Multiple Solutions Research Articles

Form-finding of thermal-adaptive pin-bar assemblies based on eigenvalue modification

Lattice structures with tunable expansion properties have been investigated in multidisciplinary fields to control the temperature effects of structures or materials. The expected thermal adaptivity can be achieved by optimizing the structural geometry. A novel method for the form-finding of thermal-adaptive pin-bar assemblies is developed in this paper by considering the control of structural temperature effects as the minimization of the potential energy of the system. Based on the stationarity condition of the potential energy with respect to the nodal coordinates, the compatibility relationship between the thermal elongations of members and the target nodal displacements is proven to be the sufficient and necessary condition for structural thermal adaptivity. The solvability of the compatibility equation is determined by the rank equality between the compatibility matrix and its augmented form, which can be measured by the number of nonzero eigenvalues of its Gramian matrix. The analytical relationship between the eigenvalues of the Gramian matrix and the nodal coordinates is established using the matrix perturbation theory. A numerical strategy based on Newton’s method is proposed in which the eigenvalues are gradually modified by adjusting the nodal coordinates until the rank equality is satisfied. To address the existence of multiple solutions with structural thermal adaptivity, structural symmetry and periodicity constraints are introduced to narrow the solution space. The thermal-adaptive configurations of three illustrative pin-bar assemblies are analyzed using the proposed form-finding method, and the expected thermal deformations are verified for the obtained configurations using the finite element software ABAQUS. Comparing the results obtained by the proposed method with those obtained by nonlinear programming and the genetic algorithm validates the advantages of the proposed method in terms of computational time, optimality of the obtained configuration and applicability to complex structural geometries.

Complexiton, complex multiple kink soliton and the rational wave solutions to the generalized (3 + 1)-dimensional kadomtsev-petviashvili equation

Some new exact solutions of the generalized (3 + 1)-dimensional Kadomtsev-Petviashvili equation (KPE) are explored in this study. Firstly, the resonant multiple soltion solutions (RMSs) are discussed via employing the linear superposition principle and weight algorithm. Then, by introducing pairs of the conjugate parameters to the RMSs, the complexiton solutions including the non-singular complexiton and singular complexiton solutions are extracted. In addition, the complex multiple kink soliton solutions are also probed by employing the bilinear approach. Finally, we investigate the rational wave solutions via the test function method and symbolic computation. By choosing the appropriate parameters, the graph descriptions of the derived solutions are presented to show the dynamical properties. The outcomes of this work are desirous to bring some new perspective to the study of the complexiton, complex solutions and rational wave solutions to the other PDEs.

Discounted nonzero-sum optimal stopping games under Poisson random intervention times

We present solutions to some discounted nonzero-sum optimal stopping games of two players related to the perpetual game-type contingent claims with payoffs representing linear functions of the running values of a geometric Brownian motion. It is assumed that the underlying process can be stopped by the both players only at certain random intervention times which coincide with the jump times of the two appropriate independent Poisson processes. The optimal stopping times forming a Nash equilibrium are shown to be the first times at which the underlying process is either below or above certain lower or upper constant boundaries at the jump times of the appropriate Poisson processes. The proof is based on the reductions of the original games to the associated coupled free-boundary problems and the solutions to the latter problems by means of the smooth-fit conditions at the optimal boundaries for every player. We show that the optimal stopping constant lower and upper boundaries are determined as (possibly multiple) solutions to the equivalent coupled systems of arithmetic equations. The obtained results can be interpreted as the rational valuation of some perpetual randomized Bermudian game-type contingent claims in the Black-Merton-Scholes model.

On the sparsity of synthetic control method

ABSTRACT Synthetic Control Method (SCM) is a popular approach for causal inference in panel data, where the optimal weights for control units are often sparse. But the sparsity of SCM has received little attention in the literature except Abadie (2021), which explores the sparsity from the perspective of predictor space. In this paper, we make three contributions. First, we show that if there is a unique solution, then the number of positive weights is upper-bounded by the number of covariates. Second, we offer a simple alternative explanation about the sparsity of SCM from the perspective of parameter space. Third, we conduct a meta-analysis of empirical studies using SCM in the literature, which shows that the sparsity of SCM decreases with the relative number of covariates. A practical implication is that if the number of positive weights exceeds the number of covariates, there are multiple solutions and possibly unstable weights.

Mobile networks expanding to space: Overview of the seranis beyond 5G testbed

In recent years, Non-Terrestrial Networks (NTNs) have gained increased attention from the 3rd Generation Partnership Project (3GPP) due to their potential to enhance cellular networks by improving coverage, resiliency, and reliability, especially in rural areas and disaster scenarios. The upcoming Sixth-Generation (6G) cellular networks aim to establish layers of cells at different altitudes with Base Stations (BSs) on Earth and in space, providing a seamless user experience. Testing and experimentation are crucial for realizing this ambitious vision. University of the Bundeswehr Munich (UniBw M) is deploying a Beyond 5G (B5G) and 6G testbed comprising both space and ground segments. The space segment of the testbed is composed of the ATHENE-1 satellite that is going to be launched in 2025. The ground segment includes the satellite ground station with several full motion antennas for the radiofrequency links and an optical ground station for the free-space optical link based on laser technology, while the Terrestrial Network (TN) component is deployed using a Fifth-Generation (5G) Non-Public Network (NPN) with multiple gNodeBs (gNBs) and multiple 5G core solutions. In its current state, the testbed includes various measurement equipment and emulators in the 5G Lab, a Gnb with two active cells, a core network, a satellite ground station, and a mobile 5G on-the-move solution. This testbed allows various experiments including interference management between existing networks, positioning and localization, Public Protection and Disaster Recovery (PPDR) using Multi-Access Edge Computing (MEC) and NTN. This paper describes the components of the Seamless Radio Access Networks for Internet of Space (SeRANIS) B5G testbed, the current status, future deployment plan, preliminary test results, and planned tests.

Multiple solution of MHD Casson fluid flow in porous channel with chemical reactions and thermal radiation effects

This study focused on evaluating the synergistic effects of magnetohydrodynamics, Casson fluid properties, thermal radiation, chemical reactions, and heat transfer mechanisms within a porous channel. Through the application of similarity transformation, nonlinear governing equations are converted into nonlinear ordinary differential equations. These modified equations were then numerically solved in MATLAB using the Runge–Kutta method alongside the shooting technique to ensure precise results. The investigation yielded various numerical solutions for the dimensionless velocity, temperature, concentration, skin friction coefficient, heat transfer coefficient, and Sherwood number, all of which are presented in both tabular and graphical formats. Three distinct solutions emerged from the analysis, differentiated by variations in the Reynolds number, Casson number, expansion or contraction ratio, and magnetic parameters. These solutions demonstrate differences in the parameters under investigation. Solutions within the ranges of γ[5,∞] and R[31.07,∞] are influenced by the specific values of the magnetic number M[0,2.0]. For each M value, there exists a unique set of solutions for γ and R that satisfy the established parameters. As the magnetic number varies, so does the range of feasible solutions, highlighting the sensitivity of the system to magnetic influence. The values of γ and R are adjusted according to the chosen M value.

Basic Jarimatika is a Multiplication Solution in Learning in the Merdeka Curriculum for Preservice Elementary Teacher

Basic Jarimatika is a Multiplication Solution in Learning in the Merdeka Curriculum for Preservice Elementary Teacher

ELECTRONIC TEST SYSTEM

Abstract : The electronic test system (ETS) will assist in speeding up the process of conducting assessment. Examiner will be able to conduct exams by integrating a set of questions. The questions can be multiple choice questions or text solution to the questions. The methodology will have the potential to do automated processing of the results of assessment based on the question which admin has put into database. The methodology will have brainy capabilities to pick the writing based solutions when not only there is an exact match, but it will also find out same solutions by verifying/scanning the synonyms of the words used in the solution. The ETS methodology engine will also avail us with the manual override specification where the examiner can manually pick up or update the result for an exam. The methodology will present an effortless to use interface for examiner, Candidates and Super Admin. Any person can act as an examiner or candidate. Once logged in, candidate will be able to see the assessments due and can take the assessment.The main aim of online network based Electronic Test System is to effectively form an idea to assess the applicant exhaustively through a fully automatic methodology that not only spares you with a lot of time but also gives speeder and exact conclusions. For Candidates, they give exam according to their comfort from any location by using net and there is no essentiality of using add-ons like pen, papers, etc. Keywords: Examination, Examiner, Candidate, Super Admin. Manual Override, Automated System

Multiple Pole Solutions of the Hirota Equation Under Nonzero Boundary Conditions by Inverse Scattering Method

Multiple Pole Solutions of the Hirota Equation Under Nonzero Boundary Conditions by Inverse Scattering Method

Robust wind farm layout optimization

Wake interactions in wind farms cause losses in annual energy production (AEP) on the order of 10%. Wind farm designers optimize the layout of the farm to mitigate wake losses, especially in the dominant site-specific wind directions. As wind turbines and wind farms grow in scale, optimization becomes more complex. Offshore wind farms regularly comprise more than 100 wind turbines and are characterized by complex boundaries due to shipping lanes, neighboring wind farms, and other constraints.Layout optimization methods are broadly split between gradient-based and gradient-free approaches. Gradient-based approaches can converge quickly and perform well for smaller, academic problems but are often sensitive to initial conditions and tuning parameters and require expert knowledge to use. On the other hand, gradient-free approaches can be more robust to problem complexities. We present a robust layout optimization approach based on a random search algorithm. The algorithm is intended for those who are not optimization experts and has few tuning parameters that need specification to achieve satisfactory results. Unlike off-the-shelf methods, which use generally available, non-domain-specific optimization routines that accept as inputs an optimization function and constraint definitions, this approach takes advantage of the relative computational costs of the different evaluations by evaluating cheaper computations first (boundary and minimum distance constraints) and running expensive AEP evaluations only if all other checks pass. Moreover, an outer genetic algorithm allows multiple solutions to evolve in parallel, enabling rapid solution development on high-performance computers. We discuss the relative ease of selecting necessary tuning parameters and demonstrate the efficacy of the genetic random search on a complex layout problem consisting of placing 70 turbines in a nonconvex and unconnected boundary region.

Bayesian Focal Mechanism Estimation from P-, S-Wave Amplitudes, and Polarities for a Microearthquake Sequence in Irpinia, Italy

ABSTRACT The P-wave peak distribution in azimuth and takeoff angles, corrected for the distance through empirical attenuation laws, can reveal the radiation pattern amplitude of the source (Tarantino et al., 2019). This piece of information, jointly combined with the available polarities and S-wave peak amplitudes, can provide the full focal mechanism, constraining the solution also when only a few seismic station records are available, that is, in the case of microseismicity. We proposed a new technique, named P-, S-wave amplitude, and polarities (P-SAP), designed to compute the focal mechanism by jointly inverting the P-, S-wave amplitude ratios and P-wave polarities in a Bayesian framework and employing the octree strategy (Fang et al., 1996) to explore the space of possible solutions. The outputs are strike, dip, and rake angles of the most likely triplet (principal and auxiliary planes) with the related uncertainties, as well as other multiple solutions, if present. We tested the methodology to synthetic data, and we applied it to a microseismic sequence that occurred in Irpinia region, southern Italy. A background microseismicity occurs in a volume delimited by the faults activated during the 1980 M 6.9 Irpinia earthquake. This faults system is complex and composed of northwest–southeast-striking normal faults along the Apennines chain and an approximately east–west-oriented strike-slip fault, deep-seated in the Potenza area. A network of three-component accelerometers and velocimeters are currently deployed to monitor the area. The major topic of this work is validating the proposed P-SAP methodology for microseismicity studies. We also inferred the optimum stress tensor of the sequence, confirming that the microseismicity is controlled by the regional stress field and can reveal characteristics useful to highlight behaviors of larger-scale seismicity.

Multiplicity of solutions for anisotropic Dirichlet problem with variable exponent

We establish some results on the existence of multiple nontrivial solutions for a general anisotropic elliptic equations. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces,combined with adequate variational methods and a variant of the Mountain Pass lemma.

Infinitely degenerate slowly rotating solutions in f(R) gravity

This work tests the no-hair conjecture in f(R) gravity models. No-hair conjecture asserts that all black holes in general relativity coupled to any matter must be Kerr–Newman type. However, the conjecture fails in some cases with non-linear matter sources. Here, we address this by explicitly constructing multiple slow-rotating black hole solutions, up to second order in rotational parameter, for a class of f(R) models ( f(R)=(α0+α1R)p,p>1 ). Such an f(R) includes all higher-powers of R. We analytically show that multiple vacuum solutions satisfy the field equations up to the second order in the rotational parameter. In other words, we show that the multiple vacuum solutions depend on arbitrary constants, which depend on the coupling parameters of the model. Hence, our results indicate that the no-hair theorem for modified gravity theories merits extending to include the coupling constants. The uniqueness of our result stems from the fact that these are obtained directly from metric formalism without conformal transformation. We discuss the kinematical properties of these black hole solutions and compare them with slow-rotating Kerr. Specifically, we show that the circular orbits for the black holes in f(R) are smaller than that of Kerr. This implies that the inner-most stable circular orbit for black holes in f(R) is smaller than Kerr’s; hence, the shadow radius might also be smaller. Finally, we discuss the implications of our results for future observations.

Hartmann Flow of Two-Layered Fluids in Horizontal and Inclined Channels

The effect of a transverse magnetic field on two-phase stratified flow in horizontal and inclined channels is studied. The lower heavier phase is assumed to be an electrical conductor (e.g., liquid metal), while the upper lighter phase is fully dielectric (e.g., gas). The flow is defined by prescribed flow rates in each phase, so the unknown frictional pressure gradient and location of the interface separating the phases (holdup) are found as part of the whole solution. It is shown that the solution of such a two-phase Hartmann flow is determined by four dimensionless parameters: the phases’ viscosity and flow-rate ratios, the inclination parameter, and the Hartmann number. The changes in velocity profiles, holdups, and pressure gradients with variations in the magnetic field and the phases’ flow-rate ratio are reported. The potential lubrication effect of the gas layer and pumping power reduction are found to be limited to low magnetic field strength. The effect of the magnetic field strength on the possibility of obtaining countercurrent flow and multiple flow states in concurrent upward and downward flows, and the associated flow characteristics, such as velocity profiles, back-flow phenomena, and pressure gradient, are explored. It is shown that increasing the magnetic field strength reduces the flow-rate range for which multiple solutions are obtained in concurrent flows and the flow-rate range where countercurrent flow is feasible.

Addressing Vulnerabilities in CAN-FD: An Exploration and Security Enhancement Approach

The rapid advancement of technology, alongside state-of-the-art techniques is at an all-time high. However, this unprecedented growth of technological prowess also brings forth potential threats, as oftentimes the security encompassing these technologies is imperfect. Particularly within the automobile industry, the recent strides in technology have brought about increased complexity. A notable flaw lies in the CAN-FD protocol, which lacks robust security measures, making it vulnerable to data theft, injection, replay, and flood data attacks. With the rising complexity of in-vehicular networks and the widespread adoption of CAN-FD, the imperative to safeguard the protocol has never been more crucial. This paper aims to provide a comprehensive review of the existing in-vehicle communication protocol, CAN-FD. It explores existing security approaches designed to fortify CAN-FD, demonstrating multiple multi-layer solutions that leverage modern techniques including Physical Unclonable Function (PUF), Elliptical Curve Cryptography (ECC), Ethereum Blockchain, and Smart contracts. The paper highlights existing multi-layer security measures that offer minimal overhead, optimal performance, and robust security. Moreover, it identifies areas where these security measures fall short and discusses ongoing research along with suggestions for implementing software and hardware-level modifications. These proposed changes aim to streamline complexity, reduce overhead while ensuring forward compatibility. In essence, the methods outlined in this study are poised to excel in real-world applications, offering robust protection for the evolving landscape of in-vehicular communication systems.

Design of 1450-1500nm Bismuth-doped Fiber Laser

With the rapid development of information technology, people's demand for the transmission capacity of fiber optic communication networks is increasing. How to broaden the bandwidth of communication systems has become one of the key issues in the field of communication. Researchers have found that the operating bandwidth of amplifiers mainly limits the bandwidth of communication systems. Although multiple solutions have been proposed and implemented to address this issue, there are still many gaps in the design of full-band multi wavelength-related light sources. By studying the three-level system of bismuth ions, the rate equation and power transfer equation of a bismuth ion doped fiber laser are simulated, and the pump power threshold and output power are calculated. Using MATLAB for simulation experiments, the relationship between laser power and pump power, as well as their variation with propagation distance, were ultimately obtained. The simulation results show that under 830 pump lights, the pump light threshold power is 10W. After reaching the threshold power, the pump light power and laser power have a linear relationship, and as the propagation distance increases, the pump light power gradually decreases and the laser power gradually increases. The analysis shows that the power generated by the signal light in this band meets the theoretical standards, which verifies the correctness of the scheme.

Impact of aeolian erosion on dust evolution in protoplanetary discs

Context. Many barriers prevent dust from forming planetesimals via coagulation in protoplanetary discs, such as bouncing, collisional fragmentation, or aeolian erosion. Modelling dust and the different phenomena that can alter its evolution is therefore necessary. Multiple solutions have been proposed, but they still need to be confirmed. Aims. In this paper, we explore the role that aeolian erosion plays in the evolution of dust. Methods. We used a mono-disperse model to account for dust growth and fragmentation, implemented in a 1D code to compute the evolution of single grains and in a 3D smoothed particle hydrodynamics (SPH) code to compute the global evolution of dust and gas. We tested the erosion model in our code and ensured it matched previous results. Results. With a disc model that reproduces observations, we show with both 1D and 3D studies that erosion is not significant during the evolution of dust when we take fragmentation into consideration. With a low-viscosity disc, fragmentation is less of a problem, but grain growth is also less important, which prevents the formation of large objects. In dust traps, close to the star, erosion is also not impactful, even when fragmentation is turned off. Conclusions. We show in this paper that aeolian erosion is negligible when radial drift, fragmentation, and dust traps are taken into account and that it does not alter the dust evolution in the disc. However, it can have an impact on later stages, when the streaming instability forms large clumps close to the star, or when planetesimals are captured.

Understanding Muslim frontline employees’ perceived religious discrimination and emotional exhaustion

PurposeThis study aims to investigate the impact of perceived subtle and overt discrimination on employees’ emotional exhaustion, along with potential mitigating factors such as social support, organizational inclusion and religiosity.Design/methodology/approachThe research is based on a sample of 359 Muslim employees working in US restaurants. The data are analyzed using fuzzy-set Qualitative Comparative Techniques.FindingsThe results reveal that high/low emotional exhaustion in tourism and hospitality sector is triggered by multiple combinations of high/low levels of subtle and overt discrimination, family and friends support and religiosity. Such findings hold important implications to both theory and practice.Research limitations/implicationsBy using fuzzy-set Qualitative Comparative Analysis, this research stands out from studies on discrimination that use conventional statistical methods. It proposes several solutions leading to a single outcome (high/low emotional exhaustion). This new approach contributes to the advancement of theory in this context.Practical implicationsThis study shows that there is no single best solution for high/low emotional exhaustion. Stated differently, multiple solutions provide several ways for firms to mitigate employees’ emotional exhaustion.Originality/valueReligious discrimination in workplaces is increasing at an alarming rate, particularly in customer facing roles, such as the tourism and hospitality industry. This is having detrimental effects on employees from minority groups, often leading to excessive levels of emotional exhaustion. Nonetheless, the extant literature has somewhat understated the consequences of this issue, creating a void that needs to be fulfilled. This study addresses this gap.

An Adaptive Orthogonal Basis Method for Computing Multiple Solutions of Differential Equations with Polynomial Nonlinearities

An Adaptive Orthogonal Basis Method for Computing Multiple Solutions of Differential Equations with Polynomial Nonlinearities

Two-phase numerical simulation of thermal and solutal transport of zero mass flux conditions over a porous deformable disc: The extension of Jeffrey-Hamel model

In recent times, numerous assertions on the thermophysical properties of nanoliquids in various flow regimes, particularly the laminar flow regimes have been documented in the literature. With this focus, this theoretical investigation is to explore multiple solutions of the laminar two-dimensional Jeffrey fluid describing the Buongiorno nanofluid model and features of heat transport near a stagnation point across a movable radial disc. Also, the study seeks to explore the effects of zero mass flux and velocity of mass transpiration embedded within a Jeffrey fluid. With the help of the ansatz similarity transformations, the study simplifies complex partial differential equations into a set of ordinary differential equations, facilitating numerical dual solutions employing the bvp4c solver. The multiple solutions become apparent in a specific range of the shrinkable parameter. The results of the present study show that the suction parameter intensifies the phenomena of friction factor in the upper solution, whereas an annulment trend is observed in the lower solution. In addition, the shear stress and heat transfer rate decline with higher impacts of the Deborah number for the first solution while a monotonical behaviour is seen for the second solution. Besides, the absolute critical value decreases owing to the change value of the Deborah number, as a result, the separation of the boundary layer accelerates. Moreover, the heat transfer rate declined by about 0.29%, 0.37%, and 0.28% for the FBS and 0.30%, 0.32%, and 0.28% for the SBS with larger values of Nta, Nba and Sca, respectively. Lastly, the outcomes of the present examination with existing data are an excellent match for the limiting cases.