i-manager's Journal on Mathematics (JMAT)


Volume 7 Issue 3 July - September 2018

Research Paper

On Lacunary Statistical Convergence and Some Properties in Fuzzy N-Normed Spaces

Muhammed Recai Turkmen *
Assistant Professor, Department of Mathematics and Science Education, The Afyon Kocatepe University, Turkey.
Türkmen, M. R. (2018). On Lacunary Statistical Convergence and Some Properties in Fuzzy N-Normed Spaces, i-manager's Journal on Mathematics, 7(3), 1-9. https://doi.org/10.26634/jmat.7.3.14868

Abstract

In this paper, the author has introduced the concept of lacunary summable and lacunary statistical convergence in fuzzy n-normed spaces. At the same time, the author has introduced condition of being lacunary statistically Cauchy sequence with respect to a fuzzy n-norm. The author has also studied the relation between these concepts and gave some properties of lacunary statistical convergence sequences in fuzzy n-normed spaces.

Research Paper

Trioengineering Interapplication and Comprehensive Cohesive Cogitation: The Use of Systemic Neuromathematical Trioinformatics to Create, Define, and Express Trichotomous Research Instrumentation and Tri-Squared Analytics

James Edward Osler II*
Associate Professor, Department of Allied Professions, North Carolina Central University, USA.
Osler, J. E., II. (2018). Trioengineering Interapplication and Comprehensive Cohesive Cogitation: The Use of Systemic Neuromathematical Trioinformatics to Create, Define, and Express Trichotomous Research Instrumentation and Tri-Squared Analytics, i-manager's Journal on Mathematics, 7(3), 10-29. https://doi.org/10.26634/jmat.7.3.15190

Abstract

This discourse provides a deeper epistemological rational for the novel discipline of “Trioinformatics” through the use of “Trioengineering” to create innovative research instrumentation from trichotomous research questions. Trioengineering uses of the novel mathematical “Ambitation” from “Neuromathematical Neuroengineering Notation” in Trioengineering as a novel operational methodology referred to as “Interapplication”. This specialized operation was first defined in the Trioinformatics article that appeared in the March-May i-manager Journal on Circuits and Systems. Trioengineering's use of the neuromathematics “Ambitation” as an “Interapplication” is the holistic, collaborative, and comprehensive expression of Trioinformatics as a sequential sequence of inquiry into a precise research analysis methodology. Neuroengineering is an innovative way of explaining the transition from trichotomous logic (Osler, 2015) into a trichotomous Triple-I (Osler, 2013d) in which research questions are implemented in a meticulously defined and mathematically associated instrument [first introduced in the i-manager Journal on Mathematics as a part of the Tri- Squared Test (Osler, 2012a)]. Trioinformatics is an in-depth way of symbolically illustrating the law of trichotomy as a mathematically-grounded rational technique for explaining the ternary nature of electronic circuitry (Osler, 2015). The use of the Trioinformatics also adds value to investigative inquiry through the efficacy of digital instruments and tools via eduscientifically - engineered (Osler, 2013) research designs (Osler, 2015).

Research Paper

Application of Multi-State Semi-Markov Models on HIV/AIDS Disease Progression

Solomon Kalayu Mengesha* , Gebregewergis Alemu Gebremedhn**, Tilahun Ferede***, Cheru Atsmegiorgis ****
*-**Lecturer, Adigrat University, Tigray, Ethiopia.
***-****Hawassa University, Awassa, Ethiopia.
Mengesha, S. K., Gebremedhn, G. A., Tilahun, F., & Atsmegiorgis, C. (2018). Application of Multi-State Semi-Markov Models on HIV/AIDS Disease Progression, i-manager's Journal on Mathematics, 7(3), 30-41. https://doi.org/10.26634/jmat.7.3.14988

Abstract

Although remarkable progress has been made in the control of the global Human Immunodeficiency Virus (HIV/AIDS) epidemic, the burden of HIV has reached contemporary at the shocking level in Sub-Saharan Africa. Understanding the cycle of HIV/AIDS disease progression can have great value on the effectiveness of the therapy. The purpose of this study is to determine factors affecting the progression between different stages of the disease and to model the progression of HIV/AIDS disease of an HIV infected patients under ART follow-up using multistate Semi-Markov model. A cohort of 526 HIV infected patients has been sampled from a Hawassa University Referral Hospital, Hawassa, Ethiopia, who have been under ART follow up from September 2012 to August 2017. States of the Markovian process are defined by the seriousness of the sickness based on the CD4 counts in cells/microliter. The five states of HIV/AIDS disease progression considered in the multi-state Semi-Markov model were defined based on of the following CD4 cell counts. State I, State II, State III, State IV and Death state. The major transiently prognostic factors between different states of HIV/AIDS disease were sex, age, ART adherence level, TB status, functional status, opportunistic infections , and body weight of patients. Hence, the progression of HIV/AIDS was significantly accelerated with poor ART adherence, patient's co-infection with TB, older patients, and patients being bedridden. The conditional probabilities of patients from any good states to worst state are increasing over time. Weibull sojourn time distribution is the appropriate and is preferably used as sojourn time distribution under multistate models. As time elapsed, the transition probability of patients is more likely to be in worse state than to be in better one. This shows that patients should aware the need to initiate therapy at early stages of the virus.

Research Paper

An Inventory Model for Two Storage System with Stock Dependent Demand

Amit Kumar Attri* , S. R. Singh**, Shweta Choudhary***
* Assistant Professor, Department of Mathematics, Delhi Technical Campus, Greater Noida, Uttar Pradesh, India.
** Professor, Department of Mathematics, CCS University Meerut, Uttar Pradesh, India.
*** Associate Professor and Head, Department of Applied Sciences, ABES Engineering College,.Dr. A. P. J. Abdul Kalam Technical University, Ghaziabad, Uttar Pradesh, India.
Attri, A. K., Singh, S. R., & Choudhary, S. (2018). An Inventory Model for Two Storage System with Stock Dependent Demand, i-manager's Journal on Mathematics, 7(3), 42-50. https://doi.org/10.26634/jmat.7.3.14668

Abstract

In this paper an inventory model to find out the buyer's optimal policy with two storage system has been developed. The buyer purchases a lot of Q units and transfers this stock in the display area in n equal lots. The demand considered here is a function of displayed stock level. The objective of this model is to optimize the total average cost for the buyer and find out the optimal number of shipments. A numerical example is presented to illustrate this study. The sensitivity analysis presented here shows that the model is quite stable and reflects the real life marketing situations.

Research Paper

Common Fixed Point Theorems for Cr-Iteration Scheme in Three Multivalued Mappings

Apurva Kumar Das* , Shailesh Dhar Diwan**, Swati Jain***
* Lecturer, Department of Mathematics, Government Polytechnic College Sukma, Chhattisgarh, India.
** Associate Professor and Head, Department of Mathematics, Government Engineering College, Raipur, Chhattisgarh, India.
*** Assistant Professor and Head, Department of Computer Science, Government J. Yoganandam Chhattisgarh College, Raipur, Chhattisgarh, India.
Das, A. K., Diwan, S. D., & Jain, S. (2018). Common Fixed Point Theorems for Cr-Iteration Scheme in Three Multivalued Mappings, i-manager's Journal on Mathematics, 7(3), 51-60. https://doi.org/10.26634/jmat.7.3.15064

Abstract

The purpose of this paper is to introduce multivalued version of CR iteration process given by Chugh, Kumar, and Kumar (2012) and provecommon fixed point theorem for this iteration in three multivalued ρ-nonexpansive mappings in modular space. Let ρϵη satisfy (UUC1) and C ⊂ Lbe nonempty ρ-bounded and convex set. Let T1, T2, T3: C →Pρ(C) be three multivalued mappings such that PT1ρ, PT2ρ and PT3ρ are ρ-nonexpansive mappings with F = Fρ(T1) ⋂ Fρ(T2) ⋂ Fρ(T3) ≠ φ. Suppose T1 , T2 and T3 satisfy condition (I). Then the sequence {fn} defined by us converges to a point of F.