Alternatives for parallel Krylov subspace basis computation

Numerical methods related to Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated via their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for constructing such bases. However, although easily parallelizable, this technique is not as scalable as expected for communications. In this work we examine alternative methods aimed at overcoming this drawback. Since they retrieve upon completion the same information as Arnoldi's algorithm does, they enable us to design a wide family of stable and scalable Krylov approximation methods for various parallel environments. We present timing results obtained from their implementation on two distributed-memory multiprocessor supercomputers: the Intel Paragon and the IBM Scalable POWERparallel SP2. (C) 1997 by John Wiley & Sons, Ltd.

Casimir invariants and characteristic identities for gl(infinity)

A full set of (higher-order) Casimir invariants for the Lie algebra gl(infinity) is constructed and shown to be well defined in the category O-FS generated by the highest weight (unitarizable) irreducible representations with only a finite number of nonzero weight components. Moreover, the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(infinity) are also determined and generalize those previously obtained for gl(n) by Bracken and Green [A. J. Bracken and H. S. Green, J. Math. Phys. 12, 2099 (1971); H. S. Green, ibid. 12, 2106 (1971)]. (C) 1997 American Institute of Physics.

Integer matrix diagonalization

We consider algorithms for computing the Smith normal form of integer matrices. A variety of different strategies have been proposed, primarily aimed at avoiding the major obstacle that occurs in such computations-explosive growth in size of intermediate entries. We present a new algorithm with excellent performance. We investigate the complexity of such computations, indicating relationships with NP-complete problems. We also describe new heuristics which perform well in practice. Wie present experimental evidence which shows our algorithm outperforming previous methods. (C) 1997 Academic Press Limited.

Growth hormone induces bone morphogenetic proteins and bone-related proteins in the developing rat periodontium

The hypothesis that growth hormone (GH) up-regulates the expression of enzymes, matrix proteins, and differentiation markers involved in mineralization of tooth and bone matrices was tested by the treatment of Lewis dwarf rats with GH over 5 days, The molar teeth and associated alveolar bone were processed for immunohistochemical demonstration of bone morphogenetic proteins 2 and 4 (BMP-2 and -4), bone morphogenetic protein type IA receptor (BMPR-IA), bone alkaline phosphatase (ALP), osteocalcin (OC), osteopontin (OPN), bone sialoprotein (BSP), and E11 protein (E11), The cementoblasts, osteoblasts, and periodontal ligament (PDL) cells responded to GH by expressing BMP-2 and -4, BMPR-IA, ALP, OC, and OPN and increasing the numbers of these cells. No changes were found in patterns of expression of the late differentiation markers BSP and E11 in response to GH, Thus, GH evokes expression of bone markers of early differentiation in cementoblasts, PDL cells, and osteoblasts of the periodontium. We propose that the induction of BMP-2 and -4 and their receptor by GH compliments the role of GH-induced insulin-like growth factor 1 (IGF-1) in promoting bone and tooth root formation.

Integrable extended hubbard models with boundary Kondo impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

Exact solution for the Bariev model with boundary fields

The Bariev model with open boundary conditions is introduced and analysed in detail in the framework of the Quantum Inverse Scattering Method. Two classes of independent boundary reflecting K-matrices leading to four different types of boundary fields are obtained by solving the reflection equations. The models are exactly solved by means of the algebraic nested Bethe ansatz method and the four sets or Bethe ansatz equations as well as their corresponding energy expressions are derived. (C) 2001 Elsevier Science B.V. All rights reserved.

A new integrable model of strongly correlated electrons with Hubbard-like interaction

A new completely integrable model of strongly correlated electrons is proposed which describes two competitive interactions: one is the correlated one-particle hopping, the other is the Hubbard-like interaction. The integrability follows from the fact that the Hamiltonian is derivable from a one-parameter family of commuting transfer matrices. The Bethe ansatz equations are derived by algebraic Bethe ansatz method.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Integrable open boundary conditions for the Bariev model of three coupled X Y spin chains

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading to nine classes of possible choices of boundary fields are found and the corresponding integrable boundary terms are presented explicitly. The boundary Hamiltonian is solved by using the coordinate Bethe ansatz technique and the Bethe ansatz equations are derived. (C) 2001 Elsevier Science B.V. All rights reserved.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Matrix-product codes over Fq

Codes C-1,...,C-M of length it over F-q and an M x N matrix A over F-q define a matrix-product code C = [C-1 (...) C-M] (.) A consisting of all matrix products [c(1) (...) c(M)] (.) A. This generalizes the (u/u + v)-, (u + v + w/2u + v/u)-, (a + x/b + x/a + b + x)-, (u + v/u - v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of /C/, d(C), the minimum Hamming distance of C, and C-perpendicular to. It also reveals an interesting connection with MDS codes. We determine /C/ when A is non-singular. To underbound d(C), we need A to be 'non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary 'Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C-perpendicular to can be described using C-1(perpendicular to),...,C-M(perpendicular to) and a transformation of A. This yields d(C-perpendicular to). Finally we show that an NSC matrix-product code is a generalized concatenated code.

Similar Markov chains

enin et al. (2000) recently introduced the idea of similarity in the context of birth-death processes. This paper examines the extent to which their results can be extended to arbitrary Markov chains. It is proved that, under a variety of conditions, similar chains are strongly similar in a sense which is described, and it is shown that minimal chains are strongly similar if and only if the corresponding transition-rate matrices are strongly similar. A general framework is given for constructing families of strongly similar chains; it permits the construction of all such chains in the irreducible case.

Veterinary drug delivery: Potential for skin penetration enhancement

A range of topical products are used in veterinary medicine. The efficacy of many of these products has been enhanced by the addition of penetration enhancers. Evolution has led to not only a highly specialized skin in animals and humans, but also one whose anatomical structure and skin permeability differ between the various species. The skin provides an excellent barrier against the ingress of environmental contaminants, toxins, and microorganisms while performing a homeostatic role to permit terrestrial life. Over the past few years, major advances have been made in the field of transdermal drug delivery. An increasing number of drugs are being added to the list of therapeutic agents that can be delivered via the skin to the systemic circulation where clinically effective concentrations are reached. The therapeutic benefits of topically applied veterinary products is achieved in spite of the inherent protective functions of the stratum corneum (SQ, one of which is to exclude foreign substances from entering the body. Much of the recent success in this field is attributable to the rapidly expanding knowledge of the SC barrier structure and function. The bilayer domains of the intercellular lipid matrices within the SC form an excellent penetration barrier, which must be breached if poorly penetrating drugs are to be administered at an appropriate rate. One generalized approach to overcoming the barrier properties of the skin for drugs and biomolecules is the incorporation of suitable vehicles or other chemical compounds into a transdermal delivery system. Indeed, the incorporation of such compounds has become more prevalent and is a growing trend in transdermal drug delivery. Substances that help promote drug diffusion through the SC and epidermis are referred to as penetration enhancers, accelerants, adjuvants, or sorption promoters. It is interesting to note that many pour-on and spot-on formulations used in veterinary medicine contain inert ingredients (e.g., alcohols, amides, ethers, glycols, and hydrocarbon oils) that will act as penetration enhancers. These substances have the potential to reduce the capacity for drug binding and interact with some components of the skin, thereby improving drug transport. However, their inclusion in veterinary products with a high-absorbed dose may result in adverse dermatological reactions (e.g., toxicological irritations) and concerns about tissue residues. These a-re important considerations when formulating a veterinary transdermal product when such compounds ate added, either intentionally or otherwise, for their penetration enhancement ability. (C) 2001 Elsevier Science B.V. All rights reserved.