Current Issue : April-June Volume : 2025 Issue Number : 2 Articles : 5 Articles
In this paper, we provide an asymptotic analysis of a nonlocal reaction-diffusion equation and with a non-local stable operator of order 0,1 . Firstly, we prove the existence and uniqueness of positive and bounded solutions for the stationary equation. Finally, we perform a long time-long range scaling in order to prove that the stable state invades the unstable state with a speed which is exponential in time....
The possibility of developing a complete graph invariant computable in polynomial time remains an open question. Consequently, creating efficient algorithms to verify non-isomorphism, including heuristic approaches, is essential. Effective implementation of these heuristics necessitates both the adaptation of existing graph invariants and the invention of novel ones, which continues to be a relevant challenge. Numerous current invariants are capable of distinguishing a significant number of graphs rapidly in real-time scenarios. In this study, we present an invariant tailored for tournaments, a specific class of directed graphs. Tournaments are particularly intriguing because the count of distinct tournaments for a given number of vertices aligns with that of undirected graphs of the same size. The introduced invariant evaluates all possible tournament subsets derived from the original digraph that share the identical arc set. For each subset tournament, standard rankings are computed and aggregated to produce the final vertex scores, which serve as the new invariant. Our analysis indicates that this newly proposed invariant diverges from the most straightforward tournament invariant, which typically assigns scores to each participant. Preliminary computational tests demonstrate that the minimal correlation between the sequences generated by these two invariants occurs at a vertex count of 15....
Transmission disequilibrium tests (TDT) is a well-known case-parents familybased method to detect the association between genetic polymorphisms and a disease phenotype. Various extensions of the TDT have been developed and widely applied in medical research. In this article, we introduced a simple simulation algorithm based on a transition model to generate general nuclear families rather than trios to simulate multiple tightly linked markers. The simulations show that the empirical distributions of the test statistics coincide with the expected distribution under the null hypothesis....
We prove in dimension d = 1 a result similar to a classical paper by Soffer andWeinstein, Jour. Diff. Eq. 98 (1992), improving it by encompassing for pure power nonlinearities the whole range of exponents p > 1. The proof is based on the virial inequality of Kowalczyk et al., J. Eur. Math. Soc. (JEMS) 24 (2022), with smoothing estimates as shown in Mizumachi J. Math. Kyoto Univ. 48 (2008)....
The behavior of objects in motion is described by the equations of motion, which are basic concepts in mathematical physics. These equations are useful in explaining how forces and torques cause body components to move around a joint when applied to joint movement, especially in biomechanics. In the orthopedic industries, biomechanics is widely used to develop orthopaedic implants for a range of body joints, dental parts, external fixations, exoskeletons, and other medical uses. In this case, the motion of a phenomenon is described using a nonlinear differential model. One of the most effective approaches for describing the qualitative behavior of a dynamical system is the introduction of Lyapunov methods. Stability analysis and boundedness of solutions of a nonlinear differential equation model, particularly in the context of knee joint movement, entails analyzing how minor perturbations (like changes in force, position, or velocity) influence the behavior of the joint and remain within a finite range over time, respectively. The goal is to determine whether the system returns to a steady state (stable) or becomes unstable when subjected to these small changes. The effect of viscous damping, external input, and angular motions at different times in seconds are all controlled to govern the shank knee movement surrounding the knee joint. Numerical simulations with Matlab and Mathematica are drawn to demonstrate the effectiveness of the shank knee motion around the knee joint....
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