*Ray Lambert is the Senior Managing Editor for Science, Technology, and Mathematics (STM) journals at Duke University Press. As part of our Journals Publishing Series, we sat down with Ray to talk about some of the unique challenges and workflows of publishing mathematics journals.*

**Tell us a little about your position and math publishing at Duke University Press.**

I first came to the Press in 2005 as an Assistant Managing Editor for Humanities and Social Sciences journals. I left in November of 2007 and came back in February of 2009 as the Editorial Manager for *Duke Mathematical Journal* (*DMJ*) and worked with *DMJ*’s staff. (*DMJ *has had its own dedicated staff for a while, as it is one of our largest journals in terms of number of pages and frequency—currently 3,000 pages over 15 issues, which will increase to 3,600 over 18 issues starting in 2016).

It was later in 2009 that the Press began to publish two additional math journals, *Kyoto Journal of Mathematics* (*KJM*) and *Nagoya Mathematical Journal* (*NMJ*) on behalf of their respective universities.

As part of our agreements, we began to provide editorial and production services for these journals as well, and our *DMJ* group became the STM group in Journals Editorial. We also now provide editorial services for *Notre Dame Journal of Formal Logic* (*NDJFL*) and, beginning this year, *Annals of Functional Analysis* (*AFA*) and *Banach Journal of Mathematical Analysis* (*BJMA*), which are two journals that we publish on behalf of the Tusi Mathematical Research Group of Ferdowsi University of Mashhad, Iran. The STM group includes Marisa Meredith, Editorial Assistant for *DMJ*; Keller Kaufman-Fox, Assistant Managing Editor for STM Journals; and Roy Pattishall, Assistant Managing Editor for STM Journals. We all work closely with our colleagues in Journals Production, our copyeditors and proofreaders, and our typesetter.

*DMJ*, *KJM*, and *NMJ* are general journals and publish research articles in several areas of theoretical mathematics. The Tusi Mathematical Research Group’s journals, *AFA* and *BJMA*, publish short and long articles, respectively, on subjects such as matrix analysis, abstract harmonic analysis, functional analysis, operator theory, and related topics. And *NDJFL *publishes in all areas of logic and the foundations of mathematics.

All of our math journals are hosted in Project Euclid (Project Euclid is a mathematics and statistics publishing platform that Duke University Press co-manages with Cornell University Library). I think that we’ve developed a good working relationship with Project Euclid over the last few years, and we’ve tried to take advantage of the technical features of the Project Euclid platform (features such as reference linking and other searching capabilities) to enhance the content of our journals.

I think that being part of Project Euclid has helped our group learn a lot more about math publishing and about how information is shared within this academic community. I think that as a publisher we’re helping our journals by facilitating that information sharing–for example, we’ve joined other publishers in starting to share bibliographic information with arXiv (also at Cornell University Library), to establish links for earlier draft (preprint) versions of articles to their final published versions on Project Euclid.

### What’s different about publishing a mathematics journal compared to journal editing in general?

Many of the humanities and social sciences journals that we publish are interdisciplinary, so, with copyediting, I think that a big part of our approach is to keep the general reader in mind. I wouldn’t say that this is as big of a concern for the math journals, since we know that our readers are mathematicians and logicians, and we don’t expect too many casual readers. Of course, we want to maintain a high standard of quality and accessibility, so we focus on making sure that the language is clear and that terms and notation are used consistently within articles. Our main goal is to work with our authors to make sure that the final articles are well presented. Our group has a lot of collective experience in editing math articles; and while our approach is thorough, particularly to citations and bibliographies, we do know when to tread carefully!

In terms of editorial tools, though, the biggest difference is that every article that we work with is not in Microsoft Word but in LaTeX, which is both a computer mark-up language and typesetting platform that is widely used in the mathematics community and in other scientific disciplines. It is excellent for writing mathematical notation and formulas and for formatting standard parts of math research papers, such as theorems, proofs, and bibliographies. LaTeX, though, can present challenges to publishers, particularly to editorial and production staff. Everyone in the STM group learned LaTeX on the job, and we’ve trained some of our freelancers as well. With their help, and the help of our typesetter, we’ve become more LaTeX-savvy as a group and, for instance, now we edit TeX files electronically, using the WYSIWYG TeX editing program BaKoMa TeX Word.

**What are the steps in the editorial process, and how does it differ from other editorial workflows?**

All of the editorial work (copyediting and proofreading) that we do occurs after an article has been accepted for publication. Shortly after we receive the TeX and figure files of accepted articles from the journals’ academic editors, we begin working with our typesetter. They facilitate the editing and typesetting process for us by formatting the files according to the journal’s LaTeX style guide (known as a class file), which governs how things like the typefaces, margins, headings, and so on will look; that preparation process allows us to copyedit articles with BaKoMa, the editing tool that I mentioned earlier.

We then start the copyediting process, some of which we do in-house and for some we hire freelancers. Our editors focus on the language and the reference list, as well as on general formatting, and our typesetter applies our style rules for the presentation of all elements in the math formulas. The copyedited manuscript is then typeset and sent to the authors for review. We also provide a marked-up version of the copyedited manuscript, so authors can see what changes were made during the copyediting and typesetting process. I think that authors appreciate having this reference file, as it no doubt makes their chore of reviewing the proofs go much quicker. This also helps us identify any of those (very rare, of course!) instances where we might have introduced some errors.

**What new projects are you working on?**

One new project that we just implemented is an “advance publication” model for *DMJ *and *NDJFL*, in which articles will be published online in Project Euclid before they appear in an assigned print issue. Working with Journals Production, we are also moving *NDJFL *to this workflow and are implementing a “growing issue” model of advance publication for *AFA *and *BJMA*. These models will help keep the time from acceptance to online publication to about three months. These articles will have been copyedited, typeset, reviewed by the authors, corrected, assigned a DOI, and then posted online in PDF.

*All Duke University Press mathematics journals are hosted on **Project Euclid*. *Read more of our Journals Publishing Series here. Stay tuned for our next post featuring an interview with Project Euclid co-director Mira Waller.*

indeed this is very important as say prof dr mircea orasanu and prof horia orasanu

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also here there is an occasion to publish as say prof dr mircea orasanu and prof horia orasanu an article as concerning some foundations and a CURRICULUM VITAE following a themes

LAGRANGIAN AND CONSTRAINTS FOR SIMPLE EXAMPLES

ABSTRACT

In order to introduce the concept of generalized coordinates, let us first consider a few simple examples.

Consider, first, the problem of a simple pendulum moving in the x-y plane. The pendulum has a length l and moves under the action of gravity, so that its potential energy is mgh. The system is illustrated in the figure below.

We could use Cartesian coordinaets x and y to describe the location of the pendulum bob, but x and y are not independent. In fact, since the length of the pendulum is constant, they are related by

displaymath443

This condition would need to be imposed as a constraint on the system, which can be inconvenient. It is more natural to use the angle tex2html_wrap_inline540 that the pendulum makes with respect to the vertical to describe the motion. But what would be the equation of motion for tex2html_wrap_inline540 ? In order to find out what this is, we only need to express the Lagrangian in terms of tex2html_wrap_inline540 . Now, the Lagrangian in terms of x and y is givn by

displaymath445

where we have introduced a general potential function, however, for this example, we know that the potential is given by U(x,y) = -mgy.

The Cartesian coordinates x and y are related to tex2html_wrap_inline540 by a set of transformation equations:

eqnarray142

In order to transform the kinetic energy, we need the time derivatives of the transformation equations:

eqnarray144

Substituting the transformations and their derivatives into the Lagrangian gives

eqnarray150

Now, given the Lagrangian, we just turn the crank on the Euler-Lagrange equation and derive the equation of motion for tex2html_wrap_inline540 :

eqnarray160

so that the equation of motion is

eqnarray168

As another example, consider again a particle moving in the x-y plane subject to a potential U that is a function only of the distance of the particle from the origin of the coordinate system. This distance is tex2html_wrap_inline566 , so that U = U(r). An example would be a radial harmonic potential tex2html_wrap_inline570 , which is a “bowl” potential shown below:

Of course, we can choose to work in Cartesian coordinates, x, and y. In this case, we would write down the Lagrangian

displaymath447

where the potential U(r) is expressed as a function of x and y through the dependence of r on x and y. Then, the equations of motion for x and y can be computed with forces obtained via the chain rule

eqnarray182

which is perfectly correct. However, it obviscates some of the important physics of the problem, which can be revealed by working in polar coordinates r and tex2html_wrap_inline540 , which are more natural for this problem. These are related to x and y via the transformations:

eqnarray194

with time derivatives

eqnarray196

Substituting into the kinetic energy gives, after some algebra

eqnarray204

so that the Lagrangian can be expressed as

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! INTRODUCTION The equations of motion of a system can be cast in the generic form

displaymath177

where, for a Hamiltonian system, the vector function tex2html_wrap_inline563 would be

displaymath180

and the incompressibility condition would be a condition on tex2html_wrap_inline563 :

displaymath186

A non-Hamiltonian system, described by a general vector funciton tex2html_wrap_inline563 , will not, in general, satisfy the incompressibility condition. That is:

displaymath191

Non-Hamiltonian dynamical systems are often used to describe open systems, i.e., systems in contact with heat reservoirs or mechanical pistons or particle reservoirs. They are also often used to describe driven systems or systems in contact with external fields.

The fact that the compressibility does not vanish has interesting consequences for the structure of the phase space. The Jacobian, which satisfies

displaymath165

will no longer be 1 for all time. Defining tex2html_wrap_inline569 , the general solution for the Jacobian can be written as

displaymath199

Note that tex2html_wrap_inline571 as before. Also, note that tex2html_wrap_inline573 . Thus, tex2html_wrap_inline575 can be expressed as the total time derivative of some function, which we will denote W, i.e., tex2html_wrap_inline579 . Then, the Jacobian becomes

eqnarray202

Thus, the volume element in phase space now transforms according to

displaymath205

which can be arranged to read as a conservation law:

displaymath207

Thus, we have a conservation law for a modified volume element, involving a “metric factor” tex2html_wrap_inline581 . Introducing the suggestive notation tex2html_wrap_inline583 , the conservation law reads tex2html_wrap_inline585 . This is a generalized version of Liouville’s theorem. Furthermore, a generalized Liouville equation for non-Hamiltonian systems can be derived which incorporates this metric factor. The derivation is beyond the scope of this course, however, the result is

displaymath211

We have called this equation, the generalized Liouville equation Finally, noting that tex2html_wrap_inline587 satisfies the same equation as J, i.e.,

displaymath216

the presence of tex2html_wrap_inline587 in the generalized Liouville equation can be eliminated, resulting in

displaymath219

which is the ordinary Liouville equation from before. Thus, we have derived a modified version of Liouville’s theorem and have shown that it leads to a conservation law for f equivalent to the Hamiltonian case. This, then, supports the generality of the Liouville equation for both Hamiltonian and non-Hamiltonian based ensembles, an important fact considering that this equation is the foundation of statistical mechanics.

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in main moments appear important circumstances so that for prof dr mircea orasanu and prof drd horia orasanu used in many situations as Legendre formula and scleronoums problem and Riemann Hilbert problem for Lebesgue function as work and paper accepted at Louis university and COLLEGE LYCEUM MAGNA ,and these can not meet at Colleg virgil magearu . buc or Colleg traian ,buc or Lyc 39 ,Buc , that must learn more and more for established. Thus in this moment we have found the occasion that to appreciate multiple situations of science biology and chapters of mathematics

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