On exact solutions of the unsteady navierstokes equations�� the vortex with instantaneous curvilinear axis

The unsteady pseudo plane motions have been investigated in which each point of the parallel planes is subjected to non-torsional oscillations in their own plane and at any given instant the streamlines are concentric circles. Exact solutions are obtained and the form of the curve , the locus of the centers of these concentric circles, is discussed. The existence of three infinite sets of exact solutions, for the flow in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks, is established. Three cases arise according to whether is greater than, equal to or less than , where is angular velocity of the basic rotation and is the frequency of the superposed oscillations. For a symmetric solution of the flow these solutions reduce to a single unique solution. The nature of the curve is illustrated graphically by considering an example of the flow between coaxial rotating disks.

A new algorithm for parallel solution of linear equations

Abstract is not available.

Structural and functional characterization of dendritic arbors and GABAergic synaptic inputs on interneurons and principal cells in the rat basolateral amygdala

The basolateral amygdala (BLA) is a complex brain region associated with processing emotional states, such as fear, anxiety, and stress. Some aspects of these emotional states are driven by the network activity of synaptic connections, derived from both local circuitry and projections to the BLA from other regions. Although the synaptic physiology and general morphological characteristics are known for many individual cell types within the BLA, the combination of morphological, electrophysiological, and distribution of neurochemical GABAergic synapses in a three-dimensional neuronal arbor has not been reported for single neurons from this region. The aim of this study was to assess differences in morphological characteristics of BLA principal cells and interneurons, quantify the distribution of GABAergic neurochemical synapses within the entire neuronal arbor of each cell type, and determine whether GABAergic synaptic density correlates with electrophysiological recordings of inhibitory postsynaptic currents. We show that BLA principal neurons form complex dendritic arborizations, with proximal dendrites having fewer spines but higher densities of neurochemical GABAergic synapses compared with distal dendrites. Furthermore, we found that BLA interneurons exhibited reduced dendritic arbor lengths and spine densities but had significantly higher densities of putative GABAergic synapses compared with principal cells, which was correlated with an increased frequency of spontaneous inhibitory postsynaptic currents. The quantification of GABAergic connectivity, in combination with morphological and electrophysiological measurements of the BLA cell types, is the first step toward a greater understanding of how fear and stress lead to changes in morphology, local connectivity, and/or synaptic reorganization of the BLA.

Generalized Burgers equations and Euler-Painleve transcendents. II

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.

A multi-microprocessor architecture for solving partial differential equations

This paper presents the architecture of a fault-tolerant, special-purpose multi-microprocessor system for solving Partial Differential Equations (PDEs). The modular nature of the architecture allows the use of hundreds of Processing Elements (PEs) for high throughput. Its performance is evaluated by both analytical and simulation methods. The results indicate that the system can achieve high operation rates and is not sensitive to inter-processor communication delay.

Exact solutions of coupled multispecies linear reaction–diffusion equations on a uniformly growing domain

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Functional dynamics of the nitrogen balance of sorghum. II. Grain filling period.

Maintenance of green leaf area during grain filling can increase grain yield of sorghum grown under terminal water limitation. This 'stay-green' trait has been related to the nitrogen (N) supply-demand balance during grain filling. This study quantifies the N demand of grain and N translocation rates from leaves and stem and explores effects of genotype and N stress on onset and rate of leaf senescence during the grain filling period. Three hybrids differing in potential height were grown at three levels of N supply under well-watered conditions. Vertical profiles of biomass, leaf area, and N% of leaves, stem and grain were measured at regular intervals. Weekly SPAD chlorophyll readings on main shoot leaves were correlated with observed specific leaf nitrogen (SLN) to derive seasonal patterns of leaf N content. For all hybrids, individual grain N demand was sink determined and was initially met through N translocation from the stem and rachis. Only if this was insufficient did leaf N translocation occur. Maximum N translocation rates from leaves and stem were dependent on their N status. However, the supply of N at canopy scale was also related to the amount of leaf area senescing at any one time. This supply-demand framework for N dynamics explained effects of N stress and genotype on the onset and rate of leaf senescence.

Functional dynamics of the nitrogen balance of sorghum: I. N demand of vegetative plant parts.

Stay-green, an important trait for grain yield of sorghum grown under water limitation, has been associated with a high leaf nitrogen content at the start of grain filling. This study quantifies the N demand of leaves and stems and explores effects of N stress on the N balance of vegetative plant parts of three sorghum hybrids differing in potential crop height. The hybrids were grown under well-watered conditions at three levels of N supply. Vertical profiles of biomass and N% of leaves and stems, together with leaf size and number, and specific leaf nitrogen (SLN), were measured at regular intervals. The hybrids had similar minimum but different critical and maximum SLN, associated with differences in leaf size and N partitioning, the latter associated with differences in plant height. N demand of expanding new leaves was represented by critical SLN, and structural stem N demand by minimum stem N%. The fraction of N partitioned to leaf blades increased under N stress. A framework for N dynamics of leaves and stems is developed that captures effects of N stress and genotype on N partitioning and on critical and maximum SLN.

Isolation and functional characterization of a lycopene beta-cyclase gene that controls fruit colour of papaya (Carica papaya L.).

The colour of papaya fruit flesh is determined largely by the presence of carotenoid pigments. Red-fleshed papaya fruit contain lycopene, whilst this pigment is absent from yellow-fleshed fruit. The conversion of lycopene (red) to beta-carotene (yellow) is catalysed by lycopene beta-cyclase. This present study describes the cloning and functional characterization of two different genes encoding lycopene beta-cyclases (lcy-beta1 and lcy-beta2) from red (Tainung) and yellow (Hybrid 1 B) papaya cultivars. A mutation in the lcy-beta2 gene, which inactivates enzyme activity, controls lycopene production in fruit and is responsible for the difference in carotenoid production between red and yellow-fleshed papaya fruit. The expression level of both lcy-beta1 and lcy-beta2 genes is similar and low in leaves, but lcy-beta2 expression increases markedly in ripe fruit. Isolation of the lcy-beta2 gene from papaya, that is preferentially expressed in fruit and is correlated with fruit colour, will facilitate marker-assisted breeding for fruit colour in papaya and should create possibilities for metabolic engineering of carotenoid production in papaya fruit to alter both colour and nutritional properties.

Direct measurement of inner prosthesis loading during activities of daily living: Proposal for classification of functional outcome

Background The purpose of this presentation is to outline the relevance of the categorization of the load regime data to assess the functional output and usage of the prosthesis of lower limb amputees. The objectives are • To highlight the need for categorisation of activities of daily living • To present a categorization of load regime applied on residuum, • To present some descriptors of the four types of activity that could be detected, • To provide an example the results for a case. Methods The load applied on the osseointegrated fixation of one transfemoral amputee was recorded using a portable kinetic system for 5 hours. The load applied on the residuum was divided in four types of activities corresponding to inactivity, stationary loading, localized locomotion and directional locomotion as detailed in previously publications. Results The periods of directional locomotion, localized locomotion, and stationary loading occurred 44%, 34%, and 22% of recording time and each accounted for 51%, 38%, and 12% of the duration of the periods of activity, respectively. The absolute maximum force during directional locomotion, localized locomotion, and stationary loading was 19%, 15%, and 8% of the body weight on the anteroposterior axis, 20%, 19%, and 12% on the mediolateral axis, and 121%, 106%, and 99% on the long axis. A total of 2,783 gait cycles were recorded. Discussion Approximately 10% more gait cycles and 50% more of the total impulse than conventional analyses were identified. The proposed categorization and apparatus have the potential to complement conventional instruments, particularly for difficult cases.

Derivation of the solution of certain singular integral equations

It is shown that the a;P?lication of the Poincare-Bertrand fcm~ulaw hen made in a suitable manner produces the s~lutiano f certain singular integral equations very quickly, thc method of arriving at which, otherwise, is too complicaled. Two singular integral equations are considered. One of these quaiions is with a Cauchy-tyge kcrnel arid the other is an equalion which appears in the a a w guide theory and the theory of dishcations. Adifferent approach i? alw made here to solve the singular integralquation> of the waveguide theor? ind this i ~ v o l v eth~e use of the inversion formula of the Cauchy-type singular integral equahn and dudion to a system of TIilberl problems for two unknowns which can be dwupled wry easily to obi& tbe closed form solutim of the irilegral equatlou at band. The methods of the prescnt paper avoid all the complicaled approaches of solving the singular integral equaticn of the waveguide theory knowr todate.

On a linear steady-state system of equations in microcontinuum fluid mechanics

Galerkin representations and integral representations are obtained for the linearized system of coupled differential equations governing steady incompressible flow of a micropolar fluid. The special case of 2-dimensional Stokes flows is then examined and further representation formulae as well as asymptotic expressions, are generated for both the microrotation and velocity vectors. With the aid of these formulae, the Stokes Paradox for micropolar fluids is established.

Expression of functional GABAc receptors in the brain

γ-aminobutyric acid (GABA) is the main inhibitory transmitter in the nervous system and acts via three distinct receptor classes: A, B, and C. GABAC receptors are ionotropic receptors comprising ρ subunits. In this work, we aimed to elucidate the expression of ρ subunits in the postnatal brain, the characteristics of ρ2 homo-oligomeric receptors, and the function of GABAC receptors in the hippocampus. In situ hybridization on rat brain slices showed ρ2 mRNA expression from the newborn in the superficial grey layer of the superior colliculus, from the first postnatal week in the hippocampal CA1 region and the pretectal nucleus of the optic tract, and in the adult dorsal lateral geniculate nucleus. Quantitative RT-PCR revealed expression of all three ρ subunits in the hippocampus and superior colliculus from the first postnatal day. In the hippocampus, ρ2 mRNA expression clearly dominated over ρ1 and ρ3. GABAC receptor protein expression was confirmed in the adult hippocampus, superior colliculus, and dorsal lateral geniculate nucleus by immunohistochemistry. From the selective distribution of ρ subunits, GABAC receptors may be hypothesized to be specifically involved in aspects of visual image motion processing in the rat brain. Although previous data had indicated a much higher expression level for ρ2 subunit transcripts than for ρ1 or ρ3 in the brain, previous work done on Xenopus oocytes had suggested that rat ρ2 subunits do not form functional homo-oligomeric GABAC receptors but need ρ1 or ρ3 subunits to form hetero-oligomers. Our results demonstrated, for the first time, that HEK 293 cells transfected with ρ2 cDNA displayed currents in whole-cell patch-clamp recordings. Homomeric rat ρ2 receptors had a decreased sensitivity to, but a high affinity for picrotoxin and a marked sensitivity to the GABAC receptor agonist CACA. Our results suggest that ρ2 subunits may contribute to brain function, also in areas not expressing other ρ subunits. Using extracellular electrophysiological recordings, we aimed to study the effects of the GABAC receptor agonists and antagonists on responses of the hippocampal neurons to electrical stimulation. Activation of GABAC receptors with CACA suppressed postsynaptic excitability and the GABAC receptor antagonist TPMPA inhibited the effects of CACA. Next, we aimed to display the activation of the GABAC receptors by synaptically released GABA using intracellular recordings. GABA-mediated long-lasting depolarizing responses evoked by high-frequency stimulation were prolonged by TPMPA. For weaker stimulation, the effect of TPMPA was enhanced after GABA uptake was inhibited. Our data demonstrate that GABAC receptors can be activated by endogenous synaptic transmitter release following strong stimulation or under conditions of reduced GABA uptake. The lack of GABAC receptor activation by less intensive stimulation under control conditions suggests that these receptors are extrasynaptic and activated via spillover of synaptically released GABA. Taken together with the restricted expression pattern of GABAC receptors in the brain and their distinctive pharmacological and biophysical properties, our findings supporting extrasynaptic localization of these receptors raise interesting possibilities for novel pharmacological therapies in the treatment of, for example, epilepsy and sleep disorders.