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Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.It is useful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics,.

You have two kidneys on either side of your spine that are each approximately the size of a human fist. They’re located posterior to your abdomen and below your rib cage.Your kidneys play several vital roles in maintaining your health. One of their most important jobs is to filter waste materials from the blood and expel them from the body as urine.

The kidneys also help control the levels of water and various essential minerals in the body. In addition, they’re critical to the production of:. vitamin D. red blood cells. hormones that regulate blood pressureIf your doctor thinks your kidneys may not be working properly, you may need kidney function tests. These are simple blood and urine tests that can identify problems with your kidneys.You may also need kidney function testing done if you have other conditions that can harm the kidneys, such as diabetes or high blood pressure.

They can help doctors monitor these conditions. To test your kidney function, your doctor will order a set of tests that can estimate your glomerular filtration rate (GFR). Your GFR tells your doctor how quickly your kidneys are clearing waste from your body. UrinalysisA screens for the presence of protein and blood in the urine. There are many possible reasons for protein in your urine, not all of which are related to disease. Infection increases urine protein, but so does a heavy physical workout. Your doctor may want to repeat this test after a few weeks to see if the results are similar.Your doctor may also ask you to provide a 24-hour urine collection sample.

This can help doctors see how fast a waste product called creatinine is clearing from your body. Creatinine is a breakdown product of muscle tissue. Serum creatinine testThis examines whether creatinine is building up in your blood. The kidneys usually completely filter creatinine from the blood. A high level of creatinine suggests a kidney problem.According to the, a creatinine level higher than 1.2 milligrams/deciliter (mg/dL) for women and 1.4 mg/dL for men is a sign of a kidney problem. Blood urea nitrogen (BUN)The also checks for waste products in your blood. BUN tests measure the amount of nitrogen in the blood.

Urea nitrogen is a breakdown product of protein.However, not all elevated BUN tests are due to kidney damage. Common medications, including large doses of aspirin and some types of antibiotics, can also increase your BUN. It’s important to tell your doctor about any medications or supplements that you take regularly. You may need to stop certain drugs for a few days before the test.A normal BUN level is between 7 and 20 mg/dL. A higher value could suggest several different health problems. Estimated GFRestimates how well your kidneys are filtering waste.

The test determines the rate by looking at factors, such as:. test results, specifically creatinine levels.

age. gender. race. height. weightAny result lower than 60 milliliters/minute/1.73m 2 may be a warning sign of kidney disease. Kidney function tests usually require a 24-hour urine sample and a blood test. 24-hour urine sampleA is a creatinine clearance test.

It gives your doctor an idea of how much creatinine your body expels over a single day.On the day that you start the test, urinate into the toilet as you normally would when you wake up.For the rest of the day and night, urinate into a special container provided by your doctor. Keep the container capped and refrigerated during the collection process. Make sure to label the container clearly and to tell other family members why it’s in the refrigerator.On the morning of the second day, urinate into the container when you get up. This completes the 24-hour collection process.Follow your doctor’s instructions about where to drop the sample off. You may need to return it either to your doctor’s office or a laboratory. Blood samplesBUN and serum creatinine tests require blood samples taken in a lab or doctor’s office.The technician drawing the blood first ties an elastic band around your upper arm.

This makes the veins stand out. The technician then cleans the area over the vein. They slip a hollow needle through your skin and into the vein. The blood will flow back into a test tube that will be sent for analysis.You may feel a sharp pinch or prick when the needle enters your arm.

The technician will place gauze and a bandage over the puncture site after the test. The area around the puncture may develop a bruise over the next few days. However, you shouldn’t feel severe or long-term pain.

Your doctor will focus on treating the underlying condition if the tests show. Your doctor will prescribe to control blood pressure if the tests indicate. They’ll also suggest lifestyle and dietary modifications.If you have, your doctor may want you to see an endocrinologist. This type of doctor specializes in metabolic diseases and can help ensure that you have the best blood glucose control possible.If there are other causes of your abnormal kidney function tests, such as and excessive use of painkillers, your doctor will take appropriate measures to manage those disorders.Abnormal test results mean you’ll probably need regular kidney function tests in the months ahead.

These will help your doctor keep an eye on your condition.

Arguments xa vector (of any mode including a ) or a factor or (forrep only) a POSIXct or POSIXlt or Dateobject; or an S4 object containing such an object. Further arguments to be passed to or from other methods.For the internal default method these can include: timesan integer-valued vector giving the(non-negative) number of times to repeat each element if oflength length(x), or to repeat the whole vector if oflength 1. Negative or NA values are an error.

Adouble vector is accepted, other inputs being coerced toan integer or double vector. Length.outnon-negative integer.

The desired length of theoutput vector. Other inputs will be coerced to a doublevector and the first element taken.

Ignored if NA or invalid. Eachnon-negative integer. Each element of xis repeated each times.

Other inputs will be coerced toan integer or double vector and the first element taken. Treated as1 if NA or invalid.times, length.outsee above.

DetailsThe default behaviour is as if the call was rep(x, times = 1, length.out = NA, each = 1). Normally just one of the additionalarguments is specified, but if each is specified with eitherof the other two, its replication is performed first, and then thatimplied by times or length.out.If times consists of a single integer, the result consists ofthe whole input repeated this many times. If times is avector of the same length as x (after replication byeach), the result consists of x1 repeatedtimes1 times, x2 repeated times2 times andso on.length.out may be given in place of times,in which case x is repeated as many times as isnecessary to create a vector of this length. If both are given,length.out takes priority and times is ignored.Non-integer values of times will be truncated towards zero.If times is a computed quantity it is prudent to add a smallfuzz or use. And analogously for each.If x has length zero and length.out is supplied and ispositive, the values are filled in using the extraction rules, that isby an NA of the appropriate class for an atomic vector( 0 for raw vectors) and NULL for a list.

NoteFunction rep.int is a simple case which was provided as aseparate function partly for S compatibility and partly for speed(especially when names can be dropped). The performance of rephas been improved since, but rep.int is still at least twice asfast when x has names.The name rep.int long precedes making rep generic.Function rep is a primitive, but (partial) matching of argumentnames is performed as for normal functions.For historical reasons rep (only) works on NULL: theresult is always NULL even when length.out is positive.Although it has never been documented, these functions have alwaysworked on vectors.