Uniqueness Of Results Research Articles

Non-linear biphasic mixture model: Existence and uniqueness results

Abstract This paper is concerned with the development and analysis of a mathematical model that is motivated by interstitial hydrodynamics and tissue deformation mechanics (poro-elasto-hydrodynamics) within an in-vitro solid tumour. The classical mixture theory is adopted for mass and momentum balance equations for a two-phase system. A main contribution of this study is we treat the physiological transport parameter (i.e., hydraulic resistivity) as anisotropic and heterogeneous, thus the governing system is strongly coupled and non-linear. We derived a weak formulation and then formulated the equivalent fixed-point problem. This enabled us to use the Galerkin method, and the classical results on monotone operators combined with the well-known Schauder and Banach fixed-point theorems to prove the existence and uniqueness of results.

New frame of fractional neutral ABC-derivative with IBC and mixed delay

In this manuscript, we describe fractional differential equations with neutral, integral boundary conditions and mixed delay using Atangana–Baleanu derivatives, which include the generalized Mittag-Leffler kernel. We determine the existence and uniqueness of results and analysis by fixed point method. Moreover, we explained the stability of the fractional differential equation in the frame of Ulam–Hyers. Then, we investigate an example with various values and illustrate the outcomes graphically.

Analysis of Existence and Stability Results for Impulsive Fractional Integro-Differential Equations Involving the Atangana–Baleanu–Caputo Derivative under Integral Boundary Conditions

In this study, we consider the existence results of solutions of impulsive Atangana–Baleanu–Caputo A B C fractional integro-differential equations with integral boundary conditions. Krasnoselskii’s fixed-point theorem and the Banach contraction principle are used to prove the existence and uniqueness of results. Moreover, we also establish Hyers–Ulam stability for this problem. An example is also presented at the end.

Indirect health monitoring of bridges using Tikhonov regularization scheme and signal averaging technique

This paper presents a novel damage identification technique for bridges based on the dynamic response of a moving vehicle. A quarter car vehicle model instrumented with two accelerometers and an inertial profilometer is used for this purpose. The method involves the coupling of Tikhonov regularization scheme with signal averaging technique to handle the problem of measurement noise and road roughness. In the first stage, a damage-dependent road roughness profile is estimated from measured acceleration response by minimizing a Tikhonov regularized least squares cost function. The second stage involves the minimization of the profile roughness residual function that depends on the location and magnitude of damage. This objective function compares the roughness profile computed from the first stage and that measured by the inertial profilometer. It is proved that efficient damage detection ensues from considering multiple runs of the vehicle and choosing the appropriate regularization parameter. The present study considers various aspects, such as the uniqueness of results, robustness of results to measurement noise, effect of modelling error, effect of vehicle speed, and uncertainty in estimation. Numerical results show that the approach is capable of detecting the magnitude as well as the location of damage. In addition, the problem of road roughness and measurement noise is handled competently.

Self-promotion and the need to be first in science

Scientists, like all humans, are subject to self-deceptive valuations of their importance and profile. Vainglorious practice is annoying but mostly harmless when restricted to an individual’s perception of self-worth. Language that can be associated with self-promotion and aggrandizement is destructive when incorporated into scientific writing. So too is any practice that oversells the novelty of research or fails to provide sufficient scholarship on the uniqueness of results. We evaluated whether such tendencies have been increasing over time by assessing the frequencies of articles claiming to be “the first”, and those that placed the requirement for scholarship on readers by using phrases such as “to the best of our knowledge”. Our survey of titles and abstracts of 176 journals in ecology and environmental biology revealed that the frequencies of both practices increased linearly over the past half century. We thus warn readers, journal editors, and granting agencies to use caution when assessing the claimed novelty of research contributions. A system-wide reform toward more cooperative science that values humility, and abhors hubris, might help to rectify the problem.

EXISTENCE AND STABILITY ANALYSIS OF SOLUTIONS FOR FRACTIONAL LANGEVIN EQUATION WITH NONLOCAL INTEGRAL AND ANTI-PERIODIC-TYPE BOUNDARY CONDITIONS

In this paper, we deal with the existence and uniqueness (EU) of solutions for nonlinear Langevin fractional differential equations (FDE) having fractional derivative of different orders with nonlocal integral and anti-periodic-type boundary conditions. Also, we investigate the Hyres–Ulam (HU) stability of solutions. The existence result is derived by applying Krasnoselskii’s fixed point theorem and the uniqueness of result is established by applying Banach contraction mapping principle. An example is offered to ensure the validity of our obtained results.

The effect of terror and economic sector in early career years on future career path

The study uses the deterioration of security situation in Israel (the “Intifada”) to investigate the uniqueness of results obtained previously in regard to Israel’s security-guard industry, as against other economic sectors, in regard to the employment stability and its implications for future career path. The findings emphasize the negative effect of a person’s mere presence in the labor market during the Intifada on his career path, irrespective of the industry in which he worked. They emphasize the variance attributed to the economic sector in which people hold their first job on their future employment career, as well as the variance attributed to working as a security guard during the Intifada, with the upturn in terror associated with it. The findings stress the role that policymakers should play for minimizing possible adverse effects on the earning trajectory and labor-market attachment of employed persons at a time of declining security and the emphasis and attention that should be given to persons employed in the security-guard industry at any time—due to the inferiority of permanent employment patterns in this industry in contrast to other industries—to minimize possible impairment to their earning trajectory and assure their long-term attachment to the labor market.

Authalic Parameterization of General Surfaces Using Lie Advection

Parameterization of complex surfaces constitutes a major means of visualizing highly convoluted geometric structures as well as other properties associated with the surface. It also enables users with the ability to navigate, orient, and focus on regions of interest within a global view and overcome the occlusions to inner concavities. In this paper, we propose a novel area-preserving surface parameterization method which is rigorous in theory, moderate in computation, yet easily extendable to surfaces of non-disc and closed-boundary topologies. Starting from the distortion induced by an initial parameterization, an area restoring diffeomorphic flow is constructed as a Lie advection of differential 2-forms along the manifold, which yields equality of the area elements between the domain and the original surface at its final state. Existence and uniqueness of result are assured through an analytical derivation. Based upon a triangulated surface representation, we also present an efficient algorithm in line with discrete differential modeling. As an exemplar application, the utilization of this method for the effective visualization of brain cortical imaging modalities is presented. Compared with conformal methods, our method can reveal more subtle surface patterns in a quantitative manner. It, therefore, provides a competitive alternative to the existing parameterization techniques for better surface-based analysis in various scenarios.