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In this paper, we analyze the auto-ignition process of hydrogen in a hot oxidizer stream composed of oxygen–nitrogen and oxygen–water vapor with nitrogen/water vapor mass fractions in a range of 0.1–0.9. The temperature of the oxidizer varies from 1100 K to 1500 K and the temperature of hydrogen is assumed to be 300 K. The research is performed in 1D mixture fraction space and in a forced homogeneous isotropic turbulent (HIT) flow field. In the latter case, the Large Eddy Simulation (LES) method combined with the Eulerian Stochastic Field (ESF) combustion model is applied. The results obtained in mixture fraction space aim to determine the most reactive mixture fraction, maximum flame temperature, and dependence on the scalar dissipation rate. Among others, we found that the ignition in H 2 - O 2 - H 2 O mixtures occurs later than in H 2 - O 2 - N 2 mixtures, especially at low oxidizer temperatures. On the other hand, for a high oxidizer temperature, the ignitability of H 2 - O 2 - H 2 O mixtures is extended, i.e., the ignition occurs for a larger content of H 2 O and takes place faster. The 3D LES-ESF results show that the ignition time is virtually independent of initial conditions, e.g., randomness of an initial flow field and turbulence intensity. The latter parameter, however, strongly affects the flame evolution. It is shown that the presence of water vapor decreases ignitability and makes flames more prone to extinction. [ABSTRACT FROM AUTHOR]

We give a new formula for the Lichnerowicz Laplacian on normal homogeneous spaces in terms of Casimir operators. We derive some practical estimates and apply them to the known list of non-symmetric, compact, simply connected homogeneous spaces G / H with 퐺 simple whose standard metric is Einstein. This yields many new examples of Einstein metrics which are stable in the Einstein–Hilbert sense, which have long been lacking in the positive scalar curvature setting. [ABSTRACT FROM AUTHOR]

Let 퐺 be a real semisimple Lie group with finite centre and without compact factors, Q < G a parabolic subgroup and 푋 a homogeneous space of 퐺 admitting an equivariant projection on the flag variety G / Q with fibres given by copies of lattice quotients of a semisimple factor of 푄. Given a probability measure 휇, Zariski-dense in a copy of H = SL 2 ⁡ (R) in 퐺, we give a description of 휇-stationary probability measures on 푋 and prove corresponding equidistribution results. Contrary to the results of Benoist–Quint corresponding to the case G = Q , the type of stationary measures that 휇 admits depends strongly on the position of 퐻 relative to 푄. We describe possible cases and treat all but one of them, among others using ideas from the works of Eskin–Mirzakhani and Eskin–Lindenstrauss. [ABSTRACT FROM AUTHOR]

This research relies on a two‐stage content analysis of Reddit to test the assumption that by emphasizing othering and polarizing opinions, homogeneous ideological spaces trigger impolite and uncivil comments towards others, as opposed to spaces that enable cross partisan‐ideological exposure, which overall are seen as positive for democracy. It examines subreddits with varying probability of occurrence of echo chamber effects to measure the prevalence and the targets of incivility and studies the interactions in which these comments emerge in discussions about immigration. Findings show that incivility is higher in subreddits that bring together users with the same ideological and political profile, in which echo chamber effects are more likely to occur, but the redditors’ reactions are similar in both types of environments. The targets of incivility vary according to the political orientation of the comments and the political context of the country. [ABSTRACT FROM AUTHOR]

The main focus of this contribution is on the harmonic Bergman spaces ℬαp on the q-homogeneous tree 픛q endowed with a family of measures σα that are constant on the horocycles tangent to a fixed boundary point and turn out to be doubling with respect to the corresponding horocyclic Gromov distance. A central role is played by the reproducing kernel Hilbert space ℬα2 for which we find a natural orthonormal basis and formulae for the kernel. We also consider the atomic Hardy space and the bounded mean oscillation space. Appealing to an adaptation of Calderón–Zygmund theory and to standard boundedness results for integral operators on Lαp spaces with Hörmander-type kernels, we determine the boundedness properties of the Bergman projection. This work was inspired by [J. M. Cohen, F. Colonna, M. A. Picardello and D. Singman, Bergman spaces and Carleson measures on homogeneous isotropic trees, Potential Anal. 44(4) (2016) 745–766, doi:10.1007/s11118-015-9529-7; F. De Mari, M. Monti and M. Vallarino, Harmonic Bergman projectors on homogeneous trees, Potential Anal. 61 (2024) 153–182]. [ABSTRACT FROM AUTHOR]

Selective oxidation of hydrocarbons using molecular oxygen as sole oxidant under mild conditions remains a challenging task. In this context, metal‐organic frameworks (MOFs) have been widely used in various oxidation reactions due to their porosity, high surface area and designability. However, the slow diffusion of substrates/products in micropores of three‐dimensional (3D) bulk MOFs hinders the efficient catalytic performance of such materials. Herein an ultrathin two‐dimensional (2D) porphyrin‐based Zr‐MOF nanosheet (Zr‐TCPP) is synthesized through modulator‐control strategy. Subsequently, various metal ions are anchored into the porphyrin ring by post synthesis modification to afford a series of 2D Zr‐TCPP(M) (M=Mn, Fe, Co, Ni, Cu and Zn). Various structural characterization techniques indicate Zr‐TCPP(M) is nanoflower structure with ultrathin nanoplate petals which provides fully exposed accessible active sites. Among them, Zr‐TCPP(Fe) shows excellent catalytic performance in styrene epoxidation reactions and benzylic C−H oxidation reactions using O2 as sole oxidant under ambient temperature and pressure. The remarkable activity arises from high density of exposed porphyrin‐Fe active sites, low diffusion barriers for substrates and products, as well as a similar homogeneous reaction space. Furthermore, Zr‐TCPP(Fe) nanosheet is easily recycled by centrifugation and reused at least five times without significant loss of catalytic activity. [ABSTRACT FROM AUTHOR]

This paper investigates some well-posedness issues of the fractional inhomogeneous Schrödinger equation i u ˙ - (- Δ) γ u = ± | x | ρ | u | p - 1 u , where 0 < γ < 1 and ρ < 0 . Here, one considers the inter-critical regime 0 < s c : = N 2 - 2 γ + ρ p - 1 < γ , where s c is the energy critical exponent, which is the only one real number satisfying ‖ κ 2 γ + ρ p - 1 u 0 (κ ·) ‖ H ˙ s c = ‖ u 0 ‖ H ˙ s c . In order to avoid a loss of regularity in Strichartz estimates, one assumes that the datum is spherically symmetric. First, using a sharp Gagliardo–Nirenberg-type estimate, one develops a local theory in the space H ˙ γ ∩ H ˙ s c . Then, one investigates the L N (p - 1) ρ + 2 γ concentration of finite-time blow-up solutions bounded in H ˙ s c . Finally, one proves the existence of non-global solutions with negative energy. Since one considers the homogeneous Sobolev space H ˙ s c , the main difficulty here is to avoid the mass conservation law. [ABSTRACT FROM AUTHOR]

In this paper, we consider the parabolic–elliptic Keller–Segel system, which is coupled to the incompressible Navier–Stokes equations through transportation and friction. It is shown that when the system is diffused by Lévy motion, the well‐posedness of the mild solution to the corresponding Cauchy problem in homogeneous Besov spaces is established by means of the Banach fixed point theorem. Furthermore, we prove the Lorentz regularity in time direction and the maximal regularity of solutions. In addition, we obtain the additional regularity and explore the time decay property of global mild solutions. [ABSTRACT FROM AUTHOR]

In this paper, we give the flag curvature formula of general (α, β)-metrics of Berwald type. We study conformally related (α, β)-metrics, especially general (α, β)-metrics that are conformally related to invariant (α, β)-metrics. Also, a necessary and sufficient condition for a Finsler metric conformally related to an (α, β)-metric is given and conformally related Douglas Randers metrics are studied. Finally, we present some examples of conformally related (α, β)-metrics. [ABSTRACT FROM AUTHOR]

In this study, some new necessary and sufficient conditions for a two-weight, weak-type maximal inequality of the form φ 1 (λ) ∫ { x ∈ X : M f (x) > λ } ϱ (x) d μ (x) ≤ c ∫ X φ 2 c | f (x) | σ (x) d μ (x) are obtained in Orlicz classes, where M f is a Hardy–Littlewood maximal function defined on homogeneous spaces and ϱ is a weight function. [ABSTRACT FROM AUTHOR]

The weak-type BMO-regularity property for couples of quasi-Banach lattices of measurable functions was recently introduced as a suitable substitute for the usual BMO-regularity in connection with characterization of the K-closedness of Hardy-type spaces on the unit circle and stability for the real interpolation. It was characterized in terms of the BMO-regularity of couples ((X, Y)α,p, (X, Y)β,q), 0 < α < β < 1, of the real interpolation spaces. In the present note, a natural characterization of this property similar to that of BMO-regularity for couples of Banach lattices (X, Y) in terms of the BMO-regularity of X′Y is extended to couples of lattices of measurable functions on homogeneous type spaces. We also derive equivalent conditions corresponding to the limit case where α = 0. [ABSTRACT FROM AUTHOR]

The traditional approach to the exponential synthesis problem for the space of solutions of a homogeneous convolution-type equation in a convex domain assumes that this space is invariant under some differential operator. This assumption makes it possible to reduce the problem of exponential synthesis to the problem of spectral synthesis. Is this assumption due to the method used to solve the problem, or is the invariance of the solution space necessary for a positive answer to the exponential synthesis problem? To answer this question, we consider special equations of the convolution type, the equations with q-sided convolution. For these equations, we show that the requirement of invariance for the solution space is necessary and cannot be omitted if we assume that the solution space admits exponential synthesis with a free choice of the convex region and the characteristic function of the equation. [ABSTRACT FROM AUTHOR]

The physical capabilities of a reconfigurable assembly system (RAS) increase the agility and responsiveness of the system in highly volatile market conditions. However, achieving optimal RAS utilization entails solving complex optimization problems effectively and efficiently. These optimizations often define homogenous sets of problem instances. While algorithm configuration in such homogeneous contexts traditionally adopts a "one-size-fits-all" approach, recent studies have shown the potential of per-instance algorithm configuration (PIAC) methods in these settings. In this work, we evaluate and compare the performance of different PIAC methods in this context, namely Hydra—a state-of-the-art PIAC method—and a simpler case-based reasoning (CBR) approach. We evaluate the impact of the tuning time budget and/or the number of unique problem instances used for training on each of the method's performance and robustness. Our experiments show that whilst Hydra fails to improve upon the default algorithm configuration, the CBR method can lead to 16% performance increase using as few as 100 training instances. Following these findings, we evaluate Hydra's methodology when applied to homogenous instance spaces. This analysis shows the limitations of Hydra's inference mechanisms in these settings and showcases the advantages of distance-based approaches used in CBR. [ABSTRACT FROM AUTHOR]

In this work, we generalize Kac's original many-particle binary stochastic model to derive a space homogeneous Boltzmann equation that includes a linear combination of higher-order collisional terms. First, we prove an abstract theorem about convergence from a finite hierarchy to an infinite hierarchy of coupled equations. We apply this convergence theorem on hierarchies for marginals corresponding to the generalized Kac model mentioned above. As a corollary, we prove propagation of chaos for the marginals associated to the generalized Kac model. In particular, the first marginal converges towards the solution of a Boltzmann equation including interactions up to a finite order and whose collision kernel is of Maxwell type with cut-off. [ABSTRACT FROM AUTHOR]

For linear control systems with bounded control range, chain controllability properties are analyzed. It is shown that there exists a unique chain control set and that it equals the sum of the control set around the origin and the center Lyapunov space of the homogeneous part. For the proof, the linear control system is extended to a bilinear control system on an augmented state space. This system induces a control system on projective space. For the associated control flow, attractor-repeller decompositions are used to show that the control system on projective space has a unique chain control set that is not contained in the equator. It is given by the image of the chain control set of the original linear control system. [ABSTRACT FROM AUTHOR]

We study the limiting distribution of dense orbits of a lattice subgroup |$\Gamma \leq \textrm{SL}(m+1,\mathbb{R})$| acting on |$H\backslash \textrm{SL}(m+1,\mathbb{R})$|⁠ , with respect to a filtration of growing norm balls. The novelty of our work is that the groups |$H$| we consider have infinitely many non-trivial connected components. For a specific such |$H$|⁠ , the homogeneous space |$H\backslash G$| identifies with |$X_{m,m+1}$|⁠ , a moduli space of rank |$m$| -discrete subgroups in |$\mathbb{R}^{m+1}$|⁠. This study is motivated by the work of Shapira-Sargent who studied random walks on |$X_{2,3}$|⁠. [ABSTRACT FROM AUTHOR]

We prove two rigidity results on holomorphic isometries into homogeneous Kähler manifolds. The first shows that a Kähler-Ricci soliton induced by the homogeneous metric of the Kähler product of a special generalized flag manifold (i.e. a flag of classical type or integral type) with a bounded homogeneous domain is trivial, i.e. Kähler-Einstein. In the second one we prove that: (i) a flat space is not relative to the Kähler product of a special generalized flag manifold with a homogeneous bounded domain, (ii) a special generalized flag manifold is not relative to the Kähler product of a flat space with a homogeneous bounded domain and (iii) a homogeneous bounded domain is not relative to the Kähler product of a flat space with a special generalized flag manifold. Our theorems strongly extend the results of Cheng and Hao [Ann. Global Anal. Geom. 60 (2021), pp. 167–180], Cheng, Di Scala, and Yuan [Internat. J. Math. 28 (2017), p. 1750027], Loi and Mossa [Proc. Amer. Math. Soc. 149 (2021), pp. 4931–4941], Loi and Mossa [Proc. Amer. Math. Soc. 151 (2023), pp. 3975–3984] and Umehara [Tokyo J. Math. 10 (1987), pp. 203–214]. [ABSTRACT FROM AUTHOR]

We say that a sequence of proper geodesic spaces Xn ​ consists of almost homogeneous spaces if there is a sequence of discrete groups of isometries Gn ​ ≤ Iso(Xn) with diam(Xn/Gn) → 0 as n → ∞. We show that if a sequence (Xn, pn) of pointed almost homogeneous spaces converges in the pointed Gromov-Hausdorff sense to a space (X, p), then X is a nilpotent locally compact group equipped with an invariant geodesic metric. Under the above hypotheses, we show that if X is semi-locally-simply-connected, then it is a nilpotent Lie group equipped with an invariant sub-Finsler metric, and for n large enough, π1(X) is a subgroup of a quotient of π1(Xn). [ABSTRACT FROM AUTHOR]

We review some works on non-classical boundary conditions, and loading devices inspired by discussions with late Professor J.L. Ericksen. For a circular contact area between a body and a linearly elastic, isotropic and homogeneous half space as a loading device, we estimate the constant in the classical Winkler's expression of the normal surface traction at a point of the contact region in terms of the normal to the surface displacement of the same point. We also provide expressions for the tangential tractions at points of the common interface between the body and the loading device. The surface tractions are in general functionals of the contact surface displacements and their tangential derivatives. It is shown that many boundary conditions fall outside the usual definition of natural boundary conditions and may require special treatments in numerically solving boundary-value problems. [ABSTRACT FROM AUTHOR]

Let X be a space of homogeneous type. Assume that L is a non negative, selfadjoint operator on L 2 (X) satisfying the sub-Gaussian upper bounds. In this paper, we prove that ‖ (I + L) - n / 2 e i τ L f ‖ 1 , ∞ ≤ C (1 + | τ |) n / 2 ‖ f ‖ 1 , ∀ τ ∈ R. By interpolation, we obtain ‖ (I + L) - n | 1 / p - 1 / 2 | e i τ L f ‖ p ≤ C (1 + | τ |) n | 1 / p - 1 / 2 | ‖ f ‖ p , ∀ τ ∈ R , 1 < p < ∞. [ABSTRACT FROM AUTHOR]

We consider families of conical Kähler–Einstein metrics on rank one horosymmetric Fano manifolds, with decreasing cone angles along a codimension one orbit. At the limit angle, which is positive, we show that the metrics, restricted to the complement of that orbit, converge to (the pull‐back of) the Kähler–Einstein metric on the basis of the horosymmetric homogeneous space, which is a projective homogeneous space. Then we show that, on the symmetric space fibers, the rescaled metrics converge to Stenzel's Ricci flat Kähler metric. [ABSTRACT FROM AUTHOR]

In this paper, we prove an existence result for a quasilinear elliptic variational inequality of the form u ∈ K ⊂ V : 0 ∈ - Δpu+aF(u) + ...IK(u) ∈ V* in the whole ℝ N under bilateral constraints K given by K = {v ∈ V : ϕ (x) ≤ v(x) ≤ Ψ(x) a.e. in ℝ N}, where Δp is the p-Laplacian, the underlying solution space V is the homogeneous Sobolev space (also called Beppo-Levi space) V = D1,p(ℝN) with 1 < p < N, and IK : V → ℝ U {+∞} is the indicator functional corresponding to K with its subdifferential ...IK. The lower order Nemytskij operator F is generated by a Carathéodory function f : ℝN x ℝ → ℝ, and the measurable and bounded coefficient α is supposed to decay like |x|- (N+α) at infinity. The growth conditions that we impose on f are such that the operator -- Δp + aF : V → V*, in general, is not coercive with respect to K which prevents us from applying standard existence results. Another difficulty, which arises due to the lack of compact embedding of V into Lq(ℝN) spaces, needs to be overcome in an appropriate way. Without assuming additional assumptions such as the existence of sub- and supersolutions, we are able not only to prove the existence of solutions, but also show the compactness of the set of all solutions in V. Finally, an extension of the theory is established, which allows us to deal with noncoercive bilateral variational-hemivariational inequalities in ℝN. The proof of our main existence result is based on a modified penalty approach. [ABSTRACT FROM AUTHOR]

Over function fields of p -adic curves, we construct stably rational varieties in the form of homogeneous spaces of SL n with semisimple simply connected stabilizers and we show that strong approximation away from a non-empty set of places fails for such varieties. The construction combines the Lichtenbaum duality and the degree 3 cohomological invariants of the stabilizers. We then establish a reciprocity obstruction which accounts for this failure of strong approximation. We show that this reciprocity obstruction to strong approximation is the only one for counterexamples we constructed, and also for classifying varieties of tori. We also show that this reciprocity obstruction to strong approximation is compatible with known results for tori. At the end, we explain how a similar point of view shows that the reciprocity obstruction to weak approximation is the only one for classifying varieties of tori over p -adic function fields. [ABSTRACT FROM AUTHOR]

We have classified in [7] all linear control systems and studied their controllability and control sets on the homogeneous spaces L ﹨ H of the 3-dimensional Heisenberg group H through its closed subgroups L. In this paper, we characterize the controllability and control sets of the induced linear control systems in the homogeneous spaces left. In particular, we focus on the singularity of the induced drift vector fields. Quite a technical analysis with many cases reveals the control sets. We give some geometric illustrations. [ABSTRACT FROM AUTHOR]

We study structurable algebras and their associated Freudenthal triple systems over commutative rings. The automorphism groups of these triple systems are exceptional groups of type E 7 , and we realize groups of type E 6 as centralizers. When 6 is invertible, we further give a geometric description of homogeneous spaces of type E 7 / E 6 , and show that they parametrize principal isotopes of Brown algebras. As opposed to the situation over fields, we show that such isotopes may be non-isomorphic. [ABSTRACT FROM AUTHOR]

We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmetric matrices, and the entire space of matrices of a given size. The construction uses twisted tensor products and their deformations combined with invariance properties derived from quantum symmetric pairs. These quantum Weyl algebras admit U q (gl N) -module algebra structures compatible with standard ones on the polynomial part, have relations that are expressed nicely via matrices, and are closely related to an algebra arising in the theory of quantum bounded symmetric domains. [ABSTRACT FROM AUTHOR]

The paper considers an axisymmetric stress state of a homogeneous elastic space with a circular disc-shaped crack, one of the edges of which is pressed into a cylindrical circular stamp with static friction. It is assumed that the contact zone is considered under the generalized law of dry friction, i.e. tangential contact stresses are proportional to normal contact pressure, while the proportionality coefficient depends on the radial coordinates of the points of the contacting surfaces and is directly proportional to them. Considering the fact that in this case the Abel images of contact stresses are also related in a similar way, the solution of the problem, with the help of rotation operators and theory of analytical functions, is reduced to an inhomogeneous Riemann problem for two functions and the closed solution in quadratures is constructed. A numerical analysis was carried out and regularities of changes in both normal and shear real contact stresses, as well as rigid displacement of the stamp depending on the physical and geometric parameters were revealed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the 3D incompressible magnetohydrodynamic equations and establish several logarithmically improved regularity criteria in the homogeneous Besov space. These criteria are based on certain assumptions made in the velocity field and pressure, respectively. The first result solely based on the velocity field indicates that the velocity field plays a dominant role in determining the regularity of weak solutions, when compared with the magnetic field. [ABSTRACT FROM AUTHOR]

In this paper we study the harmonic map heat flow on the euclidean space R d and we show an unconditional uniqueness result for maps with small initial data in the homogeneous Besov space B ˙ p , ∞ d p (R d) where d < p < ∞. As a consequence we obtain decay rates for solutions of the harmonic map flow of the form ‖ ∇ u (t) ‖ L ∞ (R d) ≤ C t − 1 2 . Additionally, under the assumption of a stronger spatial localization of the initial conditions, we show that the temporal decay happens in a self-similar way. We also explain that similar results hold for the biharmonic map heat flow and the semilinear heat equation with a power-type nonlinearity. [ABSTRACT FROM AUTHOR]

In this paper, the local existence and uniqueness of weak solutions to a d-dimensional non-resistive MHD equations in homogeneous Besov spaces are studied. Specifically we obtain the local existence of a weak solution $ (u,b) $ (u , b) of the non-resistive MHD equations for the initial data $ u_0\in \dot B^{\frac {d}{p}-1}_{p,1}(\mathbb {R}^{d}) $ u 0 ∈ B ˙ p , 1 d p − 1 (R d) and $ b_0\in \dot B^{\frac {d}{p}}_{p,1}(\mathbb {R}^{d}) $ b 0 ∈ B ˙ p , 1 d p (R d) with $ 1\le p \le \infty $ 1 ≤ p ≤ ∞ , and the uniqueness of the weak solution when $ 1\le p\le 2d $ 1 ≤ p ≤ 2 d. Compared with the previous results for the non-resistive MHD equations, in the local existence part, the range of p extends to $ 1\le p \le \infty $ 1 ≤ p ≤ ∞ from $ 1\le p\le 2d $ 1 ≤ p ≤ 2 d , but the uniqueness of the solution requires $ 1\le p\le 2d $ 1 ≤ p ≤ 2 d yet. [ABSTRACT FROM AUTHOR]

We prove effective density of random walks on homogeneous spaces, assuming that the underlying measure is supported on matrices generating a dense subgroup and having algebraic entries. The main novelty is an argument passing from high dimension to effective equidistribution in the setting of random walks on homogeneous spaces, exploiting the spectral gap of the associated convolution operator. [ABSTRACT FROM AUTHOR]

The wonderful compactification X m of a symmetric homogeneous space of type AIII (2 , m) for each m ≥ 4 is Fano, and its blowup Y m along the unique closed orbit is Fano if m ≥ 5 and Calabi–Yau if m = 4. Using a combinatorial criterion for K-polystability of smooth Fano spherical varieties obtained by Delcroix, we prove that X m admits a Kähler–Einstein metric for each m ≥ 4 and Y m admits a Kähler–Einstein metric if and only if m = 4 , 5. [ABSTRACT FROM AUTHOR]

We investigate variational, Lie and Killing symmetries of the Lagrangian of an essential class of four-dimensional (pseudo-)Riemannian manifolds, i.e., non-reductive homogeneous spaces. Moreover, a Lie algebra analysis is shown. With the help of a result of the Noether's theorem, we have presented the expressions for conservation laws corresponding to all variational symmetries. [ABSTRACT FROM AUTHOR]

An analytical solution to the dynamic response of a functionally graded cylindrical tube embedded in a full homogeneous space subjected to elastic SH waves is presented using the wavefunction expansion method. The shear modulus of the functionally graded tube is assumed to have a power-law variation with radius. The wave fields in the tube and unbounded surrounding medium are derived in a form of wavefunction series with unknown coefficients. The wave field coefficients are obtained by satisfying the boundary conditions at the inner and outer tube surfaces. The influences of the inhomogeneity exponent, shear modulus and thickness of the functionally graded tube, and the frequency of the incident SH waves on the dynamic stress concentration factor (DSCF) of the tube are systematically discussed. It is concluded that the application of functionally graded materials (FGMs) with a positive inhomogeneity exponent tends to weaken the DSCF along the inner surface of the tube significantly but intensify that along the outer surface slightly, which is beneficial to the long-term use of the tube. [ABSTRACT FROM AUTHOR]

We investigate three aspects of weak* convergence of the n-step distributions of random walks on finite volume homogeneous spaces $ G/\Gamma $ G / Γ of semisimple real Lie groups. First, we look into the obvious obstruction to the upgrade from Cesàro to non-averaged convergence: periodicity. We give examples where it occurs and conditions under which it does not. In a second part, we prove convergence towards Haar measure with exponential speed from almost every starting point. Finally, we establish a strong uniformity property for the Cesàro convergence towards Haar measure for uniquely ergodic random walks. [ABSTRACT FROM AUTHOR]

In this paper, we apply a result of the classification of a compact cohomogeneity one Riemannian manifold with a compact Lie group G to obtain a classification of compact cohomogeneity one locally conformal Kähler manifolds. In particular, we prove that the compact complex manifold is a complex one-dimensional torus bundle over a projective rational homogeneous, or cohomogeneity one manifold except of a class of manifolds with a generalized Hopf surface bundle over a projective rational homogeneous space. Additionally, it is a homogeneous compact complex manifold under the complexification G C of the given compact Lie group G under an extra condition that the related closed one form is cohomologous to zero on the generic G orbit. Moreover, the semi-simple part S of the Lie group action has hypersurface orbits, i.e., it is of cohomogeneity one with respect to the semi-simple Lie group S in that special case. [ABSTRACT FROM AUTHOR]

We show that, for any n\geq 2, there exists a homogeneous space of dimension d=8n-4 with metrics of Ric_{\frac {d}{2}-5}>0 if n\neq 3 and Ric_6>0 if n=3 which evolve under the Ricci flow to metrics whose Ricci tensor is not (d-4)-positive. Consequently, Ricci flow does not preserve a range of curvature conditions that interpolate between positive sectional and positive scalar curvature. This extends a theorem of Böhm and Wilking [Geom. Funct. Anal. 17 (2007), pp. 665–681] in the case of n=2. [ABSTRACT FROM AUTHOR]

Many matrix‐valued functions of an m×m Wishart matrix W, Fk(W), say, are homogeneous of degree k in W, and are equivariant under the conjugate action of the orthogonal group 풪(m), that is, Fk(HWHT)=HFk(W)HT, H∈풪(m). It is easy to see that the expectation of such a function is itself homogeneous of degree k in ∑, the covariance matrix, and are also equivariant under the action of 풪(m) on ∑. The space of such homogeneous, equivariant, matrix‐valued functions is spanned by elements of the type Wrpλ(W), where r∈{0,...,k} and, for each r, λ varies over the partitions of k−r, and pλ(W) denotes the power‐sum symmetric function indexed by λ. In the analogous case where W is replaced by W−1, these elements are replaced by W−rpλ(W−1). In this paper, we derive recurrence relations and analytical expressions for the expectations of such functions. Our results provide highly efficient methods for the computation of all such moments. [ABSTRACT FROM AUTHOR]

Our examination of quadratic curvature functionals in Generalized Symmetric Spaces has resulted in the comprehensive classification of critical metric sets within diverse categories of these spaces. [ABSTRACT FROM AUTHOR]

The high‐frequency sea level oscillations (SLO) associated with meteotsunamis can have hazardous consequences for coastal populations. They are triggered by high‐frequency atmospheric disturbances generating an oceanic response that is amplified mainly by Proudman and harbor resonance. So far, the lack of high‐resolution data had prevented a comprehensive characterization of these atmospheric disturbances, even in an extensively studied "hot spot" as Ciutadella (Balearic Islands). Here, we analyze atmospheric disturbances triggering meteotsunamis in Ciutadella during 2021 using data from an ultra‐dense meteorological network (BalearsMeteo). Atmospheric pressure time series with a sampling rate ≤1 min are used to estimate propagation speed and direction, spectral energy content, and the spatial homogeneity of atmospheric disturbances linked to meteotsunami events. We find that the spatial structure of the disturbances are rather heterogeneous, but the inferred propagation velocities are consistent with the occurrence of Proudman resonance on the continental shelves located upstream of Ciutadella (speeds between 24 and 36 m/s and directions from 210° to 260°). Although during meteotsunami events these velocity estimates undergo some changes both in time and in space, they show two key characteristics: (a) the atmospheric pressure disturbances are mostly non‐dispersive; and (b) the largest SLO are observed when the speed and direction of propagation velocities are more homogeneous in space and time. Nevertheless, an empirical relationship between the analyzed atmospheric features and the SLO amplitudes could not be established. That is, the prediction of meteotsunami amplitudes remains challenging due to the intricate interplay of atmospheric and oceanic processes. Plain Language Summary: Meteotsunamis are extreme sea level oscillations that can cause rapid sea level changes of several meters in just a few minutes. The flooding and currents associated with this rapid sea level change are dangerous for coastal infrastructure and even to human lives. Meteotsunamis are generated by rapid changes in the atmospheric pressure that generate a sea wave. Since the atmospheric perturbations are not strong enough to generate large sea waves, it is necessary that a chain of amplification mechanism acts on the generated sea wave to amplify it before reaching the coast. In this process the characteristics of the atmospheric disturbances is a key parameter that conditions the amplification process. In the present work, we use the atmospheric pressure data collected in the Balearic Islands by an ultra‐dense meteorological network to analyze in detail the atmospheric disturbances that generate meteotsunamis in Ciutadella harbor. This new set of data allows us to study with an unprecedented level of detail the spatial structure of the atmospheric disturbances and to estimate for first time the time evolution of their propagation velocity in different locations. Therefore, these results provide evidence of the complexity of the atmospheric disturbances that generate the meteotsunamis. Key Points: We characterize the atmospheric disturbances generating meteotsunamis in the Balearic Islands using an ultra‐dense observational networkThe atmospheric disturbances generating meteotsunamis have a significant spatial and temporal variabilityNo clear relationship is found between any of the analyzed characteristics of the perturbations and the meteotsunami magnitude [ABSTRACT FROM AUTHOR]

We extend the results about left-invariant Codazzi tensor fields on Lie groups equipped with left-invariant Riemannian metrics obtained by d’Atri in 1985 to the setting of reductive homogeneous spaces G/H, where the curvature of the canonical connection of second kind associated with the fixed reductive decomposition g = h ⊕ m enters the picture. In particular, we show that invariant Codazzi tensor fields on a naturally reductive homogeneous space are parallel. [ABSTRACT FROM AUTHOR]

We study hypersurfaces of the four‐dimensional Thurston geometry Sol04$\mathrm{Sol}^4_0$, which is a Riemannian homogeneous space and a solvable Lie group. In particular, we give a full classification of hypersurfaces whose second fundamental form is a Codazzi tensor—including totally geodesic hypersurfaces and hypersurfaces with parallel second fundamental form—and of totally umbilical hypersurfaces of Sol04$\mathrm{Sol}^4_0$. We also give a closed expression for the Riemann curvature tensor of Sol04$\mathrm{Sol}^4_0$, using two integrable complex structures. [ABSTRACT FROM AUTHOR]

This note addresses the problem of recovering a convex set of homogeneous polynomials from the subset of its extreme points, i.e., the justification of a polynomial version of the classical Krein–Milman theorem. Not much was done in this direction. The existing papers deal mostly with the description of the extreme points of the unit ball in the space of homogeneous polynomials in various special cases. Even in the case of linear operators, the classical Krein–Milman theorem does not work, since closed convex sets of operators turn out to be compact in some natural topology only in rather special cases. In the 1980s, a new approach to the study of the extremal structure of convex sets of linear operators was proposed on the basis of the theory of Kantorovich spaces, which led to an operator form of the Krein–Milman theorem. Combining the approach with the linearization method for homogeneous polynomials, we obtain a version of the Krein–Milman theorem for homogeneous polynomials. Namely, a weakly order bounded, operator convex, and pointwise order closed set of homogeneous polynomials from an arbitrary vector space to a Kantorovich space is the pointwise order closure of the operator convex hull of the extreme points of . We also establish Milman's converse of the Krein–Milman theorem for homogeneous polynomials: The extreme points of the smallest operator convex pointwise order closed set including a given set of homogeneous polynomials are pointwise uniform limits of appropriate nets of mixings in . A mixing of a family of polynomials with the values in a Kantorovich space is understood as the (infinite) sum of these polynomials multiplied by pairwise disjoint order projections with sum the identity operator in the Kantorovich space. [ABSTRACT FROM AUTHOR]

The equivalence of the Haar system in a rearrangement invariant space on and a sequence of pairwise disjoint functions in some Lorentz space is known to imply that up to the equivalence of norms. We show that the same holds for the class of uniform disjointly homogeneous rearrangement invariant spaces and obtain a few consequences for the properties of isomorphic embeddings of such spaces. In particular, the space with is the only uniform -disjointly homogeneous rearrangement invariant space on with nontrivial Boyd indices which has two rearrangement invariant representations on the half-axis . [ABSTRACT FROM AUTHOR]

• The dissimilar material and the crack are treated as inhomogeneities of different elastic modulus based on the EIM. • A semi-analytical model for two joined dissimilar materials with interfacial cracks is established and validated. • Parametric analysis on rupture performance of joined materials with interfacial cracks are carried out. Existing interfacial cracks in two joined dissimilar materials play a crucial role in determining the stress concentration and its further propagation, which severely affects the interfacial strength of the bi-materials, even leading to its debonding failure under external loading. This study proposes a semi-analytical method (SAM) to analyze the elastic field of two joined dissimilar materials with interfacial cracks. One of the two dissimilar materials is treated as an inhomogeneity having different material properties from the other and the crack is regarded as a line inhomogeneity whose elastic modulus equals to zero, hence the problem for the two joined dissimilar materials with an interfacial crack is converted to a homogeneous half space material problem with the assistance of the well-known Eshelby equivalent inclusion method (EIM). The results obtained with the SAM agree very well with those with the finite element method (FEM), providing a verification for the proposed method. Cases studies are conducted to explore the influences of the material mismatch, the length and the depth of the crack, the friction coefficient and the loading location on the elastic field of the two joined dissimilar materials, demonstrating that this work has potential in the analysis of joined dissimilar materials with interfacial cracks. [ABSTRACT FROM AUTHOR]

Graph clustering has been a hot research topic and is widely used in many fields, such as community detection in social networks. Lots of works combining auto-encoder and graph neural networks have been applied to clustering tasks by utilizing node attributes and graph structure. These works usually assumed the inherent parameters (i.e., size and variance) of different clusters in the latent embedding space are homogeneous, and hence the assigned probability is monotonous over the Euclidean distance between node embeddings and centroids. Unfortunately, this assumption usually does not hold since the size and concentration of different clusters can be quite different, which limits the clustering accuracy. In addition, the node embeddings in deep graph clustering methods are usually L2 normalized so that it lies on the surface of a unit hyper-sphere. To solve this problem, we proposed Deep Adaptive Graph Clustering via von Mises-Fisher distributions, namely DAGC. DAGC assumes the node embeddings H can be drawn from a von Mises-Fisher distribution and each cluster k is associated with cluster inherent parameters ρk which includes cluster center μ and cluster cohesion degree κ. Then we adopt an EM-like approach (i.e., (H|ρ) and (ρ|H), respectively) to learn the embedding and cluster inherent parameters alternately. Specifically, with the node embeddings, we proposed to update the cluster centers in an attraction-repulsion manner to make the cluster centers more separable. And given the cluster inherent parameters, a likelihood-based loss is proposed to make node embeddings more concentrated around cluster centers. Thus, DAGC can simultaneously improve the intra-cluster compactness and inter-cluster heterogeneity. Finally, extensive experiments conducted on four benchmark datasets have demonstrated that the proposed DAGC consistently outperforms the state-of-the-art methods, especially on imbalanced datasets. [ABSTRACT FROM AUTHOR]

We consider vector-valued elliptic boundary value problems and parabolic initial-boundary value problems on abstract Banach spaces of class HT. For a very general class of boundary conditions, which includes, but is not limited to the classical cases of Dirichlet, Neumann and Robin boundary conditions, we show L p -maximal regularity of the system. We do not restrict ourselves to the homogeneous case, but also identify the temporal and boundary trace spaces, which are both sufficient and necessary to obtain a unique solution in the L p -maximal regularity space. Our results are based on a (partial) Fourier–Laplace transform of the problem in the half-space case, leading to elliptic boundary value problems which have to satisfy variants of the Lopatinskii–Shapiro condition [34] to be solvable. The parabolic theory is then developed with use of tools from modern harmonic analysis such as the bounded H ∞ -calculus and the Kalton–Weis theorem. [ABSTRACT FROM AUTHOR]

Let F be an algebraically closed field of characteristic different from 2. We show that the images of multilinear ⁎-graded polynomials on U T 2 are homogeneous vector spaces. An analogous result holds for U T 3 endowed with non-trivial grading. We further show that these results are optimal, in the following sense: there exist multilinear ⁎-graded polynomials whose image on U T n (n ≥ 3) with the trivial grading is not a vector space, and whose image on U T n (n ≥ 4) with the natural Z n -grading is also not a vector space. In particular, an analog of the L'vov-Kaplansky conjecture can not be expected in the setting of algebras with (graded) involutions. [ABSTRACT FROM AUTHOR]

In this paper, we study left-invariant cross curvature solitons on Lorentzian three-dimensional Lie groups and classify these solitons. [ABSTRACT FROM AUTHOR]