The infinite-dimensional mechanics of fluids and plasmas can be formulated as “noncanonical” Hamiltonian systems on a phase space of Eulerian variables. Singularities of the Poisson bracket operator produce singular Casimir elements that foliate the phase space, imposing topological constraints on the dynamics. Here we proffer a physical interpretation of Casimir elements as adiabatic invariant...

‎This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$‎. ‎Some applications to these inequalities are also given‎. ‎In addi...

Antenna functions describe the infrared singular behaviour of colour-ordered QCD matrix elements due to the emission of unresolved partons inside an antenna formed by two hard partons. In this paper, we show that antenna functions for hard gluon-gluon pairs can be systematically derived from the effective Lagrangian describing Higgs boson decay into gluons, and compute the the infrared structur...

Any line is associated with a two-parameter group of polar complexes relative to a given first-order line complex that are called tangential complexes when the line belongs to the complex. The congruence that is determined by the tangential complex of a complex line is of a special kind, in that both of its directrices coincide in a single line that is the complex line itself. It is of a specia...

We give necessary and sufficient conditions for a certain class of local arithmetical congruence monoids (or ACMs) to have accepted elasticity. Let a and b be positive integers with a ≤ b and a ≡ a (mod b). Under these conditions, the arithmetic sequence a, a+ b, a+ 2b, a+ 3b, . . . is closed under multiplication and is a multiplicative semigroup. Setting M(a, b) = {a+ kb | k ∈ N0} ∪ {1} produc...

In the optimization process of a complex three-dimensional continuum structure by using the conventional evolutionary structural optimization method, some isolated groups of elements or a few elements being of rigid movements, often appear in the optimized structure, which becomes singular so that the optimization process can’t continue. In order to overcome this problem, this paper proposes an...

For certain negative rational numbers κ0, called singular values, and associated with the symmetric group SN on N objects, there exist homogeneous polynomials annihilated by each Dunkl operator when the parameter κ = κ0. It was shown by de Jeu, Opdam and the author (Trans. Amer. Math. Soc. 346 (1994), 237-256) that the singular values are exactly the values − n with 2 ≤ n ≤ N , m = 1, 2, . . . ...

Weighted cup-length calculations in singular cohomology led Farber and Grant in 2008 to general lower bounds for the topological complexity of lens spaces. We replace singular cohomology by connective complex K-theory, and weighted cup-length arguments by considerations with biequivariant maps on spheres to improve on Farber–Grant’s bounds by arbitrarily large amounts. Our calculations are base...

The standard (point-wise) linear channel model for MIMO wireless systems provides a simplistic mapping from antenna elements to continuous (operator) view point of wireless channels. Low-rank, high-dimension sampling matrices generated by Ray-Tracing may be used to estimate (with error) the “true” operator channel. In order to achieve reasonable estimation error bounds, intractably large dimens...

Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability...