Admissible Functions Research Articles

On some distributivity equation related to minitive and maxitive homogeneity of the upper n-Sugeno integral

In this paper we provide a full characterization of functions G:[0,y¯]2→[0,y¯] satisfying the distributivity equation G(a∘b,a∘c)=a∘G(b,c) for any a,b,c with a fixed binary operation ∘:[0,y¯]2→[0,y¯] generalizing minimum and maximum, where y¯∈(0,∞]. The above functional equation with an admissible function G and ∘ being minimum [resp. maximum] has appeared when studying properties of minitive [resp. maxitive] homogeneity for the recently introduced upper n-Sugeno integral.

Elastic and inelastic stability of a steel arch subjected to a crown point load under an elevated fire environment

This paper focuses on the stability of thin-walled circular arches subjected to a radially-directed concentrated load at the crown point under a temperature increase up to 800℃ induced by fire. A solution is obtained analytically to predict the critical buckling load of the elastic arch based on the principle of minimum potential energy and an admissible displacement function. Subsequently, a planar numerical model is introduced to explore the maximum load (critical buckling load) by drawing the normalized load-displacement equilibrium curves. These curves from the numerical results exhibit close trends with the analytical ones for both fixed-fixed and pinned-pinned arches. In addition, steel arches with inelastic material properties and geometric nonlinearities are considered in the numerical model, indicating that inelastic properties reduce prominently the maximum load. Furthermore, all investigations show the heating process induced by the fire reduces the load capacity (maximum load) dramatically for both elastic and inelastic arches. Finally, parametric analyses are performed to examine the effect of central angle and normalized thickness on the maximum load of the arch.

Correction to: Remarks on input-to-state stability of collocated systems with saturated feedback

The following corrections should be made to this article. In Theorem 9 and Theorem 11, one needs to add the assumption that the admissible feedback function σ is globally Lipschitz continuous. If we denote the globally Lipschitz constant by k, then in the proofs of Theorems 9 and 11 the definition of r should be omitted and the constant kr replaced by k. Otherwise, the K∞-function candidate for the functions ρ in (7) would depend on the solution x and the disturbance d in both theorems.

Applications of Inequalities in the Complex Plane Associated with Confluent Hypergeometric Function

The idea of inequality has been extended from the real plane to the complex plane through the notion of subordination introduced by Professors Miller and Mocanu in two papers published in 1978 and 1981. With this notion came a whole new theory called the theory of differential subordination or admissible functions theory. Later, in 2003, a particular form of inequality in the complex plane was also defined by them as dual notion for subordination, the notion of differential superordination and with it, the theory of differential superordination appeared. In this paper, the theory of differential superordination is applied to confluent hypergeometric function. Hypergeometric functions are intensely studied nowadays, the interest on the applications of those functions in complex analysis being renewed by their use in the proof of Bieberbach’s conjecture given by de Branges in 1985. Using the theory of differential superodination, best subordinants of certain differential superordinations involving confluent (Kummer) hypergeometric function are stated in the theorems and relation with previously obtained results are highlighted in corollaries using particular functions and in a sandwich-type theorem. An example is also enclosed in order to show how the theoretical findings can be applied.

Existence and Uniqueness of Fixed Points of Generalized F-Contraction Mappings

The newest generalization of the Banach contraction through the notions of the generalized F-contraction, simulation function, and admissible function is introduced. The existence and uniqueness of fixed points for a self-mapping on complete metric spaces by the new constructed contraction are investigated. The results of this article can be viewed as an improvement of the main results given in the references.

Severity of shock, rate of physiological stabilization and organ failure in healthy women admitted to the intensive care unit following major peripartum hemorrhage: A retrospective, descriptive study.

To describe shock severity, physiological stabilization and organ failure in healthy women admitted to the intensive care unit (ICU) after major peripartum hemorrhage (PPH). Retrospective, descriptive, single center study. Twenty-nine women median age 33years (interquartile range [IQR] 30-36) and gravidity 5 pregnancies (IQR 3-9) were studied. One woman died. The median maternal admission hematocrit was 28.8 (IQR 25.7-32.4). Median transfusion rates were nine units of packed red blood cells (IQR 7-12.25), eight fresh frozen plasma (IQR 6-12), 17 platelets (IQR 10-22) and 15 cryoprecipitate (IQR 9.75-20). Blood pressure dropped significantly in the six hours following ICU admission. Nonetheless, lactate decreased from 3.23mmol/L to 1.54mmol/L within 24h of ICU admission, renal and pulmonary function were unaffected and coagulopathy was never observed. Two-thirds of the women underwent hysterectomy. One-third underwent repeated surgery. The median length of ICU stay was <48h and that of mechanical ventilation was <24h. Increased transfusion rates correlated with lengthier ICU admission (p≤0.01 regardless of blood product). Ongoing hemorrhage in women with severe PPH manifests subtly and often requires active intervention. Hemorrhage control is required to achieve physiological stabilization and minimize organ damage.

New Conditions for Univalence of Confluent Hypergeometric Function

Since in many particular cases checking directly the conditions from the definitions of starlikeness or convexity of a function can be difficult, in this paper we use the theory of differential subordination and in particular the method of admissible functions in order to determine conditions of starlikeness and convexity for the confluent (Kummer) hypergeometric function of the first kind. Having in mind the results obtained by Miller and Mocanu in 1990 who used a,c∈R, for the confluent (Kummer) hypergeometric function, in this investigation a and c complex numbers are used and two criteria for univalence of the investigated function are stated. An example is also included in order to show the relevance of the original results of the paper.

Two meromorphic functions on annuli sharing some pairs of small functions or values

&lt;abstract&gt;&lt;p&gt;In this paper, we prove that two admissible meromorphic functions on an annulus must be linked by a quasi-Möbius transformation if they share some pairs of small function with multiplicities truncated by $ 4 $. We also give the representation of Möbius transformation between two admissible meromorphic functions on an annulus if they share four pairs of values with multiplicities truncated by $ 4 $. In our results, the zeros with multiplicities more than a certain number are not needed to be counted if their multiplicities are bigger than a certain number.&lt;/p&gt;&lt;/abstract&gt;

Free vibration analysis of circular cylindrical shell on elastic foundation using the Rayleigh-Ritz method

A general approach is presented for the free vibration analysis of circular cylindrical shell resting on elastic foundation and subjected to classical boundary conditions of any type. The Winkler/Pasternak model is utilized to simulate the elastic foundation imposed on the cylindrical shell, and then it is easily to derive the potential energy of the elastic foundation. Based on the Flugge shell theory, explicit expressions for the mass and stiffness matrices are obtained. By taking the characteristic beam modal functions as the admissible functions, the Rayleigh-Ritz method is employed to derive the frequency equations of circular cylindrical shell with all the classical boundary conditions and resting on elastic foundation. Once the frequency equation has been determined, the frequencies can be calculated numerically. The excellent accuracy and validity of the present approach are demonstrated by numerical examples and comparisons with the results available in the literature. Finally, some further numerical results are given to illustrate the comprehensive effect of geometric properties and foundation coefficients on the frequencies of circular cylindrical shell in contact with elastic foundation.

Profile of egyptian patients with borderline personality disorder with and without comorbidity

Background Borderline personality disorder (BPD) is a complex psychiatric disorder associated with a wide range of psychopathology, including unstable mood, impulsive behavior, and suicidality, which is a defining feature of borderline, as well as high rates of axis I comorbidity.Aim To identify the profile of psychiatric comorbidity among patients with BPD and to compare them with a group of patients with BPD without comorbidity regarding some demographic variables, suicidal behavior, impulsivity, and functioning.Methods Structural Clinical Interviewing was done for DSM-IV axis I and axis II diagnoses. We recruited 30 patients with BPD, without axis I comorbidity (group I) and other 31 patients with BPD with comorbidity (group II). We compared both groups regarding different demographic variables, family circumstances impulsivity, suicidality, and functioning using suicide behavior questionnaire − revised, Barratt impulsiveness scale II, and global assessment of function.Results Patients with BPD in group II had one additional diagnosis, mainly major depression (35.5%), substance-related disorder (35.5%), anxiety disorder (16.1%), whereas bipolar disorder and eating disorders were equally rated (6.5% each). Group II patients scored significantly higher in the total suicidality scores using suicide behavior questionnaire − revised than group I, yet the two groups did not differ significantly in impulsivity scores. Meanwhile, the former group was significantly younger (P=0.05), and they started their illness and seeked treatment at a younger age with more history of previous hospitalization than did group I. In addition, their global assessment of function is significantly impaired (P=0.002).Conclusion Comorbidities in patients with BPD are high, mainly major depression and substance-related disorders, which are associated with increased suicidality behavior, hospital admission, and impaired functioning. Data obtained conveys the need to give high priority to recognize the comorbidities that pose risk on the lives of patients with BPD.

Regularity results for a class of obstacle problems with p, q−growth conditions

In this paper we prove the the local Lipschitz continuity for solutions to a class of obstacle problems of the type min{ ∫ΩF(x, Dz) : z ∈ 𝛫ψ(Ω)}. Here 𝛫ψ(Ω) is the set of admissible functions z ∈ u0 + W1,p(Ω) for a given u0 ∈ W1,p(Ω) such that z ≥ ψ a.e. in Ω, ψ being the obstacle and Ω being an open bounded set of ℝn, n ≥ 2. The main novelty here is that we are assuming that the integrand F(x, Dz) satisfies (p, q)-growth conditions and as a function of the x-variable belongs to a suitable Sobolev class. We remark that the Lipschitz continuity result is obtained under a sharp closeness condition between the growth and the ellipticity exponents. Moreover, we impose less restrictive assumptions on the obstacle with respect to the previous regularity results. Furthermore, assuming the obstacle ψ is locally bounded, we prove the local boundedness of the solutions to a quite large class of variational inequalities whose principal part satisfies non standard growth conditions.

Free vibration analysis of a laminated composite sandwich plate with compressible core placed at the bottom of a tank filled with fluid

The paper addresses the free vibration problem of a laminated composite sandwich plate with compressible core, placed at the bottom of a tank filled in with fluid. The analysis is performed based on the extended higher order sandwich plate theory (EHSAPT). First-order shear deformation theory (FSDT) is used for the face sheets. Cubic and quadratic polynomials are used to describe the in-plane and transverse displacements of the core, respectively. The fluid is assumed inviscid, incompressible, and irrotational. To obtain the kinetic energy of the fluid, its velocity potential is expressed by using the compatibility and boundary conditions. The governing differential equations and corresponding boundary conditions are derived from Hamilton’s principle. A single series expansion is considered with two-variable orthogonal polynomials as a set of admissible functions satisfying the boundary conditions. The natural frequencies of the coupled sandwich plate-fluid system are calculated by using the Rayleigh-Ritz method. Convergence of the adopted strategy is first investigated. Then, comparisons are conducted with previous results reported in the literature. Also, the effects are investigated of several parameters, such as the plate side-to-thickness ratio, the core-to-face sheets thickness ratio, the face sheet-to-core flexural modulus ratio, the height and aspect ratio of the tank.

Asymptotics and Uniqueness of Solutions of the Elasticity System with the Mixed Dirichlet–Robin Boundary Conditions

We study properties of generalized solutions of the Dirichlet–Robin problem for an elasticity system in the exterior of a compact, as well as the asymptotic behavior of solutions of this mixed problem at infinity, with the condition that the energy integral with the weight |x|a is finite. Depending on the value of the parameter a, we have proved uniqueness (or non-uniqueness) theorems for the mixed Dirichlet–Robin problem, and also given exact formulas for the dimension of the space of solutions. The main method for studying the problem under consideration is the variational principle, which assumes the minimization of the corresponding functional in the class of admissible functions.

Engaging Families in Function-Focused Care: Goal Attainment and Associated Outcomes

Partnering with families to develop function-focused plans for hospitalized persons with dementia (PWD) improves both the hospital experience and patient outcomes. This secondary analysis included patients enrolled in the intervention arm of the on-going Family-centered Function-focused Care (Fam-FFC).study. This study examined the goals co-established by family caregivers, PWD, and nurses to prevent hospital-acquired complications and promote functional and cognitive recovery. The influence of goal attainment upon delirium and physical function at discharge was also examined. The majority of patients (N=162) were female (65%), black (53%) with a mean age of 82.7 (SD= 8.2). Goal attainment ranged from -2 to 2; mean = -0.24 (SD= 0.75). The goals (N=432) represent three main areas: mobility, self-care, and cognitive stimulation. Controlling for age and admission function, goal attainment was associated with less discharge delirium (F=3.2, p = .022) but not discharge function. Results support the contribution of function-focused care to improving delirium outcomes.

Free vibration behavior of bi-directional functionally graded plates with porosities using a refined first order shear deformation theory

This paper proposes the refined first order shear deformation theory to investigate the free vibration behavior of bidirectional functionally graded porous plates. This theory satisfies the transverse shear stress free conditions at the top and bottom of the plate, thus avoids the need of a shear correction factor. The rule of mixtures is employed to compute the effective material properties and assumed to be graded in both x and z-directions. The equations of motion are derived by means of Lagrange equations to investigate the free vibration response. The displacement functions in axial and transverse directions are expressed in simple algebraic polynomial series form, including admissible functions which are used to fulfill the simply supported boundary conditions. The admissible functions are generated using Pascal’s triangle. The accuracy of the present theory is assessed with the numerical results and is confirmed by comparing with 3-D exact solutions and with other higher order theories. The influence of thickness ratios, aspect ratios, gradation indexes, type of porosity distribution and the volume fraction of porosity on the free vibration behavior of bi-directional FGPs are discussed in detail. The presented numerical results can be used as benchmark solutions to assess the various plate theories and compare with solutions obtained by other analytical and finite element methods. From the present work, it can be concluded that the present theory allows examining the vibration behavior of bidirectional porous FG plates manufactured in the sintering process.

Free Vibration Characteristics of Moderately Thick Spherical Shell with General Boundary Conditions Based on Ritz Method

In this paper, the Ritz method is adopted to investigate the vibration characteristics of isotropic moderately thick annular spherical shell with general boundary conditions. The energy expressions of the annular spherical shell were established based on the first-order shear deformation theory (FSDT). The spring stiffness method is introduced to guarantee continuity and simulate various boundary conditions on the basis of the domain decomposition method. Under the current framework, the displacement admissible function along axial direction and circumferential direction of the shell structure are, respectively, expanded as the unified Jacobi polynomials and Fourier series. The final solutions can be obtained according to the Ritz method. The validity of the proposed method is proved by comparing the results of the same condition with those obtained by the finite element method (FEM) and published literatures. The results show that the current method has fast convergence and delightful accuracy through the comparative study. On this basis, the vibration characteristics of isotropic moderately thick annular spherical shell are further studied by a series of numerical examples.

A Naghdi Type Nonlinear Model for Shells with Little Regularity

In this paper a new nonlinear two-dimensional shell model of Naghdi’s type is formulated for shells which middle surface is parameterized by a $W^{1, \infty}$ function. Therefore the model inherently contains undeformed geometries with corners, so the model also includes models of junctions of nonlinear shells. Deformation of the shell is described by a pair $(\boldsymbol{\psi}, {\mathbf{R}})$ of independent unknowns, where $\boldsymbol{\psi}$ is the deformation of the middle surface and ${\mathbf{R}}$ is a function with value in rotations that describes rotation of the shell cross-section. The model is formulated as the minimization problem for the total energy functional that includes flexural, membrane, shear and drill energies differently scaled with respect to the thickness of the shell. We relate the new model for smooth enough undeformed geometry to the known shell models in two ways. First we restrict the proposed model on two particular subsets of admissible functions and obtain exactly the flexural shell model and a perturbation of the Koiter shell model. More important, we consider asymptotics, using $\Gamma$ –convergence, of the proposed model with respect to the thickness as a small parameter in the membrane and flexural regime and obtain exactly the nonlinear membrane and flexural shell model obtained as $\Gamma$ –limits starting from nonlinear three–dimensional elasticity. In that way we link rigorously the proposed model with the nonlinear three–dimensional elasticity.

Transverse Vibration Analysis of Composite Plates with Multiple Distributed Composite Patches

Transverse vibration of rectangular composite plates with multiple distributed composite patches is analyzed in this paper. Because of the geometric discrepancy between the plate and patch, analytical solutions are usually hard to achieve. The present model is formulated by using the Rayleigh–Ritz method and adopting various types of modal shape functions of uniform beam as admissible functions for different boundary conditions. The total system energies are calculated by adding the energies of the substrate plate and the energies of the patches. By imposing the displacement-matching condition at the patch domains, the coordinate systems of the substrate plate and patches are coupled. By means of the present method, it is very convenient and efficient to build the system governing equations and solve the eigenvalue problem. For the composite patches, they are also assumed to be symmetrically layered and have the same layer stacking sequence with the substrate laminate. The effects of layer stacking sequence, modulus ratio, aspect ratio, and boundary conditions on the natural frequencies are investigated and discussed. The results are also compared with the existed benchmark solutions and FEM solutions for validation. The numerical results demonstrate that the proposed approach is computationally very efficient and accurate and can be used as a tool to solve transverse vibration problems of composite plate with multiple composite patches.

Free vibration analysis of metal-ceramic matrix composite laminated cylindrical shell reinforced by CNTs

A unified method is presented to analyze free vibrations of dual-functional graded nanocomposite laminated cylindrical shells reinforced by carbon nanotubes (CNTs) under arbitrary boundary conditions. Especially, the matrix material of the carbon nanotubes is metal-ceramic functional gradient material (FGM), and the CNT is also assumed to be a gradient distribution in the matrix, constituting the dual-functional graded materials. Based on the first-order shear deformation theory (FSDT) and artificial spring technology, the Chebyshev polynomials was selected as the admissible function, and the Rayleigh-Ritz method was used to derive the vibration differential equation of the laminated shell. Further, the effects of volume fraction of CNTs, change of matrix material, the thickness of the middle layer, and geometric parameters on the natural frequency were discussed.

Residential cardiac rehabilitation (rCR) derived survival predictors in patients after transcatheter aortic valve replacement (TAVR): a retrospective multicenter study

Abstract Purpose To evaluate exercise-based rCR derived outcome predictors in patients referred after TAVR. Methods Data of 434 patients (aged 81±6 years) admitted to an average 3-week rCR program after TAVR (walking, up to 30 minutes of cycling or treadmill session twice daily, respiratory and calistenic training) from January 2009 to December 2017 and home discharged, were retrospectively collected at 10 Italian rCR Division of Istituti Clinici Maugeri SpA. Comorbidity (cumulative illness rated state-comorbidity index) (CIRS-CI) score, echocardiography on admission, Disability (Barthel Index) (BI) score, Morse Fall Scale score (MFS), six minutes walking test distance (6MWT) on admission and discharge and maximal training session intensity (MTSI expressed in METs per minutes) were collected. The mortality was assessed up to 3 years after rCR discharge. Results During a 3-years follow up there were 120 (28%) deaths. At t-test analysis non survivors compared to survivors had significantly higher CIRS CI (p=0.000), MFS score on admission (p=0.008) and discharge (p=0.017), serum creatinine level on admission (p=0.000) and discharge (p=0.000); moreover they had significantly lower BI score on admission (p=0.000) and discharge (P=0.000), left ventricle ejection fraction (p=0.008),6MWT on admission (p=0.001) and discharge (p=0.000) and MTSI (p=0.022) in comparison to survivors. At multivariate logistic stepwise analysis, BI score on admission and serum creatinine level at discharge were the only independent predictors of mortality (Table 1); the AUC of the final logistic model was 0.72. Conclusions Patients attending rCR after TAVR seem to be very old; overall mortality at 3 years follow up in patients discharged home after rCR is substantial. Disability profile on admission (measured by Barthel Index) and impaired renal function on discharge (measured by creatinine levels) are independently correlated to death at long term follow up. Funding Acknowledgement Type of funding source: None