An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups

We generalise a result of Hardy, which asserts the impossibility of a function and its Fourier transform to be simultaneously “very rapidly decreasing” to: (i) all noncompact, semi-simple Lie groups with one conjugacy class of Cartan subgroups; (ii) SL(2, R); and (iii) all symmetric spaces of the noncompact type

A CLINICAL STUDY OF MUSTA (CYPERUS ROTUNDUS LINN.) IN HYPERLIPIDAEMIA

Hyperlipidaemia is a metabolic disorder in population diagnosed by altered levels of Lipoproteins, Cholesterol and Triglycerides in plasma. This results deposition of lipids especially esterified cholesterol in the wall of arteries resulting in the narrowing and blockage of the arteries leading to heart diseases and other diseases such as cerebrovascular disease, renal disease, liver disease and peripheral vascular disease. The present work focused on comparative analysis of anti-hyperlipidaemic profile of Musta (Cyperus rotundus Linn.) in Male and female patients. The patients suffering from Hyperlipidaemia and its related disorders like non-insulin dependent diabetes etc. were divided into two groups, Group A confined to male and Group B confined to female. Each group contains 15 patients. All the patients were advised to take 3 gm powdered Musta rhizome in two or three divided doses for a period of 45 days. After treatment, Musta rhizome powder showed more significant anti-hyperlipidaemic activity in males than females. The significance in males total cholesterol (p<0.05), HDL (p<0.05), VLDL (p<0.05), triglycerides (p<0.05) is more than that of females VLDL (p>0.05), triglycerides (p>0.05). It is observed that in group A 40% patients got complete relief, 6.67 % patients got marked relief, 33.33% patients got moderate relief and 20 % patients got mild relief. Similarly, in group B patients 06.67% patients got complete relief, 6.67 % patients got marked relief, 53.33% patients got moderate relief and 33.33 % patients got mild relief

Hardy's uncertainty principle on semisimple groups

A theorem of Hardy states that, if f is a function on R such that |f(x)|≤ C e−α|x|2 for all x in R and |f(ξ)|≤ C e−β|ξ|2 for all ξ in R, where α > 0, β > 0, and αβ > 1∕4, then f = 0. Sitaram and Sundari generalised this theorem to semisimple groups with one conjugacy class of Cartan subgroups and to the K-invariant case for general semisimple groups. We extend the theorem to all semisimple groups

Effect of Gurney Flap Configuration on the Performance of a Centrifugal Fan

The present investigation is conducted to study the effect of Gurney flap configuration on the performance of a centrifugal fan at different Reynolds numbers. Gurney flaps of different configurations, such as angle, quarter round and half round corresponding to a nominal height of 1.2 mm (1.94% of the impeller blade spacing at tip) height are attached to the pressure surface of the centrifugal fan impeller blade tip. Performance tests are carried out on the centrifugal fan with a vaneless diffuser at five Reynolds numbers viz. 0.30, 0.41, 0.55, 0.69 and 0.80×105 based on the impeller tip speed, impeller blade exit height and kinematic viscosity, both with and without Gurney flaps. From the performance curves it is found that fan performance improves significantly with Gurney flaps at low Reynolds numbers and improves marginally at high Reynolds numbers. Gurney flap of angle configuration of height as small as 1.94% of the impeller blade spacing at tip increases head coefficient by 5.2% and increases the volume flow rate across the fan by 5.4% at the lowest Reynolds number of 0.30×105. Even though there is increase in both head and flow coefficients with other Gurney flap configurations (quarter round and half round), they are always less than that for the angle Gurney flap. The effect of Reynolds number on the performance curves is found to be negligible with Gurney flaps, whereas the effect of Reynolds number on the performance curves of the impeller without Gurney flap is found to be considerable. Additional experiments conducted with Gurney flaps of two configurations, viz. angle and quarter round, with a larger height of 2.5 mm (4.05% of the impeller blade spacing at tip) attached on the pressure surface of the centrifugal fan impeller blade tip have shown that the performance of the fan with quarter round GF is better than the performance of the fan with angle GF

Sensemaking for Broad Topics via Automated Extraction and Recursive Search

The availability of vast amounts of diverse information related to a broad topic makes it difficult and time-consuming for users to find and digest the right information regarding various low-level topics within the broader space. Current approaches to addressing these challenges include providing curated topical pages, relevant query refinement suggestions, list of subtopics, etc. However, these approaches do not scale and offer inadequate support for sensemaking. This disclosure describes automated techniques that extract information from online information sources by using a query related to a high-level topic to recursively formulate additional queries for subtopics to construct a hierarchical set of topics related to the broad query. The results can be utilized to provide a user interface using the hierarchical topic levels which can make it faster and easier for users to understand and navigate information regarding a high-level topic

The correct structures of the ortho-cyclized products in the cycloalkylations of 1-m-methoxybenzyl-4,4a,5,6,7,8-hexahydronaphthalen-2(3H)-one and 1-m-methoxybenzyl-octalins: X-ray structure determination of (±)-4-methoxy-9a-carbamorphinan-16-one

The previously assigned (ref.1) ortho-cycloalkylated product from the reaction of 1 and 2 respectively, with ortho-phosphosphoric acid and polyphosphoric acid, has been corrected to (±)-4-methoxy-9a-carbamorphinan-16-one (6) and the respective ether 7 by a single crystal X-ray structure determination of 6

Performance Improvement of a Centrifugal Compressor by Passive Means

The present experimental investigation deals with performance improvement of a low-speed centrifugal compressor by inexpensive passive means such as turbulence generator placed at different positions and partial shroud near the rotor blade tip. The experiments are carried out at three values of tip clearance, namely 2.2%, 5.1%, and 7.9% of rotor blade height at the exit. Performance tests are carried out for a total of 13 configurations. From these measurements, partial shroud is found to give the best performance. The improvement in the compressor performance may be due to the reduction of tip leakage flows by the small extension of partial shroud (2 mm on the pressure surface side). Although there is nominal change in performance due to turbulence generator (TG), TG has beneficial effect of increased operating range

Uncertainty principles on certain Lie groups

There are several ways of formulating the uncertainty principle for the Fourier transform on Rn. Roughly speaking, the uncertainty principle says that if a function f is 'concentrated' then its Fourier transform f~ cannot be 'concentrated' unless f is identically zero. Of course, in the above, we should be precise about what we mean by 'concentration'. There are several ways of measuring 'concentration' and depending on the definition we get a host of uncertainty principles. As several authors have shown, some of these uncertainty principles seem to be a general feature of harmonic analysis on connected locally compact groups. In this paper, we show how various uncertainty principles take form in the case of some locally compact groups including Rn, the Heisenberg group, the reduced Heisenberg group and the Euclidean motion group of the plane