Using Elimination Theory to construct Rigid Matrices

The rigidity of a matrix A for target rank r is the minimum number of entries of A that must be changed to ensure that the rank of the altered matrix is at most r. Since its introduction by Valiant (1977), rigidity and similar rank-robustness functions of matrices have found numerous applications in circuit complexity, communication complexity, and learning complexity. Almost all nxn matrices over an infinite field have a rigidity of (n-r)^2. It is a long-standing open question to construct infinite families of explicit matrices even with superlinear rigidity when r = Omega(n). In this paper, we construct an infinite family of complex matrices with the largest possible, i.e., (n-r)^2, rigidity. The entries of an n x n matrix in this family are distinct primitive roots of unity of orders roughly exp(n^2 log n). To the best of our knowledge, this is the first family of concrete (but not entirely explicit) matrices having maximal rigidity and a succinct algebraic description. Our construction is based on elimination theory of polynomial ideals. In particular, we use results on the existence of polynomials in elimination ideals with effective degree upper bounds (effective Nullstellensatz). Using elementary algebraic geometry, we prove that the dimension of the affine variety of matrices of rigidity at most k is exactly n^2-(n-r)^2+k. Finally, we use elimination theory to examine whether the rigidity function is semi-continuous.Comment: 25 Pages, minor typos correcte

Efficiency in Indian Edible Oilseed Sector: Analysis and Implications

Reversing the declining trend in productivity of oilseeds and improving the efficiency of oilseed processing is a major challenge to the policymakers and researchers. The present study has analyzed technical inefficiencies and factors responsible for inefficiencies in production and processing of four major edible oilseeds, viz. groundnut, rapeseed and mustard, soybean and sunflower. Both primary and secondary data have been used to estimate the inefficiencies. Analysis has revealed the presence of 1/4 to 1/3 technical inefficiencies in oilseed production at the average level and even more at the farm/ processing unit level along with allocative and scale inefficiencies. The combined technical inefficiencies in the oilseed sector have been found to be 1/2 to 2/3, which are enormous. If prevented/ minimized, the oil production in the country could nearly be doubled. Soil quality, seed replacement and education have been found as determinants of technical efficiency in oilseed production, whereas availability of adequate raw material and higher oil recovery determine the technical efficiency in oil production. Lack of assured market for oilseeds and lack of timely and assured supply of quality seeds and raw materials for processing are some of the important factors for the poor performance of the oilseeds industry. Study has reported that the marginal return to water is one of the highest in oilseeds. Therefore, cultivation of oilseeds in irrigated land if they really compete with other crops for profitability, needs to be given due consideration.Agricultural and Food Policy,

Results of Sever- L’ Episcopo procedure for obstetric brachial plexus palsy

Background: The reported incidence of obstetric brachial plexus palsy (OBPP) varies from 0.3 to 2.5 per 1000 live birthsresulting in internal rotation deformity and weak abduction of the involved side shoulder.Methods: To retrospectively analyse the functional results of the Sever- L‘ Episcopo procedure for OBPP with a minimum follow-up of 2 years to a maximum of 13 years using modified Mallet scoring system for shoulder.Results: A significant improvement in the range of abduction and the restoration of external rotation of shoulder was achieved with Sever- L’Episcopo procedure. Conclusions: The results of secondary reconstruction of a dysfunctional shoulder by means of a Lattismus dorsi & Teres major transfer as described by Sever- L’Episcopo is definitely beneficial. However this procedure will improve, but will not normalize, function. Apart from functional improvement this procedure corrects a deformity thereby easing the psycho-social stigma associated with it

Hydrography of Gourikere pond of Siddapur, Karnataka

Present work was pertaining to studies conducted at one lentic perinial water body at Talaguppa viz., Gourikere pond Tq:Sagar Karnataka.  The period of study undertaken it one year from May - 2007 to April - 2008. This study is intended to monitor the water quality of Gourikere pond of Talaguppa, Sagar Tq: Shimoga District and also helpful for using this water for making fisheries activity. The present investigation encompassed collection of data pertaining to various aspects such as meteorological condition, physicochemical parameter of water body of Gourikere pond. Air and surface water temperatures varied from 29.7oC to 37.5oC and from 20.6oC – 24.8oC. And the pH ranged between 8.1 to 9.1. Variation in dissolved oxygen content was from 6.4 mg/l to 10.8 mg/l  and variation in CO2 was observed from 7.4 mg/l to 12.00 mg/l.  Concentrations of nutrients viz. nitrates (0.69 mg/l to1.30 mg/l), phosphates (0.30 mg/l to 0.63 mg/l) Magnesium (11.79 mg/l to 88.64 mg/l) sulphate (2.45 mg/l to 5.16 mg/l) Calcium (33.41 to 138.10mg/l), also varied independently. The results of the study revealed that hydrographical conditions fluctuated moderately throughout the year. Keywords: Physico-chemical parameters, lentic, Nutrients, Gourikere pond

Zooplankton diversity and abundance of mangrove ecosystem of Kali estuary, Karwar, west coast of India

The present study conducted at the mangrove ecosystem of Kali estuary. Samples were collected from the three fixed stations for the period of thirteen months from January 2008 to January 2009 at regular monthly interval to identify and quantify the abundance, taxonomy and relative ratio of phytoplankton and zooplankton. In the present study of species diversity of zooplankton groups in the mangrove area, composed of twelve groups comprising fifty two species major share comes from the copepods which comprises about seventeen species.  Protozoa taxa comprised by five species, coelenterata and cladocera by two species each, ctenophore comprised by single species whereas the larval forms comprised by fourteen species. Keywords: Zooplankton, Diversity, Abundance, Estuary, Mangrove, Karwar

20W Output Broadband Amplifier with Automatic Gain Control and Thermal Protection

The requirement is to explore concept, design, fabrication and testing of a common source class B, cwrf amplifier by using readily available MOSFET that can withstand a load mismatch at all phase angles with more than a VSWR of 20:1. This amplifier must give an output of more than 20W with 13dB gain in the frequency range of 28 to 46MHz i.e. 37 ± 9MHz. This module will make one of the stages for a multistage cascaded high power cwrf solid state amplifier. The amplifier must be over current and over voltage protected by using external self-regulated dc power supply at the drain. The amplifier MOSFET device is presently to be biased at the gate with a variable dc supply. This arrangement will make it gain controlled. This will be feed backed from the cwrf output so as to make it automatic gain controlled in future. Various techniques of sampling forward and reflected power at the output must also be explored. A thermoswitch at the heat sink of MOSFET is to be added along with necessary circuitry to regulate the operating temperature, thereby protecting the device from overheating

Oestrus synchronization with fixed-time artificial insemination in smallholder pig production systems in north-east India: Success rate and benefits

Pig production is an important component of the farming systems that are practised in the north-eastern region of India and it has special significance for improving the socio-economic status of tribal farmers in the region. In an effort to optimize the production efficiency of rural pig production systems, the potential influence of oestrus synchronization and fixed-time artificial insemination (AI) on synchronizing husbandry programmes was investigated. A total of 117 crossbred sows, selected from various village production units, were randomly allocated to two (control and treatment) groups. The sows in the treatment group (n = 81) received 800 IU of equine chorionic gonadotropin (eCG), followed by 500 IU of human chorionic gonadotropin (hCG) 72 hours after the eCG injection. The sows in the control group (n = 36) served as the untreated control. The onset of oestrus, oestrus signs, oestrus intensity, and duration of oestrus were observed after treatment. The oestrus sows were inseminated twice at 24 h and 36 h, respectively, after hCG injection at various village production units. Results revealed that 86.4% of sows in the treatment group exhibited all the behavioural and physical signs of oestrus. The average interval between treatment and onset of oestrus was 84.8 ± 2.43 hours. The mean oestrus intensity of sows in the treatment group was 2.3 (when assessed on a scale of 1 to 3), which did not differ significantly from the oestrus intensity exhibited by the control group. The duration of oestrus varied from 36 to 56 hours in the treated sows, which was significantly longer when compared with the duration of oestrus in the control group. The study obtained a farrowing rate of 82.6% and litter size of 9.2 ± 0.32 after oestrus synchronization with timed insemination. Oestrus synchronization facilitated the insemination of a batch of sows at particular locations covering two to three village clusters, which drastically reduced the transport costs for the semen. Oestrus synchronization facilitated the effective implementation of AI by coordinating the insemination of batches of sows, thus reducing shipping and insemination costs. Improving heat detection contributed to shortening the weaning to oestrous interval in smallholder pig production system, which in turn decreased production costs.______________________________________________________________________________________Keywords: Assisted reproduction, farrrowing rate, insemination cost, reproduction efficienc

Collective Dynamics of One-Dimensional Charge Density Waves

The effect of disorder on the static and dynamic behaviour of one-dimensional charge density waves at low temperatures is studied by analytical and numerical approaches. In the low temperature region the spatial behaviour of the phase-phase correlation function is dominated by disorder but the roughness exponent remains the same as in the pure case. Contrary to high dimensional systems the dependence of the creep velocity on the electric field is described by an analytic function.Comment: 4 pages, 4 figure

Adaptive Fuzzy PI Current Control of Grid Interact PV Inverter

Now a day‟s, Photo Voltaic (PV) power generation rapidly increasing. This power generation highly depending on the temperature and irradiation. When this power interface with grid through the voltage source inverter with PI controller. Its gains should be updated due to the parametric changes for the better performance. In This Work Fuzzy Controller updates the gains of the proportional integral (PI)s Controller under variable parametric conditions. the gaines of the PI Controller are updated based on the error current and change in error current through the fuzzy controller. The error current in direct and quadrature frame are the Inputs to the PI controller. The PI Controller generates the reference voltage to the pulse width modulation technique. Here reference voltage is compared with the carrier signal to generate the pulses to the 3-Ph Inverter connected to the grid. This controller has given well dynamic response with less steady state error and also given The less THD of the grid current compared to the PI and Fuzzy controller.It Is implemented and verified in MATLAB Simulink