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

1. Bar-Yam, Y. Dynamics of Complex Systems; Addison-Wesley Publishing Company: Reading, MA, USA, 1997. [Google Scholar]

2. Mitchell, M. Complexity: A Guided Tour; Oxford University Press: Oxford, UK, 2009. [Google Scholar]

3. Bennett, C.H. How to define complexity in physics, and why. Complex. Entropy Phys. Inf. 1990, 8, 137–148. [Google Scholar]

4. Winfree, A.T. The Geometry of Biological Time, 2nd ed.; Interdisciplinary Applied Mathematics (Book 12); Springer: New York, NY, USA, 2000. [Google Scholar]

5. Badii, R.; Politi, A. Complexity: Hierarchical Structure and Scaling in Physics; Cambridge University Press: Cambridge, UK, 1997. [Google Scholar]

6. Nottale, L. Fractal Space-Time and Microphysics: Towards A Theory of Scale Relativity; World Scientific: Singapore, Singapore, 1993. [Google Scholar]

7. Nottale, L. Scale Relativity and Fractal Space-Time: A New Approach to Unifying Relativity and Quantum Mechanics; Imperial College Press: London, UK, 2011. [Google Scholar]

8. Agop, M.; Forna, N.; Casian-Botez, I.; Bejinariu, C. New theoretical approach of the physical processes in nanostructures. J. Comput. Theor. Nanosci. 2008, 5, 483–489. [Google Scholar]

9. Agop, M.; Murguleţ, C. El Naschie’s epsilon (infinity) space-time and scale-relativity theory in the topological dimention D = 4. Chaos Solitons Fractals 2008, 32, 1231–1240. [Google Scholar]

10. Agop, M.; Nica, X.; Gîrţu, M. On the vacuum status in Weyl-Dirac theory. Gen. Relativ. Gravit. 2008, 40, 35–55. [Google Scholar]

11. Agop, M.; Nica, P.; Niculescu, O.; Dumitru, D.G. Experimental and theoretical investigations of the negative differential resistance in a discharge plasma. J. Phys. Soc. Jpn. 2012, 81. [Google Scholar] [CrossRef]

12. Agop, M.; Păun, V.; Harabagiu, A. El Naschie’s epsilon (infinity) theory and effects of nanoparticle clustering on the heat transport in nanofluids. Chaos Solitons Fractals 2008, 37, 1269–1278. [Google Scholar

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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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here we consider some aspects and in agree with the above ideas of PROJECT EUCLID OF mathematics that must included n a form as say prof dr mircea orasanu and prof horia orasanu with these and as followed for

JOURNAL OF MATHEMATICS . PROJECT EUCLID

ABSTRACT

To graph a surface with patch x(u, v) in Mathematica is a relatively simple matter. First, input the equation for the patch. To input a function, the argument goes in square brackets, an underscore follows the variables’ names, and a colon precedes the equals sign. For example, to define the sphere, the command is: sphere[u_,v_]:={r Cos[u] Cos[v], r Sin[u] Cos[v], r Sin[v]}. Second, select an appropriate rectangle P = [u0, u1] x [v0, v1] in R2 on which to graph. Lastly, graph using the built-in function ParametricPlot3D. The syntax is as follows: ParametricPlot3D[x[u, v], {u, u0, u1}, {v, v0, v1}, Lighting->True]. (The lighting is important; otherwise the graph is all black.) It may be convenient to view the surface from a particular viewpoint (x, y, z); in this case, after Lighting->True, a comma then ViewPoint->{x,y,z} is added.

The amount of time Mathematica takes to solve a system of differential equations increases as the order of the system increases. For this reason, it is convenient to reduce the order of the system by introducing the auxiliary variables p = u’ and q = v’.

1 INTRODUCTION

This yields the system

(12)

Now, these equations are inputted into Mathematica, as in Figure 1. To make this easier, the partial derivatives of x are designated as functions of x before inputting the differential equations.

Therefore, {u0, v0} and ang give the necessary initial conditions to give a unique geodesic.

Figure 3

Take[…, {a,b}] selects the ath through bth elements of a list and outputs them in another list; First[…] gives the first element of a list as a number. So First[Take[geo…, {3,3}] gives the numeric value of u’’.

To display the solution on a surface, two different plots are made and saved. First, the equations are solved: solution1=solvetest1[ x,0,{u0,v0},ang,tfin]. Next, the geodesic is plotted:

g1=ParametricPlot3D[Evaluate[Append[x[u[t],

v[t]], AbsoluteThickness[3]] /. Solution1],

{t,0,tfin}],

and the surface is plotted:

g2=ParametricPlot3D[x[u,v], {u, u1, u2}, {v, v1,

v2}, Lighting->True].

Lastly, the two plots are shown together: Show[g1,g2,Lighting-> True,ViewPoint->{x,y,z}]. Finding the proper viewpoint depends on the geodesic, and often requires trial and error. Now, we give specific examples of

this

2 FORMULATION

In keeping with the aims of the journal the editorial hand is used very lightly. This is an international unrefereed journal which aims to stimulate the sharing of ideas for no other reason than an interest in the ideas and love of discussion among its contributors and readers. If a contribution has some relevance to the broad areas of interest concerned, and contains some features of value it will be included; and these criteria are used very liberally.

Please send any items for inclusion to the editor including an electronic copy on disc or E-mail. Word for Windows versions 6 and 7 preferred, but most word processing formats can be accommodated. Most items are welcome include papers, short contributions, letters, discussions, provocations, reactions, half-baked ideas, notices of relevant research groups, conferences or publications, reviews of books and papers, or even books or papers for review. Diagrams, figures and other inserted items are not always easy to accommodate and can use up a great deal of web space, so please use these economically in submissions.

Copyright Notice.

All materials published herein remain copyright of the named author, or editor if unattributed. Permission is given to freely copy this journal’s contents on a not-for-profit basis, provided any reproduction preserves the integrity of each article as a whole, apart from extracted quotes, and full credit is given to the author and the journal in each case.

Theme.

There is no overall theme to this issue. There are philosophical reflections on mathematics, reports of mathematics education reflections and research, items on the and news items. Although largely euro- and anglo-centric, the issue has a better representation of world issues and languages.

Acknowledgements.

The journal is made possible by the generous support of University of Exeter. Special thanks go to Mrs. Pam Rosenthal, Mathematics Technician at the School of Education for technical assistance in publishing this journal on the web. Any opinions expressed here are personal to the author(s) and not the responsibility of the University of Exeter.

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here we have some important aspects as say prof dr mircea orasanu and prof horia orasanu as followed concerning

LAGRANGIAN AND HAMILTONIAN RELATIONS WITH PARTIAL DIFFERENTIAL EQUATIONS

ABSTRACT

Jn(k4nz), etc.

This set of functions, Jn(kmnz) is orthogonal, since it is a solution to a Sturm-Liouville problem. The orthogonality condition satisfied by these functions is defined from equation [106] with a weighting function, p(z) = z, as discussed in the paragraph following equation [120]. Applying equation [106] to this problem we have the interval from 0 to R (in place of a to b) and we have a real function so we do not have to consider the complex conjugate. This gives the following orthogonality condition.

The values of mn, called the zeros of Jn, are the values of the argument of Jn for which Jn is zero. There are an infinite of values, mn, for which Jn(mn) = 0. Note the two subscripts for mn; m is an eigenfunction-counting index that ranges from one to infinity. Do not confuse this eigenfunction index with the index, n, for Jn. The index for Jn is set by the appearance of n in the original differential equation. Thus our set of eigenfunctions, for fixed n, will be Jn(k1nz), Jn(k2nz), Jn(k3nz),

[122]

We can apply the usual equation for an eigenfunction expansion from [109] to this set of Bessel functions.

1 INTRODUCTION

For convenience we define mn and kmn as follows.

[121]

[123]

If we multiply both sides of this equation by zJn(konz)dz and integrate from 0 to R we obtain the following result.

[123]

In the final step we use the orthogonality relationship which makes all terms in the sum, except for the term in which m = o, zero. We can use an integral table to evaluate the normalization integral.

[124]

Combining equations [123] and [124] and using m in place of o as the coefficient subscript gives the following result for the eigenfunction expansion coefficients.

[123]

Although this seems like an unlikely choice of eigenfunctions with which to expand an arbitrary f(x), we will see that such expansions become important in the consideration of partial differential equ. This operator for functions had properties similar to a Hermetian matrix, which could also be regarded as a Hermetian operator. We listed the following important results for Hermetian (or self-adjoint) operators in general and for the Sturm-Liouville operator in particular:

1. The eigenvalues of any self-adjoint or Hermetian operator are real.

2. The eigenfunctions of any self-adjoint or Hermetian operator defined over a region a x b form an orthogonal set over that region.

3. The eigenfunctions form a complete set if the vector space has a finite number of dimensions as in an n x n matrix.

4. The Sturm-Liouville operator has a complete set of eigenfunctions over an infinite-d

2 . FORMULATION

[98]

We noted that the Sturm-Liouville problem was an example of a Hermetian or self-adjoint operator

1. imensional vector space.

For functions, the inner product is defined in terms of the integral in equation [103]. This definition includes a weight function, p(x), which may be 1. The orthogonality condition for functions was given in equation [106], which is copied below.

[106]

If we had an orthonormal set of functions, then the value of ai in the previous equation would be one.Therefore, defining the weights

we have

The method of undetermined coefficient extends to multiple dimensions in a

straightforward manner if we consider multidimensional Taylor series expan-

sions. Thus, assuming a uniform and , we have

A finite difference approximation of the form

can be obtained by inserting the Taylor series expansions for vjk and determining

the coefficients by equating the coefficients of the different derivative terms.

Note 4

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FORM OF FORMULAS

ABSTRACT

be continuous on and differentiable on . If , then there exists at least one number c in at which .

[Intuitions:]

(1)

(2)

(3)

If (3) (figure), in . Thus, . If

(1) or (2), suppose takes on some positive values in . Intuitive, there is a number in , such that , where M is the maximum value of in . Then, .

◆

Theorem 14 (mean-value theorem):

Let be continuous on and differentiable on . If , then there exists at least one number c in at which

.

1 INTRODUCTION

Using the integral form of Gauss’ Law is perhaps the easiest way to solve most geometrically simple problems of this form. By geometrically simple, we mean those problems with a fair amount of symmetry. (WE CANNOT USE GAUSS’ LAW FOR SYSTEMS WITHOUT SYMMETRY TO GET ANALYTIC SOLUTIONS.) We can understand/determine how to solve the equation by looking at its form.

Note that the surface is closed. This implies that we can pick various surfaces that make solving the problem easier. Thus if we pick surfaces such that

or

Now for those sections of the surface where try to pick things such that . It this point the integrals become fairly straightforward and hence makes the problems easy to solve.

Note that computational versions of Gauss’ Law can still be used to solve more complex problems.

2.1.6.3. From the point form of Gauss’ Law

ADD HERE

2.1.7. Examples

2.1.7.1. Coulomb’s Law examples

Example 2.1

Electric field from a line of charges

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HISTORY OF LAGRANGIAN AND PUBLISHING

ABSTRACT

Figure 6.1 Bessel function, , , and .

Eq.(6.5) actually holds for n < 0 , also giving

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