ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study a correspondence between numerical sets and integer partitions that leads to a bijection between simultaneous core partitions and the integer points of a certain polytope. We use this correspondence to prove combinatorial results about core partitions. For small values of a, we give formulas for the number of (a,b)-core partitions corresponding to numerical semigroups. We also study the number of partitions with a given hook set.
Ubiquitous transition region (TR) network jets are considered to be substantial sources of mass and energy to the corona and solar wind. We conduct a case study of a network jet to better understand the nature of mass flows along its length and the energetics involved in its launch. We present an observation of a jet with the Interface Region Imaging Spectrograph (IRIS), while also using data from the Solar Dynamics Observatory (SDO) to provide further context. The jet was located within a coronal hole close to the disk center. We find that a blueshifted secondary component of TR emission is associated with the jet and is persistent along its spire. This component exhibits upward speeds of approximately 20-70 km s$^{-1}$ and shows enhanced line broadening. However, plasma associated with the jet in the upper chromosphere shows downflows of 5-10 km s$^{-1}$. Finally, the jet emanates from a seemingly unipolar magnetic footpoint. While a definitive magnetic driver is not discernible for this event, we infer that the energy driving the network jet is deposited at the top of the chromosphere, indicating that TR network jets are driven from the mid-atmospheric layers of the Sun. The energy flux associated with the line broadening indicates that the jet could be powered all the way into the solar wind.
Here we report small-angle neutron scattering (SANS) measurements and theoretical modeling of U$_3$Al$_2$Ge$_3$. Analysis of the SANS data reveals a phase transition to sinusoidally modulated magnetic order, at $T_{\mathrm{N}}=63$~K to be second order, and a first order phase transition to ferromagnetic order at $T_{\mathrm{c}}=48$~K. Within the sinusoidally modulated magnetic phase ($T_{\mathrm{c}} < T < T_{\mathrm{N}}$), we uncover a dramatic change, by a factor of three, in the ordering wave-vector as a function of temperature. These observations all indicate that U$_3$Al$_2$Ge$_3$ is a close realization of the three-dimensional Axial Next-Nearest-Neighbor Ising model, a prototypical framework for describing commensurate to incommensurate phase transitions in frustrated magnets.
An interacting cigar-shaped Bose-Einstein condensate (BEC) inside a driven optical cavity exhibits an intrinsic cross-Kerr (CK) nonlinearity due to the interaction with the optical mode of the cavity. Although the CK coupling is much weaker than those of the radiation pressure and the atom-atom interactions, it can affect the bistability behavior of the system when the intensity of the laser pump is strong enough. On the other hand, there is a competition between the CK nonlinearity and the atom-atom interaction so that the latter can neutralize the effect of the former. Furthermore, the CK nonlinearity causes the effective frequency of the Bogoliubov mode of the BEC as well as the quantum fluctuations of the system to be increased by increasing the cavity driving rate. However, in the dispersive interaction regime the effect of the CK nonlinearity is negligible. In addition, we show that by increasing the \textit{s}-wave scattering frequency of atomic collisions one can generate a strong stationary quadrature squeezing in the Bogoliubov mode of the BEC.
A three-level system with partially broken SU(3) symmetry immersed in a metal, comprised of a unique non-interacting ground state and two-fold degenerate excited states, exhibits a stable two-channel Kondo fixed point within a wide range of parameters, as has been shown in previous work. Such systems can, for instance, be realized by protons dissolved in a metal and bound in the interstitial space of the host lattice, where the degeneracy of excited rotational states is guaranteed by the space inversion symmetry of the lattice. We analyze the robustness of the 2CK fixed point with respect to a level splitting of the excited states and discuss how this may explain the behavior of the well-known dI/dV spectra measured by Ralph and Buhrman on ultrasmall quantum point contacts in a magnetic field.
Several shielding applications, to protect human health and electronic devices against dangerous effects of electromagnetic radiation, require solutions that fabrics can suitably fulfill. Here, we will investigate the electromagnetic interference shielding effectiveness of polypyrrole-coated polyester textiles, in the frequency range 100-1000 MHz. Insertion losses for several conductive fabrics with different surface resistivity ranging from 40 Ohm till the very low value of 3 Ohm were evaluated with a dual-tem cell. Correlations between the shielding effectiveness and the conductivity of composites are also discussed.
Let $K$ be the function field of a smooth curve over an algebraically closed field $k$. Let $X$ be a scheme, which is smooth and projective over $K$. Suppose that the cotangent bundle $\Omega_{X/K}$ is ample. Let $R:={\rm Zar}(X)(K)\cap X)$ be the Zariski closure of the set of all $K$-rational points of $X$, endowed with its reduced induced structure. We prove that there is a projective variety $X_0$ over $k$ and a finite and surjective $K^{\rm sep}$-morphism $X_{0,K^{\rm sep}}\to R_{K^{\rm sep}}$, which is birational when ${\rm char}(K)=0$.
We generalize Merel's work on universal Fourier expansions to Bianchi modular forms over Euclidean imaginary quadratic fields, under the assumption of the nondegeneracy of a pairing between Bianchi modular forms and Bianchi modular symbols. Among the key inputs is a computation of the action of Hecke operators on Manin symbols, and building upon the Heilbronn-Merel matrices constructed by Mohamed.
We study various boundary and inner regularity questions for $p(\cdot)$-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for $p(\cdot)$-harmonic functions into three disjoint classes: regular, semiregular and strongly irregular points. Regular and especially semiregular points are characterized in many ways. The discussion is illustrated by examples. Along the way, we present a removability result for bounded $p(\cdot)$-harmonic functions and give some new characterizations of $W^{1, p(\cdot)}_0$ spaces. We also show that $p(\cdot)$-superharmonic functions are lower semicontinuously regularized, and characterize them in terms of lower semicontinuously regularized supersolutions.
The detection and the research of the neutrinos background of   Universe are the attractive problems. This problems do not seem the unpromising one in the case of the high neutrinos density that is necessary for the explanation of the nucleons-antinucleons asymmetry of Universe. It was offered before to use the low energy neutrinos background of Universe for the explanation of the gravitational phenomena with the quantum position attracting the Casimir's effect for this. As a result it was connected the gravitational constant with the parameters characterizing the electroweak interactions. If now we shall be based on the results of the experements fixing the equality of the gravitation mass and the inert one then it can consider that the spectrum of the particle masses is defined by their interaction with the neutrinos background of Universe.
It is reported that a surface model of Polyakov strings undergoes a first-order phase transition between smooth and crumpled (or branched polymer) phases. The Hamiltonian of the model contains the Gaussian term and a deficit angle term corresponding to the weight of the integration measure dX in the partition function.
In this work it has been developed a new approach to study the stability of a system composed by an ELKO field interacting with dark matter, which could give some contribution in order to alleviate the cosmic coincidence problem. It is assumed that the potential which characterizes the ELKO field is not specified, but it is related to a constant parameter $\delta$. The strength of the interaction between matter and ELKO field is characterized by a constant parameter $\beta$ and it is also assumed that both ELKO field as matter energy density are related to their pressures by equations of state parameters $\omega_\phi$ and $\omega_m$, respectively. The system of equations is analysed by a dynamical system approach. It has been found the conditions of stability between the parameters $\delta$ and $\beta$ in order to have stable fixed points for the system for different values of the equation of state parameters $\omega_\phi$ and $\omega_m$, and the results are presented in form of tables. The possibility of decay of ELKO field into dark matter or vice versa can be read directly from the tables, since the parameters $\delta$ and $\beta$ satisfy some inequalities. It allows us to constrain the potential assuming that we have a stable system for different interactions terms between the ELKO field and dark matter. The cosmic coincidence problem can be alleviated for some specific relations between the parameters of the model.
We consider particular entanglement of two particles whose state vectors are in bases that are mutually unbiased (MUB), i.e. "that exhibit maximum degree of incompatibility" (J.Schwinger,Nat. Ac. Sci. (USA), 1960)). We use this link between entanglement and MUB to outline a protocol for secure key distribution among the parties that share these entangled states. The analysis leads to an association of entangled states and states in an MUB set: both carry the same labels.
An analytical model, recently developed to study the electromagnetic dissociation (EMD) energy spectra of two-neutron halo nuclei, is applied to 11-Li and 14-Be. We find that a reliable set of experimental data on EMD could help to resolve the problem concerning the structure of the 11-Li ground state. For 14-Be we find a mutual inconsistency between the existing experimental data on the binding energy, radius and EMD energy spectrum. We also conclude that the structure of 14-Be is essentially more complicated than the structure of other Borromean two--neutron halo nuclei.
A quantum group analysis is applied to the Sine-Gordon model (or may be its version) in a strong-coupling regime. Infinitely many bound states are found together with the corresponding S-matrices. These new solutions of the Yang-Baxter eqations are related to some reducible representations of the quantum $sl(2)$ algebra resembling the Kac-Moody algebra representations in the Wess-Zumino-Witten-Novikov conformal field theory.
Increasingly accurate observations are driving theoretical cosmology toward the use of more sophisticated descriptions of matter and the study of nonlinear perturbations of FL cosmologies, whose governing equations are notoriously complicated. Our goal in this paper is to formulate the governing equations for linear perturbation theory in a particularly simple and concise form in order to facilitate the extension to nonlinear perturbations. Our approach has several novel features. We show that the use of so-called intrinsic gauge invariants has two advantages. It naturally leads to: (i) a physically motivated choice of a gauge invariant associated with the matter density, and (ii) two distinct and complementary ways of formulating the evolution equations for scalar perturbations, associated with the work of Bardeen and of Kodama and Sasaki. In the first case the perturbed Einstein tensor gives rise to a second order (in time) linear differential operator, and in the second case to a pair of coupled first order (in time) linear differential operators. These operators are of fundamental importance in cosmological perturbation theory, since they provide the leading order terms in the governing equations for nonlinear perturbations.
In systems with weak ergodicity breaking, the equivalence of time averages and ensemble averages is known to be broken. We study here the computation of the power spectrum from realizations of a specific process exhibiting 1/f^beta noise, the Rebenshtok-Barkai model. We show that even the binned power spectrum does not converge in the limit of infinite time, but that instead the resulting value is a random variable stemming from a distribution with finite variance. However, due to the strong correlations in neighboring frequency bins of the spectrum, the exponent beta can be safely estimated by time averages of this type. Analytical calculations are illustrated by numerical simulations.
We calculate resistivity in the paramagnetic phase just above the curie temperature in a $2d$ ferromagnetic metal. The required dynamical susceptibility in the formalism of resistivity is calculated within the Random Phase Approximation(RPA). The mechanism of resistivity is magnetic scattering in which $s$-band electrons are scattered off the magnetic spin fluctuations of d-band electrons. We use the $s$-$d$ Hamiltonian formalism. We find that near the quantum critical point the resistivity in $2d$ scales as $T^{\frac{4}{3}}$, whereas in $3d$ it scales as $T^{\frac{5}{3}}$. In contrast to it, resistivity due to phonon scattering is given by $T^5$ in low temperature limit as is well known. Our RPA result agrees with the Self-Consistence Renormalisation(SCR) theory result.
In this paper we investigate the geometry of the Dwork pencil in any dimension. More specifically, we study the automorphism group G of the generic fiber of the pencil over the complex projective line, and the quotients of it by various subgroups of G. In particular, we compute the Hodge numbers of these quotients via orbifold cohomology.
In this paper we examine the effect of X-ray and Lyalpha photons on the intergalactic medium temperature. We calculate the photon production from a population of stars and micro-quasars in a set of cosmological hydrodynamic simulations which self-consistently follow the dark matter dynamics, radiative processes as well as star formation, black hole growth and associated feedback processes. We find that, (i) IGM heating is always dominated by X-rays unless the Lyalpha photon contribution from stars in objects with mass M<10^8 Msun becomes significantly enhanced with respect to the X-ray contribution from BHs in the same halo (which we do not directly model). (ii) Without overproducing the unresolved X-ray background, the gas temperature becomes larger than the CMB temperature, and thus an associated 21 cm signal should be expected in emission, at z<11.5. We discuss how in such a scenario the transition redshift between a 21 cm signal in absorption and in emission could be used to constraint BHs accretion and associated feedback processes.
We study when kernels of inflation maps associated to extraspecial p-groups in stable group cohomology are generated by their degree two components. This turns out to be true if the prime is large enough compared to the rank of the elementary abelian quotient, but false in general.
A recent detection of the peculiar neutron star X-ray binary Circinus X-1 with electronic very long baseline interferometry (e-VLBI) prompted the suggestion that compact, non-variable radio emission persists through the entire 16.6-day orbit of the binary system. We present the results of a high angular resolution monitoring campaign conducted with the Australian Long Baseline Array in real-time e-VLBI mode. e-VLBI observations of Circinus X-1 were made on alternate days over a period of 20 days covering the full binary orbit. A compact radio source associated with Circinus X-1 was clearly detected at orbital phases following periastron passage but no compact radio emission was detected at any other orbital phase, ruling out the presence of a persistent, compact emitting region at our sensitivity levels. The jet was not resolved at any epoch of our 1.4-GHz monitoring campaign, suggesting that the ultrarelativistic flow previously inferred to exist in this source is likely to be dark. We discuss these findings within the context of previous radio monitoring of Circinus X-1.
We introduce a block Lanczos (BL) recursive technique to construct quasi-one-dimensional models, suitable for density-matrix renormalization group (DMRG) calculations, from single- as well as multiple-impurity Anderson models in any spatial dimensions. This new scheme, named BL-DMRG method, allows us to calculate not only local but also spatially dependent static and dynamical quantities of the ground state for general Anderson impurity models without losing elaborate geometrical information of the lattice. We show that the BL-DMRG method can be easily extended to treat a multi-orbital Anderson impurity model. We also show that the symmetry adapted BL bases can be utilized, when it is appropriate, to reduce the computational cost. As a demonstration, we apply the BL-DMRG method to three different models for graphene: (i) a single adatom on the honeycomb lattice, (ii) a substitutional impurity in the honeycomb lattice, and (iii) an effective model for a single carbon vacancy in graphene. Our analysis reveals that, for the particle-hole symmetric case at half filling of electron density, the ground state of model (i) behaves as an isolated magnetic impurity with no Kondo screening while the ground state of the other two models forms a spin singlet state. We also calculate the real-space dependence of the spin-spin correlation functions between the impurity site and the conduction sites for these three models. Our results clearly show that, reflecting the presence of absence of unscreened magnetic moment at the impurity site, the spin-spin correlation functions decay as $r^{-3}$, differently from the non-interacting limit ($r^{-2}$), for model (i) and as $ r^{-4}$, exactly the same as the non-interacting limit, for models (ii) and (iii) in the asymptotic $r$, where $r$ is the distance between the impurity site and the conduction site.
We consider semilinear hyperbolic systems with a trilinear nonlinearity. Both the differential equation and the initial data contain the inverse of a small parameter $\varepsilon$, and typical solutions oscillate with frequency proportional to $1/\varepsilon$ in time and space. Moreover, solutions have to be computed on time intervals of length $1/\varepsilon$ in order to study nonlinear and diffractive effects. As a consequence, direct numerical simulations are extremely costly or even impossible. We propose an analytical approximation and prove that it approximates the exact solution up to an error of $\mathcal{O}(\varepsilon^2)$ on time intervals of length $1/\varepsilon$. This is a significant improvement over the classical nonlinear Schr\"odinger approximation, which only yields an accuracy of $\mathcal{O}(\varepsilon)$.
We prove nonuniqueness of weak solutions to multi-dimensional generalisation of the Aw-Rascle model of vehicular traffic. Our generalisation includes the velocity offset in a form of gradient of density function, which results in a dissipation effect, similar to viscous dissipation in the compressible viscous fluid models. We show that despite this dissipation, the extension of the method of convex integration can be applied to generate infinitely many weak solutions connecting arbitrary initial and final states. We also show that for certain choice of data, ill posedness holds in the class of admissible weak solutions.
The generation of parallel electric fields by the propagation of ion cyclotron waves in the plasma with a transverse density inhomogeneity was studied. It was proven that the minimal model required to reproduce the previous kinetic simulation results of E_{||} generation [Tsiklauri et al 2005, Genot et al 2004] is the two-fluid, cold plasma approximation in the linear regime. By considering the numerical solutions it was also shown that the cause of E_{||} generation is the electron and ion flow separation induced by the transverse density inhomogeneity. We also investigate how E_{||} generation is affected by the mass ratio and found that amplitude attained by E_{||} decreases linearly as inverse of the mass ratio m_i/m_e. For realistic mass ratio of m_i/m_e=1836, such empirical scaling law, within a time corresponding to 3 periods of the driving ion cyclotron wave, is producing E_{||}=14 Vm^{-1} for solar coronal parameters. Increase in mass ratio does not have any effect on final parallel (magnetic field aligned) speed attained by electrons. However, parallel ion velocity decreases linearly with inverse of the mass ratio m_i/m_e. These results can be interpreted as following: (i) ion dynamics plays no role in the E_{||} generation; (ii) E_{||} \propto 1/m_i scaling is caused by the fact that omega_d = 0.3 omega_{ci} \propto 1/m_i is decreasing with the increase of ion mass, and hence the electron fluid can effectively "short-circuit" (recombine with) the slowly oscillating ions, hence producing smaller E_{||}.
Broad Absorption Lines indicate gas outflows with velocities from thousands km/s to about 0.2 the speed of light, which may be present in all quasars and may play a major role in the evolution of the host galaxy. The variability of absorption patterns can provide informations on changes of the density and velocity distributions of the absorbing gas and its ionization status. We collected 23 photometrical and spectro-photometrical observations at the 1.82m Telescope of the Asiago Observatory since 2003, plus other 5 spectra from the literature. We analysed the evolution in time of the equivalent width of the broad absorption feature and two narrow absorption systems, the correlation among them and with the R band magnitude. We performed a structure function analysis of the equivalent width variations. We present an unprecedented monitoring of a broad absorption line quasar based on 28 epochs in 14 years. The shape of broad absorption feature shows a relative stability, while its equivalent width slowly declines until it sharply increases during 2011. In the same time the R magnitude stays almost constant until it sharply increases during 2011. The equivalent width of the narrow absorption redwards of the systemic redshift only shows a decline. The broad absorption behaviour suggests changes of the ionisation status as the main cause of variability. We show for the first time a correlation of this variability with the R band flux. The different behaviour of the narrow absorption system might be due to recombination time delay. The structure function of the absorption variability has a slope comparable with typical optical variability of quasars. This is consistent with variations of the 200 A ionising flux originating in the inner part of the accretion disk.
Synthesizing photo-realistic images from text descriptions is a challenging problem. Previous studies have shown remarkable progresses on visual quality of the generated images. In this paper, we consider semantics from the input text descriptions in helping render photo-realistic images. However, diverse linguistic expressions pose challenges in extracting consistent semantics even they depict the same thing. To this end, we propose a novel photo-realistic text-to-image generation model that implicitly disentangles semantics to both fulfill the high-level semantic consistency and low-level semantic diversity. To be specific, we design (1) a Siamese mechanism in the discriminator to learn consistent high-level semantics, and (2) a visual-semantic embedding strategy by semantic-conditioned batch normalization to find diverse low-level semantics. Extensive experiments and ablation studies on CUB and MS-COCO datasets demonstrate the superiority of the proposed method in comparison to state-of-the-art methods.