##### Non-negative Integer Power of a Hyponormal m-isometry is Reﬂexive

Pradeep Kothiyal, Rajesh Kumar Pal, Deependra Nigam

Asian Research Journal of Mathematics, Page 1-5
DOI: 10.9734/arjom/2021/v17i430288

Sarason did pioneer work on reflexive operator and reflexivity of normal operators, however, he did not used the word reflexive but his results are equivalent to say that every normal operator is reflexive. The word reflexive was suggested by HALMOS and first appeared in H. Rajdavi and P. Rosenthals book Invariant Subspaces’ in 1973. This line of research was continued by Deddens who showed that every isometry in B(H) is reflexive. R. Wogen has proved that every quasi-normal operator is reflexive’. These results of Deddens, Sarason, Wogen are particular cases of theorem of Olin and Thomson which says that all sub-normal operators are reflexive. In other direction, Deddens and Fillmore characterized these operators acting on a finite dimensional space are reflexive. J. B. Conway and Dudziak generalized the result of reflexivity of normal, quasi-normal, sub-normal operators by proving the reflexivity of Vonneumann operators. In this paper we shall discuss the condition under which m-isometries operators turned to be reflexive.

##### A Study of Fuzzy Relation and Its Application in Medical Diagnosis

Shishir Kumar, Chhaya Gangwal

Asian Research Journal of Mathematics, Page 6-11
DOI: 10.9734/arjom/2021/v17i430289

Objective: Medical diagnosis process extends within the degree to which they plan to affect different complicating aspects of diagnosis. In this research work, the concept of fuzzy relation with medical diagnosis is studied and the application of fuzzy relations to such problems by extending the Sanchez’s approach is introduced.

Method: An application of fuzzy relation with Sanchez's approach for medical diagnosis is presented. Based on the composition of the fuzzy relations, an algorithm for medical diagnosis as follows- first input the number of objects and attributes to obtain patient symptom matrix, symptom-disease matrix and the composition of fuzzy relations to get the patient-diagnosis matrix. Then find the maximum value to evaluate which patient is suffering from what disease.

Result: Using the algorithm for medical diagnosis, the disease for which the membership value is maximum gives the final decision. If almost equal values for different diagnosis in composition are obtained, the case for which non-membership is minimum and hesitation is least is considered. The output matched well with the doctor’s diagnosis.

Conclusion: In the process of medical diagnosis, state of patient are given by the patient through linguistic terminology like as temperature, cough, stomach pain etc., consideration of fuzzy sets as grades for association instead of membership grades in [0,1] is more advantageous to model the state of the patient. Similarly fuzzy relation has been introduced representing the association between symptoms and diseases. Sanchez’s approach has been extended for medical diagnosis in this reference. The approach used to form fuzzy matrix showing the association of symptoms and diseases is based on the sanchez’s approach.

##### Certain Subclass of Bi-univalent Functions Defined by Sălăgean Differential Operator Related with Horadam Polynomials

Dhirgam Allawy Hussein

Asian Research Journal of Mathematics, Page 12-19
DOI: 10.9734/arjom/2021/v17i430290

The goal of this paper is to introduce and investigate a new subclass   of bi-univalent functions using  the Horadam polynomials and Sălăgean differential operator. Furthermore, coefficient estimates are given for   and Fekete-Szegő inequalities for this subclass are obtained.

##### Modelling Bubble Lifetime of Thin Film Surfactants Solution on Fuel Spillage

Shitakha Felistus, Kimathi George, Songa Caroline

Asian Research Journal of Mathematics, Page 20-33
DOI: 10.9734/arjom/2021/v17i430291

Aims / Objectives: To find the lifetime of the bubble by plotting the rate of mass flow rate change against time. Place and Duration of Study: Department of Mathematics and Applied Science, Catholic University of Eastern Africa, Nairobi, Kenya, between February 2020 and March 2021.

Methodology: The maximum lifetime of the bubble is assumed to match the time when the mass flow rate change is zero. The study also assumes the velocity of flow rate and other fluid properties at the interface of fuel-surfactant constant other than Re. Re is varied from 0.01 to 100.

Results: The graphical plots show that for Re ! 1, and Re " 1, the stability depends on diffusive viscosity and linearized convection, respectively. The simulation suggested that the bubble formed at the fuel-surfactant interface may have Re “ 1 and its lifetime is tb » 0.28.

Conclusion: The lifetime of surfactant depends on Re while assuming other interface properties constant.

Recommendation: Future studies in the area need to consider the effect of variation in temperature, velocity, and Reynolds number in determining the lifetime of a bubble in the thin foam of the surfactant-fuel interface.

##### Identifying Minimum Effective Dose Under Heteroscedasticity

Michael J. Adjabui, Jakperik Dioggban, Irene D. Angbing

Asian Research Journal of Mathematics, Page 34-43
DOI: 10.9734/arjom/2021/v17i430292

We propose a stepwise confidence procedure for identifying minimum effective dose (MED) without multiplicity adjustment.Stepwise procedures strongly control the familywise error rate (FWER) which is a critical requirement for statistical methodologies in identification of MED. The partitioning principle is invoked to validate the control of the FWER. Our simulation study indicates that the FWER was properly controlled in the case with balanced design but failed in some cases of sample sizes for situations of unbalanced design. In addition, the power of the procedure increases with increasing mean of ratio differences and the sample sizes.

##### Edge-Complement Graphs – Another Approach

Sanal Kumar, Henah E. Vatsalya

Asian Research Journal of Mathematics, Page 44-49
DOI: 10.9734/arjom/2021/v17i430293

The collection of edge complement spanning subgraphs of a simple graph is an abelian group with respect to the symmetric difference operation.

##### Type II Topp-Leone Gumbel Type-2 distribution: Properties and Applications

Fatoki Olayode, Phillips Samuel Ademola, Adeleye Najeem Friday

Asian Research Journal of Mathematics, Page 50-60
DOI: 10.9734/arjom/2021/v17i430294

In this paper, a three parameter life time model named Type II Topp-Leone Gumbel type-2 distribution which can be used to model reliability problems, fatigue life studies, and survival data has been studied. We derived explicit expressions for some of its statistical properties such as ordinary moments, generating function, incomplete moments, and order statistics. The maximum likelihood estimation technique is used to estimate the parameters of the model. The tractability of the model was illustrated by using two real life data sets. The proposed distribution provides a better fit than some well known distributions using criteria of criteria of goodness of fit.

##### Some Inequalities on Generalized p − k Gamma and Beta Functions

Inci Ege, Emrah Yıldırım

Asian Research Journal of Mathematics, Page 61-69
DOI: 10.9734/arjom/2021/v17i430295

In this work, we firstly introduce the integral representation of the generalized p-k beta function and then employ well-known Chebychev’s and H¨older’s inequalities to obtain some inequalities on generalized p - k gamma and beta functions. Also, we show the logarithmic convexity properties
of these functions.