Introduction The investigation of Lane Emden HLEEL equation has a long standing history Hsee, e.g., @1 10D, to mention only part of a vast literatureL. Recently Schaudt @6D has shown that Picard type iteration scheme may be used to show the existence, uniqueness and regularity of global solutions of LEE , in particular, for n 3 1. In this paper it was shown that straightforward usage of Picard ...

Homotopy And Simple Homotopy Theory Feel lonely? What about reading books? Book is one of the greatest friends to accompany while in your lonely time. When you have no friends and activities somewhere and sometimes, reading book can be a great choice. This is not only for spending the time, it will increase the knowledge. Of course the b=benefits to take will relate to what kind of book that yo...

This paper reports the improvement of a bitterness sensor based on a lipid polymer membrane consisting of phosphoric acid di-n-decyl ester (PADE) as a lipid and bis(1-butylpentyl) adipate (BBPA) and tributyl o-acetylcitrate (TBAC) as plasticizers. Although the commercialized bitterness sensor (BT0) has high sensitivity and selectivity to the bitterness of medicines, the sensor response graduall...

The purpose of this paper is to show that ideas and techniques of the homotopy continuation method can be used to find the complete set of eigenpairs of a symmetric matrix. The homotopy defined by Chow, Mallet- Paret and York [I] may be used to solve this problem with 2""-n curves diverging to infinity which for large n causes a great inefficiency. M. Chu 121 introduced a homotopy equation...

Homotopy limits and colimits are homotopical replacements for the usual limits and colimits of category theory, which can be approached either using classical explicit constructions or the modern abstract machinery of derived functors. Our first goal is to explain both and show their equivalence. Our second goal is to generalize this result to enriched categories and homotopy weighted limits, s...

Working in homotopy type theory, we provide a systematic study of homotopy limits of diagrams over graphs, formalized in the Coq proof assistant. We discuss some of the challenges posed by this approach to formalizing homotopy-theoretic material. We also compare our constructions with the more classical approach to homotopy limits via fibration categories.

Certain naturally occurring spaces have isomorphic v 1-periodic homotopy groups. To each is associated a mapping telescope whose ordinary homotopy groups equal the v 1-periodic homotopy groups of the space. It is proved that the mapping telescopes of the spaces are homotopy equivalent .

Link homotopy has been an active area of research for knot theorists since its introduction by Milnor in the 1950s. We introduce a new equivalence relation on spatial graphs called component homotopy, which reduces to link homotopy in the classical case. Unlike previous attempts at generalizing link homotopy to spatial graphs, our new relation allows analogues of some standard link homotopy res...

We propose a new sheaf-theoretical method for the calculation of the monodromy zeta functions of Milnor fibrations. As an application, classical formulas of Kushnirenko [11] and Varchenko [23] etc. concerning polynomials on C will be generalized to polynomial functions on any toric variety.

Introduction 1 1. Notation 8 2. Finite group action on products of curves 9 3. The fundamental group of (C1 × C2)/G. 12 4. The structure theorem for fundamental groups of quotients of products of curves 14 5. The classification of standard isotrivial fibrations with pg = q = 0 where X = (C1 × C2)/G has rational double points 20 5.1. The singularities of X 21 5.2. The signatures 23 5.3. The poss...