bluuebunny/crossref_metadata_2025_split huggingface dataset:
Using quasiconvex functionals to bound the effective conductivity of composite materials
Authors: Nesi V. 
Published: November 2011

SynopsisIn 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

SynopsisMultiple 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.
The stability of the resonance set for a problem with jumping non-linearity
Authors: d'Aujourd'hui Marcel 
Published: November 2011

SynopsisFor 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

SynopsisIn 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

SynopsisThe paper considers the small time evolution of the interface which appears in the boundary value problemA 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

SynopsisWe 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

SynopsisIn 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

SynopsisLeading 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

SynopsisWe 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.
Nearly real fronts in a Ginzburg–Landau equation
Authors: Jones Christopher K. R. T. , Kapitula Todd M. , Powell James A. 
Published: November 2011

SynopsisSubcritical 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.
Idempotents in partial transformation semigroups
Authors: Garba G. U. 
Published: November 2011

SynopsisAn 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 thatLet 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 thatα 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

SynopsisIn 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 offor 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

SynopsisThroughout 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

SynopsisWe 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

SynopsisIf 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

SynopsisIn 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.
Landau's inequality
Authors: Kwong M. K. , Zettl A. 
Published: November 2011

SynopsisLandau'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

SynopsisFor 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

SynopsisThe 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 byThe 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

SynopsisA 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.
Homogenisation of parametrised families of hyperbolic problems
Authors: Amirat Y. , Hamdache K. , Ziani A. 
Published: November 2011

SynopsisThis 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

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

SynopsisWe 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.
Approximation properties of sets with bounded complements
Authors: Franchetti C. , Papini P. L. 
Published: November 2011

SynopsisGiven 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

SynopsisLety(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 abstract multiparameter spectral theory
Authors: Binding P. A. , Källström A. , Sleeman B. D. 
Published: November 2011

SynopsisWe consider the eigenvalue problemfor 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

SynopsisLet 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

SynopsisIt 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

SynopsisBy 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

SynopsisLet 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 propertyfor every harmonic function near m, characterizes Einstein spaces. We define super-Einstein spaces and prove that they are characterized by the property
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.
Emerging Trends of Nanotechnology towards Picotechnology: Energy and Biomolecules
Authors: Sharma Rakesh , Sharma Avdhesh , Chen Ching 
Published: November 2011

AbstractIn 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.
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

AbstractThe 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.