In this paper, we present new variants of global bi-conjugate gradient (Gl-BiCG) and global bi-conjugate residual (Gl-BiCR) methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. It is shown that these new algorithms converge faster and more smoothly than the Gl-...

Hilbert’s law of quadratic reciprocity, as reformulated by Hasse, states that for a quaternion algebra D over a number field K, the number of ramified places of D is even. In general a number field has three kinds of places: finite, real, and complex. The complex places are never ramified. If D is assumed unramified at all finite places, it follows that D is ramified at an even number of real p...

Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition fo...

A covalently linked protein--protein conjugate between ThiF and ThiS thiocarboxylate was found in a partially purified coexpressed ThiF/ThiS protein mixture by using Fourier transform mass spectrometry. The Cys-184 of ThiF and the C terminus of ThiS thiocarboxylate were identified to be involved in the formation of this complex by using both mutagenesis and chemical modification methods. A comp...

In this paper, we will introduce the notion of conjugate phase retrieval, which is a relaxed definition of phase retrieval allowing recovery of signals up to conjugacy as well as a global phase factor. It is known that frames of real vectors are never phase retrievable on C in the ordinary sense, but we show that they can be conjugate phase retrievable in complex vector spaces. We continue to d...

Let X ⊂ Pn+r be an n dimensional smooth complex projective complete intersection of type (d1, . . . , dr). CHr(X) denotes the Chow group of codimension r algebraic cycles on X modulo rational equivalence and Ar(X) denotes the subgroup of the codimension r algebraic cycles that are algebraically equivalent to zero. In 1990 James D. Lewis made a conjecture on the representability of Ar(X). We wil...

We investigate the relationship between complex symmetry of composition operators C ϕ f = ∘ induced on classical Hardy space H 2 ( D ) by an analytic self-map open unit disk and its Koenigs eigenfunction. A generalization orthogonality known as conjugate-orthogonality will play a key role in this work. show that if is Schröder map (fixes point ∈ with 0 < | ′ 1 σ eigenfunction, then symmetric on...

In [1] (Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization J. Optimization. Theory Appl. 141 (2009) 249 - 264), an efficient hybrid conjugate gradient algorithm, the CCOMB algorithm is proposed for solving unconstrained optimization problems. However, the proof of Theorem 2.1 in [1] is incorrect due to an erroneous inequality which used to indicate the descent property for the s...

The n-tuple of Laplacian characteristic values of a graph is majorized by the conjugate sequence of its degrees. Using that result we find a collection of general inequalities for a number of Laplacian indices expressed in terms of the conjugate degrees, and then with a maximality argument, we find tight general bounds expressed in terms of the size of the vertex set n and the average degree dG...