Let
T
be a self-mapping on a complete metric space (
X
,
d
). In this paper, we obtain new fixed point theorems assuming that
T
satisfies a contractive-type condition of the following form:
ψ
(
d
(
...T
x
,
T
y
)
)
≤
φ
(
d
(
x
,
y
)
)
or
T
satisfies a generalized contractive-type condition of the form
ψ
(
d
(
T
x
,
T
y
)
)
≤
φ
(
m
(
x
,
y
)
)
,
where
ψ
,
φ
:
(
0
,
∞
)
→
R
and
m
(
x
,
y
) is defined by
m
(
x
,
y
)
=
max
d
(
x
,
y
)
,
d
(
x
,
T
x
)
,
d
(
y
,
T
y
)
,
d
(
x
,
T
y
)
+
d
(
y
,
T
x
)
/
2
.
In both cases, the results extend and unify many earlier results. Among the other results, we prove that recent fixed point theorems of Wardowski (2012) and Jleli and Samet (2014) are equivalent to a special case of the well-known fixed point theorem of Skof (1977).
In this analysis, convective heat transfer characteristics of a hybrid nanofluid mixture containing magnesium oxide (MgO) and gold (Au) nanoparticles are numerically studied. The impact of slip ...effects on nodal/saddle stagnation point boundary layer flow with viscous dissipation effect is mathematically modeled. The behavior of nanofluids is studied by employing Tiwari–Das nanofluid model. Pure water is the base fluid in this analysis. The governing partial differential equations with many independent variables are reduced to ordinary differential equations with one independent variable and then numerically solved by the Runge–Kutta–Fehlberg method with the desired accuracy. The outputs showed that MgO–Au/water hybrid nanofluid sharply raises the base fluid's thermal behavior. Results reveal that in the nodal and saddle point areas, the impact of higher slip effects significantly increases the local heat transfer rate.
The excessively available solar energy storage is a very useful way to bridge the energy demand and its supply gap. This thermal energy storage (TES) can be done in the form of sensible or latent ...heat energy. The energy storage in the form of latent heat energy is better than the sensible energy storage in terms of operating temperature and storage density. Organic PCMs (O-PCMs) have great potential, especially from low to medium temperature-TES applications due to their several admirable thermal and physical characteristics. An appropriate melting point/enthalpy of O-PCMs is mainly required parameters for TES applications. In this regard, development of eutectic O-PCMs (EO-PCMs) by mixing two or more PCMs customizes the melting temperature and enthalpy so that they can be made suitable for targeted TES applications. However, their low thermal conductivity and leakage issue during the phase transition significantly restrict the practices of EO-PCM. A lot of studies were carried out to solve these changes by preparing them in form stable or shape-stabilized composite form. This review paper provides an insight on the development and thermo-physical properties of eutectic (binary and ternary) EO-PCMs as well as their composites as nano-enhanced and form stable phase change materials (FSPCMs). This paper also highlights recent studies published about the enhancement of thermal conductivity of EO-PCMs and their FSPCMs developed for LHTES practices. The use of EO-PCMs and their form stable composites in various applications, and challenges faced are also discussed. Finally, it outlooks the future directions for development of eutectic organic PCMs and their applications.
Abstract
We present and investigate two additional subclasses of bi-univalent functions corresponding to symmetric and symmetric conjugate points in the open unit disc employing the Al-Oboudi ...operator. The initial coefficients of functions assigned to these classes are estimated.
•A LeGO-LOAM-OE method for dynamic outdoor environment.•Four types of outliers are eliminated to improve the accuracy of pose estimation.•Constraining the levelness makes the segmentation of the ...ground more accurate.•The dynamic object is eliminated by the motion distance in adjacent frames.
Based on the analysis of the shortcomings of Lightweight and Ground-Optimized Lidar Odometry and Mapping (LeGO-LOAM) algorithm, an improved LeGO-LOAM method based on outlier points elimination (LeGO-LOAM-OE) was proposed. The original point cloud data generated by Light Detection and Ranging (LiDAR) was analyzed and the four types of outlier points were eliminated, which made the extracted feature points more effective and improved the accuracy of pose estimation. In ground segmentation, the levelness of the ground is constrained so that the extracted ground points are more abundant and accurate. In dynamic point elimination, dynamic objects are eliminated by the moving distance of the same cluster objects in adjacent frames, and the calculation method is simple. The simulation results show that the trajectory accuracy generated by LeGO-LOAM-OE is higher than that generated by LeGO-LOAM. Compared with LeGO-LOAM, LeGO-LOAM-OE can effectively reduce the maximum error and average error of three axes. The total maximum error is reduced by 14.3%, and the total mean error is reduced by 7.6%. LeGO-LOAM-OE had the most significant effect on reducing the Y-axis error (vertical direction), with an average error reduction of 8.5%. An experimental platform was built to test the positioning accuracy and mapping effect of the proposed algorithm in an outdoor environment. Experimental results showed that the proposed method has high accuracy in both online and offline simultaneous localization and mapping (SLAM). The maximum error of the calculated position is less than 1 m, and the average error is less than 0.1 m. Moreover, the generated point cloud map can highly reproduce the environment without deviation.
•Transition boiling and film boiling regimes, and the Leidenfrost point for spray cooling are reviewed.•Discussed are dominant mechanisms, data trends, and predictive correlations and models.•Shown ...is how to predict the quench curve using spray correlations as boundary conditions.•Also shown is how the spray system can be configured to optimize mechanical properties of a quenched alloy part.
This paper is the second part of a comprehensive two-part review of spray cooling. The first part addressed the mechanisms and predictive tools associated with the relatively low-temperature single-phase liquid cooling and nucleate boiling regimes, as well as critical heat flux (CHF). The present part is focused on the relatively high-temperature transition boiling and film boiling regimes, and the Leidenfrost point. Discussed are dominant mechanisms, data trends, and predictive correlations and models. This information is especially important to the quenching of metal alloy parts from high initial temperature during heat treating. It is shown how correlations for the different spray cooling regimes and transition points can be implemented into boundary conditions for heat diffusion models to predict the temperature-time (quench) curve everywhere within the quenched part. It is also shown how the quench curve can be combined with the alloy’s transformation kinetics to predict mechanical properties. By properly configuring the sprays used to quench complex-shaped parts, it is also possible to greatly enhance the mechanical properties while minimizing residual stresses.
Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts ...pertaining to topological phases in non-Hermitian Hamiltonians with relevant examples and realistic model setups. Discussions are devoted to both the adaptations of topological invariants from Hermitian to non-Hermitian systems, as well as origins of new topological invariants in the latter setup. Unique properties such as exceptional points and complex energy landscapes lead to new topological invariants including winding number/vorticity defined solely in the complex energy plane, and half-integer winding/Chern numbers. New forms of Kramers degeneracy appear here rendering distinct topological invariants. Modifications of adiabatic theory, time-evolution operator, biorthogonal bulk-boundary correspondence lead to unique features such as topological displacement of particles, 'skin-effect', and edge-selective attenuated and amplified topological polarizations without chiral symmetry. Extension and realization of topological ideas in photonic systems are mentioned. We conclude with discussions on relevant future directions, and highlight potential applications of some of these unique topological features of the non-Hermitian Hamiltonians.
This paper introduces a novel class of generalized $ {\alpha} $-admissible contraction types of mappings in the framework of $ {\theta} $-complete partial satisfactory cone metric spaces and proves ...the existence and uniqueness of coincidence points for such mappings. In this setting, the topology generated and induced by the partial satisfactory cone metric is associated with semi-interior points rather than interior points of the underlying cone. In addition, some applications of the paper's main coincidence point theorems are given. The results of this paper unify, extend and generalize some previously proved theorems in this generalized setting.
Vanishing point is an important geometric element in sports video. In this paper, a new calibration algorithm is proposed by using the algebraic and geometric properties of vanishing points, which ...resolves the three main problems of the traditional camera calibration technology based on vanishing points: (1) calibrating camera with varied focal length; (2) screening out outliers from a set of images; (3) estimation of distortion coefficients. The principal line passes through the principal point, and the algebraic relationship between it and the vanishing points is deduced. Using the geometry feature of the principal line, problems (1) and (2) can be easily solved. The linear relationship between the point and the line is used to estimate the distortion coefficient under the condition of obtaining the principal point. Simulation and real experiments show the validity and robustness of the proposed algorithm, and satisfactory results can be obtained by solving the above three problems.
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