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We report the detection of a rich spectrum of more than one hundred optical emission lines of vibrationally hot molecular hydrogen (H2) from the photodissociation region (PDR) around the mini-starburst cluster NGC 346 in the Small Magellanic Cloud. The lines are concentrated in the spectral range 6000 to 9300 Angstrom and have observed brightnesses ranging from 0.01% to 0.4% times that of the H beta lambda 4861 hydrogen recombination line. Analysis of the spatial distribution of the H2 lines shows that they originate from a range of depths in the PDR, intermediate between the shallow layers probed by known fluorescent lines of neutral nitrogen and oxygen, and the more shielded layers probed by neutral carbon recombination lines. Comparison with other PDRs shows that the relative strength of the H2 lines with respect to the [C I] lambda 8727 line increases rapidly with decreasing metallicity, being at least 40 times larger in NGC 346 than in the prototypical PDR of the Orion Bar. The internal PDR dust extinction is also found to be anomalously low in NGC 346. A separate result is the discovery of a high-ionization bow shock around the O2 star Walborn 3.

In this contribution, I briefly review recent progress in detecting and measuring the properties of relativistic iron lines observed in stellar-mass black hole systems, and the aspects of these lines that are most relevant to studies of similar lines in Seyfert-1 AGN. In particular, the lines observed in stellar-mass black holes are not complicated by complex low-energy absorption or partial-covering of the central engine, and strong lines are largely independent of the model used to fit the underlying broad-band continuum flux. Indeed, relativistic iron lines are the most robust diagnostic of black hole spin that is presently available to observers, with specific advantages over the systematics-plagued disk continuum. If accretion onto stellar-mass black holes simply scales with mass, then the widespread nature of lines in stellar-mass black holes may indicate that lines should be common in Seyfert-1 AGN, though perhaps harder to detect.

In this paper we address the following question: given a holomorphic function with prescribed $L^p(\mathbb{R})$ and $L^q(\mathbb{R})$ norm (with $1\leq p,q \leq \infty$) along two parallel lines in the complex plane, then what is the maximum value that this function can achieve at a given point between these lines. Here we show that this problem is well-posed in suitable Hardy-like spaces on the strip. Moreover, in this setting we completely solve this problem by providing not only an explicit formula for the optimizers but also for the optimal values. In addition, we briefly discuss some applications of these results to interpolation theory and to Lieb-Thirring inequalities.

Fine-tuning pre-trained models has become the standard approach to endow them with specialized knowledge, but it poses fundamental challenges. In particular, \textit{(i)} fine-tuning often leads to catastrophic forgetting, where improvements on a target domain degrade generalization on other tasks, and \textit{(ii)} merging fine-tuned checkpoints from disparate tasks can lead to significant performance loss. To address these challenges, we introduce LiNeS, Layer-increasing Network Scaling, a post-training editing technique designed to preserve pre-trained generalization while enhancing fine-tuned task performance. LiNeS scales parameter updates linearly based on their layer depth within the network, maintaining shallow layers close to their pre-trained values to preserve general features while allowing deeper layers to retain task-specific representations. In multi-task model merging scenarios, layer-wise scaling of merged parameters reduces negative task interference. LiNeS demonstrates significant improvements in both single-task and multi-task settings across various benchmarks in vision and natural language processing. It mitigates forgetting, enhances out-of-distribution gener

Context: The Importance of Dynamic Variability Management in Dynamic Software Product Lines. Objective: Define a protocol for conducting a systematic mapping study to summarize and synthesize evidence on dynamic variability management for Dynamic Software Product Lines in self-adaptive systems. Method: Application the protocol to conduct a systematic mapping study according the guidelines of K. Petersen. Results: A validated protocol to conduct a systematic mapping study. Conclusions: First findings show that it is necessary to visualize new ways to manage variability in dynamic software product lines.

The mass measurement of supermassive black holes (SMBHs) is a very complex task. Between several methods for SMBH mass measurements, some of them use the spectral lines, which indicate the motion of the emitting/absorbing material around an SMBH. Mostly there is assumption of virialization of line emitting gas in the region close to SMBHs that is used for their mass measurements. In this paper we will give an overview of methods for the SMBH mass measurements using broad emission spectral lines observed in Type 1 AGNs. First we give the basic idea to use the parameters of broad lines to SMBH mass measurements. After that we give an overview of broad lines from X-ray (Fe kα) to the IR (Pashen and Brecket lines) which have been used for SMBH mass estimates. Additionally, we describe and discuss a new method for SMBH mass measurements using the polarization in the broad lines emitted from Type 1 AGNs.

We list vacuum wavelengths, energy levels, statistical weights, transition probabilities and oscillator strengths for permitted resonance spectral lines of all ions of 18 astrophysically important elements (H through Si, S, Ar, Ca, Fe). Using a compilation of experimental energy levels, we derived accurate wavelengths for 5599 lines of 1828 ground-term multiplets which have gf-values calculated in the Opacity Project. We recalculated the Opacity Project multiplet gf-values to oscillator strengths and transition probabilities of individual lines. For completeness, we added 372 resonance lines of NeI, ArI, FeI and FeII ions which are not covered by the Opacity Project. Intercombination and forbidden lines are not included in the present compilation.

For each linearly normal elliptic curve $C$ in $\mathbb P^3$, we determine Galois lines and their arrangement. The results are as follows: the curve $C$ has just six $V_4$-lines and in case $j(C)=1$, it has eight $Z_4$-lines in addition. The $V_4$-lines form the edges of a tetrahedron, in case $j(C)=1$, for each vertex of the tetrahedron, there exist just two $Z_4$-lines passing through it. We obtain as a corollary that each plane quartic curve of genus one does not have more than one Galois point.

We study and quantify gravitational redshift by means of relativistic ray tracing simulations of emission lines. The emitter model is based on thin, Keplerian rotating rings in the equatorial plane of a rotating black hole. Emission lines are characterised by a generalized fully relativistic Doppler factor or redshift associated with the line core. Two modes of gravitational redshift, shift and distortion, become stronger with the emitting region closer to the Kerr black hole. Shifts of the line cores reveal an effect at levels of 0.0015 to 60 % at gravitational radii ranging from 100000 to 2. The corresponding Doppler factors range from 0.999985 to 0.4048. Line shape distortion by strong gravity, i.e. very skewed and asymmetric lines occur at radii smaller than roughly ten gravitational radii. Gravitational redshift decreases with distance to the black hole but remains finite due to the asymptotical flatness of black hole space-time. The onset of gravitational redshift can be tested observationally with sufficient spectral resolution. Assuming a resolving power of ~100000, yielding a resolution of ~0.1 Angstroms for optical and near-infrared broad emission lines, the gravitational

There are many examples for point sets in finite geometry, which behave "almost regularly" in some (well-defined) sense, for instance they have "almost regular" line-intersection numbers. In this paper we investigate point sets of a desarguesian affine plane, for which there exist some (sometimes: many) parallel classes of lines, such that almost all lines of one parallel class intersect our set in the same number of points (possibly mod $p$, the characteristic). The lines with exceptional intersection numbers are called renitent, and we prove results on the (regular) behaviour of these renitent lines.

We answer negatively a question: if $\mathcal F$ is a family of $n\geqslant 3$ non-vertical, pairwise non-parallel lines on the plane and $\bigcap \mathcal F=\emptyset$, is there a vertical line $L$ such that $L\cap\bigcup \mathcal F$ has exactly $n-1$ or $n-2$ points?

We derive a formula expressing the average number $E_n$ of real lines on a random hypersurface of degree $2n-3$ in $\mathbb{R}\textrm{P}^n$ in terms of the expected modulus of the determinant of a special random matrix. In the case $n=3$ we prove that the average number of real lines on a random cubic surface in $\mathbb{R}\textrm{P}^3$ equals: $$E_3=6\sqrt{2}-3.$$ Our technique can also be used to express the number $C_n$ of complex lines on a generic hypersurface of degree $2n-3$ in $\mathbb{C}\textrm{P}^n$ in terms of the determinant of a random Hermitian matrix. As a special case we obtain a new proof of the classical statement $C_3=27.$ We determine, at the logarithmic scale, the asymptotic of the quantity $E_n$, by relating it to $C_n$ (whose asymptotic has been recently computed D. Zagier). Specifically we prove that: $$\lim_{n\to \infty}\frac{\log E_n}{\log C_n}=\frac{1}{2}.$$ Finally we show that this approach can be used to compute the number $R_n=(2n-3)!!$ of real lines, counted with their intrinsic signs, on a generic real hypersurface of degree $2n-3$ in $\mathbb{R}\textrm{P}^n$.

We provide explicit equations of some smooth complex quartic surfaces with many lines, including all 10 quartics with more than 52 lines. We study the relation between linear automorphisms and some configurations of lines such as twin lines and special lines. We answer a question by Oguiso on a determinantal presentation of the Fermat quartic surface.

The broad emission spectral lines emitted from AGNs are our main probe of the geometry and physics of the broad line region (BLR) close to the SMBH. There is a group of AGNs that emits very broad and complex line profiles, showing two displaced peaks, one blueshifted and one redshifted from the systemic velocity defined by the narrow lines, or a single such peak. It has been proposed that such line shapes could indicate a supermassive binary black hole (SMB) system. We discuss here how the presence of an SMB will affect the BLRs of AGNs and what the observational consequences might be. We review previous claims of SMBs based on broad line profiles and find that they may have non-SMB explanations as a consequence of a complex BLR structure. Because of these effects it is very hard to put limits on the number of SMBs from broad line profiles. It is still possible, however, that unusual broad line profiles in combination with other observational effects (line ratios, quasi-periodical oscillations, spectropolarimetry, etc.) could be used for SMBs detection. Some narrow lines (e.g., [O\,III]) in some AGNs show a double-peaked profile. Such profiles can be caused by streams in the Narrow

We define a ternary Relation Algebra (RA) of relative position relations on two-dimensional directed lines (d-lines for short). A d-line has two degrees of freedom (DFs): a rotational DF (RDF), and a translational DF (TDF). The representation of the RDF of a d-line will be handled by an RA of 2D orientations, CYC_t, known in the literature. A second algebra, TA_t, which will handle the TDF of a d-line, will be defined. The two algebras, CYC_t and TA_t, will constitute, respectively, the translational and the rotational components of the RA, PA_t, of relative position relations on d-lines: the PA_t atoms will consist of those pairs <t,r> of a TA_t atom and a CYC_t atom that are compatible. We present in detail the RA PA_t, with its converse table, its rotation table and its composition tables. We show that a (polynomial) constraint propagation algorithm, known in the literature, is complete for a subset of PA_t relations including almost all of the atomic relations. We will discuss the application scope of the RA, which includes incidence geometry, GIS (Geographic Information Systems), shape representation, localisation in (multi-)robot navigation, and the representation of mo

The notion of a congruence of effective dislocation lines endowed with the nonvanishing local Burgers vector is introduced. Particularly, the class of congruences of principal Volterra-type effective dislocation lines associated with the dislocation densities (tensorial as well as scalar) is distinguished in order to investigate the geometry of continuized defective crystals in terms of these densities. It is shown that effective dislocation lines can be endowed with the dislocation line tension and with a finite self-energy.

We examine variability of absorption line strength of intervening systems along the line of sight to GRB 060206 at $z = 4.05$, by the low-resolution optical spectra obtained by the Subaru telescope from six to ten hours after the burst. Strong variabilities of Fe\emissiontype{II} and Mg\emissiontype{II} lines at $z=1.48$ during $t=$5--8 hours have been reported for this GRB \citep{Hao07}, and this has been used to support the idea of clumpy Mg\emissiontype{II} cloudlets that was originally proposed to explain the anomalously high incidence of Mg\emissiontype{II} absorbers in GRB spectra compared with quasars . However, our spectra with higher signal-to-noise ratio do not show any evidence for variability in $t=$6-10 hours. There is a clear discrepancy between our data and Hao et al. data in the overlapping time interval. Furthermore, the line strengths in our data are in good agreement with those observed at $t \sim$ 2 hours by \citet{Tho08}. We also detected Fe\emissiontype{II} and Mg\emissiontype{II} absorption lines for a system at $z = 2.26$, and these lines do not show evidence for variability either. Therefore we conclude that there is no strong evidence for variability of in

A global view is given of how emission lines have been, and may in the future, be used to enhance our understanding of AGN. Lines from the microwave to the X-ray bands all contribute. Although we have a deep understanding of the physical processes by which line photons are generated, when the circumstances of line emission are complicated, models become too unreliable to provide strong inferences about the rest of the AGN system. At present, the lines which appear the most promising for helping answer the most important questions about AGN are the 22~GHz H_2 O rotational transition and the 6.4 keV Fe Kalpha fluorescence.

We consider line defects with large quantum numbers in conformal field theories. First, we consider spin impurities, both for a free scalar triplet and in the Wilson-Fisher $O(3)$ model. For the free scalar triplet, we find a rich phase diagram that includes a perturbative fixed point, a new nonperturbative fixed point, and runaway regimes. To obtain these results, we develop a new semiclassical approach. For the Wilson-Fisher model, we propose an alternative description, which becomes weakly coupled in the large spin limit. This allows us to chart the phase diagram and obtain numerous rigorous predictions for large spin impurities in $2+1$ dimensional magnets. Finally, we also study $1/2$-BPS Wilson lines in large representations of the gauge group in rank-1 $\mathcal{N}=2$ superconformal field theories. We contrast the results with the qualitative behavior of large spin impurities in magnets.