This paper develops a technique to represent linear functionals on spaces of homogeneous polynomials between Banach spaces. This technique applies to cases that are not covered by the classical polynomial Borel transform. We provide applications to represent linear functionals on spaces of approximable, compact, hyper-nuclear and hyper-\(\sigma (p)\)-nuclear polynomials. An unexpected difference between

It is known that the lengths of closed geodesics of an arithmetic hyperbolic orbifold are related to Salem numbers. We initiate a quantitative study of this phenomenon. We show that any non-compact arithmetic 3-dimensional orbifold defines \(c Q^{1/2} + O(Q^{1/4})\) square-rootable Salem numbers of degree 4 which are less than or equal to Q. This quantity can be compared to the total number of such

Let \(k\ge 2\). A generalization of the well-known Fibonacci sequence is the k-Fibonacci sequence. For this sequence, the first k terms are \(0,\ldots ,0,1\) and each term afterwards is the sum of the preceding k terms. In this paper, we find all k-Fibonacci which are product of two Fermat numbers.

In this paper we introduce a matrix representation of the logarithmic wave operator and we study a second-order semilinear evolution equation governed by this operator. We present a result of local well-posedness for this problem and properties of the logarithmic wave operator in terms of the logarithmic negative Dirichlet Laplacian operator.

We investigate in this work some situations where it is possible to estimate or determine the upper and the lower q-generalized fractal dimensions \(D^{\pm }_{\mu }(q)\), \(q\in {\mathbb {R}}\), of invariant measures associated with continuous transformations over compact metric spaces. In particular, we present an alternative proof of Young’s Theorem by Young (Ergod. Theory Dyn. Syst. 2(1):109–124

In this note we exhibit some large sets \(\varTheta _x \subset \{1, 2, \ldots , \lfloor x \rfloor \}\) such that the sum of the Möbius function over \(\varTheta _x\) is small and independent of x. We show that the existence of some of these sets are intimately connected with the existence of the alternating series used by Tschebyschef and Sylvester to bound the prime counter function \(\varPi (x)\)

We describe the topology of the local Milnor fiber of a function f defined on a 3-dimensional subanalytic subset \(W \subset {\mathbb {R}}^3\), in terms of the embedded topological type of its link \(K_f\). Precisely, we prove that the interior of the local Milnor fiber of \(\Vert f\Vert \) is homeomorphic to the complement of \(K_f\) in the corresponding sphere, extending a result due to Milnor to

Let T be a pearl necklace consisting of the union of n consecutive tangent closed 3-balls \(B_i\) (\(i=1,2,\ldots , n\)) and consider the Kleininan group \(\Gamma _T\) generated by the reflections on the boundaries \(\partial B_i\). Let \(\Lambda (\Gamma _T)\) be a wild knot obtained as the limit set of \(\Gamma _T\) acting on the 3-sphere \(\mathbb {S}^3\). We say that a n-pearl necklace V consisting

We consider the problem of finding conformal metrics on the unit ball \({\mathbb {B}}^n\) of \({\mathbb {R}}^n\), \(n\ge 3\), with zero scalar curvature and prescribed mean curvature on the boundary. We study the lack of compactness of the problem and we prove an existence result based on an index-counting formula.

We study n-dimensional area-minimizing currents T in \(\mathbf {R}^{n+1},\) with boundary \(\partial T\) satisfying two properties: \(\partial T\) is locally a finite sum of \((n-1)\)-dimensional \(C^{1,\alpha }\) orientable submanifolds which only meet tangentially and with same orientation, for some \(\alpha \in (0,1]\); \(\partial T\) has mean curvature \(=h \nu _{T}\) where h is a Lipschitz scalar-valued

Using the knowledge about the finite-dimensional irreducible modules over \(\mathfrak {sl}_2({\mathbb {C}})\), it is possible to associate for any of them an irreducible module over the four-dimensional zero-algebra on the class of commutative power-associative algebras. This association allows to construct an embedding from the category of \(\mathfrak {sl}_2({\mathbb {C}})\)-modules into the category

In this paper we propose a definition of a distance between flows of possibly different metric spaces. This notion is then combined with the concept of topologically stable flow to obtain the notion of \(\sigma \)-topologically GH-stable flow. Afterwards, we prove that an expansive flow of a compact metric space, with the pseudo-orbit tracing property, and without singularities is \(\sigma \)-topologically

In this paper we study polynomial vector fields on \({\mathbb {C}}^{2}\) of degree larger than 2 with \(n^{2}\) isolated singularities. More precisely, we show that if two polynomial vector fields share \(n^{2}-1\) singularities with the same spectra (trace and determinant) and from these singularities \(n^{2}-2\) have the same positions, then both vector fields have identical position and spectra

Building on previous papers by Anantharaman-Delaroche (AD) we introduce and study the notion of AD-amenability for partial actions and Fell bundles over discrete groups. We prove that the cross-sectional \(C^*\)-algebra of a Fell bundle is nuclear if and only if the underlying unit fibre is nuclear and the Fell bundle is AD-amenable. If a partial action is globalisable, then it is AD-amenable if and

In this paper, we investigate the existence of free involutions on some Wall manifolds and we compute the mod 2 cohomology algebra of the correspondent orbit space.

In this paper, we investigate the Cauchy problem for the 3D incompressible Hall-MHD equations with zero viscosity. We prove the Beale–Kato–Majda regularity criterion of smooth solutions in terms of the velocity field and magnetic field in the homogeneous Besov spaces \({\dot{B}}_{\infty ,\infty }^{0} \). Then we give a criterion on extension beyond T of our local solution. Our result may be also regarded

In this paper we study the multiplicities and the asymptotic behaviour of the numbers of totients in the strata given by 2-adic valuation.

In this work we study and provide a full description, up to a finite index subgroup, of the dynamics of solvable complex Kleinian subgroups of \(\text {PSL}\left( 3,\mathbb {C}\right) \). These groups have simple dynamics, contrary to strongly irreducible groups. Because of this, we propose to define elementary subgroups of \(\text {PSL}\left( 3,\mathbb {C}\right) \) as solvable groups. We show that

A new class of alternating convolutions concerning binomial coefficients and Catalan numbers are evaluated in closed forms.

We prove that every finite-expansive homeomorphism with the shadowing property has a kind of stability. This stability will be good enough to imply both the shadowing property and the denseness of periodic points in the chain recurrent set. Next we analyze the N-shadowing property which is really stronger than the multishadowing property in Cherkashin and Kryzhevich (Topol Methods Nonlinear Anal 50(1):

In this paper, for a simple undirected connected graph G, the concept of the distance Randić matrix of G is defined and basic properties on its spectrum are derived. Moreover, the distance Randić energy of G is introduced. Bounds on this energy are obtained and for those which are sharp the extremal graphs are characterized. Finally, for \(\alpha \in [0,1]\), the concept of \(\alpha -\) distance Randić

We study finite-dimensional graded modules for hyperalgebras of twisted current algebras. In particular, we prove that local graded Weyl modules are isomorphic to the corresponding level one Demazure modules, and, moreover, that they are restrictions of corresponding local graded Weyl modules for the hyperalgebra of the untwisted current algebra.

A left Engel sink of an element g of a group G is a set \({\mathscr {E}}(g)\) such that for every \(x\in G\) all sufficiently long commutators \([...[[x,g],g],\dots ,g]\) belong to \({\mathscr {E}}(g)\). (Thus, g is a left Engel element precisely when we can choose \({\mathscr {E}}(g)=\{ 1\}\).) We prove that if a finite group G admits an automorphism \(\varphi \) of prime order coprime to |G| such

We study the equisingularity of a family of function germs \(\{f_t:(X_t,0)\rightarrow ({\mathbb {C}},0)\}\), where \((X_t,0)\) are d-dimensional isolated determinantal singularities. We define the \((d-1)\)th polar multiplicity of the fibers \(X_t\cap f_t^{-1}(0)\) and we show how the constancy of the polar multiplicities is related to the constancy of the Milnor number of \(f_t\) and the Whitney equisingularity

In this note we introduce a new technique to answer an issue posed in Fávaro et al. (Bull Braz Math Soc 51:27–46, 2020) concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.

On any odd-dimensional oriented Riemannian manifold we define a volume form called the odd Pfaffian through a certain invariant polynomial with integral coefficients in the curvature tensor. We prove an intrinsic Chern–Gauss–Bonnet formula for incomplete edge singularities in terms of the odd Pfaffian on the fibers of the boundary fibration. The same method produces a Chern–Gauss–Bonnet formula for

Is it possible to obtain unbounded minimal surfaces in certain asymptotically flat three-manifolds as a limit of solutions to a natural mountain pass problem with diverging boundaries? In this work, we give evidence that this might be true by analyzing related aspects in the case of the exact Riemannian Schwarzschild manifold. More precisely, we observe that the simplest minimal surface in this space

In this paper we will provide the exact formulas for the regularity and projective dimension of edge ideals of three types of vertex-weighted oriented m-partite graphs. We also give some examples to show that the restrictions on orientations of edges and weights of vertices can not be removed.

In this study, we find all Fibonacci and Lucas numbers which can be expressible as a product of two repdigits in the base b. It is shown that the largest Fibonacci and Lucas numbers which can be expressible as a product of two repdigits are \(F_{12}=144\) and \(L_{15}=1364\), respectively. Also, we have the presentation $$\begin{aligned} F_{12}=144=6\times (3+3\cdot 7)=(6)_{7}\times (33)_{7}=4\times

Let Co(p), \(p\in (0,1]\) be the class of all meromorphic univalent functions \(\varphi \) defined in the open unit disc \({\mathbb {D}}\) with normalizations \(\varphi (0)=0=\varphi '(0)-1\) and having simple pole at \(z=p\in (0,1]\) such that the complement of \(\varphi ({\mathbb {D}})\) is a convex domain. The class Co(p) is called the class of concave univalent functions. Let \(S_{H}^{0}(p)\) be

In our original paper the incorrect labelling of the number of vertices of the line graph L(G) in the proof of Theorem 2 has led to the inequality

In this paper, we prove the boundedness and compactness of localization operators associated with spherical mean wavelet transforms, which depend on a symbol and two spherical mean wavelets on \(L^{p}(d\nu )\), \(1 \le p \le \infty \).

Naradajah and Pal (Bull Braz Math Soc New Ser 39(1):45–60, 2008) derived explicit closed-form expressions for moments of order statistics from the gamma and generalized gamma distributions. However, the closed-form expressions provided by these authors are not correct and hence cannot be used to compute the moments of order statistics. We provide, therefore, an alternative closed-form expression for

\(\xi \)-submanifolds and \(\xi \)-translators are, respectively, the natural generalizations of self-shrinkers and translators of the mean curvature flow and, in the case of codimension one, they are previously known as \(\lambda \)-hypersurfaces and \(\lambda \)-translators, respectively. In this paper, we study the complete Lagrangian space-like \(\xi \)-surfaces and \(\xi \)-translators in \({\mathbb

In this paper we consider the following nonlinear nonlocal Choquard equation $$\begin{aligned} {{\mathcal {F}}} _{\alpha }\left( u(x)\right) +\omega u(x) = C_{n,2s} \left( |x|^{2s-n}*u^q(x)\right) u^r(x), ~ x\in {\mathbb {R}}^n, \end{aligned}$$ F α u ( x ) + ω u ( x ) = C n , 2 s | x | 2 s - n ∗ u q ( x ) u r ( x ) , x ∈ R n , where $$0

A positive integer N is called a \(\theta \)-congruent number if there is a \({\theta }\)-triangle (a, b, c) with rational sides for which the angle between a and b is equal to \(\theta \) and its area is \(N \sqrt{r^2-s^2}\), where \(\theta \in (0, \pi )\), \(\cos (\theta )=s/r\), and \(0 \le |s|

We study local equivariant maps on real finite dimensional orthogonal representations of a compact abelian Lie group G. Equivariant degree $$\deg _G$$ is an invariant applied to determine whether a given map has zeros. The goal of this paper is to present a complete, straightforward proof of the product property of $$\deg _G$$ . For that purpose, we use the otopy classification and distinguish a special

In 1972, Alniacik proved that every strong Liouville number is mapped into the set of $U_m$-numbers, for any non-constant rational function with coefficients belonging to an $m$-degree number field. In this paper, we generalize this result by providing a larger class of Liouville numbers (which, in particular, contains the strong Liouville numbers) with this same property (this set is sharp is a certain

Singular and sectional hyperbolic sets are the objects of the extension of the classical Smale Hyperbolic Theory to flows having invariant sets with singularities accumulated by regular orbits within the set. It is by now well-known that (partially) hyperbolic sets admit adapted metrics. We show the existence of singular adapted metrics for any singular hyperbolic set with respect to a $C^{1}$ vector

First, by a probabilistic approach through the Feynman-Kac representation, we obtain a sufficient condition for the blow up in infinite time of the positive solution of a nonlinear anomalous reaction-diffusion system. Afterward, by reducing our system to an ordinary differential system, we prove that, in fact, our condition implies blow up in finite time of the solution.

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

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

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 $\rho(z) = 1+\frac{1}{\textrm{dist}(z,P(f))^{1-1/d}}$, and where $P(f)$ is the postcritical set of $f$. We also show that this metric is H\"older 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

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 give an upper bound for the height of the unique element in the group which sends the point into the fundamental domain. The height is bounded by a polynomial function on some coordinates of the point whose degree does not

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 hypersurfaces

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 and the polytope duality among families of $K3$ surfaces.

This paper deals with foliations by curves [ s ] of degree $$ r \ge 2 $$ r ≥ 2 on $$ \mathbb {P}^2 $$ 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 $$ Y \subset S $$ Y ⊂ S if [ s ] is the unique foliation that vanishes on Y and say that Y is minimal for [ s ] if, moreover, the degree of

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.