its variables can still be interpreted in terms of physiological variables, since they have been derived from the physiological variables of the Hodgkin–Huxley model. The other way in which Fitzhugh derived these equations was by introducing one additional parameter in the original van der Pol oscillator equations which modifies them so that they have the qualitative features which Bonhoeffer h...

The variational method and critical point theory are employed to investigate the existence of solutions for 2nth-order difference equation Δ pk−nΔyk−n −1 n f k, yk 0 for k ∈ 1,N with boundary value condition y1−n y2−n · · · y0 0, yN 1 · · · yN n 0 by constructing a functional, which transforms the existence of solutions of the boundary value problem BVP to the existence of critical points for t...

Numerous studies have shown that biventricular pacing (BVP) improves symptoms and exercise capacity in patients with congestive cardiac failure (CCF) and left bundle branch block (LBBB). The mechanism of symptomatic improvement has been attributed to changes in ventricular synchrony. However, the degree of asynchrony is not a good predictor of response. 2 The aim of this study was to assess whe...

Cross-linked poly(N-benzyl-4-vinylpyridinium halide) (designated insoluble BVP) was previously reported to capture bacterial cells alive by contact with them. The corresponding linear polymer poly(N-benzyl-4-vinylpyridinium salt) (designated soluble BVP) was found to exhibit antibacterial activity. This soluble pyridinium-type polymer showed strong antibacterial activity against gram-positive b...

The superfamily of protein tyrosine phosphatases (PTPs) includes at least one enzyme with an RNA substrate. We recently showed that the RNA triphosphatase domain of the Caenorhabditis elegans mRNA capping enzyme is related to the PTP enzyme family by sequence similarity and mechanism. The PTP most similar in sequence to the capping enzyme triphosphatase is BVP, a dual-specificity PTP encoded by...

Plants commonly rely on photoperiodism to control flowering time. Rice development before floral initiation is divided into two successive phases: the basic vegetative growth phase (BVP, photoperiod-insensitive phase) and the photoperiod-sensitive phase (PSP). The mechanism responsible for the transition of rice plants into their photoperiod-sensitive state remains elusive. Here, we show that s...

VPM (continuation method or homotopy method) may be considered as special development and modification of classical Newton’s method, see [1] [5], [16]. The main idea of VPM admits short formulation: reducing of a given problem to some IVP for ODE. This fundamental principle of mathematical physics is well known, widely used and effective because IVP for ODE may be considered as a routine comput...

In this paper, we study sufficient conditions for the existence of at least three positive solutions for fourth-order three-point BVP.

The problem of diffraction of an electromagnetic field by a locally nonhomogeneous body in a perfectly conducting waveguide of rectangular cross section is considered. This problem is reduced to solving a volume singular integral equation (VSIE). The examination of this equation is based on the analysis of the corresponding boundary value problem (BVP) for the system of Maxwell’s equations and ...

Nonlinear two-point boundary value problems (BVPs) may have none or more than one solution. For the singularly perturbed two-point BVP εu′′ + 2u′ + f (u) = 0, 0 < x < 1, u(0) = 0, u(1) = 0, a condition is given to have one and only one solution; also cases of more solutions have been analyzed. After attention to the form and validity of the corresponding asymptotic expansions, partially based o...