The development and interaction of solitary wave pulses is critical to understanding wavy film flows on an inclined (or vertical) surface. Sufficiently far downstream, the structure consists a generally irregular sequence waves independent conditions at inlet. velocity periodic found depend their frequency amplitude. Larger travel faster; this property, plus strong inelasticity, causes larger absorb others during interactions, leaving nearly flat interface behind. These interactions lead...

The fused Lasso penalty enforces sparsity in both the coefficients and their successive differences, which is desirable for applications with features ordered some meaningful way. resulting problem is, however, challenging to solve, as non-smooth non-separable. Existing algorithms have high computational complexity do not scale large-size problems. In this paper, we propose an Efficient Fused Algorithm (EFLA) optimizing class of One key building block proposed EFLA Signal Approximator...

A bstract We establish a correspondence between supersymmetric mass deformation of the IKKT matrix integral at large N and background Euclidean type IIB string theory. Both sides have sixteen supersymmetries an SO(3) × SO(7) symmetry. In limit is dominated by fuzzy sphere saddle point. This corresponds to D 1-brane in finite, Euclidean, ellipsoidal cavity. The cavity supported three-form NSNS flux that polarises -instantons into 1-brane. furthermore use localisation show deformed can be...

Sparse learning techniques have been routinely used for feature selection as the resulting model usually has a small number of non-zero entries. Safe screening, which eliminates features that are guaranteed to zero coefficients certain value regularization parameter, is technique improving computational efficiency. screening gaining increasing attention since 1) solving sparse formulations high cost especially when large and 2) one needs try several parameters select suitable model. In this...

In this paper, we propose a fast block $\alpha$-circulant preconditioner for solving the nonsymmetric linear system arising from an all-at-once implicit discretization scheme in time wave equation. As generalization of well-known circulant preconditioning technique, proposed can also be efficiently inverted parallel-in-time manner. The complex eigenvalues preconditioned matrix are fully derived explicit expression and its diagonalizability is shown. Furthermore, mesh-independent convergence...

This paper proposes a novel exponential rational function method, modification of the well-known exp-function to find exact solutions time fractional Cahn-Allen equation and Phi-4 equation. The solution procedure is reduced solve system algebraic equations, which then solved by Wu?s method. results show that present method effective, can be applied other differential equations.

Fractional Fokas equation is studied, its exact solution obtained by the direct algebraic method. The process elucidated step step, and fractional complex transform characteristic set algorithm are emphasized.

A multiresolution method for distributed parameter estimation (or inverse problems) is studied numerically. The identification of the coefficient an elliptic equation in one dimension considered as our model problem. First, multiscale bases are used to analyze degree ill-posedness Second, based on some numerical results, it shown that scale-by-scale yields robust and fast convergence. Finally, how gives a natural regularization approach which complementary Tikhonov's regularization.

Let $p(\cdot) \colon \mathbb{R}^n \to (0,\infty]$ be a variable exponent function satisfying the globally log-Hölder continuous condition and $A$ general expansive matrix on $\mathbb{R}^n$. In this article, authors first introduce anisotropic Hardy space $H_A^{p(\cdot)}(\mathbb{R}^n)$ associated with $A$, via non-tangential grand maximal function, then establish its radial or characterizations. Moreover, also obtain various equivalent characterizations of $H_A^{p(\cdot)}(\mathbb{R}^n)$,...

In this paper, we consider the problem of learning from multiple related tasks for improved generalization performance by extracting their shared structures. The alternating structure optimization (ASO) algorithm, which couples all using a feature representation, has been successfully applied in various multitask problems. However, ASO is nonconvex and algorithm only finds local solution. We first present an formulation (iASO) based on new regularizer. then convert iASO, formulation, into...

A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with constraints. If the Hamiltonian possesses strong convexity property, then theory yields whose state and costate possess two square integrable derivatives. The based on stability result sup-norm change in solution of variational inequality relative 2-norm perturbation, Sobolev space bound error interpolation at quadrature points additional point -1. tightness examined...

Let $ \vec{p}\in(0, \infty)^n and A be a general expansive matrix on \mathbb{R}^n $. In this article, via the non-tangential grand maximal function, authors first introduce anisotropic mixed-norm Hardy spaces H_A^{\vec{p}}(\mathbb{R}^n) associated with then establish their radial or function characterizations. Moreover, characterize $, respectively, by means of atoms, finite Lusin area functions, Littlewood–Paley g $-functions g_{\lambda}^\ast establishing an Fefferman–Stein vector-valued...

The group Lasso is an extension of the for feature selection on (predefined) non-overlapping groups features. structure limits its applicability in practice. There have been several recent attempts to study a more general formulation, where features are given, potentially with overlaps between groups. resulting optimization is, however, much challenging solve due overlaps. In this paper, we consider efficient overlapping penalized problem. We reveal key properties proximal operator...