Admissible Functions Research Articles

Results on Third-Order Differential Subordination for Analytic Functions Related to a New Integral Operator

In this paper, we aim to give some results for third-order differential subordination for analytic functions in the open unit disk U=z:z∈C and z<1 involving the new integral operator μα,nm(f∗g). The results are obtained by examining pertinent classes of acceptable functions. New findings on differential subordination have been obtained. Additionally, some specific cases are documented. This work investigates appropriate classes of admissible functions, presents a novel of new integral operator, and discusses the properties of third-order differential subordination. The properties and results of the differential subordination are symmetrical to the properties of the differential superordination to form the sandwich theorems.

Analytical and numerical predictions of elastoplastic buckling behaviors of the subsea lined pipelines with ovality defects under hydrostatic pressure

The subsea pipelines may deteriorate and/or be cracked after a long period of service. A cost-effective trenchless rehabilitation technology is to install a thin-walled steel liner inside the pipelines. However, elliptical defects may occur in the liner due to issues such as insufficient inflation, deformation of the host pipelines, and joint misalignment in practical engineering. Thus, this study aims to develop a systematic analytical model and numerical model for the elastic and inelastic buckling behaviors of the thin-walled oval steel liner, respectively. An admissible radial displacement function is introduced to describe the single-lobe deformation of the liner. The governing equations are established to trace the equilibrium paths by applying the theory of thin-walled shells and the principle of minimum potential energy. A two-dimensional finite element model is developed for the elastic and inelastic buckling performance of the liner. The analytical solutions of elastic buckling are in good agreement with other closed-form solutions, numerical results, and respective test results available in the literature. Finally, parametric evaluations are carried out in terms of ovality, non-uniform liner-pipeline gap, internal pressure, and liner yield strength.

3rd-Order Differential Subordination and Superordination Results for Univalent Analytic Functions Associated with Zeta-Riemann Fractional Differential Operator

Using the results of 3rd order differential subordination, we introduce certain families of admissible functions and discuss some applications of 3rd order differential subordination for normalized analytic functions associated with novel fractional operator namely Zeta-Riemann Fractional differential operator. Some new results on differential subordination and superordination with some sandwich theorems are obtained. Moreover, several particular cases are also noted.

Some Results on Pursuit Games for an Infinite System of Ternary Differential Equations

This paper aims to study a one-pursuer, one evader pursuit differential game for a higher level of infinite system that is an infinite system of first order ternary differential equations, and prove completion of pursuit in the game. Both integral constraints and geometric constraints are subjected on the players' control functions, thus two separate cases of pursuit games are examined. In the game, the pursuer wants to take the state of the system into the origin of l2 space at some finite time interval, whereas evader avoids this from happening. For every case, we solve the control problem by establishing the admissible control function. In order to achieve the pursuer's objective, we then construct an admissible strategy for the pursuer and develop an equation for the guaranteed pursuit time of the game.

Vibration of composite open shell of hydrogen-electric fuselage with rectangular cutout in hygrothermal circumstances: theoretical and experimental research

An effective formulation is performed to approximate calculate the vibration of the typical composite fuselage battery compartment structures of the hydrogen-electric aircraft, which are highly sensitive to hygrothermal circumstances. The strain energy, kinetic energy and hygrothermal potential energy of CLOCSRC are deduced in frame of Donnell's shell assumption and a series of hypothetical elastic springs operating on the edges of divided components are introduced to simulate coupling connection and the elastic supports of the open shell, which contribute to total system energy in the form of elastic spring potential energy. The equations of motion for CLOCSRC subjected to distinct hygrothermal circumstances and arbitrary boundaries are eventually obtained in frame of the Rayleigh-Ritz method by means of the modified orthogonal polynomial as the displacement admissible function. After confirming the convergence and accuracy of the presented formulation by experiment and finite element method, several numerical examples are presented to investigative the effects of geometric parameters, elastic boundaries and hygrothermal circumstances on the vibration of CLOCSRC. Differ from traditional investigation, the present paper offers an effective approach to insight the hygrothermal mechanism of open shell with rectangular cutouts creatively. The relevant investigation demonstrated that the current strategy is beneficial for further research on the vibration characteristics of CLOCSRC.

Energy Element Method for Three-Dimensional Vibration Analysis of Stiffened Plates with Complex Geometries

A novel numerical method, the energy element method, is proposed for the three-dimensional vibration analysis of stiffened plates with complex geometries. The problem is modeled in a cuboidal domain, and a cuboidal energy element is developed for the simulation of the structural components. To simulate the energy distribution of the structure, stiffened plates are treated as discrete energy systems, where variable stiffness is used to characterize their energy distribution in a cuboidal domain and a global admissible function is used to approximate their vibrational behavior. With extended interval integral, Gauss quadrature, variable stiffness, and Legendre polynomials used for numerical integration in the cuboidal domain, the cuboidal energy element can offer sufficient precision with sufficient Gauss points for simulating the strain energy of stiffened plates with complex geometries. The Gauss–Legendre quadrature will provide accurate integration results if the integral domain is cuboidal. Otherwise, small cuboidal energy elements are generated with denser Gauss points to capture the geometric boundaries. As the numerical model is constructed on a standard geometric domain, all energy functionals and computational procedures are standard. Three-dimensional vibration problems are investigated for variously shaped stiffened plates with straight or curvilinear stiffeners. The present results are compared with analytical, numerical, and experimental results published in the literature.

Forced vibrations of an elastic triangular plate supported around its perimeter by a unilateral support via the Chebyshev polynomial expansion

The present study introduces static and dynamic analysis of an elastic triangular plate on unilateral edge supports, including forced vibrations due to loading and unloading excitation. The plate is assumed to be subjected to a uniformly distributed load and an eccentrically applied concentrated load. Furthermore, the loads are assumed to display dynamic variations. The governing equation of the problem is derived by considering the static and the dynamic responses of the plate by including inertia forces. The analytical solution is conducted by employing a series of Chebyshev polynomials for the admissible displacement functions and using Lagrange’s equations of motion. Having found the governing equation of the problem, an approximate numerical solution is accomplished using an iterative process due to the non-linear properties of the unilateral edge supports. The static behavior of the plate under a concentrated load is investigated in detail numerically by considering a wide range of parameters of the plate geometry and the stiffness of the support. In deriving the governing equation of the problem and in the numerical solution, special care is taken to use nondimensional parameters. This approach ensures that the analysis and conclusions remain valid across a wide range of parameter values. Dynamic treatment of the problem is carried out in the time domain by assuming a stepwise time variation of the concentrated load and by employing the constant acceleration procedure in the numerical solution of the system of governing differential equations derived from the equation of motion. Time variations of the displacements, the contact points, and the reactions of the plate’s support are presented in figures for various values of the parameters of the plate, as well as those of the supports, particularly focusing on the non-linearity of the problem due to the plate liftoff from the unilateral support. The effects of the parameters and the loading are investigated in detail. The results reveal that the unilateral property of the support stiffness significantly affects the static and dynamic behavior of the triangular plate. The analysis can be extended easily to cover a general type of loading as well. The main issues addressed in this study include: the analysis of a triangular plate with unilateral perimeter support that does not resist tensile forces; the use of Chebyshev polynomials as admissible functions in both directions; the consideration of static and dynamic loads; the determination of lifting areas of the support in both cases and the assessment of the global vertical force balance in the plate, including inertia forces in the dynamic case.

Vibration analysis and suppression of axially moving composite laminated plates with modified energy method and piezoelectric shunt damping circuits

This paper presents a modified variational modeling method and develops an electro-mechanical coupling based vibration control method for moving composite plate structures. Unlike the stationary structures, movement will introduce new challenges for both vibration analysis and control of the laminated plate. Based on the modified variational method, electromechanically coupled dynamic models for the moving plate with piezoelectric patches and control circuits are developed. To release limitations to the admissible functions, modified variational principles are derived for the interface and boundary constraints in both directions of the moving plate. On the basis of first-order shear deformation theory (FSDT), the energy functional expressions of the axially moving laminated plates are formulated and the governing equations are obtained. To suppress the vibration, a piezoelectric shunt damping circuit (PSDC) with negative capacitance is proposed and the control circuit parameters are optimized using the differential evolution (DE) algorithm. Through numerous numerical examples, the high accuracy, good efficiency, and flexibility in constructing admissible functions of the proposed modeling method are demonstrated. The developed PSDC possesses much better vibration suppression properties for the moving laminated plates than the series R-L PSDC. Effects of the moving speed and negative capacitance on the optimal circuit parameters are also examined. The appropriate values of the negative capacitance are shown to be near the capacitance of the patches.

Monitoring Poverty in a Data‐Deprived Environment: The Case of Lebanon

AbstractThis paper addresses the lack of data and limited statistical capacity in the Middle East and North Africa, particularly amid Lebanon's economic collapse. We apply a novel data augmentation technique to analyze poverty when traditional income data are limited or unavailable. By adapting existing methods, we recover continuous income distributions from interval data and derive dominance conditions for such data, accounting for non‐response. The proposed approach enables robustness checks by estimating the bounds of admissible cumulative distribution functions. Our empirical analysis uses Lebanese data to perform first‐order dominance tests on these bounds, highlighting the importance of the approach. We demonstrate how alternative data sources can be leveraged for essential poverty analysis.

Quantum nature of spacetime near the black hole singularity

The concept of spacetime loses its usual interpretation at the essential singularity of a black hole. In consequence, all laws of physics must fail at this classical singularity. This unphysical behavior of spacetime at the singularity originates from general relativity. In order to have a consistent description of spacetime, this singularity must disappear in a quantum mechanical description of spacetime which is expected to be given by a quantum theory of gravity. In this paper, we therefore attempt to describe the quantum nature of spacetime in the vicinity of the (classical) singularity of a black hole. We take the Kantowsi–Sachs representation for the interior spacetime of a black hole and include inevitable vacuum fluctuations of matter field in the Klein–Gordon representation. Hence we obtain the Wheeler–DeWitt equation for the black hole interior and solve this equation exactly yielding a general expression for the interior wave function of the black hole. Admissible wave functions consistent with the DeWitt boundary condition implies that the Hilbert space has three nonoverlapping sectors distinguished by the relative character of the eigenvalues. Regular quantum black holes with admissible and well-behaved wave function having no singularity can exist only in two of those sectors. However, the remaining sector does not contain any regular quantum black hole.

Fuzzy Differential Subordination for Classes of Admissible Functions Defined by a Class of Operators

Fuzzy Differential Subordination for Classes of Admissible Functions Defined by a Class of Operators

Vibration localization and reduction of double-plate structures

A thin plate-type resonator is attached to a host-stepped plate to achieve vibration localization and reduction in initial low-order global vibration modes. A semi-analytical method is proposed to analyze the free and forced vibrations of the double-plate structure, considering the geometric configuration's heterogeneity and discontinuity. The double plate structure is divided into several sub-plates for individual modeling, with admissible functions constructed for the displacements of each subdomain. These subdomains are then combined into a unified whole through displacement compatibility conditions. The no-orthogonality between global vibration and localized modes is determined using analytic mode functions obtained by the Ritz method with special admissible functions, which is crucial for suppressing the multiple resonance peaks of global vibration using the integrated plate-type resonator. An intriguing finding is that at the frequency veering point of global vibration modes and localized modes, the non-orthogonality can lead to two coupled global-localized modes that are similar to the initial localized mode, and the vibration of initial global modes can be mainly concentrated in the resonator region outside the plate during free vibration. For force vibration of the double plate, the initial resonance peak splits from one into two smaller resonance peaks due to the two coupled global-localized modes. Furthermore, the coupled global-localized mode allows for a substantial reduction in the host plate vibration while making a negligible impact on the total mass and global vibration frequency. This study presents a promising approach for reducing multimodal vibrations in lightweight structures.

Boosting optimal symbolic planning: Operator-potential heuristics

Heuristic search guides the exploration of states via heuristic functions h estimating remaining cost. Symbolic search instead replaces the exploration of individual states with that of state sets, compactly represented using binary decision diagrams (BDDs). In cost-optimal planning, heuristic explicit search performs best overall, but symbolic search performs best in many individual domains, so both approaches together constitute the state of the art. Yet combinations of the two have so far not been an unqualified success, because (i) h must be applicable to sets of states rather than individual ones, and (ii) the different state partitioning induced by h may be detrimental for BDD size. Many competitive heuristic functions in planning do not qualify for (i), and it has been shown that even extremely informed heuristics can deteriorate search performance due to (ii).Here we show how to achieve (i) for a state-of-the-art family of heuristic functions, namely potential heuristics. These assign a fixed potential value to each state-variable/value pair, ensuring by LP constraints that the sum over these values, for any state, yields an admissible and consistent heuristic function. Our key observation is that we can express potential heuristics through fixed potential values for operators instead, capturing the change of heuristic value induced by each operator. These reformulated heuristics satisfy (i) because we can express the heuristic value change as part of the BDD transition relation in symbolic search steps. We run exhaustive experiments on IPC benchmarks, evaluating several different instantiations of potential heuristics in forward, backward, and bi-directional symbolic search. Our operator-potential heuristics turn out to be highly beneficial, in particular they hardly ever suffer from (ii). Our best configurations soundly beat previous optimal symbolic planning algorithms, bringing them on par with the state of the art in optimal heuristic explicit search planning in overall performance.

Weighted boundedness of fractional integrals associated with admissible functions on spaces of homogeneous type

Weighted boundedness of fractional integrals associated with admissible functions on spaces of homogeneous type

Chaotic vibration of a curved CNT conveying magnetic fluid in the thermo-magnetic field considering the surface effects

The nonlinear chaotic vibration of curved single-walled carbon nanotube (CSWCNT) conveying magnetic fluid is studied based on the nonlocal Euler-Bernoulli beam model. The governing equation of CSWCNT is presented considering the axial thermo-magnetic load and the surface effect. By employing the Galerkin decomposition approximation method along with the admissible beam shape function satisfying the cantilevered beam boundary conditions, the nonlinear partial differential equation of the system is reduced to a nonlinear ordinary differential equation and numeric integration procedures are used to solve it. By considering the non-dimensional damping, cubic and quadratic terms, and amplitude of external force as controlling parameters, the bifurcation diagram and the largest Lyapunov exponent are employed to distinguish the chaotic, periodic, and quasi-periodic critical parameters of the curved CNT dynamics and validate the predicted results. Also, the phase plane and Poincare map for these critical parameters are provided. The results show that decreasing values of damping coefficient and quadratic term leads to quasi-periodic or chaotic motion, while system has periodic behaviour for smaller values of the external force and nonlinear cubic term. Also, magnetic field intensity and length of the CSWCNT help preventing the chaotic motion. Furthermore, adverse effects of higher values of temperature change, flow velocity and its correction factor are seen based on the obtained results.

On the semicontinuity properties of the set of trajectories of the nonlinear control systems with integral constraints on the control functions

ABSTRACT In this paper the control system described by the ordinary nonlinear differential equation is considered. The admissible control functions are chosen from the closed ball of radius r in the space L p , p ∈ [ 1 , ∞ ] , centred at the origin. The behaviour of the set of trajectories at p = 1 is studied. It is proved that the set of trajectories is the Hausdorff right upper semicontinuous and Vietoris right lower semicontinuous at p = 1. It is illustrated that it is not Hausdorff right lower semicontinuous at p = 1.

Admissibility and mean hyperbolicity for evolution equations

Mean hyperbolic systems permit non-hyperbolic behavior at certain moments during the evolution process T(t,s), owing to non-fixed error hyperbolic degree ε(t,s). Despite the coexistence of compression and expansion behaviors in generalized stable and unstable subspaces, mean hyperbolic systems admit fixed average contraction and expansion rates measured at sufficiently long time. To discuss the relationship between admissibility and mean hyperbolicity for evolution equations, our main goal is to construct admissible function classes and invariant decomposition with generalized stable and unstable subspaces. As applications, the mean hyperbolicity of damped wave equations with variable coefficients and the roughness of mean hyperbolicity are presented.

Modeling and mathematical approach for mechanical natural frequencies of structural plates with free edges

The current study aims to demonstrate an easy mathematical procedure and simple to be used by engineers to maintain the mechanical natural frequencies (Eigen values of free vibration) of thin rectangular structural plates with free edges included in boundary conditions. The reason for this easiness and simplicity is that new method of analysis depends mainly on using mechanical minimum energy concept represented in the Rayleigh–Ritz method with appropriate real polynomials as admissible functions. The new procedure guides these functions to satisfy the boundary conditions at the middle points on the free edges of the plate beside the nodal points of the vibration modes along each edge direction. Therefore, there are no complicated or imaginary terms in the developed functions while they lead to surprisingly acceptable and even accurate results when compared with other works and Ansys program models.

Effect of spatial setting angle on vibration of elastically restrained rotating beams

For a fully articulated rotor system, there may exist a spatial setting angle and elastically restrained root for each individual blade in rotation procedure due to flapping, drag and pitch hinges. Most of previous studies on rotating blades or beams focused on pitch angle and clamped root. In this paper, a three-dimensional dynamic model is proposed for elastically restrained rotating beams with spatial setting angle. The elastic deformation of the beam is expressed by three scalar variables in three-dimensional space including stretch deformation instead of the conventional axial deformation. The longitudinal shrinkage is considered to capture centrifugal forces. The penalty method is adopted to deal with the elastic constraints, which greatly simplifies the construction of admissible functions. A unified formulation is derived by a variational principle combined with Chebyshev orthogonal polynomials. One of the advantages of the present method is that any linearly independent and complete basis functions can be used as admissible function regardless of boundary conditions, and another advantage is that the present method is capable of handling arbitrary boundary conditions by only adjusting the values of penalty factor. The convergence and accuracy of the present method are validated by comparison, and the effects of boundary conditions, angular velocity and spatial setting angle on vibration characteristics are discussed in detail. The results show that natural frequencies increase as the spring stiffness rises in a certain range and the spatial setting angle plays a more significant role on dynamic characteristics for rotating beams.

The Modeling Method for Vibration Characteristics Analysis of Composite-Laminated Rotationally Stiffened Plate

The composite-laminated rotationally stiffened plate is widely applied in aviation, aerospace, ship, machinery, and other fields. For structural design and optimization, to investigate the vibration characteristics is important. In this paper, a modeling method of composite-laminated rotationally plate is established. The first-order shear deformation theory (FSDT) and the modified Fourier series are applied to construct the admissible displacement function of the stiffened plate-coupled systems. On this basis, the energy function of composite-laminated rotationally stiffened plate is established. Combined with the artificial virtual spring technology, the proposed theory could be used to analyze the vibration characteristics of composite-stiffened plate-coupled systems with various classical boundary conditions or arbitrary elastic boundary conditions. The Rayleigh–Ritz method is used to solve the energy function. Thus, the vibration characteristics of the composite-laminated rotationally stiffened plate are obtained and analyzed. The correctness of the theoretical analysis model was verified through modal experiments. On this basis, the effect of some important parameters on the vibration characteristics of stiffened plate structures is studied, such as the number, thickness, and width of the laminated stiffener, varying structural parameters, and different boundary conditions. This study can provide the theoretical basis for the vibration and noise reduction of such structures.