recurrence

Examples of recurrence in the following topics:

• Series Solutions

  • In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients.
  • After substituting the power series form, recurrence relations for $A_k$ is obtained, which can be used to reconstruct $f$.
  • We can rearrange this to get a recurrence relation for $A_{k+2}$:
  • and all coefficients with larger indices can be similarly obtained using the recurrence relation.

• Pyelonephritis

  • Pyelonephritis requires antibiotic therapy, and sometimes surgical intervention, as well as treatment of any underlying causes to prevent its recurrence.

• Counting Rules and Techniques

  • Generating functions and recurrence relations are powerful tools that can be used to manipulate sequences, and can describe if not resolve many combinatorial situations.
  • A recurrence relation defines each term of a sequence in terms of the preceding terms.
  • The Fibonacci sequence is one example of a recurrence relation.

• Tenosynovitis

  • The causes for children are even less well known and have a recurrence rate of less than 1-5% after treatment.

• Branches of Spinal Nerves

  • The meningeal branches (recurrent meningeal or sinuvertebral nerves): These branch from the spinal nerve and re-enter the intervertebral foramen to serve the ligaments, dura, blood vessels, intervertebral discs, facet joints, and periosteum of the vertebrae.

• Other Infectious Eye Diseases

  • Herpetic simplex keratitis is a form of keratitis caused by recurrent herpes simplex virus in cornea.
  • Recurrent herpes of the eye in turn is caused by reactivation of the virus in a latently infected sensory ganglion, transport of the virus down the nerve axon to sensory nerve endings, and subsequent infection of ocular surface.
  • Focal or diffuse reduction in corneal sensation develops following recurrent epithelial keratitis.
  • Serologic tests in turn may show a rising antibody titer during primary infection but are of no diagnostic assistance during recurrent episodes.

• Compromised Host

  • Patients' treatments can leave them vulnerable to infection: immunosuppression and antacid treatment undermine the body's defences, while antimicrobial therapy (removing competitive flora and only leaving resistant organisms) and recurrent blood transfusions have also been identified as risk factors.

• Other Neurological Disorders

  • While there are several different types of epilepsy, all are characterized by recurrent seizures.

• Medical Imaging and Diagnostics

  • It may also be used as part of curative therapy, to prevent tumor recurrence after surgery, or to remove a primary malignant tumor.

• Therapeutic Uses of Radiation

  • It may also be used as part of curative therapy, to prevent tumor recurrence after surgery, or to remove a primary malignant tumor.