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Existence and Concentration of Solutions for a Class of Kirchhoff–Boussinesq Equation with Exponential Growth in $${\mathbb {R}}^4$$ Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2024-03-15 Romulo D. Carlos, Gustavo S. A. Costa, Giovany M. Figuereido
This paper is concerned with the existence and concentration of ground state solutions for the following class of elliptic Kirchhoff–Boussinesq type problems given by $$\begin{aligned} \Delta ^{2} u \pm \Delta _{p} u +(1+\lambda V(x))u= f(u)\quad \text {in}\ {\mathbb {R}}^{4}, \end{aligned}$$ where \(2< p< 4,\) \(f\in C( {\mathbb {R}}, {\mathbb {R}})\) is a nonlinearity which has subcritical or critical
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Numerical Semigroups with Monotone Apéry Set and Fixed Multiplicity and Ratio Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2024-03-14 Aureliano M. Robles-Pérez, José Carlos Rosales
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On the Invariant Subspace Problem via Universal Toeplitz Operators on the Hardy Space Over the Bidisk Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2024-03-04 João Marcos R. do Carmo, Marcos S. Ferreira
The invariant subspace problem (ISP) for Hilbert spaces asks if every bounded linear operator has a non-trivial closed invariant subspace. Due to the existence of universal operators (in the sense of Rota) the ISP can be solved by proving that every minimal invariant subspace of a universal operator is one dimensional. In this work, we obtain conditions for \(T^{*}_{\varphi }|_{M}\) to have a non-trivial
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Approximation of Almost Diagonal Non-linear Maps by Lattice Lipschitz Operators Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2024-02-13 Roger Arnau, Jose M. Calabuig, Ezgi Erdoğan, Enrique A. Sánchez Pérez
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Universal Inequalities for Eigenvalues of a Clamped Plate Problem of the Drifting Laplacian Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2024-02-06 Yue He, Shiyun Pu
In this paper, we study the universal inequalities for eigenvalues of a clamped plate problem of the drifting Laplacian in several cases, and establish some universal inequalities that are different from those obtained previously in (Du et al. in Z Angew Math Phys 66(3):703–726, 2015).
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A Blowup Criteria of Smooth Solutions to the 3D Boussinesq Equations Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2024-02-02
Abstract In this work, we are concerned with the main mechanism for possible blow-up criteria of smooth solutions to the 3D incompressible Boussinesq equations. The main results state that the finite-time blowup/global existence of smooth solutions to the Boussinesq equation is controlled by either of the criteria $$\begin{aligned} u_{h}\in L^{2}\left( 0,T;\dot{B}_{\infty ,\infty }^{0}({\mathbb {R}}
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Analytical Solutions to the Cylindrically Symmetric Compressible Navier–Stokes Equations with Density-Dependent Viscosity and Vacuum Free Boundary Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2024-01-23 Jianwei Dong, Haijie Cui
In this paper, we investigate the analytical solutions to the cylindrically symmetric compressible Navier–Stokes equations with density-dependent viscosity and vacuum free boundary. The shear and bulk viscosity coefficients are assumed to be a power function of the density and a positive constant, respectively, and the free boundary is assumed to move in the radial direction with the radial velocity
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A Higher-Order Non-autonomous Semilinear Parabolic Equation Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2024-01-11 Maykel Belluzi, Flank D. M. Bezerra, Marcelo J. D. Nascimento, Lucas A. Santos
In this paper, we study results of well-posedness and regularity of higher order in time abstract non-autonomous semilinear Cauchy problems associated with Newton’s binomial theorem and the theory of sectorial operators. Our approach to parabolic problems of arbitrarily order n apparently has never been addressed earlier in the existing literature. Also, we present applications to evolutionary equations
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On the GIT-Stability of Foliations of Degree 3 with a Unique Singular Point Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-12-22 Abel Castorena, P. Rubí Pantaleón-Mondragón, Juan Vásquez Aquino
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Harmonic 1-Forms on Minimal Hypersurfaces in $${{\mathbb {S}}}^{n}\times {{\mathbb {R}}}$$ Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-12-20 Peng Zhu
We consider a complete noncompact minimal hypersurface \(\Sigma ^n\) in a product manifold \({{\mathbb {S}}}^{n}(\sqrt{2(n-1)})\times {{\mathbb {R}}}\) \((n\ge 3)\). We get that there admits no nontrivial \(L^2\) harmonic 1-forms on \(\Sigma \) if the square of \(L^n\)-norm of the second fundamental form is less than \(\frac{\alpha ^2n}{2C_0(n-1)}\) or the square of the length of the second fundamental
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Para-Abelian Varieties and Albanese Maps Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-12-20 Bruno Laurent, Stefan Schröer
We construct for every proper algebraic space over a ground field an Albanese map to a para-abelian variety, which is unique up to unique isomorphism. This holds in the absence of rational points or ample sheaves, and also for reducible or non-reduced spaces, under the mere assumption that the structure morphism is in Stein factorization. It also works under suitable assumptions in families. In fact
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Unified Grothendieck’s and Kwapień’s Theorems for Multilinear Operators Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-12-14 Daniel Núñez-Alarcón, Joedson Santos, Diana Serrano-Rodríguez
Kwapień’s theorem asserts that every continuous linear operator from \(\ell _{1}\) to \(\ell _{p}\) is absolutely \(\left( r,1\right) \)-summing for \(1/r=1-\left| 1/p-1/2\right| .\) When \(p=2\) it recovers the famous Grothendieck’s theorem. In this paper we investigate multilinear variants of these theorems and related issues. Among other results we present a unified version of Kwapień’s and Grothendieck’s
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On General Concavity Extensions of Grünbaum Type Inequalities Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-11-29 Francisco Marín Sola
Given a strictly increasing continuous function \(\phi :\mathbb {R}_{\ge 0} \longrightarrow \mathbb {R}\cup \{-\infty \}\) with \(\lim _{t\rightarrow \infty }\phi (t) = \infty \), a function \(f:[a,b] \longrightarrow \mathbb {R}_{\ge 0}\) is said to be \(\phi \)-concave if \(\phi \circ f\) is concave. When \(\phi (t) = t^p\), \(p>0\), this notion is that of p-concavity whereas for \(\phi (t) = \log
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Multiplicity of Solutions for A Semilinear Elliptic Problem Via Generalized Nonlinear Rayleigh Quotient Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-11-22 M. L. M. Carvalho, Edcarlos D. Silva, C. Goulart, M. L. Silva
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Necessary Codimension One Components of the Projection of the Jacobian Blow-Up Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-11-06 David B. Massey
For a complex analytic function, the exceptional divisor of the jacobian blow-up is of great importance. In this short paper, we show what a lemma from the thesis of Lazarsfeld tells one about the structure of the projections of this exceptional divisor into the base space.
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On the Convergence of the Fractional Relativistic Schrodinger Operator Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-10-28 V. Ambrosio, H. Bueno, A. H. S. Medeiros, G. A. Pereira
In this paper, we deal with the convergence of the fractional relativistic Schrodinger operator $$\begin{aligned}(-\Delta + m^2)^s\quad \text {as}\ s\rightarrow 1^-.\end{aligned}$$ Intuitively, this operator converges to \((-\Delta +m^2)\) but the proof of this result is not so simple and it is based on a careful analysis of the involved modified Bessel function \(K_\nu \). The convergence of the operator
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Binary Differential Equations Associated to Congruences of Lines in Euclidean 3-Space Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-10-30 J. W. Bruce, F. Tari
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Representations of Solvable Subgroups of $$\text {PSL}\left( 3,\mathbb {C}\right) $$ Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-10-15 Mauricio Toledo-Acosta
In this paper, we give a complete description of the representations of all upper triangular complex Kleinian subgroups of \(\text {PSL}\left( 3,\mathbb {C}\right) \). In Toledo-Acosta (Bull Braz Math Soc New Ser 20:1–45, 2021), we show that any solvable group is virtually triangularizable and can be constructed as the semidirect product of two layers of parabolic elements and two layers of loxodromic
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Involutions of the Second Kind on Finitary Incidence Algebras Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-10-09 Érica Z. Fornaroli
Let K be a field and X a connected partially ordered set. In the first part of this paper, we show that the finitary incidence algebra FI(X, K) of X over K has an involution of the second kind if and only if X has an involution and K has an automorphism of order 2. We also give a characterization of the involutions of the second kind on FI(X, K). In the second part, we give necessary and sufficient
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Poisson Structures on Trivial Extension Algebras Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-10-09 D. García-Beltrán, J. C. Ruíz-Pantaleón, Yu. Vorobiev
We present a class of Poisson structures on trivial extension algebras which generalizes some known structures induced by Poisson modules. We show that there exists a one-to-one correspondence between such a class of Poisson structures and some data involving (not necessarily flat) contravariant derivatives, and then we give a formulation of this result in terms of Lie algebroids. Some properties of
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On Bisectors in Quaternionic Hyperbolic Space Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-10-05 Igor A. R. Almeida, Jaime L. O. Chamorro, Nikolay Gusevskii
In this paper, we study a problem related to geometry of bisectors in quaternionic hyperbolic geometry. We develop some of the basic theory of bisectors in quaternionic hyperbolic space \({{\textrm{H}}^{\textrm{n}}_{{\mathbb {Q}}}}\). In particular, we show that quaternionic bisectors enjoy various decompositions by totally geodesic submanifolds of \({{\textrm{H}}^{\textrm{n}}_{{\mathbb {Q}}}}\). In
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Intermediate Classes of Nuclear Multilinear Operators Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-10-05 Amar Belacel, Amar Bougoutaia, Renato Macedo, Pilar Rueda
This paper introduces the class of \(\left( p_1,\ldots ,p_m,\sigma ,q,\nu \right) \)-nuclear m-linear operators between Banach spaces, as an intermediate space between the class of nuclear multilinear operators and the whole class of all bounded multilinear operators. The connection with the theory of summing m-linear operators is established. Moreover, we identify this space with a dual space by means
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On Special Holomorphic Distributions and Residues Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-10-05 Arturo Fernández-Pérez, Gilcione Nonato Costa, Allan Ramos
For a codimension one holomorphic distribution on \({\mathbb {P}}^3\) whose singular locus contains a smooth curve and closed points, we introduce the concepts of specialty and residue along a curve. We provide an upper bound for this residue, in terms of the numerical invariants of the distribution and of the curve. Furthermore, under certain conditions, we also prove a characterization of special
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On Weighted Greedy-Type Bases Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-09-27 Hùng Việt Chu
We study weights for the thresholding greedy algorithm, aiming to extend previous work on sequential weights \(\varsigma \) on \({\mathbb {N}}\) to weights \(\omega \) on \({\mathcal {P}}({\mathbb {N}}).\) We revisit major results on weighted greedy-type bases in this new setting including characterizations of \(\omega \)-(almost) greedy bases and the equivalence between \(\omega \)-semi-greedy bases
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Classification of Ruled Surfaces as Homothetic Self-Similar Solutions of the Inverse Mean Curvature Flow in the Lorentz–Minkowski 3-Space Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-09-01 Gregório Silva, Vanessa Silva
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Stratification of Spaces of Locally Convex Curves by Itineraries Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-08-30 Victor Goulart, Nicolau C. Saldanha
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Kukles Systems of Degree Three with Global Centers Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-08-30 Fabio Scalco Dias, Luis Fernando Mello, Claudia Valls
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Symmetries of $$C^r$$ -vector Fields on Surfaces Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-08-19 Wescley Bonomo, Jorge Rocha, Paulo Varandas
Given \(r\geqslant 1\), the discrete \(C^r\)-centralizer of a vector field is formed by the set of its symmetries, that is, the set of \(C^r\)-diffeomorphisms commuting with the flow generated by it. Here we prove that if M is a compact surface and \(2\leqslant r \leqslant \infty \) then there exists a \(C^r\)-open and dense subset of vector fields \(\mathcal O \subset \mathfrak {X}^r(M)\) whose \(C^r\)-discrete
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On the Spaceability of the Set of Functions in the Lebesgue Space $$L_p$$ Which are Not in $$L_q$$ Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-08-09 G. Araújo, A. Barbosa, A. Raposo, G. Ribeiro
We answer an open problem posed by Fávaro, Pellegrino and Tomáz in (Bull Braz Math Soc 51:27–46, 2020b). Namely, we prove that, for all \(0< p<\infty \), the set \(L_{p}[0,1]\smallsetminus \bigcup _{q\in \left( p,\infty \right) }L_{q}[0,1]\) is \((\alpha ,\mathfrak {c})\)-spaceable in \(L_{p}[0,1]\) if, and only if, \(\alpha <\aleph _{0}\).
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Coefficients of Multilinear Forms on Sequence Spaces Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-08-05 Anselmo Raposo, Diana M. Serrano-Rodríguez
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Coexistence Phenomena in the Hénon Family Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-07-18 Michael Benedicks, Liviana Palmisano
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Refined Long Time Existence of the Boussinesq Equation with Large Initial Data in $$\mathbb {R}^{n}$$ Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-07-09 Guowei Liu, Hao Xu
In this paper, we study the long time existence of the Boussinesq equation with large initial data in \(\mathbb {R}^{n}\). By establishing a new prior estimate and a new low-frequency Strichartz estimate, we utilize the bootstrap principle to prove the unique existence of smooth solutions on [0, T] for all \(T>0\), provided that the lower bound of dispersive coefficient is the polynomial form of the
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Cohyponormality and Complex Symmetry of Linear Fractional Composition Operators on a Half-Plane Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-07-06 V. V. Fávaro, P. V. Hai, O. R. Severiano
We investigate the bounded composition operators induced by linear fractional self-maps of the right half-plane \({\mathbb {C}}_+\) on the Hardy space \(H^2({\mathbb {C}}_+).\) We completely characterize which of these operators are cohyponormal and we find conjugations for the linear fractional composition operators that are complex symmetric.
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Stationary Solutions to a Chemo-repulsion System and a Related Optimal Bilinear Control Problem Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-07-05 Sebastián Lorca, Exequiel Mallea-Zepeda, Élder J. Villamizar-Roa
In this paper we study a stationary chemo-repulsion model and analyze a related optimal bilinear control problem. We prove the existence of strong solutions of the state equations with a non-smooth source term in the chemical concentration equation, in bounded domains of \(\mathbb {R}^N,\) \(N=1,2,3,\) for any given mass, which permit us to consider optimal bilinear control problems. We prove the existence
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Optimal Large Time Behavior of the Full Compressible Navier–Stokes System in $${\mathbb {R}}^3$$ Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-07-04 Zhengyan Luo, Yinghui Zhang
In this paper, we investigate optimal large time behavior for higher–order spatial derivatives of strong solutions to the Cauchy problem of the full compressible Navier–Stokes equations. The main novelty of this paper is two–fold: First, under the assumptions that the initial perturbation is small in \(H^3\)–norm and bounded in \(L^1\)–norm, we apply the Fourier splitting method to establish the optimal
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Weierstrass Semigroups from Cyclic Covers of Hyperelliptic Curves Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-06-28 Ethan Cotterill, Nathan Pflueger, Naizhen Zhang
The Weierstrass semigroup of pole orders of meromorphic functions in a point p of a smooth algebraic curve C is a classical object of study; a celebrated problem of Hurwitz is to characterize which semigroups \(\textrm{S} \subset \mathbb {N}\) with finite complement are realizable as Weierstrass semigroups \(\textrm{S}= \textrm{S}(C,p)\). In this note, we establish realizability results for cyclic
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A Note on the Distribution of Iwasawa Invariants of Imaginary Quadratic Fields Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-06-26 Anwesh Ray
Given an odd prime number p and an imaginary quadratic field K, we establish a relationship between the p-rank of the class group of K, and the classical \(\lambda \)-invariant of the cyclotomic \(\mathbb {Z}_p\)-extension of K. Exploiting this relationship, we prove statistical results for the distribution of \(\lambda \)-invariants for imaginary quadratic fields ordered according to their discriminant
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A Result of Rigidity for Ricci-Flat Warped Products Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-06-26 Ilton Menezes, Paula Correia, Romildo Pina
In this work we prove a result of rigidity on Ricci-flat semi-Riemannian warped products when the base is locally conformally flat with scalar curvature zero and invariant by the action of the pseudo-orthogonal group. We obtain that in these manifolds the fiber must be 1-dimensional. As an application, every metric with these characteristics is a generalized Schwarzschild metric.
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$$L_{p}$$ -Estimates for Solutions of Equations Governed by Operators like the Anisotropic Fractional Laplacian Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-06-21 Raimundo Leitão
In this paper we establish new \(L_{p}\)-estimates for solutions of anisotropic fractional equations, as the ones governed by the anisotropic fractional laplacian \(\Delta ^{\beta , s}\).
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Normal Forms of $$\omega $$ -Hamiltonian Vector Fields with Symmetries Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-06-21 Patrícia H. Baptistelli, Maria Elenice R. Hernandes, Eralcilene Moreira Terezio
In this paper, we present algebraic tools to obtain normal forms of \(\omega \)-Hamiltonian vector fields under a semisymplectic action of a Lie group, by taking into account the symmetries and reversing symmetries of the vector field. The normal forms resulting from the process preserve the Hamiltonian condition and the types of symmetries of the original vector field. Our techniques combine the classical
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A Unique Continuation Result for a 2D System of Nonlinear Equations for Surface Waves Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-06-19 Alex M. Montes, Ricardo Córdoba
In this paper, we establish a result of unique continuation for a special two-dimensional nonlinear system that models the evolution of long water waves with small amplitude in the presence of surface tension. More precisely, we will show that if \((\eta ,\Phi ) = (\eta (x,y, t),\Phi (x,y, t))\) is a solution of the nonlinear system, in a suitable function space, and \((\eta ,\Phi )\) vanishes on an
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Existence of Solutions for a Class of Quasilinear Choquard Equations with Potential Vanishing at Infinity Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-06-14 Die Hu, Xianhua Tang
In this paper, we discuss the following quasilinear Choquard equation $$\begin{aligned} - \Delta v+ V(x)v- v\Delta (v^{2})= \left( \frac{1}{|x|^{\mu }}*Q(x)F(v)\right) Q(x)f( v),~~~~~v\in D^{1,2}(\mathbb {R}^{N}), \end{aligned}$$ where \(N\ge 3\), \(\mu \in (0,N)\), V and Q are differentiable, \(f\in \mathbb {C}(\mathbb {R},\mathbb {R})\) and \(F(s)=\int ^{s}_{0}f(t)dt\). We prove that the above equation
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Independence Numbers of Johnson-Type Graphs Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-06-12 Danila Cherkashin, Sergei Kiselev
We consider a family of distance graphs in \(\mathbb {R}^n\) and find its independence numbers in some cases. Define the graph \(J_{\pm }(n,k,t)\) in the following way: the vertex set consists of all vectors from \(\{-1,0,1\}^n\) with exactly k nonzero coordinates; edges connect the pairs of vertices with scalar product t. We find the independence number of \(J_{\pm }(n,k,t)\) for an odd negative t
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Bi-Lipschitz Characterization of Space Curves Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-06-04 Alexandre Fernandes, Zbigniew Jelonek
In the paper Targino (Outer Lipschitz Geometry of Complex Algebraic Plane Curves. International Mathematics Research Notices, rnac202. https://doi.org/10.1093/imrn/rnac202, 2022) Renato Targino shows that bi-Lipschitz type of a plane curve is determined by the local ambient topological properties of curves. Here we show that it is no longer true in higher dimensions. However we show that the bi-Lipschitz
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Examples of d-sets with Irregular Projection of Hausdorff Measures Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-05-26 Yuri Lima, Carlos Gustavo Moreira
Given positive integers \(\ell 1\).
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Analytic Semiroots for Plane Branches and Singular Foliations Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-05-08 Felipe Cano, Nuria Corral, David Senovilla-Sanz
The analytic moduli of equisingular plane branches has the semimodule of differential values as the most relevant system of discrete invariants. Focusing in the case of cusps, the minimal system of generators of this semimodule is reached by the differential values attached to the differential 1-forms of the so-called standard bases. We can complete a standard basis to an extended one by adding a last
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Lie Structures and Chain Ideal Lattices Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-05-05 Pilar Benito, Jorge Roldán-López
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On the Transcendence of Some Powers Related to U-numbers Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-04-15 Diego Marques, Marcelo Oliveira
In this paper, we provide some results on the arithmetic nature of numbers related to U-numbers. In particular, we show the transcendence of \(\alpha ^{\xi }\), for all algebraic number \(\alpha \not \in \{0,1\}\) and all Liouville number \(\xi \).
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Pairs of r-Primitive and k-Normal Elements in Finite Fields Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-04-13 Josimar J. R. Aguirre, Victor G. L. Neumann
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Existence of Discrete Eigenvalues for the Dirichlet Laplacian in a Two-Dimensional Twisted Strip Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-03-29 Rafael T. Amorim, Alessandra A. Verri
We study the spectrum of the Dirichlet Laplacian operator in twisted strips on ruled surfaces in any space dimension. It is shown that a suitable twisted effect can create discrete eigenvalues for the operator. In particular, we also study the case where the twisted effect “grows” at infinity while the width of the strip goes to zero. In this situation, we find an asymptotic behavior for the eigenvalues
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On the Asymptotic Distribution of Fourier Coefficients of Cusp Forms Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-03-26 Huafeng Liu
Let \(\lambda _{f}(n)\) be the n-th normalized Fourier coefficient of primitive holomorphic cusp form of even integral weight \(k\ge 2\) for the full modular group \(SL(2,\mathbb {Z})\). In this paper, we first refine related previous results on the l-th power sums of the Fourier coefficient \(\lambda _f(n)\). Then we establish asymptotic formulas of the variance of \(\lambda _f^l(n)\).
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Genus Field and Extended Genus Field of an Elementary Abelian Extension of Global Fields Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-03-25 Juan C. Hernandez B., Gabriel D. Villa S.
In the present work we give the construction of the genus field and the extended genus field of an elementary abelian l-extension of a field of rational functions, where l is a prime number. In the Kummer case, if K is contained in a cyclotomic function field, the construction is given using Leopoldt’s ideas by means of Dirichlet characters. Following the definition of Anglès and Jaulent of extended
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Semi-Algebraic Functions with Non-Compact Critical Set Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-03-26 Nicolas Dutertre, Juan Antonio Moya Pérez
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On a Elliptic System Involving Nonhomogeneous Nonlinearities and Critical Growth Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-03-25 Elisandra Gloss, Everaldo S. Medeiros, Uberlandio Severo
Let \(\Omega \subset {\mathbb {R}}^N\) be a bounded domain with \(N\ge 3\). We address the existence and nonexistence of solutions for the following class of elliptic systems: $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u=a u+b v+ \mu |u|^{p-2}u &{} \text {in}\quad \Omega \\ -\Delta v=bu+a v+ |v|^{2^*-2}v &{} \text {in}\quad \Omega \end{array}\right. } \end{aligned}$$ with Dirichlet boundary
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Modules for Leavitt Path Algebras via Extended Algebraic Branching Systems Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-03-13 Raimund Preusser
For a graph E, we introduce the notion of an extended E-algebraic branching system, generalising the notion of an E-algebraic branching system introduced by Gonçalves and Royer. We classify the extended E-algebraic branching systems and show that they induce modules for the corresponding Leavitt path algebra L(E). Among these modules we find a class of nonsimple modules whose endomorphism rings are
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A Variational Approach to Quasilinear Elliptic Problems with Gradient Dependence Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-03-10 Gelson C. G. dos Santos, Leandro S. Tavares
In this paper, we consider a class of quasilinear elliptic equations with gradient terms which arise in several applications in the theory of Heidelberg Ferromagnetism and Magnus, Hydrodynamics, and the Condensed Matter Theory. By performing a change of variables, the original problem is transformed into an equivalent semilinear one. The semilinear equation is solved by applying an iterative method
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Singularities of Holomorphic Codimension One Foliations of the Complex Projective Plane Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-03-09 Dominique Cerveau, Julie Déserti
We prove that any holomorphic codimension 1 foliation on the complex projective plane has at most one singularity up to the action of an ad-hoc birational map. Consequently, any algebraic foliation on the affine plane has no singularities up to the action of a suitable birational self map of the complex projective plane into itself.
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Conditions for Spanning Trees Whose Internal Subtrees Have Few Branch Vertices and Leaves Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-03-04 Dang Dinh Hanh
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A Well-Posed Logarithmic Counterpart of an Ill-Posed Cauchy Problem Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-02-25 Lucas A. Santos, Flank D. M. Bezerra
In this short paper, we study a well-posed logarithmic counterpart of an ill-posed Cauchy problem associated with an abstract evolution equation of third order in time.
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Atypical Values and the Milnor Set of Real Polynomials in Two Variables Bull. Braz. Math. Soc. New Ser. (IF 0.7) Pub Date : 2023-01-27 Gabriel E. Monsalve
We give a new algorithmic method of detection of atypical values for 2-variables real polynomial functions with emphasis on the effectivity.