Semisimple classes containing no trivial near- rings

2001 ◽  
Vol 38 (1-4) ◽  
pp. 331-337
Author(s):  
R. Mlitz ◽  
R. Wiegandt
Keyword(s):  
Present Note ◽  
Point Of View ◽  
Constant Multiplication ◽  
Zero Multiplication ◽  
Trivial Multiplication

Beside near-rings with zero-multiplication or constant multiplication also other near- rings can be considered as near-rings with trivial multiplication. From a structure theoret- ical point of view it is reasonable to consider Kurosh{Amitsur radical classes which contain all near-rings with trivial multiplication. In the present note, continuing the investigations of [2], [4] and [5], we shall characterize the semisimple classes of such radical classes. Our characterizations look clumsier than those in [2], [4] and [5], but we exhibit that exact analogues of the mentioned characterizations cannot be achieved.

Anomalous Behavior of Heterogeneous Materials at Microwaves Frequencies: Introduction to Fractional Derivatives in Electromagnetism

1990 ◽  
Vol 189 ◽  
Author(s):  
F. Heliodore ◽  
D. Cottevieille ◽  
A. Le Mehaute
Keyword(s):  
Electromagnetic Wave ◽  
Physical Meaning ◽  
Fractional Derivatives ◽  
Heterogeneous Media ◽  
Present Note ◽  
Heterogeneous Materials ◽  
Anomalous Behavior ◽  
Point Of View ◽  
Unique Point ◽  
Validity Range

ABSTRACTThe present note introduces new trends in electromagnetic spectroscopy in complex media.When an electromagnetic wave propagates in heterogeneous media, some questions arise about both physical meaning and validity range of the traditional analysis. The aim of our advanced research is related to the generalisation of Maxwell's equations able todescribe both homogeneous and heterogeneous media from an unique point of view.

scholarly journals Square of Brownian motion

1975 ◽  
Vol 59 ◽  
pp. 1-8
Author(s):  
Hisao Nomoto
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Correlation Function ◽  
Finite Time ◽  
Present Note ◽  
Point Of View ◽  
Time Interval ◽  
Sample Function ◽  
Finite Time Interval ◽  
Zero Crossings

Let Xt be a stochastic process and Yt be its square process. The present note is concerned with the solution of the equation assuming Yt is given. In [4], F. A. Grünbaum proved that certain statistics of Yt are enough to determine those of Xt when it is a centered, nonvanishing, Gaussian process with continuous correlation function. In connection with this result, we are interested in sample function-wise inference, though it is far from generalities. A glance of the equation shows that the difficulty is related how to pick up a sign of . Thus if we know that Xt has nice sample process such as the zero crossings are finite, no tangencies, in any finite time interval, then observations of these statistics will make it sure to find out sample functions of Xt from those of Yt (see [2]). The purpose of this note is to consider the above problem from this point of view.

A suggested theory of electric conduction

1928 ◽  
Vol 24 (3) ◽  
pp. 438-444 ◽  
Author(s):  
W. H. McCrea
Keyword(s):  
Present Note ◽  
Point Of View ◽  
Electric Conduction ◽  
Atomic Processes ◽  
Important Advance

Sommerfeld has recently made a very important advance in the theory of electric conduction by employing the conception of electron waves and the new mechanics. His theory has been most successful in explaining a large number of phenomena. It treats them, however, from the macroscopic point of view and does not examine the atomic processes involved. The present note, intended to be merely tentative, seeks to attack the latter aspect of the problem.

On the Polygons Inscribed in one Conic and Circumscribed to Another

1924 ◽  
Vol 22 (2) ◽  
pp. 163-166
Author(s):  
W. Burnside
Keyword(s):  
Difference Equation ◽  
Present Note ◽  
Elliptic Functions ◽  
Point Of View ◽  
Image Position

This problem is in general treated in connection with the division of the periods of the elliptic functions. It is the object of the present note to shew, from a purely algebraical point of view, that the condition of closing of the polygon depends solely on a difference equation of the form

Note Introductory to the Study of Klein's Group of Order 168

1935 ◽  
Vol 31 (4) ◽  
pp. 468-481 ◽  
Author(s):  
H. F. Baker
Keyword(s):  
Present Note ◽  
Point Of View ◽  
Simplified Approach ◽  
Vast Literature

The group of order 168 discovered by Klein, which it is now known can be generated by two operations E, of order 7, and ϑ, of order 2, which satisfy the relations E7 = 1, ϑ2 = 1, (Eϑ)3 = 1, (E4ϑ)4 = 1, has a vast literature. But for the most part each author pursues the matter from his own point of view; and it seems it may be useful to present a simplified approach to the theory which takes account of various possible aspects, in particular the geometrical. This is the object of the present note; for most of its contents I have found it necessary to do fresh work, so that the paper is by no means a transcript of what is already available.

Excitation of multimode surface waves

1967 ◽  
Vol 63 (4) ◽  
pp. 1281-1283
Author(s):  
W. E. Williams
Keyword(s):  
Surface Waves ◽  
Radiation Field ◽  
Present Note ◽  
Incident Field ◽  
Point Of View ◽  
Impedance Boundary Condition ◽  
Infinite Plane ◽  
Total Field ◽  
Impedance Boundary ◽  
Impedance Condition

1. In a recent paper Karp and Karal(1) have suggested a generalization of the normal impedance boundary condition which might be applicable to surfaces which can support more than one surface wave and have determined the total field produced by a magnetic line dipole placed above an infinite plane characterized by such a condition. The theory is at this stage purely tentative and arguments concerning its plausibility are given in (1). The validity of the generalized impedance condition has also not yet been experimentally verified. From the point of view of experimental verification it would seem useful to have available a theoretical solution valid for an arbitrary electromagnetic field incident on a plane characterized by a generalized impedance condition and such a solution is given in the present note. By means of a technique used by the author in related problems (2,3) an explicit solution is given for an arbitrary incident field and it is shown that the radiation field and the amplitudes of the surface waves may be expressed in terms of the radiation field of the incident wave.

scholarly journals The Esscher Premium Principle: A Criticism

1981 ◽  
Vol 12 (1) ◽  
pp. 77-78 ◽  
Author(s):  
Benjamin Zehnwirth
Keyword(s):  
Loss Function ◽  
Utility Theory ◽  
Random Quantity ◽  
Present Note ◽  
Random Variable ◽  
Point Of View ◽  
The Other ◽  
Important Distinction ◽  
Image Position ◽  
Insight Into

The Esscher premium principle has recently had some exposure, namely, with the works of Bühlmann (1980) and Gerber (1980).Bühlmann (1980) devised the principle and coined the name for it within the framework of utility theory and risk exchange. Geruber (1980), on the other hand, gives further insight into the principle by studying it within the realm of forecasting in much the same spirit as credibility theorists forecast premiums. However, there is an important distinction: the choice of loss function.The present note sets out to criticize this relatively embryonic principle using decision theoretic arguments and indicates that the Esscher premium is essentially a small perturbation of the well established linearized credibility premium Bühlmann (1970).Let H denote the Esscher premium principle with loading h > o. That is, if X is an observable random variable and Y is a parameter (a risk or a random quantity) to be forecasted then the Esscher premium is given byThat is, H(Y ∣ X) is the Bayes decision rule for estimating Y given the data X relative to the loss functionwhere a is the estimate of Y, and of course the loading h is greater than zero.Now, for the clincher. This loss function is nonsensical from the point of view of estimation. It indicates a loss (or error) to the forecaster that is essentially the antithesis of relative loss.

scholarly journals The “Pellian Equation” and Some Series for π

1930 ◽  
Vol 26 ◽  
pp. xx-xxii
Author(s):  
A. C. Aitken
Keyword(s):  
Present Note ◽  
Point Of View ◽  
Pellian Equation

§ 1. The craze for extensive π-calculation which was so strange a feature of the last century was probably brought to an end not so much by the famous 707 decimals of W. Shanks in 1873 as by the demonstrations of Hermite and Lindemann, about the same time, regarding the transcendental nature of both e and π. Sporadic minor outbreaks of the disease still occur, of course, —Ramanujan in his earlier days was not entirely immune—and the series of the present note may seem symptomatic. It is hoped, however, that they will not be devoid of interest from the point of view of elementary trigonometry.

scholarly journals Power counting for nuclear forces in chiral effective field theory

2016 ◽  
Vol 25 (05) ◽  
pp. 1641006 ◽  
Author(s):  
Bingwei Long
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Effective Field Theory ◽  
Present Note ◽  
Effective Field ◽  
Power Counting ◽  
Point Of View ◽  
Nuclear Forces ◽  
Chiral Effective Field Theory ◽  
Group Invariance

The present note summarizes the discourse on power counting issues of chiral nuclear forces, with an emphasis on renormalization-group invariance. Given its introductory nature, I will lean toward narrating a coherent point of view on the concepts, rather than covering comprehensively the development of chiral nuclear forces in different approaches.

On a family of constructs in higher space

1926 ◽  
Vol 23 (1) ◽  
pp. 50-67
Author(s):  
C. G. F. James
Keyword(s):  
Present Note ◽  
Point Of View ◽  
Minimum Order ◽  
Linear Spaces

The constructs in question are represented by the vanishing of all determinants of two rows and columns drawn from a matrix of r + 1 rows and s + 1 columns, where r can be taken less than or equal to s. They are thus the multiple constructs of highest dimension on the well-known family of constructs generated by projective systems of linear spaces. In the present note the constructs are considered from a somewhat different point of view, the principal applications being to the determination of directrix loci of minimum order for the systems of spaces which they contain, and to the re-proof and extension of a known theorem.

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