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The challenges encountered in performing minimally invasive approaches, such as supraorbital minicraniotomy (SOMC), in services without adequate equipment are rarely reported in the literature. This study analyzes the viability of SOMC in the treatment of cerebral aneurysms, using exactly the same resources as pterional craniotomy (PC). The results of these two techniques are compared. 35 patients underwent SOMC, compared to 50 patients underwent CP (100 aneurysms in total), using the same microsurgical instruments. The following variables were compared: operative time, angiographic cure, length of intensive care unit stay during the post-operative period, surgical complications, length of hospital stay after surgery until hospital discharge, intraoperative aneurysm rupture, aesthetic satisfaction with the scar, and neurological status at discharge. SOMC had a significantly shorter operative time in relation to PC (213.9 ± 11.09 min and 268.6 ± 15.44 min, respectively) (p = 0.0081).With respect to the cosmetic parameters assessed by the Visual Analog Scale, the average for SOMC was 94.12 ± 1.92 points, and the average for PC was 83.57 ± 4.75 points (p = 0.036). SOMC was as effective as PC in relation to successful aneurysm clipping (p = 0.77). The SOMC technique did not show advantages over PC in any other variable. Even in a general neurosurgery service lacking a specific structure for minimally invasive surgeries, SOMC was feasible and effective for treating intracranial aneurysms, using the same set of microsurgical instruments used for PC, obtaining better results in operating time and cosmetic satisfaction.

Abstract BACKGROUND Transpetrosal approaches have been used for treatment of tumors in the petroclival region for many years. Injury to the temporal lobe, however, has been a potential drawback of the techniques described to date. OBJECTIVE To describe modifications of the transpetrosal surgical technique, which allows extradural manipulation of the temporal lobe during the focused combined transpetrosal approach. This extra layer of protection avoids mechanical brain retraction, direct trauma to the temporal lobe and disruption of the local venous structures. METHODS The present manuscript describes an innovative technical nuance based on the combination of the focused combined transpetrosal approach, the peeling of the dural layers of the tentorium, and the reverse peeling of the middle fossa dura mater. Ample illustrative material is provided and illustrative cases are presented. CONCLUSION Peeling of the dural layers of the tentorium is a promising modification of the transpetrosal approach to increase the safety of the temporal lobe manipulation.

We investigate the existence of families of symmetric periodic solutions of second kind as continuation of the elliptical orbits of the two-dimensional Kepler problem for certain symmetric differentiable perturbations using Delaunay coordinates. More precisely, we characterize the sufficient conditions for its existence and its type of stability is studied. The estimate on the characteristic multipliers of the symmetric periodic solutions is the new contribution to the field of symmetric periodic solutions. In addition, we present some results about the relationship between our symmetric periodic solutions and those obtained by the averaging method for Hamiltonian systems. As applications of our main results, we get new families of periodic solutions for: the perturbed hydrogen atom with stark and quadratic Zeeman effect, for the anisotropic Seeligers two-body problem and to the planar generalized Størmer problem.

In this work, we suggest a simpler model to study the motion around irregularly elongated asteroids. This new model includes a variable density for the elongated asteroid. More precisely, we consider the motion of an infinitesimal mass attracted by the gravitational force induced by a body modeled as a non-homogeneous straight segment. We consider two situations: the segment can rotate uniformly with angular velocity , or it is fixed (i.e., ). The aim of this paper is to prove the existence of different family of periodic solutions for this problem, such as those obtained by the averaging method for Hamiltonian or as the continuation method of Poincaré by using discrete symmetries. We prove the existence of several families of periodic solutions as a continuation of circular orbits of the (fixed or rotating) Kepler problem. We also obtain periodic solutions as a continuation of circular solutions of the Coriolis problem. The analysis of the linear stability of some periodic solutions is considered. The families of periodic orbits studied in this work constitute an example of the variety of orbits that can be followed by a particle orbiting an elongated asteroid from an analytic point of view. This helps us understand the dynamics around these bodies.

In this work, we advance in the study of the Lyapunov stability and instability of equilibrium solutions of Hamiltonian flows. More precisely, we study the nonlinear stability in the Lyapunov sense of equilibrium solutions in autonomous Hamiltonian systems with n -degrees of freedom, assuming the existence of two resonance vectors k 1 and k 2 without interaction ( | k 1 | ≤ | k 2 | ). We provide conditions to obtain a type of formal stability, called Lie stability. In particular, we need to normalize the Hamiltonian function to any arbitrary order, and our results take into account the sign of the components of the resonance vectors. Subsequently, we guarantee some sufficient conditions to obtain exponential stability in the sense of Nekhoroshev for Lie stable systems. In addition, we give sufficient conditions for the instability in the Lyapunov sense of the full system. For this, it is necessary to normalize the Hamiltonian function to an adequate order, and assuming that the components of at least one resonance vector change of sign.

We consider time-periodic Hamiltonians of the form H(t,Q,P,ϵ) where ϵ is a small parameter: The unperturbed function H0(Q,P)=H(t,Q,P,0) is autonomous, integrable and has periodic solutions. It is assumed that these Hamiltonian functions can be written in convenient symplectic coordinates in the form H(t,θ,ϕ,q,I,J,p,ϵ)=H0(I,J)+ϵH1(t,θ,ϕ,q,I,J,p)+O(ϵ2),where θ,ϕ∈T, I,J∈R, q,p∈Rn. The aim of this paper is to show the existence of periodic solutions of the previous family of time-dependent 2π-periodically perturbed Hamiltonian systems under different approaches.

We consider time-periodic Hamiltonians of the form H ( t , Q , P , ϵ ) where ϵ is a small parameter: The unperturbed function H 0 ( Q , P ) = H ( t , Q , P , 0 ) is autonomous, integrable and has periodic solutions. It is assumed that these Hamiltonian functions can be written in convenient symplectic coordinates in the form H ( t , θ , ϕ , q , I , J , p , ϵ ) = H 0 ( I , J ) + ϵ H 1 ( t , θ , ϕ , q , I , J , p ) + O ( ϵ 2 ) , where θ , ϕ ∈ T , I , J ∈ R , q , p ∈ R n . The aim of this paper is to show the existence of periodic solutions of the previous family of time-dependent 2 π -periodically perturbed Hamiltonian systems under different approaches.

We consider the motion of an infinitesimal mass under the Newtonian attraction of N point masses forming a ring plus a central body where a Manev potential ( - 1 / r + e / r 2 , e ∈ R ), is applied to the central body. More precisely, the bodies are arranged in a planar ring configuration. This configuration consists of N - 1 primaries of equal mass m located at the vertices of a regular polygon that is rotating on its own plane about its center of mass with a constant angular velocity ω . Another primary of mass m 0 = β m ( β > 0 parameter) is placed at the center of the ring. Moreover, we assume that the central body may be an ellipsoid, or a radiation source, which introduces a new parameter e . The existence and stability of periodic solutions of the spatial Maxwell restricted N + 1 -body problem is obtained using averaging theory. The determination of KAM 3-tori encasing some of the linearly stable periodic solutions is proved. The planar case is moreover considered.

The existence of periodic, almost periodic, and asymptotically almost periodic of periodic and almost periodic of abstract retarded functional difference equations in phase spaces is obtained by using stability properties of a bounded solution.

The spatial equilateral restricted four-body problem (ERFBP) is a four body problem where a mass point of negligible mass is moving under the Newtonian gravitational attraction of three positive masses (called the primaries) which move on circular periodic orbits around their center of mass fixed at the origin of the coordinate system such that their configuration is always an equilateral triangle. Since fourth mass is small, it does not affect the motion of the three primaries. In our model we assume that the two masses of the primaries m2 and m3 are equal to μ and the mass m1 is 1−2μ. The Hamiltonian function that governs the motion of the fourth mass is derived and it has three degrees of freedom depending periodically on time. Using a synodical system, we fixed the primaries in order to eliminate the time dependence. Similarly to the circular restricted three-body problem, we obtain a first integral of motion. With the help of the Hamiltonian structure, we characterize the region of the possible motions and the surface of fixed level in the spatial as well as in the planar case. Among other things, we verify that the number of equilibrium solutions depends upon the masses, also we show the existence of periodic solutions by different methods in the planar case.