Geometric Function Research Articles

Sandwich Theorems for a New Class of Complete Homogeneous Symmetric Functions by Using Cyclic Operator

In this paper, we discuss and introduce a new study on the connection between geometric function theory, especially sandwich theorems, and Viete’s theorem in elementary algebra. We obtain some conclusions for differential subordination and superordination for a new formula of complete homogeneous symmetric functions class involving an ordered cyclic operator. In addition, certain sandwich theorems are found.

Applications of Symmetric Quantum Calculus to the Class of Harmonic Functions

In the past few years, many scholars gave much attention to the use of q-calculus in geometric functions theory, and they defined new subclasses of analytic and harmonic functions. While using the symmetric q-calculus in geometric function theory, very little work has been published so far. In this research, with the help of fundamental concepts of symmetric q-calculus and the symmetric q-Salagean differential operator for harmonic functions, we define a new class of harmonic functions connected with Janowski functions SH0˜m,q,A,B. First, we illustrate the necessary and sufficient convolution condition for SH0˜m,q,A,B and then prove that this sufficient condition is a sense preserving and univalent, and it is necessary for its subclass TSH0˜m,q,A,B. Furthermore, by using this necessary and sufficient coefficient condition, we establish some novel results, particularly convexity, compactness, radii of q-starlike and q-convex functions of order α, and extreme points for this newly defined class of harmonic functions. Our results are the generalizations of some previous known results.

Development of solar isodose lines: Mercatorian and spatial guides for mapping solar installation areas

Mercatorian and spatial studies of solar power potential (SPP) provide technical guides for mapping actual solar installation areas for the efficient performance of photovoltaic plants. Acquisition and processing of satellite and on-station data on clearness index, relative sunshine hours, latitude, longitude and SPP preceded their modeling and simulations. The mercatorian SPP model is a geometric function of latitude and longitude, whereas the spatial SPP model is a function of x and y coordinates developed from the Haversine formula. Multiple isodose lines and a single maximum isodose line characterized the distributed and concentrated SPP contours, respectively. The present geometric SPP model validated well with the measured SPP with insignificant error results for the study areas. The Concentrated SPPs: 757.5, 635.2, 557.5 and 405.9 W/m2 with their corresponding percentage concentrated areas (actual): 28.85(29084.6), 41.48(15368.6), 4.37(1179.6) and 0.75(635.7)%(m2) for Northern Region (NR), Eastern Region (ER), Central Region (CR) and Western Region (WR), respectively. These results support the efficient performance of solar facilities within the confine of the SPP concentrated areas. The effective mercatorian coordinates were useful in identifying districts within the SPP concentrated areas. Furthermore, the high magnitude of the SPP in ER and NR supports that they are favored for the installation of solar facilities.

Applications of the q-Sălăgean Differential Operator Involving Multivalent Functions

In this article we explore several applications of q-calculus in geometric function theory. Using the method of differential subordination, we obtain interesting univalence properties for the q-Sălăgean differential operator. Sharp subordination results are obtained by using functions with remarkable geometric properties as subordinating functions and considering the conditions of expressions involving the q-Sălăgean differential operator and a convex combination using it.

Briot–Bouquet Differential Subordinations for Analytic Functions Involving the Struve Function

We define a new class of exponential starlike functions constructed by a linear operator involving normalized form of the generalized Struve function. Making use of a technique of differential subordination introduced by Miller and Mocanu, we investigate several new results related to the Briot–Bouquet differential subordinations for the linear operator involving the normalized form of the generalized Struve function. We also obtain univalent solutions to the Briot–Bouquet differential equations and observe that these solutions are the best dominant of the Briot–Bouquet differential subordinations for the exponential starlike function class. Moreover, we give an application of fractional integral operator for a complex-valued function associated with the generalized Struve function. The significance of this paper is due to the technique employed in proving the results and novelty of these results for the Struve functions. The approach used in this paper can lead to several new problems in geometric function theory associated with special functions.

Certain subclass of analytic functions involving Hurwitz–Lerch zeta function

Making use of Integral operator involving the Hurwitz-Lerch zeta function, we introduce a new subclass of analytic functions defined in the open unit disk and investigate its various characteristics. Further we obtain some usual properties of the geometric function theory such as coefficient bounds, extreme points radius of starlikness and convexity, partial sums and neighbourhood results belonging to the class.

Properties of q-Symmetric Starlike Functions of Janowski Type

The word “symmetry” is a Greek word that originated from “symmetria”. It means an agreement in dimensions, due proportion, and arrangement; however, in complex analysis, it means objects remaining invariant under some transformation. This idea has now been recently used in geometric function theory to modify the earlier classical q-derivative introduced by Ismail et al. due to its better convergence properties. Consequently, we introduce a new class of analytic functions by using the notion of q-symmetric derivative. The investigation in this paper obtains a number of the latest important results in q-theory, including coefficient inequalities and convolution characterization of q-symmetric starlike functions related to Janowski mappings.

Least-distance approach for efficiency analysis: A framework for nonlinear DEA models

We propose a class of nonlinear data envelopment analysis (DEA) models, including variants of the Russell graph measure (RM), BRWZ measure, slack-based measure (SBM), and geometric distance function (GDF). Based on linear programming, this class of DEA models provides a monotonic maximum efficiency measure and an efficient target that achieves the least Manhattan distance from the weakly efficient frontier of the production possibility set. We show that the maximum efficiency measure in this class can be explicitly expressed as a decreasing function of the least Manhattan distance. Furthermore, by adding certain consistent weight restrictions to this class of DEA models, the maximum efficiency measures satisfy strong monotonicity.

Morphology modelling and validation in nanosecond pulsed laser ablation of metallic materials

Nanosecond pulsed lasers are widely used in the surface treatment of metallic materials due to their low cost and simple operation. During pulsed laser processing, many parameters such as laser and material properties are involved. Consequently, the existing mathematical models for pulsed laser ablation of metals are complex and computationally difficult. In this paper, a simple and novel model was proposed for nanosecond pulsed laser processing based on heat transfer and geometrical mathematics. The geometrical parameters functions of the recast layer under pulsed laser single ablation and continuous superimposed ablation are presented, respectively. The feasibility of the models is validated by experiments. Errors in diameter and depth of single-pulse laser ablation craters were 2.56%–7.14% and 6.82%–18.91%. The recast layer depth error is about 3.47%–12.47% for successive pulses of superimposed ablation. It predicts the shape of the recast layer on pulsed laser ablated metal surfaces. The model is a guide to the surface morphology of laser woven materials and the preparation of surface functionalities, particularly the selection of process parameters for microstructure machining.

Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

We develop crossing symmetric dispersion relations for describing 2-2 scattering of identical external particles carrying spin. This enables us to import techniques from Geometric Function Theory and study two sided bounds on low energy Wilson coefficients. We consider scattering of photons, gravitons in weakly coupled effective field theories. We provide general expressions for the locality/null constraints. Consideration of the positivity of the absorptive part leads to an interesting connection with the recently conjectured weak low spin dominance. We also construct the crossing symmetric amplitudes and locality constraints for the massive neutral Majorana fermions and parity violating photon and graviton theories. The techniques developed in this paper will be useful for considering numerical S-matrix bootstrap in the future.

Entropic uncertainty and quantum correlations dynamics in a system of two qutrits exposed to local noisy channels

We address the dynamics of the lower bound of geometric quantum discord and quantum-memory-assisted entropic uncertainty in a two-qutrit system when exposed to classical channels characterized by power-law (PL) and random telegraph (RT) noises. The system-channel coupling strategy is examined in two contexts: common qutrit-environment (CQE) and different qutrit-environment (DQE) configurations. We show that the geometric quantum discord functions remain anti-correlated with entropic uncertainty and decline as uncertainty appears in the system. The rate of entropic uncertainty appearance seems more prevalent than the decline rate of quantum discord function, suggesting that uncertainty causes the quantum correlations to fade in quantum systems. We find that non-local correlations estimated by the lower bound of geometric quantum discord are not destroyed even at the maximum entropic disorder and entropic uncertainty. In addition, the efficacy of entropic uncertainty and the lower bound is strongly influenced by the state’s purity factor, with the former being more robust at higher purity values and the latter at lower purity values. All the parameters impact entropic uncertainty, however, the mixedness of the state is noticed to greatly alter the generation of quantum memory. Besides, PL noise caused Markovian behavioral dynamics, and the RT noise allowed non-Markovian dynamics, while the latter remains more resourceful for the quantum correlations preservation and entropic uncertainty suppression. We also demonstrate how to model longer quantum correlations and provide optimal parameter settings for suppressing the dephasing and entropic uncertainty effects.

Bioinspired Artificial Ion Pumps.

Ion pumps are important membrane-spanning transporters that pump ions against the electrochemical gradient across the cell membrane. In biological systems, ion pumping is essential to maintain intracellular osmotic pressure, to respond to external stimuli, and to regulate physiological activities by consuming adenosine triphosphate. In recent decades, artificial ion pumping systems with diverse geometric structures and functions have been developing rapidly with the progress of advanced materials and nanotechnology. In this Review, bioinspired artificial ion pumps, including four categories: asymmetric structure-driven ion pumps, pH gradient-driven ion pumps, light-driven ion pumps, and electron-driven ion pumps, are summarized. The working mechanisms, functions, and applications of those artificial ion pumping systems are discussed. Finally, a brief conclusion of underpinning challenges and outlook for future research are tentatively discussed.

Percolativity of Porous Media

Connectivity and connectedness are nonadditive geometric functionals on the set of pore scale structures. They determine transport of mass, volume or momentum in porous media, because without connectivity there cannot be transport. Percolativity of porous media is introduced here as a geometric descriptor of connectivity, that can be computed from the pore scale and persists to the macroscale through a suitable upscaling limit. It is a measure that combines local percolation probabilities with a probability density of ratios of eigenvalues of the tensor of local percolating directions. Percolativity enters directly into generalized effective medium approximations. Predictions from these generalized effective medium approximations are found to be compatible with apparently anisotropic Archie correlations observed in experiment.

Celestial insights into the S-matrix bootstrap

We consider 2-2 scattering in four spacetime dimensions in Celestial variables. Using the crossing symmetric dispersion relation (CSDR), we recast the Celestial amplitudes in terms of crossing symmetric partial waves. These partial waves have spurious singularities in the complex Celestial variable, which need to be removed in local theories. The locality constraints (null constraints) admit closed form expressions, which lead to novel bounds on partial wave moments. These bounds allow us to quantify the degree of low spin dominance(LSD) for scalar theories. We study a new kind of positivity that seems to be present in a wide class of theories. We prove that this positivity arises only in theories with a spin-0 dominance. The crossing symmetric partial waves with spurious singularities removed, dubbed as Feynman blocks, have remarkable properties in the Celestial variable, namely typically realness, in the sense of Geometric Function Theory (GFT). Using GFT techniques we derive non-projective bounds on Wilson coefficients in terms of partial wave moments.

Subordination Results on the q-Analogue of the Sălăgean Differential Operator

Aspects related to applications in the geometric function theory of q-calculus are presented in this paper. The study concerns the investigation of certain q-analogue differential operators in order to obtain their geometrical properties, which could be further developed in studies. Several interesting properties of the q-analogue of the Sălăgean differential operator are obtained here by using the differential subordination method.

Bio-inspired maple-leaf viburnum shaped 4-port compact wideband MIMO antenna with reinforced interleaved SIW cavity integration

This study proposes a maple-leaf viburnum (MLV) shaped 4-port compact MIMO antenna with SIW technology for WLAN-LTE-WiMax applications, which is inspired by nature’s flora diversity. The antenna is constituted of a monopole feed and MLV petal shapes which have been generated using standard analytical exponential curves. Then, using rotation and translation features, MLV petal radiators are extended to resemble a maple-leaf-like pattern, invoking Hutchison’s geometrical transfer function. First, a 16 mm × 16 mm 1-element antenna resonating at 3.7 GHz is designed, and then it is extended to construct a 4-port wideband antenna with a dimension of 32 mm × 32 mm that operates from (3.2–5.2) GHz. To achieve a reinforced SIW cavity integrated profile with improved performance, interleaved metallic strips are interconnected via metallized posts. Isolation coefficients have increased by >25 dB using this unique strategy. In the operational band, the envelope channel coefficient (ECC) is <0.11, and the antenna gain is >3 dBi. A prototype antenna was fabricated and tested, and the simulated and measured outcomes were found to be well correlated.

A D-InSAR method to improve snow depth estimation accuracy

<p indent="0mm">Snow depth is an important parameter that reflects the law of spatiotemporal variation in snow cover and is an indispensable observation variable for studying global and regional climate change and the hydrological cycle. Traditional manual field measurements and ground station observations have limited scopes and cannot fully reflect regional-scale snow conditions. Satellite remote sensing can simultaneously observe surface information over a large area and has been widely used in snow monitoring since the 1970s. Optical remote sensing has difficulty obtaining snow depth information directly through the visible light band and is limited by atmospheric conditions. Microwave remote sensing can penetrate clouds and fog and can effectively capture changes in snow depth. Differential interferometric synthetic aperture radar (D-InSAR) technology uses the differential interferometric phase formed by microwave penetration through the snow layer before and after snowfall to establish a geometric function relationship with the snow depth; it is widely used in regional small-scale snow depth estimation research. However, its estimation accuracy is affected by many factors, such as interferometric image pair coherence, local topography, and snow dielect capability at microwave wavelengths. Based on high-resolution Sentinel-1 SAR data, this study optimizes the snow depth differential interferometric phase unwrapping accuracy by introducing Sentinel-2 optical images and high coherence coefficient regions to select ground control points, which are phase correction benchmarks. Furthermore, introducing field-measured snow parameters such as snow density and satellite local terrain incidence angles based on digital elevation model (DEM) data reduces the error of the differential interferometric phase-slope distance relationship model, thereby enabling estimations of the spatiotemporal distribution of snow depth in the Babao River Basin in the northeastern Qinghai-Tibet Plateau during the 2021 ablation period. Simultaneously, the accuracy of the snow depth estimation ability is evaluated based on the synchronous field measurement data of snow cover satellites. The main factors affecting the accuracy of snow depth estimation are discussed and analysed. Data from 122 ground snow depth measurements (meteorological stations + field measurements) are used to verify the results. The results show that the optimized D-InSAR differential interferometry can improve the snow depth estimation accuracy. The RMSE is <sc>3.9 cm,</sc> the<italic> </italic>MAPE is 20.03%, and the <italic>R</italic>² is 0.92. However, the estimated snow depth is generally underestimated (MBE%=−16.8%), and the maximum underestimation error of the snow depth is <sc>9.1 cm.</sc> In addition to the influencing factors of D-InSAR system interferometric decorrelation, the estimations are affected by the penetration ability of microwaves in the snow and snow parameters such as stratigraphy structure, temperature and humidity. This limits the ability of differential interferometry to estimate snow depth and is more suitable for dry and homogeneous snow cover. This method allows for more precise and faster monitoring of centimetre-level snow depth changes; at the same time, the underlying surface of the study is relatively simple, and the influence of forest and other vegetation coverage is not considered. In follow-up research, snow cover should be optimized with multi-property and multi-environment interferometric models. An InSAR scattering model with a layered factor is introduced to improve the propagation information inside the snow layer then combined with the multiangle radar measurement of the ascending and descending orbits; experiments are carried out using the penetration ability of more bands in microwaves to reduce interferometric error sources and improve the accuracy of snow depth estimation. This study can provide a scientific reference for D-InSAR snow depth estimation research.

Discrete symmetries control geometric mechanics in parallelogram-based origami

Geometric compatibility constraints dictate the mechanical response of soft systems that can be utilized for the design of mechanical metamaterials such as the negative Poisson's ratio Miura-ori origami crease pattern. Here, we develop a formalism for linear compatibility that enables explicit investigation of the interplay between geometric symmetries and functionality in origami crease patterns. We apply this formalism to a particular class of periodic crease patterns with unit cells composed of four arbitrary parallelogram faces and establish that their mechanical response is characterized by an anticommuting symmetry. In particular, we show that the modes are eigenstates of this symmetry operator and that these modes are simultaneously diagonalizable with the symmetric strain operator and the antisymmetric curvature operator. This feature reveals that the anticommuting symmetry defines an equivalence class of crease pattern geometries that possess equal and opposite in-plane and out-of-plane Poisson's ratios. Finally, we show that such Poisson's ratios generically change sign as the crease pattern rigidly folds between degenerate ground states and we determine subfamilies that possess strictly negative in-plane or out-of-plane Poisson's ratios throughout all configurations.

Quantitative two-scale stabilization on the Poisson space

We establish inequalities for assessing the distance between the distribution of a (possibly multidimensional) functional of a Poisson random measure and that of a Gaussian element. Our bounds only involve add-one cost operators at the order one—that we evaluate and compare at two different scales—and are specifically tailored for studying the Gaussian fluctuations of sequences of geometric functionals displaying a form of weak stabilization—see Penrose and Yukich (Ann. Appl. Probab. 11 (2001) 1005–1041) and Penrose (Ann. Probab. 33 (2005) 1945–1991). Our main bounds extend the estimates recently exploited by Chatterjee and Sen (Ann. Appl. Probab. 27 (2017) 1588–1645) in the proof of a quantitative version of the central limit theorem (CLT) for the length of the Poisson-based Euclidean minimal spanning tree (MST). We develop in full detail three applications of our bounds, namely: (i) to a quantitative multidimensional spatial CLT for functionals of the on-line nearest neighbour graph, (ii) to a quantitative multidimensional CLT involving functionals of the empirical measure associated with the edge-length of the Euclidean MST, and (iii) to a collection of multidimensional CLTs for geometric functionals of the excursion set of heavy-tailed shot noise random fields. Application (i) is based on a collection of general probabilistic approximations for strongly stabilizing functionals, that is of independent interest.

A Spectro-geometric solution of dynamic characteristics of submarine-like structures

In this paper, the Spectro-geometric method is used to study the vibration behaviors of the submarine-like structure. The substructures of the geometric model include: cylindrical shell, conical shell, spherical shell, annular plate and rectangular plate. The energy formula of the sub-structure is deduced by the principle of first-order shear deformation. In order to satisfy the continuity conditions between the sub-structures and the related boundary conditions, the artificial spring technology is introduced in this paper. The Lagrange energy functional for the entire model is established. For efficient modeling, the displacement functions used here is the two-dimensional spectral geometric functions. Substitute the displacement function into the energy functional and solve it by the Ritz method to obtain the displacement coefficient and natural frequency of the structure. Through the convergence analysis and the comparative studies for the substructures and the whole structure under different boundary conditions, it is verified that the method in this paper is feasible. The effects of coupling parameters, material parameters, and molecular structure dimensions on the free and forced vibrations of the submarine-like structure are also investigated.