In this paper, we use the Banach fixed point theorem to obtain the existence, interval of existence and uniqueness of solutions for nonlinear hybrid implicit Caputo-Hadamard fractional differential equations. We also use the generalization of Gronwall’s inequality to show the estimate of the solutions.

Harmonic convexity is very important new class of non-convex functions, it gained prominence in the Theory of Inequalities and Applications as well as in the rest of Mathematics’s branches. The harmonic convexity of a function is the basis for many inequalities in mathematics. Furthermore, harmonic convexity provides an analytic tool to estimate several known definite integrals like \(\int_{a}^{b} \frac{e^{x}}{x^{n}}dx\), \(\int_{a}^{b} e^{x^{2}} dx\), \(\int_{a}^{b} \frac{\sin x}{x^{n}}dx\) and \(\int_{a}^{b} \frac{\cos x}{x^{n}}dx\) \(\forall n \in \mathbb{N}\), where \(a,b \in (0,\infty)\). In this article, some un-weighted inequalities of Hermite-Hadamard type for harmonic log-convex functions defined on real intervals are given.

Corrosion at the bottom of a ship’s water line can result in personnel and material safety risks. There are 2 (two) ways to protect against corrosion, they are passive protection (by painting) and active protection (by cathodic protection method). In the KRI with KCR-40 type, the design of the bottom line of the ship’s waterline protection has been carried out with ICCP, but the value of its failure risk and reliability is unknown, both functional and designs, so that the design of the tool cannot be used maximally. This research aimed to determine the factors of failure and reliability value of the design-based ICCP (Reliability by Design) with the FTA and FMEA approach, the FTA aimed to identify the risks that contribute to the failure. The main factors causing failure in the design of ICCP tools occur in the component of Steel potential indicator and rectifier indicator with a failure mode not pointing to the correct number, this will result in corrosion control which is expected to be uncontrolled properly and correctly due to incorrect data input. After analyzing the FTA, the reliability value was 33%. Mitigation of tool components that have a high level of risk among other things in the indicator of steel potential and rectifier indicators: the first was to redesign the laying of some components of the tool compilers to pay attention to the circulating circulation in the box so that the tool works more optimally, the second was to carry out periodic control while the device was operating, and third was to ensure that the electrical power used was stable so there were no problems with the ICCP device while the ICCP device was operating.

The penetration of fuel spray as a result of the mixture of fuel droplet and entrained air usually generate nonlinear models whose solutions are normally difficult to realize analytically. This present study presents general approximate analytical solution to such problem by employing Differential transform Method (DTM). At the level of two-phase flow, the spray droplets and the entrained air have the same flow velocity. In order to fully understand the process, the parameters present in the governing equations are carefully studied. The obtained solution employing DTM is verified with Numerical Runge-Kutta (RKF45) and also compared with similar past works. Furthermore, the acquired results for different ambient densities and injection velocities are depicted and discussed. The results illustrate that continuous increase in the initial velocity and orifice diameter cause a corresponding increase in spray penetration while an antonymous effect is noticed for an increased semi cone angle and density. This work will find vital applications in the optimization of systems whose operation are influence by the aforementioned spray penetration processes.

In this paper we have introduced the concept of pseudo-valuations on JU-algebras and have investigated the relationship between pseudo-valuations and ideals of JU-algebras. Conditions for a real-valued function to be a pseudo-valuation on JU-algebras are given and results based on them have been shown. We have also defined and studied pseudo-metric on JU-algebras and have proved that \(\vartheta\) being a valuation on a JU-algebras \(A\), the operation \(\diamond\) in \(A\) is uniformly continuous.

In this work, we present a newly three antimicrobial chitosan, 2-benzoxazinyl benzoic acid (BBA) and novel biopolymer of Chitosan-spiroquinazolinone (SQC) via coupling of chitosan with benzoxazinyl benzoic acid, for promoting the antimicrobial activity of inherent chitosan. Modification in the chemical structure of the synthesized product SQC was confirmed using FT-IR and UV analysis. The antimicrobial activities of Chitosan, and BBA compounds were expressively increased more than chitosan-spiroquinazolinone SQC. Minimum inhibitory concentration (MIC) of compound SQC was supposed at \(50\mu g/ml\) against tested microorganisms except for B.cereus and C.albicans. The highest concentration of Chitosan would prevent the growth of Gram-+ve upto 99%. However, compound BBA recorded the maximum inhibition percentage versus Gram-+ve approximately 82%. The findings emphasized that the developed Chitosan-Spiroquinazolinone SQC may be blocker for antimicrobial activity to pure chitosan and BBA i.e, stop reaction if possible for actions of antimicrobial treatments.

Glaucoma is a second leading cause of blindness worldwide and stands on fourth position among the cause of blindness. Two main types of Glaucoma, primary congenital Glaucoma (PCG) and primary open angle Glaucoma (POAG). Primary open angle Glaucoma is further classified in to primary juvenile open angle Glaucoma JOAG (age of onset 3-35 years) and adult onset open angle Glaucoma (after the age of 35 years). Myocilin (MYOC) gene plays a major role in the development of adult primary open angle Glaucoma (POAG). Mutations in Myocilin (MYOC) gene are well documented to cause Adult Primary Open Angle Glaucoma (POAG). Currently, very few data is available on the contribution of Myocilin (MYOC) gene in POAG in Pakistani population. In present study, fifty seven sporadic cases of autosomal recessive samples of Primary Open Angle Glaucoma (POAG) were collected from different hospitals of Lahore, Pakistan. Sequencing was performed to check the contribution of (MYOC) gene and to identify the common mutations present in Pakistani population. Sequencing results revealed previously reported one heterozygous synonymous single nucleotide polymorphism SNP and a variant in intronic exonic boundary of exon 2. Findings of this study revealed that contribution of (MYOC) gene is high. Therefore, there is need to enroll more patients and families to identify the pathogenic mutations in (MYOC) gene to report actual frequency of this gene and its mutations in our population. Mutations identified in this gene may be helpful at clinical level to diagnose the disease at early stages.

Mathematical modeling of infectious diseases has progressed dramatically over the past four decades and continues to flourish at the nexus of mathematics, epidemiology, and infectious diseases research. Now recognized as a valuable tool, mathematical models are being integrated into the public health decision-making process more than ever before. In this article, a mathematical model of Ebola virus which is named as SEIVR (susceptible, exposed, infected, vaccinated, recovered) model is considered. First, we formulate the model and present the basic properties of the proposed model. Then, basic reproductive number is obtained by using the next-generation matrix approach. Furthermore, the sensitivity analysis of \(R_0\) is also discussed, all the endemic equilibrium points related to the disease are derived, a condition to investigate all possible equilibria of the model in terms of the basic reproduction number is obtained. In last, numerical simulation is presented with and without vaccination or control for the proposed model.

This paper studies some properties of the Fourier multiplier operators on a compact group when the underlying multiplication functions (the symbols) defined on the dual object take values in a Banach algebra. More precisely, boundedness properties for such Fourier multiplier operators for the space of Bochner strong integrable functions and for the (vector) \(p\)-Fourier spaces are investigated.

Since the emergence of the avian influenza A(H7N9) in the year 2013 in China, several researches have been carried out to investigate the spread. In this paper, a mathematical model describing the transmission dynamics of avian influenza A(H7N9) between human and poultry proposed by Li et al. [1] is modified by introducing re-infections into the susceptible human compartment. The method of next generation matrix is used to calculate the reproduction number. We also establish the local and global stability of the equilibria using Lyapunov functions. Finally, we use numerical simulations to validate our results.