489 research outputs found
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
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