Path Counting and Rank Gaps in Differential Posets

We study the gaps Δp_n between consecutive rank sizes in r-differential posets by introducing a projection operator whose matrix entries can be expressed in terms of the number of certain paths in the Hasse diagram. We strengthen Miller’s result that Δp_n ≥ 1, which resolved a longstanding conjecture of Stanley, by showing that Δp_n ≥ 2r. We also obtain stronger bounds in the case that the poset has many substructures called threads

Path Counting and Rank Gaps in Differential Posets

We study the gaps Δp_n between consecutive rank sizes in r-differential posets by introducing a projection operator whose matrix entries can be expressed in terms of the number of certain paths in the Hasse diagram. We strengthen Miller’s result that Δp_n ≥ 1, which resolved a longstanding conjecture of Stanley, by showing that Δp_n ≥ 2r. We also obtain stronger bounds in the case that the poset has many substructures called threads

A SURVEY ON CONTROLLING SPEED OF DIRECT TORQUE CONTROL BASED BRUSHLESS DC MOTOR

In this work, an examination on position sensor less immediate torque control of BLDC Motor with backhanded flux control have been studied utilizing two level, six switch Voltage Source Inverter (VSI). By embracing the aberrant flux control in direct torque control, the stator flux can be adequately controlled in the steady torque locale. This plan is adjusted to three stage conduction method of VSI. Most extreme torque proficiency can be acquired in this technique since the torque is evaluated in the dq reference outline. In direct torque with aberrant flux control of BLDC in three stage conduction mode, the substitution torque swell can be minimized and additionally torque swell can be viably diminished. Since the plan is position sensor less, the electrical rotor position is evaluated utilizing stator winding inductance, stationary reference outline streams and flux linkages. The voltage vector choice is set up in the turn upward table so that quick torque reaction is conceivable. Since the impartial purpose of the engine is not accessible, ordinary 2×3 framework is supplanted by 2×2 Park's and Clarke's changes for the adjusted frameworks. The trial results are approved in MATLAB/SIMULINK

Study comparing the efficacy of platelet rich plasma versus steroid versus placebo in lateral epicondylitis

Background: Lateral epicondylitis is seen more commonly in non-athletes than athletes. Non-operative methods are the mainstay of treatment being effective in more than 95% of cases. Platelet rich plasma (PRP) has shown promising results in many studies as compared to steroid injection & other modes of conservative management. Hence, this study was done to evaluate PRP efficacy in our clinical setup and in the people of age group most commonly being affected.Methods: This randomized study was conducted at Narayana Medical College Hospital, Nellore, for a period of two years from December 2014 to June 2016 on 150 consenting patients diagnosed as suffering from lateral epicondylitis. Using lottery method for randomization the patients were divided into three groups, based on which the treatment was received. Group –N with 50 patients received 3 ml of normal saline as placebo. Group –P with 50 patients received 3 ml of extracted PRP injection. Group –S with 50 patients received depot preparation of 40 mg of methyl prednisiolone injected into the affected area. The data collected and recorded in the appropriate proforma. Post therapy assessment was done using with Oxford elbow score.Results:  The overall mean ages of the patients in the three groups (Group P, Group S and Group N) are 38.62±7.53, 37.82±7.79 and 36.3±6.93 respectively. Female preponderance was observed in all the groups. Most common presenting complaint was elbow pain seen in 100% of cases. Most common side involved was the dominant side, right side involvement was seen in 136 cases and left side in 14 cases. The Oxford elbow score pre-treatment in all the groups was not statistically significant and the Oxford elbow score at the end of 12 weeks and 24 weeks treatment showed that PRP and steroid was better than normal saline in control of pain.Conclusion: Lateral epicondylitis or tennis elbow is a painful debilitating condition of elbow, which creates disturbance in functional activities. A single injection of PRP at the site of the elbow pain resulted in relief of pain in patients with longer duration as compared to local steroids to other conservative treatments

The dermatotraction technique for closure of fasciotomy wound

Management of an open wound is a problem frequently encountered in the treatment of fractures. Skin grafting, rotational flaps, free flaps, and healing by secondary intention add a considerable amount of morbidity and cost to the patient. Therefore, it is ideal to obtain primary closure when possible. This communication describes a technique that uses 1-0 prolene suture material, skin stapler and the natural stretching ability of the skin to enable primary closure of wounds. The technique described uses dermatotraction to stretch the skin, is a cost-effective way to achieve primary closure of large wounds with supplies that are readily available in every operating room

The beta-Wishart ensemble The beta-Wishart ensemble

We introduce a "broken-arrow" matrix model for the β-Wishart ensemble, which improves on the traditional bidiagonal model by generalizing to non-identity covariance parameters. We prove that its joint eigenvalue density involves the correct hypergeometric function of two matrix arguments, and a continuous parameter β > 0. If we choose β = 1, 2, 4, we recover the classical Wishart ensembles of general covariance over the reals, complexes, and quaternions. Jack polynomials are often defined as the eigenfunctions of the Laplace-Beltrami operator. We prove that Jack polynomials are in addition eigenfunctions of an integral operator defined as an average over a β-dependent measure on the sphere. When combined with an identity due to Stanley, we derive a definition of Jack polynomials. An efficient numerical algorithm is also presented for simulations. The algorithm makes use of secular equation software for broken arrow matrices currently unavailable in the popular technical computing languages. The simulations are matched against the cdfs for the extreme eigenvalues. The techniques here suggest that arrow and broken arrow matrices can play an important role in theoretical and computational random matrix theory including the study of corners processes. We provide a number of simulations illustrating the extreme eigenvalue distributions that are likely to be useful for applications. We also compare the n → ∞ answer for all β with the free-probability prediction. C 2013 AIP Publishing LLC. [http://d

Nanolayered multilayer Ti/TiN coatings: Role of bi-layer thickness and annealing on solid particle erosion behavior at elevated temperature

Solid particle erosion is a very serious and inevitable issue faced by key components of modern machinery in various applications such as compressor blades and vanes of turbine engines, and turbine blades of advanced aircraft engines. In this direction third generation Ti/TiN nanolayered multilayered erosion resistant coatings were developed using sputtering technique. Films of around 7–10 μm total thickness with bi-layer thicknesses from 7.5–115 nm were deposited. Structural and mechanical properties such as hardness, toughness and stress of the films were studied, and correlated with the bi-layer thickness and deposition conditions. Erosion test was carried out according to ASTM G76-13 standard parameters at 30, 45, 60, and 90° impinging angles. Since the compressor blades of the gas turbine engines usually operate at 100 to 550 °C, the erosion tests were conducted at 400 °C. Films with lower bi-layer thickness showed better erosion resistance in comparison with higher bi-layer thickness films. Further, effect of bi-layer thickness, annealing and internal stress of the films on erosion resistance performance is studied. Detailed studies revealed that the optimized coating exhibited an improvement in the erosion performance by a factor of 15 compared to Ti6Al4V substrate

Ultra-thin multilayered erosion resistant Ti/TiN coatings with stress absorbing layers

In this high speed era, several machine components are operated at high speeds and at high temperatures. Machine components such as gas turbine compressor blades and vanes are exposed to high speed dust particles. Consequently, engine performance deteriorates and in extreme cases catastrophic accidents can happen. In order to protect these engine components, ultra-thin multilayered erosion resistant Ti/TiN coatings (thickness similar to 9-10 mu m) with stress absorbing layers were developed using magnetron sputtering. Stress absorbing metallic layers were introduced to control the internal stress and also to maintain balanced ductile and brittle nature of the coating. Ultra-thin (3-4 nm) metal/ceramic bilayers provided high number of interfaces and ultra-small grain sizes. Erosion resistance performance of the developed coatings and also bare Ti6Al4V substrates was tested according to the ASTM-G76-13 standard at 400 degrees C. Tests were conducted with three different erodent speeds of 30, 60 and 100 m/s at four different impinging angles 90 degrees, 60 degrees, 45 degrees and 30 degrees. The average erosion rate ratios between Ti6Al4V substrate and optimized coating were 74, 13 and 12 for the erodent speeds of 30, 60 and 100 m/s, respectively. Influence of the substrate on the coating performance was also studied. Morphological, elemental and spectral analyses of the erosion scar were also probed. Structural stability, mechanical properties and erosion resistance performance of the optimized film were tested after 100 h annealing in air and vacuum at a temperature of 400 degrees C. Erosion resistant performance of the optimized film was unaffected after 100 h annealing