摘要:

The following article arises from a case‐study involving the determination of the optimum sampling frequency in monitoring the quality of output of a continuous process. It is particularly useful in that it shows how the basic theoretical results of undergraduate statistics may be harnessed in solving a practical problem usually associated with industrial quality control.

ISSN:0020-739X    

DOI:10.1080/0020739830140111

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The article deals with the importance of the use of basic figures in mathematics. As an example the derivation of a new rule is demonstrated, by which series of cosnx and sinnx may be evolved without having to refer to a book. The starting formulae for n = 2 and n = 3 can immediately be read from adequate figures, being found by a simple reasoning. The series of higher integer values of n can be found afterwards by using the right half of Pascal's triangle. For proving this rule the complex forms of sine and cosine are needed. These formulae can be found easily from basic figures, constructed in the unit circle in the complex plane, depending on Euler's theorem. This theorem is proved by means of Maclaurin's series evolution, the starting point of which is also directly readable from a simple figure. The aim of the article is to point out a way of quickly deriving formulae, which are not inherently easy to memorize.

ISSN:0020-739X    

DOI:10.1080/0020739830140112

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A previous paper establishes a general treatment of integral transforms on the basis of Sturm‐Liouville theory and associated eigenfunction expansions [1]. In this paper the general theory is applied to the problem of flow under uniform pressure gradient of an electrically conducting incompressible viscous fluid through a uniform channel across which an initially uniform transverse magnetic field acts. The treatment is an alternative to the application of Fourier series which is often made.

ISSN:0020-739X    

DOI:10.1080/0020739830140113

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

On a regular polyhedron a particle moves from a vertex with equal probability to one of the neighbouring vertices taking a unit time. Let it start at a vertex to make a tour around. How long does it take on an average to visit every vertex at least once? Probabilistic calculations show that the expected time is 5.5 for a tetrahedron, 248/21 for an octahedron and 1996/95 for a cube. The last case needs a complicated transition schema with simultaneous equations. For an icosa‐hedron we only know that the expected time will fall between 37 and 38, which is estimated by 4000 times of simulated trials. A simple device is sufficient for programming the simulation.

ISSN:0020-739X    

DOI:10.1080/0020739830140114

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Guided reading is a teaching technique that offers advantages both in its, in some ways, more efficient use of staff and student time and in developing certain learning skills in students which are difficult to foster by other means. In this paper the introduction of guided reading courses into an Engineering Mathematics degree course is described, the students reactions to these courses is reported and some evaluatory comments made.

ISSN:0020-739X    

DOI:10.1080/0020739830140115

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A compound rule for the numerical integration of an analytic function along a directed line segment in the complex plane, basing on the Birkhoff‐Young 5‐point formula has been formulated. The rule has been tested in case of some examples and the convergence of the computed approximate values to the exact values of the integrals has been asserted.

ISSN:0020-739X    

DOI:10.1080/0020739830140116

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Using the Radon transform, we establish the weak and strong law of large numbers for a certain class of random variables. Our results are stated in terms of weighted averages for the mean. In terms of these.weighted averages an example is obtained where the Gaussian distribution does not satisfy the strong law.

ISSN:0020-739X    

DOI:10.1080/0020739830140117

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Let O be an annulus or a disc in the complex plane and let f be an analytic function on O. A lower bound for the area of the set f(O) is obtained in terms of the length of the curve f(O), where C is a certain circle concentric with O. The inequality is shown to be sharp and the cases of equality are determined. We indicate proofs which lie entirely within the domain of undergraduate mathematics.

ISSN:0020-739X    

DOI:10.1080/0020739830140118

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The electrical image of a point charge situated outside an earthed conducting sphere is found by a simple algebraic argument which does not assume that this image lies on the line joining the exterior charge to the centre of the sphere. This is a simplification of the more common methods discussed in standard textbooks.

ISSN:0020-739X    

DOI:10.1080/0020739830140119

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A 100000 variable nonlinear problem is stated and solved. A nonlinear blending problem is also presented along with a nonlinear system of equations involving trignometric, exponential and transcendental terms. These problems are solved with three different random number generators using multi‐stage Monte Carlo techniques. A further discussion of multi‐stage is presented.

ISSN:0020-739X    

DOI:10.1080/0020739830140120

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor