JOURNAL OF ADVANCES IN MATHEMATICS Interested in submitting to this journal? We recommend that you review the About the Journal page for the journal's section policies, as well as the Author Guidelines. Authors need to register with the journal prior to submitting or, if already registered, can simply log in and begin the five-step process. Council for Innovative Research en-US JOURNAL OF ADVANCES IN MATHEMATICS 2347-1921 <p>Authors retain the copyright of their manuscripts, and all Open Access articles are distributed under the terms of the&nbsp;<a href="">Creative Commons Attribution License</a>, which permits unrestricted use, distribution, and reproduction in any medium, provided that the original work is properly cited.</p> <p>&nbsp;</p> On Pompeiu Cebysev Type Inequalities for Positive Linear Maps of Selfadjoint Operators in Inner Product Spaces <p>In this work, generalizations of some inequalities for continuous synchronous (h-asynchronous) functions of linear bounded selfadjoint operators under positive linear maps in Hilbert spaces are proved.</p> Mohammad W Alomari ##submission.copyrightStatement## 2018-12-01 2018-12-01 15 8081 8092 10.24297/jam.v15i0.7927 Symmetry problem 1 <p>A symmetry problem is solved. A new method is used. The idea of this methodis to reduce to a contradiction the PDE and the over-determined boundary data on the boundary.The new method allows one to solve other symmetry problems.</p> Alexander G. Ramm ##submission.copyrightStatement## 2018-12-01 2018-12-01 15 8093 8097 Probabilistic Inventory Model Multi-Source Backlogged Probabilistic Inventory Model for Crisp and Fuzzy Environment <p>This paper proposed a multi-item multi-source probabilistic periodic review inventory model under a varying holding cost constraint with zero lead time when: (1) the stock level decreases at a uniform rate over the cycle. (2) some costs are varying. (3) the demand is a random variable that follows some continuous distributions as (two-parameter exponential, Kumerswamy, Gamma, Beta, Rayleigh, Erlang distributions).</p> <p>The objective function under a constraint is imposed here in crisp and fuzzy environment. The objective is to find the optimal maximum inventory level for a given review time that minimize the expected annual total cost. Furthermore, a comparison between given distributions is made to find the optimal distribution that achieves the model under considerations. Finally, a numerical example is applied.</p> H. A. Ferganya Osama Mahmoud Hollah ##submission.copyrightStatement## 2018-11-12 2018-11-12 15 8051 8069 The Reproducing Kernel Hilbert Space Method for Solving System of Linear Weakly Singular Volterra Integral Equations <p>The exact solutions of a system of linear weakly singular Volterra integral equations (VIE) have been a difficult to find.&nbsp; The aim of this paper is to apply reproducing kernel Hilbert space (RKHS) method to find the approximate solutions to this type of systems. At first, we used Taylor's expansion to omit the singularity. &nbsp;From an expansion the given system of linear weakly singular VIE is transform into a system of linear ordinary differential equations (LODEs). &nbsp;&nbsp;The approximate solutions are represent in the form of series in the reproducing kernel space . By comparing with the exact solutions of two examples, we saw that RKHS is a powerful, easy to apply and full efficiency in scientific applications to build a solution without linearization and turbulence or discretization.&nbsp;</p> Hameeda Oda Al-Humedi ##submission.copyrightStatement## 2018-11-14 2018-11-14 15 8070 8080 About the Dirichlet Boundary Value Problem using Clifford Algebras <p>This paper reviews and summarizes the relevant literature on Dirichlet problems for monogenic functions on classic Clifford Algebras and the Clifford algebras depending on parameters on. Furthermore, our aim is to explore the properties when extending the problem to and, illustrating it using the concept of fibres. To do so, we explore ways in which the Dirichlet problem can be written in matrix form, using the elements of a Clifford's base. We introduce an algorithm for finding explicit expressions for monogenic functions for Dirichlet problems using matrices in Finally, we illustrate how to solve an initial value problem related to a fibre.</p> Johan Ceballos ##submission.copyrightStatement## 2018-11-12 2018-11-12 15 8098 8119 10.24297/jam.v15i0.7795 Supplement to the Collatz Conjecture <p>For any natural number was created the supplement sequence, that is convergent together with the original sequence. The parameter - index was defined, that is the same tor both sequences. This new method provides the following results:</p> <ol> <li>All natural numbers were distributed into different classes according to the corresponding indexes;</li> <li>The analytic formulas ( not by computer performed routine calculations) were produced, the formulas for groups of consecutive natural numbers of different lengths, having the same index;</li> <li>The new algorithm to find index for any natural number was constructed and proved.</li> </ol> Anatoliy Nikolaychuk ##submission.copyrightStatement## 2018-12-01 2018-12-01 15 8120 8132 10.24297/jam.v15i0.7876 On Twisted Sums of Sequence Spaces <p>&nbsp;We prove the existence of non trivial twisted sums involving the p<sup>th</sup> James&nbsp;space J<sub>p</sub>(1 &lt; p &lt; 1), the Johnson-Lindenstrauss space JL; the James tree space&nbsp;JT , the Tsirelson’s space T and the Argyros and Deliyanni space AD . We also&nbsp;present non trivial twisted sums involving their duals and biduals. We show&nbsp;that there are strictly singular quasi-linear maps from the spaces T ;T<sup>*</sup> ; AD and&nbsp;JT into C[0; 1]. We discuss the Pelczynski’s property(u) for the twisted sums&nbsp;involving these spaces which extends a pthJames-Schreier spaces V<sub>p</sub>(1 &lt; p &lt;1)&nbsp;or J<sub>2.&nbsp;</sub></p> Haifa Mohammed Bin Jebreen ##submission.copyrightStatement## 2018-12-11 2018-12-11 15 8133 8144 10.24297/jam.v15i0.7901