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We present a search for transient radio sources on timescales of 2 to 9 yr at 150 MHz. This search is conducted by comparing the first Alternative Data Release of the TIFR GMRT Sky Survey (TGSS ADR1) and the second data release of the LOFAR Two-metre Sky Survey (LoTSS DR2). The overlapping survey area covers 5570 $\rm{deg}^2$ on the sky, or 14 per cent of the total sky. We introduce a method to compare the source catalogues that involves a pair match of sources, a flux density cutoff to meet the survey completeness limit and a newly developed compactness criterion. This method is used to identify both transient candidates in the TGSS source catalogue that have no counterpart in the LoTSS catalogue and transient candidates in LoTSS without a counterpart in TGSS. We find that imaging artefacts and uncertainties and variations in the flux density scales complicate the transient search. Our method to search for transients by comparing two different surveys, while taking into account imaging artefacts around bright sources and misaligned flux scales between surveys, is universally applicable to future radio transient searches. No transient sources were identified, but we are able to place an upper limit on the transient surface density of $, 14 pages, 11 figures

In the work (Bouaouid et al. in Adv. Differ. Equ. 2019:21, 2019), the authors have used the Krasnoselskii fixed point theorem for showing the existence of mild solutions of an abstract class of conformable fractional differential equations of the form: $\frac{d^{\alpha }}{dt^{\alpha }}[\frac{d^{\alpha }x(t)}{dt^{\alpha }}]=Ax(t)+f(t,x(t))$ d α d t α [ d α x ( t ) d t α ] = A x ( t ) + f ( t , x ( t ) ) , $t\in [0,\tau ]$ t ∈ [ 0 , τ ] subject to the nonlocal conditions $x(0)=x_{0}+g(x)$ x ( 0 ) = x 0 + g ( x ) and $\frac{d^{\alpha }x(0)}{dt^{\alpha }}=x_{1}+h(x)$ d α x ( 0 ) d t α = x 1 + h ( x ) , where $\frac{d^{\alpha }(\cdot)}{dt^{\alpha }}$ d α ( ⋅ ) d t α is the conformable fractional derivative of order $\alpha \in\, ]0,1]$ α ∈ ] 0 , 1 ] and A is the infinitesimal generator of a cosine family $(\{C(t),S(t)\})_{t\in \mathbb{R}}$ ( { C ( t ) , S ( t ) } ) t ∈ R on a Banach space X. The elements $x_{0}$ x 0 and $x_{1}$ x 1 are two fixed vectors in X, and f, g, h are given functions. The present paper is a continuation of the work (Bouaouid et al. in Adv. Differ. Equ. 2019:21, 2019) in order to use the Darbo–Sadovskii fixed point theorem for proving the same existence result given in (Bouaouid et al. in Adv. Differ. Equ. 2019:21, 2019) [Theorem 3.1] without assuming the compactness of the family $(S(t))_{t>0}$ ( S ( t ) ) t > 0 and any Lipschitz conditions on the functions g and h.

In this paper, we consider the asymptotic behavior of solutions to stochastic strongly damped wave equations with variable delays on unbounded domains, which is driven by both additive noise and deterministic non-autonomous forcing. We first establish a continuous cocycle for the equations. Then we prove asymptotic compactness of the cocycle by tail-estimates and a decomposition technique of solutions. Finally, we obtain the existence of a tempered pullback random attractor.

The main purpose of this article is to initiate a systematic study of Semihypergroups, first introduced by C. Dunkl [4], I. Jewett [13] and R. Spector [20] independently around 1972. We introduce and study several natural algebraic and analytic structures on semihypergroups, which are well-known in the case of topological groups and semigroups. In particular, we first study almost periodic and weakly almost periodic function spaces (basic properties, their relation to the compactness of the underlying space, introversion and Arens product on their duals among others). We then introduce homomorphisms and ideals, and thereby examine their behaviour (basic properties, structure of the kernel and relation of amenability to minimal ideals) in order to gain insight into the structure of a Semihypergroup itself. In the process, we further investigate where and why this theory deviates from the classical theory of semigroups., 26 Pages, comments are welcome

As a stronger form of multi-sensitivity, the notion of ergodic multi-sensitivity (resp. strongly ergodically multi-sensitivity) is introduced. In particularly, it is proved that every topologically double ergodic continuous selfmap (resp. topologically double strongly ergodic selfmap) on a compact metric space is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive). And for any given integer $ m\geq 2 $, $ f $ is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive) if and only if so is $ f^{m} $. Also, it is shown that if $ f $ is a continuous surjection, then $ f $ is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive) if and only if so is $ \sigma_{f} $, where $ \sigma_{f} $ is the shift selfmap on the inverse limit space $ \lim\limits_{\leftarrow}(X, f) $. Moreover, it is proved that if $ f:X\rightarrow X $ (resp. $ g:Y\rightarrow Y $) is a map on a nontrivial metric space $ (X, d) $ (resp. $ (Y, d') $), and $ \pi $ is a semiopen factor map between $ (X, f) $ and $ (Y, g) $, then the ergodic multi-sensitivity (resp. the strongly ergodic multi-sensitivity) of $ g $ implies the same property of $ f $.

This paper studies the mass-critical variable coefficient nonlinear Schrödinger equation. We first get the existence of the ground state by solving a minimization problem. Then we prove a compactness result by the variational characterization of the ground state solutions. In addition, we construct the blow-up solutions at the minimal mass threshold and further prove the uniqueness result on the minimal mass blow-up solutions which are pseudo-conformal transformation of the ground states.

A class of Dirichlet-Morrey spaces $ D_{\beta, \lambda} $ is introduced in this paper. For any positive Borel measure $ \mu $, the boundedness and compactness of the identity operator from $ D_{\beta, \lambda} $ into the tent space $ \mathcal{T}_s^1(\mu) $ are characterized. As an application, the boundedness of the Volterra integral operator $ T_g: D_{\beta, \lambda} \to F(1, \beta-s, s) $ is studied. Moreover, the essential norm and the compactness of the operator $ T_g $ are also investigated.

We revisit the flavor symmetries arising from compactifications on tori with magnetic background fluxes. Using Euler's Theorem, we derive closed form analytic expressions for the Yukawa couplings that are valid for arbitrary flux parameters. We discuss the modular transformations for even and odd units of magnetic flux, M, and show that they give rise to finite metaplectic groups the order of which is determined by the least common multiple of the number of zero-mode flavors involved. Unlike in models in which modular flavor symmetries are postulated, in this approach they derive from an underlying torus. This allows us to retain control over parameters, such as those governing the kinetic terms, that are free in the bottom-up approach, thus leading to an increased predictivity. In addition, the geometric picture allows us to understand the relative suppression of Yukawa couplings from their localization properties in the compact space. We also comment on the role supersymmetry plays in these constructions, and outline a path towards non-supersymmetric models with modular flavor symmetries., 34 pages, 3 figures, 2 tables

In this paper, we investigate the existence of stable standing waves for the nonlinear Schrodinger equation with inverse-power potential and combined power-type and Choquard-type nonlinearities $ i \partial_t\psi+\triangle \psi+\frac{\gamma}{|x|^\alpha}\psi+\lambda_1|\psi|^p\psi +\lambda_2(I_\beta\ast|\psi|^q)|\psi|^{q-2}\psi = 0,\; \; (t,x)\in [0,T^\star)\times \mathbb{R}^N. $ By using concentration compactness principle, when one nonlinearity is focusing and $ L^2 $-critical, the other is defocusing and $ L^2 $-supercritical, we prove the existence and orbital stability of standing waves. We extend the results of Li-Zhao in paper [ 14 ] to the $ L^2 $-critical and $ L^2 $-supercritical nonlinearities.

In this paper, we study the Cauchy problem of the isothermal system in a general nozzle with space-dependent friction $ \alpha(x) $. First, by using the maximum principle, we obtain the uniform bound $ \rho^{\delta, \varepsilon, \tau} \le M $, $ |m^{\delta, \varepsilon, \tau}| \le M $, independent of the time, of the viscosity-flux approximation solutions; Second, by using the compensated compactness method coupled with the convergence framework given in [5], we prove that the limit, $ (\rho, m) $ of $ (\rho^{\delta, \varepsilon, \tau}, m^{\delta, \varepsilon, \tau}) $, as $ \varepsilon, \delta, \tau $ go to zero, is a uniformly bounded entropy solution.

In this paper, we characterize completely the compactness of linear combinations of composition operators acting on the space $H^{\infty }(\mathbb{B}_{N})$ H ∞ ( B N ) of bounded holomorphic functions over the unit ball $\mathbb{B}_{N}$ B N from two different aspects. The same problems are also investigated on the space $H^{\infty }(\mathbb{D}^{N})$ H ∞ ( D N ) over the unit polydisk $\mathbb{D}^{N}$ D N .

This paper deals with nonlocal fractional p-Laplacian problems with difference. We get a theorem which shows existence of a sequence of weak solutions for a family of nonlocal fractional p-Laplacian problems with difference. We first show that there exists a sequence of weak solutions for these problems on the finite-dimensional subspace. We next show that there exists a limit sequence of a sequence of weak solutions for finite-dimensional problems, and this limit sequence is a sequence of the solutions of our problems. We get this result by the estimate of the energy functional and the compactness property of continuous embedding inclusions between some special spaces.

We obtain well behaved interior solutions describing hydrostatic equilibrium of anisotropic relativistic stars in scale-dependent gravity, where Newton's constant is allowed to vary with the radial coordinate throughout the star. Assuming i) a linear equation-of-state in the MIT bag model for quark matter, and ii) a certain profile for the energy density, we integrate numerically the generalized structure equations, and we compute the basic properties of the strange quark stars, such as mass, radius and compactness. Finally, we demonstrate that stability criteria as well as the energy conditions are fulfilled. Our results show that a decreasing Newton's constant throughout the objects leads to slightly more massive and more compact stars., Comment: 11 pages, 4 tables, 6 figures, accepted in EPJC

In this paper, we study the following Schrödinger-Poisson system with critical exponent \begin{document} $ \begin{equation*} \begin{cases} -\Delta u-k(x)\phi u=\lambda h(x)|u|^{p-2}u+s(x)|u|^{4}u, \ ~~x\in\mathbb{R}^{3},\\ -\triangle\phi=k(x)u^{2}, \ \ \ \ \ \ \ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ x\in\mathbb{R}^{3}, \\ \end{cases} \end{equation*} $ \end{document} where $1 < p < 2$ and $\lambda > 0.$ Under suitable conditions on $k$, $h$ and $s$, we show that there exists $\lambda^{\ast}>0$ such that the above problem possesses infinitely many solutions with negative energy for each $\lambda\in(0, \lambda^{\ast})$. Moreover, we prove the existence of infinitely many solutions with positive energy. The main tools are the concentration compactness principle, $Z_{2}$ index theory and Fountain Theorem. These results extend some existing results in the literature.

We present the features of a model which generalizes Schwarzschild’s homogeneous star by adding a transition zone for the density near the surface. By numerically integrating the modified TOV equations for the $$f(\mathcal {R})=\mathcal {R}+\lambda \mathcal {R}^2$$ f ( R ) = R + λ R 2 Palatini theory, it is shown that the ensuing configurations are everywhere finite. Depending on the values of the relevant parameters, objects more, less or as compact as those obtained in GR with the same density profile have been shown to exist. In particular, in some region of the parameter space the compactness is close to that set by the Buchdahl limit.

We obtain results on compactness of two linear Hammerstein integral operators with singularities, and apply the results to give new proof that Riemann–Liouville fractional integral operators of order $\alpha\in (0,1)$ map $L^{p}(0,1)$ to $C[0,1]$ and are compact for each $p\in \bigl(\frac{1}{1-\alpha},\infty\bigr]$. We show that the spectral radii of the Riemann–Liouville fractional operators are zero.

The $K$-hull of a compact set $A\subset\mathbb{R}^d$, where $K\subset \mathbb{R}^d$ is a fixed compact convex body, is the intersection of all translates of $K$ that contain $A$. A set is called $K$-strongly convex if it coincides with its $K$-hull. We propose a general approach to the analysis of facial structure of $K$-strongly convex sets, similar to the well developed theory for polytopes, by introducing the notion of $k$-dimensional faces, for all $k=0,\dots,d-1$. We then apply our theory in the case when $A=\Xi_n$ is a sample of $n$ points picked uniformly at random from $K$. We show that in this case the set of $x\in\mathbb{R}^d$ such that $x+K$ contains the sample $\Xi_n$, upon multiplying by $n$, converges in distribution to the zero cell of a certain Poisson hyperplane tessellation. From this results we deduce convergence in distribution of the corresponding $f$-vector of the $K$-hull of $\Xi_n$ to a certain limiting random vector, without any normalisation, and also the convergence of all moments of the $f$-vector., Comment: 40 pages, 3 figures; Corollary 6.6 has been corrected and new Theorem 7.3 has been added. Accepted for publication in Advances in Mathematics

Grape (Vitis vinifera) cluster compactness is an important trait due to its effect on disease susceptibility, but visual evaluation of compactness relies on human judgement and an ordinal scale that is not appropriate for all populations. We developed an image analysis pipeline and used it to quantify cluster compactness traits in a segregating hybrid wine grape (Vitis sp.) population for 2 years. Images were collected from grape clusters immediately after harvest, segmented by color, and analyzed using a custom script. Both automated and conventional phenotyping methods were used, and comparisons were made between each method. A partial least squares (PLS) model was constructed to evaluate the prediction of physical cluster compactness using image-derived measurements. Quantitative trait loci (QTL) on chromosomes 4, 9, 12, 16, and 17 were associated with both image-derived and conventionally phenotyped traits within years, which demonstrated the ability of image-derived traits to identify loci related to cluster morphology and cluster compactness. QTL for 20-berry weight were observed between years on chromosomes 11 and 17. Additionally, the automated method of cluster length measurement was highly accurate, with a deviation of less than 10 mm (r = 0.95) compared with measurements obtained with a hand caliper. A remaining challenge is the utilization of color-based image segmentation in a population that segregates for fruit color, which leads to difficulty in differentiating the stem from the fruit when the two are similarly colored in non-noir fruit. Overall, this research demonstrates the validity of image-based phenotyping for quantifying cluster compactness and for identifying QTL for the advancement of grape breeding efforts.

This paper concerns the long term behavior of the stochastic two-dimensional g-Navier–Stokes equations with additive noise defined on a sequence of expanding domains, where the ultimate domain is unbounded and of Poincaré type. We prove that the weak continuity is uniform with respect to all expanding cocycles, which yields the equi-asymptotic compactness by using an energy equation method. Finally, we show the existence of a random attractor for the equation on each domain and the upper semi-continuity of random attractors as the bounded domain is expanded to the unbounded ultimate domain.

The finite-dimensional problem of embedding a given compact D ⊂ R p into the lower Lebesgue set G(α) = {y ∈ R p : f(y) 6 α} of the convex function f(·) with the smallest value of α due to the offset of D is considered. Its mathematical formalization leads to the problem of minimizing the function φ(x) = max y∈D f(y − x) on R p . The properties of the function φ(x) are researched, necessary and sufficient conditions and conditions for the uniqueness of the problem solution are obtained. As an important case for applications, the case when f(·) is the Minkowski gauge function of some convex body M is singled out. It is shown that if M is a polyhedron, then the problem reduces to a linear programming problem. The approach to get an approximate solution is proposed in which, having known the approximation of xi to obtain xi+1 it is necessary to solve the simpler problem of embedding the compact set D into the Lebesgue set of the gauge function of the set Mi = G(ai), where ai = f(xi). The rationale for the convergence for a sequence of approximations to the problem solution is given.

We investigate level-set percolation of the discrete Gaussian free field on $\mathbb{Z}^d$, $d\geq 3$, in the strongly percolative regime. We consider the event that the level-set of the Gaussian free field below a level $\alpha$ disconnects the discrete blow-up of a compact set $A$ from the boundary of an enclosing box. We derive asymptotic large deviation upper bounds on the probability that the local averages of the Gaussian free field deviate from a specific multiple of the harmonic potential of $A$, when disconnection occurs. These bounds, combined with the findings of the recent article [12], show that conditionally on disconnection, the Gaussian free field experiences an entropic push-down proportional to the harmonic potential of $A$. In particular, due to the slow decay of correlations, the disconnection event affects the field on the whole lattice. Furthermore, we provide a certain 'profile' description for the field in the presence of disconnection. We show that while on a macroscopic scale the field is pinned around a level proportional to the harmonic potential of $A$, it locally retains the structure of a Gaussian free field shifted by a constant value. Our proofs rely crucially on the 'solidification estimates' developed in arXiv:1706.07229 by A.-S. Sznitman and the second author., Comment: Accepted in Probability Theory and Related Fields

In this work we investigate the extra packing of mass within the framework of gravitational decoupling by means of Minimal Geometric Deformation approach. It is shown that, after a suitable set of the free parameters involved, the like-Tolman IV solution extended by Minimal Geometric Deformation not only acquire extra packing of mass but it corresponds to a stable configuration according to the adiabatic index criteria. Additionally, it is shown that the extra packing condition induce a lower bound on the compactness parameter of the seed isotropic solution and a stringent restriction on the decoupling parameter.

In this paper, we are devoted to study asymptotic dynamics of the stochastic extended Brusselator system with a multiplicative noise. The stochastic extended Brusselator system is composed of three pairs of symmetrical coupling components. We firstly study the pullback absorbing property for the stochastic extended Brusselator system with a multiplicative noise. But coupling terms bring great difficulty on this problem, we use the scaling method and estimate groups to overcome this difficulty. Then, we apply the bootstrap pullback estimations to prove the pullback asymptotic compactness for the stochastic extended Brusselator system with a multiplicative noise. Finally, we show the existence of random attractors. In the study of the existence of random attractors for stochastic dynamics, we use the exponential transformation of the Ornstein-Uhlenbeck process to replace the exponential transformation of Brownian motion, which changes the structure of the original Brusselator equations and produces the non-autonomous terms. Based on this, we have to estimate groups to overcome the difficulties of coupling structure and make more complex estimates.

We study relativistic stars in the scale-dependent scenario, which is one of the approaches to quantum gravity, and where Newton's constant is promoted to a scale-dependent quantity. First, the generalized structure equations are derived here for the first time. Then they are integrated numerically assuming a linear equation-of-state in the simplest MIT bag model for quark matter. We compute the radius, the mass and the compactness of strange quarks stars, and we show that the energy conditions are fulfilled., Comment: Minor correction, references added

This paper presents a computational frequency-domain boundary value analysis of acoustic metamaterials and phononic crystals based on a general homogenization framework, which features a novel definition of the macro-scale fields based on the Floquet-Bloch average in combination with a family of characteristic projection functions leading to a generalized macro-scale continuum. Restricting to 1D elastodynamics and the frequency-domain response for the sake of compactness, the boundary value problem on the generalized macro-scale continuum is elaborated. Several challenges are identified, in particular the non-uniqueness in selection of the boundary conditions for the homogenized continuum and the presence of spurious short wave solutions. To this end, procedures for the determination of the homogenized boundary conditions and mitigation of the spurious solutions are proposed. The methodology is validated against the direct numerical simulation on an example periodic 2-phase composite structure.

In this paper we complete the study started in [P. Pucci, L. Temperini, Existence for (p,q) critical systems in the Heisenberg group, Adv. Nonlinear Anal. 9 (2020), 895–922] on some variants of the concentration-compactness principle in bounded PS domains \(\Omega\) of the Heisenberg group \(\mathbb{H}^n\). The concentration-compactness principle is a basic tool for treating nonlinear problems with lack of compactness. The results proved here can be exploited when dealing with some kind of elliptic systems involving critical nonlinearities and Hardy terms.

We study the compactness and the hypercyclicity of Toeplitz operators T ϕ ¯ , b {T_{\bar \varphi ,b}} with co-analytic and bounded symbols on de Branges-Rovnyak spaces ℋ(b). For the compactness of T ϕ ¯ , b {T_{\bar \varphi ,b}} , we will see that the result depends on the boundary spectrum of b. We will prove that there are non trivial compact operators of the form T ϕ ¯ , b {T_{\bar \varphi ,b}} , with ϕ ∈ H ∞ ∩ C(𝕋), if and only if m(σ(b) ∩ 𝕋) = 0. We will also show that, when b is non-extreme, then T ϕ ¯ , b {T_{\bar \varphi ,b}} is hypercyclic if and only if ϕ is non-constant and ϕ(𝔻) ∩ 𝕋 ≠ ∅.

In this paper, we introduce a class of stochastic variational inequalities generated from the Browder variational inequalities. First, the existence of solutions for these generalized stochastic Browder mixed variational inequalities (GS-BMVI) are investigated based on FKKM theorem and Aummann’s measurable selection theorem. Then the uniqueness of solution for GS-BMVI is proved based on strengthening conditions of monotonicity and convexity, the compactness and convexity of the solution sets are discussed by Minty’s technique. The results of this paper can provide a foundation for further research of a class of stochastic evolutionary problems driven by GS-BMVI.

In this paper we give sufficient conditions on a semi-linear differential equation ensuring the pre-compactness of its solution. The result is illustrated by two examples of vibrating strings in a network with a static damper.

Binary relations are commonly used in Computer Science for modeling data. In addition to classical representations using matrices or lists, some compressed data structures have recently been proposed to represent binary relations in compact space, such as the $k^2$-tree and the Binary Relation Wavelet Tree (BRWT). Knowing their storage needs, supported operations and time performance is key for enabling an appropriate choice of data representation given a domain or application, its data distribution and typical operations that are computed over the data. In this work, we present an empirical comparison among several compressed representations for binary relations. We analyze their space usage and the speed of their operations using different (synthetic and real) data distributions. We include both neighborhood and set operations, also proposing algorithms for set operations for the BRWT, which were not presented before in the literature. We conclude that there is not a clear choice that outperforms the rest, but we give some recommendations of usage of each compact representation depending on the data distribution and types of operations performed over the data. We also include a scalability study of the data representations., This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 690941

In this paper we continue the work that we began in arXiv:1912.07537. Given $1 0$, and a continuous function $A(r) >0\ (r>0)$, we consider the quasilinear elliptic equation \[ -\mathrm{div}\left(A(|x| )|\nabla u|^{p-2} \nabla u\right) +V\left( \left| x\right| \right) |u|^{p-2}u= K(|x|) f(u) \quad \text{in }\mathbb{R}^{N}, \] where all the potentials $A,V,K$ may be singular or vanishing, at the origin or at infinity. We find existence of nonnegative solutions by the application of variational methods, for which we need to study the compactness of the embedding of a suitable function space $X$ into the sum of Lebesgue spaces $L_{K}^{q_{1}}+L_{K}^{q_{2}}$. The nonlinearity has a double-power super $p$-linear behavior, as $f(t)= \min \left\{ t^{q_1 -1}, t^{q_2 -1} \right\}$ with $q_1,q_2>p$ (recovering the power case if $q_1=q_2$). With respect to \cite{AVK_I}, in the present paper we assume some more hypotheses on $V$, and we are able to enlarge the set of values $q_1 , q_2$ for which we get existence results., Comment: arXiv admin note: text overlap with arXiv:1510.03879, arXiv:1912.07537, arXiv:1403.3803

This letter proposes a novel form of continuous-time evolutionary game dynamics for generalized Nash equilibrium seeking in equality-constrained population games. Using Lyapunov stability theory and duality theory, we provide sufficient conditions to guarantee the asymptotic stability, non-emptiness, compactness, and optimality of the equilibria set of the proposed dynamics for certain population games. Moreover, we illustrate our theoretical developments through a numerical simulation of an equality-constrained congestion game., Juan Martinez-Piazuelo gratefully acknowledges the Universitat Politecnica de Catalunya and Banco Santander for the financial support ` of his predoctoral grant FPI-UPC. In addition, the authors would like to thank the project PID2020-115905RB-C21 (L-BEST) funded by MCIN/ AEI /10.13039/501100011033 for supporting this research.