Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42444420160901On the non validity of a recently introduced fractional calculus on time scales12859ENRui FerreiraGrupo F&iacute;sica-Matem&aacute;tica, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal.Journal Article20150813In this note we show that the semigroup property of a certain fractional integral, introduced in [A. Ahmadkhanlu and M. Jahanshahi, On the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales, Bull. Iranian Math. Soc. 38 (2012), no. 1, 241-252], does not hold. Consequently, the fractional calculus developed therein is meaningless.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42444420160901The theory of matrix-valued multiresolution analysis00860ENPing ZhaoBeijing Jiaotong UniversityChun ZhaoTianjin normal UniversityJournal Article20141011A generalization of matrix-valued multiresolution analysis (MMRA) to matrix-valued frames, and the constructions of matrix-valued frames are considered and characterized. A matrix-valued frame multiresolution analysis is defined in this paper. We provide necessary and sufficient conditions for constructing matrix-valued frames and Riesz bases of translates, and give the calculation method of matrix-valued dual Riesz basis. These conclusions are useful in providing theoretical basis for constructing matrix-valued frames and Riesz basis.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42444420160901Weak convergence of splitting algorithms in Hilbert spaces with their applications121048ENS. Y. ChoDepartment of Mathematics, Gyeongsang National University, Jinju, Korea.X. QinInstitute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Sichuan, China.Journal Article20160428In this article, we study the convergence of a splitting algorithm for solving a convex feasibility problem. Weak convergence of the purposed algorithm is obtained in the framework of real Hilbert spaces. Applications are also provided to support the main results.