We define the path coalgebra and Gabriel quiver constructions as functors between the category of k-quivers and the category of pointed k-coalgebras, for k a field. We define a congruence relation on the coalgebra side, show that the functors above respect this relation, and prove that the induced Gabriel k-quiver functor is left adjoint to the corresponding path coalgebra functor. We dualize, obtaining

We introduce several sufficient conditions to guarantee the existence of the Milnor vector field for new classes of singularities of map germs. This special vector field is related with the equivalence problem of the Milnor fibrations for real and complex singularities, if they exit.

Let C be a smooth non-rational projective curve over the complex field \(\mathbb {C}\). If A is an abelian subvariety of the Jacobian J(C), we consider the Abel-Prym map \(\varphi _A : C \rightarrow A\) defined as the composition of the Abel map of C with the norm map of A. The goal of this work is to investigate the degree of the map \(\varphi _A\) in the case where A is one of the components of an

We consider a new class of singularities called mixed maps from Oka’s class. In this new setting we prove the existence of Milnor–Hamm fibration on the tube and sphere. Moreover, we discuss the problem of existence of a Milnor vector field for this class.

We consider the stable ruled surface \(S_1\) over an elliptic curve. There is a unique foliation on \(S_1\) transverse to the fibration. The minimal self-intersection sections also define a 2-web. We prove that the 4-web defined by the fibration, the foliation and the 2-web is locally parallelizable.

We prove that unicritical polynomials \(f(z)=z^d+c\) which are semihyperbolic, i.e., for which the critical point 0 is a non-recurrent point in the Julia set, are uniformly expanding on the Julia set with respect to the metric \(\rho (z) |dz|\), where \(\rho (z) = 1+{{\,\mathrm{dist}\,}}(z,P(f))^{-1+1/d}\) has singularities on the postcritical set P(f). We also show that this metric is Hölder equivalent

In this work, we consider a quasi-homogeneous, corank 1, finitely determined map germ f from \((\mathbb {C}^2,0)\) to \((\mathbb {C}^3,0)\). We consider the invariants m(f(D(f))) and J, where m(f(D(f))) denotes the multiplicity of the image of the double point curve D(f) of f and J denotes the number of tacnodes that appears in a stabilization of the transversal slice curve of \(f(\mathbb {C}^2)\)

In this paper, we investigated influence of \({\mathcal {M}}_p\)-supplemented p-subgroups contained in a normal subgroup on structure of finite groups. We obtained some new criteria for p-supersolvability of finite groups, decided all possible non-Abelian pd-chief factors under our assumption and gave a Frobenius type theorem. Some earlier results on \({\mathcal {M}}_p\)-supplemented p-subgroups appear

We study the action of Bianchi groups on the hyperbolic 3-space \(\mathbb {H}^3 \). Given the standard fundamental domain for this action and any point in \( \mathbb {H}^3 \), we show that there exists an element in the group which sends the given point into the fundamental domain such that its height is bounded by a quadratic function on the coordinates of the point. This generalizes and establishes

We establish cross-ratio invariants for surfaces in 4-space in an analogous way to Uribe-Vargas’s work for surfaces in 3-space. We study the geometric locii of local and multi-local singularities of orthogonal projections of the surface to 3-space. Cross-ratio invariants at \(P_3(c)\)-points are used to recover two moduli in the 4-jet of a projective parametrization of the surface and identify the

This paper deals with the subject of infinitesimal variations of Euclidean submanifolds with arbitrary dimension and codimension. The main goal is to establish a Fundamental theorem for these geometric objects. Similar to the theory of isometric immersions in Euclidean space, we prove that a system of three equations for a certain pair of tensors are the integrability conditions for the differential

We fix a mistake in the argument leading to the proof that the family of foliations introduced in the paper does not have an algebraic solution apart from the line at infinity

In this paper, we classify the Einstein hypersurfaces of \(\mathbb {S}^n \times \mathbb {R}\) and \(\mathbb {H}^n \times \mathbb {R}\). We use the characterization of the hypersurfaces of \(\mathbb {S}^n \times \mathbb {R}\) and \(\mathbb {H}^n \times \mathbb {R}\) whose tangent component of the unit vector field spanning the factor \(\mathbb {R}\) is a principal direction and the theory of isoparametric

In this note we show that the exceptional algebraic set for an infinite discrete group in \(PSL(3,{{\mathbb {C}}})\) should be a finite union of: complex lines, copies of the Veronese curve or copies of the cubic \(xy^2-z^3\).

We describe the generic geometry of the 3D-crosscap (image of a stable map of a 3-manifold into \(\mathbb {R}^4\)) by means of the simultaneous analysis of the generic singularities of height and squared distanced functions on the flag composed by the 3-manifold, the surface of double points and the crosscaps curve at any point of this curve.

We study a relation between coupling introduced by Ebeling (Kodai Math J 29:319-336, 2006) and the polytope duality among families of K3 surfaces.

This paper deals with foliations by curves [s] of degree \( r \ge 2 \) on \( \mathbb {P}^2 \) with isolated singularities S, called non-degenerate if S is reduced and otherwise degenerate. Say that [s] is uniquely determined by a zero-dimensional \( Y \subset S \) if [s] is the unique foliation that vanishes on Y and say that Y is minimal for [s] if, moreover, the degree of Y is the minimal possible

We give an upper (resp. a lower) bound on the largest (resp. the least) eigenvalue of the signless Laplacian matrix of a Hamiltonian graph. These bounds are applied to obtain sufficient spectral conditions for the non-existence of Hamiltonian cycles. Under certain additional assumptions we provide a polynomial time decisive spectral criterion for the Hamiltonicity of a given graph with sufficiently

We establish q-analogues for three summation formulae about the \(\lambda \)-extended Catalan numbers.

The Brasselet number of a function fhnonisolated singularities describes numerically the topological information of its generalized Milnor fibre. In this work, using the Brasselet number, we present several formulas for germs \(f:(X,0)\rightarrow (\mathbb {C},0)\) and \(g:(X,0)\rightarrow (\mathbb {C},0)\) in the case where g has a one-dimensional critical locus. We also give applications when f has

In this paper, the authors establish some asymptotic formulas and two-sided inequalities for the ratio of the gamma function in terms of the digamma function. Considering the application of the gamma function to central Bernoulli coefficients, the authors give some better approximations and two-sided inequalities of central Bernoulli coefficients. Finally, for demonstrating the superiority of our results

In this note we give a simple proof of the following relative analog of the well known Milnor-Palamodov theorem: the Bruce-Roberts number of a function relative to an isolated hypersurface singularity is equal to its topological Milnor number (the rank of a certain relative (co)homology group) if and only if the hypersurface singularity is quasihomogeneous. The proof relies on an interpretation of

In this work we prove the existence of ground state solutions for the following class of problems $$\begin{aligned} \left\{ \begin{array}{ll} \displaystyle - \Delta _1 u + (1 + \lambda V(x))\frac{u}{|u|} &{} = f(u), \quad x \in \mathbb {R}^N, \\ u \in BV(\mathbb {R}^N), &{} \end{array} \right. \end{aligned}$$ where \(\lambda > 0\), \(\Delta _1\) denotes the 1-Laplacian operator which is formally defined

We define a groupoid from a labelled space and show that it is isomorphic to the tight groupoid arising from an inverse semigroup associated with the labelled space. We then define a local homeomorphism on the tight spectrum that is a generalization of the shift map for graphs, and show that the defined groupoid is isomorphic to the Renault-Deaconu groupoid for this local homeomorphism. Finally, we

Let \({\mathbb {G}}=({\mathbb {V}},{\mathbb {E}})\) be the graph obtained by taking the cartesian product of an infinite and connected graph \(G=(V,E)\) and the set of integers \({\mathbb {Z}}\). We choose a collection \({\mathcal {C}}\) of finite connected subgraphs of G and consider a model of Bernoulli bond percolation on \({\mathbb {G}}\) which assigns probability q of being open to each edge whose

In this paper we classify Euclidean hypersurfaces \(f:M^n\rightarrow {\mathbb {R}}^{n+1}\) with a principal curvature of multiplicity \(n-2\) that admit a genuine conformal deformation \({\tilde{f}}:M^n\rightarrow {\mathbb {R}}^{n+2}\). That \({\tilde{f}}:M^n\rightarrow {\mathbb {R}}^{n+2}\) is a genuine conformal deformation of f means that it is a conformal immersion for which there exists no open

Let M be a compact oriented Riemannian manifolds with positive scalar curvature. We first prove a vanishing theorem for p-th Betti number of M, by assuming that the norm of the concircular curvature is less than some positive multiple of the scalar curvature at each point. In the second part, we show that if M has positive scalar curvature, then the existence of non-trivial harmonic p-forms imposes

In the direction towards the question when mixed multiplicities are equal to the Hilbert–Samuel multiplicity of joint reductions, this paper not only generalizes Viet et al. (Proc Am Math Soc 142:1861–1873, 2014, Theorem 3.1) that covers the Rees’s theorem Rees (J Lond Math Soc 29:397–414, 1984, Theorem 2.4), but also removes the hypothesis that joint reductions are systems of parameters in Viet et

In dictionary learning, a matrix comprised of signals Y is factorized into the product of two matrices: a matrix of prototypical atoms D, and a sparse matrix containing coefficients for atoms in D, called X. This process has applications in signal processing, image recognition, and a number of other fields. Many procedures for solving the dictionary learning problem follow the alternating minimization

We provide explicit lower and upper bounds for the maximum number of isolated zeros of the complete Abelian integral associated with a rational polynomial, with non-trivial global monodromy, and a polynomial 1-form of degree n. Moreover, we obtain the explicit form of the relative cohomology of the polynomial 1-forms with respect to the rational polynomial.

Only two balancing numbers \(B_1=1\) and \(B_3=35\) are one away from a perfect powers. Furthermore, each balancing-like sequence has at most three terms which are one away from perfect squares.

Let \((\mathcal {X},\rho ,\mu )\) be Ahlfors-1 regular metric spaces. By developing the Littlewood–Paley characterization of Lipschitz spaces over \((\mathcal {X},\rho ,\mu )\) and establishing a density argument in the weak sense, the authors give a necessary and sufficient condition for the boundedness of Calderón–Zygmund operators on the Lipschitz spaces.

The Riemann problem for isentropic van der Waals fluid flows in a nozzle with discontinuous cross-section is investigated. The pressure, expressed as a function of the density, is increasing and admits two inflection points. The model is not strictly hyperbolic, and the characteristic fields are not genuinely nonlinear. Since the model is written in Eulerian coordinates, it is hard to directly examine

We study the existence of a solution to the mixed boundary value problem for Helmholtz and Poisson type equations in a bounded Lipschitz domain \(\Omega \subset \mathbb {R}^N\) and in \(\mathbb {R}^N{\setminus }\Omega \) for \(N\ge 3\). The boundary \(\partial \Omega \) of \(\Omega \) is the decomposition of \(\Gamma _1,\Gamma _2\subset \partial \Omega \) such that \(\partial \Omega =\Gamma =\overline{\Gamma

In the paper, we generalize the well-known Bellman’s and Popoviciu’s inequalities, and get new Bellman’s and Popoviciu’s type inequalities. These new results provide new estimates on inequalities of these type. As application, we establish a Minkowski inequality, which in special case yields the well-known dual Minkowski inequality for volumes difference.

In this paper, we establish the primal and dual second-order necessary and sufficient optimality conditions for (local) weakly efficient solutions of vector equilibrium problems with constraints in terms of contingent derivatives with 2-steady functions in real finite spaces. Using the 2-steadiness of objective and constraint functions at a given optimal point, the second-order necessary conditions

In this work, we consider a fourth-order plate equation that represents the downward displacement of suspension bridge in the presence of viscoelastic and delay damping. We establish an optimal and general decay estimates with partially hinged boundary conditions under suitable assumptions on the relaxation function. This result improves and generalizes earlier results in the literature such as Kirane