Conditional linearizability criteria for a system of third-order ordinary differential equations

We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by differentiating a system of second-order quadratically semi-linear ODEs and using the original system to replace the second derivative. The procedure developed splits into two cases, those where the coefficients are constant and those where they are variables. Both cases are discussed and examples given

Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible complex transformations can be used to obtain invertible real transformations that map a system of nonlinear partial differential equations into a system of linear partial differential equation. Explicit invariant criteria are given that provide procedures for writing down the solutions of the linearized equations. A few non-trivial examples are mentioned.Comment: This paper along with its first part ODE-I were combined in a single research paper "Linearizability criteria for systems of two second-order differential equations by complex methods" which has been published in Nonlinear Dynamics. Due to citations of both parts I and II these are not replaced with the above published articl

Appendiceal Mucocele – Unexpected Diagnosis in a Gynecology Department

Appendiceal mucocele is a rare entity, occuring in < 1% among appendicectomies, with a female predominance 4/1 (F/M) and a mean age of more than 50 years. The preoperative diagnosis is difficult; in most cases, it´s an intraoperative finding. In such work, we describe the two clinical cases occurring in last 10 years in our Department. Case 1 - 56 years old, posmenopausal, referred to our Department (02/2004) because an asymptomatic right adnexal septated cystic image, 53x48mm, with hipovascularized septa and a vascularised capsule with low flow resistance (IR 0,57). CA 125 elevated (71,3 U/mL).Exploratory laparotomy: an ovary increased, with a gelatanious consistency and an appendicular enlargement. Extemporaneous examination: a pseudomixoma peritonei, associated with a mucinous appendicular and an ovary tumor. It was performed a radical surgery. The histo-pathological analysis showed a mucinous cystadenoma of the appendix with peritoneal mucinous dissemination involving the ovary. Expectant attitude since the surgery, without clinical and imaging signs of recurrence. Case 2- 62 years old posmenopausal and asymptomatic woman, with a large adnexal mass detected on routine pelvic ultrasound: heterogeneous, 94x84mm without vascularisation signs in its interior. CEA was elevated (41,47U/ml). Exploratory laparotomy (02/2010): enlarged appendix and macroscopically normal pelvic organs. An appendicectomy was performed. The histo-pathological analysis showed a 10cm mucinous cystadenoma of the appendix and signs of localized (visceral peritoneal surface) pseudomyxoma peritonei. Currently she’s clinically well, in an expectant attitude. Despite mucoceles of the appendix are rare, they should be considered in women presenting with abnormal quadrant masses