Singularities and Global Solutions in the Schrodinger-Hartree Equation

In 1922, Louis de Broglie proposed wave-particle duality and introduced the idea of matter waves. In 1925, Erwin Schrodinger, proposed a wave equation for de Broglie’s matter waves. The Schrodinger equation is described using the de Broglie’s matter wave, which takes the wave function, and describes its quantum state over time. Herein, we study the generalized Hartree (gHartree) equation, which is a nonlinear Schrodinger type equation except now the nonlinearities are a nonlocal (convolution) type. In the gHartree equation, the influence on the behavior of the solutions is global as opposed to the case of local (power type) nonlinearities. Our first goal is to understand the behavior of finite energy solutions. We start with proving the local existence and then extend to the global existence for small data. We then, in the energy-subcritical critical regime, classify the behavior of finite energy solutions under the mass-energy assumption identifying the sharp threshold (depending on the size of the initial mass and gradient) for global (scattering) versus finite time (blow-up) solutions. Next, we revisit the problem of scattering and give an alternative proof of scattering, for both NLS and gHartree equations in the radial setting. The alternative approach provides a simpler proof of scattering, which might also be useful for other contexts. Our next aim is to understand the phenomenon of wave collapse (blow-up, the sudden energy transfer from higher levels to lower ones), i.e., solutions with finite time of existence. We first give a sufficient condition for finite time blow-up for the large data and give examples of the various thresholds available in a variety of cases (energy-subcritical, critical and supercritical) for Gaussian data. We then investigate stable singularity formations in the mass-critical gHartree equation, and in particular, rigorously prove a stable blow-up formation in dimension 3. We observe that the nonlocal nonlinearity does not destroy the blow-up dynamics, similar to the local nonlinearities. On the other hand, one of the necessary properties, namely the spectral property required for the blow-up analysis, is modified remarkably. Nevertheless, we are able to prove that stable blow-up occurs with a self-similar profile at the square root rate with a logarithmic correction. Finally, we present the reader with the conclusion and possible future research directions, wrapping up the dissertation

Scanning electron microscopic comparison of endophallus of Apis cerana and Apis mellifera

During the present investigations, the detailed morphoarchitecture of the male genitalia viz., the endophallus of the drone of A.cerana F. and A.mellifera L. was scanned under the electron microscope. Endophallus of each species was studied for its unique characteristics. Significant interspecific differences were observed in the 2 different species. These differences highlight the reproductive isolation in the genus. These species specific differences in the endophallus are highlighted in the paper

Scanning electron microscopic studies on tongue of open-nesting honey bees Apis dorsata F. and Apis florea F. (Hymenoptera: Apidae)

Taste stimuli play vital role in the life of honey bees. Sensory structures observed on tongue of the honey bees with the help of Scanning electron microscopy (SEM) have become an important tool in analyzing honey bee biodiversity which offers an advanced diagnostic tool to study honey bee biogeography and determine adaptive variations to native flora. Tongue of honey bees present a high geographic variability in regard to the floral resources visited by the bees. The present study has determined to determine differences in the tongue ofopen-nesting bees by scanning electron microscopy of Apis dorsata and Apis florea. The two bees showed distinct morphological variations with respect to the lapping and sucking apparatus. It was observed that the ridges on the proximal region exhibited rough surface on A.dorsata whereas spinous in case of A.florea. Moreover, the arrangement of hair in the middle part of the tongue also differed in the two species. The shape of flabellum differed in the two species reason being the influence of native flora. It was observed that the shape of flabellum was oval in A.dorsata whereas in A.florea it was triangular. These differences indicated for the role of native flora and honey bee biodiversity

Ultramorphology of antennal sensilla of open-nesting honey bees Apis florea F. and Apis dorsata F. (Hymenoptera: Apidae)

Antenna of honey bees is geniculate and has been known to possess a wide variety of sensilla. The sensilla are sensitive to odor, temperature, humidity, air pressure and gustatory stimuli. In the present investigation, ultrastructural study on the antenna of the two open-nesting worker honey bees- Apis florea F. - the dwarf honey bee and A. dorsata F. - the giant honey showed considerable amount of variation in the types and distribution pattern of sensilla in the two species. The antennal form as well as the sensilla arrangement has been suggested to be adapted to the pheromone perception need of regarding a particular species

Surgical management of intracapsular fracture neck femur by hemiarthroplasty between uncemented bipolar prosthesis and Austin Moore’s prosthesis: a comparative study in elderly population

Background: Intracapsular femoral neck fractures are common in elderly population after a simple fall. To avoid the drawbacks of internal fixation and for the early mobilization, hemiarthroplasty is performed in elderly. The aim of this study is to compare the outcome AMP with uncemented bipolar prosthesis in geriatric patients.Methods: 51 patients above 60 years and an acute displaced fracture of the femoral neck were randomly allocated to treatment by either AMP (Austin Moore prosthesis) or bipolar hemiarthroplasty, in the Department of Orthopaedics, Sri Siddhartha medical college, Tumkur between April 2014 and May 2017. The patients were summoned at 6 weeks, 12 weeks, 6 months and 1 year. Functional outcome was assessed and compared with modified Harris hip score and radiological parameters.Results: The mean Harris hip score in bipolar and AMP group was 86.31±12.1 and 79.86±15.42, respectively (p=0.182). The range of motion was 204.52±28.2 and 183.62±36 (p=0.014) respectively. Functional activities like use of public transport and ability to wear shoe or socks was better with bipolar group. Incidence of complications like painful hip, posterior dislocation, periprosthetic fracture and acetabular erosion was encountered in AMP group.Conclusions: The use of uncemented bipolar endoprosthesis in the management of displaced femoral neck fractures in the elderly was associated with better mean Harris hip score and incidence of complications was limited. Hence, bipolar would be a better option in elderly patients with fracture neck of femur.

RESEARCH AND REVIEWS: JOURNAL OF MEDICAL AND HEALTH SCIENCES An Anthropometric Study of the Humerus in Adults

ABSTRACT The long bones are most commonly used for identification of unknown bodies and parts of bodies. Seventy two adult dried humeri (36 right and 36 left) were obtained from the Anatomy Department of University College of Medical College and GTB Hospital. Somatometry was done by means of an osteometric board, a vernier caliper and a tapeline. The maximum height was found to be 306.41± 25.8mm on the right bone and 304.43 ± 23.4mm on the left bone. In the upper third the mean circumference of the shaft was 60.6 ± 6.6mm and 58.85 ± 6.0mm whereas the mean transverse diameter was 18.6 ± 2.1mm and 18.2 ± 2 mm on right and left sides respectively. The mean sagittal diameter of upper third of the shaft was measured to be 19.63 ± 2.1mm and 19.52 ±2.3mm on right and left sides respectively. In the middle third of the shaft the mean circumference was measured to be 56.79 ± 4.8mm and 55.51 ± 4.4mm on the right and left humerus. The mean transverse diameter was 17.37 ± 2.4mm and 16.55 ± 2.2mm whereas the mean sagittal diameter was 18.67 ± 2.7 mm and 18.32 ± 2.6mm in right and left sided bones respectively. In the lower third the mean circumference of the shaft was measured to be 55.57 ± 5.3mm and 54.47 ± 4.8mm and the mean transverse diameter was 18.31± 1.8mm and 18.21 ± 2.0mm on the right and left humerus respectively. However, the mean sagittal diameter was 16.84 ± 1.5mm and 16.7 ± 1.5mm for the lower third of the shaft in right and left humerus respectively. Obtained data was statistically analyzed

Effect of Monomer Content in the Polymer-Monomer Ratio on the Displacement of Maxillary Teeth and Dimensional Accuracy of the Maxillary Denture Base in Microwave and Conventional Polymerization - An in Vitro Study

The purpose of the study was to verify the linear displacement of teeth and dimensional accuracy in maxillary complete dentures influenced by different monomer- polymer ratios - according to the manufacture