Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system

In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability.We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method

Effects of Dissolving Solutions on the Accuracy of an Electronic Apex Locator-Integrated Endodontic Handpiece

The effects of three dissolving agents on the accuracy of an electronic apex locator- (EAL-) integrated endodontic handpiece during retreatment procedures were evaluated. The true lengths (TLs) of 56 extracted incisor teeth were determined visually. Twenty teeth were filled with gutta-percha and a resin-based sealer (group A), 20 with gutta-percha and a zinc oxide/eugenol-based sealer (group B), and 16 roots were used as the control group (group C). All roots were prepared to TL. Guttasolv, Resosolv, and Endosolv E were used as the dissolving solutions. Two evaluations of the handpiece were performed: the apical accuracy during the auto reverse function (ARL) and the apex locator function (EL) alone. The ARL function of the handpiece gave acceptable results. There were significant differences between the EL mode measurements and the TL (P<0.05). In these comparisons, Tri Auto ZX EL mode measurements were significantly shorter than those of the TL

On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem

This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented

Preparation of Ion Imprinted SPR Sensor for Real-Time Detection of Silver(I) Ion from Aqueous Solution

The aim of the submitted study is to develop molecular imprinting based surface plasmon resonance (SPR) sensor for real-time silver ion detection. For this purpose polymeric nanofilm layer on the gold SPR chip surface was prepared via UV polymerization of acrylic acid at 395 nm for 30 minutes. N-methacryloyl- L cysteine used as the functional monomer to recognize the silver(I) ions from the aqueous solutions and methylene bisacrylamide used as the crosslinker for obtaining structural rigidity of the formed cavities. Silver(I) solutions with different concentrations were applied to SPR system to investigate the efficiency of the imprinted SPR sensor in real time. For the control experiments, non-imprinted SPR sensor was also prepared as described above without addition of template “silver(I) ions”. Prepared SPR sensors were characterized with atomic force microscopy (AFM). In order to show the selectivity of the silver(I) imprinted SPR sensor, competitive adsorption of Cu(II), Pb(II), Ni(II) ions was investigated. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3489

Weak field and slow motion limits in energy-momentum powered gravity

We explore the weak field and slow motion limits, Newtonian and Post-Newtonian limits, of the energy-momentum powered gravity (EMPG), viz., the energy-momentum squared gravity (EMSG) of the form $f(T_{\mu\nu}T^{\mu\nu})=\alpha (T_{\mu\nu}T^{\mu\nu})^{\eta}$ with $\alpha$ and $\eta$ being constants. We have shown that EMPG with $\eta\geq0$ and general relativity (GR) are not distinguishable by local tests, say, the Solar System tests; as they lead to the same gravitational potential form, PPN parameters, and geodesics for the test particles. However, within the EMPG framework, $M_{\rm ast}$, the mass of an astrophysical object inferred from astronomical observations such as planetary orbits and deflection of light, corresponds to the effective mass $M_{\rm eff}(\alpha,\eta,M)=M+M_{\rm empg}(\alpha,\eta,M)$, $M$ being the actual physical mass and $M_{\rm empg}$ being the modification due to EMPG. Accordingly, while in GR we simply have the relation $M_{\rm ast}=M$, in EMPG we have $M_{\rm ast}=M+M_{\rm empg}$. Within the framework of EMPG, if there is information about the values of $\{\alpha,\eta\}$ pair or $M$ from other independent phenomena (from cosmological observations, structure of the astrophysical object, etc.), then in principle it is possible to infer not only $M_{\rm ast}$ alone from astronomical observations, but $M$ and $M_{\rm empg}$ separately. For a proper analysis within EMPG framework, it is necessary to describe the slow motion condition (also related to the Newtonian limit approximation) by $|p_{\rm eff}/\rho_{\rm eff}|\ll1$ (where $p_{\rm eff}=p+p_{\rm empg}$ and $\rho_{\rm eff}=\rho+\rho_{\rm empg}$), whereas this condition leads to $|p/\rho|\ll1$ in GR.Comment: 12 pages, no figures and table

Screening Λ\Lambda in a new modified gravity model

We study a new model of Energy-Momentum Squared Gravity (EMSG), called Energy-Momentum Log Gravity (EMLG), constructed by the addition of the term $f(T_{\mu\nu}T^{\mu\nu})=\alpha \ln(\lambda\,T_{\mu\nu}T^{\mu\nu})$, envisaged as a correction, to the Einstein-Hilbert action with cosmological constant $\Lambda$. The choice of this modification is made as a specific way of including new terms in the right-hand side of the Einstein field equations, resulting in constant effective inertial mass density and, importantly, leading to an explicit exact solution of the matter energy density in terms of redshift. We look for viable cosmologies, in particular, an extension of the standard $\Lambda$CDM model. EMLG provides an effective dynamical dark energy passing below zero at large redshifts, accommodating a mechanism for screening $\Lambda$ in this region, in line with suggestions for alleviating some of the tensions that arise between observational data sets within the standard $\Lambda$CDM model. We present a detailed theoretical investigation of the model and then constrain the free parameter $\alpha'$, a normalisation of $\alpha$, using the latest observational data. The data does not rule out the $\Lambda$CDM limit of our model ($\alpha'= 0$), but prefers slightly negative values of the EMLG model parameter ($\alpha'= -0.032\pm 0.043$), which leads to the screening of $\Lambda$. We also discuss how EMLG relaxes the persistent tension that appears in the measurements of $H_0$ within the standard $\Lambda$CDM model.Comment: 17 pages, 11 figures, 1 table; matches the version published in EPJ

Evaluation of the effect of mitral stenosis severity on the left ventricular systolic function using isovolumic myocardial acceleration

Background: Isovolumic acceleration (IVA) is a new tissue Doppler parameter in the as­sessment of systolic function of both left and right ventricles. It remains unaffected with the changes in pre- and after-load within the physiological range. The aim of our study was to assess the effect of mitral stenosis degree, which is determined by echocardiography, on the left ventricular (LV) function using IVA. Methods: A total number of 62 patients with mitral stenosis (MS) and 32 healthy controls were examined. The severity of MS (mild, moderate, and severe) was determined on the basis of mitral valve area (MVA) and the mean diastolic mitral gradient findings. The peak myocardial velocities during isovolumic contraction, systole, early diastole and late diastole were measured by using tissue Doppler imaging (TDI). Results: All TDI-derived global LV basal wall systolic (peak myocardial isovolumic contra­ction velocity, peak myocardial systolic velocity and IVA), and diastolic velocities (peak early and late diastolic velocities) were significantly decreased in the patients with MS, compared to the healthy patients (p &lt; 0.001, for all). However, IVA was not different when the degree of MS was evaluated (p = 0.114). In addition, IVA was not correlated with the MVA (r = 0.185, p = 0.150). Conclusions: Left ventricular function is impaired in patients with MS regardless of the severity of the disease.

A repertoire of biomedical applications of noble metal nanoparticles

Noble metals comprise any of several metallic chemical elements that are outstandingly resistant to corrosion and oxidation, even at elevated temperatures. This group is not strictly defined, but the tentative list includes ruthenium, rhodium, palladium, silver, osmium, iridium, platinum and gold, in order of atomic number. The emerging properties of noble metal nanoparticles are attracting huge interest from the translational scientific community and have led to an unprecedented expansion of research and exploration of applications in biotechnology and biomedicine. Noble metal nanomaterials can be synthesised both by top-down and bottom up approaches, as well as via organism-assisted routes, and subsequently modified appropriately for the field of use. Nanoscale analogues of gold, silver, platinum, and palladium in particular, have gained primary importance owing to their excellent intrinsic properties and diversity of applications; they offer unique functional attributes, which are quite unlike the bulk material. Modulation of noble metal nanoparticles in terms of size, shape and surface functionalisation has endowed them with unusual capabilities and manipulation at the chemical level, which can lead to changes in their electrical, chemical, optical, spectral and other intrinsic properties. Such flexibility in multi-functionalisation delivers ‘Ockham's razor’ to applied biomedical science. In this feature article, we highlight recent advances in the adaptation of noble metal nanomaterials and their biomedical applications in therapeutics, diagnostics and sensing

The effect of residual calcium hydroxide on the accuracy of a contemporary electronic apex locator

Objective. The aim of this study was to evaluate the effect of residual calcium hydroxide [Ca(OH)(2)] on the accuracy of an electronic apex locator (EAL). Materials and methods. Working lengths (WLs) of 56 extracted maxillary incisors were determined initially by two different methods. The first method used the ` APEX' reading of the EAL as a reference point, 0.5 mm was subtracted and recorded as WL0. The second method used the '0.5' reading and the score was recorded as WL0.5 without subtraction. The roots were prepared to WL0 and divided randomly into three experimental groups (n = 16) (1 mm in group A, 2 mm in group B and 4 mm in group C) and a control (n = 8). Specimens in all experimental groups were filled with Ca(OH)(2) paste. Following its removal, WLs were re-determined with the same methods. Results. In group C, pre/ post WLs were significantly different (p < 0.05). No significant difference was observed between the other experimental groups and the control group. Conclusion. Accuracy of EAL decreased proportionally with the amount of paste remaining at the +/- 0.5-mm tolerance level. Ca(OH)(2) paste remnants may cause incorrect EAL readings