41,402 Results Found

Background/Objectives: Transient neonatal diabetes mellitus (TNDM) is a form of neonatal diabetes mellitus (NDM) arising in the first weeks of life and remitting in infancy. Epigenetic aberrations at the imprinted 6q24 locus (overexpression of PLAGL1...

The main purpose of this paper is to consider q-sine-based and q-cosine-Based q-Fubini polynomials and is to investigate diverse properties of these polynomials. Furthermore, multifarious correlations including q-analogues of the Genocchi, Euler and...

In recent years, $(p,q)$-special polynomials, such as $\left(p,q\right)$-Euler, $\left(p,q\right)$-Genocchi, $\left(p,q\right)$-Bernoulli, and $\left(p,q\right)$-Frobenius-Euler, have been studied and investigated by many mathematicians, as well physicists. It is important that any polynomial have explicit form...

In this paper, we introduce a fractional q-extension of the q-differential operator $D_{q^{-1}}$ and prove some of its main properties. Next, fractional q-extensions of some classical q-orthogonal polynomials are introduced and some of the main propert...

In this paper, we apply a general family of basic (or q-) polynomials with double q-binomial coefficients as well as some homogeneous q-operators in order to construct several q-difference equations involving seven variables. We derive the Rogers typ...

In this article, the authors introduce the q-analogue of the $\mathbb{M}$-function, and establish four theorems related to the Riemann–Liouville fractional q-calculus operators pertaining to the newly defined q-analogue of $\mathbb{M}$-functions. In addition, to est...

One finds several q-differential equations of a higher order for q-Euler polynomials and q-Genocchi polynomials. Additionally, we have a few q-differential equations of a higher order, which are mixed with q-Euler numbers and q-Genocchi polynomials....

In the geometric function theory of complex analysis, the investigation of the geometric properties of analytic functions using q-analogues of differential and integral operators is an important area of study, offering powerful tools for applications...

Our investigation is motivated essentially by the demonstrated applications of the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and basic (or q-) hypergeometric polynomials, in many diverse...

This paper aims to find Hermite–Hadamard-type inequalities for a generalized notion of integrals called $q-h$-integrals. Inequalities for q-integrals can be deduced by taking $h=0$ and are connected with several known results of q-Hermite&nda...

The rich history of prime numbers includes great names such as Euclid, who first analytically studied the prime numbers and proved that there is an infinite number of them, Euler, who introduced the function $\zeta \left(s\right)\equiv {\sum }_{n=1}^{\infty }{n}^{-s}={\&}_{}$...

Real-time quantitative polymerase chain reaction is subject to inhibition by substances that co-purify with nucleic acids during isolation and preparation of samples. Such materials alter the activity of reverse transcriptase (RT) and thermostable DN...

In this paper, we present the q-Lidstone polynomials which are q-Bernoulli polynomials generated by the third Jackson q-Bessel function, based on the Green’s function of a certain q-difference equation. Also, we provide the q-Fourier series exp...

In this paper, we make use of the Riemann–Liouville fractional q-integral operator to discuss the class $S_{q,\delta }^{*}\left(\alpha \right)$ of univalent functions for $\delta >0,\alpha \in \mathbb{C}-\left\{0\right\}$, and $0<\left|q\right|<1$. Then, we develop convolution resul...

Certain new classes of q-convex and q-close to convex functions that involve the q-Janowski type functions have been defined by using the concepts of quantum (or q-) calculus as well as q-conic domain $\left(\right)$...

The purpose of this article is to study how q-real numbers can be used for computations of convergence regions, q-integral representations of certain multiple triple q-Lauricella functions. The corresponding q-difference equations are also given with...

In this paper, binomial convolution in the frame of quantum calculus is studied for the set ${\mathcal{A}}_q$ of q-Appell sequences. It has been shown that the set ${\mathcal{A}}_q$ of q-Appell sequences forms an Abelian group under the operation of binomial convolution. Several...

In this paper, we introduce q-cosine and q-sine Euler polynomials and determine identities for these polynomials. From these polynomials, we obtain some special properties using a power series of q-trigonometric functions, properties of q-exponential...

In this article, the $(p,q)$-analogs of the $\alpha$-th fractional Fourier transform are provided, along with a discussion of their characteristics in specific classes of $(p,q)$-generalized functions. Two spaces of infinitely $(p,q)$-differentiable functio...

Since Gottlieb introduced and investigated the so-called Gottlieb polynomials in 1938, which are discrete orthogonal polynomials, many researchers have investigated these polynomials from diverse angles. In this paper, we aimed to investigate the q-e...

In this paper, we first discuss some important properties of fractional q-calculus. Then, based on these properties and the q-Laplace transform, we translate a class of fractional q-differential equations into the equivalent q-differential equations...

The q-Stirling numbers (polynomials) of the second kind have been investigated and applied in a variety of research subjects including, even, the q-analogue of Bernstein polynomials. The $(p,q)$-Stirling numbers (polynomials) of the second kind have be...

A class of power series q-distributions, generated by considering a q-Taylor expansion of a parametric function into powers of the parameter, is discussed. Its q-factorial moments are obtained in terms of q-derivatives of its series (parametric) func...

This paper establishes a new characterization of symmetric q-Dunkl-classical orthogonal polynomials through a second structure relation. These symmetric polynomials generalize the $q^2$-analogues of Hermite and Gegenbauer polynomials. Our main result pr...

This article presents the theory of trivariate q-truncated Gould–Hopper polynomials through a generating function approach utilizing q-calculus functions. These polynomials are subsequently examined within the framework of quasi-monomiality, le...

Let f be analytic in open unit disc $E=\{z:|z|<1\}$ with $f\left(0\right)=0$ and $f^{{}^{\prime }}\left(0\right)=1$ . The q-derivative of f is defined by: $D_{q}f\left(z\right)=\frac{f\left(z\right)-f\left(qz\right)}{(1-q)z},q\&i$...

In this article, we make use of the q-binomial theorem to introduce and study two new subclasses $\aleph (\alpha q,q)$ and $\aleph (\alpha ,q)$ of meromorphic functions in the open unit disk $\mathbb{U}$, that is, analytic functions in the punctured unit disk ${\mathbb{U}}^{}$...

The q-Bernoulli numbers and polynomials can be given by Witt’s type formulas as p-adic invariant integrals on ${\mathbb{Z}}_p$ . We investigate some properties for them. In addition, we consider two variable q-Bernstein polynomials and operators and derive...

Trichorhinophalangeal syndrome type II (TRPS II) is a rare disease caused by a contiguous gene deletion in the 8q23.3–q24.11 region. Three genes (TRPS1, RAD21, and EXT1) are considered responsible for the most common clinical features, which in...

Andrews gave a remarkable interpretation of the Rogers–Ramanujan identities with the polynomials ${\rho }_e(N,y,x,q)$, and it was noted that ${\rho }_e(\infty ,-1,1,q)$ is the generation of the fifth-order mock theta functions. In the present investigation, several interest...

We study a q-analogue of Euler numbers and polynomials naturally arising from the p-adic fermionic integrals on ${\mathbb{Z}}_p$ and investigate some properties for these numbers and polynomials. Then we will consider p-adic fermionic integrals on ${\mathbb{Z}}_p$ of the two va...

In this paper, we address the lack of general Janowski-type subclasses for analytic functions involving higher-order q-derivatives, unifying cases with both positive and negative coefficients. Using a combination of higher-order q-derivative techniqu...

An accurate and easy-to-use Q3 system for on-chip quantitative real-time Polymerase Chain Reaction (qPCR) is hereby demonstrated, and described in detail. The qPCR reactions take place inside a single-use Lab-on-a-Chip with multiple wells, each with...

Many diverse subclasses of analytic functions, q-starlike functions, and symmetric q-starlike functions have been studied and analyzed by using q-analogous values of integral and derivative operators. In this paper, we define a q-analogous value of d...

We present a unique case of a young woman with acute myeloid leukemia (AML) with complex karyotype. The presence of the t(4;11)(q23;p15) is extremely rare in myeloid leukemias, while t(4;8)(q32;q13) has not yet been described in any leukemia referenc...

Queuosine (Q) is a complex modification of the wobble base in tRNAs with GUN anticodons. The full Q biosynthesis pathway has been elucidated in Escherichia coli. FolE, QueD, QueE and QueC are involved in the conversion of guanosine triphosphate (GTP)...

In our present investigation, we extend the idea of q-symmetric derivative operators to multivalent functions and then define a new subclass of multivalent q-starlike functions. For this newly defined function class, we discuss some useful properties...

Utilizing $\left(p,q\right)$-numbers and $\left(p,q\right)$-concepts, in 2016, Duran et al. considered $\left(p,q\right)$-Genocchi numbers and polynomials, $\left(p,q\right)$-Bernoulli numbers and polynomials and $\left(p,q\right)$-Euler polynomials and numbers and provided multifarious formulas and properties for these pol...

Using the q-integral representation of Sears’ nonterminating extension of the q-Saalschütz summation, we derive a reduction formula for a kind of double q-integrals. This reduction formula is used to derive a curious double q-integral formula, and al...

Background and Objectives: Only nine patients with interstitial de novo 8q22.2q22.3 microdeletions have been reported to date. The objective of this report is to present clinical features of a new patient with an 8q22.2q22.3 microdeletion, to compare...

In mathematical analysis, the q-analogue of a function refers to a modified version of the function that is derived from q-series expansions. This paper is focused on the q-analogue of the exponential function and investigates a class of convex funct...

Originally identified as a key component of the mitochondrial respiratory chain, Coenzyme Q (CoQ or CoQ₁₀ for human tissues) has recently been revealed to be essential for many different redox processes, not only in the mitochondria, but elsewhere wi...

Background: Polycythemia vera (PV) is a clonal myeloid stem cell disease characterized by a growth-factor independent erythroid proliferation with an inherent tendency to transform into overt acute myeloid malignancy. Approximately 95% of the PV pati...

Many properties of special polynomials, such as recurrence relations, sum formulas, and symmetric properties have been studied in the literature with the help of generating functions and their functional equations. In this paper, using the $(p,q)$&ndas...

This paper constructs and introduces $(p,q)$ -cosine and $(p,q)$ -sine Bernoulli polynomials using $(p,q)$ -analogues of ${(x+a)}^n$ . Based on these polynomials, we discover basic properties and identities. Moreov...

Recently, a number of researchers from different fields have taken a keen interest in the domain of fractional q-calculus on the basis of fractional integrals and derivative operators. This has been used in various scientific research and technology...

The 15q11.2q13 chromosomal region is particularly susceptible to chromosomal rearrangements due to low-copy repeats (LCRs) located inside this area. Specific breakpoints (BP1-BP5) that lead to deletions and duplications of variable size have been ide...

Coenzyme Q₁₀ (CoQ₁₀) deficiency syndrome includes clinically heterogeneous mitochondrial diseases that show a variety of severe and debilitating symptoms. A multiprotein complex encoded by nuclear genes carries out CoQ₁₀ biosynthesis. Mutations in an...

The Q-system and Q-slope are empirical methods developed for classifying and assessing rock masses for tunneling, underground mining, and rock slope engineering. Both methods have been used extensively to guide appropriate ground support design for u...

This paper aims to unify q-derivative/q-integrals and h-derivative/h-integrals into a single definition, called $q-h$-derivative/$q-h$-integral. These notions are further extended on the finite interval $[a,b]$ in the form of left and right $q\&m$...