Duke University Press, MSP (Mathematical Sciences Publishers), and Project Euclid announce a new publishing partnership, Alloy: A Publishing Services Alliance.

Alloy was forged with two goals in mind: to offer journals the finest suite of nonprofit publishing services available in the field, and to welcome publishers into a collaboration that treats journals as true partners, not just as clients or profit centers.

MSP founder and president Rob Kirby said, “MSP was conceived as an alternative to the big, profit-driven publishers. We are thrilled to join forces with Duke University Press and Project Euclid in pursuit of our goal to strengthen, defend, and expand independent scientific publishing.”

Each organization will bring its own set of strengths, skills, and experience to the partnership. Alloy features:

- editorial management supported by EditFlow from MSP,
- editing and production from MSP,
- marketing, sales, and customer relations from Duke University Press,
- and online presence from Project Euclid.

Duke University Press Director Steve Cohn said, “We are delighted to bring MSP into the long and very successful collaboration between DUP and Project Euclid. They will bring to this partnership deep knowledge of mathematics and the math community, plus the very best peer-review system in existence for use with math-related subject matter.”

“Providing publishers with the hosting services they need to be competitive and discoverable has always been at the core of Project Euclid’s mission. With MSP and Duke University Press, we have found like-minded partners who can offer publishers truly excellent solutions to the rest of the publication process,” said Leslie Eager, Project Euclid’s Director of Publishing Services.

For more information about collaborating with Alloy, contact Erich Staib at erich.staib[at]dukeupress[dot]edu.

To learn more about Duke University Press, MSP, and Project Euclid, read the full press release.

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LAGRANGIAN AND DEFINING A CONSTRAINT

Author Horia Orasanu

ABSTRACT

There are many instances in which the basic physics is known (or postulated), and the behavior of a complex system is to be determined. A typical example is that in which there are too many particles for the problem to be tractable in terms of single-particle equations, and too few for a statistical analysis to apply. In such situations, use of a computer may furnish information on enough specific cases for the general behavior of the system to be discernable. If the basis physics is postulated but not known, a computer simulation can relate the theory to observations on complex systems and thus test the theory.

1 INTRODUCTION

sophisticated methods, such as annealing, an algorithm for finding global minima which was inspired by an actual physical process. Some of the techniques are repetitive applications of deterministic equations. Others invoke stochastic processes (using “random” numbers), to focus on the important features.

While most applications of such simulations yield expected results, surprises do occur. This is analogous to an unexpected result from an experiment. Either the simulation/experiment went wrong (usual) or a new aspect of nature has been uncovered (rare). Examples of the latter are the identification of constants of motion in chaotic systems and the discovery of runaway motion in the drift and diffusion of ions in gas. Such discoveries are followed by “proper” theories and “proper” experiments, but the computer plays a vital role in the researchIn this lecture we recall the definitions of autonomous and non autonomous Dynamical Systems as well as their different concepts of attractors. After that we introduce the different notions of robustness of attractors under perturbation (Upper semicontinuity, Lower semicontinuity, Topological structural stability and Structural stability) and give conditions on the dynamical systems so that robustness is attained. We show that enforcing the appropriately defined virtual holonomic constraints for the configuration variables implies that the robot converges to and follows a desired geometric path. Numerical simulations and experimental rMethods

2 FORMULATION

In particular, we use the word ‘constructive’ in the sense that through the feedback action, we shape the dynamics of the system such that it possesses the desired structural properties, i.e. positive invariance and exponential stability of an appropriately defined constraint manifold. To this end, we define a constraint manifold for the system, and we design the control input of (29) to exponentially stabilize the constraint manifold. The geometry of this manifold is defined based on specified geometric relations among the generalized coordinates of the system which are called virtual holonomic constraints. In particular, we call them virtual constraints because they do not arise from a physical connection between two variables but rather from the actions of a feedback controller [20].

At this point, we augment the state vector of the system with three new states that in the following will be used in the control design. The introduction of these new variables to the state vector of the system, which will be used as constraint variables, is inspired by the notion of dynamic virtual holonomic constraints [21], i.e. virtual holonomic constraints which depend on the solutions of a dynamic compensator. The idea is to make the virtual holonomic constraints to depend on the variations of a dynamic parameter, which is used for controlling the system on the constraint manifold. The purpose of these additional states is explained below.

1. We introduce two new states [ϕo,ϕ˙o]T∈R2 where the second-order time derivative of ϕo will be used as an additional control input that drives the snake robot towards the desired path by modifying the orientation of the robot in accordance with a path following guidance law.

2. In the previous section, we defined the control objective for the joints and the head angle of the robot as a trajectory tracking problem. However, it is known that holonomic constraints are coordinate-dependent equality constraints of the form Φi(x)=0, where Φi is a time-independent function [25]. Thus, we remove this explicit time dependency from the reference joint trajectories by augmenting the state vector of the system with a new variable η, with η˙=2π/T and η(0)=0, where T denotes the period of the cyclic motion of the shape variables of the robot.

Subsequently, we denote the augmented coordinate vector of the system by

xˆ=[q1,…,qN−1,θN,px,py,ϕo,η]T∈RN+4

References

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sure here we must consider some aspects as say prof dr mircea orasanu and prof horia orasanu as followed and

a CURRICULUM VITAE

ABSTRACT

Example ( Other Indeterminate Forms )

Example Evaluate Example Evaluate .

Example Evaluate

Want to prove that

(1) Consider

Try to prove that

Hence, we have is strictly increasing on

(2) Try to prove that is continuous on

Then we have

(3) Try to prove that

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