Introduction. In this paper the structure of graphs is studied by purely combinatorial methods. The concepts of rank and nullity are fundamental. The first part is devoted to a general study of non-separable graphs. Conditions that a graph be non-separable are given ; the decomposition of a separable graph into its non-separable parts is studied; by means of theorems on circuits of graphs, a me...

This paper proposes a closed-form weighted least-squares solution for designing variable two-dimensional (2-D) finite-impulse response (FIR) digital filters with continuously variable 2-D fractional delay responses. First, the coefficients of the variable 2-D transfer function are represented by using the polynomials of a pair of fractional delays ( 1 2). Then the weighted squared-error functio...

The Fortran 90 separable Hamiltonian system solver Hamint 90 permits a wide choice of symplectic and non-symplectic integrators, and xed step size and local error-controlled (variable step size) integrations. We report on numerical experiments comparing xed step size and error-controlled strategies for various Hamiltonian systems and time scales.

For implementation of various model based techniques such as in control and fault diagnosis, data-driven identification is key for enabling cheap and rapid development of models of hybrid systems of industrial interest. In the present work, a novel identification method is proposed for a class of hybrid systems which are linear and separable in the discrete variables (that is discrete states an...

The problems studied are the separable variational inequalities with linearly coupling constraints. Some existing decomposition methods are very problem specific, and the computation load is quite costly. Combining the ideas of proximal point algorithm PPA and augmented Lagrangian method ALM , we propose an asymmetric proximal decomposition method AsPDM to solve a wide variety separable problem...

In order to solve the convex minimization problem with at least two variables, the augmented Lagrangian method is often used and improved to the alternating direction method of multipliers (ADMM) in the Gauss-Seidel or Jacobian fashion. Though various versions of the ADMM were developed for solving the two-block separable convex problem with linear equality constraint, there are a few feasible ...

Learned image features can provide great accuracy in many Computer Vision tasks. However, when the convolution filters used to learn image features are numerous and not separable, feature extraction becomes computationally demanding and impractical to use in real-world situations. In this thesis work, a method for learning a small number of separable filters to approximate an arbitrary non-sepa...

‎Given a frame of a separable Hilbert space $H$‎, ‎we present some‎ ‎iterative methods for solving an operator equation $Lu=f$‎, ‎where $L$ is a bounded‎, ‎invertible and symmetric‎ ‎operator on $H$‎. ‎We present some algorithms‎ ‎based on the knowledge of frame bounds‎, ‎Chebyshev method and conjugate gradient method‎, ‎in order to give some‎ ‎approximated solutions to the problem‎. ‎Then we i...

Fe3O4 nanoparticles were employment as an efficient and magnetically separable Nano catalyst for the synthesis of amides via one-pot Beckmann rearrangement of ketones under solvent-free conditions. Various secondary amides were synthesized by this method in moderate to good yields. The catalyst showed high thermal stability and was recovered and reused at least five times without any considerab...