Open Disk Research Articles

Complex Generalized Stancu-Schurer Operators

Abstract In the present study, we determine a Schurer type of complex generalized Stancu operators and examine its some approximation properties. Firstly, we obtain upper quantitative estimates for the convergence and then we get lower estimates from a qualitative Voronovskaja-type result for these specified operators attached to the analytic functions in an open disk centered at the origin. Hence, we present the exact order of simultaneous approximation by using obtained upper and lower estimates.

On a Degenerating Limit Theorem of DeMarco–Faber

One of our aims is to complement the proof of DeMarco–Faber’s degenerating limit theorem for the family of the unique maximal entropy measures parametrized by a punctured open disk associated to a meromorphic family of rational functions on the complex projective line, degenerating at the puncture. This complementation is done by our main result, which rectifies a key computation in their argument. We also establish and use a direct and explicit translation from degenerating complex dynamics into quantized Berkovich dynamics, instead of using DeMarco–Faber’s more conceptual transfer principle between those dynamics.

Nocturnal burst emissions of germacrene D from the open disk florets of pyrethrum flowers induce moths to oviposit on a nonhost and improve pollination success.

Recent studies show that nocturnal pollinators may be more important to ecosystem function and food production than is currently appreciated. Here, we describe an agricultural field study of pyrethrum (Tanacetum cinerariifolium) flower pollination. Pyrethrum is genetically self-incompatible and thus is reliant on pollinators for seed set. Our pollinator exclusion experiment showed that nocturnal insects, particularly moths, significantly contribute to seed set and quality. We discovered that the most abundant floral volatile, the sesquiterpene (-)-germacrene D (GD), is key in attracting the noctuid moths Peridroma saucia and Helicoverpa armigera. Germacrene D synthase (GDS) gene expression regulates the specific GD production and accumulation in flowers, which, in contrast to related species, lose the habit of closing at night. We did observe that female moths also oviposited on pyrethrum leaves and flower peduncles, but found that only a small fraction of those eggs hatched. Larvae were severely stunted in development, most likely due to the presence of pyrethrin defense compounds. This example of exploitative mutualism, which blocks the reproductive success of the moth pollinator and depends on nocturnal interactions, is placed into an ecological context to explain why it may have developed.

The influence of open disc repositioning surgery on the internal derangement of the contralateral temporomandibular joint: a prospective study of 96 patients.

To assess the influence of unilateral open disc repositioning surgery (ODRS) of the temporomandibular joint (TMJ) on the internal derangement (ID) of the contralateral joint. Patients with bilateral ID of TMJ who underwent unilateral ODRS were enrolled and followed-up for one year. They were divided into two groups based on the contralateral disease: the anterior disc displacement with reduction (ADDWR) and without reduction (ADDWoR). Postoperative evaluation included clinical and MRI evaluation. Indices measured were unilateral intermaxillary distance (UID), visual analogue scale (VAS), disc length (DL), condylar height (CH), and disc-condyle angle (DCA). Paired t tests were used to compare the clinical and MRI indices between different time points. Ninety-six patients were enrolled, including 47 in the ADDWR group and 49 in the ADDWoR group. One-year post-surgery, ODRS led to significant increases in MMO, DL, and CH, and decrease in VAS and DCA on the operated side (P < 0.05). In ADDWR group, UID, DL, and CH increased significantly, and VAS decreased (P < 0.05), with no significant change in DCA (P > 0.05). In ADDWoR group, clinical and MRI variables worsened slightly, except for UID, which remained unchanged (P > 0.05). ODRS is a promising method for correcting TMJ ID and may improve condition of ADDWR and decrease progress of ADDWoR at the contralateral joint. Preoperative bilateral TMJ evaluation is essential for better outcomes. ODRS can effectively treat TMJ ID and produce adaptive changes in the contralateral ID, for which continuous monitoring of the contralateral joint is essential.

Automorphisms and isomorphisms of maps in linear time

A map is a \(2\) -cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. An automorphism of a map can be thought of as a permutation of the vertices which preserves the vertex-edge-face incidences in the embedding. Every automorphism of a map determines an angle-preserving homeomorphism of the surface. While it is conjectured that there is no “truly subquadratic” algorithm for testing map isomorphism for unconstrained genus, we present a linear-time algorithm for computing the generators of the automorphism group of a map on an orientable surface of genus \(g\neq 0\) , parametrized by the genus \(g\) . A map on an orientable surface is uniform if the cyclic vector of sizes of faces incident to a vertex \(v\) does not depend on the choice of \(v\) . The algorithm applies a sequence of local reductions and produces a uniform map, while preserving the automorphism group. The automorphism group of the original map can be reconstructed from the automorphism group of the associated uniform map in linear time. We also extend the algorithm to non-orientable surfaces by making use of the antipodal double-cover. The algorithm can be used to solve the map isomorphism problem between maps (orientable or non-orientable) of bounded negative Euler characteristic.

Majorization and Quasi-Subordination Problems for Certain Subclasses of Holomorphic Functions Utilizing Differential Operator

In the current paper, we define some subclasses of holomorphic functions in the open disk that are defined by the differential operator. These subclasses are defined in the open disk . We make some estimates for the bounds of the Fekete-Szego inequality as well as the coefficients and for functions that belong to these subclasses. Also, some of the results of these subclasses have been generalized, particularly those that involve the majorization and quasi-subordination concepts.

A study On Quasi- Hadamard Product of A class of Analytic Functions Defined by Sălăgean Operator

The purpose of this paper is to study some known properties for certain class of uniformly functions defined in the open unite disk Especially, is to obtain quasi-Hadamard products for certain class of univalent functions which are defined by means of the Sălăgean operator. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.

Holonomy and (stated) skein algebras in combinatorial quantization

The algebra \mathcal{L}_{g,n}(H) was introduced by Alekseev, Grosse, and Schomerus and by Buffe­noir and Roche and quantizes the character variety of the Riemann surface \Sigma_{g,n}\setminus D (where D is an open disk). In this article we define a holonomy map in that quantized setting, which associates a tensor with components in \mathcal{L}_{g,n}(H) to tangles in (\Sigma_{g,n}\setminus\!D) \times [0,1] , generalizing previous works of Buffenoir and Roche and of Bullock, Frohman, and Kania-Bartoszynska. We show that holonomy behaves well for the stack product and the action of the mapping class group; then we specialize this notion to links in order to define a generalized Wilson loop map. Thanks to the holonomy map, we give a geometric interpretation of the vacuum representation of \mathcal{L}_{g,0}(H) on \mathcal{L}_{0,g}(H) . Finally, the general results are applied to the case H=U_{q^2}(\mathfrak{sl}_{2}) in relation to skein theory and the most important consequence is that the stated skein algebra of a compact oriented surface with just one boundary edge is isomorphic to \mathcal{L}_{g,n}(U_{q^2}(\mathfrak{sl}_{2})) . Throughout the paper, we use a graphical calculus for tensors with coefficients in \mathcal{L}_{g,n}(H) which makes the computations and definitions very intuitive.

Applications of q-Borel distribution series involving q-Gegenbauer polynomials to subclasses of bi-univalent functions

This study introduces a new class of bi-univalent functions in the open disk using q-Borel distribution series and q-Gegenbauer polynomials. It provides estimates for the Taylor coefficients |μ2| and |μ3| for this family of functions, as well as solutions for the Fekete-Szegö functional problems associated with this subclass. The study presents various innovative findings that result from the unique parameters used in the main results.

Evaluation of clinical impact of two types of Temporomandibular joint disc reduction and fixation

ObjectiveTo evaluate the clinical effectiveness and stability of open suture versus micro-screw anchored disc reduction and fixation in treating disc displacement without reduction in the anterior temporomandibular joint. MethodsA total of 38 patients (51 sides) with anterior disc displacement without reduction (ADDwR) of the TMJ treated in our hospital from August 2021 to January 2023 were selected, including 19 cases in group A (23 sides) treated with open temporomandibular joint disc reduction and anchorage, and 19 cases in group B (28 sides) treated with temporomandibular joint disc reduction and suture. The Magnetic Resonance Imaging (MRI) data of the two groups before and after operation were compared to evaluate the effective rate of articular disc reduction, the change of articular disc length, The Maximal Interincisal Opening (MIO) and Numeric Rating Scale (NRS) were measured before and after operation. ResultsIn group A, the MRI effective rate 6 months after disc reduction was 95.65 % (22/23), the disc length gain was 1.74 mm, MIO was 40.32±5.067 mm, and NRS was 0.47±0.697. The MRI effective rate 6 months after disc reduction in group B was 100 % (28/28). The disc length gain was 1.78 mm, MIO was 41.58±3.746 mm, and NRS was 0.00. There was no significant difference between the two groups (P > 0.05). ConclusionsTMJ disc reduction and suture and open TMJ disc anchorage can effectively reduce the TMJ disc. The TMJ disc stability is high at 6 months after operation, and the pain and mouth opening can be improved, which is worthy of further promotion in clinical practice.

The Generalized Fox–Wright Function: The Laplace Transform, the Erdélyi–Kober Fractional Integral and Its Role in Fractional Calculus

In this paper, we consider and study in detail the generalized Fox–Wright function Ψ˜qp introduced in our recent work as an extension of the Fox–Wright function Ψqp. This special function can be seen as an important case of the so-called I-functions of Rathie and H¯-functions of Inayat-Hussain, that in turn extend the Fox H-functions and appear to include some Feynman integrals in statistical physics, in polylogarithms, in Riemann Zeta-type functions and in other important mathematical functions. Depending on the parameters, Ψ˜qp is an entire function or is analytic in an open disc with a final radius. We derive its basic properties, such as its order and type, and its images under the Laplace transform and under classical fractional-order integrals. Particular cases of Ψ˜qp are specified, including the Mittag-Leffler and Le Roy-type functions and their multi-index analogues and many other special functions of Fractional Calculus. The corresponding results are illustrated. Finally, we emphasize the role of these new generalized hypergeometric functions as eigenfunctions of operators of new Fractional Calculus with specific I-functions as singular kernels. This paper can be considered as a natural supplement to our previous surveys “Going Next after ‘A Guide to Special Functions in Fractional Calculus’: A Discussion Survey”, and “A Guide to Special Functions of Fractional Calculus”, published recently in this journal.

Multiplicativity of linear functionals on function spaces on an open disc

Multiplicativity of linear functionals on function spaces on an open disc

Continuity of inner-outer factorization and cross sections from invariant subspaces to inner functions

Let H∞ be the Banach algebra of bounded analytic functions on the unit open disc D equipped with the supremum norm. As well known, inner functions play an important role in the study of bounded analytic functions. In this paper, we are interested in the study of inner functions. Following by the canonical inner-outer factorization decomposition, define Qinn and Qout the maps from H∞ to I the set of inner functions and F the set of outer functions, respectively. In this paper, we study the H2-norm continuity and H∞-norm discontinuity of Qinn and Qout on some subsets of H∞. On the other hand, the Beurling theorem connects inner functions and invariant subspaces of the multiplication operator Mz. We show the nonexistence of continuous cross section from some certain invariant subspaces to inner functions in the supremum norm. The continuity problem of Qinn and Qout on Hol(D‾), the set of all analytic functions in the closed unit disk, are considered. In addition, we also study the factor maps Q[inn] and Q[out] from H∞ to I/T and F/T, where I/T is the quotient space of I mod T and F/T is the quotient space of F mod T.

Norm and Numerical Radius Inequalities for Sums of Power Series of Operators in Hilbert Spaces

The main focus of this paper is on establishing inequalities for the norm and numerical radius of various operators applied to a power series with the complex coefficients h(λ)=∑k=0∞akλk and its modified version ha(λ)=∑k=0∞|ak|λk. The convergence of h(λ) is assumed on the open disk D(0,R), where R is the radius of convergence. Additionally, we explore some operator inequalities related to these concepts. The findings contribute to our understanding of operator behavior in bounded operator spaces and offer insights into norm and numerical radius inequalities.

Hölder-Type Inequalities for Power Series of Operators in Hilbert Spaces

Consider the power series with complex coefficients h(z)=∑k=0∞akzk and its modified version ha(z)=∑k=0∞|ak|zk. In this article, we explore the application of certain Hölder-type inequalities for deriving various inequalities for operators acting on the aforementioned power series. We establish these inequalities under the assumption of the convergence of h(z) on the open disk D(0,ρ), where ρ denotes the radius of convergence. Additionally, we investigate the norm and numerical radius inequalities associated with these concepts.

Comparison of disc position stability and condylar bone remodelling between two open disc repositioning surgeries: a retrospective single-centre cohort study.

Open suturing (OSu) and mini-screw anchor (MsA) are two commonly used open disc repositioning surgeries for anterior disc displacement (ADD) of the temporomandibular joint (TMJ). This study assesses the differences in disc position stability (DPS) and condylar bone remodelling (CBR) between these two surgical procedures in a single centre. A retrospective cohort study using MRI scans (pre-operation, 1 week and 12months post-operation) of all patients who had open TMJ disc repositioning surgery from January 2016 to June 2021 at one centre through two surgical techniques (OSu and MsA) was performed. The predictor variable was technique (OSu and MsA). Outcome variables were DPS and CBR. During follow-up, DPS was rated as good, acceptable and poor, and CBR was graded as improved, unchanged, and degenerated. Multivariate analysis was used to compare the DPS and CBR at 12 months after adjusting five factors including age, sex, Wilkes stage, preoperative bone status (normal, mild/moderate abnormal) and the degree of disc repositioning (normal, overcorrected, and posteriorly repositioned). Relative risk (RR) for DPS and CBR was calculated by multivariate logistic regression. Three hundred eighty-five patients with 583 joints were included in the study. MRIs at 12 months showed that 514 joints (93.5%) had good DPS, and 344 joints (62.5%) had improved CBR. Multivariate analysis revealed that OSu had higher DPS (RR=2.95; 95% CI, 1.27-6.85) and better CBR (RR=1.58; 95% CI, 1.02-2.46) than MsA. Among the factors affecting DPS, females had better results than males (RR=2.63; 95% CI, 1.11-6.26) and overcorrected or posteriorly repositioned discs were more stable than normally repositioned discs (RR=5.84; 95% CI, 2.58-13.20). The improvement in CBR decreased with age increasing (RR=0.91; 95% CI, 0.89-0.93). Preoperative mild/moderate abnormal bone status had a higher probability of improved CBR compared to normal preoperative bone status (RR=2.60; 95% CI, 1.76-3.83). OSu had better DPS and CBR than MsA. Sex and the degree of disc repositioning impacted DPS, while age and preoperative bone status affected CBR.

P-Summing Bloch mappings on the complex unit disc

The notion of p-summing Bloch mapping from the complex unit open disc D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {D}$$\\end{document} into a complex Banach space X is introduced for any 1≤p≤∞.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\le p\\le \\infty .$$\\end{document} It is shown that the linear space of such mappings, equipped with a natural seminorm πpB,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi ^{\\mathcal {B}}_p,$$\\end{document} is Möbius-invariant. Moreover, its subspace consisting of all those mappings which preserve the zero is an injective Banach ideal of normalized Bloch mappings. Bloch versions of the Pietsch’s domination/factorization Theorem and the Maurey’s extrapolation Theorem are presented. We also introduce the spaces of X-valued Bloch molecules on D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {D}$$\\end{document} and identify the spaces of normalized p-summing Bloch mappings from D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {D}$$\\end{document} into X∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X^*$$\\end{document} under the norm πpB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi ^{\\mathcal {B}}_p$$\\end{document} with the duals of such spaces of molecules under the Bloch version of the p∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p^*$$\\end{document}-Chevet–Saphar tensor norms dp∗.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d_{p^*}.$$\\end{document}

The Raducanu-Orhan operator associated with subclass of meromorphic bi-univalent functions

In this study, we create a subclass of meromorphic bi-univalent functions related to the Raducanu-Orha operator. Σδμ* (k, β). Additionally, estimates of the general coefficients and estimates of the beginning coefficients |c0|, |c1| and |c2| and obtain important properties of subclasses to the Raducanu-Orha operator defined on the open unite disk U.

POLYNOMIALS LEAST DEVIATING FROM ZERO IN \(L^p(-1;1)\), \(0 \le p \le \infty \), WITH A CONSTRAINT ON THE LOCATION OF THEIR ROOTS

We study Chebyshev's problem on polynomials that deviate least from zero with respect to \(L^p\)-means on the interval \([-1;1]\) with a constraint on the location of roots of polynomials. More precisely, we consider the problem on the set \(\mathcal{P}_n(D_R)\) of polynomials of degree \(n\) that have unit leading coefficient and do not vanish in an open disk of radius \(R \ge 1\). An exact solution is obtained for the geometric mean (for \(p=0\)) for all \(R \ge 1\); and for \(0&lt;p&lt;\infty\) for all \(R \ge 1\) in the case of polynomials of even degree. For \(0&lt;p&lt;\infty\) and \(R\ge 1\), we obtain two-sided estimates of the value of the least deviation.

P-VALENTLY BAZILEVIˇ C FUNCTIONS DEFINED WITH HIGHER ORDER DERIVATIVES

The object of this paper is to derive various properties and characters for a class of p-valently Bazileviˇ c functions defined with higher order derivatives. Using the technique of Briot-Bouquet differential subordination we obtained several results, some of them presented here generalize and improve a few earlier results, and several others are new ones involving differential inequalities. These last implications deal with the symmetric open disc and symmetric conic domains with respect to the real axe. Our results extends and improves many other previous ones, and some of them are the best possible under the given assumptions.