The Structural Summary Method (SSM) provides a central framework for evaluating constructs within circumplex models, yet guidance for prospective power analysis has remained unavailable. Here, I extend the SSM from a retrospective tool to one supporting a priori inference. Across two studies, I derive and validate power functions for amplitude and angular displacement. Study 1 establishes analytical power functions for amplitude, demonstrating that meaningful interpersonal differentiation can be detected with modest sample sizes. Study 2 extends this framework to angular displacement, showing that displacement precision depends critically on amplitude, with important implications for displacement-focused hypotheses. Validation using simulation and resampling across multiple datasets confirms that the proposed formulas provide reliable guidance for study design. These results clarify the distinct inferential properties of amplitude and displacement and strengthen the SSM as a tool for prospective research planning within circumplex models. This study's code and materials are available at https://osf.io/63wyf.

Analytic wave functions of quasistable quantum systems with arbitrary angular momentum

A Hybrid-Displacement POD-based finite element formulation: Application to a linear elastic perforated plate

Microfluidics in separation science: Fabrication, applications and intelligent systems.

Corrigendum to: “Cesàro-type operators on derivative-type Hilbert spaces of analytic functions II” [J. Funct. Anal. 290 (5) (2026) 111287

Aim. To identify the linguistic and stylistic features of N. S. Leskov’s idiostyle based on his early journalistic work “Note on Buildings” and to determine the system-forming techniques in the context of journalistic discourse. Methodology. The study is based on a comprehensive linguistic and stylistic analysis of the text, including lexical-semantic analysis (identifying thematic groups of vocabulary, analyzing metaphors and epithets), and contextual analysis of irony and sarcasm. Special attention is paid to the consideration of the oppositions “high / low”, “abstract / physiological,” and “official / everyday” as the basis of the author’s style. Results. It has been revealed that the system-forming technique of Leskov’s idiostyle in “A Note on Buildings” is contrast, which is implemented at all levels of the text. A consistent collision of elevated abstract vocabulary with physiological vocabulary has been identified, which creates an estrangement effect and reveals the conflict between official magnificence and the real conditions of life. Key author’s metaphors and epithets, which conceptualize the criticism of the bureaucratic system and social indifference, have been analyzed. The article provides evidence that irony and sarcasm serve as an expressive and an analytical function in the text, allowing the author to reveal deep contradictions of contemporary reality through tragicomic grotesque. Research implications. The article deepens our understanding of the nature of N. S. Leskov’s idiostyle, demonstrating the unity of artistic and journalistic techniques in his works and identifying the role of contrast as a tool for social analysis in 19 th century journalistic discourse. The findings of the study can be used in university courses on the history of 19 th century Russian literature, text linguistics, special courses on N. S. Leskov’s works, and in the analysis of journalistic texts.

Abstract We consider application of the analytic functional approach to the conformal field theories associated with mean field theory and Wilson–Fisher fixed point. We study the constraints imposed by the crossing symmetry on the coefficients of the operator product expansion. Making use of these constraints along with a few other additional inputs, we obtain expressions of the coefficients of the operator product expansion up to first order of $$\epsilon $$ ϵ .

We consider Banach spaces ℓp(C),1≤p<∞, where the index set C is the classical Cantor set and study various groups of symmetries of ℓp(C), associated with the binary representation of C. The main purpose of the paper is the investigation of polynomials on ℓp(C) that are symmetric (i.e., invariant) with respect to the constructed groups G. We are interested in finding systems of generators of algebras of G-symmetric polynomials for different groups G and we discuss possible applications of G-symmetric polynomials to highly composite physical systems. The generators are useful for descriptions of spectra of algebras of G-symmetric analytic functions on ℓp(C), and for the construction of some nontrivial complex homomorphisms of these algebras. Finally, we establish the topological transitivity and hypercyclicity of some shift-like operators on ℓp(C) and its subspaces, and translation operators on algebras of symmetric analytic functions on ℓp(C).

Sharp upper bounds for the Hankel, generalized Zalcman and Krushkal coefficient functionals are investigated for the class of normalized analytic functions f defined in an open unit disk with the quantity zf′ / f lying in the evolute of a nephroid curve in the right-half plane. The similar analysis is also carried out when the expression zf′/f is replaced with . Moreover, the sharp radii constants concerning the class are also computed.

Abstract This paper studies the bidiagonal factorization of the collocation matrices of analytic bases using symmetric functions. Explicit formulas for their initial minors are derived in terms of Schur functions. The structure of these formulas permits establishing sufficient conditions for the total positivity of generic systems of analytic functions. In addition, they have been found to lead to generalizations of the Cauchy identity for certain families of functions.

It has been known for over a century that certain large classes of functions defined on a compact nowhere dense subset X X of the complex plane, and obtained as limits of analytic functions in various metrics, can sometimes inherit the property of unique continuation characteristic of the approximating family. The first example of the transfer of the uniqueness property in this way to R ( X ) R(X) , the space of functions that can be uniformly approximated on X X by a sequence of rational functions whose poles lie outside of X X , was obtained by M. V. Keldysh around 1940, but apparently never published. Years later in 1975 A. A. Gonchar exhibited a qualitatively definitive improvement of Keldysh’s example, and our goal here is to extend that result to R p ( X , d A ) R^p(X,dA) , p ≥ 2 p\geq 2 , the evidently larger space obtained as the closure of the rational functions in L p ( X , d A ) L^p(X,dA) , where d A dA denotes 2 2 -dimensional Lebesgue, or area, measure.

Abstract Let $\mathcal {A}$ denote the class of normalised analytic functions f in the open unit disk $\mathbb {D}:=\{z\in \mathbb {C}:|z|<1\}$ with $f(0)=0$ and $f'(0)=1$ . A function $f\in \mathcal {A}$ is said to be convex if $f(\mathbb {D})$ is convex. We establish a sharp upper bound for the third Hankel determinant corresponding to the inverse coefficients of convex univalent (that is, one-to-one) functions in the unit disk $\mathbb {D}$ .

Analytical soft functions for heavy-quark final states at hadron colliders

Background: Students’ prior mathematical knowledge plays a critical role in their success in university mathematics, yet it is often treated diagnostically rather than instructionally. Aim: This study examines students’ prior mathematical knowledge at the start of a university calculus course, with the purpose of identifying conceptual and procedural strengths and weaknesses that are relevant for subsequent learning and for a mathematical modelling intervention. Setting: The study was conducted in South Africa and involved three cohorts of first-year science and engineering students (1874 participants) across the years 2020, 2021 and 2022. Methods: A mixed-methods sequential explanatory design was employed. Quantitative data were collected using a diagnostic test. Welch’s one-way analyses of variance (ANOVAs) and Games–Howell post hoc tests were used to compare cohort performance across content areas. Qualitative analyses of written solutions from a stratified random sample of 90 students were conducted to examine errors and misconceptions. Results: Although overall test performance showed modest improvement across cohorts, students’ results remained low across most content areas. Algebra emerged as a relative strength, indicating procedural fluency, whilst weaknesses were evident in Analytical geometry, Functions and Modelling. Qualitative analyses revealed persistent conceptual and representational difficulties, in interpreting inequalities, graphing functions and constructing and using linear models. Conclusion: The findings suggest that apparent improvements in preparedness may cover structural weaknesses. The study highlights the importance of using diagnostic evidence not merely to identify at-risk students, but to inform responsive teaching that addresses conceptual gaps. Contribution: By integrating large-scale diagnostic data with qualitative error analysis, students’ prior knowledge can be leveraged as an instructional resource to support modelling-oriented teaching in university mathematics.

Given a positive Borel measure μ \mu on [ 0 , 1 ) [0,1) and a parameter β > 0 \beta >0 , we consider the Cesàro-type operator C μ , β \mathcal {C}_{\mu ,\beta } acting on the analytic function f ( z ) = ∑ n = 0 ∞ a n z n f(z)=\sum _{n=0}^{\infty } a_{n} z^{n} on the unit disc of the complex plane D \mathbb {D} , defined by C μ , β ( f ) ( z ) = ∑ n = 0 ∞ μ n ( ∑ k = 0 n Γ ( n − k + β ) ( n − k ) ! Γ ( β ) a k ) z n = ∫ 0 1 f ( t z ) ( 1 − t z ) β d μ ( t ) , \begin{equation*} \mathcal {C}_{\mu ,\beta }(f)(z)= \sum _{n=0}^{\infty } \mu _{n} \left ( \sum _{k=0}^{n} \frac {\Gamma (n-k+\beta )}{(n-k)! \Gamma (\beta )} a_{k} \right ) z^{n} = \int _{0}^{1} \frac {f(tz)}{(1-tz)^{\beta }} d\mu (t), \end{equation*} where μ n = ∫ 0 1 t n d μ ( t ) \mu _{n}=\int _{0}^{1} t^{n} d\mu (t) . This operator generalizes the classical Cesàro operator (corresponding to the case where μ \mu is the Lebesgue measure and β = 1 \beta =1 ) and includes other relevant cases previously studied in the literature. In this paper we study the boundedness of C μ , β \mathcal {C}_{\mu ,\beta } on mixed norm spaces H ( p , q , γ ) H(p,q,\gamma ) for 0 > p , q ≤ ∞ 0>p,q\leq \infty and γ > 0 \gamma >0 . Our results extend and unify several known characterizations for the boundedness of Cesàro-type operators acting on spaces of analytic functions.

ABSTRACT Based on the complex variable method and the corresponding principle of viscoelasticity, viscoelastic solutions for the stress and displacement of a lined non‐circular tunnel subjected to in‐situ stresses and internal water pressure is derived. The basic equations for solving the analytic functions are established according to the stress boundary condition along the inner boundary of the lining and the stress and displacement continuity conditions along the rock‐lining interface. The analytic functions are expressed as Laurent series and the Laplace transformation is performed on the basic equation. Herein, the power series method is applied to obtain the linear equations which are expressed by the analytic function coefficients in the Laplace domain. The stress and displacement solutions of tunnel in Laplace domain can be addressed by solving the equations, and then the viscoelastic solutions are obtained through Laplace Inverse transformation. Subsequently, an example for the horseshoe‐shaped tunnel is performed. The example used the generalized Kelvin model to simulate the rheological properties of surrounding rock mass. The obtained solution is compared with the numerical solution. The influences of the lateral pressure coefficient and the internal water pressure on the stresses and displacements of lining are analyzed.

We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace transform. We start by applying this transform to the evolution problem, thus yielding a time-independent boundary value problem solely depending on the complex Laplace variable. In an offline stage, we judiciously sample the Laplace variable and numerically solve the corresponding collection of high-fidelity or full-order problems. Next, we apply a proper orthogonal decomposition (POD) to this collection of solutions in order to obtain a reduced basis in the Laplace domain. We project the linear parabolic problem onto this basis and then, using any suitable time-stepping method, we solve the evolution problem. A key insight to justify the implementation and analysis of the proposed method consists of using Hardy spaces of analytic functions and establishing, through the Paley-Wiener theorem, an isometry between the solution of the time-dependent problem and its Laplace transform. As a result, one may conclude that computing a POD with samples taken in the Laplace domain produces an exponentially accurate reduced basis for the time-dependent problem. Numerical experiments illustrate the performance of the method in terms of accuracy and, in particular, speed-up when compared to the solution obtained by solving the full-order model.

ABSTRACT In this study, an ad hoc analytical model is developed to describe the axial profile of the time-averaged heat release rate in the diffusion flame of a Liquid Rocket Engine coaxial injector operating under transcritical conditions (resulting in a simple density stratification, without vaporization). The model is derived from the Burke-Schumann diffusion flame model with the infinitely fast combustion assumption, augmented by adding turbulent diffusivity and velocity dispersion. It is therefore built upon a series of physically motivated assumptions which are systematically validated against experimental and numerical data. The predictive capability of the model is then assessed through detailed comparisons with Large Eddy Simulation results from the literature, demonstrating its ability to capture key features of the flame structure as it gives an accurate representation of the flame profile and effectively captures the total time-averaged heat release rate. Furthermore, a preliminary extension explores the ability of the model to predict the effects of forcing amplitude and frequency on the flame response. The model exhibits some key features of the flame response to acoustic forcing. Designed to be integrated into flame transfer function models, this work represents a milestone toward fully analytical flame transfer functions.

This study investigates third-order differential subordination and its influence on classes of analytic functions associated with the Lommel function of the first kind. By employing a newly defined operator Lwjf(z), we identify and characterize the admissible function classes that satisfy the corresponding third-order differential subordinations. These admissibility conditions enable the derivation of several key results, including a sandwich-type theorem obtained as a direct consequence of the established framework. The findings contribute to a broader understanding of analytic functions governed by higher-order differential constraints and highlight the significant role played by the Lommel function in shaping these geometric properties.

The theoretical and practical foundations for intensifying investment activity of enterprises in the tourism and recreation complex (TRC) of Ukraine through the prism of strategic management are substantiated. The importance of developing effec­tive tools for improving investment in conditions of economic instability and market environment transformations is emphasized. It has been establi­shed that the investment attractiveness of TRC enterprises is a dynamic characteristic that is formed under the influence of external and internal factors of a strategic nature. The main barriers that hinder investment activity in the industry are identified as the insufficient level of project readiness of enterprises, weak integration with cluster initiatives, and a low level of strategic planning. As a result of the analysis of modern approaches to activating investment attraction, proposals have been formulated to improve the strategic mana­gement of investment activities, in particular through the introduction of public-private partner­ships, the development of municipal investment support programs, and the strengthening of the analytical function of strategic management. Effective practices from regions of Ukraine where tourist activity continues despite wartime restric­tions are considered examples. A model for the strategic support of investment activities of TRC enterprises as part of the overall strategy for sustainable development of the industry is proposed. Two hypotheses were put forward during the study: the first is that insufficient stimulation of investment in the TRC sector in Ukraine is a consequence of imperfect state regulation mecha­nisms, which limit the investment activity of TRC enterprises; the second is that the introduction of new strategic management approaches to investment processes will contribute to the growth of resource efficiency and attract investment in TRC enterprises, as it will allow them to adapt to dynamic market conditions. The methodological basis of the study consists of methods of analysis and synthesis, SWOT analysis, and expert assessment. To deter­mine the priorities for intensifying investment activity, a matrix multi-criterion ranking (Priority score) was applied with the formation of a system of key performance indicators (KPI). Comparative analysis was used to generalize regional case studies