available information, one of the eight sources is confirmed as an LBV, four stars are designated as high-probability cLBVs, and the remaining three stars await further photometric observations to secure their classification. Given the current scarcity of known cLBVs, our study has the potential to make a significant increase in the number of LBVs in M31 and M33.

Quantum communication between distant superconducting qubits on separate chips using itinerant microwave photons has been studied to realize distributed quantum information processing. To enhance information capacity and fault tolerance in quantum networks, it is beneficial to encode a large quantity of quantum information using auxiliary degrees of freedom of these photons. In this work, we experimentally investigate the use of temporal modes of photon wave packets. Through the photon-shaping technique with a fixed-frequency transmon qubit, we generate single microwave photons in four orthogonal temporal modes propagating along a waveguide. We demonstrate mode-selective absorption across orthogonal modes via the time-reversed process of emission, achieving absorption efficiencies exceeding 0.89 for mode-matched cases, while remaining below 0.13 for orthogonal modes. Photons rejected by a given receiver mode can remain mutually orthogonal, enabling selective absorption at subsequent receivers in future multi-node architectures. These results highlight the feasibility of temporal-mode engineering for constructing a higher-dimensional orthogonal basis for multiplexed quantum networks.

A three-component plasma model composed of ions, cool electrons, and hot electrons is adopted to investigate the existence of large amplitude electron-acoustic solitons not only for the model for which inertia and pressure are retained for all plasma species which are assumed to be adiabatic but also neglecting inertial effects of the hot electrons. Using the Sagdeev potential formalism, the Mach number ranges supporting the existence of large amplitude electron-acoustic solitons are presented. The limitations on the attainable amplitudes of electron-acoustic solitons having negative potentials are attributed to a number of different physical reasons, such as the number density of either the cool electrons or hot electrons ceases to be real valued beyond the upper Mach number limit, or, alternatively, a negative potential double layer occurs. Electron-acoustic solitons having positive potentials are found to be supported only if inertial effects of the hot electrons are retained and these are found to be limited only by positive potential double layers.

Topologically trivial and non-trivial semimetals with a high degree of carrier compensation are well known for demonstrating large transverse magnetothermopower ($S_{yx}$). However, in such systems, the longitudinal magnetothermopower ($S_{xx}$) is typically suppressed due to nearly perfect electron-hole compensation. Here, we show that the half-Heusler topological semimetal DyPtBi exhibits simultaneously large $S_{xx}$ and $S_{yx}$ magnetothermopowers, defying this conventional trade-off. In $B=14$\,T, thermopower of DyPtBi reaches peak values of $S_{xx}=131\,μ\rm{V/K}$ at $T=149$\,K and $S_{yx}=-297\,μ\rm{V/K}$ at $T=200$\,K, and transverse component remains significantly large even at $290$\,K ($S_{yx}=-213\,μ\rm{V/K}$). Remarkably, at $T=290$\,K and in relatively weak magnetic field of $1$\,T, both relevant for practical applications, DyPtBi shows $S_{yx}=-18\,μ\rm{V/K}$, which is one of the largest values reported under such conditions. The large transverse thermopower originates from an ambipolar effect associated with thermal excitation occurring in zero-gap semiconductors. Due to the imperfect electron-hole compensation, an intrinsic asymmetry between hole- and electron-type carriers enables pronounced values of both $S_{xx}$ and $S_{yx}$, resulting in high effective thermopower ($S_{xx}+|S_{yx}|=379\,μ\rm{V/K}$) in DyPtBi at 200\,K. A comparative analysis with DyPdBi, another half-Heusler material that demonstrates large $S_{xx}=123\,μ\rm{V/K}$ but small $S_{yx}=-16\,μ\rm{V/K}$ (both values obtained at $T=293$\,K and $B=14$\,T), highlights the critical role of band structure and compensation tuning. These findings underscore the potential of chemical doping and band engineering in rare-earth-based half-Heusler materials for optimizing both transverse and longitudinal thermoelectric properties.

As AI capabilities and deployment accelerate toward a post-AGI era, concerns are growing about electricity demand and carbon emissions from AI computing, yet it is rarely represented explicitly in long term energy-economy-climate scenario models. In such a setting, digital infrastructure scaling may be constrained by power system dynamics. We introduce an AI computing sector into the Global Change Analysis Model (GCAM) and run U.S. scenarios that couple AI service growth with time varying compute energy intensity and economic drivers. We find that service growth does not translate linearly into electricity demand: outcomes depend on efficiency trajectories and demand responsiveness. With sustained efficiency improvements, AI electricity demand remains moderated; with slower or saturating gains, income-driven demand dominates by mid-century. Sensitivity analyses show weak responsiveness to price signals but strong dependence on income growth, implying limited leverage from price-based mechanisms alone. Rather than offering a single forecast, we map conditions under which efficiency-dominant versus demand-dominant regimes emerge, providing a compact template for long run AI electricity-demand scenarios and their implications for power sector emissions.

Several hadronic observables are nowadays computed in lattice QCD with a sub-percent precision which requires the inclusion of strong isospin-breaking and electromagnetic effects. Most of the methods that implement the photon propagator in finite-volume lead to power-law suppressed finite-size effects and do not allow for a straightforward crosscheck against phenomenology and other calculations. Both issues can be avoided by working with a Pauli-Villars regulated photon propagator defined directly in the continuum and infinite volume. This methodology can be profitably exploited to improve the determination of leading-order electromagnetic corrections to several observables such as the HVP or nucleon masses. In this work we apply the strategy to the charged/neutral pion mass difference using CLS ensembles.

Skyrmions are a particle-like topology with a quantised skyrmion number, realised across condensed matter and photonic platforms alike. In quantum photonics, they constitute an emerging resource, promising robust quantum information encoding, so far realised as single photon and bi-photon entangled states. Here we report the first visualisation of tripartite entanglement dynamics through topological structure using spin-skyrmion entangled states, where the topology of a single photon is remotely controlled through the spin of its entangled partner. We visualise our tripartite state theoretically by introducing the notion of a topological Bloch sphere that completely captures the entanglement and topolological features of the state. By leveraging this state, we realise the first quantum multiskyrmions, comprising multiple localised skyrmions within a single structure, that emulate signatures of their magnetic counterparts. We verify this experimentally and show that traversing our topological sphere reveals entanglement-driven particle-like motion of the localised topological structures. These dynamics unveil a physical manifestation of tripartite entanglement correlations which we illustrate by example of GHZ-like states, enabling a visualisation of multiple Bell states encoded within our system. Our work opens exciting possibilities for quantum sensing by mapping complex quantum channel features onto topological observables of multipartite states and offers a promising avenue for harnessing quantum topologies for multi-level encoding quantum communication schemes.

We develop a parabolic-cylinder approach to valley-polarized conductance in tilted anisotropic Dirac-Weyl systems, showing that the smooth-interface scattering problem can be reduced analytically to the Weber equation, which belongs to the same differential-equation class as the quantum harmonic oscillator. This reduction yields closed-form expressions for the angular transmission envelope and clarifies the distinct roles of the tilt components: the perpendicular tilt renormalizes the tunneling-envelope width, while the parallel tilt shifts the Fabry-Perot resonance structure differently in opposite valleys. Combined with the nonlinear mapping between the fixed device frame and the rotated barrier frame, this analytical structure provides a direct route from valley-dependent interface tunneling to net valley-polarized conductance. We apply the formalism to rotated electrostatic barriers and construct phase diagrams over barrier angle, tilt strength, width, height, and Fermi energy. The results reveal a robust optimum near t = 0.2 over the parameter range studied, identify the crossover from oscillatory to monotonic polarization regimes, and delineate practical operating windows for candidate materials including 8-Pmmn borophene and WTe2.

The universal prevalence of cooperation is puzzling, as defection typically yields higher payoffs than cooperation, motivating searches for hidden pathways to cooperation. Here we study a game-theoretic model on a lattice structured population in which interaction payoffs are scaled by the minimum of participants' accumulated wealth, reflecting real-world heterogeneity and incorporating the influence of past strategic choices. This wealth scaling allows frequent cooperators to surpass defectors in payoffs through their greater wealth even at high cooperation costs where defection would otherwise dominate. At the elevated critical cost-benefit ratio, the wealth gradient at the cooperator-defector boundary in one dimension exhibits a discontinuous transition. We show that slowing and effective stalling of the boundary trigger an explosive buildup of the wealth gradient, driving the dominance of cooperation below the critical ratio. Remarkably, this promotion of cooperation is stronger at higher temperatures, revealing a constructive role of fluctuations.

Charge density waves (CDW) are ubiquitous in the complex phase diagram of cuprate superconductors and exhibit both short- and long-range correlations. Using time-resolved resonant X-ray scattering, we investigate the photo-induced dynamics of CDW in YBa$_2$Cu$_3$O$_{6.67}$. We discover an excitation threshold ($Φ$$_\mathrm{C}$ $\approx$ 65 $μ$J/cm$^2$) above which long-range CDW disappear, revealing a persistent CDW peak with short-range correlation length. Ultrafast photo-excitation promptly uncovers this residual short-range CDW correlations, appearing within $\approx$ 0.2 ps. Long-range CDW coherence recovers within $\approx$ 0.6 ps, while the peak intensity remains partially suppressed. We rationalize the dichotomic behavior in the fluence and temporal dependencies as the signature of two coexisting CDW peaks, arising from short- and long-range correlations, which we disentangle through their distinct response to photo-excitation. We provide evidence that the collapse of long-range correlations is driven by an electronic process, while short-range correlations are characterized by distinct timescales and stiffness against photo-excitation. This approach establishes ultrafast X-ray scattering as an effective tool for disentangling coexisting density waves and correlations in quantum materials.

This paper studies the near field refraction problem with loss of energy in negative refractive index material. Based on the relative refractive index $κ$, the analysis is categorized into two cases, namely $κ< -1$ and $-1 < κ< 0$. For each case, we give the definition of the refractor and discuss some crucial properties of it. The properties of Fresnel coefficients are also discussed. Based on these properties, the existence of the weak solution when the target measure is either discrete or a finite Radon measure are proved. Besides, the critical case $κ= -1$ is also discussed briefly at the end of this paper.

Infrared (IR) excess observed around white dwarfs (WDs) is typically attributed to companions or debris disks. These systems are interesting because they offer a unique opportunity to study the late stages of stellar evolution and the interactions between WDs and surrounding material. The 11th data release (DR11) of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) - one of the largest spectroscopic surveys to date - has recently provided spectra for 3092 WDs, many of which have yet to be systematically investigated for IR excess. In this study, we cross-correlated the LAMOST DR11 WD catalog with optical and IR surveys, including the Sloan Digital Sky Survey (SDSS), Two Micron All-Sky Survey (2MASS), UKIRT Infrared Deep Sky Survey (UKIDSS), and Wide-field Infrared Survey Explorer (WISE). We performed spectral energy distribution fitting using the VOSA tool for 1818 WDs and identified 167 IR excess WD candidates. After excluding 23 sources with potential contamination within 6" and five additional sources identified through WISE ccf flag analysis, we identified 139 objects with candidate IR excess. These include 30 candidate WD + M dwarf binaries (18 new systems), 19 candidate WD + brown dwarf (BD) binaries (eight new systems), 66 candidate WD + dust disks (38 new systems), and 24 candidate either WD + BD or WD + dust disks (19 new systems). Given the limited spatial resolution of WISE, all candidate systems require follow-up IR observations for confirmation, such as high spatial resolution imaging or IR spectroscopy. This will help expand the parameter space of dust disks, allowing us to explore a broader range of possibilities.

Continuous-variable quantum key distribution (CV-QKD) is a promising quantum-safe alternative to classical asymmetric cryptography that enables two authenticated parties to establish a shared secret over a potentially eavesdropped quantum channel. A key step in CV-QKD post-processing is information reconciliation, which leverages forward error correction (FEC) techniques to extract identical bit strings from noisy correlated data. In this work, we analyze the strict limitations on operating distance that are imposed by constant-rate FEC, severely limiting the practicability of CV-QKD systems in deployed optical networks. To overcome the distance limitations, we evaluate three strategies: (i) tuning modulation variance, (ii) adding controlled amounts of trusted detector loss, and (iii) the use of rate-adaptive FEC. All approaches are validated experimentally, compared in terms of performance, and we discuss implementation aspects. Our results show that while methods (i) and (ii) extend the operational distance of constant-rate FEC without the need for additional hardware components, they incur a significant penalty in secret key rate (SKR). In contrast, rate-adaptive FEC enables CV-QKD operation with performance close to the asymptotic SKR over a wide range of distances, provided that the reconciliation efficiency is chosen appropriately.