Uniqueness for boundary value problems for second order finite difference equations

We establish maximum principles for second order difference equations and apply them to obtain uniqueness for solutions of some boundary value problems.

First- and second-order stimulus length selectivity in New World monkey striate cortex

Motion is a powerful cue for figure-ground segregation, allowing the recognition of shapes even if the luminance and texture characteristics of the stimulus and background are matched. In order to investigate the neural processes underlying early stages of the cue-invariant processing of form, we compared the responses of neurons in the striate cortex (V1) of anaesthetized marmosets to two types of moving stimuli: bars defined by differences in luminance, and bars defined solely by the coherent motion of random patterns that matched the texture and temporal modulation of the background. A population of form-cue-invariant (FCI) neurons was identified, which demonstrated similar tuning to the length of contours defined by first- and second-order cues. FCI neurons were relatively common in the supragranular layers (where they corresponded to 28% of the recorded units), but were absent from layer 4. Most had complex receptive fields, which were significantly larger than those of other V1 neurons. The majority of FCI neurons demonstrated end-inhibition in response to long first- and second-order bars, and were strongly direction selective, Thus, even at the level of V1 there are cells whose variations in response level appear to be determined by the shape and motion of the entire second-order object, rather than by its parts (i.e. the individual textural components). These results are compatible with the existence of an output channel from V1 to the ventral stream of extrastriate areas, which already encodes the basic building blocks of the image in an invariant manner.

Solvability of singular second order m-point boundary value problems of Dirichlet type

Let f : [0, 1] x R2 -> R be a function satisfying the Caxatheodory conditions and t(1 - t)e(t) epsilon L-1 (0, 1). Let a(i) epsilon R and xi(i) (0, 1) for i = 1,..., m - 2 where 0 < xi(1) < xi(2) < (...) < xi(m-2) < 1 - In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem [GRAPHICS] The proof of our main result is based on the Leray-Schauder continuation theorem.

Multiplicity results for second-order two-point boundary value problems with nonlinearities across several eigenvalues

We consider the boundary value problems for nonlinear second-order differential equations of the form u '' + a(t)f (u) = 0, 0 < t < 1, u(0) = u (1) = 0. We give conditions on the ratio f (s)/s at infinity and zero that guarantee the existence of solutions with prescribed nodal properties. Then we establish existence and multiplicity results for nodal solutions to the problem. The proofs of our main results are based upon bifurcation techniques. (c) 2004 Elsevier Ltd. All rights reserved.

Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t) f(u) = 0, t epsilon (0, 1), u(0) = u(1) = 0, where a epsilon C([0, 1], (0, infinity)) and f : R --> R is continuous and satisfies f (s)s > 0 for s not equal 0. We establish existence and multiplicity results for nodal solutions to the problems if either f(0) = 0, f(infinity) = infinity or f(0) = infinity, f(0) = 0, where f (s)/s approaches f(0) and f(infinity) as s approaches 0 and infinity, respectively. We use bifurcation techniques to prove our main results. (C) 2004 Elsevier Inc. All rights reserved.

Late pleistocene to holocene composite speleothem O-18 and C-13 chronologies from south island, new Zealand-did a global younger dryas really exist?

Oxygen and carbon data from eight stalagmites from northwest South Island are combined to produce composite records of delta(18)O and delta(13)C from 23.4 ka to the present. The chronology is anchored by 43 thermal ionization mass spectrometry (TIMS) uranium series ages. Delta O-18 values are interpreted as having a first order positive relationship to temperature, but also to be influenced by precipitation in a complex manner. Delta C-13 is interpreted as responding negatively to increases in atmospheric CO, concentration, biological activity and precipitation amount. Six climatic phases are recognized. After adjustment of 1.2parts per thousand for the ice volume effect, the delta(18)O record between 23 and 18 ka varies around -3.72parts per thousand compared to the Holocene average of -3.17parts per thousand. Late-glacial warming commenced between 18.2 and 17.8 ka and accelerated after 16.7 ka, culminating in a positive excursion between 14.70 and 13.53 ka. This was followed by a significant negative excursion between 13.53 and 11.14 ka of up to 0.55parts per thousand depth that overlapped the Antarctic Cold Reversal (ACR) and spanned the Younger Dryas (YD). Positive delta(18)O excursions at 11.14 ka and 6.91-6.47 ka represent the warmest parts of the Holocene. The mid-Holocene from 6 to 2 ka was marked by negative excursions that coincide with increased glacial activity in the South Island. A short positive excursion from 0.71 to 0.57 ka was slightly later than the Medieval Warm Period of Europe. Delta C-13 values were high until 17.79 ka after which there was an abrupt decrease to 17.19 ka followed by a steady decline to a minimum at 10.97 ka. Then followed a general increase, suggesting a drying trend, to 3.23 ka followed by a further general decline. The abrupt decrease in delta-values after 17.79 ka probably corresponds to an increase in atmospheric CO2 concentration, biological activity and wetness at the end of the Last Glaciation, but the reversal identified in the delta(18)O record from 13.53 to 11.14 ka was not reflected in delta(13)C changes. The lowest delta(13)C values coincided with the early Holocene climatic suboptimum when conditions were relatively wet as well as mild. Major trends in the delta(18)O(c) record are similar to the Northern Hemisphere, but second order detail is often distinctly different. Consequently, at the millennial scale, a more convincing case can be made for asymmetric climatic response between the two hemispheres rather than synchronicity. (C) 2004 Elsevier B.V. All rights reserved.

Random vibration of the functionally graded laminates in thermal environments

This work deals with the random free vibration of functionally graded laminates with general boundary conditions and subjected to a temperature change, taking into account the randomness in a number of independent input variables such as Young's modulus, Poisson's ratio and thermal expansion coefficient of each constituent material. Based on third-order shear deformation theory, the mixed-type formulation and a semi-analytical approach are employed to derive the standard eigenvalue problem in terms of deflection, mid-plane rotations and stress function. A mean-centered first-order perturbation technique is adopted to obtain the second-order statistics of vibration frequencies. A detailed parametric study is conducted, and extensive numerical results are presented in both tabular and graphical forms for laminated plates that contain functionally graded material which is made of aluminum and zirconia, showing the effects of scattering in thermo-clastic material constants, temperature change, edge support condition, side-to-thickness ratio, and plate aspect ratio on the stochastic characteristics of natural frequencies. (c) 2005 Elsevier B.V. All rights reserved.