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Notes: Abstract Minimum onset latency (Lmin) of single- and multiple-unit responses were mapped in the primary auditory cortex (AI) of barbiturate-anesthetized cats. Contralateral Lmin for multiple units was non-homogeneously distributed along the dorso-ventral/isofrequency axis of the AI. Responses with shorter latencies were more often located in the central, more sharply tuned region while longer latencies were more frequently encountered in the dorsal and ventral portions of the AI. For single units, a large scatter of Lmin values was found throughout the extent of the AI including cortical depth. The relationship between Lmin and previously reported spectral, intensity and temporal parameters was analyzed and revealed statistically significant correlations between minimum onset latency and the following response properties in some but not all studied animals: sharpness of tuning of a frequency response area 10 dB above threshold, broadband transient response, strongest response level, monotonicity of rate/level functions, dynamic range, and preferred frequency modulation sweep direction. This analysis suggests that Lmin is determined by several independent factors and that the prediction of Lmin based on relationships with other spectral and temporal response properties is inherently weak. The spatial distribution and the functional relationship between these response parameters may provide an important aspect of the time-based cortical representation of specific features in the animal's natural environment.

Notes: Abstract The reinnervation pattern of crural pacinian corpuscles was examined by light and electron microscopy in eight adult cats of both sexes 3–18 months after sciatic nerve crush. Normal pacinian corpuscles are each supplied with a single myelinated axon and a single cylindrical axon terminal which may branch in the distal part of the inner core. Reinnervation of these vibroreceptors was very satisfactory after sciatic nerve crush: in a sample of 68 corpuscles examined 3–18 months after the operation, 92.6% were found reinnervated, while only 7.4% remained denervated. At the nerve entry, 84.2% of the reinnervated corpuscles were supplied with a single myelinated axon, while 15.8% received two myelinated axons; some of the axons branched before or after entering the inner core. Near the mid-level of the inner core, 60.3% of 63 reinnervated corpuscles were innervated with a single axon terminal, 22.2% were biterminal, while 17.5% had three or more terminals. Regenerated axon terminals induced the formation of thin lamellar layers in the axial region of the original core and, exceptionally, also at the outer aspect of the original core. In monoterminal corpuscles, the shape and ultrastructure of regenerated endings resembled those of normal controls, whereas in multiterminal corpuscles their shape and profiles were variable. In contrast to previous reports, reinnervated corpuscles did not ultimately become monoterminal. On the contrary, the mean number of 1.3 terminals found in reinnervated crural corpuscles at 3–5 months increased to 1.9 terminals per corpuscle 6–18 months after axotomy.

Notes: Abstract  In this study we examined connections between the moment-generating capacity of the neck muscles and their patterns of activation during voluntary head-tracking movements. Three cats lying prone were trained to produce sinusoidal (0.25 Hz) tracking movements of the head in the sagittal plane, and 22.5º and 45º away from the sagittal plane. Radio-opaque markers were placed in the cervical vertebrae, and intramuscular patch electrodes were implanted in five neck muscles, including biventer cervicis, complexus, splenius capitis, occipitoscapularis, and rectus capitis posterior major. Videofluoroscopic images of cervical vertebral motion and muscle electromyographic responses were simultaneously recorded. A three-dimensional biomechanical model was developed to estimate how muscle moment arms and force-generating capacities change during the head-tracking movement. Experimental results demonstrated that the head and vertebrae moved synchronously, but neither the muscle activation patterns nor vertebral movements were constant across trials. Analysis of the biomechanical model revealed that, in some cases, modification of muscle activation patterns was consistent with changes in muscle moment arms or force-generating potential. In other cases, however, changes in muscle activation patterns were observed without changes in muscle moment arms or force-generating potential. This suggests that the moment-generating potential of muscles is just one of the variables that influences which muscles the central nervous system will select to participate in a movement.

Notes: Abstract  For an understanding of how various degrees of altered use (training, disuse) affect the properties of skeletal muscles, it is important to know how much they are used normally. The main aim of the present project was to produce such background knowledge for hindlimb muscles of the cat. In four adult female cats, each one being studied in several experimental sessions, ankle muscles were chronically implanted with electrodes for electromyographic (EMG) recording. The muscles recorded from were: extensor digitorum longus (EDL), peroneus longus (PL), tibialis anterior (TA), lateral gastrocnemius (LG) and soleus (SOL). For PL, TA and LG, there were anterior as well as posterior recording sites. During 24-h experimental sessions, the studied animal stayed, together with another cat, in a box large enough for playing and walking around. Using telemetric techniques, samples of EMG signals were recorded on tape for 4 min every 30 min. In an off-line analysis, measurements were made of the total accumulated duration of activity from each one of the studied muscle regions. These ”duty times” were expressed as a percentage of total sampling duration. When averaged over the whole 24-h experimental period, the mean duty times per muscle region varied from 1.9% for EDL up to about 13.9% for SOL. Also, among predominantly fast muscles of mixed-fibre composition (i.e. all studied muscles except SOL), marked and statistically significant differences in duty time were found, mean values varying fivefold from 1.9% (EDL) to 9.5% (PL, posterior site). For all three muscles with simultaneous recordings from different sites, consistent and statistically significant differences in daily duty time were found between anterior and posterior regions (anterior less than posterior for TA and PL; anterior more than posterior for LG). We also measured the extent to which each 4-min sampling period was filled with activity (if any). As compared to muscles with a low mean 24-h duty time, those with high duty times were not active during more sampling periods per day, but, whenever being used, their activity lasted relatively longer. Such results were consistent with the view that differences in mean 24-h duty time might largely reflect differences in the extent to which the various muscles and muscle regions were used for long-lasting stabilizing contractions.

Notes: Abstract Results of previous studies have indicated that the rostral superior colliculus (SC) plays an important part in the control of accommodation. The present study was carried out to investigate retinal projections to the accommodation-related area in the rostral SC. We injected WGA-HRP into the accommodation-related area in the rostral SC of the cat, where accommodative responses were elicited by stimulation with weak currents of less than 20 μA. Following injection of WGA-HRP into the accommodation-related area in the rostral SC, retrogradely labeled ganglion cells were observed mainly in the area centralis. Projections from the contralateral eye were denser than those from the ipsilateral eye. Almost all retrogradely labeled cells were classified as γ-cells owing to their small cell-body diameters and thin dendrites, although a few were classified as α-cells. These findings suggest that the accommodation-related area in the rostral SC is located in the portion corresponding to the area of representation of the central visual field and receives mainly γ-cell projections

Notes: Abstract  In decerebrate cats that had been acutely hemilabyrinthectomized (HL), the extracellular activities of vestibular nuclear neurons on the lesioned and labyrinth-intact sides were studied during constant-velocity off-vertical axis rotations (OVAR) in the clockwise (CW) and counterclockwise (CCW) directions (at 10° tilt). Over the range of 1.75–15°/s, two types of neuronal responses were identified on both sides. Some neurons showed symmetric and velocity-stable bidirectional response sensitivity (δ defined as the CW gain over the CCW gain) while other neurons exhibited asymmetric and velocity-variable δ. The mathematically derived gain tuning ratios of these two groups of neurons were within the range of one-dimensional and two-dimensional neurons respectively. The best response orientations in one-dimensional neurons and the orientations of the maximum response vector, S max, in two-dimensional neurons were found to point in all directions on the horizontal plane. On the labyrinth-intact side, both the one-dimensional and two-dimensional neurons showed asymmetry in the neuron numbers and/or the response gains between the two roll quadrants as well as between the two pitch quadrants. In addition, both the neuron number and gain were significantly higher for neurons in the head-down/ipsilateral-side-down half-circle than those in the head-up/contralateral-side-down half-circle. None of the aforementioned asymmetries was observed on the lesioned side. That a comparable pattern of distribution was observed in the one-dimensional and two-dimensional neurons suggests that these neurons maintain a common spatial reference frame in encoding head orientational signals arising from the ipsilateral and contralateral otoliths. Furthermore, a predominance of two-dimensional neurons that exhibited a greater gain with CW rotations was observed on both sides of HL cats. Of the response dynamics observed amongst neurons on the two sides of HL cats, no difference was found with regard to the response gain and the pattern of response lead. However, a difference in response lag was observed between neurons on the two sides of HL cats. These suggest that there is a segregation of otolithic signals to reach the ipsilateral and contralateral vestibular nuclei. Taken together, the present study demonstrates that one-dimensional and two-dimensional neuronal responses could be elicited with inputs arising solely from the ipsilateral or contralateral otoliths. The observed orientational tuning and the CW-CCW asymmetry to bidirectional rotation may provide the essential directional coding of head orientations. Further, the imbalance of spatial/dynamic response patterns between the bilateral vestibular nuclei following the restriction of otolith inputs by HL implies that converging otolithic inputs from the bilateral labyrinths are essential for producing the neuronal responses in control animals. The results are also discussed in terms of the possible contribution of the various neural asymmetries between neuronal subpopulations in the bilateral vestibular nuclei to the behavioral symptoms accompanying acute HL.

Notes: Abstract  A technique was developed to measure, in the anesthetized and paralyzed cat under artificial ventilation, changes of excitability to intraspinal stimulation simultaneously in two different afferent fibers or in two collaterals of the same afferent fiber. Intraspinal stimulation reduced the threshold of single muscle afferent fibers ending in the intermediate nucleus. This effect was seen with strengths below those required to activate the afferent fiber tested (1.5–12 μA), occurred at a short latency (1.5–2.0 ms), reached a maximum between 15 and 30 ms, and lasted up to 100 ms. The effects produced by graded stimulation applied at the shortest conditioning-testing stimulus time intervals increased by fixed steps, suggesting recruitment of discrete elements, most likely of last-order interneurons mediating primary afferent depolarization (PAD). The short-latency increases in excitability produced by the weakest effective intraspinal stimuli were usually detected only in the collateral closest to the stimulating micropipette, indicating that the stimulated interneurons mediating PAD have spatially restricted actions. The short-latency PAD produced by intraspinal stimuli, as well as the PAD produced by stimulation of the posterior biceps and semitendinosus (PBSt) nerve or by stimulation of the bulbar reticular formation (RF), was depressed 19–30 min after the i.v. injection of 0.5 mg/kg of picrotoxin, suggesting that all these effects were mediated by GABAergic mechanisms. The PAD elicited by stimulation of muscle and/or cutaneous nerves was depressed following the i.v. injection of (–)-baclofen, whereas the PAD elicited in the same collateral by stimulation of the RF was baclofen-resistant. The short-latency PAD produced by intraspinal stimulation was not always depressed by i.v. injections of (–)-baclofen. Baclofen-sensitive and baclofen-resistant monosynaptic PADs could be produced in different collaterals of the same afferent fiber. The results suggest that the intraspinal terminals of single muscle afferents receive synapses from more than one PAD-mediating GABAergic interneuron and that a single last-order interneuron has synaptic connections with a restricted number of intraspinal terminals and/or collaterals of the same afferent fiber. In addition, they support the existence of separate subsets of last-order baclofen-sensitive and baclofen-resistant interneurons that respond predominantly to segmental and to descending inputs. It is suggested that the restricted nature of the PAD plays an important role in the central control of the synaptic effectiveness of group I muscle afferents.

Notes: Abstract  The purpose of this study was to determine (1) whether the nucleus retroambigualis (NRA) plays an essential role in periaqueductal gray (PAG)-induced vocalization and (2) which NRA neurons are involved in the projection from the PAG to laryngeal motoneurons. Bilateral injections of the neurotoxin kainic acid into the NRA in decerebrate cats abolished PAG-induced vocalization; PAG stimulation after the injections no longer modulated vocal fold adductor or tensor activity, and only tonically, but no longer phasically, activated the abdominal muscles. In contrast, PAG-induced inspiratory excitation remained even after the injections. These results suggest that the NRA is essential for the vocal activation of the laryngeal adductor and abdominal muscles, and that an additional pathway from the PAG to respiratory motoneurons other than through the NRA is important for mediating PAG-induced inspiratory activation. Secondly, axonal projections of NRA neurons to the contralateral nucleus ambiguus (NA) were studied electrophysiologically. Five expiratory neurons, which had decrementing (n=4) or constant (n=1) firing patterns, were identified as both having axonal projections to the NA and receiving inputs from the PAG. Furthermore, following NA stimulation many constant-latency action potentials of silent cells were recorded in the vicinity of the NRA, where many silent cells were also orthodromically activated by PAG stimulation. No NRA augmenting expiratory neurons could be antidromically activated from the NA. It is suggested that the NRA and adjacent reticular formation integrate inputs from the PAG and send outputs to laryngeal motoneurons for vocalization.

Notes: Abstract  Previous studies have reported that stimulation of group I afferents from extensor muscles prolongs stance duration during walking in decerebrate cats. The main objective of this investigation was to determine whether this phenomenon occurs during walking in conscious cats. In conscious cats without lesions of the central nervous system (CNS), stimulation of group I afferents in the lateral gastrocnemius/soleus (LGS) nerve during stance prolonged extensor burst duration and increased the cycle period in five of seven animals. The mean increases in cycle period were modest, ranging from 6 to 22%. In five of six animals that walked both quadrupedally and bipedally at the same rate, the effects on cycle period were stronger during bipedal stepping (18% mean increase in cycle period compared with 9%). The stimulated nerves were transected and the experimental procedure was usually delayed in the conscious animals for 2–3 days following implantation of the stimulating electrodes. To assess whether chronic axotomy of the LGS nerve was a factor in the decreased effectiveness, four of the cats with chronic nerve section were decerebrated and their LGS nerves were stimulated after the animals began to spontaneously walk on a motorized treadmill. In all four of these animals, the effects of stimulating the chronically cut LGS nerve on the step cycle period became stronger following decerebration. However, these effects were not as strong as those produced when an acutely sectioned LGS nerve was stimulated. During both quadrupedal and bipedal walking, stimulation of the LGS nerve increased the amplitude of the medial gastrocnemius (MG) electromyogram. The augmented activity of the MG muscle contributed to an increased extension of the ankle during stimulated steps. The conclusion from these experiments is that stimulation of the group I afferents in extensor nerves can prolong stance in the conscious cat, but this effect is weaker than in decerebrate animals. It is likely that transmission in the polysynaptic group I pathways controlling stance duration is regulated in a complex fashion by descending signals from the brain in the conscious animal.

Notes: Abstract  In the ventral horn of the lumbar spinal cord of cats anaesthetised with pentobarbitone sodium, microelectrophoretically administered (–)-baclofen, but not (+)-baclofen, reversibly reduced the duration of the orthodromic action potential of muscle group Ia afferent terminations, but not those of muscle group I afferent myelinated fibres. The presumably submicromolar concentrations are already known to reversibly reduce excitatory transmitter release from muscle group Ia afferent terminations. Action potential durations were estimated from threshold recovery curves after an orthodromic impulse using an extracellular microstimulation technique. Both of these presynaptic effects of (–)-baclofen were blocked by baclofen antagonists, and neither appeared to be reduced by the potassium channel blocking agents tetraethylammonium and 4-aminopyridine. Tetraethylammonium and 4-aminopyridine also did not significantly modify the reduction by (–)-baclofen of monosynaptic field potentials in the lumbar cord of rats anaesthetised with pentobarbitone sodium. In the cat the maximum reduction by (–)-baclofen of termination action potentials was considerably less than that produced by cadmium ions, which, unlike (–)-baclofen, also reduced the action potential duration of group I myelinated fibres. These findings are consistent with a reduction by (–)-baclofen of the influx of calcium through voltage-activated channels in the membrane of group Ia terminations, a proposal which also accounts for the reduction by (–)-baclofen of the release of GABA at axo-axonic depolarizing synapses on these terminations. The results are discussed in relation to the mode of action of (–)-baclofen and the different sensitivities of transmitter release at various central synapses.

Notes: Abstract  A region of the caudal ventrolateral medullary reticular formation (CVLM) participates in baroreceptor, vestibulosympathetic, and somatosympathetic reflexes; the adjacent retroambigual area is involved in generating respiratory-related activity and is essential for control of the upper airway during vocalization. However, little is known about the connections of the CVLM in the cat. In order to determine the locations of terminations of CVLM neurons, the anterograde tracers Phaseolus vulgaris leucoagglutinin and tetramethylrhodamine dextran amine were injected into this region. These injections produced a dense concentration of labeled axons throughout the lateral medullary reticular formation (lateral tegmental field), including the retrofacial nucleus and nucleus ambiguus, regions of the rostral ventrolateral medulla, the lateral and ventrolateral aspects of the hypoglossal nucleus, nucleus intercalatus, and the facial nucleus. A smaller number of labeled axons were located in the medial, lateral, and commissural subnuclei of nucleus tractus solitarius, the A5 region of the pontine reticular formation, the ventral and medial portions of the spinal and motor trigeminal nuclei, locus coeruleus, and the parabrachial nucleus. We confirmed the projection from the CVLM to both the rostral ventrolateral medulla and lateral tegmental field using retrograde tracing. Injections of biotinylated dextran amine or Fluorogold into these regions resulted in retrogradely labeled cell bodies in the CVLM. However, the neurons projecting to the lateral tegmental field were located mainly dorsal to those projecting to the rostral ventrolateral medulla, suggesting that these neurons form two groups, possibly with different inputs. Injections of retrograde tracers into the lateral tegmental field and rostral ventrolateral medulla also produced labeled cell bodies in other regions, including the medial and inferior vestibular nuclei and nucleus solitarius. These data are consistent with the view that the CVLM of the cat is a multifunctional area that regulates blood pressure, produces vocalization, affects the shape of the oral cavity, and elicits contraction of particular facial muscles.

Notes: Abstract  This study was primarily aimed at investigating the selectivity of the cortico-spinal actions exerted on the pathways mediating primary afferent depolarization (PAD) of muscle spindle and tendon organ afferents ending within the intermediate nucleus at the L6–L7 segmental level. To this end we analyzed, in the anesthetized cat, the effects produced by electrical stimulation of sensory nerves and of the cerebral cortex on (a) the intraspinal threshold of pairs of single group I afferent fibers belonging to the same or to different hindlimb muscles and (b) the intraspinal threshold of two collaterals of the same muscle afferent fiber. Afferent fibers were classified in three categories, according to the effects produced by stimulation of segmental nerves and of the cerebral cortex. Twenty-five of 40 fibers (62.5%) were depolarized by stimulation of group I posterior biceps and semitendinosus (PBSt) or tibialis (Tib) fibers, but not by stimulation of the cerebral cortex or of cutaneous and joint nerves, which instead inhibited the PBSt- or Tib-induced PAD (type A PAD pattern, usually seen in Ia fibers). The remaining 15 fibers (37.5%) were all depolarized by stimulation of the PBSt or Tib nerves and the cerebral cortex. Stimulation of cutaneous and joint nerves produced PAD in 10 of those 15 fibers (type B PAD pattern) and inhibited the PBSt- or Tib-induced PAD in the 5 remaining fibers (type C PAD pattern). Fibers with a type B or C PAD pattern are likely to be Ib. Not all sites in the cerebral cortex inhibited with the same effectiveness the segmentally induced PAD of group I fibers with a type A PAD pattern. With the weakest stimulation of the cortical surface, the most effective sites that inhibited the PAD of individual fibers were surrounded by less effective sites, scattered all along the motor cortex (area 4γ and 6) and sensory cortex (areas 3, 2 and 1), far beyond the area of projection of group I fibers from the hindlimb. With higher strengths of cortical stimulation, the magnitude of the inhibition was also increased, and previously ineffective or weakly effective sites became more effective. Maps obtained when using the weakest cortical stimuli have indicated that the most effective regions that produced PAD of group I fibers with a type B or type C PAD pattern were also scattered throughout the sensory-motor cortex, in the same general area as those that inhibited the PAD of group I afferents with a type A PAD pattern. In eight fibers with a type A PAD pattern it was possible to examine the intraspinal threshold of two collaterals of the same single afferent fiber ending within the intermediate nucleus at the L7 segmental level. In six fibers, stimulation of the PBSt nerve with trains of pulses between 1.5 and 1.86 times threshold (×T) produced a larger PAD in one collateral than in the other. In seven fibers, stimulation of the sensory-motor cortex and of cutaneous nerves produced a larger inhibition of the PBSt-induced PAD in one collateral than in the other. The ratio of the cortically induced inhibition of the PAD elicited in the two collaterals could be modified by changing the strength of cortical and of PBSt stimulation. In three fibers it was possible to inhibit almost completely the background PAD elicited in one collateral while having little or no effect on the PAD in the other collateral. Changes in the intraspinal threshold of pairs of collaterals following electrical stimulation of segmental nerves and of the somato-sensory cortex were examined in three fibers with a type B and two fibers with a type C PAD pattern. In four fibers the PAD elicited by stimulation of cutaneous (4–20×T) and muscle nerves (1.54–3.7×T), or by stimulation of the sensory-motor cortex, was of different magnitude in the two collaterals. In two experiments it was possible to find cortical sites in which weak surface stimulation produced PAD in one collateral only. The magnitude of the PAD elicited in pairs of collaterals of group I afferents with a type B or C PAD pattern, or the inhibition of the PAD in pairs of collaterals of fibers with a type A PAD pattern, appeared not to be topographically related to the site of spinal projection of the cutaneous and cortico-spinal fibers used for conditioning stimulation. The present demonstration of a differential control of the PAD exerted on two collaterals of the same afferent fiber suggests that the profuse intraspinal branching of muscle spindle and tendon organs is a potentially rich substrate for information transmission. By means of presynaptic control mechanisms, the terminal arborizations of the afferent fibers could function either as a simple unit or in a fractionated manner, allowing funneling of information to selected groups of central neurons.

Notes: Abstract  The central cervical nucleus (CCN) of the cat receives input from upper cervical muscle afferents, particularly primary spindle afferents. Its axons cross in the spinal cord, and while in the contralateral restiform body give off collaterals to the vestibular nuclei. In order to study the connections between CCN axons and vestibular neurons, we stimulated the area of the CCN in decerebrate cats while recording intra- or extracellularly from neurons in the contralateral vestibular nuclei. CCN stimulation evoked excitatory postsynaptic potentials (EPSPs) or extracellularly recorded firing in the lateral, medial and descending vestibular nuclei. The latency of EPSPs (mean 1.6 ms) was on average 0.4 ms longer than the latency of antidromic spikes evoked in the CCN by stimulation of the contralateral vestibular nuclei (mean 1.2 ms), demonstrating that the excitation was typically monosynaptic. The results provide further evidence that the CCN is an important excitatory relay between upper cervical muscle afferents and neurons in the contralateral vestibular nuclei.

Notes: Abstract  The ventrolateral (VL) thalamus in mammals is a site well-situated to show vocalization-related neural activity if there is general or classical motor system involvement in vocal production. It receives input from both the basal ganglia and cerebellum, and forms reciprocal connections with motor cortical areas. The current study examined the activity in cat VL thalamus neurons during instrumentally conditioned vocalization. Units in our sample showed irregular spontaneous firing which could be modulated by slowly occurring fluctuations in intensity of vocalization task performance. Two main types of behavioral events were associated with changes in neural firing rate. The first of these was the ingestion of food reward. More than half of all recordings showed phasic bursting patterns during licking; a similar number had increases in firing preparatory to this phasic activity. The second behavioral event modulating unit responses was vocalization. Approximately 60% of recordings showed activity changes time-locked to vocalization. These responses were almost always excitatory, and often involved changes in firing that preceded vocalization onset. No spatial organization of differences in firing pattern between neurons could be distinguished. Our results suggest that VL thalamus may well be involved in mediating vocal behavior, although its functional role remains an object of speculation. Results are compared with previous studies of vocalization-related activity and of VL thalamus activity.

Notes: Abstract  In a proportion of simple cells of the striate cortex, the weighting functions of the receptive fields (RFs) had more periods than could be established by mapping using responses to light bars and dark bars. In these multiperiodical cells, side subfields do not respond to single bars, as they have lower weights than central zones and the excitation is under the threshold of impulse response if a single bar is applied. This fact has been established by different methods: conditioning and testing stimuli, grating patches, and inverse Fourier transform of the amplitude-phase characteristic, combining them in one cell. We assume that this type of nonlinarity can be used in analyzing the image, as it acts as a spatial-frequency filter of the area overlapped by the RF. The responses to complex gratings composed by two sinusoidal gratings of different frequency, contrast, and phase shift were compared with the sum of the responses to the gratings when they were presented separately. The results show that the principle of superposition holds a reasonable approximation even if the response is evoked from the side subzones. Some simple cells have nonlinear properties beyond the classic zone of RF (2nd type of nonlinearity). Linear cells have a tendency to be localized in layer 4 of striate cortex, cells with a nonlinear surround in layers 2, 3, 5, and 6. The significance of both types of nonlinearities in simple cells is discussed.

Notes: Abstract  Axonal pathways, projection levels, conduction velocities, and locations of the cell bodies of saccular nerve-activated vestibulospinal neurons were studied in decerebrated cats and anesthetized cats, using a collision test of orthodromic and antidromic spikes. The saccular nerve was selectively stimulated by bipolar tungsten electrodes. Three monopolar electrodes were inserted into the left and right lateral vestibulospinal tract (LVST) and medial vestibulospinal tract (MVST) of the C1 segment, to determine the pathway of axons. Three pairs of similar electrodes were positioned bilaterally in the C3–4, T1, and L3 segments to examine projection levels. Another monopolar electrode was placed in the oculomotor nucleus to determine whether saccular nerve-activated vestibulospinal neurons have branches ascending to the oculomotor nucleus. Of 145 vestibular neurons orthodromically activated by stimulation of the saccular nerve, 46 were activated from the C1 segment antidromically. Forty-three were second-order vestibulospinal neurons and 3 were third-order vestibulospinal neurons. Four saccular nerve-activated vestibulospinal neurons were also antidromically activated from the oculomotor nucleus. Sixty-three percent of the saccular nerve-activated vestibulospinal neurons descended through the MVST; one-third of these terminated in the upper cervical segments, one-third reached the lower cervical segments and the remaining one-third reached the upper thoracic segments. Thirty percent of the saccular nerve-activated vestibulospinal neurons descended through the ipsilateral LVST; most of these reached the upper thoracic segments. Seven percent of the saccular nerve-activated vestibulospinal neurons descended through the contralateral vestibulospinal tracts terminating in the upper cervical segments. Most of the saccular nerve-activated vestibulospinal neurons originated in the caudal part of the lateral nucleus and rostral part of the descending nucleus.

Notes: Abstract  The aim of this investigation was to understand the functions of long horizontal connections projecting from area 17 to area 18 in cats. The animals were anesthetized and prepared for recording single-cell responses to sine-wave gratings in area 18. Neuronal activity was analyzed under three conditions: prior to, during, and after inactivation of a circumscribed region of area 17. The latter was depressed with micro-injections of GABA. Cells in both areas were in close retinotopic correspondence. Cells were classified as simple and complex types. Globally, simple cells were less affected than complex units, and those which were affected shifted their optimal spatial frequency to higher values. Complex neurons were more often influenced by the interruption of area 17 input. Namely, the peaks of the tuning curves were displaced on the x-axis to a new optimal spatial frequency. This effect was obtained by a dual change: a decline in the discharge strength to the optimal spatial frequency and an enhancement to nonoptimal spatial frequency. Contrast sensitivity function disclosed similar shifts of optimal spatial frequencies. Likewise bandwith, spatial resolution, high cutoff, and low cutoff were modified to a greater extent in complex cells. It appears that there is no relationship between areas 17/18 orientation difference and the modifications observed in tuning curves to spatial frequencies. The results suggest that neurons of area 18 may carry multiple-frequency channels and that area 17 facilitates the emergence of one particular spatial frequency.

Notes: Abstract  In the lumbar ventral horn of pentobarbitone-anaesthetised cats, (-)-baclofen reduces both the synaptic release of excitatory transmitter from muscle group Ia afferent terminations and the duration of the presynaptic action potentials of these terminations, presumably by interfering with the influx of calcium ions through voltage-activated channels. Baclofen, however, has little or no effect on cholinergic excitation at motor axon collateral synapses on spinal Renshaw cells and, in the present study, was found not to reduce the duration of the action potential of axon collateral terminations located in the vicinity of Renshaw cells in pentobarbitone-anaesthetised cats. Furthermore, in contrast to group Ia terminations, a 4-aminopyridine-sensitive potassium conductance could not be detected as contributing to axon collateral termination action potentials. These results suggest that there may be differences in presynaptic ion fluxes associated with transmitter release at the intraspinal terminations of group Ia afferent fibres and motor axon collaterals in the cat spinal cord.

Notes: Abstract  The effect of exposure to repeated angular velocity steps about the earth-vertical axis on the vertical vestibulo-ocular reflex (VOR) during onside pitch rotation was investigated in normal cats. By contrast with the VOR in the horizontal plane, the amplitude and duration of the vertical VOR did not progressively decrease throughout the repetition of velocity steps alternated in both directions. Instead, the amplitude of VOR decreased by about 40% during the very first trials in naive cats and then stayed unchanged with repeated stimuli. Habituation of the amplitude of the vertical VOR was observed when the velocity steps were always directed in the same direction. However, the duration of the vertical VOR did not show any signs of habituation. The habituation of the amplitude of the vertical VOR during unidirectional training was due to the progressive development of an initial inhibition of the VOR. This initial inhibition appeared much earlier during the bidirectional protocol, and was presumably responsible for the larger reduction in VOR amplitude observed during the very first session. These results support the model of two distinct mechanisms for VOR habituation, one producing an increasing inhibition of nystagmus, and the other depressing the response duration, and suggest that only the first mechanism is generated during repeated stimulation in the vertical plane. The low-frequency information provided by the velocity storage mechanism during onside pitch rotation, when the otoliths are positioned so they do not signal head tilt relative to gravity, could prevent a decrease in the overall response by the second mechanism.

Notes: Abstract  Neurophysiological studies of the blink reflex to supraorbital nerve stimulation were conducted in eight alert, adult male cats. The cat, like other mammals, shows both short-latency (R1) and long-latency (R2) orbicularis oculi electromyographic (OOemg) components. Measures of OOemg latency, duration, integrated area, and maximum amplitude (MA) were obtained at a stimulus magnitude of 1.5×R2 threshold. The mean (±SE) minimal latencies for R1 and R2 were 8.26±0.85 and 22.97±1.53 ms, respectively. On average, R1 MA was larger than R2 MA. R1 and R2 area measures were similar. Three stimulus paradigms were tested. In a paired-stimulus paradigm, the interstimulus interval (ISI) was randomly varied from 100 to 1200 ms. Ratios were constructed for the OOemg area and MA by dividing the test response by the conditioning response. In this paradigm, although a significant linear relationship was observed only between ISI and R2 MA, conditioning effects were noted on both R1 and R2 area and MA test responses at several ISIs. In a habituation paradigm, both R2 and R1 showed habituation at stimulus frequencies from 0.5 to 2 Hz. In a stimulus-response paradigm, stimulus magnitude was randomly varied between threshold and 2×threshold. In this paradigm, OOemg area and MA of both R1 and R2 were linearly related to stimulus magnitude. Neither the systemically administered centrally acting α2-adrenergic antagonist yohimbine nor agonist clonidine had significant effects on blink reflex parameters, habituation, or the paired-stimulus paradigm. Overall, these results suggest that there are important similarities in the control and modulation of the R1 and R2 components of the blink reflex to supraorbital nerve stimulation in cats.

Notes: Abstract  Somaesthetic input to rubrospinal cells, bypassing the cerebellum and cerebral cortex, has been demonstrated in the cat. The detailed organization of this somatic afferent system was studied using electrophysiological methods on multiple-lesion, chloralose-anaesthetized preparations. Stimulation of the dorsal column (DC) at upper cervical cord segments induced significant responses in magnocellular red nucleus (RNm) cells in cats without a cerebellum and with ablation of the frontal cortex. As classic descriptions state that primary afferents fibres have ascending and descending branches in the DC, with many collaterals arborizing in the grey matter at the segmental level of the cord, this procedure is equivalent to stimulating the somatic fibres coming from a large portion of the body, leading to the simultaneous activation of most ascending spinal pathways. To show that the pathway responsible for the rubral responses ascends in the ventral spinal cord, and that the synaptic relays are located at the segmental level, the stimulation was applied to the DC, caudally to the sectioned dorsal spinal half. Various tests confirmed that the activation was conducted to rubral cells through antidromically activated primary afferents. Their multiple collaterals relay the messages to cells located caudal to the spinal lesion, with fibres ascending in the ventral cord. Any relay of the somatic rubral responses in the DC’s nuclei was excluded. When the DC was sectioned and its rostral end was dissected free and lifted onto two hook electrodes for stimulation, no response was obtained in the rubral cells. This dissection indeed sectioned all DC fibre collaterals entering the grey matter, thus excluding the possibility of segmental relay. Single shocks applied to the ventral quadrant of the cord or in the medial lemniscus (LM) in the medulla oblongata induced monosynaptic excitatory post-synaptic potentials (EPSPs) in most rubrospinal cells. The spinal EPSPs could be collided by stimulation in the LM, thus demonstrating the existence of direct connections from the cord to the RNm. This somaesthetic pathway to the RNm could be involved in on-line correction of movements and in learning new motor strategies.

Notes: Abstract. We investigated the binding characteristics of two monoclonal antibodies, 4F3 and 3F8, which in the retina specifically stain Müller cells, both with protein blots and immunohistochemically in sections of various regions of the central nervous system of neonatal and adult cats and rats. Clear differences emerged between the two antibodies. In addition, some species-specific as well as developmental differences within the staining pattern of each individual antibody were evident. The epitopes recognized by 4F3 lay mainly in the 57–63 kDa range. Histologically, 4F3 labelled mainly glia cells: oligodendrocytes and astrocytes in optic nerve, astrocytes in neocortex and cerebellum, Bergmann glia in the cerebellum and radial glia in neonatal animals. This was confirmed by double-immunofluorescence with the astrocyte marker GFAP. By contrast, 3F8 epitopes lay mainly in the 47–49 kDa range. Histologically, 3F8 labelled oligodendrocytes in the optic nerve, but only neurons in cerebellum and neocortex as confirmed by double-labelling with neuronal markers. Neither 4F3 nor 3F8 recognized GFAP or vimentin. These results clearly indicate (1) that the two antibodies identify new epitopes/molecules, (2) that the antigens are not retina-specific, and (3) that Müller cells share epitopes with other glial cells as well as with neurons outside the retina.

Notes: We use Hodge-Helmholtz decompositions of weighted Sobolev spaces to solve time-harmonic exterior-boundary value problems for perturbations of the (aδd+bdδ)-system (δ: the co-differential, a, b〉0). We prove, that a Fredholm alternative holds true, the eigensolutions decay polynomially at infinity, and that the positive eigenvalues do not accumulate. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The Neumann problem for the Laplace equation in an exterior connected plane region bounded by closed and open curves is studied. The existence of classical solution is proved by potential theory. The problem is reduced to the Fredholm equation of the second kind, which is uniquely solvable. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: A new numerical method is derived for the calculation of high-frequency asymptotic expansions of the scalar wave scattered by curved periodic structures. Optimal error estimates for this method are established. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We give a complete classification for breakdown in finite time or global existence of continuously differentiable solutions to hyperbolic systems of two first-order partial differential equations posed on a real bounded interval, with boundary damping and initial data of small magnitude. Structural bounds for the derivatives of the initial data which govern the behavior of the solution are brought to light. We isolate two classes of boundary damping: the strong damping forbids the solution to blow up after a time that we exhibit while the weak damping permits a late breakdown. The results are applied to nonlinear elasticity. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: No Abstract

Notes: Solutions of linear elliptic partial differential equations in unbounded domains can be represented by boundary potentials if they satisfy certain conditions at infinity. These radiation conditions depend on the fundamental solution chosen for the integral representation. We prove some basic results about radiation conditions in a rather general framework.Fundamental solutions G are considered that are defined only on the complement of a compact set. It turns out, however, and we present examples for this, that the more interesting results only hold if G is defined on all of ∝n or if it is a Green function for an exterior boundary value problem. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notes: In the present paper, we deal with the long time behaviour of solutions for the generalized Benjamin-Bona-Mahony equation. By a priori estimates methods, we show this equation possesses a global attractor in Hk for every integer k≥2, which has finite Hausdorff and fractal dimensions. We also construct approximate inertial manifolds such that every solution enters their thin neighbourhood in a finite time. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notes: An explicit factorization of the Fourier symbol matrix functions generated by Sommerfeld diffraction problems with oblique derivatives is obtained. For this purpose a new prefactorization procedure is developed which makes use of factorization through weighted L2 spaces. These results yield a representation of a generalized inverse of the corresponding matrix Wiener-Hopf operator and the asymptotic behaviour of the solution at the edge of the screen. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We study a high-field version of the periodic Schrödinger-Poisson system, for which the Poisson equation includes nonlinear terms corresponding to a field-dependent dielectric constant. Using a Galerkin scheme, we prove global existence and uniqueness, and present the matrix equations for the numerical evaluation of the potential. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: A generalized Hele-Shaw flow is derived and analysed in injection and compression moulding which contains non-isothermal and non-Newtonian rheological behaviour of the molten polymers as well as non-symmetric effects. The corresponding fixed domain formulations for the flow are investigated from a mathematical point of view. Different approaches for the determination of the temperature and some viscosity models are discussed. Together with an outline of the proposed solution algorithm special finite element techniques are described for the numerical treatment of this complex non-linear moving boundary problem. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The Ginzburg-Landau equation which describes nonlinear modulation of the amplitude of the basic pattern does not give a good approximation when the Landau constant (which describes the influence of the nonlinearity) is small. In this paper a derivation of the so-called degenerate (or generalized) Ginzburg-Landau (dGL)-equation is given. It turns out that one can understand the dGL-equation as an example of a normal form of a co-dimension two bifurcation for parabolic PDEs. The main body of the paper is devoted to the proof of the validity of the dGL as an equation whose solution approximate the solution of the original problem. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The paper deals with the Dirichlet problem for the Stokes linear equation in a domain exterior to an open surface. With the help of the theory of boundary integral (pseudo-differential) equations uniqueness and existence theorems are proved in the Bessel-potential and Besov spaces and Cα-smoothness (with α〈1/2) of solution is established in the neighbourhood of the boundary of the open surface. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In this paper the authors consider the initial boundary value problem of the ferromagnetic spin chain equation and prove the existence of the global attractor and finiteness of the Hausdorff and the fractal dimensions of the attractor. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We regard the Schrödinger-Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three-dimensional domain and establish the method of steepest descent. The electrostatic potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schrödinger operator, the Fermi level and the quantum mechanical electron density operator for square integrable electrostatic potentials. On bounded sets of potentials the Fermi level is continuous and bounded, and the electron density operator is monotone and Lipschitz continuous. As a tool we develop a Riesz-Dunford functional calculus for semibounded self-adjoint operators using paths of integration which enclose a real half-axis. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We investigate an initial-value problem modelling fragmentation processes where particles split into two or more pieces at a rate, γ, that not only depends on the sizes of the particles involved but also on time. The existence of non-negative, mass-conserving solutions is established by considering a truncated version of an associated non-autonomous abstract Cauchy problem. The latter has solutions of the form u(t)=Un(t,t0)f, t≥t0, where f is the known data at some fixed time t0≥0 and {Un(t,s)}t0≤s≤t≤T is a uniformly continuous evolution system. A limit evolution system {U(t,s)}t0≤s≤t≤T is shown to exist. Depending on the form of the known data f at time t0, the scalar-valued function u, obtained from the limit evolution system via u(x, t)=[U(t, t0)f](x) for a.e. x〉0, t≥t0, is a solution of either the original initial-value problem or an integral version of this problem. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We study the boundedness and a priori bounds of global solutions of the problem Δu=0 in Ω×(0, T), (∂u/∂t) + (∂u/∂ν) = h(u) on ∂Ω×(0, T), where Ω is a bounded domain in ∝N, ν is the outer normal on ∂Ω and h is a superlinear function. As an application of our results we show the existence of sign-changing stationary solutions. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In this note we investigate spatial bounds for the heat conduction equation with three relaxation times. We use energy methods similar to those considered in the study of the backward parabolic heat equation. Finally, we show that for any positive choice of the coefficients we may take initial data for which the solution is unstable when we suppose that the body is bounded. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: Continuous sedimentation of solid particles in a liquid takes place in a clarifier-thickener unit, which has one feed inlet and two outlets. The process is vital in a waste water treatment plant, where the particles consist of several biological components. The concentrations of these are modelled by a one-dimensional system of conservation laws with source term. It is shown how a unique solution can be obtained, and how analytical solutions are used to form a conservative numerical algorithm. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: This paper is concerned with the existence and uniqueness of the steady-state solution of hydrodynamic model for semiconductor devices. Boundary conditions are prescribed by vorticity on inflow boundary as well as by electron density, temperature, and normal component of electron velocity on whole boundary. If the ambient temperature is large, and if both vorticity on inflow boundary and the variation of density on boundary are small, a unique subsonic solution exists. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The theory of high-frequency waves has been used to calculate first and second-order asymptotic solutions for the propagation of non-linear waves in a cylindrical symmetric flow of an electron plasma. The behaviour of acceleration waves and weak shock waves has been analysed through these solutions and Whitham's rule for a weak shock wave on any wavelet has been confirmed through the first-order solution. The appearance of a weak shock wave on any wavelet has been determined and its strength, the location, and the speed of propagation have been found from the asymptotic solution presented in this paper. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: Of concern are factored Euler-Poisson-Darboux equations of the type∏Nj=1(d2/dt2+(ρ/t)d/dt+Aj)u(t)=0,where, for example, Aj=-cjΔ, Δ being the Dirichlet Laplacian acting on L2(Ω), Ω⊂∝n, and 0〈c1〈…〈cN. More generally -Aj can be the square of the generator of a (C0) group on a Banach space. When the constant ρ is negative, the initial value problem for the factored EPD equation is ill-posed. Nevertheless, we determine how many initial conditions are necessary to guarantee uniqueness of a solution. This number jumps up as ρ crosses a negative integer from right to left. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We study on the initial-boundary value problem for some degenerate non-linear wave equations of Kirchhoff type with a strong dissipation:\documentclass{minimal} \begin{document} \[ u_{tt}=\left\| \nabla u\right\| ^{2\gamma }\Delta u-\Delta u_t=\left| u\right| ^\alpha u,\quad u(0)=u_0,\;u_t(0)=u_1,\;u|_{\partial \Omega }=0. \] \end{document}When the initial energy $E(u_0,u_1)\equiv \left\| u_1\right\| ⁁2+\frac 1{\gamma +1}\left\| \nabla u_0\right\| ⁁{2(\gamma +1)}-\frac 2{\alpha+2}\left\| u_0\right\| _{\alpha +2}⁁{\alpha +2}$ associated with the equations is non-negative and small, a unique (weak) solution exists globally in time and has some decay properties. When the initial energy E(u0,u1) is negative, the solution blows up at some finite time. In the proof we use the ‘modified potential well’ and ‘Concavity’ methods. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notes: We prove existence, in a small time interval, of a classical solution having a regular free boundary, (i.e. the level set {u=0}) of a multidimensional filtration problem. The key point to get the regularity of the level set {u=0} is the proof of an a priori estimate for the L∞-norm of ut. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notes: We study stationary solutions of the relativistic Vlasov-Maxwell system of plasma physics which have a special form introduced (in the classical setting) by Rudykh, Sidorov and Sinitsy and establish their existence under suitable assumptions on the ansatz functions. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 667-677 (1997).

Notes: This paper addresses the question: when the frequency of collisions vanishes, will the solutions of the Landau system converge to the solutions of the Vlasov system? We give a positive answer to the question for solutions satisfying certain regularity conditions. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 679-688 (1997).

Notes: The paper considers the non-linear stability of a non-hyperbolic system of conservation laws with both relaxation and diffusion, which is commonly used for the modeling of two-phase fluid flows. Global existence in time is proved for initial data with a sufficiently small H1 norm. This result heavily depends on the nice structure of the relaxation system, derived from the initial system by setting the relaxation variables to zero. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The goal of this paper is to establish that even for strongly non-linear Darcy's laws and strongly non-linear leaky boundary conditions on the bottom of the reservoirs the fluid flow through a porous dam is a well-posed problem for which existence of a solution can be established. In a simple case we provide also the exact solution to the problem. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: Consider the problem of heat flow in a convex domain in ∝n with Dirichlet boundary condition and constant initial temperature. We show that the solution has a fixed hot spot if the domain is invariant under the action of an essential symmetry group. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The paper considers a particular type of closed-loop for the wave equation in one space dimension with damping acting at an arbitrary internal point, for which the uniform stabilization with exponential decay rate is shown. Applications to chains of coupled strings are also discussed. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The paper is concerned with optimal control problem for a non-linear parabolic equation with non-homogenous boundary condition and quadratic cost. The control is acting in a nonlinear equation. We derive some results on the existence of optimal controls. Then we treat optimal control problem by Galerkin method and we prove the convergence of optimal values for approximated control problems to the one for the original problem. Finally, we apply the results to give a simple example. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: It is proved that there is a (weak) solution of the equationut=a*uxx+b*g(ux)x+f,on ∝+ (where * denotes convolution over (-∞, t)) such that ux is locally bounded. Emphasis is put on having the assumptions on the initial conditions as weak as possible. The kernels a and b are completely monotone and if a(t)=t-α, b(t)=t-β, and g(ξ)∼sign(ξ)∣ξ∣γ for large ξ, then the main assumption is that α〉(2γ+2)/(3γ+1)β+(2γ-2)/(3γ+1). © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: This article treats the initial-boundary-value problem of viscoplasticity using unified constitutive models without a yield surface. Semi-discretization with the finite element method (FEM) leads to a system of differential-algebraic equations (DAE) with strongly non-linear evolution equations for the internal state variables. A special family of partitioned Runge-Kutta methods is introduced which allows an efficient time integration of the semidiscrete system. Coefficients for methods of order one, two, and three are given. Finally, numerical results for some two- and three-dimensional examples using the model of Hart are presented. In a second part we will give the theoretical background and state a proof of convergence for the algorithm presented in this paper. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We prove that any solution of the problem(u+K*u)t+∑ai(u)uxi=0 on (0,∞)×∝Nwith spatially periodic initial data converges to a constant provided some non-degeneracy conditions on the kernel K and the non-linear functions ai,i=1,…,N are imposed. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We continue the study of the operators of generalized linear elasticity and investigate the behaviour of the solutions as the frequency tends to zero. We identify degenerate operators in terms of special solutions to the static problem which must be added to the usual Neumann series in order to describe the low frequency behaviour adequately. As a byproduct we construct solutions to the homogeneous static operator (‘spherical elastics’) which generalize the spherical harmonics and give rise to a ‘spherical elastics expansion’. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The Dirichlet initial-boundary-value problem in the half-space ∝t×∝3+ for a non-linear hyperbolic system is studied. About the nonlinearity the null condition structure is imposed. Under the smallness conditions on the initial data the existence of low regularity solutions, on a given interval of time, is proved. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We develop aspects of Clifford analysis over the sphere and hyperbolae. We focus primarily on the hyperbola lying in the Minkowski type space ∝n,1. We show that in order to give a proper extension of basic results on Clifford analysis in Euclidean space to this context one needs to consider both hyperbolae lying in ∝n,1. We also introduce Bergman spaces of Lp left monogenic sections in this context and consider the decomposition of square integrable sections over suitable bundles constructed over subdomains of spheres and hyperbolae. The results presented here cover the necessary background to enable one to set up and solve boundary value problems for field-type equations over hyperbolae. In particular, one can study analogues of the Dirichlet problem for analogues of the Laplacian over hyperbolae and spheres. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The limiting behaviour of solutions of a system of singularly perturbed equations is studied. The goal is to construct a dissipative feedback control synthesis that stabilizes the prescribed output functional along trajectories of solutions. The results are applied to a singularly perturbed Johnson-Sagelman-Oldroyd model of shearing motions of a piston driven flow of a non-Newtonian fluid. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notes: The three-dimensional steady state oscillation problems of the elasticity theory for homogeneous anisotropic bodies are studied. By means of the limiting absortion principle the fundamental matrices maximally decaying at infinity are constructed and the generalized Sommerfeld-Kupradze type radiation conditions are formulated. Special functional spaces are introduced in which the basic and mixed exterior boundary value problems of the steady state oscillation theory have unique solutions for arbitrary values of the oscillation parameter. Existence theorems are proved by reduction of the original boundary value problems to equivalent boundary integral (pseudodifferential) equations. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notes: The two-dimensional frictionless contact problem of linear isotropic elasticity in the half-space is treated as a boundary variational inequality involving the Poincare-Steklov operator and discretized by linear boundary elements. Quadratic growth of the energy near the solution is shown under weak regularity assumptions if the central axis of external forces intersects the boundary of the domain in a Lebesgue null set. Estimating the numerical range of the discrete Poincare-Steklov operator and properly modifying it, enables the application of an error estimate for semi-coercive variational inequalities. Optimal order of convergence is obtained in the underlying Sobolev space H1/2(∂Ω)2. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notes: The dependence on the small parameter ε of constants in Korn's inequalities is investigated for domains which are obtained by joining thin rods to an elastic spatial body. The external ends of the rods are clamped. The asymptotic accuracy of the derived inequalities is achieved by certain distribution of weight multipliers and powers of ε in L2-norms of displacements and their derivatives while the introduced weights differ for longitudinal and transversal components of displacement fields in the rods. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notes: The aim of this paper is to investigate the behaviour as t→∞ of solutions to the Cauchy problem ut-Δut-νΔu-(b, ∇u)=∇⋅F(u), u(x, 0)=u0(x), where ν〉0 is a fixed constant, t≥0, x∊∝n. First, we prove that if u is the solution to the linearized equation, i.e. with ∇⋅F(u)≡0, then u decays like a solution for the analogous problem to the heat equation. Moreover, the long-time behaviour of u is described by the heat kernel. Next, analogous results are established for the non-linear equation with some assumptions imposed on F, p, and the initial condition u0. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notes: The article treats the question of how to numerically solve the Dirichlet problem for the Stokes system in the exterior of a three-dimensional bounded Lipschitz domain. In a first step, the solution of this problem is approximated by functions solving the Stokes system in a truncated domain and satisfying a suitable artificial boundary condition on the outer boundary of this truncated domain. In a second step, this new problem is approximately solved in finite element spaces related to a graded mesh as introduced by Goldstein [Math. Comp., 36, 387-404 (1981)]. The difference between this finite element approximation and the exact solution of the exterior Stokes problem is estimated in the norm of suitable unweighted L2-Sobolev spaces. These estimates are analogous to corresponding results which are known for the Poisson equation. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notes: Inverse problems for identification of the memory kernel in the linear constitutive stress-strain relation of Boltzmann type are reduced to a non-linear Volterra integral equation using Fourier's method for solving the direct problem. To this equation the contraction principle in weighted norms is applied. In this way global existence of a solution to the inverse problem is proved and stability estimates for it are derived. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We consider exact controllability of a system of two Schrödinger equations. These represent matter waves in adjacent potential wells with different potentials, one zero, the other a positive constant V0. The problem is formulated as a simultaneous boundary controllability problem, with Dirichlet control. Estimates for the controls, including an observability inequality, are proved using multiplier techniques. Then the Hilbert uniqueness method is used to obtain the exact controllability result. If V0 is sufficiently small, there exists a time T^(V0) such that the system is exactly controllable in times T〉T^(V0). © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The Dirichlet problem for the Stokes system in a dihedral angle is considered. An explicit description of special solutions to the homogeneous problem which have the form\documentclass{minimal} \begin{document} \begin{eqnarray*} U(x) &=&\left| x\right| ^\lambda \sum_{0\leq k\leq \kappa }\frac{(\log \left| x\right|)^{\kappa -k}}{(\kappa -k)!}u^{(k)}(x/\left| x\right|), \\ P(x) &=&\left| x\right| ^{\lambda -1}\sum_{0\leq k\leq \kappa }\frac{(\log \left| x\right|)^{\kappa -k}}{(\kappa -k)!}p^{(k)}(x/\left| x\right|) \end{eqnarray*} \end{document}is given. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We consider an initial value problem for a system of equations describing the motion and the heat convection in a viscous and incompressible fluid which occupies a smooth region Ωt⊂∝3 depending on time.In the equation for the distribution of temperature in the fluid we take into account not only the convective term but also the term responsible for the dissipation of energy.We prove local in time existence and uniqueness of solutions of the considered problem, and global in time existence for sufficiently small data. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The work deals with boundary equations appearing if non-stationary problems for Maxwell system are solved with the help of surface-retarded potentials. The solvability of these equations is proved in some functional spaces of Sobolev type. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We consider the electromagnetic inverse scattering problem of determining the index of refraction of an isotropic inhomogeneous medium from a knowledge of the total electric near field data. We consider both the case of scattering by an infinite inhomogeneous cylinder and a bounded inhomogeneous region in space. We conclude by giving an application of our method to the problem of imaging leukemia in the upper leg by means of microwaves. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: Here we consider initial boundary value problems for parabolic equations in non-bounded (with respect to time) domains by using the single-layer potential. We discuss the solvability in anisotropic Hölder spaces of the boundary integral equations, to which original parabolic problems are reduced. We construct the special operators (regularizers) for these integral equations which transform them to equivalent integral Volterra equations of the second kind with weakly singular kernels. As a corollary we obtain the theorem about the classical solvability in anisotropic Hölder spaces for initial boundary value parabolic problems. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In this paper we prove an a posteriori error estimate for the symmetric coupling of finite elements and boundary elements applied to linear parabolic-elliptic interface problems. The discontinuous Galerkin method is used for the discretization in time. We present an adaptive algorithm for choosing the mesh size in space and time and we analyse the Hybrid Modified Conjugate Residual (HMCR) method as a solution method for the linear systems which arise. Computational results show that the number of HMCR-iterations grows slowly with the problem size. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: No Abstract

Notes: Implicit one-step difference methods for quasilinear parabolic initial boundary value problems in two space variables and in polar coordinates are considered. Problems of this kind are suitable for the description of diffusion processes in plasma physics. Therefore, because of its special physical interest the dependence of the coefficients both on the solution and on its space derivatives (the fluxes) is included. The first part of this paper deals with proving convergence of the discrete approximations for vanishing step sizes. For this purpose, bounds for the inverse difference operators have to be derived previously. The nonlinear systems arising from the discretizations have exactly one solution for all step sizes being sufficiently small. In the second part of the article numerical tests are performed. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: This article establishes the existence of trapped-mode solutions of a linearized water-wave problem. The fluid occupies a symmetric horizontal channel that is uniform everywhere apart from a confined region which either contains a thin vertical plate spanning the depth of the channel or has indentations in the channel walls. A trapped mode corresponds to an eigenvalue of a non-local Neumann-Dirichlet operator for an elliptic boundary-value problem in the fluid domain. The existence of such an eigenvalue is established by generalizing previous results concerning spectral theory for differential operators to this non-local operator. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The existence of the classical global solutions for the non-linear Klein-Gordon-Schrödinger equations is proved in H1-subcritical cases for space dimensions n≤5. For higher space dimensions 6≤n≤9, we will give a subsequent paper to deal with. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We show that any solution of the scalar conservation law(u+k*u)t+σ(u)x=0starting from spatially periodic initial datum stabilizes to its integral mean as time goes to infinity. No convexity or ‘genuinely non-linear’ like conditions are assumed concerning σ. © 1997 by B. C. Teubner stuttgart-John Wiley & Sons Ltd.

Notes: We consider the initial-boundary value problem for quasi-linear symmetric hyperbolic systems with dissipation and characteristic boundary of constant multiplicity. We investigate the global existence and decay property of small regular solutions in suitable functions spaces which take into account the loss of regularity in the normal direction to the characteristic boundary. We also show the existence, uniqueness and stability of the time periodic solutions. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The uniqueness for unbounded classical solutions of the magnetohydrodynamic (MHD) equations in the whole space is investigated. Under suitable growth condition, it is shown that the solution to the initial value problem is unique. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The steady-state problem of the non-linear reaction-diffusion systemut-uxx=u(av-b),vt-vxx=cuis considered. The existence of positive steady-solutions is established by using a fixed point theorem in ordered Banach space. The uniqueness of ordered positive steady-state solutions and an application to the associated reaction-diffusion system are presented. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: A class of diffraction problems for the two-dimensional Helmholtz equation is studied where the boundary conditions on a canonical screen contain oblique derivatives. The problem in weak formulation is reduced to a system of pseudodifferential equations on a half-line. The Fredholm property is characterized in dependence of the parameters, index formulas are given, and, if necessary, a normalization of the problem is implemented. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In this paper a time-discrete dynamic model for the process of disarmament is investigated. The state variables of the system are costs and security values. We assume that the costs can be controlled, and we aim at reducing the costs to zero and achieving non-negative security values after a finite number of time steps. In the case where the opponents behave cooperatively this leads to the solution of a linear programming problem. If the opponents behave non-cooperatively, then a Nash equilibrium has to be determined under linear constraints. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 653-666 (1997).

Notes: In this paper we prove the existence of a weak solution to the non-stationary drift-diffusion equations (van Roosbroeck's system) of semiconductor theory involving discontinuous permittivities. The proof is based on an approximation of these equations by a system with bounded non-linearities, deriving a priori estimates on the approximate solutions and then carrying out the passage to limit. The discussion is completed by some regularity results for the weak solution under consideration. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 689-706 (1997).

Notes: We study the free streaming operator T∧ in a slab domain with boundary conditions described by a linear matrix operator Λ acting between the ‘incoming’ and ‘outgoing’ particle fluxes. Under suitable assumptions on the entries of Λ, it is proved that the resolvent operator of T∧ is positive. It is proved also that T∧ is the generator of a positive strongly continuous semigroup, whose type depends on the norm of the entries of Λ. Some examples are given. In particular the case of Maxwell type boundary conditions is studied and the location of the spectrum of T∧ is improved. © 1997 by B. G. Teubner Stuttgart - John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 717-736 (1997).

Notes: In the present paper we prove Cα-estimates for ∇u using components of boundary values of u, div u, curl u and quantities given by components of boundary values of u as well as boundary values of elements belonging to de Rhams cohomology modules. The vector field u is defined on a bounded set G¯⊂∝3, meanwhile the cohomology group will be defined with regard to ∝3-G. Our inequalities turn out to be a priori estimates concerning well-known boundary value problems for vector fields. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We consider in this paper a system of equations modelling a steady-state induction heating process for ‘two-dimensional geometries’. Existence of a solution is stated in W1,p(Ω) Sobolev spaces and is derived using the Leray-Schauder's fixed point theory. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We extend the recently developed Riesz-Clifford monogenic functional calculus (based on Clifford analysis) for a set of unbounded non-commuting operators. Connections with quantum mechanics are discussed. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: Existence and nonexistence of solutions (both stationary and evolution) for a parabolic-elliptic system describing the electrodiffusion of ions are studied. The answers to some questions concerning a generalization of a problem posed by I. Rubinstein are given. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: No Abstract

Notes: We consider a free boundary value problem arising from a non-symmetric problem of electrochemical machining (ECM). After a conformal mapping of the unknown domain the problem is transformed to a non-smooth non-linear Riemann-Hilbert problem for holomorphic functions in the complex unit disk. A special technique allows to remove the singularities in the boundary condition. Utilizing existence results for smooth non-orientable Riemann-Hilbert problems, existence and uniqueness of a solution are shown. Finally, we propose an iterative method of Newton type for the effective numerical computation of the free boundary of the anode and present some test results. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5]. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We prove the existence of a wide collection of finite sets of functionals that completely determine the long-time behaviour of strong solutions to the von Karman evolution equations. This collection contains finite sets of determining modes, nodes and local volume averages. The approach presented relies on the concept of a completeness defect for a set of linear functionals and it involves some ideas from abstract approximation theory. Our method is general enough and also can be applied to other non-linear partial differential equations which are of second order in time. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In this paper, we study a system of biharmonic equations coupled by the boundary conditions. These boundary conditions contain some combinations of the values, div, curl, and grad. Applications in mathematical physics are possible and the investigations will be done with the help of hypercomplex methods. It is also the aim of the paper to demonstrate the application of Clifford analytic methods to the solution of boundary value problems. The results on a special boundary value problem for the biharmonic equation will be used for the investigation of some first-order systems of partial differential equations. We study a theoretical problem connected with the ∂¯-problem and the solution of a Beltrami system by using a fixed-point iteration. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: Modified fundamental solutions are used to show that the system of boundary integral equations in a direct method for the interior Dirichlet problem for the two-dimensional biharmonic equation has at most one solution on any smooth closed boundary contour. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: The non-homogeneous magnetohydrodynamics equation is studied, with emphasis on the singularities due to Alfvén resonance. It is shown that for any arbitrary function defined on the singular set, there exists a unique solution of the problem coinciding with this function. Then the values on the singular set which correspond to the correct physical solution are determined proving that this is unique except for a discrete set of geometrical configurations. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In this paper we present some new results of symmetry for inhomogeneous Dirichlet eigenvalue problems overdetermined by a condition involving the gradient of the first eigenfunction on the boundary. One specificity of the problem studied is the dependence of the equation and the boundary condition on the distance to the origin. The method of investigation is based on the use of continuous Steiner symmetrization together with some domain derivative tools. An application is given to the study of an overdetermined eigenvalue problem for a wedge-like membrane. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We consider the initial-boundary value problem for a linear thermoelastic plate equation and we prove that the energy associated to the system decays exponentially to zero as time goes to infinity. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: In this paper, we consider the Cauchy problem:(ECP)ut-Δu+p(x)u=u(x,t)∫∝3u2(y,t)/∣x-y∣dy; x∊∝3, t〉0,u(x, 0)=u0(x)≥0 x∊∝3, (0.2)The stationary problem for (ECP) is the famous Choquard-Pekar problem, and it has a unique positive solution ū(x) as long as p(x) is radial, continuous in ∝3, p(x)≥ā〉0, and lim∣x∣→∞p(x)=p¯〉0. In this paper, we prove that if the initial data 0≤u0(x)≤(≢)ū(x), then the corresponding solution u(x, t) exists globally and it tends to the zero steady-state solution as t→∞, if u0(x)≥(≢)ū(x), then the solution u(x,t) blows up in finite time. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We consider the incompressible limit of the compressible Euler equation in the half-space ∝n+. It is proved that the solutions of the non-dimensionalized compressible Euler equation converge to the solution of the incompressible Euler equation when the Mach number tends to zero. If the initial data v∞0 do not satisfy the condition ‘∇⋅v∞0=0’, then the initial layer will appear. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notes: We study the linearized stability of planer flows of incompressible, viscous fluid in two-dimensional annular domains. A certain family of steady, explicit solutions which have spiral streamlines are considered. The Navier-Stokes equations are linearized at these solutions and we show analytically or numerically that these solutions are stable to perturbation of steady states, whatever the Reynolds number or the aspect ratio of the annuli may be. Hopf bifurcations from them are also examined numerically. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.