bluuebunny/crossref_metadata_2025 huggingface dataset:
The quasiconvex envelope of the Saint Venant–Kirchhoff stored energy function
Authors: Le Dret Hervé , Raoult Annie
Published: November 2011

We give an explicit expression for the quasiconvex envelope of the Saint Venant–Kirchhoff stored energy function in terms of the singular values. This envelope is also the convex, polyconvex and rank 1 convex envelope of the Saint Venant–Kirchhoff stored energy function. Moreover, it coincides with the Saint Venant–Kirchhoff stored energy function itself on, and only on, the set of matrices whose singular values arranged in increasing order are located outside an ellipsoid. It vanishes on, and only on, the set of matrices whose singular values are less than 1. Consequently, a Saint Venant–Kirchhoff material can be compressed under zero external loading.
On the stability of the saddle solution of Allen–Cahn's equation
Authors: Schatzman M.
Published: November 2011

Letfbe an odd,C2function on [− 1, 1], which vanishes at ± 1, and such thatf′(O) < 0,f′ (±1) > 0 andu↦f(u)/uis increasing. Dang, Fife and Peletier [5] showed that there is a unique solutionuwith values in [−1, 1] of

which has the same sign asxy. The linearised operator arounduisBdefined by

It is proved here that the spectrum of B contains at least one negative eigenvalue, that all eigenfunctions corresponding to negative eigenvalues have the symmetries of the square, and that for Allen–Cahn's nonlinearity (f(u) = 2u3− 2u), there is exactly one negative eigenvalue.
Global resolvability for a viscoelastic model with relaxation
Authors: Changjiang Zhu
Published: November 2011

In this paper, we prove the existence of the global smooth solution for the equation of a viscoelastic model with relaxation in time under the only assumption that the C0-norm of the initial data is small, without smallness hypothesis for the C1-norm.
Contracting sets and dissipation
Authors: Carvalho Alexandre N.
Published: November 2011

In this work we study reaction–diffusion systems in fractional power spaces Xα which are embedded in L∞. We prove that the solution operators T(t) to these problems are globally defined, point dissipative, locally bounded and compact. That ensures the existence of global attractors. We also find a set containing the range of every function in the attractor, providing good estimates on asymptotic concentrations. This is done under very few hypotheses on the reaction term. These hypotheses are natural and easy to verify in many applications. The tools employed are the theory of invariant regions for systems of parabolic partial differential equations, the notion of contracting sets and the variation of constants formula. Several examples are considered to emphasise the applicability of these techniques.
The spectra of well-posed operators
Authors: Ibrahim Sobhy El-sayed
Published: November 2011

In this paper, the general ordinary quasidifferential expression M of nth order, with complex coefficients, and its formal adjoint M− are considered. It is shown in the case of two singular endpomts and when all solutions of the equation and the adjoint equation are in (the limit-circle case) that all well-posed extensions of the minimal operator T0(M) have resolvents which are Hilbert Schmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all of the standard essential spectra to be empty. These results extend those for the formally symmetric expression M studied in [1] and [14], and also extend those proved in [8] for one singular endpoint.
Large-time asymptotic behaviour of a step for the Benjamin–Bona–Mahony–Burgers equation
Authors: Naumkin P. I.
Published: November 2011

The asymptotic behaviour for large-time values of solutions of the initial-boundary-value problem for the Benjamin–Bona–Mahony–Burgers (BBMB) equation is studied. The solution of the initial-boundary-value problem is proved to converge to the standing wave as t → ∞ uniformly with respect to x ∈ R1. The estimate obtained of the time-decay rate of the remainder appears to depend on the rate of decay at infinity of the deviation of initial data from the standing wave. Due to the known expansion formulae with respect to the eigenfunctions associated to the stationary Schrodinger operator with the standing wave as a potential, it is possible to find the second term of the large-time asymptotic expansion of the solution to the initial-boundary-value problem for the BBMB equation.
On the number of nonorientable Wicks forms in a free group
Authors: Vdovina A.
Published: November 2011

The paper is concerned with the estimation of the number of maximal-length genus n nonorientable Wicks forms for n → ∞. It is shown how to apply a graph theory for this problem. It is proved that if M(n) be the number of all nonequivalent nonorientable genus n Wicks forms of maximal length, then
Long-time behaviour for a model of phase-field type
Authors: Laurençot Ph.
Published: November 2011

In this paper, we study a model of phase-field type for the kinetics of phase transitions which was considered by Halperin, Hohenberg and Ma and which includes the phase-field equations. We study the well-posedness of the corresponding initial boundary value problem in an open bounded subset in space dimension lower than or equal to 3 and prove that, under suitable conditions, the long-time behaviour of the solutions to this problem is described by a maximal attractor.
Singular sets of anisotropic weighted capacity zero and degenerate quasilinear parabolic equations
Authors: Saraiva Luis M. R.
Published: November 2011

The aim of this paper is to characterise sets of anisotropic weighted capacity zero. In this we generalise previous known results for the isotropic equivalent. A particular case of this zero capacity set is used to generalise removable singularity results for weak solutions of degenerate quasilinear parabolic equations and for their elliptic equivalent when its structure is still essentially isotropic, with the anisotropy confined to the mixed norms of the generalised Lebesgue spaces involved.
Oriented and nonoriented curvature varifolds
Authors: Delladio S. , Scianna G.
Published: November 2011

In a recent work, G. Anzellotti and the present authors introduced a notion of variation for functions defined over a rectifiable current. In this paper, we give a definition of a curvature varifold slightly different from that of Hutchinson (equivalent in the nonoriented case) and we study the variation properties, in the sense of [2], of the normal to a rectifiable current when the associated varifold is a curvature varifold.
The syntactic monoid of the semigroup generated by a comma-free code
Authors: Petrich Mario , Reis C. M.
Published: November 2011

A sequence of lemmas leads to a two-fold characterisation of the syntactic monoid in the title. Some alternatives as well as special cases, in particular when the code consists of a singleton, are considered.
Perpendicular bisectors, duality and local symmetry of plane curves
Authors: Giblin Peter , Tari Farid
Published: November 2011

For a smooth, simple closed curve α in the plane, the perpendicular bisector map P associates to each pair of distinct points (p, q) on α the perpendicular bisector of the chord joining p and q. To a pair (p, p), the map P associates the normal to α at p. The set of critical values of this map is the union of the dual of the symmetry set of α and the dual of the evolute. (The symmetry set is the locus of the centres of circles bitangent to α.) We study the mapP and use it to give a complete list of the transitions which take place on the dual of the symmetry set and the dual of the evolute, as α varies in a generic one-parameter family of plane curves.
Using quasiconvex functionals to bound the effective conductivity of composite materials
Authors: Nesi V.
Published: November 2011

Synopsis

In this paper we establish bounds constraining the effective conductivity tensor of composites made of an arbitrary number n of possibly anisotropic phases in prescribed volume fractions. The bounds are valid in any spatial dimension d≧2. The bounds have a very simple and concise form and include those previously obtained by Hashin and Shtrikman, Murat and Tartar, Lurie and Cherkaev, Kohn and Milton, Avellaneda, Cherkaev, Lurie and Milton and Dell'Antonio and Nesi.
Weak lower semicontinuity of polyconvex integrals
Authors: Malý Jan
Published: November 2011

Synopsis

Multiple integrals with polyconvex integrands are studied on the class of all sense-preserving diffeomorphisms from W1,p(Ω, Rn) where Ω is an open subset of Rn. They are proved to be sequentially weakly lower semicontinuous if 1 < p = n –1. An example is presented showing that a similar result is not valid if p <n –1.
Actions of locally nilpotent groups on Λ-trees
Authors: Chiswell I. M.
Published: November 2011

For certain classes of groups, it is shown that there are restrictions on the type of action a group in the class can have on a Λ-tree, where Λ is an arbitrary ordered abelian group, generalizing results by other authors in the case Λ = ℝ. The main classes considered are locally nilpotent, polycyclic by finite, locally (polycyclic by finite) and locally (hyperabelian by finite). The arguments involve an investigation of the relation between the type of action a group has on a Λ-tree and the type of action of its subgroups by restriction.
On the unboundedness below of the Sturm—Liouville operator
Authors: Möller Manfred
Published: November 2011

We show that if the leading coefficient p in a Sturm-Liouville expression is negative on a set E with positive Lebesgue measure, then the minimal operator (and hence any self-adjoint realization of the Sturm-Liouville expression) is not bounded below. The case when E contains an interval follows from standard methods but these methods fail when E contains no interval, e.g. when E is a Cantor-like set. This is the case considered here.
The stability of the resonance set for a problem with jumping non-linearity
Authors: d'Aujourd'hui Marcel
Published: November 2011

Synopsis

For Q ∊ L2(0, 1) we investigate the set Γ ∊ ℝ2 of pairs (α β,) for which the problem

has a nontrivial solution which has exactly one zero in (0,1) and is positive near x = 0. We show that Γ is stable in a certain sense under small perturbations of Q. The dependence of Γ upon Q is illustrated by an example.
Tight stable surfaces, I
Authors: Coghlan Leslie
Published: November 2011

Synopsis

In this paper we begin a systematic study of smooth tight maps with singularities of surfaces into E3, particularly C∞-stable maps. The class of C∞-stable tight maps of surfaces into E3 is much larger and richer than the class of C∞ (or even topological) tight immersions. We describe the general structure of C∞-stable tight maps of surfaces into E3. We show that, given any integer n ≧ 2 and a compact surface X other than the sphere or the projective plane, there is a C∞ -stable tight map X → E3 with exactly n topcycles. This is very different from the situation for tight topological immersions, where Cecil and Ryan have shown that the number α(f) of topcycles of a map f: X → E3, X a compact surface other than S2, satisfies the bound 2 ≦ α(f) ≦ 2 − Euler number of X. We prove also an analogue of the Cecil–Ryan result for C∞-stable maps.
Short time behaviour of a singular solution to the heat equation with absorption
Authors: Grundy R. E. , Peletier L. A.
Published: November 2011

Synopsis

The paper considers the small time evolution of the interface which appears in the boundary value problem

A diffusion dominated small time outer expansion is not uniformly valid when x = O(t½ log t) and has to be supplemented by an inner expansion valid in a region where diffusion and absorption are of equal importance. For p < 1 a zero order inner solution is constructed, which is consistent with a moving interface where u is zero, and the small time development of this is given.

These results are first derived in a heuristic way using the method of matched expansions. However, an important aim of the paper is to give rigorous proofs, being one of the very few cases in nonlinear diffusion where this has been done.
On the time-asymptotic behaviour of solutions in thermoelasticity
Authors: Racke Reinhard
Published: November 2011

Synopsis

We consider initial boundary value problems for the equations of linear thermoelasticity in both bounded and unbounded domains and for both nonhomogeneous and anisotropic media. For bounded domains, it is shown that the unique solution of the problem is time-asymptotically equal to the solution of a particular initial boundary value problem which is obtained from a natural decomposition of the original initial data and which represents a (in general non-vanishing) time harmonic part. For the unbounded case similar results are obtained, but now in the sense of weak convergence which lead to the result of local energy decay: the solution tends to zero in every compactum.
Expansion theorems for Birkhoff-regular differential-boundary operators
Authors: Möller Manfred
Published: November 2011

Synopsis

In this paper we consider differential-boundary operators T over a finite interval depending on a complex parameter. A differential-boundary operator admits boundary conditions in the differential part. The boundary part contains multipoint boundary conditions and integral conditions. For Birkhoff-regular boundary conditions we prove that every Lp -function is expansible into a series with respect to the eigenfunctions and the associated functions of the differential-boundary operator. Here the Birkhoff-regularity only depends on the boundary conditions at the endpoints of the interval, i.e. T is Birkhoff-regular if and only if T0 is Birkhoff-regular where T0 arises from T by omitting the boundary part in the differential equations, the interior point boundary conditions and the integral condition.
A shadowing approach to passage through resonance
Authors: Murdoch James A.
Published: November 2011

Synopsis

Leading order approximations are given by a patching method for passage through resonance in the case when the resonance zone contains saddle points. The approximations are uniformly valid regardless of the length of time required to pass through the resonance. Accuracy for extended time periods is obtained by asking not for approximate solutions with specified initial values, but for approximate solutions which are “shadowed” by exact solutions in the resonance zone.
Hopf bifurcation for equivariant conservative and time-reversible systems
Authors: Vanderbauwhede A.
Published: November 2011

Synopsis

We study the bifurcation of small periodic solutions at a non-semi-simple 1:1-resonance in equivariant conservative or equivariant time-reversible systems. By using an equivariant Liapunov-Schmidt method and restricting to solutions with an appropriate isotropy, we reduce the problem to a scalar bifurcation equation. The analysis of this equation shows a bifurcation behaviour similar to that found for the Hamiltonian Hopf bifurcation.
An Lp inequality
Authors: Webb J. R. L. , Zhao Weiyu
Published: November 2011

Synopsis

We obtain an inequality for Lp spaces (1
2) which corrects an inequality claimed by Xu and Xu [6] and has connections with some quantities of interest in fixed point theory.
Nearly real fronts in a Ginzburg–Landau equation
Authors: Jones Christopher K. R. T. , Kapitula Todd M. , Powell James A.
Published: November 2011

Synopsis

Subcritical fronts are shown to exist in a quintic version of the well-known complex Ginzburg–Landau equation, which has a subcritical pitchfork as well as a supercritical saddle-node bifurcation. The fronts connect a finite amplitude plane wave state to a stable zero solution. The unstable manifold at finite amplitude and stable manifold of vanishing amplitude solutions are shown to intersect transversely on an invariant zero-wavenumber manifold with parameters set to be real. By the persistence of transverse intersection, frontal connections exist for a continuum of nearly real fronts parametrised by appropriate variables that exhibit some interesting changes in dimension.
Development of interfaces in ℝN
Authors: de Mottoni P. , Schatzman M.
Published: November 2011

Consider the reaction-diffusion equation in ℝN × ℝ+: ut − h2 Δu + Φ(u) = 0, where Φ is the derivative of a bistable even potential, and h is a small parameter. If the initial data have a smooth noncritical zero set, we prove that an interface appears in time O(log (h−1)), and that the solution stays close to it for at least time O(1/√h).
On the equation grad f = M grad g
Authors: Jodeit Max , Olver Peter J.
Published: November 2011

Synopsis

The system of differential equations ∇f = M∇g, where M is a given square matrix, arises in many contexts. A complete solution to this problem in the case when M is a constant matrix is presented here. Applications to continuum mechanics and biHamiltonian systems are indicated.
Idempotents in partial transformation semigroups
Authors: Garba G. U.
Published: November 2011

Synopsis

An element α of Pn, the semigroup of all partial transformations of {1,2,…, n}, is said to have projection characteristic (r, s), or to belong to the set [r, s], if dom α= r, im α = s. Let E be the set of all idempotents in Pn\[n, n] and E1, the set of those idempotents with projection characteristic (n, n − 1) or (n − 1, n − 1). For α in Pn\[n, n], we define a number g(α), called the gravity of α and closely related to the number denned in Howie [5] for full transformations, and we obtain the result that

Let d(α) be the defect of α, and for any real number x let [x] be the least integer m such that m ≧ x. Then by analogy with the results of Saito [9] we have that

α ϵ Ek(α) and α ∉ Ek(α)

where k(α) = [g(α)/d(α)] or [g(α)/d(α)+ 1. Following Howie, Lusk and McFadden [6] we then explore connections between the defect and the gravity of α. Letting K(n, r) be the subsemigroup of Pn consisting of all elements of rank r or less, we prove a result, corresponding to that of Howie and McFadden [7] for total transformations, that the idempotent rank, defined as the cardinality of a minimal generating set of idempotents, of K(n, r) is S(n + 1, r + 1), the Stirling number of the second kind.
Existence and non-existence results for semilinear elliptic problems in unbounded domains
Authors: Esteban M. J. , Lions P. L.
Published: November 2011

Synopsis

In this paper, we prove various existence and non-existence results for semilinear elliptic problems in unbounded domains. In particular we prove for general classes of unbounded domains that there exists no solution distinct from 0 of

for any smooth f satisfying f(0) = 0. This result is obtained by the use of new identities that solutions of semilinear elliptic equations satisfy.
A radical for near-rings
Authors: Hartney J. F. T.
Published: November 2011

Synopsis

Throughout this paper the near-ring N is assumed to be zero symmetric and to satisfy the right distributive law. That is, x · 0 = 0 and (x + y)z = xz + yz for all x, y, z ∈ N. In what follows we generalise the notion of s-primitivity first introduced in an earlier paper by the author (1968), where only distributively generated (d.g.) near-rings with identity were considered. We define a Jacobson type radical Js (N) and show that J1(N)⊇Js(N) ⊇ Q(N), where Q(N) is the intersection of all 0-modular left ideals of N (Pilz). In addition we settle some of the problems remaining from Hartney (1968).
Inequalities for the tail probabilities of weighted sums of independent random variables with applications to rates of convergence to zero
Authors: Dunnage J. E. A.
Published: November 2011

Synopsis

We obtain inequalities for where Wn = anlX1 + … + annXn, the Xr being independent random variables and the Mn being certain truncated means. We then use these inequalities to study the rate at which this probability tends to zero as N→ ∞, noting that in the special case Wn = (X1 + … + Xn)/n, we obtain the estimate given by L. E. Baum and M. Katz which they show is, in a sense, best possible.

A desire to find an inequality which would lead to the result of Baum and Katz was, indeed, the impetus behind this paper.
Lifting homotopies through fixed points
Authors: Armstrong M. A.
Published: November 2011

Synopsis

If G is a discontinuous group of homeomorphisms of a connected, locally path connected space X, which acts freely on X, then the projection π: X → X/G is a covering map and has the homotopy lifting property. Here we allow the elements of G to have fixed points and use work of Rhodes to investigate how two loops in X are related if their projections are homotopic in X/G. This enables us to establish a formula for the fundamental group of the orbit space of a discontinuous group under very general conditions. Finally we show by means of an example that some restriction on the action near fixed points is needed for the formula to be valid.
Counting singularities
Authors: Bruce J. W.
Published: November 2011

Synopsis

In this paper we obtain information on the parity of the number of singularities associated with generic mappings and families of functions. More generally we obtain results relating homology cycles (with ℤ2 coefficients) associated with certain singularity types. The methods employed are elementary, and rely on computations of local incidence numbers associated with certain manifold partitions or stratifications. These computations are carried out for some stratifications arising naturally within singularity theory.
Essential self-adjointness and self-adjointness for even order elliptic operators
Authors: Dung Nguyen Xuan
Published: November 2011

Synopsis

We consider elliptic operators of the form , on L2(Rn), and establish conditions under which T is essentially self-adjoint on , and self-adjoint on H2m(Rn)∩D(q).
Asymptotics and deficiency indices for certain pairs of differential operators
Authors: Braaksma B. L. J.
Published: November 2011

Synopsis

Asymptotic approximations to solutions of perturbations of Meijer's differential equation are derived. These are used to determine deficiency indices for certain subspaces associated with related pairs of symmetric differential expressions.
Landau's inequality
Authors: Kwong M. K. , Zettl A.
Published: November 2011

Synopsis

Landau's inequality ∥y′∥2≦4∥y∥∥y″∥ is extended to ∥y′∥2≦K(a)∥y∥1−a ∥y″ ∣y∣a∥, K(a) = 4/(l−a), 0≦ a<1. The proof is elementary and new even in the case a = 0 considered by Landau.
Spectral functions of a symmetric linear relation with a directing mapping, I
Authors: Langer H. , Textorius B.
Published: November 2011

Synopsis

For a symmetric linear relation S with a directing mapping, the notion of a spectral function is defined by means of a Bessel–Parseval inequality, and a description of all such spectral functions is given. As an application, we describe the set of all spectral functions of a canonical regular first order differential system.
The Froude number for solitary waves
Authors: McLeod J. B.
Published: November 2011

Synopsis

The paper is concerned with the problem of a solitary wave moving with constant form and constant velocity c on the surface of an incompressible, inviscid fluid over a horizontal bottom. The motion is assumed to be two-dimensional and irrotational, and if h is the depth of the fluid at infinity and g the acceleration due to gravity, then the Froude number F is defined by

The result that F>1 has recently been proved by Amick and Toland by means of a long and complicated argument. Here we give a short and simple one.
Upper and lower solutions and semilinear second order elliptic equations with non-linear boundary conditions
Authors: Mawhin J. , Schmitt K.
Published: November 2011

Synopsis

A general framework is presented for the proof of the existence of classical solutions of second order elliptic equations which satisfy non-linear boundary conditions. The results obtained contain many of the known theorems for such problems and the approach used unifies the various methods of study based upon upper and lower solutions.
Criterion of global equivalence of linear differential equations
Authors: Neuman František
Published: November 2011

Synopsis

A criterion of global equivalence of linear homogeneous differential equations of then-th order,n≧ 3, is derived, which is in general effective, i.e. expressible in terms of coefficients and quadratures.
Homogenisation of parametrised families of hyperbolic problems
Authors: Amirat Y. , Hamdache K. , Ziani A.
Published: November 2011

Synopsis

This paper is concerned with homogenisation processes for parametrised families of transport equations in ℝn symmetric hyperbolic systems in several space dimensions and anisotropic wave equations. The main tools for carrying out the homogenisation are the Young measures and Radon transform combined with the integral representation of holomorphic functions of Nevanlinna-Pick's type.
From sine waves to square waves in delay equations
Authors: Chow S.-N. , Hale J. K. , Huang W.
Published: November 2011

Synopsis

Suppose fλ: ℝ→ℝ, fλ(0) = 0 and the fixed point zero undergoes a generic supercritical period doubling bifurcation at λ = 0. We characterise those small values of ε > 0, λ ∈ ℝ for which there are periodic solutions of period approximately two of the equation

As ε → 0, these solutions approach square waves.
Generalized systems of linear differential equations
Authors: Pfaff Rainer
Published: November 2011

Synopsis

We consider ordinary linear differential systems of first order with distributional coefficients and distributional nonhomogeneous terms. Firstly the coefficients are assumed to be functions, secondly to be first order distributions (i.e. first derivatives of functions which are integrable or of bounded variation), and thirdly to be distributions of higher order.
Corrigendum: On the Dirichlet problem for weakly non-linear elliptic partial differential equations
Authors: Dancer E. N.
Published: November 2011

The proof of Lemma 6 (and thus of Theorem 9) has a gap in it. While m(B) → 0 as r → ∞ for each fixed h in Ni, it is not clear (and probably false) that this holds uniformly for h in . However Lemma 6 (and thus Theorem 9) holds with only trivial modifications of the given proof if one of the following holds: (i) ygi(y) → ∞ as |y| → ∞; (ii) m{x∈Ω: h(x) = 0} = 0 for every h in (iii) Niis one dimensional; (iv) there is a subset A of Ω such that h(x) = 0 if x ∈ A and h ∈ and m{x∈Ω\A: h(x) = 0} = 0 for every h ∈ . Assumption (ii) holds under very weak conditions. For example, the methods in [1] and regularity theorems imply that (ii) holds if there is a closed subset T of Ω of measure zero such that either (a) Ω\T is connected and aij (i, j = 1, …, n) are locally Lipschitz continuous on Ω\T or (b) for each component A of Ω\T, the aij have Lipschitz extensions to Ā and T is a “nice” set. (For example, it suffices to assume that T is a smooth submanifold of Ω though much weaker conditions would suffice.) Remember that we are assuming Ω is connected.
Approximation properties of sets with bounded complements
Authors: Franchetti C. , Papini P. L.
Published: November 2011

Synopsis

Given a Banach space X, we investigate the behaviour of the metric projection PF onto a subset F with a bounded complement.

We highlight the special role of points at which d(x, F) attains a maximum. In particular, we consider the case of X as a Hilbert space: this case is related to the famous problem of the convexity of Chebyshev sets.
On the differential invariants of a linear ordinary differential equation
Authors: Kung Joseph P. S. , Rota Gian-Carlo
Published: November 2011

Synopsis

Lety(n)+a1y(n−1+…+an−1y(1)+an= 0 (*) be a linear ordinary differential equation of ordern. A (relative) differential invariant of (*) is a differential polynomial function π(xi) defined on the solution space of (*) satisfying: there is an integergsuch that for all invertible linear transformations α ofVinto itself, π(αxi) = (det α)βπ(xi). We prove in a purely algebraic manner the following two theorems: A. The differential invariants of (*) are generated algebraically by the WronskianWand the coefficientsala2, …,anof (*). B. Every generic differential relation (i.e. differential relation which holds for every linear ordinary differential equation of ordern) amongW, a1…,ancan be deduced algebraically from Abel's identity,W′ = −a1W. The second theorem may be considered as an algebraic version of the existence theorem for linear ordinary differential equations.
An eigenfunction expansion associated with a two-parameter system of differential equations. I
Authors: Faierman M.
Published: November 2011

Synopsis

Techniques from the theory of partial differential equations are employed to prove the uniform convergence of the eigenfunction expansion associated with a left definite two-parameter system of ordinary differential equations of the second order.
An abstract multiparameter spectral theory
Authors: Binding P. A. , Källström A. , Sleeman B. D.
Published: November 2011

Synopsis

We consider the eigenvalue problem

for self-adjoint operators Ai and Bij on separable Hilbert spaces Hi. It is assumed that and Bij are bounded with compact. Various properties of the eigentuples λi, and xi are deduced under a “definiteness condition” weaker than those used by previous authors, at least in infinite dimensions. In particular, a Parseval relation and eigenvector expansion are derived in a suitably constructed tensor product space.
Group algebras of finite p-solvable groups with radicals of the fourth power zero
Authors: Koshitani Shigeo
Published: November 2011

Synopsis

Let J(KG) be the Jacobson radical of the group algebra KG of a finite p-solvable group G over a field K of characteristic p > 0, and let t(G) be the least positive integer t such that J(KG)t = 0. In this paper we determine the structure of G with t(G) = 4 under the assumption that H is abelian, H is metacyclic, or the order of H is not divisible by 3 where H = O2'(G).
The number of Dirichlet solutions of a fourth order differential equation
Authors: Read Thomas T.
Published: November 2011

Synopsis

It is shown that the equation (p2y”)”–(p1y’)’+ p0y = 0 has exactly two linearly independent solutions on [0,∞) with finite Dirichlet integral when the coefficients are nonnegative and p2 satisfies a condition which includes all nondecreasing functions. An inequality for the Dirichlet form is derived and used to extend characterizations of the domains of certain self-adjoint operations associated with the differential expression to arbitrary symmetric boundary conditions at 0.
Regular semigroups with a multiplicative inverse transversal
Authors: Blyth T. S. , McFadden R.
Published: November 2011

Synopsis

By an inverse transversal of a regular semigroup S we mean an inverse subsemigroup that contains a single inverse of every element of S. A certain multiplicative property (which in the case of a band is equivalent to normality) is imposed on an inverse transversal and a complete description of the structure of S is obtained.
Mean-value theorems for Riemannian manifolds
Authors: Gray A. , Willmore T. J.
Published: November 2011

Synopsis

Let Mm (r, f) denote the mean-value of a real-valued integrable function f over a geodesic sphere with centre m and radius r in an n-dimensional Riemannian manifold M. We obtain an expansion of Mm (r, f) in powers of r, thereby generalizing Pizzetti's formula valid in euclidean space. From this expansion we prove that the property

for every harmonic function near m, characterizes Einstein spaces. We define super-Einstein spaces and prove that they are characterized by the property
Existence of the free boundary in a multi-dimensional combustion problem
Authors: Gianni Roberto
Published: November 2011

In this paper, we consider an n-dimensional semilinear equation of parabolic type with a discontinuous source term arising from combustion theory. We prove local existence for a classical solution having a ‘regular’ free boundary. In this regard, the free boundary is a surface through which the discontinuous source term exhibits a switch-like behaviour. We specify conditions under which this solution and its free boundary are global in time; moreover, we exhibit a special domain for which, for t tending to infinity, such a global-in-time solution converges, together with its free boundary, to the solution of the stationary problem and to its regular free boundary (which is proved to exist), respectively. We also prove uniqueness and continuous dependence theorems.
Completely integrable holonomic systems of first-order differential equations
Authors: Izumiya Shyuichi
Published: November 2011

We classify completely integrable holonomic systems of first-order differential equations for one real-valued function by equivalence under the group of point transformations in the sense of Sophus Lie. In order to pursue the classification, we use the notion of one parameter Legendrian unfoldings which induces a special class of divergent diagrams of map germs which are called integral diagrams. Our normal forms are represented by integral diagrams.
Correspondences of completely regular semigroups and -isomorphisms of semigroups
Authors: Goberstein Simon M.
Published: November 2011

A correspondence of a semigroup S is any subsemigroup of S × S, and the set of all correspondences of S, with the operations of composition and involution and the relation of set-theoretic inclusion, forms the bundle of correspondences of S, denoted by (S). For semigroups S and T, any isomorphism of (S) onto (T) is called a -isomorphism of S upon T. Similar notion can be introduced for other types of algebras and in the general frame of category theory. The principal goal of this paper is to study -isomorphisms of completely regular semigroups (that is, unions of groups) and of one other interesting class of semigroups.
The deliberative turn in participation: the problem of inclusion and deliberative opportunities in participatory budgeting
Authors: Ganuza Ernesto , Francés Francisco
Published: November 2011

Participation has undergone a communicative shift, which has favoured the organization of new participatory processes based on classic principles of deliberation theory. These experiments go beyond traditional protest: they include a communicative element with the aim of defining a public politics, which places them alongside models of deliberative governance. The present work sets out the characteristics of these new instruments (participatory budgeting, PB) in order to find out which problems deliberative governance initiatives are faced with. The conclusions tell us that the inequalities in participation are significant. Nevertheless, PB enables most participants to make effective use of their opportunities for deliberation. From this standpoint, the challenge for deliberative governance does not seem to be the deliberative capabilities of individuals, but rather the design of participatory procedures and the participation of individuals. We may question whether the administration can guarantee impartial political spaces that are as inclusive as possible.
The role of dissolved organic matter in arctic surface waters in the photolysis of hexachlorobenzene and lindane
Authors: Grannas Amanda M. , Cory Rose M. , Miller Penney L. , Chin Yu‐Ping , McKnight Diane M.
Published: November 2011

Terrestrially derived dissolved organic matter (DOM) can impact the fate of persistent organic pollutants (POPs) that are transported to the Arctic via global distillation. Interactions between DOM and POPs through hydrophobic binding processes may influence their photofate in arctic surface waters. We examined the DOM‐mediated photodegradation of γ‐hexachlorocyclohexane (lindane) and hexachlorobenzene (HCB) in arctic surface waters. These two halogenated organic compounds are commonly detected in the Arctic. We examined how different sources of DOM affect the indirect photolysis of these compounds. We conducted our study using DOM from arctic streams and lakes near the Toolik Lake Long‐term Ecological Research Site. HCB or lindane was irradiated in the presence and absence of DOM from these sources, both at the surface of an arctic lake and at 10 cm depth, to investigate the indirect phototransformation of these two compounds and the depth dependence of the observed chemistry. In both artificial and natural sunlight, two of four DOM sources studied stimulated the photodegradation of HCB but not of lindane, suggesting that the indirect phototransformation is a selective process depending on the interactions between DOM and POPs. Through solubility studies, we found that HCB readily partitions to isolated Toolik Lake DOM, while lindane shows no affinity for DOM, findings that corroborate results previously reported in the literature. We demonstrate for the first time DOM's role as a sensitizer for photodegradation of some POPs under field conditions, thus confirming that this process may be an important control on the fate of POPs exhibiting a strong affinity for DOM.
On the response of the ionospheric F region over Indian low‐latitude station Gadanki to the annular solar eclipse of 15 January 2010
Authors: Madhav Haridas M. K. , Manju G.
Published: November 2011

The response of the ionospheric F region over Indian low‐latitude regions to the annular solar eclipse of 15 January 2010 is investigated. The foF2 corresponding to an electron density increase of ∼21% at the F2 peak is seen over Gadanki (13.5°N, 79°E) during the course of the eclipse in comparison with the control day behavior. After the peak phase the foF2 shows a large decrease (∼19%) compared to the mean control day pattern. The total electron content (TEC) at Bangalore (13°N, 78°E) which is located very close to Gadanki is expected to follow a similar pattern of temporal evolution. This TEC shows reduction with respect to control day both at the peak phase (17%) and in the postpeak phase (30%). The enhanced foF2 from the start to the peak phase of the eclipse is attributed to the effect of the weakened equatorial ionization anomaly (EIA). At altitude regions below 270 km, the eclipse induced cutoff of solar insolation results in chemical recombination becoming dominant and thus contributes to the decrease in columnar content in spite of foF2 increase. The post peak phase steep decrease of both foF2 and TEC is attributed to the substantial increase in the poleward meridional winds, the inhibition of the EIA, and persistent depletion in the lower‐altitude electron densities. In summary, this study demonstrates the modifications in electrodynamics, recombination, and neutral dynamics acting in concert to produce the observed effects at low latitudes during an eclipse.
Comparison of Earth rotation excitation in data‐constrained and unconstrained atmosphere models
Authors: Neef Lisa J. , Matthes Katja
Published: November 2011

Changes in Earth rotation are strongly related to fluctuations in the angular momentum of the atmosphere, and therefore contain integral information about the atmospheric state. Here we investigate the extent to which observed Earth rotation parameters can be used to evaluate and potentially constrain atmospheric models. This is done by comparing the atmospheric excitation function, computed geophysically from reanalysis data and climate model simulations constrained only by boundary forcings, to the excitation functions inferred from geodetic monitoring data. Model differences are assessed for subseasonal variations, the annual and semiannual cycles, interannual variations, and decadal‐scale variations. Observed length‐of‐day anomalies on the subseasonal timescale are simulated well by the simulations that are constrained by meteorological data only, whereas the annual cycle in length‐of‐day is simulated well by all models. Interannual length‐of‐day variations are captured fairly well as long as a model has realistic, time‐varying SST boundary conditions and QBO forcing. Observations of polar motion are most clearly relatable to atmospheric dynamics on subseasonal to annual timescales, though angular momentum budget closure is difficult to achieve even for data‐constrained atmospheric simulations. Closure of the angular momentum budget on decadal timescales is difficult and strongly dependent on estimates of angular momentum fluctuations due to core‐mantle interactions in the solid Earth.
Estimation of the strike angle of an empty tunnel in different rocks using a cross‐borehole pulse radar
Authors: Kim Sang‐Wook , Kim Se‐Yun
Published: November 2011

The finite difference time domain method is employed to calculate the radar signatures of an obliquely penetrating tunnel in various background media. The relatively faster propagation of electromagnetic signal and stronger distortion in the first peak were discovered due to the existence of an empty tunnel as its penetration angle becomes more oblique. It renders the arrival time of the first peak to be increased relatively slower than that of the first received signal. To analyze the different behaviors of two arrival times, those data are compared with the straight line model and the ray‐tracing model. Finally, the relation between the penetration angle of an empty tunnel and the arrival time of received pulse signatures is evaluated with the curve fitting model in three different background media. These results are compared with the measured data in a well suited tunnel test site.
Smart licensing and environmental flows: Modeling framework and sensitivity testing
Authors: Wilby R. L. , Fenn C. R. , Wood P. J. , Timlett R. , LeQuesne T.
Published: November 2011

Adapting to climate change is just one among many challenges facing river managers. The response will involve balancing the long‐term water demands of society with the changing needs of the environment in sustainable and cost effective ways. This paper describes a modeling framework for evaluating the sensitivity of low river flows to different configurations of abstraction licensing under both historical climate variability and expected climate change. A rainfall‐runoff model is used to quantify trade‐offs among environmental flow (e‐flow) requirements, potential surface and groundwater abstraction volumes, and the frequency of harmful low‐flow conditions. Using the River Itchen in southern England as a case study it is shown that the abstraction volume is more sensitive to uncertainty in the regional climate change projection than to the e‐flow target. It is also found that “smarter” licensing arrangements (involving a mix of hands off flows and “rising block” abstraction rules) could achieve e‐flow targets more frequently than conventional seasonal abstraction limits, with only modest reductions in average annual yield, even under a hotter, drier climate change scenario.
Emerging Trends of Nanotechnology towards Picotechnology: Energy and Biomolecules
Authors: Sharma Rakesh , Sharma Avdhesh , Chen Ching
Published: November 2011

In nature, metal oxide particles display their existence at the level of picomolecules in solution state and bioactive states in the body. We present evidence of picomolar behavior of molecules different than nanomolar behavior of particles. These particles can be encapsulated in polymers and can be functionalized with protein, nucleotides, and drugs to develop as smart intracellular targeting pico-devices. The preparation technique and physiological conditions decide the size and functionality of these pico-carrier devices. Their usable success rate, feasibility and potentials are yet to be proven or we do not know. The major difference between nanodevices and pico-devices is their intermolecular and intramolecular thermodynamics in medium and their molecular conformational interaction with molecular assembly in cytoarchitecture of the neurofilament, actin-myosin, microtubule proteins. Pico-carrier devices can be presumed as potential spears without interacting with host signal transduction and immunoprotection. In conclusion, the ultrafine size of newer picotechnology products may be better suited and easier to functionalize for design of particle based picodrugs, picochemicals, and pico-targeting molecules.
Protein repellent hydrophilic grafts prepared by surface-initiated atom transfer radical polymerization from polypropylene
Authors: Fristrup Charlotte Juel , Jankova Katja , Eskimergen Rüya , Bukrinsky Jens T. , Hvilsted Søren
Published: November 2011

Cross-linked hydrophilic poly(PEGMA) grafts (red) on PP repel fluorescence labelled insulin (green) when the PP plate is pulled out of the protein solution.
Identification of 4-hydroxy-2-nonenal–histidine adducts that serve as ligands for human lectin-like oxidized LDL receptor-1
Authors: Kumano-Kuramochi Miyuki , Shimozu Yuuki , Wakita Chika , Ohnishi-Kameyama Mayumi , Shibata Takahiro , Matsunaga Shigeru , Takano-Ishikawa Yuko , Watanabe Jun , Goto Masao , Xie Qiuhong , Komba Shiro , Uchida Koji , Machida Sachiko
Published: November 2011

LOX-1 (lectin-like oxidized low-density lipoprotein receptor-1) is an endothelial scavenger receptor that is important for the uptake of OxLDL (oxidized low-density lipoprotein) and contributes to the pathogenesis of atherosclerosis. However, the precise structural motifs of OxLDL that are recognized by LOX-1 are unknown. In the present study, we have identified products of lipid peroxidation of OxLDL that serve as ligands for LOX-1. We used CHO (Chinese-hamster ovary) cells that stably express LOX-1 to evaluate the ability of BSA modified by lipid peroxidation to compete with AcLDL (acetylated low-density lipoprotein). We found that HNE (4-hydroxy-2-nonenal)-modified proteins most potently inhibited the uptake of AcLDL. On the basis of the findings that HNE-modified BSA and oxidation of LDL resulted in the formation of HNE–histidine Michael adducts, we examined whether the HNE–histidine adducts could serve as ligands for LOX-1. The authentic HNE–histidine adduct inhibited the uptake of AcLDL in a dose-dependent manner. Furthermore, we found the interaction of LOX-1 with the HNE–histidine adduct to have a dissociation constant of 1.22×10−8 M using a surface plasmon resonance assay. Finally, we showed that the HNE–histidine adduct stimulated the formation of reactive oxygen species and activated extracellular-signal-regulated kinase 1/2 and NF-κB (nuclear factor κB) in HAECs (human aortic endothelial cells); these signals initiate endothelial dysfunction and lead to atherosclerosis. The present study provides intriguing insights into the molecular details of LOX-1 recognition of OxLDL.
Luteolin induces apoptotic cell death through AIF nuclear translocation mediated by activation of ERK and p38 in human breast cancer cell lines
Authors: Kim Moon Jung , Woo Jae Suk , Kwon Chae Hwa , Kim Jae Ho , Kim Yong Keun , Kim Ki Hyung
Published: November 2011

The flavonoid, luteolin, has been shown to have anticancer activity in various cancer cells; however, the precise molecular mechanism of its action is not completely understood, and studies were conducted to find out how it induces apoptosis in breast cancer cells. Luteolin induced a reduction of viability in a dose‐ and time‐dependent manner. The pro‐apoptotic effect of luteolin was demonstrated by cell cycle measurement and Hoechst 3325 staining. Western blot analysis showed that luteolin activates ERK (extracellular‐signal‐regulated kinase) and p38. Pharmacological inhibition or knockdown of ERK and p38 protected against luteolin‐induced cell death; however, the caspase‐3‐specific inhibitor had no effect. Immunocytochemical examination indicated that luteolin induced nuclear translocation of AIF (apoptosis‐inducing factor), which was mediated by activation of ERK and p38. Transfection of a vector expressing the miRNA (microRNA) of AIF prevented luteolin‐induced apoptosis. The data suggest that luteolin induces a caspase‐dependent and ‐independent apoptosis involving AIF nuclear translocation mediated by activation of ERK and p38 in breast cancer cells.