Search Results (10)

Ultra-high contrast (UHC) MRI describes forms of MRI in which little or no contrast is seen on conventional MRI images but very high contrast is seen with UHC techniques. One of these techniques uses the divided subtracted inversion recovery (dSIR) sequence, which, in modelling studies, can produce ten times the contrast of conventional inversion recovery (IR) sequences. When used in cases of mild traumatic brain injury (mTBI), the dSIR sequence frequently shows extensive abnormalities in white matter that appears normal when imaged with conventional T₂-fluid-attenuated IR (T₂-FLAIR) sequences. The changes are bilateral and symmetrical in white matter of the cerebral and cerebellar hemispheres. They partially spare the anterior and posterior central corpus callosum and peripheral white matter of the cerebral hemispheres and are described as the whiteout sign. In addition to mTBI, the whiteout sign has also been seen in methamphetamine use disorder and Grinker’s myelinopathy (delayed post-hypoxic leukoencephalopathy) in the absence of abnormalities on T₂-FLAIR images, and is a central component of post-insult leukoencephalopathy syndromes. This paper describes the concept of ultra-high contrast MRI, the whiteout sign, the theory underlying the use of dSIR sequences and post-insult leukoencephalopathy syndromes. Full article

The present paper examines the plane wave’s reflection in a semiconducting magneto-thermoelastic rotating nonlocal half-space medium, which is stress-free, thermally insulated, and with a diffusion transport process at the boundaries. The novel mathematical model of extended three-phase-lag (TPL) heat transfer law with memory-dependent derivative (MDD) and two temperatures (2T) is used to model this problem. The investigated 2D model shows that a longitudinal wave, when striking the surface z = 0, produces four reflected waves. The characteristics of the plane wave such as phase velocity, amplitude ratios, penetration depth, attenuation-coefficients-specific loss, and energy ratios of various reflected waves are obtained. The symmetric and asymmetric tensor representations of all physical quantities are used. The effects of various theories of thermoelasticity, two temperatures, and rotation on wave characteristics are illustrated graphically using MATLAB software. Full article

The paper studies the bifurcations that occur in the T-system, a 3D dynamical system symmetric in respect to the Oz axis. Results concerning some local bifurcations (pitchfork and Hopf bifurcation) are presented and our attention is focused on a special bifurcation, when the system has infinitely many equilibrium points. It is shown that, at the bifurcation limit, the phase space is foliated by infinitely many invariant surfaces, each of them containing two equilibrium points (an attractor and a saddle). For values of the bifurcation parameter close to the bifurcation limit, the study of the system’s dynamics is done according to the singular perturbation theory. The dynamics is characterized by mixed mode oscillations (also called fast-slow oscillations or oscillations-relaxations) and a finite number of equilibrium points. The specific features of the bifurcation are highlighted and explained. The influence of the pitchfork and Hopf bifurcations on the fast-slow dynamics is also pointed out. Full article

Considered herein is the initial-boundary value problem for a semilinear parabolic equation with a memory term and non-local source $w_t-{\mathrm{\Delta }}_{\mathbb{B}}w-{\mathrm{\Delta }}_{\mathbb{B}}{w}_t+{\int }_0^{t}g(t-\tau ){\mathrm{\Delta }}_{\mathbb{B}}w\left(\tau \right)d\tau ={|w|}^{p-1}w-\frac{1}{|\mathbb{B}|}{\int }_{\mathbb{B}}{|w|}^{p-1}w\frac{d{x}_1}{x_1}d{x}^{\prime }$ on a manifold with conical singularity, where the Fuchsian type Laplace operator ${\mathrm{\Delta }}_{\mathbb{B}}$ is an asymmetry elliptic operator with conical degeneration on the boundary $x_1=0$. Firstly, we discuss the symmetrical structure of invariant sets with the help of potential well theory. Then, the problem can be decomposed into two symmetric cases: if $w_0\in W$ and $\mathrm{\Pi }\left(w_0\right)>0$, the global existence for the weak solutions will be discussed by a series of energy estimates under some appropriate assumptions on the relaxation function, initial data and the symmetric structure of invariant sets. On the contrary, if $w_0\in V$ and $\mathrm{\Pi }\left(w_0\right)<0$, the nonexistence of global solutions, i.e., the solutions blow up in finite time, is obtained by using the convexity technique. Full article

Droughts, considered one of the most dangerous and costly water cycle expressions, always occurs over a certain region, lasting several weeks or months, and involving multiple variables. In this work, a multivariate approach was used for the statistical characterization of hydrological droughts in Shaying River Basin with data from 1959–2008. The standard runoff index (SRI) and the run theory were employed to defined hydrological drought character variables (duration, severity, and intensity peak). Then, a multivariate joint probability analysis with four symmetric and corresponding asymmetric Archimedean Copulas was presented; and the multivariate frequency analysis with the joint return periods ($T_{and}$ and $T_{or}$) were estimated. The results showed that the hydrological droughts have a severity of 4.79 and 5.09, and the drought intensity peak is of 1.35 and 1.50 in Zhoukou station and Luohe station, respectively; the rank correlation coefficients τ are more than 0.5, which means multivariate copulas can effectively describe the joint frequency distributions among multivariate variables. Drought risk shows a spatial variation: the downstream observed at Zhoukou station is characterized by a higher multivariate drought risk. In general, multivariate copulas provide a reliable method when constructing a comprehensive drought index and evaluating multivariate drought characteristics. Thus, this paper can provide useful indications for the multi-dimensional droughts’ risks assessment in Shaying River Basin. Full article

Motivated by q-analogue theory and symmetric conic domain, we study here the q-version of the Ruscheweyh differential operator by applying it to the starlike functions which are related with the symmetric conic domain. The primary aim of this work is to first define and then study a new class of holomorphic functions using the q-Ruscheweyh differential operator. A new class $k-S{T}_q^{\tau }\left[C,D\right]$ of k-Janowski starlike functions associated with the symmetric conic domain, which are defined by the generalized Ruscheweyh derivative operator in the open unit disk, is introduced. The necessary and sufficient condition for a function to be in the class $k-S{T}_q^{\tau }\left[C,D\right]$ is established. In addition, the coefficient bound, partial sums and radii of starlikeness for the functions from the class of k-Janowski starlike functions related with symmetric conic domain are included. Full article

We describe 4D evaporating black holes as quantum field configurations by solving the semi-classical Einstein equation $G_{\mu \nu }=8\pi G⟨\psi |T_{\mu \nu }|\psi ⟩$ and quantum matter fields in a self-consistent manner. As the matter fields, we consider N massless free scalar fields (N is large). We find a spherically symmetric self-consistent solution of the metric $g_{\mu \nu }$ and the state $|\psi ⟩$ . Here, $g_{\mu \nu }$ is locally $Ad{S}_2\times S^2$ geometry, and $|\psi ⟩$ provides $⟨\psi |T_{\mu \nu }|\psi ⟩=⟨0|T_{\mu \nu }|0⟩+T_{\mu \nu }^{\left(\psi \right)}$ , where $|0⟩$ is the ground state of the matter fields in the metric and $T_{\mu \nu }^{\left(\psi \right)}$ consists of the excitation of s-waves that describe the collapsing matter and Hawking radiation with the ingoing negative energy flow. This object is supported by a large tangential pressure $⟨0\left|{T^{\theta }}_{\theta }\right|0⟩$ due to the vacuum fluctuation of the bound modes with large angular momenta $l\gg 1$ . This describes the interior of the black hole when the back reaction of the evaporation is taken into account. In this picture, the black hole is a compact object with a surface (instead of horizon) that looks like a conventional black hole from the outside and eventually evaporates without a singularity. If we count the number of configurations $\left\{\right|\psi ⟩\}$ that satisfy the self-consistent equation, we reproduce the area law of the entropy. This tells that the information is carried by the s-waves inside the black hole. $|\psi ⟩$ also describes the process that the negative ingoing energy flow created with Hawking radiation is superposed on the collapsing matter to decrease the total energy while the total energy density remains positive. Finally, as a special case, we consider conformal matter fields and show that the interior metric is determined by the matter content of the theory, which leads to a new constraint to the matter contents for the black hole to evaporate. Full article

In this study at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of quantum-mechanical theory it was explored conformational variety of the isolated quercetin molecule due to the mirror-symmetrical hindered turnings of the O3H, O5H and O7H hydroxyl groups, belonging to the A and C rings, around the exocyclic C–O bonds. These dipole active conformational transformations proceed through the 72 transition states (TSs; C₁ point symmetry) with non-orthogonal orientation of the hydroxyl groups relatively the plane of the A or C rings of the molecule (HO7C7C8/HO7C7C6 = ±(89.9–93.3), HO5C5C10 = ±(108.9–114.4) and HO3C3C4 = ±(113.6–118.8 degrees) (here and below signs ‘±’ corresponds to the enantiomers)) with Gibbs free energy barrier of activation ΔΔG_TS in the range 3.51–16.17 kcal·mol⁻¹ under the standard conditions (T = 298.1 K and pressure 1 atm): ΔΔG_TS^O7H (3.51–4.27) < ΔΔG_TS^O3H (9.04–11.26) < ΔΔG_TS^O5H (12.34–16.17 kcal mol⁻¹). Conformational dynamics of the O3H and O5H groups is partially controlled by the intramolecular specific interactions O3H…O4, C2′/C6′H…O3, O3H…C2′/C6′, O5H…O4 and O4…O5, which are flexible and cooperative. Dipole-active interconversions of the enantiomers of the non-planar conformers of the quercetin molecule (C₁ point symmetry) is realized via the 24 TSs with C₁ point symmetry (HO3C3C2C1 = ±(11.0–19.1), HC2′/C6′C1′C2 = ±(0.6–2.9) and C3C2C1′C2′/C3C2C1′C6′ = ±(1.7–9.1) degree; ΔΔG_TS = 1.65–5.59 kcal·mol⁻¹), which are stabilized by the participation of the intramolecular C2′/C6′H…O1 and O3H…HC2′/C6′ H-bonds. Investigated conformational rearrangements are rather quick processes, since the time, which is necessary to acquire thermal equilibrium does not exceed 6.5 ns. Full article

In the current article, the hydrodynamic forces of single-stepped planing hulls were evaluated by an analytical method and compared against towing tank tests. Using the 2D + T theory, the pressure distribution over the wedge section entering the water and the normal forces acting on the 2D sections have been computed. By integrating the 2D sectional normal forces over the entire wetted length of the vessel, the lift force acting on it has been obtained. Using lift forces as well as the consequence pitch moment, the equilibrium condition for the single-stepped planing hull is found and then resistance, dynamic trim, and the wetted surface are computed. The obtained hydrodynamic results have been compared against the experimental data and it has been observed that the presented mathematical model has reasonable accuracy, in particular, up to Froude number 2.0. Furthermore, this mathematical model can be a useful and fast tool for the stepped hull designers in the early design stage in order to compare the different hull configurations. It should also be noted that the mathematical model has been developed in such a way that it has the potential to model the sweep-back step and transverse the vertical motions of single-stepped planing hulls in future studies. Full article

In this paper, we comprehensively review the five-dimensional (5D) fully-covariant theory of gravitation developed by Zhang two decades ago and its recent applications in astrophysics and cosmology. This 5D gravity describes not only the fields, but also the matter and its motion in a 5D spacetime. The greatest advantage of this theory is that there does not exist any unknown parameter, so that we can apply it to explain astrophysical and cosmological issues by quantitatively comparing the results obtained from it with observations and to predict new effects that could not be derived from any other gravitational theories. First, the 5D covariant description of matter and its motion enabled Zhang to analytically derive the fifteenth component of the 5D energy-momentum tensor of matter (${\stackrel{-}{T}}^{44}$ ), which significantly distinguishes this 5D gravity from other 5D gravitational theories that usually assumed a ${\stackrel{-}{T}}^{44}$ with an unknown parameter, called the scalar charge s, and, thus, to split the 5D covariant field equation into (4 + 1) splitting form as the gravitational, electromagnetic, and scalar field equations. The gravitational field equation turns into the 4D Einstein’s field equation of general relativity if the scalar field is equal to unity. Then, Zhang solved the field equations and obtained an exact static spherically-symmetric external solution of the gravitational, electromagnetic and scalar fields, in which all integral constants were completely determined with a perfect set of simple numbers and parameters that only depend on the mass and electric charge of the matter, by comparing with the obtained weak internal solution of the fields at a large radial distance. In the Einstein frame, the exact field solution obtained from the 5D fully-covariant theory of gravitation reduces to the Schwarzschild solution when the matter is electrically neutral and the fields are weak in strength. This guarantees that the four fundamental tests (light deflection, gravitational redshift, perihelion advance and radar echo delay) of the 4D Einstein’s general relativity in the case of weak fields are also the tests of the 5D fully-covariant theory of gravitation. In the case of strong fields, especially when the matter is highly charged, however, the results from the 5D fully-covariant theory of gravitation are significantly different from the 4D Einstein’s general relativity. Applying this 5D gravity and its exact field solution, Zhang has recently developed a new redshift mechanism, called electric redshift, a new supernova explosion mechanism with gravitational field shielding, a new gravitationless black hole model, a modified neutron star mass-radius relation, a modified Friedmann equation for the accelerating universe, and so on. This paper provides an overview of this 5D fully-covariant theory of gravitation, including also its solution properties and astrophysical applications. Full article