Impulsive Nonlocal Neutral Integro-Differential Equations Controllability results on Time Scales

In this work, we studied the controllability results for neutral differential time-varying equation with impulses on time scales & extend these results into nonlocal controllability of neutral functional integro-differential time-varying equation with impulses on time scales. The solutions are obtained employing standard fixed point theorems

Local invariants of fronts in 3-manifolds

An invariant is a quantity which remains unchanged under certain classes of transformations. A wave front (or a front) in a 3-manifold is the image of a surface under a Legendrian map. The aim of this thesis is the description of all local invariants of fronts in 3-manifolds. The front invariants under consideration are those whose increments in generic homotopies are determined entirely by diffeomorphism types of local bifurcations of the fronts. Such invariants are dual to trivial codimension 1 cycles supported on the discriminant in the space of corresponding Legendrian maps. We describe the spaces of the discriminantal cycles (possibly non-trivial) for various orientation and co-orientation settings of the fronts in an arbitrary oriented 3-manifold, both for the integer and mod2 coefficients. For the majority of these cycles we find homotopy-independent interpretations which guarantee the triviality required. In particular, in the case of framed fronts we show that all integer local invariants of Legendrian maps without corank 2 points are essentially exhausted by the numbers of points of isolated singularity types of the fronts

Discussion on iterative process of nonlocal controllability exploration for Hilfer neutral impulsive fractional integro-differential equation

This manuscript primarily focuses on the nonlocal controllability results of Hilfer neutral impulsive fractional integro-differential equations of order $0\leq w\leq1$ and 0 < g < 1 in a Banach space. The outcomes are derived from the strongly continuous operator, Wright function, linear operator, and bounded operator. First, we explore the existence and uniqueness of the results of the mild solution of Hilfer's neutral impulsive fractional integro-differential equations using Schauder's fixed point theorem and an iterative process. In order to determine nonlocal controllability, the Banach fixed point technique is used. We employed some specific numerical computations and applications to examine the effectiveness of the results

Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problems

A new form of basis functions structures has been constructed. These basis functions constitute a mix of Chebyshev polynomials and Legendre polynomials. The main purpose of these structures is to present several forms of differentiation matrices. These matrices were built from the perspective of pseudospectral approximation. Also, an investigation of the error analysis for the proposed expansion has been done. Then, we showed the presented matrices' efficiency and accuracy with several test functions. Consequently, the correctness of our matrices is demonstrated by solving ordinary differential equations and some initial boundary value problems. Finally, some comparisons between the presented approximations, exact solutions, and other methods ensured the efficiency and accuracy of the proposed matrices

Existence criteria for fractional differential equations using the topological degree method

In this work, we analyze the fractional order by using the Caputo-Hadamard fractional derivative under the Robin boundary condition. The topological degree method combined with the fixed point methodology produces the desired results. Finally to show how the key findings may be utilized, applications are presented

Mucormycosis co-infection in COVID-19 patients: An update

Mucormycosis (MCM) is a rare fungal disorder that has recently been increased in parallel with novel COVID-19 infection. MCM with COVID-19 is extremely lethal, particularly in immunocompromised individuals. The collection of available scientific information helps in the management of this co-infection, but still, the main question on COVID-19, whether it is occasional, participatory, concurrent, or coincidental needs to be addressed. Several case reports of these co-infections have been explained as causal associations, but the direct contribution in immunocompromised individuals remains to be explored completely. This review aims to provide an update that serves as a guide for the diagnosis and treatment of MCM patients’ co-infection with COVID-19. The initial report has suggested that COVID-19 patients might be susceptible to developing invasive fungal infections by different species, including MCM as a co-infection. In spite of this, co-infection has been explored only in severe cases with common triangles: diabetes, diabetes ketoacidosis, and corticosteroids. Pathogenic mechanisms in the aggressiveness of MCM infection involves the reduction of phagocytic activity, attainable quantities of ferritin attributed with transferrin in diabetic ketoacidosis, and fungal heme oxygenase, which enhances iron absorption for its metabolism. Therefore, severe COVID-19 cases are associated with increased risk factors of invasive fungal co-infections. In addition, COVID-19 infection leads to reduction in cluster of differentiation, especially CD4+ and CD8+ T cell counts, which may be highly implicated in fungal co-infections. Thus, the progress in MCM management is dependent on a different strategy, including reduction or stopping of implicit predisposing factors, early intake of active antifungal drugs at appropriate doses, and complete elimination via surgical debridement of infected tissues

Outcomes of orthodontic treatment performed by individual orthodontists versus two orthodontists collaborating on treatment

Objectives: The aim of this study was to evaluate orthodontic treatment quality, length and efficiency when two orthodontists collaborated on treatment compared to cases treated by either orthodontist. Methods: The sample consisted of 150 consecutively treated subjects gathered from three groups of patients (A, B and C), each group included 50 patients. Group A patients were treated by orthodontist A, group B by orthodontist B, and group C by both orthodontists. PAR index, ICON, ABO-DI and ABO-CRE assessed the pre- and post-treatment status. Variables including age, gender, type of malocclusion, extraction versus non-extraction, orthognathic surgery, treatment length, number of visits, frequency of missed, cancelled and emergency appointments were collected for statistical analysis. Treatment efficiency Index (TEI) was also assessed. Results: There was no statistical significant difference in the pre-treatment status, age, gender, type of malocclusion or number of extractions between the three groups. Post-treatment PAR and ICON indices showed excellent results in all three groups, with no statistical significant difference between groups. ABO-CRE was significantly higher in group C (25.3 points) than either group A (21.5 points) or group B (22.0 points) (P=0.014). Group A cases, on average, had significantly less treatment time (23 months) than either group B or C (26 months) (P=0.011). Group C patients required more appointments (27 visits) than either group A or B (23 and 25 visits, respectively). The treatment efficiency index showed no statistical significant differences between the three groups (P=0.113). Conclusions: Good outcomes were achieved in all three groups as assessed by PAR index and ICON, with no difference between providers. Cases treated by a collaboration of both orthodontists required 2 to 4 more visits and had higher ABO-CRE scores than those treated by a single orthodontist.Dentistry, Faculty ofGraduat

Quasi Semi-Border Singularities

We obtain a list of simple classes of singularities of function germs with respect to the quasi m-boundary equivalence relation, with m &ge; 2 . The results obtained in this paper are a natural extension of Zakalyukin&rsquo;s work on the new non-standard equivalent relation. In spite of the rather artificial nature of the definitions, the quasi relations have very natural applications in symplectic geometry. In particular, they are used to classify singularities of Lagrangian projections equipped with a submanifold. The main method that is used in the classification is the standard Moser&rsquo;s homotopy technique. In addition, we adopt the version of Arnold&rsquo;s spectral sequence method, which is described in Lemma 2. Our main results are Theorem 4 on the classification of simple quasi classes, and Theorem 5 on the classification of Lagrangian submanifolds with smooth varieties. The brief description of the main results is given in the next section

Hosoya Polynomials of Power Graphs of Certain Finite Groups

Assume that G is a finite group. The power graph P(G) of G is a graph in which G is its node set, where two different elements are connected by an edge whenever one of them is a power of the other. A topological index is a number generated from a molecular structure that indicates important structural properties of the proposed molecule. Indeed, it is a numerical quantity connected with the chemical composition that is used to correlate chemical structures with various physical characteristics, chemical reactivity, and biological activity. This information is important for identifying well-known chemical descriptors based on distance dependence. In this paper, we study Hosoya properties, such as the Hosoya polynomial and the reciprocal status Hosoya polynomial of power graphs of various finite cyclic and non-cyclic groups of order pq and pqr, where p,q and r(p&ge;q&ge;r) are prime numbers