The origin of the cosmic-ray (CR) knee remains one of the central open questions in particle astrophysics. Recent measurements by the Large High Altitude Air Shower Observatory revealed a pronounced feature in the proton spectrum at $\sim3-4$~PeV, while observations of diffuse gamma rays above $100$~TeV do not exhibit a corresponding spectral break. This apparent discrepancy challenges the standard interpretation, in which the local CR distribution is representative of the Galactic CR sea. Here, we investigate whether the CR knee can instead originate from the Cygnus region as a nearby PeVatron. By combining CR measurements at Earth with very-high-energy gamma-ray observations from LHAASO and the Tibet-AS$γ$ experiment, we identify an additional hard gamma-ray component in the inner Galaxy consistent with a source located in the Cygnus region. We show that our results provide a concordance multimessenger picture. The required properties are compatible with the PeVatron candidate detected by LHAASO in the Cygnus bubble and with the Galactic neutrino flux observed by the IceCube Neutrino Observatory.

We review existing classical simulation methods for performing fermionic Gaussian operations and develop new methods to address the gap by adhering to the fundamental theoretical framework established by Bravyi [Quantum Info. Comput. 5, 216 (2005)] for the most general fermionic Gaussian processes. Throughout this attempt, the focus remains on the unified approach that can be applied to generic fermionic Gaussian operations. This is beneficial since the selection of simulation methods has often been based on an ad hoc choice, heavily influenced by the specific model and circumstances, rather than on a systematic approach.

The growing demand for multi-DNN workloads with unpredictable task arrival times has highlighted the need for interruptible scheduling on edge accelerators. However, existing preemptive frameworks typically assume known task arrival times and rely on CPU-based offline scheduling, which incurs heavy runtime overhead and struggles to handle unpredictable task arrivals. Even worse, prior studies have shown that multi-DNN scheduling requires solving an NP-hard subgraph isomorphism problem on large directed acyclic graphs within limited time, which is extremely challenging. To tackle this, we propose IMMSched, a parallel subgraph isomorphism method that combines Multi-Particle Optimization with the Ullmann algorithm based on a probabilistic continuous-relaxation scheme, eliminating the serial data dependencies of previous works. Finally, a quantized scheduling scheme and a global controller in the hardware architecture further combine multi-particle results for consensus-guided exploration. Evaluations demonstrate that IMMSched achieves orders-of-magnitude reductions in scheduling latency and energy consumption, enabling real-time execution of unpredictable DNN tasks on edge accelerators.

This study demonstrates that thermal-evaporated SAM (eSAM) films, particularly in a thick configuration, spontaneously adopt a heterogeneous molecular orientation, forming a vertical-to-horizontal gradient in molecular packing. This unique architecture establishes a graded energy barrier, which is shown to facilitate more efficient hole transport compared with the single energy barrier presented by conventional thin SAMs. In conclusion, while solution-processed SAMs present formidable scalability challenges, the thermal evaporation of SAMs offers a viable pathway toward industrial-scale fabrication. The strategy of employing thick eSAM films with gradient molecular packing not only circumvents the uniformity issues of solution methods but also introduces a superior structure for charge transport, positioning it as a promising enabler for the commercialization of high-efficiency perovskite photovoltaics. The inability to achieve uniform hole transport with solution-processed self-assembled monolayers (SAMs) constitutes a fundamental bottleneck for scaling perovskite photovoltaics. Herein, we demonstrate that thermal-evaporated SAMs (eSAMs) overcome this limitation by enabling precise thickness control. Crucially, a thickened eSAM spontaneously forms a vertical-to-horizontal gradient in molecular orientation, which creates a descending energy barrier that directionally facilitates hole transport. This tailored interface also ensures excellent surface coverage and directs the growth of high-quality perovskite films. Consequently, the resultant photovoltaic devices set new benchmarks, delivering impressive power conversion efficiencies (PCEs) of 21.46% (small-area, 0.108 cm2) and 19.38% (large-area module, 15.52 cm2) for fully vacuum-evaporated devices, while also setting an impressive PCE of 23.67% for eSAM-based devices with solution-processed perovskites.

We study the use of a learned forward operator in the inverse problem of photoacoustic tomography. The Fourier neural operator to approximate the photoacoustic wave propagation is used. Further, the inverse problem is solved using a gradient-based approach with automatic differentiation. The methodology is evaluated using numerical simulations, and the results are compared to a conventional approach, where the forward operator is approximated using the pseudospectral $k$-space method. The results show that the learned forward operator can be used to approximate the photoacoustic wave propagation with good accuracy, and that it can be utilised as a computationally efficient forward operator in solving the inverse problem of photoacoustic tomography.

Uncertainties in balancing generation and load in low-carbon industrial microgrids (IMGs) make hybrid energy storage systems (HESS) crucial for their stable and economic operation. Existing model predictive control (MPC) techniques typically enforce periodic state of charge (SOC) constraints to maintain long term stability. However, these hard constraints compromise dispatch flexibility near the end of the prediction horizon, preventing sufficient energy release during critical peaks and leading to optimization infeasibility. This paper eliminates the periodic SOC constraints of individual storage units and proposes a novel full-timescale hierarchical MPC scheduling framework. Specifically, comprehensive physical and cost models are established for the HESS composed of flywheel, battery, compressed-air, and hydrogen-methanol energy storage. The control problem is decoupled into a hierarchical MPC architecture. Furthermore, a novel adaptive feedback mechanism based on micro trajectory inverse projection (MTIP) is embedded into the scheduling process, accurately mapping the high frequency dynamic buffering capabilities of lower tier storages into the upper decision space to generate dynamic boundaries. Experiments using 14 consecutive months of second-level data from a real-world IMG validate the effectiveness of the proposed method, demonstrating its significant superiority over existing approaches. By effectively preventing limit violations and deadlocks in lower-tier storages under extreme fluctuations, it achieves a 97.4\% net load smoothing rate and a 62.2\% comprehensive cycle efficiency.

We investigate optimal band structures in band-converged systems to achieve high zT using numerical calculations based on a virtual spectral conductivity model. We consider a two parabolic band system, in which multiple band parameters can be independently controlled. Despite its simplicity, this model provides theoretical validation of empirical trends observed in thermoelectric materials. Our results provide a physically transparent set of design principles for band-structure engineering, offering quantitative design guidelines for the development of a wide range of thermoelectric materials. The main conclusions are as follows: (i) When a band does not cross the chemical potential and |μ-E_edge |>5k_B T, the contribution of the band to zT is negligibly small; (ii) To suppress the bipolar effect, a band gap E_g satisfying E_g>5k_B T_op, where T_op is the operating temperature, is required; (iii) In band-converged systems, the energy separation between the band edge ΔE should satisfy ΔE~0 to maximize zT when interband scattering is insignificant; (iv) Achieving high spectral conductivity Σ (high band degeneracy N, density of states effective mass m_DOS^*, and relaxation time τ) near the band edge is essential for achieving high zT.

We demonstrate a single-arm optical platform for phase-retrieval-free, quantitative dynamic phase mapping of continuous transparent media via field-correlation ghost imaging. By modeling the medium as a dynamic pure-phase object, we spatially encode and compress its two-dimensional (2D) complex transmittance into a single bucket detector. Balanced heterodyne detection downconverts the optical frequencies for direct digitization. Crucially, by mapping spatial information into the temporal domain, this single-pixel architecture exploits high-speed digitization to continuously resolve 2D phase dynamics, effectively bypassing the frame-rate bottlenecks of traditional array sensors. Coupled with intermediate-frequency spectral analysis, this establishes a direct linear mapping from the recorded signal to the physical phase. The complex amplitude is thus deterministically extracted via field-correlation, enabling the spatial reconstruction of 2D acoustic pressure distributions using a pseudo-inverse algorithm. Experimental validations in an acoustic levitator confirm that the optically extracted acoustic wavelengths strictly match theoretical dispersion models, exhibiting a robust linear correlation between the retrieved phase shift and local sound pressure levels. This deterministic methodology provides a real-time-capable metrological tool for characterizing rapidly evolving phenomena, including transient aeroacoustic flows, shockwaves, and microfluidic biological dynamics.

In this paper, we study the hydrodynamic and acoustic limit from Boltzmann equations for two species gas mixture with potential $γ\in \left(-3, 1\right]$. % in the whole space $(x \in \mathbb{R}^3)$.Here the particle masses are different which derives to the loss of symmetry to the linearized collision operator. %This paper resolves it precisely by using a framework based on vector-valued functions. We construct the hydrodynamic limit for two species based on the Hilbert expansion method when the Knudsen number is small. The key observation is the precise properties of the linearized collision operators, including the extra operators due to the different particle masses $(m^A \neq m^B)$. In additional, the acoustic limit of the Boltzmann equations for gas mixtures is rigorously justified by assuming the strength of the initial data depends on the Knudsen number.

We construct automata with input(s) in Fibonacci representation (also known as Zeckendorf representation) recognizing some basic arithmetic relations and study their number of states. We also consider some basic operations on Fibonacci-automatic sequences and discuss their state complexity. Furthermore, as a consequence of our results, we improve a bound in a recent paper of Bosma and Don. We also discuss the state complexity and runtime complexity of using a reasonable interpretation of Büchi arithmetic to actually construct some of the studied automata recognizing relations.

We prove the existence of time-periodic leapfrogging vortex rings for the three-dimensional incompressible Euler equations, thereby providing a rigorous realization of a phenomenon first conjectured by Helmholtz (1858). In the leapfrogging motion, two coaxial vortex rings periodically exchange positions, a striking behavior repeatedly observed in experiments and numerical simulations, yet lacking complete mathematical justification. Our construction relies on a desingularization of two interacting vortex filaments within the contour dynamics formulation, which yields a Hamiltonian description of nearly concentric vortex rings. The main difficulty stems from a singular small-divisor problem arising in the linearized transport dynamics, where the effective time scale degenerates with the ring thickness parameter. To overcome this obstruction, we develop a degenerate KAM-type analysis combined with pseudo-differential operator techniques to control the linearized dynamics around symmetric configurations. Combining these tools with a Nash-Moser iteration scheme, we construct families of nontrivial time-periodic solutions in an almost uniformly translating frame. This establishes the first rigorous construction of classical leapfrogging motion for axisymmetric Euler flows without swirl, with no restriction on the time interval of existence.

Neutral atom arrays have seen tremendous progress in quantum simulation, quantum metrology, and fault-tolerant quantum computing. However, hardware constraints such as atom loss and heating remain significant challenges. In this work, we introduce a comprehensive ancilla-based toolbox for optical tweezer experiments that utilizes high-fidelity Rydberg entangling gates and ancilla atoms to mitigate these physical limitations. First, we demonstrate repeated ancilla-based atom readout, achieving improved detection fidelity over multiple rounds with minimal perturbation to data atoms. Second, leveraging the quantized motional states in tweezer-trapped strontium atoms, we transduce quantum information from the electronic to the motional manifold. This enables us to perform mid-circuit ancilla-based atom loss detection in a coherence-preserving fashion. Finally, we demonstrate algorithmic cooling, a circuit-based sequence that deterministically cools data atoms by transferring their motional entropy to the electronic states of ancilla atoms. We observe a marked reduction in the atomic temperature of data atoms. These tools offer a pathway to continuous operation in tweezer clocks and complement recent developments in continuous reloading experiments.

Prompt injection is listed as the number-one vulnerability class in the OWASP Top 10 for LLM Applications that can subvert LLM guardrails, disclose sensitive data, and trigger unauthorized tool use. Developers are rapidly adopting AI-assisted development tools built on the Model Context Protocol (MCP). However, their convenience comes with security risks, especially prompt-injection attacks delivered via tool-poisoning vectors. While prior research has studied prompt injection in LLMs, the security posture of real-world MCP clients remains underexplored. We present the first empirical analysis of prompt injection with the tool-poisoning vulnerability across seven widely used MCP clients: Claude Desktop, Claude Code, Cursor, Cline, Continue, Gemini CLI, and Langflow. We identify their detection and mitigation mechanisms, as well as the coverage of security features, including static validation, parameter visibility, injection detection, user warnings, execution sandboxing, and audit logging. Our evaluation reveals significant disparities. While some clients, such as Claude Desktop, implement strong guardrails, others, such as Cursor, exhibit high susceptibility to cross-tool poisoning, hidden parameter exploitation, and unauthorized tool invocation. We further provide actionable guidance for MCP implementers and the software engineering community seeking to build secure AI-assisted development workflows.

The Model Context Protocol (MCP) has emerged as a standard for connecting Large Language Models (LLMs) to external tools and data. However, MCP servers often expose privileged capabilities, such as file system access, network requests, and command execution that can be exploited if not properly secured. We present mcp-sec-audit, an extensible security assessment toolkit designed specifically for MCP servers. It implements static pattern matching for Python-based MCP servers and dynamic sandboxed fuzzing and monitoring via Docker and eBPF. The tool detects risky capabilities through configurable rule-based analysis and provides mitigation recommendations.

This paper studies distributed stochastic nonconvex optimization problems with compressed communication and differential privacy, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. To this end, we propose a compressed distributed stochastic gradient descent algorithm, which is robust under a general class of compression operators that allow both relative and absolute compression errors. We then show that the proposed algorithm finds the first-order stationary point for smooth nonconvex functions with the linear speedup convergence rate $\mathcal{O}(1/\sqrt{nT})$ and converges to the optimum if the global cost function additionally satisfies the Polyak--Łojasiewicz (P--Ł) condition with the convergence rate $\mathcal{O}(1/(nT^θ)),θ\in(0,1)$, where $T$ is the total number of iterations and $n$ is the number of agents. Furthermore, if the P--Ł~constant is known in advance, we show that the proposed algorithm achieves a convergence rate $\mathcal{O}(1/(nT))$. Finally, we show that the proposed algorithm is able to achieve $(0,δ)$-differential privacy without sacrificing convergence accuracy. Numerical experiments are carried out to

Exploratory data analysis (EDA) is often hindered by cold-start friction; when users lack specific analytic goals, they struggle to configure complex visualization parameters. While existing visualization tools mostly rely on explicit user input to frame data, we propose leveraging the physical environment as an implicit framing mechanism. We introduce a conceptual framework that uses the geometric and spatial properties of physical containers in Augmented Reality (AR) to guide data interpretation. We characterize how container attributes, such as number of faces, size, proportion, and shape, give rise to distinct perceptual tendencies. For example, a circular container may encourage cyclic interpretation, while juxtaposed planar faces may facilitate comparative analysis. By treating physical forms as environmental framing conditions, we show how AR can orient a user's attention and structure their exploration without requiring manual encoding or prescribing fixed conclusions. We demonstrate this framework through a series of AR design examples illustrating how container morphology foregrounds cyclic, comparative, and sequential analytic patterns.

We study population dynamics through a general growth/degrowth-fragmentation process, with resource consumption and unbounded growth/degrowth, birth and death rates. Our model is structured in a positive trait called energy (which is a proxy for any biological parameter such as size, age, mass, protein quantity...), and the jump rates of the process can be arbitrarily high depending on individual energies, which has not been considered yet in the literature. After a preliminary study to construct well-defined objects (which is necessary contrary to similar works, because of the explosion of individual rates), we consider a classical sequence of renormalizations of the underlying process and obtain a tightness result for the associated laws in large-population asymptotics. We characterize the accumulation points of this sequence as solutions of an integro-differential system of equations, which proves the existence of measure solutions to this system. Furthermore, if such a measure solution is unique, then our tightness result becomes a convergence result towards this unique process. We illustrate our work with the case of allometric rates (i.e. they are assumed to be power functions) and eventually present numerical simulations in this allometric setting.

A central challenge in understanding the origin of collective flow-like signatures in small collision systems calls for a reliable method to disentangle genuine collective flow from substantial background correlations, especially those arising from transverse momentum conservation (TMC). A Bayesian inference framework is developed to integrate TMC calculations with the LHC-ATLAS data on long-range multiparticle azimuthal correlation observables, thereby extracting genuine collective flow in small systems. Our analysis indicates that while the genuine elliptic and triangular flow ($v_{2}$ and $v_{3}$) are similar, the $p$+$p$ and $p$+Pb systems exhibit distinct TMC backgrounds, TMC-flow interplay, and $v_{2}$--$v_{3}$ correlations. We demonstrate that the genuine $v_{2}$ and $v_{3}$ are well described by the measured four-particle $v_2\{4\}$ and two-particle $v_3\{2\}$ in $p$+Pb collisions, whereas these measurements systematically underestimate the genuine flow in $p$+$p$ collisions, due to competing contributions from TMC effects. This establishes a robust and data-driven approach, providing renewed theoretical insight into collective behavior free from TMC contamination in small collision systems.

The frequency range around 7 GHz has emerged as a promising upper mid-band spectrum for 6th generation (6G), offering a practical balance between coverage and capacity. To fully exploit this band, however, future systems require substantially stronger beamforming and spatial multiplexing capability than today's 5G 64-port commercial deployments. This article investigates extreme multiple-input multiple-output (X-MIMO) with 256 digital ports as a practical 6G architecture for 7 GHz operation. First, through system-level simulations, we examine the throughput benefits and design trade-offs of increasing the number of base station (BS) and user equipment (UE) digital antenna ports, including comparisons between 128-port and 256-port configurations. We then present a 256-port 7 GHz BS and UE prototype and report field-trial results obtained in urban outdoor environments. The measurements demonstrate the feasibility of 8-layer downlink single-user MIMO over a 100 MHz bandwidth, achieving more than 3 Gbps for a single user under urban outdoor propagation conditions. Channel analysis based on measured data further suggests how the large digital aperture of X-MIMO supports high-order spatial multiplexing even with limited dominant angular clusters. Finally, we identify key challenges and outline research directions toward practical deployment of 7 GHz X-MIMO systems for 6G.

The potential of quantum computing is fundamentally constrained by the inherent susceptibility of qubits to noise and crosstalk, particularly during multi-qubit gate operations. Existing strategies, such as hardware isolation and dynamical decoupling, face limitations in scalability, experimental feasibility, and robustness against complex noise sources. In this manuscript, we propose a physics-guided neural control (PGNC) framework to generate robust control pulses for superconducting transmon qubit systems, specifically targeting crosstalk mitigation. By combining a hardware aware parameterization with a Hamiltonian-informed objective that accounts for condition-dependent crosstalk distortions, PGNC steers the search toward smooth and physically realizable pulses while efficiently exploring high dimensional control landscapes. Numerical simulations for the CZ gate demonstrate superior fidelity and pulse smoothness compared to a Krotov baseline under matched constraints. Taken together, the results show consistent and practically meaningful improvements in both nominal and perturbed conditions, with pronounced gains in worst-case fidelity, supporting PGNC as a viable route to robust control on near-term transmon devices.

We establish a sparsity in terms of $\ell_p$-summability and weighted $\ell_2$-summability for the coefficients of the Laguerre generalized piecewise-polynomial chaos expansion of solutions to parametric elliptic PDEs with log-Laplace random inputs. From the sparsity, we derive convergence rates for semi-discrete approximations with respect to parametric variables. These rates are valid for sparse-grid, piecewise-polynomial interpolations and the generated quadratures, and to related extended least-squares approximations and generated quadratures.

The Gilbert graph $\text{Gilbert}(q,n,d)$, which arises naturally in graph theory and coding theory, is the regular graph on $\mathbb{F}_q^n$ in which two vertices are adjacent if their Hamming distance is less than $d$, and it is vertex-transitive. We classify all parameters $(q,n,d)$ for which $\text{Gilbert}(q,n,d)$ is edge-transitive or distance-transitive, and separately classify all parameters for which its complement has these properties. We prove that $\text{Gilbert}(q,n,d)$ is edge-transitive if and only if it is distance-transitive, and that this occurs precisely when $d=2$, $(q,d)=(2,3)$, or $(q,d)=(2,n)$. For the complement graphs, we determine all parameters yielding edge- or distance-transitivity using spectral methods based on Krawtchouk polynomials and the structure of the Hamming association scheme. In contrast to the Gilbert graphs, where the parameter sets corresponding to edge- and distance-transitivity coincide, we show that for their complements the set of parameters yielding distance-transitivity is strictly contained in the set yielding edge-transitivity. As an application, we compute the exact values of the Lovász $\vartheta$-function of Gilbert graphs, as well as of their complements, in all cases where either one of them is edge-transitive.

Existing computational studies of popular music primarily model aggregate trends or predict chart performance, offering limited support for interpreting artist-level alignment against historical stylistic baselines. We introduce an interactive visual analytics framework that treats each artist-decade as a unit defined relative to an era-specific baseline, characterized along two complementary dimensions: profile shape similarity, capturing directional correspondence with the era's feature pattern, and profile contrast ratio, capturing stylistic intensity relative to the era's dispersion. Together, these dimensions define a quadrant-based trajectory space for reasoning about conformity, divergence, and amplification over time. Applied to weekly U.S. Billboard Hot 100 chart entries from the all-time top-10 artists across six decades (1960s-2010s), linked with Spotify audio features, the framework reveals that alignment and intensity can meaningfully diverge across artist trajectories.

The conventional description of time-varying media assumes that electromagnetic fields evolve according to fixed continuity conditions during parameter jumps. Here we reveal that these conditions are not physical constraints but tunable design degrees of freedom. By developing a unified framework that treats continuity rules as engineerable parameters, we expand the scope of time-varying metamaterials and enable wave phenomena previously considered impossible. For instance, non-resonant, reflectionless wave amplification without momentum bandgaps, and reversible conversion between propagating waves and static fields for optical memory, etc. This work opens a new dimension for controlling light-matter interactions.

In 2014, Juul, Kurlberg, Madhu and Tucker asked the following: given $K$ a number field and $f$ a rational function with coefficients in $K$, if $f_\mathfrak{p}$ denotes the reduction of $f$ modulo a prime ideal $\mathfrak{p}$ in the ring of integers of $K$, what is the limit inferior of the proportion of periodic points of $f_\mathfrak{p}$ when the norm of $\mathfrak{p}$ goes to infinity? Recent results of Fariña-Asategui and the author show that when $f$ is a polynomial of degree $d \geq 2$ non-linearly conjugate over $\mathbb{C}$ to a Chebyshev polynomial then the limit is zero. In this article, we address the remaining cases to give a complete classification of the problem in the case of polynomials.

We consider the problem of triangulating a polygon with $n$ vertices and $h$ holes, or relatedly the problem of computing the trapezoidal decomposition of a collection of $h$ disjoint simple polygonal chains with $n$ vertices total. Clarkson, Cole, and Tarjan (1992) and Seidel (1991) gave randomized algorithms running in $O(n\log^*n + h\log h)$ time, while Bar-Yehuda and Chazelle (1994) described deterministic algorithms running in $O(n+h\log^{1+\varepsilon}h)$ or $O((n+h\log h)\log\log h)$ time, for an arbitrarily small positive constant $\varepsilon$. No improvements have been reported since. We describe a new $O(n + h\log h)$-time algorithm, which is optimal and deterministic. More generally, when the given polygonal chains are not necessarily simple and may intersect each other, we show how to compute their trapezoidal decomposition (and in particular, compute all intersections) in optimal $O(n + h\log h)$ deterministic time when the number of intersections is at most $n^{1-\varepsilon}$. To obtain these results, Chazelle's linear-time algorithm for triangulating a simple polygon is used as a black box.

We contrast three perspectives on engagement from three projects on the design of Digital Behavior Change Interventions (DBCIs), all conducted as part of the PhD thesis of the second author. We provide a reflection on this work with respect to engagement, discussing the motivation, the assumed effects of engagement, the measures of engagements and key insights of each project, as the well as the strategies employed to increase engagement.

During solar flares, a considerable portion of the flare atmosphere becomes heated; however, the energy deposition process is still unclear, especially in the lower solar atmosphere. Here, we present spectroscopic and imaging observations of a small-scale transient of lifetime $<$1-min and further formation of a hot loop of lifetime $\approx$2-min in a solar active region. The observed transient shows the appearance of hot plasma $>$10 MK at the loop foot-point and the subsequent formation of a small-scale transient loop with a loop-top temperature $>$8 MK. The transient shows an enhancement in intensities in several AIA and IRIS passbands. Light curves obtained from several lower atmospheric passbands show consistent time lags in several peak intensities, which, to our knowledge, has never been reported before. Beneath the transient, associated HMI magnetogram shows evidence of flux emergence of both polarities. Using the IRIS \ion{O}{IV} line pair, we obtained the average electron number density of $10^{11.22}$ cm$^{-3}$ at the transient. IRIS transition region lines such as \ion{O}{IV} and \ion{Si}{IV} show a redshift of 10-15 km s$^{-1}$, whereas neutral lines such as \ion{C}{I} and \ion{S}{I} show a redshift of about 5 km s$^{-1}$. These Doppler shifts suggest a down-flowing warmer plasma in the lower atmosphere. The appearance of \ion{Mg}{II} triplets in emission is also observed. We interpret these enhancements in intensities in the lower atmosphere as a result of heating due to both non-thermal electrons and thermal conduction operating simultaneously.

We report here the results of a detailed magnetic, thermodynamic, and neutron powder diffraction (NPD) studies carried out on the double perovskite iridates Pr(2-x)SrxMgIrO6 (x = 0 and 0.5). Temperature dependent bulk DC susceptibility data clearly reveals a sharp antiferromagnetic (AFM) transition at 14.5 K in Pr2MgIrO6(x = 0). Next, a weaker signature of an AFM transition at a lower temperature (6 K) is observed in x = 0.5 i.e., Pr1.5Sr0.5MgIrO6 (PSMIO1505). The observed magnetic transitions are further corroborated by the presence of anomalies around the same temperatures in our T-dependent specific heat results. The charge states of both Pr and Ir cations have been confirmed to be the expected ones (3+ for Pr in both the compounds, while Ir is in a pure 4+ state for x = 0 and in a mixed 4+/5+ state for x = 0.5) from the core-level x-ray photoemission spectroscopy (XPS) measurements. Using neutron powder diffraction (NPD) the magnetic ground states and the magnetic moment values were determined for both compounds. Both the Pr- and Ir-sites undergo AFM ordering below the respective transition temperatures, designated by the propagation vector k = ( 1/2 , 0, 1/2 ), in both the compounds.

In this work we consider the focusing, energy-critical wave equation in 3D radial case. It has been verified that any global or type II blow-up solution decomposes into a superposition of several decoupled grounds states, a free wave and a small error, as time tends to infinity or the blow-up time. This is usually called soliton resolution. However, all known examples of soliton resolution in the 3D radial case come with no more than one soliton. In this work we prove the nonexistence of any global or type II blow up solution with two or more solitons, thus give a complete classification of asymptotic behaviours of radial solutions.