This paper refines the relationship between centrally quasi-morphic and centrally morphic modules, correcting earlier equivalences and extending them to a broader module-theoretic framework. We prove that if a module \(M\) is image-projective and generates its kernels, then the following are equivalent: \(M\) is centrally morphic, \(M\) is centrally quasi-morphic, and its endomorphism ring \(S=\operatorname{End}_R(M)\) is right centrally morphic. This characterization clarifies the role of image-projectivity and kernel-generation in transferring morphic behavior between a module and its endomorphism ring. Furthermore, if \(R\) is a semiprime right centrally quasi-morphic ring with a von Neumann regular center \(Z(R)\), then \(R\) is strongly \(π\)-regular. In the module setting, when the endocenter \(Z(S)\) is von Neumann regular and the kernels and images of powers of endomorphisms are fully invariant, an image-projective module \(M\) is strongly \(π\)-endoregular if and only if its endomorphism ring \(S\) is semiprime and \(M\) is centrally quasi-morphic.
Let E be a point in the plane of a convex quadrilateral ABCD. The lines from E to the vertices of the quadrilateral form four triangles. If we locate a triangle center in each of these triangles, the four triangle centers form another quadrilateral called a central quadrilateral. For each of various shaped quadrilaterals, and each of 1000 different triangle centers, and for various choices for E, we examine the shape of the central quadrilateral. Using a computer, we determine when the central quadrilateral has a special shape, such as being a rhombus or a cyclic quadrilateral. A typical result is the following. Let E be the centroid of equidiagonal quadrilateral ABCD. Let F, G, H, and I be the X(591)-points of triangles ABE, BCE, CDE, and DAE, respectively. Then FGHI is an orthodiagonal quadrilateral
Muhammed Adil Yatkin, Mihkel Korgesaar, Jani Romanoff
et al.
Current neural network (NN) models can learn patterns from data points with historical dependence. Specifically, in natural language processing (NLP), sequential learning has transitioned from recurrence-based architectures to transformer-based architectures. However, it is unknown which NN architectures will perform the best on datasets containing deformation history due to mechanical loading. Thus, this study ascertains the appropriateness of 1D-convolutional, recurrent, and transformer-based architectures for predicting deformation localization based on the earlier states in the form of deformation history. Following this investigation, the crucial incompatibility issues between the mathematical computation of the prediction process in the best-performing NN architectures and the actual values derived from the natural physical properties of the deformation paths are examined in detail.
Dislocations in ceramics have enjoyed a long yet underappreciated research history. This brief historical overview and reflection on the current challenges provides new insights into using this line defect as a rediscovered tool for engineering functional ceramics.
The $γ$-ray deposition history in an expanding supernova (SN) ejecta has been mostly used to constrain models for Type Ia SN. Here we expand this methodology to core-collapse SNe, including stripped envelope (SE; Type Ib/Ic/IIb) and Type IIP SNe. We construct bolometric light curves using photometry from the literature and we use the Katz integral to extract the $γ$-ray deposition history. We recover the tight range of $γ$-ray escape times, $t_0\approx30-45\,\textrm{d}$, for Type Ia SNe, and we find a new tight range $t_0\approx80-140\,\textrm{d}$, for SE SNe. Type IIP SNe are clearly separated from other SNe types with $t_0\gtrsim400\,\textrm{d}$, and there is a possible negative correlation between $t_0$ and the synthesized $^{56}$Ni mass. We find that the typical masses of the synthesized $^{56}$Ni in SE SNe are larger than those in Type IIP SNe, in agreement with the results of Kushnir. This disfavours progenitors with the same initial mass range for these explosions. We recover the observed values of $ET$, the time-weighted integrated luminosity from cooling emission, for Type IIP, and we find hints of non-zero $ET$ values in some SE SNe. We apply a simple $ γ$-ray radiation transfer code to calculate the $γ$-ray deposition histories of models from the literature, and we show that the observed histories are a powerful tool for constraining models.
Foliations on the space of $p$-divisible groups were studied by Oort in 2004. In his theory, special leaves called central stream play an important role. In this paper, we give a complete classification of the boundary components of the central streams for an arbitrary Newton polygon in the unpolarized case. Hopefully this classification would help us to know the boundaries of other leaves and more detailed structure of the boundaries of central streams.
This talk sketches the main milestones of the path towards cubic kilometer neutrino telescopes. It starts with the first conceptual ideas in the late 1950s and describes the emergence of concepts for detectors with a realistic discovery potential in the 1970s and 1980s. After the pioneering project DUMAND close to Hawaii was terminated in 1995, the further development was carried by NT200 in Lake Baikal, AMANDA at the South Pole and ANTARES in the Mediterranean Sea. In 2013, more than half a century after the first concepts, IceCube has discovered extraterrestrial high-energy neutrinos and opened a new observational window to the cosmos - marking a milestone along a journey which is far from being finished.
A new parametrization of the reionization history is presented to facilitate robust comparisons between different observations and with theory. The evolution of the ionization fraction with redshift can be effectively captured by specifying the midpoint, duration, and asymmetry parameters. Lagrange interpolating functions are then used to construct analytical curves that exactly fit corresponding ionization points. The shape parametrizations are excellent matches to theoretical results from radiation-hydrodynamic simulations. The comparative differences for reionization observables are: ionization fraction $|Δx_\text{i}| \lesssim 0.03$, 21cm brightness temperature $|ΔT_\text{b}| \lesssim 0.7\, \text{mK}$, Thomson optical depth $|Δτ| \lesssim 0.001$, and patchy kinetic Sunyaev-Zel'dovich angular power $|ΔD_\ell | \lesssim 0.1\, μ\text{K}^2$. This accurate and flexible approach will allow parameter-space studies and self-consistent constraints on the reionization history from 21cm, CMB, and high-redshift galaxies and quasars.
Alessandro Checco, Gianluca Demartini, Alexander Loeser
et al.
A core business in the fashion industry is the understanding and prediction of customer needs and trends. Search engines and social networks are at the same time a fundamental bridge and a costly middleman between the customer's purchase intention and the retailer. To better exploit Europe's distinctive characteristics e.g., multiple languages, fashion and cultural differences, it is pivotal to reduce retailers' dependence to search engines. This goal can be achieved by harnessing various data channels (manufacturers and distribution networks, online shops, large retailers, social media, market observers, call centers, press/magazines etc.) that retailers can leverage in order to gain more insight about potential buyers, and on the industry trends as a whole. This can enable the creation of novel on-line shopping experiences, the detection of influencers, and the prediction of upcoming fashion trends. In this paper, we provide an overview of the main research challenges and an analysis of the most promising technological solutions that we are investigating in the FashionBrain project.
Patricia B. Tissera, Rubens E. G. Machado, Daniela Carollo
et al.
We study the properties of the central spheroids located within 10 kpc of the centre of mass of Milky Way mass-sized galaxies simulated in a cosmological context. The simulated central regions are dominated by stars older than 10 Gyr, mostly formed in situ, with a contribution of ~30 per cent from accreted stars. These stars formed in well-defined starbursts, although accreted stars exhibit sharper and earlier ones. The fraction of accreted stars increases with galactocentric distance, so that at a radius of ~8-10 kpc a fraction of ~40 per cent, on average, are detected. Accreted stars are slightly younger, lower metallicity, and more $α$-enhanced than in situ stars. A significant fraction of old stars in the central regions come from a few ($2-3$) massive satellites ($\sim 10^{10}{\rm M}_\odot$). The bulge components receive larger contributions of accreted stars formed in dwarfs smaller than $\sim 10^{9.5}{\rm M}_\odot$. The difference between the distributions of ages and metallicities of old stars is thus linked to the accretion histories -- those central regions with a larger fraction of accreted stars are those with contributions from more massive satellites. The kinematical properties of in situ and accreted stars are consistent with the latter being supported by their velocity dispersions, while the former exhibit clear signatures of rotational support. Our simulations demonstrate a range of characteristics, with some systems exhibiting a co-existing bar and spheroid in their central regions, resembling in some respect the central region of the Milky Way.
A hypersurface $M$ in $\mathbb{R}^n$, $n \geq 4$, has central ovaloid property if $M$ intersects some hyperplane transversally along an ovaloid and every such ovaloid on $M$ has central symmetry. We show that a complete, connected, smooth hypersurface with central ovaloid property must either be a cylinder over a central ovaloid or else quadric.
We study the growth of the central polynomials for the algebras $G$ and $M_k(F)$, the infinite dimensional Grassmann algebra and the $k\times k$ matrices over a field $F$ of characteristic zero. In particular it follows that $M_k(F)$ satisfy many proper central polynomials.
Central configurations have been of great interest over many years, with the earliest examples due to Euler and Lagrange. There are numerous results in the literature demonstrating the existence of central configurations with specific symmetry properties, using slightly different techniques in each. The aim here is to describe a uniform approach by adapting to the symmetric case the well-known variational argument showing the existence of central configurations. The principal conclusion is that there is a central configuration for every possible symmetry type, and for any symmetric choice of masses. Finally the same argument is applied to the class of balanced configurations introduced by Albouy and Chenciner.
Over the past two decades, an avalanche of data from multiwavelength imaging and spectroscopic surveys has revolutionized our view of galaxy formation and evolution. Here we review the range of complementary techniques and theoretical tools that allow astronomers to map the cosmic history of star formation, heavy element production, and reionization of the Universe from the cosmic "dark ages" to the present epoch. A consistent picture is emerging, whereby the star-formation rate density peaked approximately 3.5 Gyr after the Big Bang, at z~1.9, and declined exponentially at later times, with an e-folding timescale of 3.9 Gyr. Half of the stellar mass observed today was formed before a redshift z = 1.3. About 25% formed before the peak of the cosmic star-formation rate density, and another 25% formed after z = 0.7. Less than ~1% of today's stars formed during the epoch of reionization. Under the assumption of a universal initial mass function, the global stellar mass density inferred at any epoch matches reasonably well the time integral of all the preceding star-formation activity. The comoving rates of star formation and central black hole accretion follow a similar rise and fall, offering evidence for co-evolution of black holes and their host galaxies. The rise of the mean metallicity of the Universe to about 0.001 solar by z = 6, one Gyr after the Big Bang, appears to have been accompanied by the production of fewer than ten hydrogen Lyman-continuum photons per baryon, a rather tight budget for cosmological reionization.
We present a quantitative star formation history of the nearby dwarf galaxy UGCA 92. This irregular dwarf is situated in the vicinity of the Local Group of galaxies in a zone of strong Galactic extinction (IC 342 group of galaxies). The galaxy was resolved into stars with HST/ACS including old red giant branch. We have constructed a model of the resolved stellar populations and measured the star formation rate and metallicity as function of time. The main star formation activity period occurred about 8 - 14 Gyr ago. These stars are mostly metal-poor, with a mean metallicity [Fe/H] ~ -1.5 -- -2.0 dex. About 84 per cent of the total stellar mass was formed during this event. There are also indications of recent star formation starting about 1.5 Gyr ago and continuing to the present. The star formation in this event shows moderate enhancement from ~ 200 Myr to 300 Myr ago. It is very likely that the ongoing star formation period has higher metallicity of about -0.6 -- -0.3 dex. UGCA 92 is often considered to be the companion to the starburst galaxy NGC 1569. Comparing our star formation history of UGCA 92 with that of NGC 1569 reveals no causal or temporal connection between recent star formation events in these two galaxies. We suggest that the starburst phenomenon in NGC 1569 is not related to the galaxy's closest dwarf neighbours and does not affect their star formation history.
The ALICE experiment at the Large Hadron Collider (LHC) at CERN consists of a central barrel, a muon spectrometer and of additional detectors for trigger and event classification purposes. The low transverse momentum threshold of the central barrel gives ALICE a unique opportunity to study the low mass sector of central production at the LHC. I will report on first analysis results of meson production in double gap events in minimum-bias proton-proton collisions at sqrt{s} = 7 TeV, and will describe a dedicated double gap trigger for future data taking.
We gauge the central charge of the N=2 supersymmetry algebra in rigid superspace. The Fayet Sohnius hypermultiplet with gauged central charge coincides on-shell with N=2 supersymmetric electrodynamics. The gauge couplings of the vector-tensor multiplet turn out to be nonpolynomial.