bluuebunny/crossref_metadata_2025_split huggingface dataset:
Small Machines in the Garden: Everyday technology and revolution in the Mekong Delta
Authors: BIGGS DAVID 
Published: November 2011

AbstractTwentieth-century industrialization in the agricultural landscapes of the Mekong Delta in Vietnam took a very different form from other places, characterized less by a continuous spread of large-scale technology than by its destruction in mid-century and the subsequent spread of small technology which powered scooters, water pumps, and boats. The numbers of these portable motors, an everyday technology in 1960, rose from a few thousand units in 1963 to millions in the present day. The colonial and post-colonial state in Vietnam played a key role in the demise of large technology and, ultimately, of the water infrastructure. Its failures during wartime spurred farmers to adopt cheap, small engines to survive; however, the state's role was complex during this time. Several key factors, including the influence of American aid programmes and the contributions of Taiwanese agricultural advisers, especially those pushing high-yield rice, favoured the adoption of small engines. From an ecological viewpoint, the post-1960 explosion in the use of small motors, especially as water pumps, has brought people and states in Southeast Asia to an ecological impasse as unrestricted use has impacted on water tables, salinity levels, and the long-term sustainability of agriculture in many places. This paper examines the state's indirect role in shaping this silent revolution, and it considers the political and ideological factors underpinning its history.
Stiffness analysis of a compliant precision positioning stage
Authors: Jia X. , Liu J. , Tian Y. , Zhang D. 
Published: November 2011

SUMMARYIn this paper a 3-degree of freedom compliant parallel positioning stage utilizing flexure hinges is explored for nanoimprint lithography. The performance of the stage is extensively analyzed using a pseudo-rigid body model and finite element method. The position and velocity models are established. Accordingly, the stiffness at driving point of the active arm is obtained on the basis of Castigliano's first theorem. The system stiffness of the compliant stage is explored using the compliant matrix methodology and matrix transformation, and the influence of the geometry parameters on stiffness factors in three directions has been graphically evaluated as well. Finite element analysis has been conducted to verify that the established models faithfully predict device performance.
Self-organizing approach for learning the forward kinematic multiple solutions of parallel manipulators
Authors: Assal Samy F. M. 
Published: November 2011

SUMMARYContrary to the inverse kinematics, the forward kinematics of parallel manipulators involves solving highly non-linear equations and provides more than one feasible end-effector pose, which are called the assembly modes, for a given set of link lengths or joint angles. Out of the multiple feasible solutions, only one solution can be achieved from a certain initial configuration. Therefore, in this paper, the Kohonen's self-organizing map (SOM) is proposed to learn and classify the multiple solution branches of the forward kinematics and then provide a unique real-time solution among the assembly modes. Each solution of the multiple feasible ones is coded using IF-THEN rules based on the values of the passive joint variables. Due to not only the classification but also the associative memory learning abilities of the SOM, the passive joint variables vector, the end-effector pose vector, and this class code are associated with the active joint variables vector constituting the input vector to the SOM in the offline learning phase. In the online testing phase, only the active joint variables vector and the class code are fed to the SOM to obtain the unique end-effector pose vector. The Jacobian matrix calculated at the SOM output layer is used for further fine tuning this output to obtain an accurate end-effector pose vector. Simulations are conducted for 3-RPR and 3-RRR planar parallel manipulators to evaluate the performance of the proposed method. The results proved high accuracy of the desired unique solution in real-time.
Classes of groups related to Fa,b,c
Authors: Campbell C. M. , Robertson E. F. 
Published: November 2011

SynopsisGroups having two generators and two relations are studied. The Reidemeister-Schreier algorithm is used to determine presentations for their derived groups. This enables the orders of the groups to be found. Necessary and sufficient conditions are given for the groups to be metabelian. Certain classes closely related to the class are also discussed.
Cyclic Banach spaces and reflexive operator algebras
Authors: Gillespie T. A. 
Published: November 2011

SynopsisLet X be a Banach space and let ℬ be a σ-complete Boolean algebra of projections on X with a cyclic vector. It is shown that there exists a normed Köthe space Lρ, the norm of which has the Fatou property, such that X is linearly homeomorphic to the subspace of Lρ consisting of those functions of absolutely continuous norm and such that, under this homeomorphism, the projections ℬ correspond to operators consisting of multiplication by characteristic functions. This representation theorem for X is used to show that certain operator algebras associated with ℬ are reflexive. As an immediate corollary of the reflexivity result, it is shown that, if T is a scalar type spectral operator whose resolution of the identity has a cyclic vector, then T is reflexive.
The condition of gram matrices and related problems
Authors: Taylor J. M. 
Published: November 2011

SynopsisIt has been known for some time that certain least-squares problems are “ill-conditioned”, and that it is therefore difficult to compute an accurate solution. The degree of ill-conditioning depends on the basis chosen for the subspace in which it is desired to find an approximation. This paper characterizes the degree of ill-conditioning, for a general inner-product space, in terms of the basis.The results are applied to least-squares polynomial approximation. It is shown, for example, that the powers {1, z, z2,…} are a universally bad choice of basis. In this case, the condition numbers of the associated matrices of the normal equations grow at least as fast as 4n, where n is the degree of the approximating polynomial.Analogous results are given for the problem of finite interpolation, which is closely related to the least-squares problem.Applications of the results are given to two algorithms—the Method of Moments for solving linear equations and Krylov's Method for computing the characteristic polynomial of a matrix.
A nonlinear singularly perturbed Volterra integrodifferential equation occurring in polymer rheology
Authors: Lodge A. S. , McLeod J. B. , Nohel J. A. 
Published: November 2011

SynopsisWe study the initial value problem for the nonlinear Volterra integrodifferential equationwhere μ > 0 is a small parameter, a is a given real kernel, and F, g are given real functions; (+) models the elongation ratio of a homogeneous filament of a certain polyethylene which is stretched on the time interval (— ∞ 0], then released and allowed to undergo elastic recovery for t > 0. Under assumptions which include physically interesting cases of the given functions a, F, g, we discuss qualitative properties of the solution of (+) and of the corresponding reduced problem when μ = 0, and the relation between them as μ → 0+, both for t near zero (where a boundary layer occurs) and for large t. In particular, we show that in general the filament does not recover its original length, and that the Newtonian term —μy′ in (+) has little effect on the ultimate recovery but significant effect during the early part of the recovery.
Convergence to travelling fronts in semilinear parabolic equations
Authors: Rothe Franz 
Published: November 2011

SynopsisWe study the convergence to the stationary state for the parabolic equation u, = uxx + F(u). There exist wave-type solutions u(x, t) = φ(x − ct) for a continuum of velocities c. In the asymptotic behavior of this equation was investigated for a step function as initial data. In this paper we obtain the asymptotic behavior for a large class of monotone initial data.All solutions with initial data in this class evolve to wave-type solutions, where the rate of decay of the initial data determines the asymptotic speed.
Acoustic tunnelling
Authors: Jones D. S. 
Published: November 2011

SynopsisGeneral formulae are obtained for the reflection and transmission of harmonic acoustic waves by a curved interface between two media when the frequency is high. In addition to refracted rays there turn up tunnelling rays, if the surface is concave to the source, which are emitted from an evanescent region when the phenomenon of total internal reflection would be anticipated. Uniformly valid formulae dealing with the transition from refraction to tunnelling in both transmission and reflection are derived.The theory is applied to the circular cylinder and to the top-hat circular jet. In the latter case it is suggested that radiation may tend to be more significant at inclinations of 50°-65° (downstream) and 25°-40° (upstream) to the axis of the cylinder. The augmentation due to tunnelling rays in propagation upstream is mentioned.
Weak containment and Clifford semigroups
Authors: Paterson Alan L. T. 
Published: November 2011

SynopsisLet S be a Clifford semigroup with identity. The weak containment question is posed for S, and answered affirmatively when each of the maximal groups Se in S is amenable. The amenability of S itself is characterised in terms of PL(S), the set of normalised positive definite functions on S arising from the left regular representation of S. A type of mean associated with PL(S) and satisfying a condition weaker than left invariance is introduced.
Asymptotic formulas for solutions of a singular linear ordinary differential equation
Authors: Gilbert Richard C. 
Published: November 2011

SynopsisBy use of the theory of asymptotic expansions for first-order linear systems of ordinary differential equations, asymptotic formulas are obtained for the solutions of annth order linear homogeneous ordinary differential equation with complex coefficients having asymptotic expansions in a sector of the complex plane. These asymptotic formulas involve the roots of certain polynomials whose coefficients are obtained from the asymptotic expansions of the coefficients of the differential operator.
On a class of weighted Sobolev spaces and the minimization of quadratic forms
Authors: Penning Frans , Sauer Niko 
Published: November 2011

SynopsisIn this paper a class of weighted Sobolev spaces defined in terms of square integrability of the gradient multiplied by a weight function, is studied. The domain of integration is either the spaceRnor a half-space ofRn. Conditions on the weight functions that will ensure density of classes of smooth functions or functions with compact support, and compact embedding theorems, are derived. Finally the results are applied to a class of isoperimetrical problems in the calculus of variations in which the domain of integration is unbounded.
The treatment of a Neumann boundary value problem for force-free fields by an integral equation method
Authors: Kress Rainer 
Published: November 2011

SynopsisA Neumann boundary value problem for the equation rot μ − λμ = u is considered. The approach is by an integral equation method based on Cauchy's integral formula for generalized harmonic vector fields. Results on existence and uniqueness are obtained in terms of the familiar Fredholm alternative.
A coordinatisation of implicative (semi-)lattices by Baer semigroups
Authors: Blyth T. S. 
Published: November 2011

SynopsisWe show that if L is a bounded (semi-)lattice and f is a range-closed idempotent residuated mapping on L then f is multiplicative if and only if it is decreasing. We then use this to prove that a bounded (semi-)lattice is implicative if and only if it can be coordinatised by a weakly multiplicative (right) Baer semigroup.
The essential self-adjointness of differential operators
Authors: Keller R. G. 
Published: November 2011

SynopsisWe consider the formally self-adjoint 2mth-order elliptic differential operator in ℝn given by where lt is an operator of order t, and establish conditions under which the operator on is essentially self-adjoint in L2. A feature is that the major conditions have to be imposed only in an increasing sequence of annular regions surrounding the origin.
Reflection and transmission of discontinuity waves through a shock wave. General theory including also the case of characteristic shocks
Authors: Boillatt Guy , Ruggeri Tommaso 
Published: November 2011

SynopsisAn incident wave creates a discontinuity in the acceleration of the shock front. The amplitudes of the reflected and transmitted waves are also determined. Special attention is given to the case of the weak shocks and the characteristic shocks.
Hyponormal and essentially normal operators
Authors: Putnam C. R. 
Published: November 2011

SynopsisLet T be a hyponormal operator on a Hilbert space, so that T*T – TT*≧ 0. Let T have the Cartesian representation T = H + iJ where H has the spectral family {Et} and suppose that EtJ − JEt is compact for almost all t on a Borei set α satisfying E(α) = I. The principal result (Theorem 3) is that under these hypotheses T must be normal. In case T is hyponormal and essentially normal some sufficient conditions are given assuring that, for a fixed t, EtJ − JEt is compact.
Solution of dual integral equations of Titchmarsh type using generalised functions
Authors: McBride Adam C. 
Published: November 2011

SynopsisThe theories of fractional calculus and of the Hankel transform developed in for the spaces F′p, μ of generalised functions are used to study distributional analogues of dual integral equations of Titchmarsh type. These are shown to have infinitely many solutions in F′p, μ under very general conditions on the parameters involved. These results are used to study the corresponding classical problem in weighted Lp spaces. Existence and uniqueness of classical solutions are investigated and examples given of both uniqueness and non-uniqueness for the classical problem.
Some comments on a singular elliptic problem associated with a rectangle
Authors: Nye V. A. 
Published: November 2011

SynopsisThe construction of the approximate solution within a rectangle of a singular elliptic problem is discussed. It is found that, provided the boundary data satisfy certain continuity conditions at the corners of the rectangle, ordinary boundary layers and parabolic boundary layers only are necessary to describe the solution. A correction term, however, has to be added to the solution if the continuity conditions on the boundary data are not satisfied.
Boundary value problems for linear systems
Authors: Neuberger J. W. 
Published: November 2011

SynopsisSuppose H and K are Hilbert spaces and H′0, H′ are closed subspaces of H so that H′0 ⊂ H′. Denote by P the orthogonal projection of H onto H′0, denote by g an element of k and by C a bounded linear transformation from H to K so that CC* = I, the identity on K. Denote CPC* by M. Given w in H′ one has the problem of finding u in H′ so thatThere are given conditions on M (or certain operators related to M) which imply convergence of a certain iteratively generated sequence to a solution to this problem. The equation Cu = g represents an inhomogeneous system of linear differential equations (ordinary, partial or functional) and the condition P(u − w) = u − w is an abstract representation of inhomogeneous boundary conditions for u.
On the location of the essential spectra and regularity fields of complex Sturm—Liouville operators
Authors: Race David 
Published: November 2011

SynopsisIn this paper the Sturm-Liouville expression τy= −(py′)′ +qy, with complex-valued coefficients is considered, and a number of results concerning the location of the essential spectrum of associated operators are obtained. Some of these are extensions or generalizations of results due to Birman, and Glazman, whilst others are new. These lead to criteria for the non-emptiness of the regularity field of the corresponding minimal operator—a condition which is needed in the theory ofJ-selfadjoint extensions. A complete determination of the regularity field is made when the equation τy= λ0yhas two linearly independent solutions inL2[a,∞) for some complex λ0.
Nonlinear eigenvalue problems for the whirling of heavy elastic strings
Authors: Antman Stuart S. 
Published: November 2011

SynopsisThis paper combines the global bifurcation theory of Rabinowitz with Sturmian theory and careful estimates to obtain a detailed qualitative description of bifurcating branches of solutions to the equations for whirling nonuniform, nonlinearly elastic strings. These results generalize earlier work of Kolodner and Stuart on inextensible strings. It is shown that the location of solution branches for the generalization of Kolodner's problem is especially sensitive to the material properties of the string, whereas that for Stuart's problem is not. The analysis of a third problem illuminates the source of this dichotomy.
Non-trivial solutions of elliptic equations at resonance
Authors: Thews Klaus 
Published: November 2011

SynopsisIn this paper we show that Dirichlet problems at resonance, being of the type −Δu(x) = λku(x) + g(u(x)), x є G, u(x) = 0 for x є ∂G, g(−u) = −g(u), admit multiple non-trivial solutions provided the non-linearity interacts in some sense with the spectrum of −Δ. In contrast to other work on this subject we deal with the case that g(u) is very small for large arguments, for instance g(u) = 0 for |u| large. On the other hand if and g satisfies a certain concavity condition at 0 the existence of infinitely many solutions is shown independent of the asymptotic behaviour of g.
Monotone continuity of the spectral resolution and the eigenvalues
Authors: Weidmann Joachim 
Published: November 2011

SynopsisLet (Tn) be a non-decreasing sequence of self-adjoint operators which are semi-bounded from below and converge to some self-adjoint operator T in the sense of strong resolvent convergence. For every λ which is eventually below the essential spectrum of Tn it is shown that ‖En(λ)−E(λ)‖→0 for n→∞, where En(·) and E(·) are the spectral resolution of Tn and T, respectively.
Normal AW*-algebras
Authors: Maitland Wright J. D. 
Published: November 2011

SynopsisIn recent years it has become clear that AW*-algebras can be much more pathological and unlike von Neumann algebras than was originally expected. When AW*-algebras are monotone complete, then the work of Kadison and Pederson shows that a particularly smooth and elegant theory can be developed. A technically weaker requirement on an AW*-algebra is that it be “normal”. This condition, which says that the lattice of projections is embedded in a well-behaved way in the partially ordered set of all self-adjoint elements, can sometimes be used as a substitute for monotone completeness. In this note we prove that when an AW*-algebra is of finite type (that is x*x = 1 implies xx* = 1) then it is normal.
Existence of periodic orbits of autonomous ordinary differential equations
Authors: Smith Russell A. 
Published: November 2011

SynopsisThe Poincaré-Bendixson theorem, concerning the existence of periodic orbits of plane autonomous systems, is extended to higher order systems under certain conditions. Under similar conditions, a complementary theorem on the existence of recurrent orbits is also proved. For the feedback control equation, these conditions are reduced to a form which can be easily verified in practice.
Gewöhnliche lineare Differentialgleichungen n−ter Ordnung mit Distributionskoeffizienten
Authors: Pfaff Rainer 
Published: November 2011

SynopsisWe give a formula (4) for a variety of ordinary linear differential equations of order n with distributional coefficients. There appear as coefficients distributions of order k ≦ n/2, i.e. these distributions are kth distributional derivatives of locally L-integrable functions. With a suitable transformation (7) the differential equations can be transformed into first order systems (8) with integrable coefficients. From this follows the existence of a continuous solution, which can be uniquely determined by proper initial conditions.The coefficients in the differential equations considered are chosen as general as possible but such that a transformation into a system with integrable coefficients can be performed, and that all products are defined by Leibniz' formula.
Eigenfunction expansions for a class of J-selfadjoint ordinary differential operators with boundary conditions containing the eigenvalue parameter
Authors: Dijksma Aalt 
Published: November 2011

SynopsisIn provided with a J-innerproduct we characterize the J-selfadjoint operators generated by a symmetric ordinary differential expression on an open real interval ι. For a subclass of these operators we prove eigenfunction expansion results using Hilbertspace-techniques.
Weighted inequalities for the Stieltjes transformation and Hubert's double series
Authors: Andersen Kenneth F. 
Published: November 2011

SynopsisThe non-negative weight functions U(x), V(x) for which the generalized Stieltjes transformation Sλ is a bounded operator from LP(V) into La(U) are characterized. This extends certain classical inequalities and some recent results of Erdélyi. In particular, our results provide weighted extensions of a classical inequality known as Hubert's double series theorem.
N-series and tame near-rings
Authors: Lyons C. G. , Meldrum J.D.P. 
Published: November 2011

SynopsisLet N be a zero-symmetric near-ring with identity and let G be an N-group. We consider in this paper nilpotent ideals of N and N-series of G and we seek to link these two ideas by defining characterizing series for nilpotent ideals. These often exist and in most cases a minimal characterizing series exists. Another special N-series is a radical series, that is a shortest N-series with a maximal annihilator. These are linked to appropriate characterizing series. We apply these ideas to obtain characterizing series for the radical of a tame near-ring N, and to show that these exist if either G has both chain conditions on N-ideals or N has the descending chain condition on right ideals. In the latter case this provides a new proof of the nilpotency of the radical of a tame near-ring with DCCR, and an internal method for constructing minimal and maximal characterizing series for the radical.
Maximum modulus algebras and singularity sets
Authors: Wermer John 
Published: November 2011

SynopsisA classical theorem of Hartogs gives conditions on the singularity set of an analytic function of several complex variables in order for such a set to be an analytic variety. A result of E. Bishop from 1963 gives an analogous condition of the maximal ideal space of a uniform algebra in order for this space to have analytic structure. We show that algebras of functions satisfying a maximum principle serve to explain both of these results.
Asymptotic methods for fourth-order differential equations
Authors: Grudniewicz C. G. M. 
Published: November 2011

SynopsisA new method is developed for obtaining the asymptotic form of solutions of the fourth-order differential equationwherem, nare integers and 1 ≦m,n≦ 2. The method gives new, shorter proofs of the well-known results of Walker in deficiency index theory and covers the cases not considered by Walker.
An inverse for the Gohberg-Krupnik symbol map
Authors: Costabel Martin 
Published: November 2011

SynopsisIt is shown that the elements of the closed operator algebra generated by one-dimensional singular integral operators with piecewise continuous coefficients with a fixed finite set of points of discontinuity can be written as the sum of a singular integral operator, a compact operator, and generalized Mellin convolutions. Their Gohberg-Krupnik symbol is given in terms of the Mellin transform. This gives an explicit construction of an operator with prescribed Gohberg—Krupnik symbol.