Bulletin of Pure and Applied Sciences- Math & Stat.

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Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)

Year : 2020, Volume & Issue : BPAS-Maths & Stat 39E(1), JAN-JUN 2020

Bulletin of Pure and Applied Sciences Section-E-Math. & Stat. is devoted to the international advancement of organized knowledge on all aspects of Mathematics and Statistics. It is serving as a forum to publish refereed, well-written original research articles and studies that describe the latest research and developments in the area of mathematics and statistics. Scope of the journal includes: Finance, economics, mathematics, statistics and probability, theoretical developments and techniques. It provides a forum for comments by publishing original research contributions, scientific survey, case studies, book review and letter to the Editor-in-Chief. Bulletin of Pure and Applied Sciences Section-E-Math. & Stat. is issued six monthly, i.e. June and December of every year. The Editor-in-Chief/Managing Editor/Editorial Board etc. assumes no responsibility for the statements and opinions advanced by the contributors. The editorial staff in its work of examining papers, received for possible publication is assisted, in an honorary capacity, by a large number of distinguished scientists working in various parts of the world. Bulletin of Pure and Applied Sciences Section-E-Math. & Stat. is copy-righted. Manuscripts published in the Bulletin should not be reproduced without the written permission of the Editor-in-Chief.

About Editor-in-chief:

Prof. Dr. Lalit Mohan Upadhyaya

Dept. of Mathematics, MPG College, Mussoorie, Dehradun, Uttarakhand 248179, India

E-mail: lmupadhyaya@rediffmail.com


National Editorial Advisory Board

Prof. Dr. Naggor Gani

Dept. of Mathematics, Jamal Mohmmed College, Trichy, Tamil Nadu 620020, India E-mail: ganijmc@yahoo.co.in

Prof. Dr. D.K. Phukan

Dept. of Mathematics, Moran College, Moranhat, Assam 785670, India E-mail: drdevakanta@yahoo.com

Prof. Dr. S. Lakshmi

Dept. of Mathematics, K.N. Govt Arts College, Thanjavur, Tamil Nadu 613007, India E-mail: Seetalakshmi_lakshmi@yahoo.co.in

Prof. Dr. V.K. Tyagi

Dept. of Mathematics, SLCE, University of Delhi, Delhi-110032, India E-mail: vinodtyagi@hotmail.com

Dr. B. Selvaraj

School of Science and Humanities, Karunya University, Coimbatore, Tamil Nadu 641114, India E-mail: selvaraj@karunya.edu

Prof. Dr. C.P.S. Hungund

Dept. of Statistics, Gulbarga University, Gulbarga, Karnataka 585106, India E-mail: chidghana@yahoo.co.in

Prof. Dr. M.A. Goalie

Dept. of Mathematics, Saranathan College of Engineering, Trichy, Tamil Nadu 620012, India E-mail: gopalanma@yahoo.com

Prof. Dr. M.V. Khaparde

Dept. of Statistics, RTM Nagpur University, Nagpur, Maharashtra 440033, India E-mail: mvkkhaparde@yahoo.co.in

Prof. Dr. P. Rajasekhara Reddy

Department of Statistics, S.V. University, Tirupati, Andhra Pradesh 517502, India. E-mail: putharsr@yahoo.co.in

Prof. Dr. P.L. Sharma

Dept. of Mathematics, H. P. University, Shimla, Himachal Pradesh 171005, India E-mail: plsharma1964@gmail.com, pl.sharma@hpuniv.ac.in

Dr. N.Ch. Bhatra Charyulu

Department of Statistics, University College of Science, Osmania University, Hyderabad, Telangana 500007, India E-mail: dwarakbhat@osmania.ac.in; vedithbhat@gmail.com

Prof. Dr. S.C. Malik

Dept. of Statistics, M.D. University, Rohtak, Haryana124 011, India E-mail: sc_malik@rediffmail.com

Prof. Dr. S.C.P. Halakatti

Dept. of Mathematics, Karnataka University, Dharwad, Karnataka 580 003, India. E-mail: scphalakatti@gmail.com

Prof. Dr. M.C. Raju

Annamacharya Institute of Technology and Sciences, Rajampet, Andhra Pradesh 516126. India E-mail: drmcraju@yahoo.co.in

Dr. Pankaj Kumar Das

Department of Mathematical Sciences, Tezpur University, Napaam, Tezpur, Assam 784028 India E-mail: pankaj4thapril@yahoo.co.in

Dr. Rajani Ballav Dash

Ravenshaw University, Cuttack, Odisha 753003, India E-mail Id-rajani_bdash@rediffmail.com,rajaniballavdash@gmail.com

Dr. Viresh Sharma

Department of Mathematics, N.A.S. (P.G.) College, Meerut, Uttar Pradesh 250003, India E-mail: vireshsharma1@yahoo.com

Dr. Vikas Poply

Department of Mathematics, K.L.P. College, Rewari, Haryana 123401, India E-mail: vikaspoply@gmail.com

Dr. PR Jayashree

Department of Mathematics, Presidency College, Chennai, Tamil Nadu 600005, India E-mail: vprjaya@gmail.com

Dr. Sai Lakshmi Radhika

Department of Mathematics, BITS Pilani, Hyderabad, Telangana 500078, India E-mail: radhikatsl@hyderabad.bits-pilani.ac.in

Dr. Ganesh Mahto

S.N. Sinha College, Warisaliganj (Nawada), Magadh University, Bodh Gaya, Bihar 805120, India. E-mail: ganeshmahto0201@gmail.com

Dr. Dinesh Kumar Madan

Chairperson, Department of Mathematics, Ch Bansi Lal University, Bhiwani, Haryana 127021, India.E-mail: dineshmadan@cblu.ac.in, dk_madaan@rediffmail.com

Dr. P. Chandra Reddy

Department of Humanities and Sciences, Annamacharya Institute of Technology and Sciences (Autonomous)Rajampet, Andhra Pradesh 516126, India E-mail: chandramsc01@gmail.com

Dr. Jyotindra C. Prajapati

Department of Mathematics, Vallabh Vidyanagar, Anand, Gujarat 388120, India E-mail: drjyotindra18@gmail.com

Prof. Dr. V.K. Tyagi

Dept. of Mathematics, SLCE, University of Delhi, Delhi-110032, India E-mail:Â vinodtyagi@hotmail.com

International Editorial Advisory Board

Prof. Dr. Florentin Smarandache Dept. of Mathematics, University of New Maxico, Gallup, USA E-mail: smarand@unm.edu

Prof. Dr. Dmitri Robounsk P O Box 1546, Sunshine Plaza 4558, Queensland, Australia E-mail: rabounski@ptep-online.co

Dr. Zhong Li Dept. of Mathematics, Guangdong University of Petrochemical Technology, China E-mail: zhongli559@163.com

Prof. Dr. Aliakbar Montazer HaghighiDepartment of Mathematics, Prairie View A &M University, Texas E-mail: amhghaighi@pvamu.edu

Prof. Dr. Temur Z. Kalanov Home of Physical Problems, Pisatelskaya, Tashkent, Uzbekistan E-mail: tzk_uz@yahoo.com, t.z.kalanov@mail.ru

Prof. Dr. H.M. Srivastava Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada E-mail: harimsri@math.uvic.ca

Dr. Ayman Shehata Mohammed Ahmed Osman El-Shazly, Department of Mathematics , Faculty of Science, Assiut University, Assiut 71516, Egypt E-mail: drshehata2006@yahoo.com, ayman.ahmed1@science.au.edu.eg

Prof. Dr. Kuldeep Kumar Saxena Department of Statistics, University of Dodoma, Dodoma, Tanzania. E-mail: haufiles@gmail.com


The purpose of the Guide to Authors is to provide instructions and guidelines that will assist authors, editors, and reviewers in preparing material for publication in Bulletin of Pure and Applied Sciences (BPAS).

The style guidelines presented here should be followed by authors preparing a scientific research papers for publication in Bulletin of Pure and Applied Sciences (BPAS).

Manuscripts that do not adhere to the following instructions will be returned to the corresponding author for technical revision before undergoing peer review.

When you prepare your research paper,  it must contains  the following order:






List here all author affiliations including position in the department, department, institute, city, state, country, E-mail




Phone numbers

Facsimile numbers

E-mail address




Phone numbers

Facsimile numbers

E-mail address


The second page should carry the full title of the manuscript and an abstract (of no more than 150 words for case reports, brief reports and 250 words for original articles). The abstract should be structured and state the Context (Background), Aims, Settings and Design, Methods and Material, Statistical analysis used, Results and Conclusions.


Include up to six keywords that describe your paper for indexing and for web searches.


State the purpose of the article and summarize the rationale for the study or observation.


The methods section should include only information that was available at the time the plan or protocol for the study was written; all information obtained during the conduct of the study belongs in the Results section.


Present your results in logical sequence in the text, tables, and illustrations, giving the main or most important findings first. Do not repeat in the text all the data in the tables or illustrations; emphasize or summarize only important observations. Extra or supplementary materials and technical detail can be placed in an appendix where it will be accessible but will not interrupt the flow of the text; alternatively, it can be published only in the electronic version of the journal.


Include Summary of key findings (primary outcome measures, secondary outcome measures, results as they relate to a prior hypothesis); Strengths and limitations of the study (study question, study design, data collection, analysis and interpretation); Interpretation and implications in the context of the totality of evidence (is there a systematic review to refer to, if not, could one be reasonably done here and now?, what this study adds to the available evidence, effects on patient care and health policy, possible mechanisms); Controversies raised by this study; and Future research directions (for this particular research collaboration, underlying mechanisms, clinical research). Do not repeat in detail data or other material given in the Introduction or the Results section.


Summarize what the reviewer should take away from your case report both in terms of the topic and your management of the patient


Standard abbreviations should be used and be spelt out when first used in the text. Abbreviations should not be used in the title or abstract.


List here any individuals who contributed in the work but do not qualify for authorship base on the above criteria



Declare here if any financial interest or any conflict of interest exists


Recent and relevant references only;  (Surname First Name Middle Name, Surname First Name Middle Name. Title of article. Journal Name Year;Volume(Number):Full inclusive page numbers.)


Manuscript file format:

We request to submit article in Microsoft Word format (.DOC). If you are using another word processor please save final version of the manuscript (using ‘Save As’ option of the file menu) as a Word document. In this case please double check that the saved file can be opened in Microsoft Word. We cannot accept Acrobat .PDF or any other text files.

Page Setup:

Main Text: (Page Size-A4 (width 8.27″ X Height 11.69”),

Page Margin: Top:1”; Bottom:1”; Left:1.5”; Right:1”; Gutter:0”; Gutter position :Left),

Font Size for Title-14 Pt. Book New Times Roman,

Font size for Text-10 pt,

Line Space for Text-1 line space,

Table and Figures– Center Align.

Language and grammar:

Uniformly American English or Hindi (Kruti Dev 010 Font)

Abbreviations spelt out in full for the first time. Numerals from 1 to l0 spelt out

Numerals at the beginning of the sentence spelt out

General Format:

Before submission of the new manuscript authors should consider the following general rules for preparation of the manuscript. Please read these instructions carefully and follow the guidelines strictly.

Manuscripts must be typed on A4 (210 × 297 mm) paper, double-spaced throughout and with ample margins of at least 2.5 cm. All pages must be numbered consecutively. Starting with the title page as p.1, the text, which begins with p.2, is to be arranged in the following order: abstract, brief introduction, materials and methods, results, discussion, acknowledgements, references, figure legends, tables.

The first page of the full manuscript must begin with the title of the paper centered on the page in 14 point Bold Title Case (title case means first letter of each main word capitalized), the names of the authors (Initials – followed by a period each – Family Name) with the main author’s name mentioned first, the names and locations of the authors’ affiliations (Title Case), and the e-mail address of the main author. The title page must provide the title in English, a short title of not more than 45 characters (including spaces) to be used as running head, up to five topical key words in English for subject indexing, the full postal address of the corresponding author to whom proofs will be sent. The title should be brief and should indicate the species studied. Subtitles are not encouraged.

The abstract should not exceed 250 words, should be one paragraph and should be free of references and abbreviations. It should indicate clearly the scope and main conclusions of the paper.

The introduction should give the pertinent background to the study and should explain why the work was done.

The materials and methods (or methodology) should give essential details, including experimental design and statistical analysis.

The results should present the findings of the research. They should be free from discussion. Results should be written in the past tense.

The discussion should cover, but not simply repeat the new findings and should present the author’s results in broader context of other work on the subject interpreting them with a minimum of speculation.

The acknowledgements should be as brief as possible.

Equations should be typewritten and with the number placed in parentheses at the right margin. Reference to the equation should use the form ‘Eq. (3)’ or ‘(3)’


While presenting data, authors should anticipate the limitations set by the size and layout of the journal. Large and complex tables, figures and maps should be avoided in the main paper, but can be included in a data appendix for use by the reviewers.

Figures should be saved in a neutral data format such as JPEG, TIFF or EPS. PowerPoint and Word graphics are unsuitable for reproduction. Please do not use any pixel-oriented programmes. Scanned figures (in JPEG and TIFF formats) should have a resolution of 300 dpi (halftone) or 600 to 1200 dpi (line drawings) in relation to the reproduction size.

Any tables and figures that are included in the main text of the paper should be numbered separately, in the sequence that they are mentioned in the text.

Each table and figure should be presented on a separate page of the manuscript, with a brief and self-explanatory title. All text should be clearly legible, and all graphics and legends should be easily distinguished when printed in black and white. Tables should use horizontal lines only, with only blank space to separate columns.

Notes under each table and figure should be used to explain and specify the source of all data shown.


References must be cited in the text in superscript digits at end of sentence or paragraph before punctuation or full stop1. In case of two or more references, separate the superscript digits by comma1,2,6. Moreover, If there are more references but in continuous numbers then use dash between superscript digits2-6.Citation may be direct or indirect, see the following examples;

Direct citation

  1. a) Farooq et al. 1 studied the temperature effect on cuticular hydrocarbons of termite.
  2. b) According to Shafqat and Saba2, cuticular hydrocarbons can be used to identify termite species.
  3. c) Variations in cuticular hydrocarbons may also assist for species recognition and foraging behaviour, investigated by Zeeshan and Pasha3.

Indirect citation

  1. a) Temperature affects cuticular hydrocarbons of termite1. Cuticular hydrocarbons can be used to identify termite species2. Variations in cuticular hydrocarbons may also assist for species recognition and foraging behavior3


Generally, units must be abbreviated according to the International System of Units (SI units).  It is important to maintain the capital letters and lower case letters as they appear in the abbreviation to avoid confusion with the other abbreviations.


The list of references appears at the end of your work and gives the full details of everything that you have used, according to same chronological order as cited in the text.

 All sources must be referred in a consistent manner. Choose from the list of sources below, the examples given, provide a guide to the format and punctuation you should use.

  • Journal (Print)
  • Journal (Electronic)
  • Book
  • Book Chapter
  • Conference Papers

Journal Article (Print)


  1. Author’s surname, Initial
  2. Publication Year
  3. Article Title
  4. Name of Journal (in standard abbreviation)
  5. Volume
  6. Starting Pages
  7. Ending Pages
  8. Digital Object Identifier (DOI)
  9. Direct link of the published article


Sepaskhah, A.R. and M.M. Ghasemi, 2008. Every-other-furrow irrigation with different irrigation intervals for grain sorghum. Pak. J. Biol. Sci., 11: 1234-1239. DOI: 10.3923/pjbs.2008.1234.1239; PMID 236548759;

Journal Article (Electronic)


  1. Author’s surname, Initial
  2. Publication Year
  3. Article Title
  4. Name of Journal (with/without abbreviations)
  5. Volume
  6. Page Numbers (if applicable)
  7. Available at
  8. Accessed on (enter date you viewed the article)
  9. Digital Object Identifier (DOI)


Brittion, A., 2006. How much and how often should we drink? Br. Med. J., 332: 1224-1225.

Available from: http://bmj.bjjournals.com/cgi/content/full/332/7552/1224 [Accessed 2 June 2006].


  • Author/Editor’s Surname and initials
  • Year of publication
  • Title of Book
  • Edition (if applicable)
  • Place of publication: (followed by a colon)
  • Name of publisher
  • ISBN Number


Anderson, J. and M. Poole, 1998. Assignment and thesis writing. 3re Edn., John While and Sons.

Book Chapter

  • Author/Editor’s Surname and initials
  • Year of publication
  • Title of Chapter
  • In: (enter editor’s surname and initials)
  • Book Title
  • Edition (if applicable)
  • Place of publication: (followed by a colon)
  • Name of publisher
  • Page number
  • ISBN


Mason, J., 1999. Recent Developments in the Prediction of Global Warming. In: Energy Demand and Planning, McVeigh, J.C. and J.G. Morgue, (Eds.). E&FN Spon., pp: 34-52.

 Conference Papers

Conference paper’s should be referenced using the following format and punctuation.

  • Author’s surname, initials
  • Date of publication
  • Title of paper
  • In: Editor’s surname, initials, (if applicable)
  • Title of proceeding
  • Place of conference
  • Date of conference
  • Publishers
  • Page numbers of contribution


Clifton, J.J., 1999. Hazard prediction. In: Disaster prevention, planning and limitation. University of Bradford, 12-13 September 1989. Technical Communications Ltd., pp: 54-64.


Authors are asked to facilitate the review process by providing the names and e-mail addresses of at least three suitable reviewers, on the understanding that the editor is not bound by any such nomination. Failure to follow this request may delay the handling of your paper, since the editorial office may specifically ask you to nominate potential reviewers for papers covering unfamiliar areas.


Manuscript should be submitted electronically to Bulletin of Pure and Applied Sciences (BPAS) to facilitate rapid publication and minimize administrative costs. All manuscripts should be submitted through online submission system. A user ID and password for the site can be obtained on first use. Online submission ensures the quickest possible review and allows authors to track the progress of their papers. It is recommended that text files are uploaded as Microsoft Word documents or generic rich text format (RTF) files and figures as JPEG, GIF, TIFF or EPS files. Authors should read Guide to Authors carefully before submission of their manuscripts.

Note: In order to submit a NEW Manuscript to Bulletin of Pure and Applied Sciences (BPAS), you must be a registered user of BPAS Publications, if you do not register, please register before you submit a NEW Manuscript.

Submissions by anyone other than one of the authors will not be accepted. The submitting author takes responsibility for the paper during submission and peer review. If for some technical reason submission through the online submission system is not possible, the author may contact editorial office for help via e-mail (bpaspublications@gmail.com).

You can submit your article through mail across our mail id.

E-mail: bpaspublications@gmail.com

Online Submission of the Manuscripts

For online Submission go through link


Alternatively, please contact the Journal’s Editorial Office for further assistance.


The next step in the publication process involves reviewing the galley proofs for your article. Please return the checked galley proofs via e-mail (bpaspublications@gmail.com) or via online submission system within 72 hours of receipt. Late return of galley proofs may mean postponement to a later issue. Please make a copy of the corrected proofs before returning them; keep the copy for your records.

 This step is entirely the responsibility of the corresponding author. The galley proofs will not be read by editorial staff. Errors that you fail to mark will be published.

 The corresponding author of an accepted manuscript will receive e-mail notification and complete instructions when page proofs are available for review via a secure Web site. Final proof will be provided in Portable document format (PDF) files of the typeset pages. The attention of the authors is directed to the instructions which accompany the proof, especially the requirement that all corrections, revisions, and additions be entered on the proof and not on the manuscript.

 Note that you are being asked to correct errors, not to revise the paper. You will not be charged for our editing mistakes or typographical errors, but you will be charged for any alterations from the original text that you make on the galley proofs. Extensive alteration may require Editorial Board approval, possibly delaying publication.


Please follow these guidelines when reviewing the galley proofs:

Mark your corrections, in red ink, directly on the galley proofs. Make sure that your corrections are noticeable and easy to understand.

Check all type on the galley proofs. Check the title, the abbreviations list, and the author–paper documentation paragraph.

Check the table data against that in your original tables.

Check any equations against those in your original manuscript. Make sure special characters have not dropped out.

Check to be sure that figures are entirely legible, including any small-print text.

If you find an error, look again at the lines around the error. Mistakes tend to cluster.


The next step in the publication process is to submit finally checked galley proof.  Take the following steps to provide the final proof corrections:

Scan only those pages marked with corrections.

Save each scanned page in JPG format.

Submit all scanned pages via e-mail to bpaspublications@gmail.com

Write the statement like “No modification on page number 1, 2, 3, 7, 8” about the pages required no corrections.


Manuscripts submitted for publication must comply with the following ethical considerations:

Informed Consent:

Informed consent of the patients must be taken before they are considered for participation in the study. Patient identifying information, such as names, initials, hospitals numbers, or photographs should not be included in the written descriptions. Patient consent should be obtained in written and archived with the author.

Protection of Human Subjects and Animals in Research:

When conduction experiments on Human Subjects, appropriate approval must have been obtained by the relevant ethics committees. All the procedures must be performed in accordance with the ethical standards of the responsible ethics committee both (Institutional and national) on human experimentation and the Helsinki Declaration of 1964 (as revised in 2008). When reporting experiments on animals, authors must follow the institutional and national guidelines for the care and use laboratory animals.


The right to give or withhold authorization of disclosures: The patient generally has the right to control who has access to confidential information except as otherwise provided by law. The patient needs to give specific authorization or permission to allow a third party to have access to confidential information.

The right to maintain privacy: Only those persons directly involved in the care of the patient’s health problem should have access to private information. Health care workers should protect information revealed during provider-health care worker encounters, including all written or electronic records of these encounters.

The right to have autonomy: Autonomy is the right of a patient to determine what will be done with his or her body, personal belongings, and personal information; this concept applies to any adult person who is mentally competent. Sometimes the right to autonomy can be overridden in the interest of protecting others who may be harmed by the patient’s decisions.

The right to be given information: The patient has a right to information about his or her medical diagnosis, treatment regimen, and progress. This allows the patient to make appropriate, informed decisions about his or her health care.


For Authors:

All manuscripts for articles, original research article, review article, editorials, comments, book reviews and letters that are submitted to BPAS Publication’s journal(s) must be accompanied by a conflict of interest disclosure statement, or a declaration by the authors that they have no conflicts of interest to declare. All articles that are published in BPAS Publication’s journal(s) will be accompanied by a conflict-of-interest disclosure statement, or a statement that the authors have replied that they have no conflicts of interest to declare.

Authors should also disclose to editors any conflict of interest that may have influenced either the conduct or the presentation of research, including but not limited to close relationships with those who might be helped or hurt by the publication, academic interests and rivalries, and any personal, religious or political convictions relevant to the topic at hand.

In the paper, authors should include a draft statement that discloses all relevant conflicts of interest and affiliations. Relevance for financial conflicts of interest with private firms is defined as a relationship of any value with a firm with a stake in the subject of the manuscript, or its competitors. Relevance for patents is defined as any invention or pending invention connected in any way to the subject.


Any financial relationship of any size should be disclosed. These Potential conflicts of interest in relation to your submitted manuscript could include:

 Direct employment, either full or part-time;

Grants and research funding Consultancies;

Travel grants, speaking fees, writing fees and other honoraria;

Advocacy group;

Patents granted, whether or not generating royalties;

Stock ownership, investment in related “sector” funds, or stock options;

Membership on private sector scientific or other advisory boards, whether paid or unpaid.

In addition, any current negotiations regarding future employment or current job offers, either full- or part-time, must be disclosed.

Non-Financial Conflicts of Interest:

These may be personal, political, or intellectual and may include any expression of strongly held views relevant to the subject of the submission. Disclosable non-financial conflicts of interest would also include membership or affiliation with non-governmental organizations that have an interest in the submission.

For Editors, Articles Editors, and Peer Reviewers:

As a general rule, BPAS Publication’s journal(s) should require that all senior editorial personnel (editors in chief, managing editors, full-time assistant editors) avoid all financial relationships that might constitute a conflict of interest. Editorial managers should also avoid personal, political, or intellectual entanglements, organizational or otherwise, that could be construed as establishing a particular bias that might influence one’s judgments. Editors who maintain financial ties with companies or institutions that have an interest in the content of a journal undermine the editorial independence that is crucial to a journal’s credibility. Requiring editors to remain conflict-of-interest free assures rejected authors that bias or potential bias did not enter into the editorial decision to reject their manuscript.

Peer reviewers have traditionally remained anonymous. Whatever the journal’s policy, peer reviewers and articles editors should follow the same rules as authors for disclosing conflicts of interest. This gives editors the tools they need to ensure that peer review panels for individual papers are fairly balanced.

Manuscript will be published only if Conflict of Interest information will be in a published statement.

You should also include a relevant disclosure statement with your article, in conjunction with any acknowledgements and details of funders.


Peer review is an essential component of scholarly research publishing. If peer review is not meant to detect fraud, what is its purpose? Unfortunately, there is no one text to which authors, reviewers or editors alike can refer. Peer review is an imprecise term and varies across disciplines. Authors wished to review papers relevant to their area of expertise. Despite various criticisms and a number of shortcomings, peer review is still the only widely accepted method for research validation. But the ways peer review is put into practice vary across journals and disciplines. 

BPAS Publications employ post-publication double-blind peer review process, in which author(s) and reviewer(s) are unaware of the identity of each other, throughout the process for unbiased peer review process and reducing the amount of repeat research publication. Every article submitted to the journal is subjected to strict plagiarism check through software.


BPAS Publications aims at rapid publication of high quality research while maintaining rigorous but sympathetic peer review process. Manuscripts (other than those that are of insufficient quality or unlikely to be competitive enough for publication) will be peer-reviewed by two or more experts in the fields, and a decision is returned to the authors in about one month. If due to special circumstance, the review process takes more time, authors will be informed by email. Manuscripts with significant results will be reviewed and published at the highest priority and speed. Possible decisions on a manuscript are:

  • accepted as it is
  • accepted after minor revision
  • accepted after major revision
  • rejected

If minor revision is required, authors should return a revised version as soon as possible within 15 days. If major revision is required, authors should return a revised version within 25 days.

These impartial reviewers are charged with carefully evaluating the quality of the submitted manuscript. Peer reviewers check the number of issues in the manuscript including assessing the validity of the research methodology and procedures. If appropriate, they may recommend revisions and re submission of an article. In other cases, they may recommend rejection for various reasons. But the final decision to publish is made by the Editor-in-Chief.


Papers must be submitted with the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture or thesis) and are not currently under consideration by another journal published by or any other publisher. The submitting (corresponding) author is responsible for ensuring that the article’s publication has been approved by all the other co-authors. It is also the authors’ responsibility to ensure that the articles emanating from a particular institution are submitted with the approval of the necessary institution. Only an acknowledgment from the editorial office officially establishes and confirms the date of receipt. Further correspondence and proofs will be sent to the corresponding author(s) before publication unless otherwise indicated. It is a condition for submission of a paper that the authors permit editing of the paper for readability. All enquiries concerning the publication of accepted papers should be addressed to support@bpasjournals.com

About Authorship

Authorship is an explicit way of assigning responsibility and giving credit for intellectual work. These both are linked together. Authorship practices should be judged by how honestly they reflect actual contributions to the final product. Authorship has its importantance for the reputation, academic promotion, and grant support of the individuals involved as well as to the strength and reputation of their institution.


Disputes sometimes arise about who should be listed as authors of an intellectual product and the order in which they should be listed. When disagreements over authorship arise, they can take a substantial toll on the good will, effectiveness, and reputation of the individuals involved and their academic community. Many such disagreements result from misunderstanding and failed communication among colleagues and might have been prevented by a clear, early understanding of standards for authorship that are shared by the academic community as a whole.

Journals do not require all the authors of a research paper have to sign the letter of submission, nor do impose an order on the list of authors. Submission to journal means that all the listed authors have agreed all of the contents. The corresponding (submitting) author is responsible for having ensured that this agreement has been attained and for managing all communication between the journal and all co-authors, before and after publication. Any change to the authors list after submission, such as a change in the order of the authors or the deletion or addition of authors needs to be approved by a signed letter from every author.

Minimum Requirements for Authorship

All persons designated as authors should qualify for authorship, and all those who qualify should be listed. Each author should have participated sufficiently in the work to take public responsibility for appropriate portions of the content. One or more authors should take responsibility for the integrity of the work as a whole, from inception to published article.

Authorship credit should be based only on:

  1. a) substantial contributions to conception and design, or acquisition of data, or analysis and interpretation of data and
  2. b) final approval of the version to be published.

Conditions a and b must meet the criteria. Acquisition of funding, the collection of data, or general supervision of the research group, by themselves, do not justify authorship.Authors should provide a description of what each contributed, and editors should publish that information. All others who contributed to the work who are not authors should be named in the Acknowledgments, and what they did should be described.

Minimum Requirements for Acknowledgments

List all contributors who do not meet the criteria for authorship, such as a person who provided purely technical help, writing assistance, or a department chair who provided only general support. Financial and material support should also be acknowledged.

Groups of persons who have contributed materially to the paper but whose contributions do not justify authorship may be listed under a heading such as “clinical investigators” or “participating investigators,” and their function or contribution should be described, e.g., “served as scientific advisors,” “critically reviewed the study proposal,” “collected data,” or “provided and cared for study”. Because readers may infer their endorsement of the data and conclusions, all persons must have given written permission to be acknowledged.

Co-author contributions

Authors are strongly encouraged to include a statement in the end noted to specify the actual contribution of each co-author to the completed work. Journal allows two co-authors to be specified as having contributed equally to the work being described.

About Plagiarism

Plagiarism is the use or close imitation of the language and ideas of another author and representation of them as one’s own original work. Duplicate publication, sometimes called self-plagiarism, occurs when an author reuses substantial parts of his or her own published work without providing the appropriate references. This can range from getting an identical paper published in multiple journals, where authors add small amounts of new data to a previous paper.

Plagiarism can be said to have clearly occurred when large chunks of text have been copied and pasted. Such manuscripts would not be considered for publication in the Journals. But minor plagiarism without dishonest intent is relatively frequent, for example when an author reuses parts of an introduction from an earlier paper. The editors will judge any case of which they become aware (either by their own knowledge of and reading about the literature, or when alerted by referees) on its own merits.

If a case of plagiarism comes to light after a paper is published in BPAS Journals, the journal will conduct a preliminary investigation. If plagiarism is found, the journal will contact the author’s institute and funding agencies. A determination of misconduct will lead the Journal to run a statement, bidirectionally linked online to and from the original paper, to note the plagiarism and to provide a reference to the plagiarized material. The paper containing the plagiarism will also be obviously marked on each page of the PDF. Depending on the extent of the plagiarism, the paper may also be formally retracted.

Duplicate Publication

The Journal will not accept duplicate publication of scientific data. Manuscripts submitted to International Journal of current trends should not have been published/ accepted for publication or simultaneously submitted. The “possible” duplicate manuscript should be submitted with the original publication (s) and the authors should provide documentation/ statement to justify the originality of the newly submitted manuscript.

Prior Publication

The Journal will accept original manuscripts that contain material that has not been reported elsewhere, except in the form of an abstract of not more than 250 words, or an alternative short communication. If any preliminary report other than an abstract has been published or submitted, copies must be submitted with the manuscript and this must be noted in the cover letter to the editor. Prior abstract presentations must be described in a footnote to the title. Initial submissions must be accompanied by the copyright assignment form, with original signatures of all authors.

Article Withdrawal

Only used for Articles in Press which represent early versions of articles and sometimes contain errors, or may have been accidentally submitted twice. Occasionally, but less frequently, the articles may represent infringements of professional ethical codes, such as multiple submission, bogus claims of authorship, plagiarism, fraudulent use of data or the like. Articles in Press (articles that have been accepted for publication but which have not been formally published and will not yet have the complete volume/issue/page information) that include errors, or are discovered to be accidental duplicates of other published article(s), or are determined to violate our journal publishing ethics guidelines in the view of the editors (such as multiple submission, bogus claims of authorship, plagiarism, fraudulent use of data or the like), may be “Withdrawn” from us. Withdrawn means that the article content (HTML and PDF) is removed and replaced with a HTML page and PDF simply stating that the article has been withdrawn according to the BPAS Publication Policy on Article in Press Withdrawal with a link to the current policy document.

Article Retraction

Infringements of professional ethical codes, such as multiple submission, bogus claims of authorship, plagiarism, fraudulent use of data or the like. Occasionally a retraction will be used to correct errors in submission or publication. The retraction of an article by its authors or the editor under the advice of members of the scholarly community has long been an occasional feature of the learned world. Standards for dealing with retractions have been developed by a number of library and scholarly bodies, and this best practice is adopted for article retraction by 

 Article Replacement

In cases where the article, if acted upon, might pose a serious health risk, the authors of the original article may wish to retract the flawed original and replace it with a corrected version. In these circumstances the procedures for retraction will be followed with the difference that the database retraction notice will publish a link to the corrected re-published article and a history of the document.

 Sending a revised manuscript

The authors revise the manuscript as advised by reviewers and submit the revised version. Typically, at this stage, authors are advised to prepare the manuscript by closely following the journal’s instructions about style and format and to submit the manuscript in electronic form.

Proofs and Reprints

Usual practice will involve corresponding authors receiving email notification with a password and web address from which to download a PDF. Hard copies of proofs will not be mailed. To avoid delays in publication, corrections to proofs must be returned within 48 hours, by electronic transmittal, fax or mail. Authors will be charged for excessive correction at this stage of production. If authors do not return page proofs promptly, the Publisher reserves the choice to either delay publication to a subsequent issue or to proceed to press without author corrections. The Publisher reserves the right to proceed to press without submitting page proofs to the author.

Bulletin of Pure and Applied Sciences Section-E-Math. & Stat. is devoted to the international advancement of organized knowledge on all aspects of Mathematics and Statistics. It is serving as a forum to publish refereed, well-written original research articles and studies that describe the latest research and developments in the area of mathematics and statistics. Scope of the journal includes: Finance, economics, mathematics, statistics and probability, theoretical developments and techniques. It provides a forum for comments by publishing original research contributions, scientific survey, case studies, book review and letter to the Editor-in-Chief. Bulletin of Pure and Applied Sciences Section-E-Math. & Stat. is issued six monthly, i.e. June and December of every year. The Editor-in-Chief/Managing Editor/Editorial Board etc. assumes no responsibility for the statements and opinions advanced by the contributors. The editorial staff in its work of examining papers, received for possible publication is assisted, in an honorary capacity, by a large number of distinguished scientists working in various parts of the world. Bulletin of Pure and Applied Sciences Section-E-Math. & Stat. is copy-righted. Manuscripts published in the Bulletin should not be reproduced without the written permission of the Editor-in-Chief.

Comparative study of exponential smoothing models and Box- Jenkins ARIMA model of partitioned data of daily stock prices of the CRDB Bank in Tanzania
K.K. Saxena1 and Juma Salehe Kamnge2

Author’s Affiliation : 1,2. Department of Statistics, University of Dodoma, Dodoma, Tanznia.

Corresponding Author : K.K. Saxena,




Data mining techniques and other analytical techniqueshave played a significant role in analysing data from different sources. Data from stock market consist of high volatility and hence it needs a special care to fit amodel for forecasting future stock prices values. In the stock market, investors trade to get positive returns through buying at a lower price and selling at a higher price. However, not all investors get positive returns on their investment in stock market because oflarge amount of risk involvedin the stock market due to vast fluctuation in the stockmarket prices.This study isconducted to compare and select the best model amongautoregressive integrated moving average (ARIMA), single exponential smoothed model (SES), double exponential smoothed model (DES), and Damped trend linear exponential smoothed model. The modelling process was preceded by analysing the time series which revealed the presence of non-stationarity. The resultant models were found as ARIMA(1,1,2), Simple Exponential Smoothing(SES) and Double exponential smoothing (DES) whoseparameters’ estimateswere also found to bestatistically significant. Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC) were used toselect the best model among all the three fitted models. The performance of the fittedmodel isanalyzed and the market behavior for future forecast is studied. ARIMA(1,1,2) is selected as the best model for daily stock forecasting forthe CRDB bank in Tanzania.


Power of control chart for zero-truncated Poisson distribution under inspection error
J.R. Singh1 and U. Mishra2

Author’s Affiliation : 1,2. School of Studies in Statistics, Vikram University, Ujjain, Madhya Pradesh, India. 1. E-mail: jrsinghstat@gmail.com , 2. E-mail: uttamamishra@gmail.com

Corresponding Author : J.R. Singh,




In this paper, an effort is made to study the Power Function and Average Run Length (ARL) of Zero-Truncated Poisson Distribution (ZTPD) under inspection error. An investigation is also made to calculate the power function of control chart for variable sample size for ZTPD under inspection error.

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