A New Approach to Nonstandard Analysis

Internal Set Theory: a New Approach to Nonstandard Analysis

1. Internal set theory. We present here a new approach to Abraham Robinson's nonstandard analysis [10] with the aim of making these powerful methods readily available to the working mathematician. This approach to nonstandard analysis is based on a theory which we call internal set theory (1ST). We start with axiomatic set theory, say ZFC (Zermelo-Fraenkel set theory with the axiom of choice [1...

a new approach to credibility premium for zero-inflated poisson models for panel data

هدف اصلی از این تحقیق به دست آوردن و مقایسه حق بیمه باورمندی در مدل های شمارشی گزارش نشده برای داده های طولی می باشد. در این تحقیق حق بیمه های پبش گویی بر اساس توابع ضرر مربع خطا و نمایی محاسبه شده و با هم مقایسه می شود. تمایل به گرفتن پاداش و جایزه یکی از دلایل مهم برای گزارش ندادن تصادفات می باشد و افراد برای استفاده از تخفیف اغلب از گزارش تصادفات با هزینه پائین خودداری می کنند، در این تحقیق ...

A Constructive Approach to Nonstandard Analysis

In the present paper we introduce a constructive theory of nonstandard arithmetic in higher types. The theory is intended as a framework for developing elementary nonstandard analysis constructively. More specifically, the theory introduced is a conservative extension of HA” + AC. A predicate for distinguishing standard objects is added as in Nelson’s internal set theory. Weak transfer and idea...

A New Approach to Buckling Analysis of Lattice Composite Structures

Buckling strength of composite latticed cylindrical shells is one of the important parameters for studying the failure of these structures. In this paper, new governing differential equations are derived for latticed cylindrical shells and their critical buckling axial loads. The nested structure under compressive axial buckling load was analyzed. Finite Element Method (FEM) was applied to mode...

Comments on Edward Nelson’s “internal Set Theory: a New Approach to Nonstandard Analysis”

Do infinitesimals exist? This question arises naturally in calculus when one wants to write f(x+Δx) f(x) + f ′(x)Δx. This equation should hold for infinitesimal Δx where the notation a b means that a− b is infinitesimal. Much calculus can be done without bothering to define infinitesimal and using the equation above as a working definition of f ′(x). For mathematicians, of course, this is not a...

FOUNDATIONS OF NONSTANDARD ANALYSIS A Gentle Introduction to Nonstandard Extensions