Research and application of tristable stochastic resonance based on harmonic and pinning potential model

In view of the unique potential barrier and complex potential function of the pining model, as well as the lack of researches on two-dimensional stochastic resonance, two new potential tristable models are proposed: one-dimensional tristable model and two-dimensional tristable model. The stochastic resonance mechanism and application of two potential systems under Gaussian white noise and weak external driving force are discussed and the differences and advantages of the two systems are analyzed in detail for the first time. First, the potential function and mean first passage time are analyzed. Second, according to the linear response theory, the probability flow method is used to calculate the spectral amplification. The effects of system parameters on spectral amplification of the two models are studied, and the two models are compared. Finally, the two models are applied to the detection of actual bearing fault signals together with the classical tristable system and the performance is compared. Both algorithms can detect fault signals effectively, but the two-dimensional model has better amplitude and difference, and the one-dimensional model has less interference burrs. The theoretical basis and reference value of the system are provided for further application in practical engineering testing.

Conformal $ \eta $-Ricci solitons within the framework of indefinite Kenmotsu manifolds

<abstract><p>The present paper is to deliberate the class of $ \epsilon $-Kenmotsu manifolds which admits conformal $ \eta $-Ricci soliton. Here, we study some special types of Ricci tensor in connection with the conformal $ \eta $-Ricci soliton of $ \epsilon $-Kenmotsu manifolds. Moving further, we investigate some curvature conditions admitting conformal $ \eta $-Ricci solitons on $ \epsilon $-Kenmotsu manifolds. Next, we consider gradient conformal $ \eta $-Ricci solitons and we present a characterization of the potential function. Finally, we develop an illustrative example for the existence of conformal $ \eta $-Ricci soliton on $ \epsilon $-Kenmotsu manifold.</p></abstract>

Exact Solution of Navier-Stokes Equations

In Navier-Stokes equations (NASA’s Navier-Stokes Equations, 3-dimensional-unsteady), wed iscover the exact solution by Newton potential function and time-function. We think the solution likely Newton potential function that be able to solve Laplace equation

Imperfect Fluid Generalized Robertson Walker Spacetime Admitting Ricci-Yamabe Metric

In the present paper, we investigate the nature of Ricci-Yamabe soliton on an imperfect fluid generalized Robertson-Walker spacetime with a torse-forming vector field ξ . Furthermore, if the potential vector field ξ of the Ricci-Yamabe soliton is of the gradient type, the Laplace-Poisson equation is derived. Also, we explore the harmonic aspects of η -Ricci-Yamabe soliton on an imperfect fluid GRW spacetime with a harmonic potential function ψ . Finally, we examine necessary and sufficient conditions for a 1 -form η , which is the g -dual of the vector field ξ on imperfect fluid GRW spacetime to be a solution of the Schrödinger-Ricci equation.

NON-UNIFORM RATIONAL B-SPLINE BASED ISO-GEOMETRIC ANALYSIS FOR A CLASS OF HYDRODYNAMIC PROBLEMS

Herein, we present the design and development of a ‘Non-uniform Rational B-spline (NURBS)’ based iso-geometric approach for the analysis of a number of ‘Boundary Value Problems (BVPs)’ relevant in hydrodynamics. We propose a ‘Potential Function’ based ‘Boundary Element Method (BEM)’ and show that it holds the advantage of being computationally efficient over the other known numerical methods for a wide range of external flow problems. The use of NURBS is consistent, as inspired by the ‘iso-geometric analysis’, from geometric formulation for the body surface to the potential function representation to interpolation. The control parameters of NURBS are utilised and they have been explored to arrive at some preferable values and parameters for parameterization and the knot vector selection. Also, the present paper investigates the variational strength panel method, and its computational performance is analyzed in comparison with the constant strength panel method. The two variations have been considered, e.g. linear and quadratic. Finally, to illustrate the effectiveness and efficiency of the proposed NURBS based iso-geometric approach for the analysis of boundary value problems, five different problems (i.e. flow over a sphere, effect of the knot vector selection on analysis, flow over a rectangular wing section of NACA 0012 aerofoil section, performance of DTMB 4119 propeller (un-skewed), performance of DTNSDRC 4382 propeller (skewed)) are considered. The results show that in the absence of predominant viscous effects, a ‘Potential Function’ based BEM with NURBS representation performs well with very good computational efficiency and with less complexity as compared to the results available from the existing approaches and commercial software programs, i.e. low maximum errors close to 110−3 , faster convergence with even up to 75 % reduction in the number of panels and improvements in the computational efficiency up to 32.5 % even with low number of panels.

Finite Difference Method in Fluid Potential Function and Velocity Calculation

There is no deterministic solution for many fluid problems but by applying analytical solutions many of them are approximated. In this study an implicit finite difference method presented which solves the potential function and further expanded to drive out the velocity components in 2D-space by applying a point-by-point swiping approach. The results showed the rotational behavior of both potential function as well as velocity components while encountering central obstacle.

The circular RNA expression profile in ovarian serous cystadenocarcinoma reveals a complex circRNA–miRNA regulatory network

Background Ovarian serous cystadenocarcinoma is one of the most serious gynecological malignancies. Circular RNA (circRNA) is a type of noncoding RNA with a covalently closed continuous loop structure. Abnormal circRNA expression might be associated with tumorigenesis because of its complex biological mechanisms by, for example, functioning as a microRNA (miRNA) sponge. However, the circRNA expression profile in ovarian serous cystadenocarcinoma and their associations with other RNAs have not yet been characterized. The main purpose of this study was to reveal the circRNA expression profile in ovarian serous cystadenocarcinoma. Methods We collected six specimens from three patients with ovarian serous cystadenocarcinoma and adjacent normal tissues. After RNA sequencing, we analyzed the expression of circRNAs with relevant mRNAs and miRNAs to characterize potential function. Results 15,092 unique circRNAs were identified in six specimens. Approximately 46% of these circRNAs were not recorded in public databases. We then reported 353 differentially expressed circRNAs with oncogenes and tumor-suppressor genes. Furthermore, a conjoint analysis with relevant mRNAs revealed consistent changes between circRNAs and their homologous mRNAs. Overall, construction of a circRNA–miRNA network suggested that 4 special circRNAs could be used as potential biomarkers. Conclusions Our study revealed the circRNA expression profile in the tissues of patients with ovarian serous cystadenocarcinoma. The differential expression of circRNAs was thought to be associated with ovarian serous cystadenocarcinoma in the enrichment analysis, and co-expression analysis with relevant mRNAs and miRNAs illustrated the latent regulatory network. We also constructed a complex circRNA–miRNA interaction network and then demonstrated the potential function of certain circRNAs to aid future diagnosis and treatment.

A proteomics study identifying interactors of the FSHD2 gene product SMCHD1 reveals RUVBL1-dependent DUX4 repression

Structural Maintenance of Chromosomes Hinge Domain Containing 1 (SMCHD1) is a chromatin repressor, which is mutated in > 95% of Facioscapulohumeral dystrophy (FSHD) type 2 cases. In FSHD2, SMCHD1 mutations ultimately result in the presence of the cleavage stage transcription factor DUX4 in muscle cells due to a failure in epigenetic repression of the D4Z4 macrosatellite repeat on chromosome 4q, which contains the DUX4 locus. While binding of SMCHD1 to D4Z4 and its necessity to maintain a repressive D4Z4 chromatin structure in somatic cells are well documented, it is unclear how SMCHD1 is recruited to D4Z4, and how it exerts its repressive properties on chromatin. Here, we employ a quantitative proteomics approach to identify and characterize novel SMCHD1 interacting proteins, and assess their functionality in D4Z4 repression. We identify 28 robust SMCHD1 nuclear interactors, of which 12 are present in D4Z4 chromatin of myocytes. We demonstrate that loss of one of these SMCHD1 interacting proteins, RuvB-like 1 (RUVBL1), further derepresses DUX4 in FSHD myocytes. We also confirm the interaction of SMCHD1 with EZH inhibitory protein (EZHIP), a protein which prevents global H3K27me3 deposition by the Polycomb repressive complex PRC2, providing novel insights into the potential function of SMCHD1 in the repression of DUX4 in the early stages of embryogenesis. The SMCHD1 interactome outlined herein can thus provide further direction into research on the potential function of SMCHD1 at genomic loci where SMCHD1 is known to act, such as D4Z4 repeats, the inactive X chromosome, autosomal gene clusters, imprinted loci and telomeres.

ON THE MAXIMUM NUMBER OF PERIOD ANNULI FOR SECOND ORDER CONSERVATIVE EQUATIONS

We consider a second order scalar conservative differential equation whose potential function is a Morse function with a finite number of critical points and is unbounded at infinity. We give an upper bound for the number of nonglobal nontrivial period annuli of the equation and prove that the upper bound obtained is sharp. We use tree theory in our considerations.