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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]

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 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 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]

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]

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]

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]

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 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]

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]

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]

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 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]

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]

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

This article, titled "Sub-Riemannian Coarea Formula for Classes of Noncontact Mappings of Carnot Groups," discusses the metric properties of level sets of noncontact mappings on Carnot groups. The author explores the possibility of extracting "sub-Riemannian" properties for such mappings and presents the sub-Riemannian analogs of differentiability for classes of mappings. The article also introduces definitions and theorems related to the sub-Riemannian metric properties of noncontact mappings. The results provide insights into the structure of the kernel of the differential and the Hausdorff dimension of level sets. The article concludes with the coarea formula for open sets not containing characteristic points. This research was supported by the Mathematical Center in Akademgorodok. [Extracted from the article]

In this paper, the class of homogeneous Siklos space-times is considered from algebraic point of view and the generalized Ricci solitons are completely classified. [ABSTRACT FROM AUTHOR]

An algebraic variety X is called a homogeneous variety if the automorphism group Aut (X) acts on X transitively, and a homogeneous space if there exists a transitive action of an algebraic group on X. We prove a criterion of smoothness of a suspension to construct a wide class of homogeneous varieties. As an application, we give criteria for a Danielewski surface to be a homogeneous variety and a homogeneous space. Also, we construct affine suspensions of arbitrary dimension that are homogeneous varieties but not homogeneous spaces. [ABSTRACT FROM AUTHOR]

A bosonic Laplacian is a conformally invariant second order differential operator acting on smooth functions defined on domains in Euclidean space and taking values in higher order irreducible representations of the special orthogonal group, in this case, the irreducible representation spaces of homogeneous harmonic polynomials. In this paper, we study boundary value problems involving bosonic Laplacians in the upper-half space and the unit ball. Poisson kernels in the upper-half space and the unit ball are constructed, which give us solutions to the Dirichlet problems with L p boundary data, 1 ≤ p ≤ ∞ . We also prove the uniqueness for solutions to the Dirichlet problems with continuous data for bosonic Laplacians and provide analogs of some properties of harmonic functions for null solutions of bosonic Laplacians, for instance, Cauchy's estimates, the mean-value property, Liouville's Theorem, etc. [ABSTRACT FROM AUTHOR]

We prove that any region \Gamma in a homogeneous n-dimensional and locally compact separable metric space X, where n\geq 2, cannot be irreducibly separated by a closed (n-1)-dimensional subset C with the following property: C is acyclic in dimension n-1 and there is a point b\in C\cap \Gamma having a special local base \mathcal B_C^b in C such that the boundary of each U\in \mathcal B_C^b is acyclic in dimension n-2. In case X is strongly locally homogeneous, it suffices to have a point b\in C\cap \Gamma with an ordinary base \mathcal B_C^b satisfying the above condition. The acyclicity means triviality of the corresponding Čech cohomology groups. This implies all known results concerning the separation of regions in homogeneous connected locally compact spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider homogeneous quasideviation means generated by real functions (defined on (0, ∞)) which are concave around the point 1 and possess certain upper estimates near 0 and ∞. It turns out that their concave envelopes can be completely determined. Using this description, we establish su˚cient conditions for the Hardy property of the homogeneous quasideviation mean and we also furnish an upper estimates for its Hardy constant. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated the projective action of the Lie group SL(3;R) on the homogeneous space RP2. In particular, we have studied the action of the subgroups of SL(3;R) on the non-degenerate conics in the space RP2. Using the Iwasawa decomposition of SL(2;R), we demonstrate that the isotropy subgroup of the projective unit circle is isomorphic to PSL(2;R) under certain conditions. [ABSTRACT FROM AUTHOR]

An existence of invariant hypercomplex structure on compact homogeneous spaces implies strong restrictions on their root structure and consequently on their characteristic Pontrjagin classes and the corresponding Chern classes. We describe these constraints by making use of Lie theory. [ABSTRACT FROM AUTHOR]

In this article, we are concerned with minimal-time optimal problems for the class of controllable linear control system on low-dimensional nonnilpotent solvable Lie groups and their homogeneous spaces.

It was shown that Yang-Mills instantons on an internal space can trigger the expansion of our four-dimensional universe as well as the dynamical compactification of the internal space. We generalize the instanton-induced inflation and dynamical compactification to general Einstein manifolds with positive curvature and also to the FLRW metric with spatial curvature. We explicitly construct Yang-Mills instantons on all Einstein manifolds under consideration and find that the homogeneous and isotropic universe is allowed only if the internal space is homogeneous. We then consider the FLRW metric with spatial curvature as a solution of the eight-dimensional Einstein-Yang-Mills theory. We find that open universe (k = −1) admits bouncing solutions unlike the other cases (k = 0, +1). [ABSTRACT FROM AUTHOR]

We discuss the rolling, without slipping and without twisting, of Stiefel manifolds equipped with α -metrics, from an intrinsic and an extrinsic point of view. We, however, start with a more general perspective, namely, by investigating the intrinsic rolling of normal naturally reductive homogeneous spaces. This gives evidence as to why a seemingly straightforward generalization of the intrinsic rolling of symmetric spaces to normal naturally reductive homogeneous spaces is not possible, in general. For a given control curve, we derive a system of explicit time-variant ODEs whose solutions describe the desired rolling. These findings are applied to obtain the intrinsic rolling of Stiefel manifolds, which is then extended to an extrinsic one. Moreover, explicit solutions of the kinematic equations are obtained, provided that the development curve is the projection of a not necessarily horizontal one-parameter subgroup. In addition, our results are put into perspective with examples of the rolling Stiefel manifolds known from the literature. [ABSTRACT FROM AUTHOR]

We consider mixed-norm Bergman spaces on homogeneous Siegel domains. In the literature, two different approaches have been considered and several results seem difficult to be compared. In this paper, we compare the results available in the literature and complete the existing ones in one of the two settings. The results we present are as follows: natural inclusions, density, completeness, reproducing properties, sampling, atomic decomposition, duality, continuity of Bergman projectors, boundary values, and transference. [ABSTRACT FROM AUTHOR]

Let L be a non-negative self-adjoint operator acting on L 2 (X) where X is a space of homogeneous type with a dimension n. Suppose that the heat kernel of L satisfies the Davies-Gaffney estimates of order m ≥ 2. Let H L 1 (X) be the Hardy space associated with L. In this paper we obtain the sharp endpoint estimate for the Schrödinger group e i t L associated with L such that ‖ (I + L) − n / 2 e i t L f ‖ L 1 (X) + ‖ (I + L) − n / 2 e i t L f ‖ H L 1 (X) ≤ C (1 + | t |) n / 2 ‖ f ‖ H L 1 (X) , t ∈ R for some constant C = C (n , m) > 0 independent of t. We further apply our result to provide the sharp estimate for Schrödinger group of the Kohn Laplacian □ b on polynomial model domains treated by Nagel–Stein [41] , where e − t □ b satisfies only the second order Davies-Gaffney estimates. Moreover, when the heat kernel of L satisfies a Gaussian upper bound, by a duality and interpolation argument, it gives a new proof of a recent result of [13] for sharp endpoint L p -Sobolev bound for e i t L : ‖ (I + L) − s e i t L f ‖ L p (X) ≤ C (1 + | t |) s ‖ f ‖ L p (X) , t ∈ R , s ≥ n | 1 2 − 1 p | for every 1 < p < ∞ , which extends the classical results due to Miyachi ([39,40]) for the Laplacian on the Euclidean space R n. [ABSTRACT FROM AUTHOR]

Let H denote the 3-dimensional Heisenberg Lie group. The main purpose of this paper is to classify all possible linear control systems on the homogeneous spaces of H through its closed subgroups. We expose a detailed study on the control behavior (i.e., controllability property and control sets) of some particular dynamics evolving on non simply connected homogeneous (state) spaces of dimension two and three. [ABSTRACT FROM AUTHOR]

Given a connected simply connected semisimple group G and a connected spherical subgroup K\subseteq G we determine the generators of the extended weight monoid of G/K, based on the homogeneous spherical datum of G/K. Let H\subseteq G be a reductive subgroup and let P\subseteq H be a parabolic subgroup for which G/P is spherical. A triple (G,H,P) with this property is called multiplicity free system and we determine the generators of the extended weight monoid of G/P explicitly in the cases where (G,H) is strictly indecomposable. The extended weight monoid of G/P describes the induction from H to G of an irreducible H-representation \pi :H\to \operatorname {GL}(V) whose lowest weight is a character of P. The space of regular \operatorname {End}(V)-valued functions on G that satisfy F(h_{1}gh_{2})=\pi (h_{1})F(g)\pi (h_{2}) for all h_{1},h_{2}\in H and all g\in G is a module over the algebra of H-biinvariant regular functions on G. We show that under a mild assumption this module is freely and finitely generated. As a consequence the spherical functions of such a type \pi can be described as a family of vector-valued orthogonal polynomials with properties similar to Jacobi polynomials. [ABSTRACT FROM AUTHOR]

Predicting cellular responses to perturbations is an unsolved problem in biology. Traditional approaches assume that different cell types respond similarly to perturbations. However, this assumption does not take into account the context of genome interactions in different cell types, which leads to compromised prediction quality. More recently, deep learning models used to discover gene–gene relationships can yield more accurate predictions of cellular responses. The huge difference in biological information between different cell types makes it difficult for deep learning models to encode data into a continuous low-dimensional feature space, which means that the features captured by the latent space may not be continuous. Therefore, the mapping relationship between the two conditional spaces learned by the model can only be applied where the real reference data resides, leading to the wrong mapping of the predicted target cells because they are not in the same domain as the reference data. In this paper, we propose an information-navigated variational autoencoder (INVAE), a deep neural network for cell perturbation response prediction. INVAE filters out information that is not conducive to predictive performance. For the remaining information, INVAE constructs a homogeneous space of control conditions, and finds the mapping relationship between the control condition space and the perturbation condition space. By embedding the target unit into the control space and then mapping it to the perturbation space, we can predict the perturbed state of the target unit. Comparing our proposed method with other three state-of-the-art methods on three real datasets, experimental results show that INVAE outperforms existing methods in cell state prediction after perturbation. Furthermore, we demonstrate that filtering out useless information not only improves prediction accuracy but also reveals similarities in how genes in different cell types are regulated following perturbation. [ABSTRACT FROM AUTHOR]

We study the double-scaling limit of SYK (DS-SYK) model and elucidate the underlying quantum group symmetry. The DS-SYK model is characterized by a parameter q, and in the q → 1 and low-energy limit it goes over to the familiar Schwarzian theory. We relate the chord and transfer-matrix picture to the motion of a "boundary particle" on the Euclidean Poincaré disk, which underlies the single-sided Schwarzian model. AdS2 carries an action of sl (2, ℝ) ≃ su (1, 1), and we argue that the symmetry of the full DS-SYK model is a certain q-deformation of the latter, namely U q (su (1, 1)). We do this by obtaining the effective Hamiltonian of the DS-SYK as a (reduction of) particle moving on a lattice deformation of AdS2, which has this U q (su (1, 1)) algebra as its symmetry. We also exhibit the connection to non-commutative geometry of q-homogeneous spaces, by obtaining the effective Hamiltonian of the DS-SYK as a (reduction of) particle moving on a non-commutative deformation of AdS3. There are families of possibly distinct q-deformed AdS2 spaces, and we point out which are relevant for the DS-SYK model. [ABSTRACT FROM AUTHOR]

The characterization of Finsler spaces with Ricci curvature is an ancient and cumbersome one. In this paper, we have derived an expression of Ricci curvature for the homogeneous generalized Matsumoto change. Moreover, we have deduced the expression of Ricci curvature for the aforementioned space with vanishing the S-curvature. These findings contribute significantly to understanding the complex nature of Finsler spaces and their curvature properties. [ABSTRACT FROM AUTHOR]

In this paper we study Riesz, Green and logarithmic energy on two-point homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projective spaces. For each of these spaces we provide upper estimates for the mentioned energies using determinantal point processes. Moreover, we determine lower bounds for these energies of the same order of magnitude. [ABSTRACT FROM AUTHOR]

In this paper, we consider homogeneous Finsler spaces with generalized m-Kropina metric. First, we find the formula for the Ricci curvature of a homogeneous Finsler space with aforesaid metric. Further, we derive the formula of the Ricci curvature for generalized m-Kropina metric having vanishing S-curvature. Finally, we derive the formula for the projective Ricci curvature of generalized m-Kropina Finsler metric. [ABSTRACT FROM AUTHOR]

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

We prove an effective version of a result due to Einsiedler, Mozes, Shah and Shapira who established the equidistribution of primitive rational points on expanding horospheres in the space of unimodular lattices in at least three dimensions. Their proof uses techniques from homogeneous dynamics and relies in particular on measure-classification theorems - an approach which does not lend itself to effective bounds. We implement a strategy based on spectral theory, Fourier analysis andWeil's bound for Kloosterman sums in order to quantify the rate of equidistribution for a specific horospherical subgroup in any dimension. We apply our result to provide a rate of convergence to the limiting distribution for the appropriately rescaled diameters of random circulant graphs. [ABSTRACT FROM AUTHOR]

Image segmentation is the process of dividing an image into homogeneous regions according to certain features and is widely used in image processing. Complexly structured images usually contain complex and essential objects. These images are non-linear structural images and they contain a large number of elements with required specifications. The main goal of the proposed EPSO (Exponential Particle Swarm Optimization) algorithm is to prevent local solutions and find the exact global optimal solutions for the task of segmenting medical images. The execution time is compared with well-known segmentation algorithms. The EPSO method is superior to the segmentation methods studied, including the graph algorithm. Comparisons were made with existing segmentation algorithms (Grow cut, Random Walker, DPSO, K-means PSO, and hybrid-K-means ant colony optimization algorithm) in tabular form. [ABSTRACT FROM AUTHOR]

A translation curve in a homogeneous space is a curve such that for a given unit vector at the origin, translation of this vector is tangent to the curve in its every point. Translation curves coincide with geodesics in most Thurston spaces, but not in twisted product Thurston spaces. Moreover, translation curves often seem more intuitive and simpler than geodesics. In this paper, we determine translation curves in Sol 1 4 space. Their curvature properties are discussed and translation spheres are presented. Finally, characterization of geodesics in Sol 1 4 space is given. [ABSTRACT FROM AUTHOR]

In this work, our main concern is to study the existence and multiplicity of solutions for the following sub-elliptic system with Hardy type potentials and multiple critical exponents on Carnot group where is a sub-Laplacian on Carnot group , , is the -natural gauge, and is the horizontal gradient associated to. The positive parameters , satisfy , , and , with , here , and are the critical Hardy-Sobolev exponents, is the homogeneous dimension of the space. By means of variational methods and the mountain-pass theorem of Ambrosetti and Rabonowitz, we study the existence of multiple solutions to the sub-elliptic system. In this work, our main concern is to study the existence and multiplicity of solutions for the following sub-elliptic system with Hardy type potentials and multiple critical exponents on Carnot group where is a sub-Laplacian on Carnot group , , is the -natural gauge, and is the horizontal gradient associated to. The positive parameters , satisfy , , and , with , here , and are the critical Hardy-Sobolev exponents, is the homogeneous dimension of the space. By means of variational methods and the mountain-pass theorem of Ambrosetti and Rabonowitz, we study the existence of multiple solutions to the sub-elliptic system. [ABSTRACT FROM AUTHOR]

In this paper we have studied the growth of meromorphic solutions of higher order homogeneous and non-homogeneous linear difference equations with entire and meromorphic coefficients. We have extended and improved some results of Zhou and Zheng (2017), Belaidi and Benkarouba (2019) by using (p,q)-order and (p,q)-type. [ABSTRACT FROM AUTHOR]

In this paper, we study the bifurcation of nontrivial steady state solutions for a cross-diffusion prey-predator model with homogeneous Neumann boundary conditions. The existence of positive steady state solutions near a bifurcation point is proved using a crossing curve bifurcation theorem. We consider a situation where the transversality condition is not satisfied. Unlike the case in saddle-node bifurcation, the solution set is a pair of transversally intersecting curves. [ABSTRACT FROM AUTHOR]

We propose a new method to construct degenerate 3-(α, δ)-Sasakian manifolds as fiber products of Boothby-Wang bundles over hyperkähler manifolds. Subsequently, we study homogeneous degenerate 3-(α, δ)-Sasakian manifolds and prove that no non-trivial compact examples exist aswell as that there is exactly one family of nilpotent Lie groups with this geometry, the quaternionic Heisenberg groups.

Recent advances in satellite observations of methane provide increased opportunities for inverse modeling. However, challenges exist in the satellite observation optimization and retrievals for high latitudes. In this study, we examine possibilities and challenges in the use of the total column averaged dry-air mole fractions of methane ( XCH 4 ) data over land from the TROPOspheric Monitoring Instrument (TROPOMI) on board the Sentinel 5 Precursor satellite in the estimation of CH 4 fluxes using the CarbonTracker Europe- CH 4 (CTE- CH 4 ) atmospheric inverse model. We carry out simulations assimilating two retrieval products: Netherlands Institute for Space Research's (SRON) operational and University of Bremen's Weighting Function Modified Differential Optical Absorption Spectroscopy (WFM-DOAS). For comparison, we also carry out a simulation assimilating the ground-based surface data. Our results show smaller regional emissions in the TROPOMI inversions compared to the prior and surface inversion, although they are roughly within the range of the previous studies. The wetland emissions in summer and anthropogenic emissions in spring are lesser. The inversion results based on the two satellite datasets show many similarities in terms of spatial distribution and time series but also clear differences, especially in Canada, where CH 4 emission maximum is later, when the SRON's operational data are assimilated. The TROPOMI inversions show higher CH 4 emissions from oil and gas production and coal mining from Russia and Kazakhstan. The location of hotspots in the TROPOMI inversions did not change compared to the prior, but all inversions indicated spatially more homogeneous high wetland emissions in northern Fennoscandia. In addition, we find that the regional monthly wetland emissions in the TROPOMI inversions do not correlate with the anthropogenic emissions as strongly as those in the surface inversion. The uncertainty estimates in the TROPOMI inversions are more homogeneous in space, and the regional uncertainties are comparable to the surface inversion. This indicates the potential of the TROPOMI data to better separately estimate wetland and anthropogenic emissions, as well as constrain spatial distributions. This study emphasizes the importance of quantifying and taking into account the model and retrieval uncertainties in regional levels in order to improve and derive more robust emission estimates. [ABSTRACT FROM AUTHOR]

The curvature characteristics of particular classes of Finsler spaces, such as homogeneous Finsler spaces, are one of the major issues in Finsler geometry. In this paper, we have obtained the expression for S-curvature in homogeneous Finsler space with a generalized Matsumoto metric and demonstrated that the homogeneous generalized Matsumoto space with isotropic S-curvature has to vanish the S-curvature. We have also derived the expression for the mean Berwald curvature by using the formula of S-curvature. [ABSTRACT FROM AUTHOR]

The problem of the classification of the exact solutions to Maxwell's vacuum equations for admissible electromagnetic fields and homogeneous space-time with the group of motions G 3 (V I I I) according to the Bianchi classification is considered. All non-equivalent solutions are found. The classification problem for the remaining groups of motion, G 3 (N) , has already been solved in other papers. All non-equivalent solutions of empty Maxwell equations for all homogeneous spaces with admissible electromagnetic fields are now known. [ABSTRACT FROM AUTHOR]

Topological spaces can be induced by various algebraic ordering relations such as, linear, partial and the inclusion-ordering of open sets forming chains and chain complexes. In general, the classifications of covering spaces are made by using fundamental groups and lifting. However, the Riesz ordered n-spaces and Urysohn interpretations of real-valued continuous functions as ordered chains provide new perspectives. This paper proposes the formulation of covering spaces of n-space charts of a foliated n-manifold containing linearly ordered chains, where the chains do not form topologically separated components within a covering section. The chained subspaces within covering spaces are subjected to algebraic split–join operations under a bijective function within chain-subspaces to form simply directed chains and twisted chains. The resulting sets of chains form simply directed chain-paths and oriented chain-paths under the homotopy path-products involving the bijective function. It is shown that the resulting embedding of any chain in a leaf of foliated n-manifold is homogeneous and unique. The finite measures of topological subspaces containing homotopies of chain-paths in covering spaces generate multiplicative and cyclic group varieties of different orders depending upon the types of measures. As a distinction, the proposed homotopies of chain-paths in covering spaces and the homogeneous chain embedding in a foliated n-manifold do not consider the formation of circular nerves and the Nachbin topological preordering, thereby avoiding symmetry/asymmetry conditions. [ABSTRACT FROM AUTHOR]

This paper classifies the exact solutions of the Maxwell vacuum equations for the case when the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group G 3 (I X) . All the appropriate non-equivalent exact solutions of the Maxwell vacuum equations are found. [ABSTRACT FROM AUTHOR]