The Open Mathematics Journal is an Open Access online journal, which publishes Research articles, Reviews and Letters in the field of mathematics, aiming at providing the most complete and reliable source of information on current developments in the field.

Manuscripts may be submitted directly to tomatj@benthamopen.org. Each peer-reviewed article that is published in a Bentham OPEN Journal is universally and freely accessible via the Internet in an easily readable and printable PDF format.

ONLINE MANUSCRIPT SUBMISSION: An online submission and tracking service via Internet facilitates a speedy and cost-effective submission of manuscripts.¹ The full manuscript has to be submitted online via our online submission service available via FTP at www.bentham-ftp.org/open/?tomatj

Manuscripts must be submitted by one of the authors of the manuscript, and should not be submitted by anyone on their behalf. The principal/corresponding author will be required to submit a Covering Letter along with the manuscript, on behalf of all the co-authors (if any). The author(s) will confirm that the manuscript (or any part of it) has not been published previously or is not under consideration for publication elsewhere. Furthermore, any illustration, structure or table that has been published elsewhere must be reported, and copyright permission for reproduction must be obtained.

For all online submissions, please provide your complete manuscript in the form of a single zipped folder containing soft copies of all the materials (main text in MS word format, figures / illustrations in TIFF, PDF or JPEG, tables in MS Word, and mathematical expressions in *TeX / MathML as separate files, while a PDF version of the entire manuscript must also be included, embedded with all the figures / illustrations / tables / mathematical expressions).

A successful electronic submission of a manuscript will be followed by a system-generated acknowledgement to the principal/corresponding author within 72 hours of the dispatch of the manuscript. Any questions with regards to the preparation of and submission of your manuscript to the journal should be addressed to tomatj@benthamopen.org and copied to atifa@benthamscience.org

NOTE: Any queries therein should be addressed to oa@bentham.org and copied to Jalil@bentham.org

Manuscript Preparation: The manuscript should be written in English in a clear, direct and active style. All pages must be numbered sequentially, facilitating in the reviewing and editing of the manuscript.

It is advisable that authors prepare their manuscript using the template available on the Web, which will assist in expediting. The template can be downloaded from www.bentham.org/open/template/ (Mac and Windows compatible; Microsoft Word XP/2000).

For further convenience, the customer support team available at Bentham Publication Services (www.benthampublishingservices.com) can provide assistance to authors for the preparation of manuscripts.

TeX/LaTeX File Users:
Though Bentham OPEN prefers manuscripts in MS Word format prepared using Template, users of *TeX/LaTeX processor may submit the original/source file of their manuscript along with a camera-ready PDF file in a presentable form (refer to Sample File).

Manuscript Length:

Letters: The maximum total page length for Letter type articles published in the journal is eight journal pages.

Research Articles: The minimum total page length for Research articles is ten journal pages. There is no maximum page length limit for research articles.

Review Articles: There is no page length limit for comprehensive Review articles. For Mini-Review articles, the maximum page length is eight journal pages.

There is no restriction on the number of figures, tables or additional files e.g. video clips, animation and datasets, that can be included with each article online. Authors should include all relevant supporting data with each article.

Manuscripts Published: The Journal accepts letters/ short communications, original research articles, and mini- and full-length review articles written in English. Supplements and proceedings of conferences may also be considered for publication.

Supplements: The journal will consider for publication supplements. A supplement will be a collection of articles (6 to 10 articles) based on a theme or topic of great importance to the field. A short summary proposal for editing a supplement should be submitted to the Editor at e-mail tomatj@benthamopen.org with a copy to oa@bentham.org

Conference Proceedings: The journal will consider for publication proceedings of relevant conferences in the field. Proposals for publishing conference proceedings should be submitted to the Editor at e-mail tomatj@benthamopen.org with a copy to oa@bentham.org

MANUSCRIPT SECTIONS FOR PAPERS: Manuscripts for research articles and letters submitted to the respective journals should be divided into the following sections; however, there can be an extension in the number of sections in review articles in accordance with the requirements of the topic.

Covering letter
Title page
Abstract
Text organization
List of abbreviations (if any)
Conflict of interest (if any)
Acknowledgements (if any)
References
Figures/illustrations (if any)
Formulae and Mathematical Expression (if any)
Tables and captions (if any)
Supportive/supplementary material (if any)

MICROSOFT WORD TEMPLATE: Although we accept manuscripts prepared as Microsoft Word, Word Perfect, or RTF files, the preferable mode of submission would be the Microsoft Word template that has been designed to generate a standard style and format for your article compatible to Bentham OPEN style.. Download the template

COVERING LETTER: A mandatory requirement is a covering letter that should be provided with the submitted manuscript, delineating the scope of your submitted article, declaring any potential competing interests, acknowledging contributions from authors and funding agencies, and certifying that the paper is prepared according to the ‘Instructions for Authors’. All inconsistencies in the text and in the reference section, and any typographical errors must be carefully checked and corrected before submission of the manuscript. Download the Covering letter

TITLE: The title should be precise and brief and must not be more than 120 characters. Authors should avoid the use of non-standard abbreviations. The title must be written in title case except for articles, conjunctions and prepositions.

Authors should also provide a short ‘running title’.

ABSTRACT: The abstract should not exceed 100-150 words for review and research papers and should be limited to only 50 words for letters, summarizing the essential features of the article. The use of abbreviations should be reduced to a minimum and the references should not be cited in the abstract.

TEXT ORGANIZATION: The main text should begin on a separate page and should be divided into separate sections. For Research articles, the preparation of the main text must be structured into separate sections as Introduction, Materials and Methodology, Results, Discussion and Conclusion. For Review and Letter articles, the manuscript should be divided into title page, abstract and the main text. The text may be subdivided further according to the areas to be discussed, which should be followed by the Acknowledgement (if any) and Reference sections. The review article should mention any previous important reviews in the field and contain a comprehensive discussion starting with the general background of the field. It should then go on to discuss the salient features of recent developments. The authors should avoid presenting material which has already been published in a previous review. For further details regarding the journals’ requirements, refer to the journal’s Template. The authors are advised to present and discuss their observations in brief. The manuscript style must be uniform throughout the text and 10 pt Times New Roman font should be used. The full term for an abbreviation should precede its first appearance in the text unless it is a standard unit of measurement. The reference numbers should be given in square brackets in the text.

Greek Symbols and Special Characters: Greek symbols and special characters play a prominent role in the manuscript. These symbols often undergo formatting changes and get corrupted or lost during preparation of a manuscript for publication. To ensure that all special characters used are embedded in the text, these special characters should be inserted as a symbol but should not be a result of any format styling (Symbol font face) otherwise they will be lost during conversion to PDF/XML.²

Authors are encouraged to consult reporting guidelines. These guidelines provide a set of recommendations comprising a list of items relevant to their specific research design. All kinds of measurements should be reported only in International System of Units (SI).

Equations and Mathematical Expressions

1.	Avoid the use of built-up fractions in the text. If not avoided by the author(s), built-up fractions will be converted to equivalent expressions on the line when the paper is copyedited. In display matter, however, built-up fractions are preferred for clarity.
2.	Avoid the use of small-type mathematical expressions centered above or below arrows. If possible, try to use an alternative format.
3.	In the exponential function, avoid exponents having more than one or two characters.
4.	Avoid the use of reference numbers for equations that are not subsequently referred to in the paper. Costs are reduced if short mathematical equations and other expressions in the text are run in (instead of each being displayed on a separate line). Authors must expect that, when accepted papers are copyedited, "excess" equation reference numbers will be deleted and short equations will be run in with text.
5.	Be sure to indicate special marking for symbols (e.g., italics, boldface) and clearly identify any unusual symbols. Try to avoid underscored symbols because they often require hand composition and opening up lines and thus are expensive. In vector notations, indicate which letters or notations, if any, may be set in boldface type. Indicate if asterisks are to be set in superscript position or centered on the line.
6.	All equations should be indented and numbered as follows: (1)
7.	Equation number should be right justified. Put three dots(...) midway between the end of the equation and the equation number.
8.	Punctuation should not be used at the end of an equation.
9.	Particular care should be taken to distinguish between the number zero (0) and the letter O; the number one (1) and the letter l, the Roman letter v and the Greek letter nu (n). The decimal logarithm should be written "log" and the natural log "ln". The abbreviation of the exponential function is a roman e (for example, e x ) or exp (for example, exp (u2 + n)). In expressions of the type dxdt, the letter d (derivative function) is always written in roman, whereas the physical parameter (x or t) is always in italics. Numbers are written in numerals when they are followed by units, these being represented by their SI symbols (10 % but a few percent).
10.	In numerals, each group of three letters should be separated by a space (except for dates and postal codes).

Authors should provide the equations in *TeX/LaTeX file format separately as well as embedded in the manuscript.

Mathematical Materials
Mathematical symbols must be defined immediately where they are introduced.

Characters

Character fonts

The italic font should be used for mathematical symbols (this is the default font in *TeX/LaTeX’s math mode). In addition to variables and constants, the italic font should be used for particle symbols, symbols of quantum states, and group-theoretic designations.

Diacritical signs:

A diacritical sign is a marking placed directly above or below symbols, e.g., the arrow in .



Subscripts and superscripts:

All available characters can be used as subscripts or superscripts.
Position of a subscript or superscript is dictated by standard notation.

Examples:



Abbreviations in math:

Some abbreviations, such as those for mathematical functions and those used in superscripts or subscripts require special handling and are discussed below.

Abbreviations designating mathematical functions:

• Roman multiletter abbreviations must be closed up to the argument following and separated from any preceding symbol by a thin space, that is,

• To treat a function of a function enclose it in bold round parentheses, i.e.,

g(f(x))

• e and exp (for exponent) notation

The e form is appropriate when the argument is short and simple, i.e., e^ik·r, whereas exp should be used if the argument is more complicated.

Equation breaking (multilinear equations):

Mathematical expressions often need to be displayed on two or more lines (“broken”)

The best place for a break is just before an operator or sign of relation. These signs should begin the next line of the equation.

Equation numbering:

A principal equation and subordinate equations may be numbered (1), (1a), (1b), etc.

Bracketing and Grouping sequence:

For the purpose of grouping, the sequence of bracketing preferred is {[()]}, working outwards in sets ( ), [ ], and {}.

{ [ ( { [ ( ) ] } ) ] }

Limits and indices:

In text, however, space limitations require that single limit sums or integrals use subscripts and superscripts, for example

Fractions

Fractions can be “built up” with a fraction bar, a+b c , “slashed” with a solidus, (a + b)/c, or written with a negative exponent, (a + b)c^__1. In text all fractions must be either slashed or written with a negative exponent.

Multiplication signs:

The primary use of the multiplication sign is to indicate a vector product of three-vectors (e.g., k x A). Do not use it to express a simple product.

The center dot (•) should not be used to mean a simple product. Use the dot to represent inner products of vectors (k • r).

Mathematical terms:

The use of the following standard symbols is recommended.

LIST OF ABBREVIATIONS: If abbreviations are used in the text either they should be defined in the text where first used, or a list of abbreviations can be provided.

CONFLICT OF INTEREST: Financial contributions to the work being reported should be clearly acknowledged, as should any potential conflict of interest.

ACKNOWLEDGEMENTS: Please acknowledge anyone (individual/company/institution) who has contributed to the study by making substantial contributions to conception, design, acquisition of data, or analysis and interpretation of data, or who was involved in drafting the manuscript or revising it critically for important intellectual content. Please list the source(s) of funding for the study, for each author, and for the manuscript preparation in the acknowledgements section.

REFERENCES: References must be listed in the numerical system (Vancouver). All references should be numbered sequentially [in square brackets] in the text and listed in the same numerical order in the reference section. The reference numbers must be finalized and the bibliography must be fully formatted before submission.

See below few examples of references listed in the correct Vancouver style:

Typical Paper Reference:
[1] Marklof J. Pair correlation densities in homogenous quadratic forms. Ann Math 2003; 158: 419-71.

Book Reference:
[2] Ruelle D. Thermodynamic formalism. New York: Addison Wesley 1978.

Edited Book:
[3] Series C. Geometrical methods of symbolic coding. In: Ergodic theory, symbolic dynamics, and hyperbolic spaces (Trieste, 1989), Bedford T, Keane M, Series C, Eds. Oxford: Oxford University Press 1991; pp. 125-51.

Typical Chapter Reference:
[4] Romberg TA. Designing middle school mathematics materials using problems created to help students progress from informal to formal mathematical reasoning. In: Leutzinger LP, Smith SP, Ed. Mathematics in the middle, National Council of Teachers of Mathematics 1998; pp. 107-19.

Conference Paper and Proceedings:
[5] Williams MC, Sharp J. A collaborative parabolic quilt, in bridges: Mathematical connections in art, music, and science, conference proceedings, Sarhangi R, Ed. 2002; 143-9.

[6] Williams MC. Quilts inspired by mathematics, in meeting Alhambra, ISAMA-BRIDGES conference proceedings, Sarhangi R, Sequin C, Eds. 2003; 393-9.

Published Book (Monograph):
[7] Crane D. Invisible colleges: Diffusion of knowledge in scientific communities. Chicago: University of Chicago Press 1972.

Company Report:
[8] Carbonell JR 1970. Mixed-Initiative Man-Computer Instructional Dialogues, Technical Report 1971, USC/Information Sciences Institute, Marina del Rey, California.

University Technical Report:
[9] Rice J. Poligon: A system for parallel problem solving. Technical report, KSL-86-19, Dept. of Computer Science, Stanford Univ. 1986.

Dissertation or Thesis:
[10] Clancey WJ. Transfer of Rule-Based Expertise through a Tutorial Dialogue. Ph.D. diss., Dept. of Computer Science, Stanford Univ 1979b.

Forthcoming Publication:
[11] Barr A, Feigenbaum E. The handbook of artificial intelligence,1999; Vol. 12. Forthcoming.

Some important points to remember:

* References must be complete and accurate.
* Online citations should include the date of access.
* Journal titles should conform to the present ACM Guide to Computing Literature/Chemical Abstracts etc. abbreviations.
* If the number of authors exceeds six then et al will be used after three names (the term “et al.” should be in italics).
* Take special care of the punctuation convention as described in the above-mentioned examples.
* Avoid using superscript in the in-text citations and reference section.
* Abstracts, unpublished data and personal communications (which can only be included if prior permission has been obtained) should not be given in the reference section but they may be mentioned in the text and details provided as footnotes.
* The authors are encouraged to use a recent version of EndNote (version 5 and above) or Reference Manager (version 10) when formatting their reference list, as this allows references to be automatically extracted.

FIGURES / ILLUSTRATIONS: The authors should provide the illustrations as separate files, as well as embedded in the text file, numbered consecutively in the order of their appearance. Each figure should include a single illustration. No charges will be levied on the use of color figures except in the reprints. Each figure should be closely cropped to minimize the amount of white space surrounding the illustration.

If a figure consists of separate parts, it is important that a single composite illustration file be submitted, containing all parts of the figure.

Photographs should be provided with a scale bar if appropriate, as well as high-resolution component files.

Scaling/Resolution

For Line Art image type, which is generally an image based on lines and text and does not contain tonal or shaded areas, the preferred file format is TIFF or EPS, with colour mode being Monochrome 1-bit or RGB, in a resolution of 900-1200 dpi.

For Halftone image type, which is generally a continuous tone photograph and contains no text, the preferred file format is TIFF, with colour mode being or RGB or Grayscale, in a resolution of 300 dpi.

For Combination image type, which is generally an image containing halftone in addition to text or line art elements, the preferred file format is TIFF, with colour mode being or RGB or Grayscale, in a resolution of 500-900 dpi.

Formats

For illustrations, the following file formats are acceptable:

• Illustrator
• EPS (preferred format for diagrams)
• PDF (also especially suitable for diagrams)
• PNG (preferred format for photos or images)
• Microsoft Word (version 5 and above; figures must be a single page)
• PowerPoint (figures must be a single page)
• TIFF
• JPEG (conversion should be done using the original file)
• BMP
• CDX (ChemDraw)
• TGF (ISIS/Draw)

Bentham OPEN does not process figures submitted in GIF format.

If the large size of TIFF or EPS figures acts as an obstacle to online submission, authors may find that conversion to JPEG format before submission results in significantly reduced file size and upload time, while retaining acceptable quality. JPEG is a 'lossy' format, however. In order to maintain acceptable image quality, it is recommended that JPEG files are saved at High or Maximum quality.

Files should not be compressed with tools such as Zipit or Stuffit prior to submission as these tools will in any case produce negligible file-size savings for JPEGs and TIFFs, which are already compressed.

Image Conversion Tools

There are many software packages, many of them freeware or shareware, capable of converting to and from different graphics formats, including PNG.

Good general tools for image conversion include GraphicConverter on the Macintosh, PaintShop Pro, for Windows, and ImageMagick, which is available on Macintosh, Windows and UNIX platforms.

Note that bitmap images (e.g. screenshots) should not be converted to EPS, since this will result in a much larger file size than the equivalent JPEG, TIFF, PNG or BMP, with no increase in the quality. EPS should only be used for images produced by vector-drawing applications such as Adobe Illustrator or CorelDraw. Most vector-drawing applications can be saved in, or exported as, EPS format. In case the images have been originally prepared in an Office application, such as Word or PowerPoint, then the original Office files should be directly uploaded to the site, instead of being converted to JPEG or another format that may be of low quality.

TABLES:

* Data Tables should be submitted in Microsoft Word table format.
* Each table should include a title/caption being explanatory in itself with respect to the details discussed in the table. Detailed legends may then follow.
* Table number in bold font i.e. Table 1, should follow a title. The title should be in small case with the first letter in caps. A full stop should be placed at the end of the title.
* Tables should be embedded in the text exactly according to their appropriate placement in the submitted manuscript.
* Columns and rows of data should be made visibly distinct by ensuring that the borders of each cell are displayed as black lines.
* Tables should be numbered in Arabic numerals sequentially in order of their citation in the body of the text.
* If a reference is cited in both the table and text, please insert a lettered footnote in the table to refer to the numbered reference in the text.
* Tabular data provided as additional files can be submitted as an Excel spreadsheet.

SUPPORTIVE/SUPPLEMENTARY MATERIAL: We strongly encourage to append supportive material, for example a Power-point file containing a talk about the study, a Power-point file containing additional screenshots, a Word, RTF, or PDF document showing the original instrument(s) used, a video, or the original data (SAS/SPSS files, Excel files, Access Db files etc.). Published/reproduced material should not be included unless you have obtained written permission from the copyright holder, which should be forwarded to the Editorial Office in case of acceptance of your article for publication.

Supportive/Supplementary material intended for publication must be numbered and referred to in the manuscript. In-text citations (for example "see Power-point Appendix 1") as well as a section with the heading "Supportive/Supplementary Material" before the "References" section should be provided. Here, list all Supportive/Supplementary Material and include a brief caption line for each file describing its contents.

Any additional files will be linked into the final published article in the form supplied by the author, but will not be displayed within the paper. They will be made available in exactly the same form as originally provided. Please also make sure that each additional file is a single table, figure or movie (please do not upload linked worksheets or PDF files larger than one sheet). Supportive/ Supplementary material must be provided in a single zipped file.

Authors must clearly indicate if these files are not for publication but meant for the reviewers'/editors' perusal only.

AUTHORS AND INSTITUTIONAL AFFILIATIONS: The author will be required to provide their full names, the institutional affiliations and the location, with an asterisk in front of the name of the principal/corresponding author. The corresponding author(s) should be designated and their complete address, business telephone and fax numbers and e-mail address must be stated to receive correspondence and galley proofs.

REVIEWING AND PROMPTNESS OF PUBLICATION: All manuscripts submitted for publication will be immediately subjected to peer-reviewing, usually in consultation with the members of the Editorial Advisory Board and a number of external referees. Authors may, however, provide in their Covering Letter the contact details (including e-mail addresses) of four potential peer reviewers for their paper. Any peer reviewers suggested should not have recently published with any of the authors of the submitted manuscript and should not be members of the same research institution.

All peer-reviewing will be conducted via the Internet to facilitate rapid reviewing of the submitted manuscripts. Every possible effort will be made to assess the manuscripts quickly with the decision being conveyed to the authors in due course.

LANGUAGE AND EDITING: Manuscripts must be written in good English in a clear and correct style. In order to maintain uniformity throughout the text, the manuscript should be written in either American or British English. Submitted manuscripts will not be edited for style or language, and reviewers may advise rejection of a manuscript if it is compromised by grammatical errors. Non-native speakers of English may choose to make use of a copyediting and language editing service such as that provided by Bentham Publication Service (please contact at email: info@benthampublishingservices.com).

PROOF CORRECTIONS: Authors are required to proofread the PDF versions of their manuscripts before submission. To avoid delays in publication, proofs should be checked immediately for typographical errors and returned within 48 hours. Major changes are not acceptable at the proof stage. If unable to send corrections within 48 hours due to some reason, the author(s) must at least send an acknowledgement on receiving the galley proofs or the article will be published exactly as received and the publishers will not be responsible for any error occurring in the manuscript in this regard.

The corresponding author will be solely responsible for ensuring that the revised version of the manuscript incorporating all the submitted corrections receives the approval of all the authors of the manuscript.

COPYRIGHT: Authors who publish in Bentham OPEN Journals retain copyright to their work. Submission of a manuscript to a journal implies that all authors have read and agreed to the content of the Covering Letter. It is a condition of publication that manuscripts submitted to this journal have not been published and will not be simultaneously submitted or published elsewhere. Once submitted to the journal, the authors will not withdraw their manuscript at any stage prior to publication. Plagiarism is strictly forbidden.

PUBLICATION FEES: The publication fee details for each article published in the journal are given below:

Letters: The publication fee for each published Letter article submitted is $600.

Research Articles: The publication fee for each published Research article is $800.

Mini-Review Articles: The publication fee for each published Mini-Review article is $600.

Review Articles: The publication fee for each published Review article is $900.

Once the paper is accepted for publication, the author will receive by email an electronic invoice. The fee form is also available on the Web site at www.bentham.org/open/feeform Submissions from the Editorial Board Members of the journals will receive a special discount of 50% on the total publication fee. Submissions by authors from developing countries will receive a discount of 30% on the total publication fee charge.

REPRINTS: High quality printed reprints of published articles are available for purchase, if ordered, with a minimum number of 100 reprints.

¹ The submission process is compatible with version 3.0 or later of Internet Explorer and Netscape Navigator, and with most other modern Web browsers. It can be used from PC, Mac, or Unix platforms.

² In this connection, we recommend the use of Microsoft Word version 2000 and above.