1. Morley, Marsh, Baldwin/Lachlan, Zilber; and Macintyre 2 2. The Borovik Program: CFSG and tameness 3 2.1. The setting: tame or not 3 2.2. The basic framework: even, odd, mixed, degenerate 4 3. Mixed type 5 3.1. Strong and weak embedding 5 3.2. Toward weak embedding: U(G) 6 3.3. The subgroups B(G) and D(G) 6 3.4. The strategy 7 3.5. The curious incident of the dog in the night 8 3.6. Weak embe...

Dependent type theory has several practical applications in the fields of theorem proving, program verification and programming language design. Ivor is a Haskell library designed to allow easy extending and embedding of a type theory based theorem prover in a Haskell application. In this paper, I give an overview of the library and show how it can be used to embed theorem proving technology in...

The 4-dimensional topological surgery conjecture has been established for a class of groups, including the groups of subexponential growth (see [6], [13] for recent developments), however the general case remains open. The full surgery conjecture is known to be equivalent to the question for a class of canonical problems with free fundamental group [5, Chapter 12]. The proof of the conjecture f...

Goemans showed that any n points x1, . . . xn in d-dimensions satisfying l 2 2 triangle inequalities can be embedded into l1, with worst-case distortion at most √ d. We extend this to the case when the points are approximately low-dimensional, albeit with average distortion guarantees. More precisely, we give an l2-to-l1 embedding with average distortion at most the stable rank, sr (M), of the ...

numerical analyses have shown that successful flow simulations and the accuracy of solution noticeably depend on the number of nodes used in computational meshing. a suitable meshing should have the capability of adapting with main flow parameters. because the number of total nodes that can be used in numerical simulation is limited, making such grid for complex flows is almost difficult, if it...

A Gorenstein sequence H is a sequence of nonnegative integers H = (1, h1, . . . , hj = 1) symmetric about j/2 that occurs as the Hilbert function in degrees less or equal j of a standard graded Artinian Gorenstein algebra A = R/I , where R is a polynomial ring in r variables and I is a graded ideal. The scheme PGor(H) parametrizes all such Gorenstein algebra quotients of R having Hilbert functi...

This paper introduces a novice solution methodology for multi-objective optimization problems having the coefficients in the form of uncertain variables. The embedding theorem, which establishes that the set of uncertain variables can be embedded into the Banach space C[0, 1] × C[0, 1] isometrically and isomorphically, is developed. Based on this embedding theorem, each objective with uncertain...