Class Of Functions Research Articles

A global method for relaxation for multi-levelled structured deformations

We prove an integral representation result for a class of variational functionals appearing in the framework of hierarchical systems of structured deformations via a global method for relaxation. Some applications to specific relaxation problems are also provided.

Non occurrence of the Lavrentiev gap for a class of nonautonomous functionals

Non occurrence of the Lavrentiev gap for a class of nonautonomous functionals

Some properties of a class of holomorphic functions associated with tangent function

Abstract In this study, we define new class of holomorphic functions associated with tangent function. Furthermore, we examine the differential subordination implementation results related to Janowski and tangent functions. Also, we investigate some extreme point theorem and partial sums results, necessary and sufficient conditions, convex combination, closure theorem, growth and distortion bounds, and radii of close-to-starlikeness and starlikeness for this newly defined functions class of holomorphic functions.

Distortion, Radius of Concavity and Several Other Radii Results for Certain Classes of Functions

Distortion, Radius of Concavity and Several Other Radii Results for Certain Classes of Functions

Long-term prognostic value of the H2FPEF score in patients undergoing transcatheter aortic valve implantation.

A considerable proportion of candidates for transcatheter aortic valve implantation (TAVI) have underlying heart failure (HF) with preserved ejection fraction (HFpEF), which can be challenging for diagnosis because significant valvular heart disease should be excluded before diagnosing HFpEF. This study investigated the long-term prognostic value of the pre-procedural H2FPEF score in patients with preserved ejection fraction (EF) undergoing TAVI. Patients who underwent TAVI between October 2013 and May 2017 were enrolled from the Optimized CathEter vAlvular iNtervention-Transcatheter Aortic Valve Implantation Japanese multicentre registry. After excluding 914 patients, 1674 patients with preserved EF≥50% (median age: 85years, 72% female) were selected for calculation of the H2FPEF score and were dichotomized into two groups: the low H2FPEF score [0-5 points; n=1399 (83.6%)] group and the high H2FPEF score [6-9 points; n=275 (16.4%)] group. Patients with high H2FPEF scores were associated with a higher prevalence of New York Heart Association Functional Class III/IV (59.3% vs. 43.7%, P<0.001), diabetes (24.4% vs. 18.5%, P=0.03), and paradoxical low-flow, low-gradient aortic stenosis (15.9% vs. 6.2%, P<0.001). These patients showed worse prognoses than those with low H2FPEF scores regarding the cumulative 2year all-cause mortality (26.3% vs. 15.5%, log-rank P<0.001), cardiovascular mortality (10.5% vs. 5.4%, log-rank P<0.001), HF hospitalization (16.2% vs. 6.7%, log-rank P<0.001), and the composite endpoint of cardiovascular mortality and HF hospitalization (23.8% vs. 10.8%, log-rank P<0.001). After adjustment for several confounders, the high H2FPEF scores were independently associated with increased risk for all-cause mortality [adjusted hazard ratio (HR), 1.48; 95% confidence interval (CI), 1.09-2.00; P=0.011] and for the composite endpoint of cardiovascular mortality and HF hospitalization (adjusted HR, 1.95; 95% CI, 1.38-2.74; P<0.001). Subgroup analysis confirmed the excess risk of high H2FPEF scores relative to low H2FPEF scores for the composite endpoint of cardiovascular mortality and HF hospitalization increased with a lower Society of Thoracic Surgeons (STS) score (STS score <8%: adjusted HR, 2.40; 95% CI, 1.50-3.85; P<0.001; STS score ≥8%: adjusted HR, 1.34; 95% CI, 0.79-2.28; P=0.28; Pinteraction=0.030). The H2FPEF score is useful for predicting long-term adverse outcomes after TAVI, including all-cause mortality, cardiovascular mortality, and HF hospitalization for patients with preserved EF. More aggressive interventions targeting HFpEF in addition to the TAVI procedure might be relevant in patients with high H2FPEF scores, particularly in those with a lower surgical risk.

Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces

This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical Kurdyka–Łojasiewicz inequality for a large class of parameter functions. Our assumptions are given in terms of the initial data, without any reference to an equilibrium point. The main results are convergence statements for gradient flow curves and proximal point sequences to a global minimiser, together with sharp quantitative estimates on the speed of convergence. These convergence results apply in the general setting of lower semicontinuous functionals on complete metric spaces, generalising recent results for smooth functionals on R n \mathbb {R}^n . While the non-smooth setting covers very general spaces, it is also useful for (non)-smooth functionals on R n \mathbb {R}^n .

Physiological and metabolic responses of Parabadminton athletes to field simulated effort.

Due to the increase in the number of Parabadminton (PBd) athletes and the lack of scientific knowledge of the sport, it is important to evaluate performance variables in different game stimuli. Thus, this study sought to examine the physiological and metabolic responses in a simulated effort protocol in PBd athletes. Forty-seven volunteers (WH1=7; WH2=9; SL3=8; SL4=9; SU5=6; SH6=8) performed a simulated effort protocol, consisting of 2 blocks of activities (1st change of direction + 1st simulated effort; 2nd change of direction + 2nd simulated effort). Peak and average oxygen consumption (VO<inf>2</inf>peak and VO<inf>2</inf>avg), peak, percentage, and average heart rate (HRmax, %HRmax, and HRavg), percentage of carbohydrates and lipids contributions (%CARB and %FAT), and average and total energy expenditure (EEavg and EEtotal) were evaluated. The data was compared between protocol stages, functional classes (FCs), and court size. It was adopted P<0.05. Differences were found between the stages of the protocol in VO<inf>2</inf>peak (P=0.0008), VO<inf>2</inf>avg (P=0.0004); HRmax (P<0.0001); %HRmax (P=0.0001), HRavg (P=0.0001), %CARB (P=0.0001), %FAT (P=0.0001), EEavg (P=0.0002), and EEtotal (P=0.008). Among FCs, SL4 athletes were superior to WH1 athletes for VO<inf>2</inf>peak (P=0.075), VO<inf>2</inf>avg (P=0.022), EEavg (P=0.011), and EEtotal (P=0.022). Athletes who completed protocol in the full court were greater than half court for VO<inf>2</inf>peak (P<0.001), VO<inf>2</inf>avg (P<0.001), %HRmax (P=0.032), HRavg (P=0.018), %CARB (P=0.022), %FAT (P=0.022), and EEavg (P=0.016). PBd athletes belonging to higher FCs (4, 5, and 6) and who cover greater distances on the court exhibit physiological and metabolic responses under greater influence of the type of disability.

Optimal solution of nonlinear 2D variable-order fractional optimal control problems using generalized Bessel polynomials

This study aims to propose a new optimization method based on the generalized Bessel polynomials (GBPs) as a class of basis functions for a category of nonlinear two-dimensional variable-order fractional optimal control problems (N-2D-VOFOCPs) involved in fractional-order dynamical systems and Caputo derivatives. For the optimal solution of such problems, the optimization method is developed on the basis of operational matrices (OMs) scheme of derivatives, 2D Gauss–Legendre quadrature rule, and Lagrange multiplier technique. The state and control functions are expanded in terms of the GBPs to reduce the complexity of these problems. The proposed method focuses on a system of nonlinear algebraic equations in the process of finding solution to the problems. The convergence of the method based on GBPs is proved, and the accuracy of the method is analyzed by solving several examples.

Ozaki-Type Bi-Close-to-Convex and Bi-Concave Functions Involving a Modified Caputo’s Fractional Operator Linked with a Three-Leaf Function

The focus of the present work is on the establishment and investigation of the coefficient estimates of two new subclasses of bi-close-to-convex functions and bi-concave functions; these are of an Ozaki type and involve a modified Caputo’s fractional operator that is associated with three-leaf functions in the open unit disc. The classes are defined using the notion of subordination based on the previously established fractional integral operators and classes of starlike functions associated with a three-leaf function. For functions in these classes, the Fekete-Szegö inequalities and the initial coefficients, |a2| and |a3|, are discussed. Several new implications of the findings are also highlighted as corollaries.

On a Class of Multivalent Functions with Negative Coefficients Involving (r, q)− Calculus

In this research, we focused on presenting a novel subclass of multivalent analytic functions situated in the open unit disk, characterized by the use of Jackson’s derivative operator. Our investigation systematically establishes the requisite inclusion conditions in this class, offering detailed coefficient characterizations. The exploration encompasses an array of significant properties intrinsic to this subclass, encompassing coefficient estimates, growth and distortion theorems, identification of extreme points, and the determination of the radius of starlikeness and convexity for functions falling within this specialized category. Expanding the preliminary findings, this research extended the inquiry to delve deeper into the intriguing features and implications associated with this new subclass of multivalent analytic functions. The research concentrated the light on the nuanced intricacies of coefficient estimates, providing a comprehensive understanding of how these functions evolve within the open unit disk through exploring the growth and distortion theorems, unraveling the underlying mathematical principles governing the behavior of functions in this subclass as they extend beyond the unit disk. The findings of this research contribute to the broader understanding of multivalent analytic functions, paving the way for further exploration and applications in diverse mathematical contexts.

Relevant sampling in a reproducing kernel subspace of Orlicz space

In this paper, we aim to provide a general paradigm for dealing with the sampling and random sampling problem in a reproducing kernel subspace of Orlicz space [Formula: see text]. We consider the function space [Formula: see text] as the image of an idempotent integral operator on [Formula: see text], where the integral kernel satisfies certain off-diagonal decay and regularity conditions. The model example of such reproducing kernel subspace of [Formula: see text] includes the finitely generated shift-invariant space and signal space with a finite rate of innovation. We show that a signal in [Formula: see text] can be stably reconstructed from its samples at distinct points separated by a sufficiently small gap. Next, we deduce that the random sampling inequality holds with a high probability for the class of functions in [Formula: see text] concentrated on a cube [Formula: see text], when the samples collected at i.i.d. random points are drawn on [Formula: see text] of order [Formula: see text].

In-hospital results of therapy with the NGLT-2 inhibitor dapagliflozin in patients with acute decompensation of heart failure: prospective randomized study

BACKGROUND: This study focuses on the development of new approaches to the management of patients with acute decompensation of heart failure (ADHF) using sodium-glucose cotransporter type 2 (iHLT-2) inhibitors, particularly dapagliflozin, and its role in early treatment initiation.&#x0D; AIM: Our aim was to determine the predictors of severe ADHF outcomes in patients with low left ventricular ejection fraction (LVEF) and the role of early initiation of iGLT-2 therapy (within the first 24 h).&#x0D; MATERIALS AND METHODS: This prospective randomized study included a total of 140 patients hospitalized with ADHF between January 1 to September 1, 2023. The patients were randomized into two groups: in group 1, iGLT-2 therapy was started within 24 h from the moment of admission (n=70), and in group 2, standard therapy was implemented (n=70). Hospital data were analyzed. The endpoint was the persistence of congestion in one or both circulatory circuits with New York Heart Association Functional Classes III–IV, indicating severe ADHF.&#x0D; RESULTS: The initial demographic and clinical characteristics of both groups were comparable. In both groups 47% patients did not receive optimal drug therapy (excluding iGLT-2) for chronic heart failure, and no differences were found in this indicator (p=0.081). iGLT-2 therapy did not demonstrate a significant effect on the likelihood of an adverse ADHF outcome (odds ratio [OR]=0.88; 95% confidence interval [CI] 0.43–1.78, p=0.719). Multivariate analysis showed an increase in the probability of this outcome for every 1000 pg/mL increase in N-terminal propeptide of brain natriuretic hormone (NT-proBNP) (OR=1.72, 95% CI 1.37–2.17; p 0.001), blood urea per 1 mmol/L (OR=1.54, 95% CI 1.21–1.97; p=0.001), pulmonary hypertension (OR=7.08, 95% CI 2.15–23.34; p=0.001), and a decrease in the probability of outcome with a 1% increase in LVEF (OR=0.91, 95% CI 0.84–0.99; p=0.031). The sensitivity and specificity of the adverse outcome model were 91.3 and 85.1%, respectively.&#x0D; CONCLUSION: The leading predictors of an unfavorable ADHF outcome include increased levels of NT-proBNP and blood urea, pulmonary hypertension, and decreased LVEF.

A comprehensive study on Milne-type inequalities with tempered fractional integrals

AbstractIn the framework of tempered fractional integrals, we obtain a fundamental identity for differentiable convex functions. By employing this identity, we derive several modifications of fractional Milne inequalities, providing novel extensions to the domain of tempered fractional integrals. The research comprehensively examines significant functional classes, including convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation.

Integration of a sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions

In this paper, the inverse spectral problem method is used to integrate a nonlinear sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of three times continuously differentiable periodic infinite-gap functions is proved. It is shown that the sum of a uniformly convergent functional series constructed by solving the system of Dubrovin equations and the first trace formula satisfies sine-Gordon-type equations with an additional term.

Relationship between New York functional class and duke activity status index with the severity of mitral valve stenosis and echocardiographic parameters: is left atrial strain a better predictor?

Purpose This study aimed to investigate the relationship between symptoms of patients with severe mitral stenosis (MS), evaluated by the New York Heart Association (NYHA) functional class and Duke Activity Status Index (DASI) score, and echocardiographic parameters. We evaluated patients with severe rheumatic MS diagnosed as mitral valve area (MVA) less than 1.5 cm2. All patients underwent transthoracic echocardiography and the left atrium (LA) reservoir auto-strain (LASr) analysis. In addition, DASI and NYHA scores were determined to evaluate the functional capacity and symptoms of MS patients. We evaluated 60 patients with MS with a mean age of 50.13 ± 10.28 and a median DASI score of 26.95 (26.38). There were 6 (10%) and 28 (46.7%) patients with NYHA class I and II, and 25 (40.0%) and 2 (3.3%) patients with NYHA class III and IV, respectively. NYHA class was positively correlated with LA area (LAA, r = 0.638), LA volume (LAV, r = 0.652), LAV index (LAVI, r = 0.62), E (r = 0.45), A (r = 0.25), and pulmonary artery pressure (PAP, r = 0.34), while negatively correlated with LASr (r=-0.73) and MVA (r=-0.417). Furthermore, the DASI score was positively associated with LASr (r = 0.81) and MVA (r = 0.52) while negatively correlated with LAA (r=-0.62), LAV (r=-0.65), LAVI (r=-0.56), E (r=-0.46), A (r=-0.3), and PAP (r= -0.32). Our findings indicate that LAA, LAV, LAVI, E, A, PAP, MVA, and LASr are associated with NYHA and DASI scores in MS patients. Additionally, the LASr had the strongest correlation between all measured parameters in severe MS patients.

On some classes of multiplicative functions

AbstractAn arithmetical function f is multiplicative if $$f(1)=1$$ f ( 1 ) = 1 and $$f(mn)=f(m)f(n)$$ f ( m n ) = f ( m ) f ( n ) whenever m and n are coprime. We study connections between certain subclasses of multiplicative functions, such as strongly multiplicative functions, over-multiplicative functions and totients. It appears, among others, that the over-multiplicative functions are exactly same as the totients and the strongly multiplicative functions are exactly same as the so-called level totients. All these functions satisfy nice arithmetical identities which are recursive in character.

Paley Wiener Theorem on a Reductive Lie Group

Let G be a locally compact group, K a maximal compact subgroup of G and δ on arbitrary class of irreducible unitary representations of K. The spherical Grassmannian Gp,δ is an equivalence class of spherical functions of type δ−positive of height p. In this work, we give an extension of orbital integral with respect to δ, when G is reductive Lie group. Moreover, if the discret serie is not empty, we give an extension of Paley-Wiener theorem using a compact Cartan subgroup of G.

On Constrained Mixed-Integer DR-Submodular Minimization

Diminishing returns (DR)–submodular functions encompass a broad class of functions that are generally nonconvex and nonconcave. We study the problem of minimizing any DR-submodular function with continuous and general integer variables under box constraints and, possibly, additional monotonicity constraints. We propose valid linear inequalities for the epigraph of any DR-submodular function under the constraints. We further provide the complete convex hull of such an epigraph, which, surprisingly, turns out to be polyhedral. We propose a polynomial-time exact separation algorithm for our proposed valid inequalities with which we first establish the polynomial-time solvability of this class of mixed-integer nonlinear optimization problems. Funding: This work was supported by the Office of Naval Research Global [Grant N00014-22-1-2602].

Stability properties of ultraholomorphic classes of Roumieu-type defined by weight matrices

We characterize several stability properties, such as inverse or composition closedness, for ultraholomorphic function classes of Roumieu type defined in terms of a weight matrix. In this way we transfer and extend known results from J. Siddiqi and M. Ider, from the weight sequence setting and in sectors not wider than a half-plane, to the weight matrix framework and for sectors in the Riemann surface of the logarithm with arbitrary opening. The key argument rests on the construction, under suitable hypotheses, of characteristic functions in these classes for unrestricted sectors. As a by-product, we obtain new stability results when the growth control in these classes is expressed in terms of a weight sequence, or of a weight function in the sense of Braun–Meise–Taylor.

Unconditional convergence of eigenfunction expansions for abstract and elliptic operators

We study the most general class of eigenfunction expansions for abstract normal operators with pure point spectrum in a complex Hilbert space. We find sufficient conditions for such expansions to be unconditionally convergent in spaces with two norms and also estimate the degree of this convergence. Our result essentially generalizes and complements the known theorems of Krein and of Krasnosel'skiĭ and Pustyl'nik. We apply it to normal elliptic pseudodifferential operators on compact boundaryless $C^{\infty }$ -manifolds. We find generic conditions for eigenfunction expansions induced by such operators to converge unconditionally in the Sobolev spaces $W^{\ell }_{p}$ with $p&gt;2$ or in the spaces $C^{\ell }$ (specifically, for the $p$ -th mean or uniform convergence on the manifold). These conditions are sufficient and necessary for the indicated convergence on Sobolev or Hörmander function classes and are given in terms of parameters characterizing these classes. We also find estimates for the degree of the convergence on such function classes. These results are new even for differential operators on the circle and for multiple Fourier series.