Differential subordination and superordination studies involving symmetric functions using a q-analogue multiplier operator

The present investigation focus on applying the theories of differential subordination, differential superordination and related sandwich-type results for the study of some subclasses of symmetric functions connected through a linear extended multiplier operator, which was previously defined by involving the $q$-Choi-Saigo-Srivastava operator. The aim of the paper is to define a new class of analytic functions using the aforementioned linear extended multiplier operator and to obtain sharp differential subordinations and superordinations using functions from the new class. Certain subclasses are highlighted by specializing the parameters involved in the class definition, and corollaries are obtained as implementations of those new results using particular values for the parameters of the new subclasses. In order to show how the results apply to the functions from the recently introduced subclasses, numerical examples are also provided

Characterization of greater middle eastern genetic variation for enhanced disease gene discovery

The Greater Middle East (GME) has been a central hub of human migration and population admixture. The tradition of consanguinity, variably practiced in the Persian Gulf region, North Africa, and Central Asia1-3, has resulted in an elevated burden of recessive disease4. Here we generated a whole-exome GME variome from 1,111 unrelated subjects. We detected substantial diversity and admixture in continental and subregional populations, corresponding to several ancient founder populations with little evidence of bottlenecks. Measured consanguinity rates were an order of magnitude above those in other sampled populations, and the GME population exhibited an increased burden of runs of homozygosity (ROHs) but showed no evidence for reduced burden of deleterious variation due to classically theorized ‘genetic purging’. Applying this database to unsolved recessive conditions in the GME population reduced the number of potential disease-causing variants by four- to sevenfold. These results show variegated genetic architecture in GME populations and support future human genetic discoveries in Mendelian and population genetics

Applications of <i>q</i>-Calculus Multiplier Operators and Subordination for the Study of Particular Analytic Function Subclasses

In this article, a new linear extended multiplier operator is defined utilizing the q-Choi–Saigo–Srivastava operator and the q-derivative. Two generalized subclasses of q—uniformly convex and starlike functions of order δ—are defined and studied using this new operator. Necessary conditions are derived for functions to belong in each of the two subclasses, and subordination theorems involving the Hadamard product of such particular functions are stated and proven. As applications of those findings using specific values for the parameters of the new subclasses, associated corollaries are provided. Additionally, examples are created to demonstrate the conclusions’ applicability in relation to the functions from the newly introduced subclasses

Some vertex/edge-degree-based topological indices of r-apex trees

In chemical graph theory, graph invariants are usually referred to as topological indices. For a graph G, its vertex-degree-based topological indices of the form BIDG=∑uv∈EGβdu,dv are known as bond incident degree indices, where EG is the edge set of G, dw denotes degree of an arbitrary vertex w of G, and β is a real-valued-symmetric function. Those BID indices for which β can be rewritten as a function of du+dv-2 (that is degree of the edge uv) are known as edge-degree-based BID indices. A connected graph G is said to be r-apex tree if r is the smallest nonnegative integer for which there is a subset R of VG such that R=r and G-R is a tree. In this paper, we address the problem of determining graphs attaining the maximum or minimum value of an arbitrary BID index from the class of all r-apex trees of order n, where r and n are fixed integers satisfying the inequalities n-r≥2 and r≥1.Published versionThis research was funded by Scientific Research Deanship at University of Ha'il, Saudi Arabia, through project no. RG-20 050

Differential Subordination and Superordination Results Associated with Mittag–Leffler Function

In this paper, we derive a number of interesting results concerning subordination and superordination relations for certain analytic functions associated with an extension of the Mittag&ndash;Leffler function

Admissible Classes of Multivalent Meromorphic Functions Defined by a Linear Operator

The results from this paper are related to the geometric function theory. In order to obtain them, we use the technique based on differential subordination, one of the newest techniques used in the field, also known as the technique of admissible functions. For that, the appropriate classes of admissible functions are first defined. Based on these classes, we obtain some differential subordination and superordination results for multivalent meromorphic functions, analytic in the punctured unit disc, related to a linear operator ℑρ,τp(ν), for τ>0,ν,ρ∈C, such that Re(ρ−ν)≧0, Re(ν)>τp,(p∈N). Moreover, taking into account both subordination and superordination results, we derive a sandwich-type theorem. The connection with some other known results and an example are also provided

On Some Relationships of Certain K−Uniformly Analytic Functions Associated with Mittag-Leffler Function

In this paper, we introduce and investigate several inclusion relationships of new k-uniformly classes of analytic functions defined by the Mittag-Leffler function. Also, integral-preserving properties of these classes associated with the certain integral operator are also obtained

Differential Subordination and Differential Superordination for Classes of Admissible Multivalent Functions Associated with a Linear Operator

In this paper, we first introduce a linear integral operator ℑp(a,c,μ)(μ>0;a,c∈R;c>a>−μp;p∈N+:={1,2,3,…}), which is somewhat related to a rather specialized form of the Riemann–Liouville fractional integral operator and its varied form known as the Erdélyi–Kober fractional integral operator. We then derive some differential subordination and differential superordination results for analytic and multivalent functions in the open unit disk U, which are associated with the above-mentioned linear integral operator ℑp(a,c,μ). The results presented here are obtained by investigating appropriate classes of admissible functions. We also obtain some Sandwich-type results

Effects of M-Truncated Derivative and Multiplicative Noise on the Exact Solutions of the Breaking Soliton Equation

In this article, the fractional–space stochastic (2+1)-dimensional breaking soliton equation (SFSBSE) is taken into account in the sense of M-Truncated derivative. To get the exact solutions to the SFSBSE, we use the modified F-expansion method. There are several varieties of obtained exact solutions, including trigonometric and hyperbolic functions. The attained solutions of the SFSBSE established in this paper extend a number of previously attained results. Moreover, in order to clarify the influence of multiplicative noise and M-Truncated derivative on the behavior and symmetry of the solutions for the SFSBSE, we employ Matlab to plot three-dimensional and two-dimensional diagrams of the exact fractional–stochastic solutions achieved here. In general, a noise term that destroy the symmetry of the solutions increases the solution’s stability

NFI-A Disrupts Myeloid Cell Differentiation and Maturation in Septic Mice

Mounting evidence supports that sepsis-associated immunosuppression increases mortality. As potential contributors to poor sepsis outcomes, myeloid-derived suppressor cells, which are Gr1+ CD11b+ innate-immune cell progenitors unable to differentiate and possess suppressive activities, expand dramatically in septic mice by a process requiring increased microRNA-21 and microRNA-181b expression. The inhibition of these microRNAs in vivo in septic mice restores Gr1+ CD11b+ cell differentiation and maturation and improves survival. Here, we show that during sepsis-induced generation of myeloid-derived suppressor cells, transcription factor nuclear factor 1 A type represses cyclin-dependent kinase inhibitor p21 to arrest differentiation of Gr1+ CD11b+ cells. Our findings include the following: 1) Gr1+ CD11b+ myeloid cells from late septic mice genetically lacking nuclear factor 1 A type cannot suppress CD4+ T cell proliferation and activation; 2) the reconstitution of nuclear factor 1 A type in microRNA-21 and microRNA-181b-depleted Gr1+ CD11b+ myeloidderived suppressor cells inhibits cyclin-dependent kinase inhibitor p21 and restores the immunesuppressor phenotype; 3) ex vivo nuclear factor 1 A type knockdown in Gr1+ CD11b+ myeloid-derived suppressor cells from late septic mice restores cyclindependent kinase inhibitor p21 expression and promotes monocyte and dendritic cell differentiation; and 4) ectopic nuclear factor 1 A type expression in normal Gr1+ CD11b+ cells generates an immunosuppressive phenotype. We suggest that therapeutically targeting nuclear factor 1 A type during late sepsis might improve survival