It is well-known that the automorphism towers of infinite centre-less groups of cardinality κ terminate in less than (2 κ) + steps. But an easy counting argument shows that (2 κ) + is not the best possible bound. However, in this paper, we will show that it is impossible to find an explicit better bound using ZF C.

Loop Calculus introduced in [1], [2] constitutes a new theoretical tool that explicitly expresses the symbol Maximum-A-Posteriori (MAP) solution of a general statistical inference problem via a solution of the Belief Propagation (BP) equations. This finding brought a new significance to the BP concept, which in the past was thought of as just a loop-free approximation. In this paper we continue...

In the past, the creators of numerical programs had to choose between simple expression of mathematical formulas and static type checking. While the Lisp family and its dynamically typed relatives support the straightforward expression via a rich numeric tower, existing statically typed languages force programmers to pollute textbook formulas with explicit coercions or unwieldy notation. In thi...

In this paper the changes in the heat capacity of cooling towers has been investigated as a result of injecting combustion products of boilers. In the tower, the air is re-heated through mixing with hot flue gas after passing through the heat exchangers. As a result of this process, the draft of the cooling tower is increased. The additional produced draft depends on the ambient temperature and...

In this paper the changes in the heat capacity of cooling towers has been investigated as a result of injecting combustion products of boilers. In the tower, the air is re-heated through mixing with hot flue gas after passing through the heat exchangers. As a result of this process, the draft of the cooling tower is increased. The additional produced draft depends on the ambient temperature and...

Today, tower cranes are in widespread use on construction sites all around the world. An important issue that arises when operating these cranes is the oscillatory behavior that occurs during payload transportation, which can have severe effects on safety as well as accuracy of payload delivery. Due to the nonlinear nature of the rotating crane motion, controlling these oscillations is a comple...

This paper presents a mixed-integer nonlinear programming (MINLP) model for the optimal design of mechanical counter-flow cooling towers, subjected to standard design constraints. The objective function consists of the minimization of the total annual cost, which includes the capital cost of the cooling tower (that depends on the filling material and the air flowrate) and the operating cost (th...

Scale invariance provides a principled reason for the physical importance of Hilbert space, the Virasoro algebra, the string mode expansion, canonical commutators and Schroedinger evolution of states, independent of the assumptions of string theory and quantum theory. The usual properties of dimensionful fields imply an infinite, projective tower of conformal weights associated with the tangent...