Mucormycosis with extensive cranial nerve involvement as the first presentation of diabetes mellitus: A case report

Mucormycosis, a rare fungal infection, mainly affects individuals with diabetes mellitus and those who were immunocompromised and has a high mortality rate. Its most common presentation is similar to that of acute bacterial sinusitis with symptoms of nasal congestion, headache, and fever. The involvement of multiple cranial nerves in mucormycosis was rarely reported in the literature and indicates severe disease. Herein, we report the case of a 56-year-old man who was referred to the ophthalmology outpatient clinic for facial nerve palsy. He was treated with systemic steroids for 10 days with no improvement. On examination, he had a loss of vision and a frozen orbit due to involvement of cranial nerves II, III, IV, V, VI, and VII. An extensive workup revealed a hemoglobin A1C of 10%. However, he was never diagnosed with diabetes mellitus previously and denied any of the classical symptoms of diabetes mellitus. He underwent ethmoidectomy, maxillectomy, and drainage of an intraorbital abscess after appropriate imaging studies. Histopathology confirmed the diagnosis of mucormycosis, and the patient was started on systemic amphotericin B. This case emphasizes the importance of screening for diabetes mellitus. Early recognition of underlying diabetes mellitus in this patient may have prevented the development of mucormycosis along with its devastating complications.

Global searches of frozen orbits around an oblate Earth-like planet

A frozen orbit is beneficial for observation owing to its stationary apsidal line. The traditional gravitational field model of frozen orbits only considers the main zonal harmonic terms J2 and limited high-order terms, which cannot meet the stringent demands of all missions. In this study, the gravitational field is expanded to J15 terms and the Hamiltonian canonical form described by the Delaunay variables is used. The zonal harmonic coefficients of the Earth are chosen as the sample. Short-periodic terms are eliminated based on the Hori-Lie transformation. An algorithm is developed to solve all equilibrium points of the Hamiltonian function. A stable frozen orbit with an argument of perigee that equals neither 90° nor 270° is first reported in this paper. The local stability and topology of the equilibrium points are obtained from their eigenvalues. The bifurcations of the equilibrium points are presented by drawing their global long-term evolution of frozen orbits and their orbital periods. The relationship between the terms of the gravitational field and number of frozen points is addressed to explain why only limited frozen orbits are found in the low-order term case. The analytical results can be applied to other Earth-like planets and asteroids.

Effects of Geopotential and Atmospheric Drag Effects on Frozen Orbits Using Nonsingular Variables

The concept of frozen orbit has been applied in space missions mainly for orbital tracking and control purposes. This type of orbit is important for orbit design because it is characterized by keeping the argument of perigee and eccentricity constant on average, so that, for a given latitude, the satellite always passes at the same altitude, benefiting the users through this regularity. Here, the system of nonlinear differential equations describing the motion is studied, and the effects of geopotential and atmospheric drag perturbations on frozen orbits are taken into account. Explicit analytical expressions for secular and long period perturbations terms are obtained for the eccentricity and the argument of perigee. The classical equations of Brouwer and Brouwer and Hori theories are used. Nonsingular variables approach is used, which allows obtaining more precise previsions for CBERS (China Brazil Earth Resources Satellite) satellites family and similar satellites (SPOT, Landsat, ERS, and IRS) orbital evolution.