Fractional Reverse Coposn's Inequalities via Conformable Calculus on Time Scales

This paper provides novel generalizations by considering the generalized conformable fractional integrals for reverse Copson's type inequalities on time scales. The main results will be proved using a general algebraic inequality, chain rule, Hölder's inequality, and integration by parts on fractional time scales. Our investigations unify and extend some continuous inequalities and their corresponding discrete analogues. In addition, when α = 1, we obtain some well-known time scale inequalities due to Hardy, Copson, Bennett, and Leindler inequalities

Improved results for testing the oscillation of functional differential equations with multiple delays

In this article, we test whether solutions of second-order delay functional differential equations oscillate. The considered equation is a general case of several important equations, such as the linear, half-linear, and Emden-Fowler equations. We can construct strict criteria by inferring new qualities from the positive solutions to the problem under study. Furthermore, we can incrementally enhance these characteristics. We can use the criteria more than once if they are unsuccessful the first time thanks to their iterative nature. Sharp criteria were obtained with only one condition that guarantees the oscillation of the equation in the canonical and noncanonical forms. Our oscillation results effectively extend, complete, and simplify several related ones in the literature. An example was given to show the significance of the main results

The Emergence of New Islamic Economic and Business Moralities

This article aims to explore the sources of the observed transformation in the embeddedness of economic, business, and financial practices of Muslim individuals in comparison to premodern period Muslims. It argues that the predomination of instrumental reasoning in modern times, as opposed to substantive morality in everyday practice, is one of the main reasons behind the transformation of embeddedness of Muslim individuals. Instrumental reasoning, being the dominant methodology, leads to diminished submergence in social relations; that is not limited to interpersonal relationships, but further extended to the core religious acts. How such an emergent economic and business morality is reconciled with the Islamic substantive morality is examined. It is argued that “transformation of exception into norm” is the main method used to reconcile instrumental reasoning with Islamic law in fulfilling religious obligations, at least in terms of fulfilling the form and in complying with the necessities of modern life. This has led to the emergence of new economic and business moralities

Diagnostic implications of pitfalls in causal variant identification based on 4577 molecularly characterized families

Despite large sequencing and data sharing efforts, previously characterized pathogenic variants only account for a fraction of Mendelian disease patients, which highlights the need for accurate identification and interpretation of novel variants. In a large Mendelian cohort of 4577 molecularly characterized families, numerous scenarios in which variant identification and interpretation can be challenging are encountered. We describe categories of challenges that cover the phenotype (e.g. novel allelic disorders), pedigree structure (e.g. imprinting disorders masquerading as autosomal recessive phenotypes), positional mapping (e.g. double recombination events abrogating candidate autozygous intervals), gene (e.g. novel gene-disease assertion) and variant (e.g. complex compound inheritance). Overall, we estimate a probability of 34.3% for encountering at least one of these challenges. Importantly, our data show that by only addressing non-sequencing-based challenges, around 71% increase in the diagnostic yield can be expected. Indeed, by applying these lessons to a cohort of 314 cases with negative clinical exome or genome reports, we could identify the likely causal variant in 54.5%. Our work highlights the need to have a thorough approach to undiagnosed diseases by considering a wide range of challenges rather than a narrow focus on sequencing technologies. It is hoped that by sharing this experience, the yield of undiagnosed disease programs globally can be improved

Characterizing the morbid genome of ciliopathies

Background Ciliopathies are clinically diverse disorders of the primary cilium. Remarkable progress has been made in understanding the molecular basis of these genetically heterogeneous conditions; however, our knowledge of their morbid genome, pleiotropy, and variable expressivity remains incomplete. Results We applied genomic approaches on a large patient cohort of 371 affected individuals from 265 families, with phenotypes that span the entire ciliopathy spectrum. Likely causal mutations in previously described ciliopathy genes were identified in 85% (225/265) of the families, adding 32 novel alleles. Consistent with a fully penetrant model for these genes, we found no significant difference in their “mutation load” beyond the causal variants between our ciliopathy cohort and a control non-ciliopathy cohort. Genomic analysis of our cohort further identified mutations in a novel morbid gene TXNDC15, encoding a thiol isomerase, based on independent loss of function mutations in individuals with a consistent ciliopathy phenotype (Meckel-Gruber syndrome) and a functional effect of its deficiency on ciliary signaling. Our study also highlighted seven novel candidate genes (TRAPPC3, EXOC3L2, FAM98C, C17orf61, LRRCC1, NEK4, and CELSR2) some of which have established links to ciliogenesis. Finally, we show that the morbid genome of ciliopathies encompasses many founder mutations, the combined carrier frequency of which accounts for a high disease burden in the study population. Conclusions Our study increases our understanding of the morbid genome of ciliopathies. We also provide the strongest evidence, to date, in support of the classical Mendelian inheritance of Bardet-Biedl syndrome and other ciliopathies

Mutations in DONSON disrupt replication fork stability and cause microcephalic dwarfism

To ensure efficient genome duplication, cells have evolved numerous factors that promote unperturbed DNA replication and protect, repair and restart damaged forks. Here we identify downstream neighbor of SON (DONSON) as a novel fork protection factor and report biallelic DONSON mutations in 29 individuals with microcephalic dwarfism. We demonstrate that DONSON is a replisome component that stabilizes forks during genome replication. Loss of DONSON leads to severe replication-associated DNA damage arising from nucleolytic cleavage of stalled replication forks. Furthermore, ATM- and Rad3-related (ATR)-dependent signaling in response to replication stress is impaired in DONSON-deficient cells, resulting in decreased checkpoint activity and the potentiation of chromosomal instability. Hypomorphic mutations in DONSON substantially reduce DONSON protein levels and impair fork stability in cells from patients, consistent with defective DNA replication underlying the disease phenotype. In summary, we have identified mutations in DONSON as a common cause of microcephalic dwarfism and established DONSON as a critical replication fork protein required for mammalian DNA replication and genome stability

Optimal Control Problems for Hilfer Fractional Neutral Stochastic Evolution Hemivariational Inequalities

In this paper, we concentrate on a control system with a non-local condition that is governed by a Hilfer fractional neutral stochastic evolution hemivariational inequality (HFNSEHVI). By using concepts of the generalized Clarke sub-differential and a fixed point theorem for multivalued maps, we first demonstrate adequate requirements for the existence of mild solutions to the concerned control system. Then, using limited Lagrange optimal systems, we demonstrate the existence of optimal state-control pairs that are regulated by an HFNSEHVI with a non-local condition. In order to demonstrate the existence of fixed points, the symmetric structure of the spaces and operators that we create is essential. Without considering the uniqueness of the control system’s solutions, the best control results are established. Lastly, an illustration is used to demonstrate the major result

On Hardy–Knopp Type Inequalities with Kernels via Time Scale Calculus

In this paper, we study the inequalities of Hardy–Knopp type with kernel functions which have two nonnegative different weighted functions in two different spaces, in a general domain called a time scale calculus. A time scale calculus T is considered as a unification of the continuous calculus and the discrete calculus. We will prove these inequalities in a time scale calculus to avoid proving them twice once in the continuous case and the second in the discrete case. Also, as special cases of the time scale calculus, we can prove some new inequalities in new different domains. Our results will be proved by using the definition of a general Hardy operator on time scale. These inequalities (when T=ℕ) are essentially new

Some Dynamic Inequalities of Hilbert’s Type

This paper is concerned with deriving some new dynamic Hilbert-type inequalities on time scales. The basic idea in proving the results is using some algebraic inequalities, Hölder’s inequality and Jensen’s inequality, on time scales. As a special case of our results, we will obtain some integrals and their corresponding discrete inequalities of Hilbert’s type