Abstract In this paper we provide a criterion for bi-Lipschitz and differential $${\mathcal {R}}$$ -sufficiency of filtered jets of maps in the context of Newton filtration, taking into account the effect of a singular metric. We adopt a singular metric which is a generalization of another one used by O. M. Abderrahmane in the characterization of $${\mathcal {V}}$$ -sufficiency from the Newton filtration point of view.
A ring R (not necessary associative) is normal with respect to involution σ if xx^σ=x^σx for every x from R. We construct some class of diassociative loops, named Q-loops, with normal loop rings. By definition a loop L is a Q-loop if every two generated subloop of L is a subgroup of some group H⊆ L isomorphic to quaternion group Q_8 .
In this paper we present a family of branch groups that extend the Hanoi Tower group on three pegs in such a manner that many key properties that lead to it having non-trivial rigid kernel are preserved and explicitly calculate the rigid kernel of the commutator subgroups of this family, showing them to be non-trivial.
In this article, we describe all rank-two varieties of nilpotent class-two loops of exponent two. Recall that a variety has rank two if it can be defined by identities involving two variables.
Abstract In the present article, we first introduce the problem of the diffusive logistic equation with memory in Bessel potential spaces, discussing the parameters $$\alpha $$ and $$\widetilde{\eta }$$ and, in particular, their influence on the memory term of the model. Next, we present a result via a lemma that provides an estimate for the integral of a Mittag-Leffler function in terms of the memory effect. Based on this, using the Banach Fixed Point Theorem, Gronwall’s inequality, and the lemma estimating the Mittag-Leffler function, we investigate the existence, uniqueness, regularity, and continuous dependence of weak solutions to the diffusive logistic equation.
This research expository paper analyzes the interplay between symmetric spaces, holonomy groups, and the geometry of submanifolds. We begin by reviewing the Berger holonomy theorem, which classifies the possible holonomy groups of irreducible Riemannian manifolds and reveals their associated geometric structures. We then explore the role of symmetric spaces in submanifold geometry, with a focus on the normal holonomy of Euclidean submanifolds. This result was applied to homogeneous submanifolds and those with constant principal curvatures, highlighting the rigidity and symmetry of such structures. Finally, we investigate complex hyperbolic submanifolds by introducing new tools, in particular the so-called weakly polar actions, for studying pseudo-Riemannian submanifolds. This extends the techniques developed in [7] for obtaining a Berger-type theorem for submanifolds of complex projective space. These new results are based on [6].We hope this overview might provide useful perspectives on these classical yet evolving topics.
The lattice of preradicals over a local uniserial ring has been studied some years ago. In this paper, we study the lattice of quotients of preradicals, which were defined by M.L. Teply and J.E. van den Berg for any associative ring R with identity. When R is a local uniserial ring, we describe these quotients as ternary sequences of length n (the composition length of R) and also as w-paths, which are defined here. These one-to-one correspondences allow us to see the set of quotients of preradicals as a finite distributive lattice with some properties, and whose cardinality we obtain in terms of Motzkin numbers. We explore quotients of certain types of preradicals. We also present a monoid embedding from to , where R and R' have, respectively, composition length n and n+1 .
In this paper, we introduce a differential calculus for functions between totally disconnected spaces within the context of Colombeau’s full generalized numbers and functions. We then study the properties of the Colombeau full differential algebra, including the Embedding Theorem, the Open Mapping Theorem, and the Fundamental Theorem of Calculus. Furthermore, we investigate the existence and uniqueness of solutions to differential equations in the space of Colombeau’s full-tempered generalized functions.
Abstract In this work, we investigate pro- $$\mathcal {C}$$ groups acting on locally finite pro- $$\mathcal {C}$$ trees, where $$\mathcal {C}$$ denotes a class of finite groups closed under taking subgroups, quotients, and extensions. In particular, we focus on a pro- $$\mathcal {C}$$ version of the generalized Baumslag–Solitar group, commonly referred to as a GBS-group.
In this paper we introduce the concepts of Lie g-digroups and the affine g-digroup for a Lie g-digroup. Some properties are studied and geometrical aspects of the actions of sub g-digroups of the affine g-digroup are established like in the Lie group case. Moreover, we use infinitesimal action of Lie algebras to determine whether the tangent space to a bar-unit in a g-digroup has a Leibniz algebra structure.
A polynomial f ∈ℂ[x,y] is a Jacobian mate if the Jacobian J(f,g) = 1 for some g ∈ℂ[x,y] . It is not known that then ℂ[f,g] = ℂ[x,y] and a conjecture that this is the case is the Jacobian conjecture (JC). In this note we will assume that a counterexample to JC exists and obtain additional restrictions on f.
The idempotents elements of the magma monoid (ℳ(S), ◃ ) are characterized. The characterization is used to determine, when S has n elements, the number of idempotents in ℳ(S) (also called ℳ(n) ). A combinatorial argument is inferred and then this generalized principle is used in a larger setting, that is, analogs to the magma monoid are introduced for s-ary operations, and the generalized combinatorial principle is used to determine the number of idempotent elements in those new monomials.In addition, the kernel-cokernel decomposition of idempotents in the binary magma monoid is analyzed and its properties and relations with anticommutative and pseudo-anticommutative operations are established.
We study, in this article, the stochastic Allen–Cahn–Navier–Stokes model in a bounded domain of ℝ^2 . The model consists of the Navier–Stokes equations for the velocity, coupled with a Allen–Cahn model for the order (phase) parameter. We prove the regularity of the solutions in a higher space. The proof uses the It ô formula and the energy method.
This paper presents a new category of tests for assessing time series independence using (h, ϕ ) -divergence and quantile-based symbolization. We derived the test statistic’s asymptotic distribution and proposed a bootstrap version to enhance reliability. Simulation analyses identified optimal parameter values and showed that the proposed tests outperform existing methods in size-corrected power, particularly in Jensen-Shannon, Pearson, Cubic, and Total Variation divergences for various sample sizes. Finally, we applied these tests to stock price data from the Tehran Stock Exchange, confirming the presence of dependence and validating model adequacy.
This paper presents a survey of the Fermat principle within the framework of general relativity, tracing its evolution from classical optics to its modern variational formulation in Lorentzian geometry. In particular, we provide its proof in the framework of smooth lightlike curves. We also analyze the mathematical difficulties inherent in the relativistic setting, specifically demonstrating that the space of lightlike curves in the Sobolev topology does not admit a C^1 -manifold structure due to the cone nature of the null condition. To address these variational obstacles, we discuss alternative frameworks highlighting the role of the quadratic arrival time functional in establishing multiplicity results for light rays. Furthermore, we explore significant extensions of the principle, such as its application to extended sources and receivers, arbitrary arrival curves, timelike geodesics with prescribed proper time, Finsler spacetimes, or settings with a non-continuous interface giving rise to a Snell law.
In the present article, we first introduce the problem of the diffusive logistic equation with memory in Bessel potential spaces, discussing the parameters alpha and (eta) over tilde and, in particular, their influence on the memory term of the model. Next, we present a result via a lemma that provides an estimate for the integral of a Mittag-Leffler function in terms of the memory effect. Based on this, using the Banach Fixed Point Theorem, Gronwall's inequality, and the lemma estimating the Mittag-Leffler function, we investigate the existence, uniqueness, regularity, and continuous dependence of weak solutions to the diffusive logistic equation.
We prove that renormalized solutions of problems for the variation flow can be built as the limit of the corresponding p-Laplacian problems as p goes to 1.
In the present article, we first introduce the problem of the diffusive logistic equation with memory in Bessel potential spaces, discussing the parameters α and η and, in particular, their influence on the memory term of the model. Next, we present a result via a lemma that provides an estimate for the integral of a Mittag-Leffler function in terms of the memory effect. Based on this, using the Banach Fixed Point Theorem, Gronwall’s inequality, and the lemma estimating the Mittag-Leffler function, we investigate the existence, uniqueness, regularity, and continuous dependence of weak solutions to the diffusive logistic equation.
In this paper we provide a criterion for bi-Lipschitz and differential ℛ -sufficiency of filtered jets of maps in the context of Newton filtration, taking into account the effect of a singular metric. We adopt a singular metric which is a generalization of another one used by O. M. Abderrahmane in the characterization of 𝒱 -sufficiency from the Newton filtration point of view.
In this work, we investigate pro- 𝒞 groups acting on locally finite pro- 𝒞 trees, where 𝒞 denotes a class of finite groups closed under taking subgroups, quotients, and extensions. In particular, we focus on a pro- 𝒞 version of the generalized Baumslag–Solitar group, commonly referred to as a GBS-group.
