the concept of mathematical proof has been controversial for the past few decades. different philosophers have offered different theories about the nature of mathematical proof, among which theories presented by lakatos and hersh have had significant similarities and differences with each other. it seems that a comparison and critical review of these two theories will lead to a better understan...

It is commonly recognized that a convenient formulation for problems in planar kinematics is obtained by considering links to be vectors in the complex plane. However, scant attention has been paid to the natural interpretation of complex vectors as isotropic coordinates. These coordinates, often considered a special trick for analyzing four-bar motion, are in fact uniquely suited to two new te...

Newton's claim to provide experimental proofs is often criticized. It argued that his are based on hypotheses and not inferred from the experiments alone. This criticism, however, applies a hypothetico-deductive analysis reasoning. Such an consistent with own understanding of proof method. The following reconstruction method intended do justice by applying conception iconic experiment. main pur...

An unsatisfiability proof is a series of applications of proof rules on an input formula to deduce false. Unsatisfiability proofs for a Boolean formula can find many applications in verification. For instance, one application is automatic learning of abstractions for unbounded model checking by analyzing proofs of program safety for bounded steps [6, 5, 4]. We can also learn unsatisfiable cores...

in this paper direct proofs of some common fixed point results for two and three mappings under weak contractive conditions are given. some of these results are improved by using different arguments of control functions. examples are presented showing that some generalizations cannot be obtained and also that our results are distinct from the existing ones.

design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structures are presented. these include techniques for designing non-separable multidimensional paraunitary matrices. properties of the structures are obtained and proofs given. paraunitary matrices play a central role in signal processing, in particular in the areas of filterbanks and wavelets.

A complete discussion of our results along with the proofs of the theorems noted here will appear in [3] and [4]. In this note we shall restrict ourselves to a description of the semiflow generated by (1), and we do this in the case where x, ƒ, a and g are real-valued. Because of the generality of our methods, they can be applied to many problems. Some of these applications are treated in [4]. ...