Physical Sciences and Mathematics Commons^™

Note On The Greatest Integer Function, M. A. Basoco

Department of Mathematics: Faculty Publications

In this note we wish to record certain finite sums involving the greatest integer function E(x), which seem to be of some interest. Hermite* has shown that the generating function for E(x) has the simple form, (1) x^b ÷(1 -x)(1 -x^a) = Σ_(n)E[(n + a - b) ÷ a]xⁿ, where a, b are positive integers. To him is due, likewise, the development (2) ) x^b ÷(1 -x)(1 + x^a) =Σ_(n)E₁[( …

Palaeontologic And Geologic Consideration Of Early Man In Nebraska, Erwin Hinckley Barbour, C. Bertrand Schultz

Bulletin of the University of Nebraska State Museum

There has been much discussion recently relative to the geologic age of Yuma and Folsom artifacts. The writers submit the following palaeontological and geological data which may aid in a better interpretation of the subject. This paper deals with three localities in Nebraska where Yuma and Folsom implements have been found with extinct mammals; namely, the Scottsbluff Bison Quarry, the Sand Hill blow-out sites, and the Sioux County artifact sites.

Test 252: Oliver Hart-Parr Row Crop 70 Hc, Nebraska Tractor Test Lab

Nebraska Tractor Tests

No abstract provided.

Test 267: Oliver Hart-Parr Row Crop 70 Kd, Nebraska Tractor Test Lab

Nebraska Tractor Tests

No abstract provided.

Test 255: Caterpiller Model Rd-7 (Diesel) 1000 R. P. M., Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 262: Cletrac Model Fg, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 275: Co-Op Number 2, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 268: Mccormick-Deering Model Wk-40 1600 R. P. M., Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 270: M-M Twin City Model Fta, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 274: Co-Op Number 3, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 264: Farmall F-20, Nebraska Tractor Test Lab

Nebraska Tractor Tests

EXPLANATION OF TEST REPORT: Farmall F-20

TEST A: The manufacturer's representative operates the tractor for a minimum of 12 hours using light to heavy drawbar loads in each gear.

This serves as a period for limber up, general observation and adjustments. Adjustments that are permissible include valve tappet clearance, breaker, point gap, spark plug gaps, clutch and others of a similar nature. No new parts or accessories can be installed without having mention made of it in the report. No data' are recorded during this preliminary run except the time that the engine is operated.

BELT HORSEPOWER TESTS

TEST B: …

Test 251: Case Rc, Nebraska Tractor Test Lab

Nebraska Tractor Tests

EXPLANATION OF TEST REPORT: Case RC

TEST A: The manufacturer's representative operates the tractor for a minimum of 12 hours using light to heavy drawbar loads in each gear.

This serves as a period for limber up, general observation and adjustments. Adjustments that are permissible include valve tappet clearance, breaker, point gap, spark plug gaps, clutch and others of a similar nature. No new parts or accessories can be installed without having mention made of it in the report. No data' are recorded during this preliminary run except the time that the engine is operated.

BELT HORSEPOWER TESTS

TEST B: …

Test 249: Twin City M-M Model Kta (Hc), Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 250: Silver King 3-Wheel, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 253: Caterpiller Model Rd-7 (Diesel) 61 H.P. At 850 R.P.M., Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 254: Caterpiller Model Rd-7 (Diesel) 69 H. P. At 850 R. P. M., Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 256: Caterpiller Model Rd-8 (Diesel) 850 R. P. M., Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 257: Caterpiller Model Rd-8 (Diesel) 1000 R. P. M., Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 258: Cletrac Model Cg, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 259: Cletrac Bg, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 260: Cletrac Ag, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 261: Cletrac E, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 261: Cletrac Model E, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 263: Cletrac Model Fd, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 265: Massey-Harris Challenger, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 266: Massey-Harris Pacemaker, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 269: Mccormick-Deering Model Wk-40, Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 271: Caterpiller Model 30 (Distillate), Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 272: Caterpiller Model 30 (Gasoline), Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …

Test 273: Caterpiller Model Rd-4 (Diesel), Nebraska Tractor Test Lab

Nebraska Tractor Tests

All tractors tested at the Nebraska Tractor Test Laboratory were certified by their manufacturers as being stock model machines, conforming to specifications filed with the application for test. No special or high-test fuels were used except as recommended by the manufacturer as necessary.

All results within the official tractor test report were actually attained in tests and are without correction or allowances for friction, temperature, altitude, etc. The results were initially accomplished with the tractor in charge of skilled operators employed by the University.

Unless otherwise noted, each tractor was apparently in good condition at the end of the testing …