Related papers: Another look at e
Limit can be defined by two axioms: 1. Strict inequality between limits implies, ultimately, strict inequality between functions. 2. For constant functions limit is trivial. How can basic results on convergence be derived from these axioms?…
In discriminating between objects from different classes, the more separable these classes are the less computationally expensive and complex a classifier can be used. One thus seeks a measure that can quickly capture this separability…
In an earlier paper we provided an alternative to the standard gauge concept for deriving the classical electromagnetic wave equations. This alternative involves recognition of two previously overlooked basic equations and represents a…
Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
A new integral representation is derived using a definite integral given by Cauchy and used to evaluate a number of integrals containing the finite series of special functions.
These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
In this paper, a problem of testing is discussed when the samples have been drawn from the normal distribution. The study of hypothesis testing is also extended to Baye's set up.
In this short note we are presenting a method of finding particular solutions of nonhomegeneous linear equations. This approach is different from methods of undetermined coefficients or variation of parameters presented in virtually every…
These notes deal with finite-dimensional normed algegras, some basic examples, and the definition of the spectrum.
In this note, we derive a Leibniz rule for difference quotient.
We introduce the E-measure: a measure-like generalization of the E-value to a class of hypotheses. Unlike classical measures, E-measures are closed under infimums instead of addition. They arise from a compatibility axiom with logical…
This Note revisits the Leibnitz integral calculus method based on differentiation under the integral sign with respect to a parameter either already existing or introduced ad hoc. Through several cases exemplifying the method, it is shown…
By presenting the proofs of a few sample results, we introduce the reader to the use of nonstandard analysis in aspects of combinatorics of numbers.
In this short note, we derive an upper-bound for the sum of two comparison functions, namely for the sum of a class K and an extended class K function. To the best of our knowledge, the relations derived in this note have not been…
Distributed delay equations have been used to model situations in which there is some sort of delay whose duration is uncertain. However, the interpretation of a distributed delay equation is actually very different from that of a delay…
We define a proof system for exceptions which is close to the syntax for exceptions, in the sense that the exceptions do not appear explicitly in the type of any expression. This proof system is sound with respect to the intended…
Errors quoted on results are often given in asymmetric form. An account is given of the two ways these can arise in an analysis, and the combination of asymmetric errors is discussed. It is shown that the usual method has no basis and is…
This note imparts heuristic arguments and theorectical evidences that contradict the abc conjecture over the rational numbers. In addition, the rudimentary datails for transforming this problem into the doimain of equidistribution theory…