Logarithmic Picard groups, chip firing, and the combinatorial rank

Illusie has suggested that one should think of the classifying group of M_X^{gp}-torsors on a logarithmically smooth curve $X$ over a standard logarithmic point as a logarithmic analogue of the Picard group of $X$. This logarithmic Picard group arises naturally as a quotient of the algebraic Picard group by lifts of the chip firing relations of the associated dual graph. We connect this perspective to Baker and Norine’s theory of ranks of divisors on a finite graph, and to Amini and Baker’s metrized complexes of curves. Moreover, we propose a definition of a combinatorial rank for line bundles on $X$ and prove that an analogue of the Riemann–Roch formula holds for our combinatorial rank. Our proof proceeds by carefully describing the relationship between the logarithmic Picard group on a logarithmic curve and the Picard group of the associated metrized complex. This approach suggests a natural categorical framework for metrized complexes, namely the category of logarithmic curves

Chronic Neck Pain and Neck Muscle Strength

INTRODUCTION: Neck pain is one of the most common musculoskeletal disorders, with an estimated 1-year prevalence of 31.4% to 35.6% of adults in the general population. The course of neck pain is characterized by exacerbations and remissions and only a small part of the patients experience complete resolution of their symptoms within 1 year. A substantial proportion of the neck pain patients will thus develop chronic neck pain. The definition of chronic pain differs between studies, in terms of either 3 or 6 months duration of complaints. Nevertheless, the estimates of their one year prevalence in the general population are similar: 8.7% to 17.8% for the 3-months definition, and 8% to 13.8% for the 6-months definition. OBJECTIVES: There is not much scientific evidence to support the standard treatments of neck pain (including things like hot and cold packs, ultrasound and massage.) The aim of this study is to assess the neck muscle strength in chronic neck pain patients and in control group and compare the difference in these two groups. This study will give an idea of the difference if at all present in neck muscle strength in these two groups. This also may give an indication of the necessity to improve the neck muscles in the neck pain group. MATERIAL AND METHOD: In this study we assessed the cervical spine muscle strength in persons with chronic neck pain and in control group without history of neck pain. With this data the strength of the neck muscles are compared and the difference in muscle strength is found out. SELECTION OF THE SUBJECTS: It is well known that the acute pain inhibits the muscle contraction. In this study only patient who is totally pain free is taken up for the study. These are the patients who have chronic pain for more than six months and they are in remission during the evaluation. They should not have any organic lesion, fracture, infection, post operative problems. From all the persons consent to join in the study is received. METHODOLOGY: Isometric neck muscle strength is assessed in sitting posture. A spring balance [Pic – 6] was mounted on a stand and the height is fixed. According to the height of the subject the stool height is adjusted. SUMMARY: • Neck muscles are weaker in Chronic Neck Pain patients. • Neck extensors are more than two times stronger than flexors. • In the control group the neck muscles are stronger in the active group. The sedentary people in the control group have weaker muscles. • The lateral flexors are stronger on the left side. CONCLUSION: 1. In Chronic Neck Pain patients due to their weak neck muscles the protection to the cervical spine is less to prevent further injury during stressful situations. So they require regular and specific neck muscle strengthening exercise to prevent recurrence of symptom. These specific cervical exercises strengthen the spinal muscles and provide better support by spinal bracing. 2. The role of cervical brace is also important. They may be used in situations where the person with chronic neck pain is subjected to prolonged stresses as in occupation or while traveling. 3. The sedentary people in the control group were found to have weaker muscles. Are they prone to neck pain? Only long term study can prove this aspect of finding. Follow up - All the Chronic Neck Pain patients were given a program of exercise. The neck pain feed back form is also given to them. Follow up in future will confirm the usefulness of the exercise in preventing frequent recurrences

Analysis of Shrinkage Compensation Factor (SCF) of FDM uPrint SE for Accuracy Enhancement

This paper scrutinizes the shrinkage of a component manufactured using Additive Manufacturing (AM) and emphasizes mainly on the change in dimensions of an AM component after printing. The physical model can be easily manufactured by having the CAD data in STL format for real time AM. However, deviation of product size in CAD model transforming to physical model will be existing due to the deformation of the material mainly because of shrinkage. So here an analysis is carried out to find the optimal shrinkage compensation factor (SCF) of the part manufactured by Fusion Deposition Modelling (FDM) machine which uses ABS P430 as the base raw material. To achieve the latter a suitable model part is considered taking all the dimension and geometrical constraints which are essential for finding SCF and through regression analysis with the help of Co-ordinate Measuring Machine (CMM) and Solid Works modeling, SCF is calculated. Based on the experimental study, dimensional accuracy of the part significantly improved after applying the SCF value of 0.068% which is assumed to be constant in all directions

Study of drug utilization pattern in the department of radiotherapy in a tertiary care teaching hospital

Background: Drug utilization studies are an important tool in evaluating the rationality of therapeutic practice and also it is said to improvise the therapeutic use of drugs. The present study will be undertaken to evaluate the drug utilization pattern in the department of Radiotherapy.Methods: This was a prospective, observational study that was undertaken in the department of Radiotherapy in a tertiary care teaching hospital. The study was conducted for a period of 6 months after obtaining permission from Institutional Ethical Committee. The study was conducted among cancer patients undergoing radiotherapy. The data was collected from the patient case records and was analyzed as per the WHO prescribing indicators.Results: In the present study it was observed that the average number of drugs prescribed per encounter was 7.7. The drugs prescribed by generic name were 41.4%. Percentage of encounters with an antibiotic prescribed was 100. Percentage of encounters with an injection prescribed was 20.5%. Percentage of drugs prescribed from essential drugs list was 35.8%.Conclusions: Drug utilization studies helps in modifying the prescription pattern and helps in making the drug usage more rational

Logarithmic Picard groups, chip firing, and the combinatorial rank

Illusie has suggested that one should think of the classifying group of MgpX -torsors on a logarithmically smooth curve X over a standard logarithmic point as a logarithmic analogue of the Picard group of X. This logarithmic Picard group arises naturally as a quotient of the algebraic Picard group by lifts of the chip firing relations of the associated dual graph. We connect this perspective to Baker and Norine’s theory of ranks of divisors on a finite graph, and to Amini and Baker’s metrized complexes of curves. Moreover, we propose a definition of a combinatorial rank for line bundles on X and prove that an analogue of the Riemann–Roch formula holds for our combinatorial rank. Our proof proceeds by carefully describing the relationship between the logarithmic Picard group on a logarithmic curve and the Picard group of the associated metrized complex. This approach suggests a natural categorical framework for metrized complexes, namely the category of logarithmic curves

Hydrogen bonding and tautomeric equilibria in Schiff bases derived from 2-amino pyridines: electronic spectral evidence for substituent effects

Schiff bases of the type C6H3(R)(OH) CH = NC5H3N(Y)[where R = H, 3-OCH3, 5,6-benzo, 3-CHO-5-CH3,5-CI, 5-Br, 5-CH3, 4-CH3, 3-nitro and 5-nitro and Y=H, 3-CH3 4-CH3, 5-CH3, 6-CH3, 4,6-demethyl and 5-CI) have now been, synthesised and evidence sought for the electronic interaction between the substituents R (in the benzene ring) and Y (in the pyridine ring) in the molecule. The effects of substituents R and Y on the strength of hydrogen bond between OH and CH = N, is coupled to keloenamine ⇌ phenoliminc equilibrium. The groups which increase the acidity of the phenolic hydroxyl and the, basicity of the azomethine nitrogen facilitate quinonoid structures with characteristic visible absorption bands in the region 400-600 nm. In those compounds where R = 5,6-benzo, the intensity and the energy of band ~400 nm show a correlation with the electron releasing tendency of Y. Thus there appears an electronic communication between the substituents R and Y causing deviations from the generally accepted model for schiff base structures

C-H...O interactions and stacking of water molecules between pyrimidine bases in 5-nitro-1-([beta]-D-ribosyluronic acid)-uracil monohydrate [1-(5-nitro-2,4-dioxopyrimidinyl)-[beta]-D-ribofuranoic acid monohydrate]: a neutron diffraction study at 80 K

This is the publisher's version, also available electronically from http://scripts.iucr.org/cgi-bin/paper?S0567740879006506.See article for abstract.Research carried out at Brookhaven National Laboratory under contract with the US Department of Energy, and supported by its Office of Basic Energy Sciences

Thermal and photochemical reactions of chromium (IV)-diperoxo complexes with organic substrates- evidence for hydroxylation of proline and phenol

The diperoxo complexes of chromium in an unusual oxidation number viz. 4, react with organic substrates such as proline and phenol to give bydroxyproline and o-benzoquinone as products respectively. The organic products were identified by electronic spectra as well as by their characteristic R1 values in thin layer chromatography using n-propanol-water(1:1v/v) mixure and chloroform as solvents for proline and phenol reaction products respectively. the studies reveal that the hydroperoxide radicals formed during the decomposition of Cr(IV)-diperoxo complexes give rise to the hydroxylation processes observed. The hydroxylation reactions are facilitated by light and yields of hydroxyproline upto 9% (from proline) have been obtained . The study presents one of the first examples of the use of Cr(IV) systems for biologically relevant processes such as hydroxylation