Conditions For Uniqueness Research Articles

Viscoelastic Kelvin–Voigt model on Ulam–Hyer’s stability and T-controllability for a coupled integro fractional stochastic systems with integral boundary conditions via integral contractors

We discuss the existence, uniqueness, Ulam–Hyer’s stability, and Trajectory (T-) controllability for solutions of coupled nonlinear fractional order stochastic differential systems (FSDEs) with integral boundary conditions via integral contractors. Using Banach space, we obtain some relaxed conditions for existence and uniqueness for the mentioned problem via successive approximation techniques. Furthermore, to demonstrate the results, the concept of bounded integral contractors is combined with a fractional order coupled system using regularity conditions. The Green’s function is used to find the solution for the coupled system with boundary conditions. Through Integral Contractors (ICs), we examine the existence and uniqueness results for a higher-order nonlinear fractional coupled stochastic system with integral boundary conditions on Time Scales. Further, we develop some conditions for Ulam–Hyer’s stability for the non-linear fractional order coupled systems. To demonstrate our main result, we provide a proper example. The real-life application of a coupled fractional stochastic Kelvin–Voigt model on viscoelastic elastomer is investigated to justify the theoretical model with the numerical comparison with a single and a double fractional stochastic Kelvin–Voigt model.

Performance study of fin structure in air-cooled thermal management system for column power battery

The Battery Thermal Management System (BTMS) is pivotal in regulating the temperature and prolonging the lifespan of battery packs. This paper introduces an innovative BTMS design that simultaneously addresses thermal regulation and mitigates the risk of thermal runaway spread. Unlike traditional air-cooled systems, which are tailored for a singular operational condition, our proposed design features a novel approach with annular fins of varying lengths attached to a single battery sleeve, enhancing the conventional air-cooling mechanism for batteries. Simulation outcomes reveal that the integration of these non-uniform notched annular fins significantly lowers the maximum temperature of the battery pack by 2.20 °C, 2.17 °C, 2.01 °C, and 1.91 °C, under various conditions, and decreases the maximum temperature disparity to 82.38 %, 74.32 %, 72.97 %, 70.54 % of its initial value across different thermal management scenarios, discharge rates of 2C, and inlet wind velocities of 1 m/s, 1.5 m/s,2 m/s, 2.5 m/s. This method not only efficiently reduces the peak temperature and the temperature variance within the battery pack under thermal management conditions but also acts as a deterrent against the spread of thermal runaway among adjacent cells during extreme conditions.

Unspecified asthma, childhood-onset, and adult-onset asthma have different causal genes: a Mendelian randomization analysis.

Asthma is a heterogeneous condition that is characterized by reversible airway obstruction. Childhood-onset asthma (COA) and adult-onset asthma (AOA) are two prominent asthma subtypes, each with unique etiological factors and prognosis, which suggests the existence of both shared and distinct risk factors. Here, we employed a two-sample Mendelian randomization analysis to elucidate the causal association between genes within lung and whole-blood-specific gene regulatory networks (GRNs) and the development of unspecified asthma, COA, and AOA using the Wald ratio method. Lung and whole blood-specific GRNs, encompassing spatial eQTLs (instrumental variables) and their target genes (exposures), were utilized as exposure data. Genome-wide association studies for unspecified asthma, COA, and AOA were used as outcome data in this investigation. We identified 101 genes that were causally linked to unspecified asthma, 39 genes causally associated with COA, and ten genes causally associated with AOA. Among the identified genes, 29 were shared across some, or all of the asthma subtypes. Of the identified causal genes, ORMDL3 had the strongest causal association with both unspecified asthma (OR: 1.49; 95% CI:1.42-1.57; p=7.30x10-51) and COA (OR: 3.37; 95% CI: 3.02-3.76; p=1.95x10-102), whereas PEBP1P3 had the strongest causal association with AOA (OR: 1.28; 95% CI: 1.16-1.41; p=0.007). This study identified shared and unique genetic factors causally associated with different asthma subtypes. In so doing, our study emphasizes the need to move beyond perceiving asthma as a singular condition to enable the development of therapeutic interventions that target sub-type specific causal genes.

Overview of Tensor-Based Cooperative MIMO Communication Systems-Part 2: Semi-Blind Receivers.

Cooperative MIMO communication systems play an important role in the development of future sixth-generation (6G) wireless systems incorporating new technologies such as massive MIMO relay systems, dual-polarized antenna arrays, millimeter-wave communications, and, more recently, communications assisted using intelligent reflecting surfaces (IRSs), and unmanned aerial vehicles (UAVs). In a companion paper, we provided an overview of cooperative communication systems from a tensor modeling perspective. The objective of the present paper is to provide a comprehensive tutorial on semi-blind receivers for MIMO one-way two-hop relay systems, allowing the joint estimation of transmitted symbols and individual communication channels with only a few pilot symbols. After a reminder of some tensor prerequisites, we present an overview of tensor models, with a detailed, unified, and original description of two classes of tensor decomposition frequently used in the design of relay systems, namely nested CPD/PARAFAC and nested Tucker decomposition (TD). Some new variants of nested models are introduced. Uniqueness and identifiability conditions, depending on the algorithm used to estimate the parameters of these models, are established. Two families of algorithms are presented: iterative algorithms based on alternating least squares (ALS) and closed-form solutions using Khatri-Rao and Kronecker factorization methods, which consist of SVD-based rank-one matrix or tensor approximations. In a second part of the paper, the overview of cooperative communication systems is completed before presenting several two-hop relay systems using different codings and configurations in terms of relaying protocol (AF/DF) and channel modeling. The aim of this presentation is firstly to show how these choices lead to different nested tensor models for the signals received at destination. Then, by capitalizing on these models and their correspondence with the generic models studied in the first part, we derive semi-blind receivers to jointly estimate the transmitted symbols and the individual communication channels for each relay system considered. In a third part, extensive Monte Carlo simulation results are presented to compare the performance of relay systems and associated semi-blind receivers in terms of the symbol error rate (SER) and channel estimate normalized mean-square error (NMSE). Their computation time is also compared. Finally, some perspectives are drawn for future research work.

Nonlinear Model for LTB Prediction of RHS Beams Under Combined Axial and Bending Loads With Distortional Deformation Allowed

ABSTRACTThe aim of the present study is to develop an efficient and accurate analytical model for the lateral torsional buckling (LTB) prediction of RHS beams. To this end, a coherent nonlinear geometric theory is formulated assuming large torsion angles. This theory is based on a new kinematic model that incorporates the distortion deformations in addition to the bending and torsion ones. Ritz's method is employed to discretize the governing equilibrium equations basing on trigonometric shape functions, and then the eigenvalue problem is defined according to the fundamental state. The Buckling loads are obtained by imposing the singularity condition of the tangential stiffness matrix. The numerical investigation is carried out to prove the accuracy of the proposed model in LTB load evaluation, when compared with the nonlinear shell finite element simulation using Abaqus software. The numerical results reveal that the classical linear models associated with moderate torsion angles, such as those provided by Generalized Beam Theory (GBT) and the classical eigenvalue shell finite element method, tend to underestimate the correct value of LTB loads of simply supported RHS beams. In accordance with linear and non‐linear models, the numerical study is focused on the impact of load height, intensity of introduced compressive load and section ratio b/h in the LTB loads prediction.

Riemann–Hilbert problem and soliton solutions with their asymptotic analysis for the focusing nonlocal Hirota equation with step-like initial data

The Riemann–Hilbert (RH) problem is developed to study the Cauchy problem of focusing space symmetric nonlocal Hirota (fsNH) equation with step-like initial data. Firstly, we analyze the characteristics of the Jost solutions and spectral functions, including analyticity, symmetry, and asymptotics as k→∞ and k→0. Then, we discuss three cases of zero point distributions of the spectral functions, and derive the expressions of spectral functions by constructing the special analytic functions and establishing the scalar RH problem. Furthermore, the constraint relations among the zeros of the spectral functions are analyzed. Next, the corresponding RH problem equipped with residual and singularity conditions is successfully derived. These singularity conditions are then transformed into a general residue condition, which reduces the problem of solving the RH problem with reflection-less potential to solving a system of algebraic equations. Ultimately, the corresponding soliton solutions of the fsNH equation and their asymptotics are derived from the solution of the RH problem.

Mathematical Evaluation and Dynamic Transmissions of a Tumor Growth Model Using a Generalized Singular and Non-Local Kernel

Currently, fractional calculus plays a critical role in improving control techniques, analyzing disease transmission dynamics, and solving several other real-world problems. This research investigates the time-fractional tumor growth model using an innovative approach. The new modified fractional derivative operator employs a singular and non-local kernel, based on Atangana and Baleanu's concepts with the Caputo derivative. The tumor growth model used the newly modified fractional operator, which provided numerical simulation. With the introduction of this new operator, we provide significant analysis for the tumor growth epidemic model. We have proven the uniqueness and stability conditions of the model by utilizing Banach's fixed point theory and the Picard successive approximation method. Using the Laplace-Adomian decomposition method (LADM), we found the numerical solution to the Modified Atangana-Baleanu-Caputo derivative model. We have verified the convergence analysis of the suggested scheme. We ultimately utilize the suggested method to obtain numeric outcomes and simulations for the tumor growth model. The study investigates the effect of multiple biological variables on the transmission of tumor growth dynamics.

Spatial Equilibria: The Case of Two Regions

In this paper we characterize the set of equilibria in a generalized version of the canonical two-region economic geography model that nests the class of models in Allen and Arkolakis (2014) as well as Krugman (1991) and features an input–output loop. We provide sufficient conditions for uniqueness of equilibria that — in contrast to the well-know result in Allen and Arkolakis (2014) — allow for positive agglomeration externalities, which concentrate economic activity, even in the absence of congestion effects, which disperse it, and highlight the key role played by three additional parameters: the trade elasticity, which regulates the strength of the dispersion force associated with the decline in the terms of trade caused by migration into a region; trade costs, which weaken this dispersion force by limiting trade across regions; and the importance of the agricultural sector, which pushes against agglomeration forces in manufacturing.

Characterization of transport optimizers via graphs and applications to Stackelberg–Cournot–Nash equilibria

AbstractWe introduce graphs associated to transport problems between discrete marginals, that allow to characterize the set of all optimizers given one primal optimizer. In particular, we establish that connectivity of those graphs is a necessary and sufficient condition for uniqueness of the dual optimizers. Moreover, we provide an algorithm that can efficiently compute the dual optimizer that is the limit, as the regularization parameter goes to zero, of the dual entropic optimizers. Our results find an application in a Stackelberg–Cournot–Nash game, for which we obtain existence and characterization of the equilibria.

Modified F(R,T2)-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry

In the present research note, we discuss the energy–momentum squared gravity model F(R,T2) coupled with perfect fluid. We obtain the equation of state for the perfect fluid in the F(R,T2)-gravity model. Furthermore, we deal with the energy–momentum squared gravity model F(R,T2) coupled with perfect fluid, which admits the hyperbolic Ricci solitons with a conformal vector field. We provide a clue in this series to determine the density and pressure in the radiation and phantom barrier periods, respectively. Also, we investigate the rate of change in hyperbolic Ricci solitons within the same vector field. In addition, we determine the different energy conditions, black holes and singularity conditions for perfect fluid attached to F(R,T2)-gravity in terms of hyperbolic Ricci solitons. Lastly, we deduce the Schrödinger equation for the potential Un with hyperbolic Ricci solitons in the F(R,T2)-gravity model coupled with perfect fluid and a phantom barrier.

A hypergraph on modules and singularity condition

A hypergraph on modules and singularity condition

Witte’s conditions for uniqueness of solutions to a class of Fractal-Fractional ordinary differential equations

In this paper, Witte's conditions for the uniqueness solution of nonlinear differential equations with integer and non-integer order derivatives are investigated. We present a detailed analysis of the uniqueness solutions of four classes of nonlinear differential equations with nonlocal operators. These classes include classical and fractional ordinary differential equations in fractal calculus. For each case, theorems and lemmas and their proofs are presented in detail.

Classical echoes of quantum boundary conditions

Abstract We consider a non-relativistic particle in a one-dimensional box with all possible quantum boundary conditions that make the kinetic-energy operator self-adjoint. We determine the Wigner functions of the corresponding eigenfunctions and analyze in detail their classical limit, governed by their behavior in the high-energy regime. We show that the quantum boundary conditions split into two classes: all local and regular boundary conditions collapse to the same classical boundary condition, while a dependence on singular non-local boundary conditions persists in the classical limit.

Interest rate dynamics and commodity prices

In economic studies and popular media, interest rates are routinely cited as a major factor behind commodity price fluctuations. At the same time, the transmission channels are far from transparent, leading to long-running debates on the sign and magnitude of interest rate effects. Purely empirical studies struggle to address these issues because of the complex interactions between interest rates, prices, supply changes, and aggregate demand. To move this debate to a solid footing, we extend the competitive storage model to include stochastically evolving interest rates. We establish general conditions for existence and uniqueness of solutions and provide a systematic theoretical and quantitative analysis of the interactions between interest rates and prices.

Uniqueness and Non-Uniqueness Results for Spacetime Extensions

Abstract Given a function $f: A \to{\mathbb{R}}^{n}$ of a certain regularity defined on some open subset $A \subseteq{\mathbb{R}}^{m}$, it is a classical problem of analysis to investigate whether the function can be extended to all of ${\mathbb{R}}^{m}$ in a certain regularity class. If an extension exists and is continuous, then certainly it is uniquely determined on the closure of $A$. A similar problem arises in general relativity for Lorentzian manifolds instead of functions on ${\mathbb{R}}^{m}$. It is well-known, however, that even if the extension of a Lorentzian manifold $(M,g)$ is analytic, various choices are in general possible at the boundary. This paper establishes a uniqueness condition for extensions of globally hyperbolic Lorentzian manifolds $(M,g)$ with a focus on low regularities: any two extensions that are anchored by an inextendible causal curve $\gamma : [-1,0) \to M$ in the sense that $\gamma $ has limit points in both extensions must agree locally around those limit points on the boundary as long as the extensions are at least locally Lipschitz continuous. We also show that this is sharp: anchored extensions that are only Hölder continuous do in general not enjoy this local uniqueness result.

The performance relationship between the EQ-5D-5L composite “Anxiety/Depression” dimension and anxiety and depression symptoms in a large, general population sample

PurposeThis cross-sectional study aims to understand the relationship between responses on the Anxiety/Depression (A/D) dimension of the EQ-5D-5L and symptoms of anxiety and depression on the GAD-7 and PHQ-9 instruments. In doing so, we investigate the comparative performance of the dimension between diagnostic groups (i.e. anxiety (GAD-7); depression (PHQ-9); anxiety & depression versus none). We additionally investigate the discriminatory performance between sub-populations based on gender, age, education and self-reported chronic conditions.Methods19,902 general population participants completed a health survey in May/June 2020, from five European countries and the United States. Performance of A/D was calculated using the Area Under the Receiver Operating Characteristic curve (AUROC), and was compared to having anxiety (GAD-7 ≥ 8), depression (PHQ-9 ≥ 10) and both versus none for the total population and sub-populations. Several additional sensitivity analyses were conducted, including calculations of the optimal A/D cut-off.ResultsThe performance in the total sample was good (AUROC > 0.8) and did not differ significantly between diagnostic groups. The performance differed significantly between the age groups, with worse performance in the younger groups, and differed between those with a singular chronic condition, with worse performance in those indicating having an anxiety or depression disorder. The performance did not differ significantly by gender, education, nor total chronic conditions.ConclusionThe A/D dimension captures symptoms of anxiety, depression or both equally well. Performance is worse in the younger population. Interpretation in those with a self-reported anxiety or depression disorder should be further investigated. This is the first-of-its-kind large population sample performance analysis, where we present evidence that the performance of the A/D dimension differs between ages, and thus intra-age comparative results may be flawed.

Identifying physiological indicators of the cognitive, thermal, and combined (cognitive-thermal) stress conditions.

Physiologically based stress detection systems have proven to be effective in identifying different stress conditions in the body to determine the source of stress and be able to counteract it. However, some stress conditions have not been widely studied, including thermal stress, cognitive stress, and combined (thermal-cognitive) stress conditions, which are frequently encountered in work or school environments. In order to develop systems to detect and differentiate these conditions, it is necessary to identify the physiological indicators that characterize each of them. The present research aims to identify which physiological indicators (heart rate, respiratory rate, galvanic skin response, and local temperature) could differentiate different stress conditions (no-stress, cognitive stress, thermal stress, and combined (thermal-cognitive) stress conditions). Thirty participants were exposed to cognitive, thermal, and combined stress sources while recording their physiological signals. The findings indicate that both mean heart rate and mean galvanic skin response identify moderate thermal and cognitive stress conditions as distinct from a no-stress condition, yet they do not differentiate between the two stress conditions. Additionally, heart rate uniquely identifies the cognitive-thermal stress condition, effectively distinguishing this combined stress condition from the singular stress conditions and the no-stress condition. Mean local temperature specifically signals thermal stress conditions, whereas mean respiratory rate accurately identifies cognitive stress conditions, with both indicators effectively separating these conditions from each other and from the no-stress condition. This is the first basis for differentiating thermal and cognitive stress conditions through physiological indicators.

Hierarchical attitude stabilization controller design and analysis for underactuated spacecraft on SO(3)

In this paper, the complete attitude stabilization of underactuated spacecraft with two parallel single gimbal control moment gyroscopes (SGCMGs) is explored on 3-dimensional special orthogonal group (SO(3)) and its corresponding Lie algebra (so(3)). Instead of assumption on zero total angular momentum in existing article, a less conservative criterion is adopted to ensure system controllability, which does not simplify system dynamics. On the kinematic level, an ideal controller is proposed to globally stabilize attitude without singular initial condition and stagnation behavior. Besides, the ideal kinematic controller is developed on so(3), which avoids singularity or unwinding phenomenon caused by other attitude parameters. On the dynamic level, a hierarchical controller consisting of two parts is proposed. The high-level sliding mode part enforces finite time stabilization of angular velocity about underactuated axis while the low-level part tracks ideal angular velocity commands about actuated axes. A rigorous proof of the whole dynamic-kinematic system that has not been explored before is given. Analysis of hierarchical control from the perspective of linear algebra provides a novel insight into controller design for underactuated systems. Furthermore, the paradigm of controller design which is applicable to other underactuated systems is derived. Simulation results validate the effectiveness of the proposed control logic.

Construction of mathematical models of thermal conductivity for modern electronic devices with elements of a layered structure

This paper considers a heat conduction process for isotropic layered media with internal thermal heating. As a result of the heterogeneity of environments, significant temperature gradients arise as a result of the thermal load. In order to establish the temperature regimes for the effective operation of electronic devices, linear and non-linear mathematical models for determining the temperature field have been constructed, which would make it possible to further analyze the temperature regimes in these heat-active environments. The coefficient of thermal conductivity for the above structures was represented as a whole using asymmetric unit functions. As a result, the conditions of ideal thermal contact were automatically fulfilled on the surfaces of the conjugation of the layers. This leads to solving one heat conduction equation with discontinuous and singular coefficients and boundary conditions at the boundary surfaces of the medium. For linearization of nonlinear boundary value problems, linearizing functions were introduced. Analytical solutions to both linear and nonlinear boundary value problems were derived in a closed form. For heat-sensitive environments, as an example, the linear dependence of the coefficient of thermal conductivity of structural materials on temperature, which is often observed when solving many practical problems, was chosen. As a result, analytical relations for determining the temperature distribution in these environments were obtained. Based on this, a numerical experiment was performed, and it was geometrically represented depending on the spatial coordinates. This proves that the constructed linear and nonlinear mathematical models testify to their adequacy to the real physical process. They make it possible to analyze heat-active media regarding their thermal resistance. As a result, it becomes possible to increase it and protect it from overheating, which can cause the destruction of not only individual nodes and their elements but also the entire structure

Solution of Fuzzy System of Linear Equation Under Different Fuzzy Difference Ideology

In this article, we solve fuzzy system of linear equations under Hukuhara difference and generalized Hukuhara difference using analytical technique. We also give necessary condition for existence and uniqueness of the fuzzy solution of system in parametric form. Under this proposed concept, nonnegativity of parameters is also taken care. Lastly, a numerical illustration is solved under both differences and graphically displayed.