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We use the underlying structure of then coadjoint orbits of a semidirect product of a connected Lie group and a vector space to obtain families of Lagrangian submanifolds in the adjoint orbits of complex semisimple Lie groups with respect to the symplectic hermitian form. This construction is a generalization of a type of semi-direct orbit previously studied by the authors.

We construct an action of the Thompson group F on a compact space built from pairs of infinite, binary rooted trees. The action arises as an F-equivariant compactification of the action of F by translations on one of its homogeneous spaces, F/H2, corresponding to a certain subgroup H2 of F. The representation of F on the Hilbert space ` 2 (F/H2) is faithful on the complex group algebra C[F]. [ABSTRACT FROM AUTHOR]

The three-distance theorem (also known as the three-gap theorem or Steinhaus problem) states that, for any given real number |$\alpha $| and integer |$N$|⁠ , there are at most three values for the distances between consecutive elements of the Kronecker sequence |$\alpha , 2\alpha ,\ldots , N\alpha $| mod 1. In this paper, we consider a natural generalization of the three-distance theorem to the higher-dimensional Kronecker sequence |$\vec \alpha , 2\vec \alpha ,\ldots , N\vec \alpha $| modulo an integer lattice. We prove that in 2D, there are at most five values that can arise as a distance between nearest neighbors, for all choices of |$\vec \alpha $| and |$N$|⁠. Furthermore, for almost every |$\vec \alpha $|⁠ , five distinct distances indeed appear for infinitely many |$N$| and hence five is the best possible general upper bound. In higher dimensions, we have similar explicit, but less precise, upper bounds. For instance, in 3D, our bound is 13, though we conjecture the truth to be 9. We furthermore study the number of possible distances from a point to its nearest neighbor in a restricted cone of directions. This may be viewed as a generalization of the gap length in 1D. For large cone angles, we use geometric arguments to produce explicit bounds directly analogous to the three-distance theorem. For small cone angles, we use ergodic theory of homogeneous flows in the space of unimodular lattices to show that the number of distinct lengths is (1) unbounded for almost all |$\vec \alpha $| and (2) bounded for |$\vec \alpha $| that satisfy certain Diophantine conditions. [ABSTRACT FROM AUTHOR]

For a space (X, d, μ) of homogeneous type and a fractional type integral operator Kα defined on (X, d, μ) we find a necessary and sufficient condition on the exponent q governing the compactness of Kαfrom Lp(X) to Lq(X), where 1 ≤ p, q < ∞ and μ(X) < ∞. [ABSTRACT FROM AUTHOR]

In this paper, we make a correction to Theorem 1.2 of the aforementioned paper [J. Liu, Fano manifolds containing a negative divisor isomorphic to a rational homogeneous space of Picard number one, Int. J. Math. 31(9) (2020) 2050066]. [ABSTRACT FROM AUTHOR]

The classification of exact solutions of Maxwell vacuum equations for the case where the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group G 3 (V I I) was completed. All non-equivalent exact solutions of Maxwell vacuum equations for electromagnetic fields and spaces with such symmetry were obtained. The vectors of the canonical frame of a homogeneous space of type VII according to the Bianchi classification and the electromagnetic field potentials were found. [ABSTRACT FROM AUTHOR]

Species with broader niches may have the opportunity to occupy larger geographic areas, assuming no limitations on dispersal and a relatively homogeneous environmental space. Here, we use data on a large set of mammal (n = 1225), bird (n = 1829) and tree (n = 341) species to examine the 1) relationship between geographic range size and climatic niche area, 2) influence of species traits on species departures from this relationship and 3) sensitivity of these relationships to how species range size and climatic niche area are estimated. We find positive geographic range size–climatic niche area relationships for all taxa, with residual variation dependent on latitude, and differing from a null model for mammals and birds, but not for trees. Together, we provide support for this general macroecological relationship which is dependent on space, weakly influenced by species traits, and different enough from a null model to suggest that geographic and demographic processes are important. [ABSTRACT FROM AUTHOR]

It is known that, under a necessary non-compactness assumption, the Brauer-Manin obstruction is the only one to strong approximation on homogeneous spaces X under a linear group G (or under a connected algebraic group, under assumption of finiteness of a suitable Tate-Shafarevich group), provided that the geometric stabilizers of X are connected. In this work we prove, under similar assumptions, that the étale-Brauer-Manin obstruction to strong approximation is the only one for homogeneous spaces with arbitrary stabilizers. We also deal with some related questions, concerning strong approximation outside a finite set of valuations. Finally, we prove a compatibility result, suggested to be true by work of Cyril Demarche, between the Brauer-Manin obstruction pairing on quotients G/H, where G and H are connected algebraic groups and H is linear, and certain abelianization morphisms associated with these spaces. [ABSTRACT FROM AUTHOR]

For any G$G$‐invariant metric on a compact homogeneous space M=G/K$M=G/K$, we give a formula for the Lichnerowicz Laplacian restricted to the space of all G$G$‐invariant symmetric 2‐tensors in terms of the structural constants of G/K$G/K$. As an application, we compute the G$G$‐invariant spectrum of the Lichnerowicz Laplacian for all the Einstein metrics on most generalized Wallach spaces and any flag manifold with b2(M)=1$b_2(M)=1$. This allows to deduce the G$G$‐stability and critical point types of each of such Einstein metrics as a critical point of the scalar curvature functional. [ABSTRACT FROM AUTHOR]

In this article we demonstrate robust estimation of the model parameters of a fully-linear data-driven BRDF model from a reflectance map under known natural lighting. To regularize the estimation of the model parameters, we leverage the reflectance similarities within a material class. We approximate the space of homogeneous BRDFs using a Gaussian mixture model, and assign a material class to each Gaussian in the mixture model. We formulate the estimation of the model parameters as a non-linear maximum a-posteriori optimization, and introduce a linear approximation that estimates a solution per material class from which the best solution is selected. We demonstrate the efficacy and robustness of our method using the MERL BRDF database under a variety of natural lighting conditions, and we provide a proof-of-concept real-world experiment. [ABSTRACT FROM AUTHOR]

We give some new formulae relating an obstruction to the weak approximation on homogeneous spaces to the set of local and global Brauer and R-equivalence classes. [ABSTRACT FROM AUTHOR]

Let G be a locally compact group and H be a compact subgroup of G. The aim of this paper is to characterize some homological properties of L¹ (G/H), C0(G/H) and M(G/H) as left Banach L¹(G)-modules such as flatness, injectivity and projectivity. Moreover, we study the projectivity of C0(G/H) and M(G/H) as Banach left L¹(G/H)-modules and M(G)-modules. [ABSTRACT FROM AUTHOR]

We investigate the action of the Lie group SL(3, R) on the two-dimensional homogeneous space. All the one-parameter subgroups (up to conjugacy) of SL(3, R) are considered. We discuss the orbits and curvatures of these one-parameter subgroups. We also classify these subgroups in terms of Fixed points. [ABSTRACT FROM AUTHOR]

Let G be a simple non-compact linear connected Lie group and H ⊂ G be a closed non-compact semisimple subgroup. We are interested in finding classes of homogeneous spaces G / H admitting proper actions of discrete non-virtually abelian subgroups Γ ⊂ G. We develop an algorithm for finding such homogeneous spaces. As a testing example we obtain a list of all non-compact homogeneous spaces G / H admitting proper action of a discrete and non virtually abelian subgroup Γ ⊂ G in the case when G has rank at most 8, and H is a maximal proper semisimple subgroup, provided that the pair (g , h) is contained in a database created by De Graaf and Marrani. [ABSTRACT FROM AUTHOR]

Let (핏 , d , μ) be a space of homogeneous type in the sense of R. R. Coifman and G. Weiss, and let X ⁢ (핏) be a ball quasi-Banach function space on 핏 . In this article, the authors introduce the weak Hardy space W ⁢ H ~ X ⁢ (핏) associated with X ⁢ (핏) via the Lusin area function. Then the authors characterize W ⁢ H ~ X ⁢ (핏) by the molecule, the grand maximal function, and the Littlewood–Paley g-function and g λ * -function. Moreover, all these results have a wide generality. Particularly, the results of this article are also new even when they are applied, respectively, to weighted Lebesgue spaces, Orlicz spaces, and variable Lebesgue spaces, which actually are new even on RD-spaces (that is, spaces of homogeneous type with additional reverse doubling condition). The main novelties of this article exist in that the authors take full advantage of the geometrical properties of 핏 expressed by both the dyadic cubes and the exponential decay of the approximations of the identity to overcome the difficulties caused by the deficiencies of both the explicit expression of the quasi-norm of X ⁢ (핏) and the reverse doubling condition of μ, and that the authors use the tent space on 핏 × ℤ to characterize W ⁢ H ~ X ⁢ (핏) by the Littlewood–Paley g λ * -function, where the range of λ might be best possible in some cases. [ABSTRACT FROM AUTHOR]

We show that a four-dimensional homogeneous manifold with half-harmonic Weyl curvature tensor is symmetric or homothetic either to the only nonsymmetric anti-self-dual homogeneous manifold or to the 3-symmetric space. [ABSTRACT FROM AUTHOR]

We make the first steps towards generalising the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph over a homogeneous metric space where the probability of two vertices to be connected is an arbitrary function of the distance. We give sufficient conditions under which the locations can be recovered (up to an isomorphism of the space) in the sparse regime. Moreover, we define a geometric counterpart of the model of flow of information on trees, due to Mossel and Peres, in which one considers a branching random walk on a sphere and the goal is to recover the location of the root based on the locations of leaves. We give some sufficient conditions for percolation and for non-percolation of information in this model. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We prove a general existence theorem for collapsed ancient solutions to the Ricci flow on compact homogeneous spaces and we show that they converge in the Gromov–Hausdorff topology, under a suitable rescaling, to an Einstein metric on the base of a torus fibration. This construction generalizes all previous known examples in the literature. [ABSTRACT FROM AUTHOR]

Let be a field of characteristic with algebraic closure. Let be a connected reductive -group, and let be a spherical variety over (a spherical homogeneous space or a spherical embedding). Let be a -model (-form) of. We give necessary and sufficient conditions for the existence of a -equivariant -model of. [ABSTRACT FROM AUTHOR]

The quadric Q 2 n is the Z -scheme defined by the equation ∑ i = 1 n x i y i = z (1 − z). We show that Q 2 n is a homogeneous space for the split reductive group scheme SO 2 n + 1 over Z. The quadric Q 2 n is known to have the A 1 -homotopy type of a motivic sphere and the identification as a homogeneous space allows us to give a characteristic independent affine representability statement for motivic spheres. This last observation allows us to give characteristic independent comparison results between Chow–Witt groups, motivic stable cohomotopy groups and Euler class groups. [ABSTRACT FROM AUTHOR]

In contrast to SPD matrices, few tools exist to perform Riemannian statistics on the open elliptope of full-rank correlation matrices. The quotient-affine metric was recently built as the quotient of the affine-invariant metric by the congruence action of positive diagonal matrices. The space of SPD matrices had always been thought of as a Riemannian homogeneous space. In contrast, we view in this work SPD matrices as a Lie group and the affine-invariant metric as a left-invariant metric. This unexpected new viewpoint allows us to generalize the construction of the quotient-affine metric and to show that the main Riemannian operations can be computed numerically. However, the uniqueness of the Riemannian logarithm or the Fréchet mean are not ensured, which is bad for computing on the elliptope. Hence, we define three new families of Riemannian metrics on full-rank correlation matrices which provide Hadamard structures, including two flat. Thus the Riemannian logarithm and the Fréchet mean are unique. The two (flat) vector space structures are particularly appealing because they reduce the manifold of full-rank correlation matrices to a vector space. We also define a nilpotent group structure for which the affine logarithm and the group mean are unique. We provide the main Riemannian/group operations of these four structures in closed form. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of orbit equivalence for semigroup actions and the concept of generalized linear control system on smooth manifold. We prove that, under certain conditions, the semigroup system of a generalized linear control system on a smooth manifold is orbit equivalent to the semigroup system of a linear control system on a homogeneous space. [ABSTRACT FROM AUTHOR]

Risk contributions of portfolios form an indispensable part of risk-adjusted performance measurement. The risk contribution of a portfolio, e.g. in the Euler or Aumann-Shapley framework, is given by the partial derivatives of a risk measure applied to the portfolio profit and loss in the direction of the asset units. For risk measures that are not positively homogeneous of degree 1, however, known capital allocation principles do not apply. We study the class of lambda quantile risk measures that includes the well-known Value-at-Risk as a special case but for which no known allocation rule is applicable. We prove differentiability and derive explicit formulae of the derivatives of lambda quantiles with respect to their portfolio composition, that is, their risk contribution. For this purpose, we define lambda quantiles on the space of portfolio compositions and consider generic (also non-linear) portfolio operators. We further derive the Euler decomposition of lambda quantiles for generic portfolios and show that lambda quantiles are homogeneous in the space of portfolio compositions, with a homogeneity degree that depends on the portfolio composition and the lambda function. This result is in stark contrast to the positive homogeneity properties of risk measures defined in the space of random variables, which admit a constant homogeneity degree. We introduce a generalised version of Euler contributions and Euler allocation rule, which are compatible with risk measures of any homogeneity degree and non-linear but homogeneous portfolios. These concepts are illustrated by a non-linear portfolio using financial market data. [ABSTRACT FROM AUTHOR]

Let k be a number field, G an algebraic group defined over k, and G(k) the group of k-rational points in G. We determine the set of functions on G(k) which are of positive type and conjugation invariant, under the assumption that G(k) is generated by its unipotent elements. An essential step in the proof is the classification of the G(k)-invariant ergodic probability measures on an adelic solenoid naturally associated to G(k). This last result is deduced from Ratner's measure rigidity theorem for homogeneous spaces of S-adic Lie groups; this appears to be the first application of Ratner's theorems in the context of operator algebras. [ABSTRACT FROM AUTHOR]

Let G be a homogeneous group and X1, X2, …, Xm be left invariant real vector fields satisfying Höormander's rank condition on G. We also assume that X1, X2, … Xm are homogeneous of degree one, by applying Moser iterations method, we lift the regularity of solutions for the following equation -Σj-1m Xj²u = λu = |u|p-1u, where λ > 0, 1 < p Q+2/Q-2 and Q is the homogeneous dimension of G. [ABSTRACT FROM AUTHOR]

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0 x 3 v space homogeneous geometry and a 1 x 3 v slab geometry. We use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD. [ABSTRACT FROM AUTHOR]

Novel magnetoencephalography (MEG) systems based on optically pumped magnetometers (OPMs) have undergone rapid development in recent years. However, environmental interference significantly degrades data quality. When the number of sensors in the OPM-MEG system is small, the traditional subspace projection denoising algorithms reliant on sensor space oversampling will be difficult to apply. Although the recently proposed homogeneous field correction (HFC) method resolves this problem by constructing a low-rank spatial model, it lacks the ability to suppress complex environmental interference such as nonhomogeneous fields. Therefore, this paper proposes a novel OPM-MEG environmental interference suppression method based on HFC. We first use a projection operator constructed from a sensor orientation matrix to project original data and empty-room noise data onto the null space of the homogeneous field; this enables dimensionality reduction to eliminate homogeneous field interference. The remaining interference is then suppressed through subspace projection in the space and time domains. We compare our method to four benchmark algorithms based on simulations and somatosensory-evoked experiments. The experimental results demonstrate that the proposed method has better interference suppression performance than the benchmark algorithms. Therefore, our method can provide high signal-to-noise ratio data for subsequent clinical applications and brain scientific research. • An improved subspace projection algorithm for OPM-MEG based on HFC. • Improved ability of HFC to suppress complex environmental interference. • Verified on simulations and somatosensory-evoked data. [ABSTRACT FROM AUTHOR]

We realize steady curved shapes from homogeneous hydrogel flat structures which are in contact with two environments at different chemical conditions. We numerically investigate the behaviour of beam-like and plate-like structures during the transient state, which realize osmotic pumps. Through numerical experiments, we determine the relationship between the difference in the chemical potentials at the top and bottom of a beam and the curvature of the bent beam as well as the Gaussian curvature of a spherical cap morphed from a flat plate. We also propose an approximate modeling of both the beam and the plate, to evaluate explicitly that relationship and show the good agreement between those formulas and the outcomes of the numerical simulations. [ABSTRACT FROM AUTHOR]

We establish the mapping properties of the fractional integral operators on the Herz-Hardy spaces with variable exponents by using extrapolation. In particular, our main results yield the mapping properties for the fractional integral operators on the Herz-Hardy spaces. [ABSTRACT FROM AUTHOR]

This article notably targets the more general (extended) function spaces by investigating the regularity of the weak solutions or turbulent solutions to the Cauchy problem of the 3D magnetic Bénard system by converting it into mathematical symmetric form, in the absence of thermal diffusion, in terms of pressure. In that regard, we successfully improved the results by obtaining sufficient integrable regularity conditions for the pressure and gradient pressure in the homogeneous Besov spaces. [ABSTRACT FROM AUTHOR]

We discuss a gauging procedure that allows us to construct lagrangians that dictate the dynamics of an underlying Cartan geometry. In a sense to be made precise in the paper, the starting datum in the gauging procedure is a Klein pair corresponding to a homogeneous space. What the gauging procedure amounts to is the construction of a Cartan geometry modelled on that Klein geometry, with the gauge field defining a Cartan connection. The lagrangian itself consists of all gauge-invariant top-forms constructed from the Cartan connection and its curvature. After demonstrating that this procedure produces four-dimensional General Relativity upon gauging Minkowski spacetime, we proceed to gauge all four-dimensional maximally symmetric carrollian spaces: Carroll, (anti-)de Sitter-Carroll and the lightcone. For the first three of these spaces, our lagrangians generalise earlier first-order lagrangians. The resulting theories of carrollian gravity all take the same form, which seems to be a manifestation of model mutation at the level of the lagrangians. The odd one out, the lightcone, is not reductive and this means that although the equations of motion take the same form as in the other cases, the geometric interpretation is different. For all carrollian theories of gravity we obtain analogues of the Gauss-Bonnet, Pontryagin and Nieh-Yan topological terms, as well as two additional terms that are intrinsically carrollian and seem to have no lorentzian counterpart. Since we gauge the theories from scratch this work also provides a no-go result for the electric carrollian theory in a first-order formulation. [ABSTRACT FROM AUTHOR]

Nonparametric univariate regression via wavelets is usually implemented under the assumptions of dyadic sample size, equally spaced fixed sample points, and i.i.d. normal errors. In this work, we propose, study and compare some wavelet based nonparametric estimation methods designed to recover a one-dimensional regression function for data that not necessary possess the above requirements. These methods use appropriate regularizations by penalizing the decomposition of the unknown regression function on a wavelet basis of functions evaluated on the sampling design. Exploiting the sparsity of wavelet decompositions for signals belonging to homogeneous Besov spaces, we use some efficient proximal gradient descent algorithms, available in recent literature, for computing the estimates with fast computation times. Our wavelet based procedures, in both the standard and the robust regression case have favorable theoretical properties, thanks in large part to the separability nature of the (non convex) regularization they are based on. We establish asymptotic global optimal rates of convergence under weak conditions. It is known that such rates are, in general, unattainable by smoothing splines or other linear nonparametric smoothers. Lastly, we present several experiments to examine the empirical performance of our procedures and their comparisons with other proposals available in the literature. An interesting regression analysis of some real data applications using these procedures unambiguously demonstrate their effectiveness. [ABSTRACT FROM AUTHOR]

We examine which of the compact connected Lie groups that act transitively on spheres of different dimensions leave the unique spin structure of the sphere invariant. We study the notion of invariance of a spin structure and prove this classification in two different ways; through examining the differential of the actions and through representation theory. [ABSTRACT FROM AUTHOR]

We study the trace inequality for fractional integrals Kα in central Morrey spaces. In particular, we establish necessary condition and sufficient condition governing the inequality ... where (X, ρ, μ) is a space of homogeneous type, a is a point in X and ν is another measure on X. As a corollary, we have necessary and sufficient conditions on power-type weights dν(x) = d(a, x)βdμ(x) for the trace inequality. The results are new even for the Euclidean spaces. [ABSTRACT FROM AUTHOR]

An almost Abelian Lie group is a non-Abelian Lie group with a codimension 1 Abelian normal subgroup. The majority of 3-dimensional real Lie groups are almost Abelian, and they appear in all parts of physics that deal with anisotropic media—cosmology, crystallography etc. In theoretical physics and differential geometry, almost Abelian Lie groups and their homogeneous spaces provide some of the simplest solvmanifolds on which a variety of geometric structures, such as symplectic, Kähler, spin etc., are currently studied in explicit terms. Recently, almost Abelian Lie algebras were classified and studied in details. However, a systematic investigation of almost Abelian Lie groups has not been carried out yet, and the present paper is devoted to an explicit description of properties of this wide and diverse class of groups. The subject of investigation are real almost Abelian Lie groups with their Lie group theoretical aspects, such as the exponential map, faithful matrix representations, discrete and connected subgroups, quotients and automorphisms. The emphasis is put on explicit description of all technical details. [ABSTRACT FROM AUTHOR]

We survey recent work, published since 2015, on equivariant Oka theory. The main results described in the survey are as follows. Homotopy principles for equivariant isomorphisms of Stein manifolds on which a reductive complex Lie group G acts. Applications to the linearisation problem. A parametric Oka principle for sections of a bundle E of homogeneous spaces for a group bundle G , all over a reduced Stein space X with compatible actions of a reductive complex group on E, G , and X. Application to the classification of generalised principal bundles with a group action. Finally, an equivariant version of Gromov's Oka principle based on a notion of a G-manifold being G-Oka. [ABSTRACT FROM AUTHOR]

We present efficient algorithms for computing the N-point correlation functions (NPCFs) of random fields in arbitrary D-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences and provide a natural tool to describe stochastic processes. Typically, algorithms for computing the NPCF components have O(nN) complexity (for a dataset containing n particles); their application is thus computationally infeasible unless N is small. By projecting the statistic onto a suitably defined angular basis, we show that the estimators can be written in a separable form, with complexityO(n²) orO(ng log ng) if evaluated using a Fast Fourier Transform on a grid of size ng. Our decomposition is built upon the D-dimensional hyperspherical harmonics; these form a complete basis on the (D - 1) sphere and are intrinsically related to angular momentum operators. Concatenation of (N - 1) such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As N and D grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: However, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a Julia package implementing our estimators and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. Theefficiency of such estimators will allowhigher-order correlators to become a standard tool in the analysis of random fields. [ABSTRACT FROM AUTHOR]

Lateral inhomogeneity in Earth's mantle affects the tidal response. In this study, the analytical method for determining the effect of lateral inhomogeneity on tidal gravity, presented by Molodenskiy (1980), is introduced. Moreover, the current study reformulates the expressions for estimating the lateral inhomogeneity effects with respect to the unperturbed Earth and supplements some critical derivation process to enhance the method. The effects of lateral inhomogeneity are calculated using several real Earth models. By considering the collective contributions of seismic wave velocity disturbance and density disturbance, the global theoretical changes of semidiurnal gravimetric factor are obtained, which vary from −0.22 % to 0.17 % compared with those in a layered Earth model, no more than 1/3 of the ellipticity's effect. The gravity changes caused by laterally-inhomogeneous disturbance are also computed, and turn out to be up to 0.16 % compared with the changes caused by tide-generating potential. The current study tests the importance of lateral inhomogeneity and other factors. The results indicate that the rotation, ellipticity, and inelasticity on tidal gravity are the most dominant factors, the ocean tide loading is the moderate one, and the lateral inhomogeneity is the least but not negligible factor, because the three-dimensional effect is comparable with ocean tide loading at some locations. Moreover, the amplitude of tidal gravity caused by lateral inhomogeneity is noticeable larger than the precision of superconducting gravimeters. [ABSTRACT FROM AUTHOR]

In this paper, a reaction–diffusion SIRE epidemic model in contaminated environments is proposed, in which the effect of protection for susceptible individuals is included by the nonlinear incidence functions b(S)E$b(S)E$ and g(S)I$g(S)I$. When the space is heterogeneous, the basic reproduction number R0$\mathcal {R}_{0}$ is derived, by which we find that if R0≤1$\mathcal {R}_{0}\le 1$, the disease‐free steady state is globally asymptotically stable, while R0>1$\mathcal {R}_{0}>1$, the disease is uniform persistent. Furthermore, when R0>1$\mathcal {R}_{0}>1$ and additional conditions hold, the global asymptotic stability of special endemic steady state is obtained in homogeneous space. Finally, the theoretical results are validated by numerical simulations, some open questions are illustrated. [ABSTRACT FROM AUTHOR]

For a class of character systems of compact Abelian groups and for homogeneous Banach spaces satisfying some additional regularity conditions, we prove the following alternative: either the Fourier series of an arbitrary function in converges almost everywhere, or there exists a function in whose Fourier series diverges everywhere. We also prove that the classes of divergence sets of Fourier series in such function systems in the above-mentioned spaces are closed under at most countable unions and contain all sets of measure zero. As corollaries, we obtain some well-known and new results on everywhere divergent Fourier series in the trigonometric system as well as in the Walsh and Vilenkin systems and their rearrangements. [ABSTRACT FROM AUTHOR]

We prove a family of sharp multilinear integral inequalities on real spheres involving functions that possess some symmetries that can be described by annihilation by certain sets of vector fields. The Lebesgue exponents involved are seen to be related to the combinatorics of such sets of vector fields. Moreover, we derive some Euclidean Brascamp–Lieb inequalities localized to a ball of radius R, with a blow-up factor of type R δ , where the exponent δ > 0 is related to the aforementioned Lebesgue exponents, and prove that in some cases δ is optimal. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of nonlinear space-time fractional stochastic kinetic equations in R d with Gaussian noise which is white in time and homogeneous in space. This type of equation constitutes an extension of the nonlinear stochastic heat equation involving fractional derivatives in time and fractional Laplacian in space. We firstly give a necessary condition on the spatial covariance for the existence and uniqueness of the solution. Furthermore, we also study various properties of the solution, such as Hölder regularity, the upper bound of second moment, and the stationarity with respect to the spatial variable in the case of linear additive noise. [ABSTRACT FROM AUTHOR]

We present schemes for simulating Brownian bridges on complete and connected Lie groups and homogeneous spaces. We use this to construct an estimation scheme for recovering an unknown left- or right-invariant Riemannian metric on the Lie group from samples. We subsequently show how pushing forward the distributions generated by Brownian motions on the group results in distributions on homogeneous spaces that exhibit a non-trivial covariance structure. The pushforward measure gives rise to new non-parametric families of distributions on commonly occurring spaces such as spheres and symmetric positive tensors. We extend the estimation scheme to fit these distributions to homogeneous space-valued data. We demonstrate both the simulation schemes and estimation procedures on Lie groups and homogenous spaces, including SPD (3) = GL + (3) / SO (3) and S 2 = SO (3) / SO (2) . [ABSTRACT FROM AUTHOR]

Let G be a real Lie group, Λ ≤ G a lattice, and Ω = G / Λ . We study the equidistribution properties of the left random walk on Ω induced by a probability measure μ on G. It is assumed that μ has a finite first moment, and that the Zariski closure of the group generated by the support of μ in the adjoint representation is semisimple without compact factors. We show that for every starting point x ∈ Ω , the μ -walk with origin x has no escape of mass, and equidistributes in Cesàro averages toward some homogeneous measure. This extends several fundamental results due to Benoist-Quint and Eskin-Margulis for walks with finite exponential moment. [ABSTRACT FROM AUTHOR]

We obtain the characterizations of commutators of several versions of maximal functions on spaces of homogeneous type. In addition, with the aid of interpolation theory, we provide weighted version of the commutator theorems by establishing new characterizations of the weighted BMO space. Finally, a concrete example shows that the local version of commutators also has an independent interest. [ABSTRACT FROM AUTHOR]

Rubio de Francia's extrapolation in weighted grand Morrey spaces with weights beyond the Muckenhoupt range is established. Based on this result, the boundedness of maximal and Calderón-Zygmund operators, and commutators of singular integrals in weighted grand Morrey spaces for appropriate class of weights is obtained. The problems are studies for spaces and operators defined on quasi-metric measure spaces (spaces of homogeneous type) but the results are new even for particular cases of spaces of homogeneous type. [ABSTRACT FROM AUTHOR]

Mexico has a sizeable indigenous population, most of whom, although not a homogeneous group, are part of the poorest, most discriminated against, disadvantaged strata of society whose living conditions are below the national and regional average. The authors of this article use information from the Viral Respiratory Diseases Epidemiological Surveillance System to analyze the sociodemographic and health factors associated with the Covid-19-related deaths, looking particularly at this sector of the population. Using a logistical regression model, they identify the factors associated with structural inequalities found among the most significant predictors of death from Covid-19 in the country, showing up the vulnerability of those sectors of the population especially marginalized in the face of the pandemic. [ABSTRACT FROM AUTHOR]