Eigenvalues of matrix commutators ∗

We characterize the eigenvalues of [X,A]=XA?AX, where A is an n by n fixed matrix and X runs over the set of the matrices of the same size.     

The minimal polynomial of a matrix ∗

Let Rbe a finite dimensional central simple algebra over a field F A be any n× n matrix over R. By using the method of matrix representation, this paper obtains the structure formula of the minimal polynomial q_A (λ) of A over F. By using q_A (λ), this paper discusses the structure of right (left) eigenvalues set of A, and obtains the necessary and sufficient condition that a matrix over a finite dimensional central division algebra is similar to a diagonal matrix.     

Relative invariants of 3 × 3 matrix triples ∗

We present primary and secondary generators for the algebra of polynomial invariants of the direct product of two copies of the special linear group Sl ₃ acting naturally on triples of 3 × 3 matrices over a field of characteristic zero. We handle also the analogous problem for triples and quadruples of 2 × 2 matrices.     

Singular values of some modular functions and their applications to class fields

Since the modular curve has genus zero, we have a field isomorphism where X ₂(z) is a product of Klein forms. We apply it to construct explicit class fields over an imaginary quadratic field K from the modular function j _Δ,25(z):=X ₂(5z). And, for every integer N≥7 we further generate ray class fields K _(N) over K with modulus N just from the two generators X ₂(z) and X ₃(z) of the function field , which are also the product of Klein forms without using torsion points of elliptic curves. J.K. Koo was supported by Korea Research Foundation Grant (KRF-2002-070-C00003).     

A note on the second largest eigenvalue of the laplacian matrix of a graph ∗

In this note, a lower bound for the second largest eigenvalue of the Laplacian matrix of a graph is given in terms of the second largest degree of the graph.     

The ‘window problem’ for series of complex exponentials

Under a suitable sparsity condition on the exponents Λ=(λ_k=τ_k+iσ_k), it is shown that the individual terms can be obtained from observation of the L² function through the ‘window’ t∈[0, δ]—with an l² estimate (uniform for such Λ) asymptotically as t, δ→0. Some applications are given to control theory for partial differential equations.     

A Class of Singular Integral Operators

Our main tool is the block decomposition of functions defined on∑_(n-1). Definition 1 A function b(x')defined on ∑_(n-1) is called a q-block,1相似文献   

On the Singular Direction of Entire Functions

In this paper, after defining a normal criterion with a parameter and a singular direction of an entire function corresponding to a normal criterion, we shall prove the following theorem.Theorem 1 Suppose that f(z) is a transcendental entire function. Then there exists a direction Δ: argz = θ0 (0≤0<2π) which is a singular direction of f(z) corresponding to every normal criterion with a parameter.From theorem 1 we deduce at once existence of some singular directions.     

Graded Singular Properties of Graded Quotient Rings

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A note on maximizing the permanent of a positive definite hermitian matrix,given the eigenvalues ∗

As a step toward understanding the unsolved problem of determining how large the permanent of a positive semi-definite matrix can be, given the eigenvalues, we note that a necessary condition for A to be a permanent maximizing matrix is that A commute with its permanental adjoint.     

∗-Polynomial Identities of a Nonsymmetric ∗-Minimal Algebra

Let F be an infinite field of characteristic ≠?2. We study the ?-polynomial identities of the ?-minimal algebra R?=?UT _?(F?⊕?F, F). We describe the generators of T _?(R) and a linear basis of the relatively free algebra of R. When char.F?=?0, these results allow us to provide a complete list of polynomials generating irreducible GL × GL-modules decomposing the proper part of the relatively free algebra of R. Finally, the ?-codimension sequence of R is explicitly computed.     

Properties of the Boundary Flux of a Singular Diffusion Process

Consider a nonhomogeneous fluid flowing through a homogeneous porous medium occupyinga bounded domain ΩR~n.Let u=u(x,t)represent the density of the fluid at the positionx∈Ω and time t,which satisfies the following singular diffusion equation     

Existence of Nonnegative Solutions to Singular Semi-positone Problems

In this paper we study a class of semi-positone singular boundary value problem. With prior bounds estimate and topology degree method, some existence results of nonnegative solution will be shown.     

Singular surfaces and the rigidity of ℙ3

In this paper we give two elementary proofs for the rigidity of the complex projective space ₃ with respect to global deformations.     

Computing α-Invariants of Singular del Pezzo Surfaces

We prove a new local inequality for divisors on surfaces and utilize it to compute α-invariants of singular del Pezzo surfaces, which implies that del Pezzo surfaces of degree one whose singular points are of type $\mathbb{A}_{1}$ , $\mathbb{A}_{2}$ , $\mathbb{A}_{3}$ , $\mathbb{A}_{4}$ , $\mathbb{A}_{5}$ , or $\mathbb{A}_{6}$ are Kähler-Einstein.     

Product of matrical discs ∗

We determine the matrical disc with minimal radius for the set of products XY when X and Y run over a (possibly distinct) matrical disc, respectively. Also we determine the union of the numerical ranges W(XY).     

Existence of Solutions for Singular Boundary Value Problems

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