The paper deals with an inverse problem of determining the right-hand side of the linear equation of oscillations of thin plates. The problem is reduced to the optimal control problem. Differentiability of the functional is studied. Necessary condition of optimality is derived.

Journal of Mathematics Research wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.
 
 Many authors, regardless of whether Journal of Mathematics Research publishes their work, appreciate the helpful feedback provided by the reviewers.
 
 Reviewers for Volume 12, Number 1
 
  
 
 Ahmed Saad Rashed, Zagazig University, Egypt
 
 Bachioua Lahcene, University of Hail, Saudi Arabia
 
 Chung-Chuan Chen, National Taichung University of Education, Taiwan
 
 Cibele Cristina Trinca Watanabe, Federal University of Tocantins (UFT), Brazil
 
 Denis Khleborodov, Lomonosov Moscow State University, Russia
 
 Francisco Bulnes, Research Department in Mathematics and Engineering, TESCHA, Mexico
 
 Gabriela Ciuperca, University Lyon 1, France
 
 Gane Sam Lo, Universite Gaston Berger de Saint-Louis, Senegal
 
 Gener Santiago Subia, Wesleyan University, Philippines
 
 Guy Biyogmam, Georgia College & State University, USA
 
 Hayat REZGUI, Ecole normale Supérieure de Kouba, Algeria
 
 Kuldeep Narain Mathur, University Utara Malaysia, Malaysia
 
 Maria Alessandra Ragusa, University of Catania, Italy
 
 Mashadi Ali, Riau University, Indonesia
 
 Mustapha El Moudden, Moulay Ismail University, Morocco
 
 Omur Deveci, Kafkas University, Turkey
 
 Philip Yordanoff Philipoff, Bulgarian Academy of Sciences, Bulgaria
 
 Rami Ahmad El-Nabulsi, Athens Institute for Education and Research, Greece
 
 Sanjib Kumar Datta, University of Kalyani, India
 
 Sergiy Koshkin, University of Houston Downtown, USA
 
 Sofian Obeidat, University of Hail, Jordan
 
 Xingbo WANG, Foshan University, China
 
 Yaqin Feng, Ohio University, USA
 
  
 
 Sophia Wang
 
 On behalf of,
 
 The Editorial Board of Journal of Mathematics Research
 
 Canadian Center of Science and Education

A mixed mode crack problem in functionally graded materials is formulated to a system of Cauchy singular Fredholm integral equations, then the system is solved by the singular integral equation method (SIEM). This specific crack problem has already been solved by N. Konda and F. Erdogan (Konda & Erdogan 1994). However, many mathematical details have been left out. In this paper we provide a detailed derivation, both analytical and numerical, on the formulation as well as the solution to the system of singular Fredholm integral equations. The research results include crack displacement profiles and stress intensity factors for both mode I and mode II, and the outcomes are consistent with the paper by Konda & Erdogan (Konda & Erdogan 1994).

In this paper we will apply a polynomial for directed weighted graph. We will introduce notion of deletion and contraction in directed weighted graph. Some examples and propositions will be illustrated.

The paper considers the problem of testing error serial correlation of partially linear additive measurement error model. We propose a test statistic and show that it converges to the standard chi-square distribution under the null hypothesis. Finally, a simulation study is conducted to illustrate the performance of the test approach.

In this paper, we present a new practical criteria for H-matrix based on γ-diagonally dominant matrix. In order to make the judgment conditions convenient and effective, we give two new definitions, one is called strong and weak diagonally dominant degree, the other is called the sum of non-principal diagonal element for the matrix. Further, we obtain a new practical method for the determination of the H-matrix by combining the properties of γ-diagonally dominant matrix, constructing positive diagonal matrix, and adding the appropriate parameters. Finally, we offer numerical examples to verify the validity of the judgment conditions, corresponding numerical examples compared the new criteria and the existing results are presented to verify the advantages of the new determination method.

In the first part of this paper we point out some basic properties of the critical cones used in second-order optimality conditions and give a simple proof of a strong second-order necessary optimality condition by assuming a “modified” first-order Abadie constraint qualification. In the second part we give some insights on second-order constraint qualifications related to second-order local approximations of the feasible set.

Journal of Mathematics Research wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.
 
 Many authors, regardless of whether Journal of Mathematics Research publishes their work, appreciate the helpful feedback provided by the reviewers.
 
 Reviewers for Volume 11, Number 3
 
  
 
 Abdessadek Saib, University of Tebessa, Algeria
 
 Arman Aghili, University of Guilan, Iran
 
 Cinzia Bisi, Ferrara University, Italy
 
 Gabriela Ciuperca, University Lyon 1, France
 
 Gener Santiago Subia, NUeva Ecija University of Science and Technology, Philippines
 
 Kong Liang, University of Illinois at Springfield, USA
 
 Kuldeep Narain Mathur, University Utara Malaysia, Malaysia
 
 Maria Alessandra Ragusa, University of Catania, Italy
 
 Rami Ahmad El, Athens Institute for Education and Research, Greece
 
 Rovshan Bandaliyev, National Academy of Sciences of Azerbaijan, Azerbaijan
 
 Sanjib Kumar Datta, University of Kalyani, India
 
 Shenghua Ni, Vanderbilt University Medical Center, USA
 
 Sreedhara Rao Gunakala, The University of The West Indies, Trinidad and Tobago
 
 Xiaofei Zhao, Texas A&M University, United States
 
 Yaqin Feng, Ohio University, USA
 
 Yifan Wang, University of Houston, USA
 
  
 
 Sophia Wang
 
 On behalf of,
 
 The Editorial Board of Journal of Mathematics Research
 
 Canadian Center of Science and Education

We propose an original mathematical model according to a Bayesian approach explaining uncertainty from a point of view connected with vector spaces. A parameter space can be represented by means of random quantities by accepting the principles of the theory of concordance into the domain of subjective probability. We observe that metric properties of the notion of $\alpha$-product mathematically fulfill the ones of a coherent prevision of a bivariate random quantity. We introduce fundamental metric expressions connected with transformed random quantities representing changes of origin. We obtain a posterior probability law by applying the Bayes' theorem into a geometric context connected with a two-dimensional parameter space.

Reviewer Acknowledgements
 
 Journal of Mathematics Research wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.
 
 Many authors, regardless of whether Journal of Mathematics Research publishes their work, appreciate the helpful feedback provided by the reviewers.
 
 Reviewers for Volume 11, Number 2
 
  
 
 Ahmed Saad Rashed, Zagazig University, Egypt
 
 Alan Jalal Abdulqader, Al-Mustansiriyah University, Iraq
 
 Amjad Salari, Razi University, Iran
 
 Arman Aghili, University of Guilan, Iran
 
 Denis Khleborodov, Lomonosov Moscow State University, Russia
 
 Gane Sam Lo, Universite Gaston Berger de Saint-Louis, Senegal
 
 Gener Santiago Subia, NUeva Ecija University of Science and Technology, Philippines
 
 Ivan Drazic, University of Rijeka, Croatia
 
 Maria Alessandra Ragusa, University of Catania, Italy
 
 Maria Cecília Santos Rosa, Instituto Politecnico da Guarda, Portugal
 
 Martin Anokye, University of Cape Coast, Ghana
 
 Mohammad A. AlQudah, German Jordanian University, Jordan
 
 N. V. Ramana Murty, Andhra Loyola College, India
 
 Neha Hooda, New Jersey City University, United States
 
 Paul J. Udoh, University of Uyo., Nigeria
 
 Rovshan Bandaliyev, National Academy of Sciences of Azerbaijan, Azerbaijan
 
 Sanjib Kumar Datta, University of Kalyani, India
 
 Sergiy Koshkin, University of Houston Downtown, USA
 
 Suzana Blesic, Italy
 
 Vishnu Narayan Mishra, Indira Gandhi National Tribal University, India
 
 Zhongming Wang, Florida International University, USA
 
  
 
 Sophia Wang
 
 On behalf of,
 
 The Editorial Board of Journal of Mathematics Research
 
 Canadian Center of Science and Education