Bulletin of the Brazilian Mathematical Society, New Series最新文献

In Kim et al. (Nagoya Math J 178: 37-53, 2005), Lee and Lee (J Geometry Phys 56(10): 2011-2023, 2006), the authors developed a nice formula to compute the Nielsen number of a self-map on an infra-nilmanifold. For the case of nilmanifolds this formula was extended to n-valued maps in Deconinck and Dekimpe (J Fixed Point Theory Appl 25(4): Paper No. 84, 29, 2023). In this paper, we extend these results further and establish the averaging formula to compute the Nielsen number of any n-valued affine map on an infra-nilmanifold.

In this paper, we explore various transforms associated with a bounded linear operator T on a Hilbert space. These transforms include the Aluthge, (lambda )-Aluthge, Duggal, generalized mean, and (lambda )-mean transforms. Our aim is to investigate the connections between T and these transforms, focusing on aspects such as norm inequalities and numerical ranges, while also highlighting certain essential properties. Furthermore, we aim to determine the conditions under which an operator T coincides in norm with its transformed counterparts through these transformations. Several characterizations and properties are also derived.

In this paper, we introduce the notions of (lambda )-limited sets and (lambda )-L-sets in a Banach space X and its dual (X^*) respectively, using the vector valued sequence spaces (lambda ^{w^*}(X^*)) and (lambda ^{w}(X)). We find characterizations for these sets in terms of absolutely (lambda )-summing operators and investigate the relationship between (lambda )-compact sets and (lambda )-limited sets, with a particular focus on the crucial role played by a norm iteration property. We also consider (lambda )-limited operators and show that this class is an operator ideal containing the ideal of (lambda )-compact operators for a suitably restricted (lambda ). Furthermore, we define a generalized Gelfand-Philips property for Banach spaces corresponding to an abstract sequence space.

In this paper, we deal with the existence of r-primitive elements, a generalisation of primitive elements, in arithmetic progression by using a new formulation of the characteristic function for r-primitive elements in (mathbb {F}_q). In fact, we find a condition on q for the existence of (alpha in mathbb {F}_q^times ) for a given (ngeqslant 2) and (beta in mathbb {F}_q^times ) such that each of (alpha , alpha +beta ,alpha +2beta , dots , alpha + (n-1)beta subset mathbb {F}_q^times ) is r-primitive in (mathbb {F}_q^times .) This result is utilized with the help of an inequality due to Robin also to produce an explicit bound on q; this, in turn, shows that for any (n, rin mathbb {N},) for all but finitely many prime powers q, for any (beta in mathbb {F}_q^times ), there exists (alpha in mathbb {F}_q) such that (alpha ,alpha +beta ,dots ,alpha +(n-1)beta ) are all r-primitive whenever (r mid q-1). The number of arithmetic progressions in (mathbb {F}_q) consisting of r-primitive elements of length n, is asymptotic to (frac{q}{(q-1)^n}varphi (frac{q-1}{r})^n).

In this paper, we classify the non-degenerate ruled surfaces which are homothetic (alpha )-self-similar solutions to the mean curvature flow (MCF) in Minkowski 3-space (mathbb {E}^3_1). Other than cylindrical surfaces as in (mathbb {E}^3), we find a class of non-cylindrical ruled surface with null rulings, in particular, the null scrolls. Further, we investigate the non-degenerate surfaces of revolutions generated by non-null curve as homothetic (alpha )-self-similar solutions to the MCF according to the causality of their rotation axes as spacelike, timelike and lightlike.

Let (X, Y subset mathbb {C}^{2n-1}) be n-dimensional strong complete intersections in a general position. In this note, we consider the set of midpoints of chords connecting a point (x in X) to a point (y in Y). This set is defined as the image of the map (Phi (x,y)=frac{x+y}{2}.) Under geometric conditions on X and Y, we prove that the symmetry defect of X and Y, which is the bifurcation set B(X, Y) of the mapping (Phi ), is an algebraic variety, characterized by a topological invariant. We introduce a hypersurface that approximates the set B(X, Y) and we present an estimate for its degree. Moreover, for any two n-dimensional strong complete intersections (X,Ysubset mathbb {C}^{2n-1}) (including the case (X=Y)) we introduce a generic symmetry defect set (tilde{B}(X,Y)) of X and Y, which is defined up to homeomorphism. The set (tilde{B}(X,Y)) is an algebraic variety. Finally we show that in the real case if X, Y are compact, then the set (tilde{B}(X,Y)) is a hypersurface and it has only Thom-Boardman singularities. In particular if X is compact, then (tilde{B}(X)) is a hypersurface, which has only Thom-Boardman singularities.

We establish refined exponent ranges for anisotropic Hardy–Littlewood type of inequalities concerning m-linear operators. We further explore the optimality of these novel exponents.

The main purpose of this paper is to establish regularity criteria of the 3D damped Boussinesq equations with zero thermal diffusion. It is shown that if two components of the velocity or the gradient of velocity belong to some Lorentz spaces in both time and spatial directions, then the weak solution is regular on [0, T].

We investigate vertices for plane curves with singular points. As plane curves with singular points, we consider Legendre curves (respectively, Legendre immersions) in the unit tangent bundle over the Euclidean plane and frontals (respectively, fronts) in the Euclidean plane. We define a vertex using evolutes of frontals. After that we define a vertex of a frontal in the general case. It is also known that the four vertex theorem does not hold for simple closed fronts. We give conditions under which a frontal has a vertex and the four vertex theorem holds for closed frontals. We also give examples and counter examples of the four vertex theorem.

We introduce the notion of a (strongly) inner non-degenerate mixed function (f:{mathbb {C}}^2rightarrow {mathbb {C}}.) We show that inner non-degenerate mixed polynomials have weakly isolated singularities and strongly inner non-degenerate mixed polynomials have isolated singularities. Furthermore, under one additional assumption, which we call “(Gamma )-niceness”, the links of these singularities can be completely characterized in terms of the Newton boundary of f. In particular, adding terms above the Newton boundary does not affect the topology of the link.