Let Π be an open, relatively compact period annulus of real analytic vector field X0 on an analytic surface. We prove that the maximal number of limit cycles which bifurcate from Π under a given multiparameter analytic deformation Xλ of X0 is finite, provided that X0 is either Hamiltonian, or generic Darbouxian vector field. 1 Statement of the result Let S be a real analytic surface without bor...

The terminology and notation used here have been introduced in the following articles: [3], [7], [17], [2], [4], [12], [13], [14], [16], [1], [5], [9], [15], [18], [10], [8], [20], [21], [19], [11], [22], and [6]. For simplicity, we use the following convention: n, i denote elements of N, X, X1 denote sets, r, p, s, x0, x1, x2 denote real numbers, f , f1, f2 denote partial functions from R to R...

It is known that if f : R → R is continuous then ẋ = f(x) with x(0) = x0 has at least one solution on some time interval [0, T (x0)). However, when f is not Lipschitz one cannot guarantee that the solutions are unique. In this paper we show that the set of points x0 ∈ R is a countable, nowhere dense set. (In particular, we show that if f(x0) 6= 0 then the solution must be locally unique.)

In many real-life applications, physical considerations lead to the necessity to consider the smoothest of all signals that is consistent with the measurement results. Usually, the corresponding optimization problem is solved in statistical context. In this paper, we propose a quadratic-time algorithm for smoothing an interval function. This algorithm, given n + 1 intervals x0, . . . ,xn with 0...

The terminology and notation used here have been introduced in the following articles: [3], [7], [17], [2], [4], [12], [13], [14], [16], [1], [5], [9], [15], [18], [10], [8], [20], [21], [19], [11], [22], and [6]. For simplicity, we use the following convention: n, i denote elements of N, X, X1 denote sets, r, p, s, x0, x1, x2 denote real numbers, f , f1, f2 denote partial functions from R to R...

We study modular subspaces corresponding to two deformation functors associated to an isolated singularity X0: the functor DefX0 of deformations of X0 and the functor Def X0 of deformations with section of X0. After recalling some standard facts on the cotangent cohomology of analytic algebras and the general theory of deformations with section, we give several criteria for modularity in terms ...

Our aim is to establish some signatures of the extra neutral gauge boson X0, predicted in a version of the SU(3)C×SU(3)L×U(1)X model with right-handed neutrinos, by considering the process p+ p−→X0 +X0∗+ X . In this work, we show some results concerning the LHC energy regime ( √ s = 14 TeV) and projected luminosity. Some distributions are shown and the X0 width is calculated. We conclude that h...

When n ≥ 2, we show that for a non-negative solution of the Aronsson equation AH(u) = DxH(Du(x)) · Hp(Du(x)) = 0 an isolated singularity x0 is either a removable singularity or u(x) = b+CH k (x− x0)+ o(|x− x0|) ( or u(x) = b−C Ĥ k (x− x0)+ o(|x− x0|) ) for some k > 0 and b ∈ R . Here CH k and C Ĥ k are general cone functions. This generalizes the asymptotic behavior theory for infinity harmonic...

It is shown that Ramanujan’s cubic transformation of the Gauss hypergeometric function 2F1 arises from a relation between modular curves, namely the covering of X0(3) by X0(9). In general, when 2 N 7, the N-fold cover of X0(N) by X0(N) gives rise to an algebraic hypergeometric transformation. The N = 2, 3, 4 transformations are arithmetic–geometric mean iterations, but the N = 5, 6, 7 transform...