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We introduce an impartial combinatorial game on Steiner triple systems called Nofil. Players move alternately, choosing points of the triple system. If a player is forced to fill a block on their turn, they lose. We explore the play of Nofil on all Steiner triple systems up to order 15 and a sampling for orders 19, 21, and 25. We determine the optimal strategies by computing the nim-values for each game and its subgames. The game Nofil can be thought of in terms of play on a corresponding hypergraph. As game play progresses, the hypergraph shrinks and will eventually be equivalent to playing the game Node Kayles on an isomorphic graph. Node Kayles is well studied and understood. Motivated by this, we study which Node Kayles positions can be reached, i.e. embedded into a Steiner triple system. We prove necessary conditions and sufficient conditions for the existence of such graph embeddings and conclude that the complexity of determining the outcome of the game Nofil on Steiner triple systems is PSPACE-complete.

In this paper, we consider an analog of the well-studied extremal problem for triangle-free subgraphs of graphs for uniform hypergraphs. A loose triangle is a hypergraph $T$ consisting of three edges $e,f$ and $g$ such that $|e \cap f| = |f \cap g| = |g \cap e| = 1$ and $e \cap f \cap g = \emptyset$. We prove that if $H$ is an $n$-vertex $r$-uniform hypergraph with maximum degree $\triangle$, then as $\triangle \rightarrow \infty$, the number of edges in a densest $T$-free subhypergraph of $H$ is at least \[ \frac{e(H)}{\triangle^{\frac{r-2}{r-1} + o(1)}}.\] For $r = 3$, this is tight up to the $o(1)$ term in the exponent. We also show that if $H$ is a random $n$-vertex triple system with edge-probability $p$ such that $pn^3\rightarrow\infty$ as $n\rightarrow\infty$, then with high probability as $n \rightarrow \infty$, the number of edges in a densest $T$-free subhypergraph is \[ \min\Bigl\{(1-o(1))p{n\choose3},p^{\frac{1}{3}}n^{2-o(1)}\Bigr\}.\] We use the method of containers together with probabilistic methods and a connection to the extremal problem for arithmetic progressions of length three due to Ruzsa and Szemer\'{e}di., Comment: Small typos were corrected

GK Cep is an eclipsing binary that contains two A-type components with an orbital period of 0.936 d. The high mass ratio and the contact or near-contact configuration make it a key target to understand binary evolution. However, the physical properties and evolutionary state are still unknown. Here we present the UV light curve obtained by using the lunar-based ultraviolet telescope (LUT) and several eclipse times obtained with the Sino-Thai 70-cm telescope and the 1.0-m telescope at Yunnan Observatories. Analysis of the LUT light curve suggests that GK Cep is a near-contact semidetached system where the slightly less massive component is the hotter one that is filling the critical Roche lobe. Meanwhile, a hotspot is found on the neck of the more massive but cooler component. By using all available times for the light minimum, it is detected that the O–C curve shows a cyclic oscillation while it undergoes an upward parabolic change. The increase of the orbital period, the high mass ratio, the semidetached configuration with a lobe-filling less massive component, and the presence of a hotspot on the more massive component all suggest that GK Cep is in a key evolutionary state just after the shortest-period evolutionary stage during the rapid mass transfer. The cyclic change in the O–C curve reveals that GK Cep contains a solar-type stellar companion in a triply hierarchical system that is in agreement with the spectroscopic result. The third body contributes about 2.6 per cent to the total light of the triple system.

With the discovery of more and more retrograde minor bodies, retrograde orbits’ production mechanism has attracted much attention. However, almost all of the current research on the flip mechanism is based on the hierarchical approximation. In this paper, we study the flip mechanism of Jupiter-crossing orbits in a non-hierarchical Sun–Jupiter triple system. Numerical experiments summarize the characteristics of flipping orbits, and this provides essential guidance for the semi-analytical method. The i − Ω portraits of flipping particles are obtained and verified by numerical integrations. Based on the previous numerical experiments, 200 000 test particles in a particular range are generated and integrated over 1 Myr. The flip region on the entire a − e parameter space is obtained. For each grid of the flip area, we plot the i − Ω portrait and measure the corresponding Jupiter’s flip ability. The gaps around the mean motion resonances (MMRs) in the flip region are also investigated. The MMRs protect the particles in these gaps from flips. Different resonant widths cause the differences in the size of these gaps. The flip mechanism is systematically studied in a planet-crossing system. The complete map of Jupiter’s flip ability in the entire flip region is depicted. Given the orbital parameters of the particle, we can assess whether the flip will occur in Jupiter’s presence. Our work can also apply to build the flip maps of other massive planets. And it may help understand the evolution of retrograde minor bodies.

Let $n$ and $\ell$ be positive integers. Recent papers by Kreher, Stinson and Veitch have explored variants of the problem of ordering the points in a triple system (such as a Steiner triple system, directed triple system or Mendelsohn triple system) on $n$ points so that no block occurs in a segment of $\ell$ consecutive entries (thus the ordering is locally block-avoiding). We describe a greedy algorithm which shows that such an ordering exists, provided that $n$ is sufficiently large when compared to $\ell$. This algorithm leads to improved bounds on the number of points in cases where this was known, but also extends the results to a significantly more general setting (which includes, for example, orderings that avoid the blocks of a design). Similar results for a cyclic variant of this situation are also established. We construct Steiner triple systems and quadruple systems where $\ell$ can be large, showing that a bound of Stinson and Veitch is reasonable. Moreover, we generalise the Stinson--Veitch bound to a wider class of block designs and to the cyclic case. The results of Kreher, Stinson and Veitch were originally inspired by results of Alspach, Kreher and Pastine, who (motivated by zero-sum avoiding sequences in abelian groups) were interested in orderings of points in a partial Steiner triple system where no segment is a union of disjoint blocks. Alspach~\emph{et al.}\ show that, when the system contains at most $k$ pairwise disjoint blocks, an ordering exists when the number of points is more than $15k-5$. By making use of a greedy approach, the paper improves this bound to $9k+O(k^{2/3})$.

This article attempts to understand if we can speak of a transition from Feminist Marxism to Feminist Materialism and Social Reproduction Theory, using a critical apparatus consisting of theorists such as Silvia Federici, Heidi Hartmann, as well as SRT feminists like Cinzia Arruzza, Tithi Bhattacharaya, Nancy Fraser, and Susan Ferguson. Starting from the proponents of the “Wages for Housework” campaign, I will make a short incursion into dual and triple system theory, to the unitary theory of Social Reproduction.

We report the discovery of a compact triply eclipsing triple star system in the southern continuous viewing zone of the TESS space telescope. TIC 278825952 is a previously known, but unstudied circular eclipsing binary with a period of 4.781 d with a tertiary component in a wider, circular orbit of 235.55-d period that was found from three sets of third-body eclipses and from light travel-time effect dominated eclipse timing variations. We performed a joint photodynamical analysis of the eclipse timing variation curves, photometric data, and the spectral energy distribution, coupled with the use of PARSEC stellar isochrones. We find that the inner binary consists of slightly evolved, near twin stars of masses of 1.12 and 1.09 M⊙ and radii of 1.40 and 1.31 R⊙. The third, less massive star has a mass of 0.75 M⊙ and radius of 0.70 R⊙. The low mutual inclination and eccentricities of the orbits show that the system is highly coplanar and surprisingly circular.

Интерес к изучению систем, содержащих сульфиды формулой АIВIIIСVI2, обусловлен, прежде всего, открывающимися возможностями их практического использования в изготовлении нелинейных оптических приборов, детекторов, солнечных батарей, фотодиодов, люминофоров и др. Поэтому в связи с поиском новых перспективных материаловна основе тиогаллата серебра и железа целью этой работы является исследование квазибинарного разреза FeGa2S4–AgGaS2 четырехкомпонентной системы Fe–Ag–Ga–S.Синтез сплавов системы AgGaS2–FeGa2S4 проводили из лигатур с использованием высокой чистоты: железа – 99.995 %, галлия – 99.999 %, серебра – 99.99 % и серы – 99.99 %. Исследование сплавов проводили методами дифференциально-термического, рентгенофазового, микроструктурного анализов, а также измерением микротвердости и определениемплотности.Методами физико-химического анализа впервые изучена и построена Т-x фазовая диаграмма разреза AgGaS2–FeGa2S4, который является внутренним сечением квазитройной системы FeS–Ga2S3–Ag2S. Установлено, что система относится к простому эвтектическому типу. Состав эвтектической точки: 56 мол. % FeGa2S4 и Т = 1100 К. На основе исходных компонентов были определены области твердых растворов. Растворимость на основе FeGa2S4 и AgGaS2 при эвтектической температуре достигает до 10 и 16 мол. % соответственно. С уменьшением температуры твердые растворы сужаются и при комнатной температуре составляют на основе тиогаллата железа (FeGa2S4) 4 мол. % AgGaS2,а на основе тиогаллата серебра (AgGaS2) 11 мол. % FeGa2S4. ЛИТЕРАТУРА 1. Zhаo B., Zhu S., Li Z., Yu F., Zhu X., Gao D. Growth of AgGaS2 single crystal by descending cruciblewith rotation method and observation of properties. Chinese Sci. Bull. 2001; 46(23): 2009–2013. DOI:https://doi.org/10.1007/BF029019182. Горюнова Н. А. Сложные алмазоподобные полупроводники. М.: Сов. радио; 1968. 215 с.3. Абрикосов Н. Х., Шелимова Л. Е. Полупроводниковые материалы на основе соединений АIVBVI..М.:Наука; 1975. 195 с.4. Kushwaha A. 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Wide- and small-angle X-ray scattering is used to study the structure of the single-phase glass of the Bi2O3–GeO2 system and three-component Bi2O3–GeO2–SiO2 system in three sections with the GeO2/SiO2 molar ratios of 3, 1, and 1/3. The Bi2O3 content is changed from 20 to 50 mol % in the first two sections; and from 10 to 50 mol %, in the third one. Based on the data of wide-angle X-ray scattering, it can be concluded that structural groupings containing BiO3 triangles and SiO2 and GeO4 tetrahedra connected with them are formed in the glass of the studied triple system due to the chemical reactions of Bi2O3, SiO2, and GeO2. When the Bi2O3 content is increased the structural groupings are combined and local areas with three-dimensional structure are formed. As a result, each BiO3 triangle is connected with three tetrahedra, and each tetrahedron is connected with four triangles. It is established that the initial stages of the appearance of crystalline phases during the cooling of the melts are observed in the glass containing not less than 40 mol % of Bi2O3.

In this paper, we present the analysis of the stellar system HIP 101227 to determine the actual number of components in the system, and their properties. We use dynamical modeling and complex spectrophotometric (involving atmospheric modeling) techniques with recent data, to determine the physical properties and orbital solution for the system, respectively, with better accuracy than past studies. Based on our analysis, we found that the system is more consistent with being a quadruple rather than a binary, or a triple system as that suggested by previous studies. The total mass of the system determined from our SED analysis is 3.42 $\pm$ 0.20 $M_{\odot}$, which are distributed almost equally between the four stars. The stars are found to be zero-age main sequence stars; i.e., at the last stage of pre-main sequence,with age less than 200 Myr and spectral types K0. All four stars have very similar physical characteristics, suggesting that fragmentation process is the most likely theory for the formation and evolution of the system., 9 pages, 8 figures and 9 tables

A recent paper by Rivinius et al. proposed that HR 6819 is a triple system, with a distant Be star and a binary of 40-day orbit, composed of a B3 III giant and a dormant black hole (BH). We suggest that the evidence for this model is not conclusive. In an alternative model, the companion of the giant is by itself a short-period binary in, say, a $\sim$$4$-day orbit, consisting, for example, of two A0 stars. Each of the two A0 stars should contribute $\sim$$4\%$ of the total brightness of the system in the $V$ band, and their spectral lines are moving due to their assumed orbital motion with an unknown period. Therefore, only a careful analysis of the observed spectra can exclude such a model. Before such an analysis is presented and upper limits for the depths of the hypothetical A0 star absorption lines are derived, the model of a hidden close pair is more probable than the BH model., Accepted for publication by MNRAS Letters. 6 pages and 1 figure

The precise determination of the physical and dynamical parameters of the HIP 109951 triple star system (WDS J22161-0705AB) which is formed by the A, Ba, and Bb components are presented. The binary nature of component B was recently confirmed by studying the radial velocities. The analysis of the system follows Al-Wardat's complex method for analyzing CVBS which employs Kurucz (Atlas9) line blanketed plane-parallel atmospheres simultaneously with an analytic method for dynamical analysis (we used Docobo's method) to calculate the parameters of this triple system. The result of our study yielded the following parameters: $T^{A}_{\rm eff}=5836\pm 80$ K, $R^{A}=1.090\pm0.039R_\odot$, $\log$g$^{A}=4.45\pm0.06$, $\mathcal{M}^{A}=1.05\pm0.16\mathcal{M}_\odot$; $T^{Ba}_{\rm eff}=5115\pm 80$ K, $R^{Ba}=0.596\pm0.05R_\odot$, $\log$ g$^{Ba}=4.60\pm0.07$, $\mathcal{M}^{Ba}=0.83\pm0.16\mathcal{M}_\odot$, $T^{Bb}_{\rm eff}=4500\pm 80$ K, $R^{Bb}=0.490\pm0.06R_\odot$, $\log$ g$^{Bb}=4.65\pm0.07$, and $\mathcal{M}^{Bb}=0.67\pm0.16\mathcal{M}_\odot$ based on the revised \textit{Hipparcos} parallax. The orbital solution gave a total mass as $\mathcal{M}=2.59\mathcal{M}_\odot$ based on Gaia parallax and $\mathcal{M}=2.15\mathcal{M}_\odot$ based on the revised \textit{Hipparcos} parallax. The synthetic spectral energy distributions (SED) and synthetic stellar photometry of the entire system and individual components are given and compared with the available observational ones. Finally, the positions of the system components on the HR diagram and the evolutionary tracks are given and their formation and the evolution of the system are discussed., 13, 4, 10

We define the $m$th Veronese power of a weight graded operad $\mathcal{P}$ to be its suboperad $\mathcal{P}^{[m]}$ generated by operations of weight $m$. It turns out that, unlike Veronese powers of associative algebras, homological properties of operads are, in general, not improved by this construction. However, under some technical conditions, Veronese powers of quadratic Koszul operads are meaningful in the context of the Koszul duality theory. Indeed, we show that in many important cases the operads $\mathcal{P}^{[m]}$ are related by Koszul duality to operads describing strongly homotopy algebras with only one nontrivial operation. Our theory has immediate applications to objects as Lie $k$-algebras and Lie triple systems. In the case of Lie $k$-algebras, we also discuss a similarly looking ungraded construction which is frequently used in the literature. We establish that the corresponding operad does not possess good homotopy properties, and that it leads to a very simple example of a non-Koszul quadratic operad for which the Ginzburg--Kapranov power series test is inconclusive., Comment: 21 pages, comments are welcome

A numerical thermodynamic model is proposed for one of the most important geological fluid system – triple system H 2 O-CO 2 -CaCl 2 at P-T conditions of the middle and lower crust, as well as for the crust-mantle boundary. The model is based on the equation for concentration dependence of the excess Gibbs free energy, proposed earlier, and for the first time obtained P-T dependencies of the coefficients of the equation of state (EOS) expressed via molar volumes of the components. The EOS allows predictions of the properties of the fluid, participating in the majority of the processes of depth petrogenesis: its phase state (homogeneous or multi-phase), densities of the fluid phases, concentrations of the components in the co-existing phases, and chemical activities of the components. The model precisely reproduces all available experimental data on the phase state of the ternary fluid system H 2 O-CO 2 -CaCl 2 in the ranges of temperature 773.15–1073.15 K and pressures 0.1-0.9 GPa and allows, as well, correct application of the EOS beyond the experimentally studied domain of temperatures and pressures – namely up to P = 2 GPa and up to T = 1673.15 K. The possibility of the correct extrapolation of our EOS is ensured by using the parametrization of P-T dependencies via the molar volume of water. The latter remains in the experimental domain of values or very near to its boundaries, when increasing temperatures and pressures.

We study General Freudenthal Transformations (GFT) on black hole solutions in Einstein-Maxwell-Scalar (super)gravity theories with global symmetry of type $E_7$. GFT can be considered as a 2-parameter, $a, b\in {\mathbb R}$, generalisation of Freudenthal duality: $x\mapsto x_F= a x+b\tilde{x}$, where $x$ is the vector of the electromagnetic charges, an element of a Freudenthal triple system (FTS), carried by a large black hole and $ \tilde{x}$ is its Freudenthal dual. These transformations leave the Bekenstein-Hawking entropy invariant up to a scalar factor given by $a^2\pm b^2$. For any $x$ there exists a one parameter subset of GFT that leave the entropy invariant, $a^2\pm b^2=1$, defining the subgroup of Freudenthal rotations. The Freudenthal plane defined by span$_\mathbb{R}\{x, \tilde{x}\}$ is closed under GFT and is foliated by the orbits of the Freudenthal rotations. Having introduced the basic definitions and presented their properties in detail, we consider the relation of GFT to the global sysmmetries or U-dualites in the context of supergravity. We consider explicit examples in pure supergravity, axion-dilaton theories and $N=2,D=4$ supergravities obtained from $D=5$ by dimensional reductions associated to (non-degenerate) $ reduced$ FTS's descending from cubic Jordan Algebras., 65 pages

In this work we we prove that all involutive Hom-Lie triple systems are whether simple or semi-simple. Moreover, we prove that an involutive simple Lie triple system give a rise of Involutive Hom-Lie triple system.

Let q : V → K be the form of degree 4 and H the alternating bilinear form that together give rise to a Freudenthal triple system when the characteristic of K is different from 2 and 3. We give a form Θ of degree 4 on a central cover of V over an arbitrary field in arbitrary characteristic and determine the group of similitudes of Θ. This group coincides with the intersection of the group of similitudes of q and the isometry group of H when the characteristic is different from 2 and 3 and has the expected structure of a suitable Levi subgroup in general. We extend known results about the stabilizers of elements of V and orbits of the group of similitudes and show, in particular, the existence of an exotic set of orbits when char ( K ) = 2 and K is not perfect.

A Berge-K_4 in a triple system is a configuration with four vertices $v_1,v_2,v_3,v_4$ and six distinct triples $\{e_{ij}: 1\le i< j \le 4\}$ such that $\{v_i,v_j\}\subset e_{ij}$ for every $1\le i...

The equivalence Principles of general relativity are an open question of physics – the relationship between the gravitational mass (mg) and the inertial mass (mi) of an object is unknown. Solving this problem is essential for testing variants of alternative theories of gravity, predicting the failure of the relationship mg = mi. Experimental tests of the relationship mg = mi, are based on the Universal Free Fall (UFF) approach: “a comparison of accelerations of two masses, having a variety of material compositions, falling into an external gravitational field”. The UFF approach can only confirm the relationship mg ≠ mi, but not the relationship mg = mi because of experimental errors. We confirm the relationship mg = mi using a new approach: “a study of a single mass at rest relative to a massive object”. We also show that conservation of energy is a sufficient condition for mg = mi. We conclude that alternative theories of gravity must be constrained by the relationship mg = mi.

Time series of spectroscopic, speckle-interferometric, and optical long-baseline-interferometric observations confirm that $\nu$ Gem is a hierarchical triple system. It consists of an inner binary composed of two B-type stars and an outer classical Be star. Several photospheric spectral lines of the inner components were disentangled, revealing two stars with very different rotational broadening ($\sim$260 and $\sim$140 kms$^{-1}$, respectively), while the photospheric lines of the Be star remain undetected. From the combined spectroscopic and astrometric orbital solution it is not possible to unambiguously cross-identify the inner astrometric components with the spectroscopic components. In the preferred solution based on modeling of the disentangled line profiles, the inner binary is composed of two stars with nearly identical masses of 3.3 M$_\odot$ and the more rapidly rotating star is the fainter one. These two stars are in a marginally elliptical orbit ($e$ = 0.06) about each other with a period of 53.8 d. The third star also has a mass of 3.3 M$_\odot$ and follows a more eccentric ($e$ = 0.24) orbit with a period of 19.1 yr. The two orbits are co-directional and, at inclinations of 79$^{\circ}$ and 76$^{\circ}$ of the inner and the outer orbit, respectively, about coplanar. No astrometric or spectroscopic evidence could be found that the Be star itself is double. The system appears dynamically stable and not subject to eccentric Lidov-Kozai oscillations. After disentangling, the spectra of the components of the inner binary do not exhibit peculiarities that would be indicative of past interactions. Motivations for a wide range of follow-up studies are suggested., Comment: accepted to ApJ

We study gravitational wave (GW) emission in the strong-field regime by a hierarchical triple system composed of a binary system placed in the vicinity of a supermassive black hole (SMBH). The LIGO-Virgo collaboration recently reported evidence for coalescences with this dynamical origin. These systems are common in galactic centers and thus are a target for the space-based LISA mission as well as other advanced detectors. Doppler shifts, aberration, lensing and strong amplitude modulations are features present in the GW signal from these systems, built into our framework and with no need for phenomenological patches. We find that the binary can resonantly excite the quasinormal modes of the SMBH, as in the resonant excitation of two tuning forks with matching frequencies. The flux of energy crossing the SMBH horizon can be significant, when compared with that from standard extreme-mass-ratio inspirals. Therefore, these triple systems are an outstanding probe of strong-field physics and of the BH nature of compact objects., Comment: 6 pages, 4 figures, v2: version to appear in Physical Review D Letters

In combinatorial design theory, clustering elements into a set of three elements is the heart of classifying data, which has recently received considerable attention in the fields of network algorithms, cryptography, design and analysis of algorithms, statistics, and Information theory. This article provides insight into formulating algorithm for a new type of triple system, called a Butterfly triple system. Basically, in this algorithm development, a starter of cyclic near-resolvable ((v-1)/2)-cycle system of the 2-fold complete graph 2Kvis employed to construct the starter of cyclic ((v-1)/2)-star decomposition of 2Kv. These starters are then decomposed into triples and classified as a starter of cyclic Butterfly triple. The obtained starter set generates a triple system of order v. A special reference for case ν ≡ 9 (mod 12) is presented to demonstrate the development of the Butterfly triple system.

We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the Brutus N-body code to include Post-Newtonian pairwise terms up to 2.5 order, and the first order Taylor expansion to the Einstein-Infeld-Hoffmann equations of motion. The degree to which our system is relativistic depends on the scaling of the total mass (the unit size was 1 parsec). Using the Brutus method of convergence, we test for time-reversibility in the conservative regime, and demonstrate that we are able to obtain definitive solutions to the relativistic three-body problem. It is also confirmed that the minimal required numerical accuracy for a successful time-reversibility test correlates with the amplification factor of an initial perturbation. When we take into account dissipative effects through gravitational wave emission, we find that the duration of the resonance, and the amount of exponential growth of small perturbations depend on the mass scaling. For a unit mass = 1e9 MSun, all systems result in a gravitational wave merger upon the first close encounter. Relativistic three-body encounters thus provide an efficient pathway for resolving the final parsec problem. The onset of mergers at the characteristic mass scale of 1e7 MSun potentially leaves an imprint in the mass function of supermassive black holes., Accepted by Phys Rev D. 10 pages, 6 figures

The 2-block intersection graph (2-BIG) of a twofold triple system (TTS) is the graph whose vertex set is composed of the blocks of the TTS and two vertices are joined by an edge if the corresponding blocks intersect in exactly two elements. The 2-BIGs are themselves interesting graphs: each component is cubic and 3-connected, and a 2-BIG is bipartite exactly when the TTS is decomposable to two Steiner triple systems. Any connected bipartite 2-BIG with no Hamilton cycle is a counter-example to a conjecture posed by Tutte in 1971. Our main result is that there exists an integer $N$ such that for all $v\geq N$, if $v\equiv 1$ or $3\mod{6}$ then there exists a TTS($v$) whose 2-BIG is bipartite and connected but not Hamiltonian. Furthermore, $132u$ in such a way that, after a single trade, the 2-BIG of the resulting TTS($v$) is bipartite connected and non-Hamiltonian., Comment: 16 pages, 3 figures

HR 6819 was recently claimed to be a hierarchical triple system of a Be star in a wide orbit around an inner binary system of a black hole (BH) and a B III type star. We argue that this system is unlikely to be a hierarchical triple due to three reasons: (i) Given that this system is discovered in a magnitude limited Bright Star Catalog, the expected number of such systems in the Milky Way amounts to about $10^4$ while the estimate for the MW budget for such systems is between $10^2-10^3$ systems under generous assumptions. Such a large gap cannot be reconciled as it would otherwise likely overflow the MW budget for BHs; (ii) The dynamical stability of this system sets lower bounds on the orbital separation of the outer Be star, while it not being resolved by Gaia places an upper limit on its projected sky separation. We show that these two constraints would imply a narrow range for the outer orbit without resorting to geometrical fine-tuning; (iii) The triple system should have survived the stellar evolution prior to the formation of the BH in the inner binary. We perform numerical simulations starting with conservative initial conditions of this system and show that a small parameter space for BH progenitor star's mass loss, BH natal kicks, and initial orbital separation can reproduce HR 6819. Therefore, we propose this system is a chance superposition of a Be star with a binary., Matches the published version at ApJ Letters

BD And is a fairly bright (V = 10.8), active and close (P = 0.9258 days) eclipsing binary. The cyclic variability of the apparent orbital period as well as third light in the light curves indicate the presence of an additional late-type component. The principal aim is the spectroscopic testing of the third-body hypothesis and determination of absolute stellar parameters for both components of the eclipsing binary. First medium and high-resolution spectroscopy of the system was obtained. The broadening-function technique appropriate for heavily-broadened spectra of close binaries was used. The radial velocities were determined fitting the Gaussian functions and rotational profiles to the broadening functions. A limited amount of photometric data has also been obtained. Although the photometric observations were focused on the obtaining the timing information, a cursory light-curve analysis was also performed. Extracted broadening functions clearly show the presence of a third, slowly-rotating component. Its radial velocity is within error of the systemic velocity of the eclipsing pair, strongly supporting the physical bond. The observed systemic radial-velocity and third-component changes do not support the 9 year orbit found from the timing variability. Masses of the components of the eclipsing pair are determined with about 0.5% precision. Further characterization of the system would require long-term photometric and spectroscopic monitoring., 23 pages, 6 figures, online data table

GW Ori is a hierarchical triple system which has a rare circumtriple disk. We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of 1.3 mm dust continuum and 12CO J=2-1 molecular gas emission of the disk. For the first time, we identify three dust rings in the disk at ~46, 188, and 338 AU, with estimated dust mass of ~70-250 Earth masses, respectively. To our knowledge, the outer ring in GW Ori is the largest dust ring ever found in protoplanetary disks. We use visibility modelling of dust continuum to show that the disk has misaligned parts and the innermost dust ring is eccentric. The disk misalignment is also suggested by the CO kinematics modelling. We interpret these substructures as evidence of ongoing dynamical interactions between the triple stars and the circumtriple disk., 17 pages, 3+3 figures, 2 tables; accepted by ApJL on 2020-04-29

The $VRI$ passbands light curves of V344 Lac were presented and analyzed by using the latest version of the W-D code. The observed spectrum reveals that V344 Lac is not an A3 type but would be a later F type star according to the yielded temperature. The results of solution show that V344 Lac is an A-subtype contact binary, with a moderate photometric mass ratio of $0.387\pm 0.003$ and a moderate contact factor of $44.6\pm 3.0\%$. Based on the parallax given by Gaia, the parameters of the components are estimated as: $M_{1}=1.16~\mathrm{M}_{\odot }$, $M_{2}=0.45~\mathrm{M}_{\odot }$, $R_{1}=1.31~\mathrm{R}_{\odot }$, $R_{2}=0.88~\mathrm{R}_{\odot }$, $L_{1}=2.512~\mathrm{L}_{\odot }$, $L_{2}=1.057~\mathrm{L}_{\odot }$. The period investigation indicates that V344 Lac may have an eccentric orbital oscillation, with $P_{3}=12.4\pm 0.5~\text{yr}$, $A_{3}=0.0020\pm 0.0002~\text{d}$, and $e=0.38\pm 0.16$. Analysis shows such oscillation would be caused by a magnetic activity which can be explained by the Applegate mechanism. Meanwhile, according to the value of $l_{3}$ and the estimated physical parameters of V344 Lac, the mass of the third companion may be $0.79~\mathrm{M}_{\odot }$. This third body could be a wide company.

Se dectriben las detecciones en: HgMn Primary in the Triple System χ Lup realizadas con instrumentos del CASLEO. Fil: Järvinen, Silva. Leibniz Institute For Astrophysics Potsdam; Alemania Fil: Chojnowski, Drew. New Mexico State University.; Estados Unidos Fil: Gonzalez, Jorge Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Instituto de Ciencias Astronómicas, de la Tierra y del Espacio. Universidad Nacional de San Juan. Instituto de Ciencias Astronómicas, de la Tierra y del Espacio; Argentina Fil: Hubrig, Swetlana. Leibniz Institute For Astrophysics Potsdam; Alemania Fil: Schöller, Marcus. European Southern Observatory; Alemania Fil: Ilyin, llya. Leibniz Institute For Astrophysics Potsdam; Alemania Fil: Hummel, Christian. European Southern Observatory; Alemania Fil: Korhonen, Heidi. Universidad de Copenhagen; Dinamarca Fil: Scholz, Ralf. Leibniz Institute For Astrophysics Potsdam; Alemania

We present new findings about KIC 8043961. We find the effective temperatures of the components as 6900 +/- 200 K for the primary, and 6598 +/- 200 K for the secondary, while the logarithm of the surface gravities are found to be 4.06 cm s(-2) and 3.77 cm s(-2), respectively. Combination of the light curve with the spectroscopic orbit model results leads to a mass ratio of 1:09 +/- 0:07 with an orbital inclination of 73:71 +/- 0:14 and a semi-major axis of 8:05 +/- 0:22 R-circle dot. Masses of the primary and secondary components are calculated as 1:379 +/- 0:109 M-circle dot and 1:513 +/- 0:181 M-circle dot, while the radii are found to be 1:806 +/- 0:084 R-circle dot and 2:611 +/- 0:059 R-circle dot. In addition, we obtain a considerable light contribution (approximate to 0.54%) of a third body. We compute a possible mass for the third body as 0:778 +/- 0:002 M-circle dot. We find that the primary component exhibits gamma Dor type pulsations with 137 frequencies., Turkish Scientific and Technical Research Council (TUBITAK) [116F349, 14BRTT150-667], We thank the referee for useful comments that have contributed to the improvement of the paper. We also wish to thank the Turkish Scientific and Technical Research Council (TUBITAK) for supporting this work through Grant No. 116F349 and for partial support in using the RTT-150 (RussianTurkish 1.5-m telescope in Antalya) with Project Number 14BRTT150-667.

In this article, we introduce equivariant formal deformation theory of Lie triple systems. We introduce an equivariant deformation cohomology of Lie triple systems and using this we study the equivariant formal deformation theory of Lie triple systems., Comment: arXiv admin note: text overlap with arXiv:1905.03607

We present results from adaptive optics imaging of the T Tauri triple system obtained at the Keck and Gemini Observatories in 2015-2019. We fit the orbital motion of T Tau Sb relative to Sa and model the astrometric motion of their center of mass relative to T Tau N. Using the distance measured by Gaia, we derived dynamical masses of M_Sa = 2.05 +/- 0.14 Msun and M_Sb = 0.43 +/- 0.06 Msun. The precision in the masses is expected to improve with continued observations that map the motion through a complete orbital period; this is particularly important as the system approaches periastron passage in 2023. Based on published properties and recent evolutionary tracks, we estimate a mass of ~ 2 Msun for T Tau N, suggesting that T Tau N is similar in mass to T Tau Sa. Narrow-band infrared photometry shows that T Tau N remained relatively constant between late 2017 and early 2019 with an average value of K = 5.54 +/- 0.07 mag. Using T Tau N to calibrate relative flux measurements since 2015, we found that T Tau Sa varied dramatically between 7.0 to 8.8 mag in the K-band over timescales of a few months, while T Tau Sb faded steadily from 8.5 to 11.1 mag in the K-band. Over the 27 year orbital period of the T Tau S binary, both components have shown 3-4 magnitudes of variability in the K-band, relative to T Tau N., Comment: 13 pages, 8 figures, 5 tables, accepted for publication in AJ

A special four-cycle F in a triple system consists of four triples inducing a C 4 . This means that F has four special vertices v 1 , v 2 , v 3 , v 4 and four triples in the form w i v i v i + 1 (indices are understood ( mod 4 ) ) where the w j s are not necessarily distinct but disjoint from { v 1 , v 2 , v 3 , v 4 } . There are seven non-isomorphic special four-cycles, their family is denoted by F . Our main result implies that the Turan number ex ( n , F ) = Θ ( n 3 / 2 ) . In fact, we prove more, ex ( n , { F 1 , F 2 , F 3 } ) = Θ ( n 3 / 2 ) , where the F i -s are specific members of F . This extends previous bounds for the Turan number of triple systems containing no Berge four cycles. We also study ex ( n , A ) for all A ⊆ F . For 16 choices of A we show that e x ( n , A ) = Θ ( n 3 / 2 ) , for 92 choices of A we find that ex ( n , A ) = Θ ( n 2 ) and the other 18 cases remain unsolved.

The Turan number of hypergraphs has been studied extensively. Here we deal with a recent direction, the linear Turan number, and restrict ourselves to linear triple systems, a collection of triples on a set of points in which any two triples intersect in at most one point. For a fixed linear triple system F , the linear Turan number ex L ( n , F ) is the maximum number of triples in a linear triple system with n points that does not contain F as a subsystem. We initiate the study of the linear Turan number for an acyclic F . In this case ex L ( n , F ) is linear in n and we aim for good bounds. Since the case of trees is already difficult for graphs (Erdős–Sos conjecture), we concentrate on matchings, paths and small trees. In case of matchings, where M k is the set of k pairwise disjoint triples, we prove that for fixed k and large enough n , ex L ( n , M k ) = f ( n , k ) where f ( n , k ) is the maximum number of triples that can meet k − 1 points in a linear triple system on n points. This is an analogue of an old result of Erdős on hypergraph matchings. For the k -edge linear path P k we show (extending some standard path increasing methods used for graphs) that ex L ( n , P k ) ≤ 1 . 5 k n which is probably far from best possible. Finding ex L ( n , F ) relates to difficult problems on Steiner triple systems and interesting even for small trees. For example, for P 4 , the path with four triples, ex L ( n , P 4 ) ≤ 4 n 3 with equality only for disjoint union of affine planes of order 3. On the other hand, for E 4 , the tree having three pairwise disjoint triples and a fourth one meeting all of them, we have bounds only: 6 ⌊ n − 3 4 ⌋ ≤ ex L ( n , E 4 ) ≤ 2 n .

Using Campaign 15 data from the K2 mission, we have discovered a triply-eclipsing triple star system: EPIC 249432662. The inner eclipsing binary system has a period of 8.23 days, with shallow $\sim$3% eclipses. During the entire 80-day campaign, there is also a single eclipse event of a third-body in the system that reaches a depth of nearly 50% and has a total duration of 1.7 days, longer than for any previously known third-body eclipse involving unevolved stars. The binary eclipses exhibit clear eclipse timing variations. A combination of photodynamical modeling of the lightcurve, as well as seven follow-up radial velocity measurements, has led to a prediction of the subsequent eclipses of the third star with a period of 188 days. A campaign of follow-up ground-based photometry was able to capture the subsequent pair of third-body events as well as two further 8-day eclipses. A combined photo-spectro-dynamical analysis then leads to the determination of many of the system parameters. The 8-day binary consists of a pair of M stars, while most of the system light is from a K star around which the pair of M stars orbits., Comment: 20 pages, accepted for publication in MNRAS

Simple finite dimensional Kantor triple systems over the complex numbers are classified in terms of Satake diagrams. We prove that every simple and linearly compact Kantor triple system has finite dimension and give an explicit presentation of all the classical and exceptional systems., Comment: 46 pages, 3 tables; v2: Major revision of the introduction; v3: Final version to appear in Journal of Algebra

The paper reports on an investigation of structure of block-transitive automorphism groups of a triple system. We prove that if G is a block-transitive automorphism group of a triple system T , then G cannot be of simple diagonal or twisted wreath product type. Furthermore, if G is of product type, then Soc ( G ) = A 5 × A 5 and T is the unique T S ( 25 , 12 ) .

The millisecond pulsar PSR J0337+1715 is in a mildly relativistic hierarchical triple system with two white dwarfs. This offers the possibility of testing the universality of free fall: does the neutron star fall with the same acceleration as the inner white dwarf in the gravity of the outer white dwarf? We have carried out an intensive pulsar timing campaign, yielding some 27000 pulse time-of-arrival (TOA) measurements with a median uncertainty of 1.2 μs. Here we describe our analysis procedure and timing model.