Khanfogh8025

Complete stability of the singular modes is accurately predicted by the anti-Vakhitov-Kolokolov criterion (under the assumption that it applies to the model), as verified by means of numerical methods. In 2D, the NLSE with a quintic self-focusing term admits singular-soliton solutions with intrinsic vorticity too, but they are fully unstable. We also mention that dissipative singular solitons can be produced by the model with a complex coefficient in front of the nonlinear term.The classical theory of liquid crystal elasticity as formulated by Oseen and Frank describes the (orientable) optic axis of these soft materials by a director n. The ground state is attained when n is uniform in space; all other states, which have a nonvanishing gradient ∇n, are distorted. This paper proposes an algebraic (and geometric) way to describe the local distortion of a liquid crystal by constructing from n and ∇n a third-rank, symmetric, and traceless tensor A (the octupolar tensor). The (nonlinear) eigenvectors of A associated with the local maxima of its cubic form Φ on the unit sphere (its octupolar potential) designate the directions of distortion concentration. The octupolar potential is illustrated geometrically and its symmetries are charted in the space of distortion characteristics, so as to educate the eye to capture the dominating elastic modes. Special distortions are studied, which have everywhere either the same octupolar potential or one with the same shape but differently inflated.In every network, a distance between a pair of nodes can be defined as the length of the shortest path connecting these nodes, and therefore one may speak of a ball, its volume, and how it grows as a function of the radius. check details Spatial networks tend to feature peculiar volume scaling functions, as well as other topological features, including clustering, degree-degree correlation, clique complexes, and heterogeneity. Here we investigate a nongeometric random graph with a given degree distribution and an additional constraint on the volume scaling function. We show that such structures fall into the category of m-colored random graphs and study the percolation transition by using this theory. We prove that for a given degree distribution the percolation threshold for weakly connected components is not affected by the volume growth function. Additionally, we show that the size of the giant component and the cyclomatic number are not affected by volume scaling. These findings may explain the surprisingly good performance of network models that neglect volume scaling. Even though this paper focuses on the implications of the volume growth, the model is generic and might lead to insights in the field of random directed acyclic graphs and their applications.An alternative analysis approach, namely, orthogonal detrended fluctuation analysis (ODFA), is proposed to quantify the long-range correlation exponent. This method uses an orthogonal polynomial to attenuate any trends and quantify the (auto-) correlations in the data. The method is tested using numerically simulated data with long-range correlation. A matrix formalism of this approach is also proposed. Furthermore, the extension to high-order polynomial detrending is discussed. The proposed approach quantifies the long-range exponent with an error rate of about 8% for short datasets (3000 samples) and an error rate of about 1% for long datasets (100 000 samples). ODFA can find applications that involve processing long datasets as well as in real-time processing.We investigate interlayer synchronization in a stochastic multiplex hypernetwork which is defined by the two types of connections, one is the intralayer connection in each layer with hypernetwork structure and the other is the interlayer connection between the layers. Here all types of interactions within and between the layers are allowed to vary with a certain rewiring probability. We address the question about the invariance and stability of the interlayer synchronization state in this stochastic multiplex hypernetwork. For the invariance of interlayer synchronization manifold, the adjacency matrices corresponding to each tier in each layer should be equal and the interlayer connection should be either bidirectional or the interlayer coupling function should vanish after achieving the interlayer synchronization state. We analytically derive a necessary-sufficient condition for local stability of the interlayer synchronization state using master stability function approach and a sufficient condition for global stability by constructing a suitable Lyapunov function. Moreover, we analytically derive that intralayer synchronization is unattainable for this network architecture due to stochastic interlayer connections. Remarkably, our derived invariance and stability conditions (both local and global) are valid for any rewiring probabilities, whereas most of the previous stability conditions are only based on a fast switching approximation.Using molecular dynamical simulations, compressional shocks in two-dimensional (2D) dusty plasmas are quantitatively investigated under various conditions. A universal relationship between the thermal and the drift velocities after shocks is discovered in 2D Yukawa systems. Using the equation of state of 2D Yukawa liquids, and the obtained pressure from the Rankine-Hugoniot relation, an analytical relation between the thermal and the drift velocities is derived, which well agrees with the discovered universal relationship for various conditions.Background/Aims We evaluated the efficacy of docetaxel and epirubicin as neoadjuvant chemotherapy in locally advanced breast cancer and assessed the predictive factors for response to neoadjuvant chemotherapy and prognostic factors related to relapse-free survival. Methods Forty patients who received docetaxel and epirubicinas neoadjuvant chemotherapy for locally advanced breast cancer were evaluated retrospectively. Neoadjuvant chemotherapy consisted of intravenous injection of 75 mg/m2 docetaxel and 60 mg/m2 epirubucin on day 1, every 21 days, and two to six cycles. Results Twenty-five (62.5%) patients showed a partial response, and 15 (37.5%) patients showed a stable disease in the first response evaluation after two or three cycles of neoadjuvant chemotherapy. In the second response evaluation of nine patients who received six cycles of neoadjuvant chemotherapy, one patient achieved a complete response, but two patients with hormone receptor-negative, human epidermal growth factor receptor 2-positive breast cancer experienced disease progression.