9 resultados para Starlike and Convex Functions
em Cochin University of Science
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Department of Biotechnology, Cochin University of Science and Technology
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The study on the fuzzy absolutes and related topics. The different kinds of extensions especially compactification formed a major area of study in topology. Perfect continuous mappings always preserve certain topological properties. The concept of Fuzzy sets introduced by the American Cyberneticist L. A Zadeh started a revolution in every branch of knowledge and in particular in every branch of mathematics. Fuzziness is a kind of uncertainty and uncertainty of a symbol lies in the lack of well-defined boundaries of the set of objects to which this symbol belongs. Introduce an s-continuous mapping from a topological space to a fuzzy topological space and prove that the image of an H-closed space under an s-continuous mapping is f-H closed. Here also proved that the arbitrary product fi and sum of fi of the s-continuous maps fi are also s-continuous. The original motivation behind the study of absolutes was the problem of characterizing the projective objects in the category of compact spaces and continuous functions.
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The brain with its highly complex structure made up of simple units,imterconnected information pathways and specialized functions has always been an object of mystery and sceintific fascination for physiologists,neuroscientists and lately to mathematicians and physicists. The stream of biophysicists are engaged in building the bridge between the biological and physical sciences guided by a conviction that natural scenarios that appear extraordinarily complex may be tackled by application of principles from the realm of physical sciences. In a similar vein, this report aims to describe how nerve cells execute transmission of signals ,how these are put together and how out of this integration higher functions emerge and get reflected in the electrical signals that are produced in the brain.Viewing the E E G Signal through the looking glass of nonlinear theory, the dynamics of the underlying complex system-the brain ,is inferred and significant implications of the findings are explored.
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Coded OFDM is a transmission technique that is used in many practical communication systems. In a coded OFDM system, source data are coded, interleaved and multiplexed for transmission over many frequency sub-channels. In a conventional coded OFDM system, the transmission power of each subcarrier is the same regardless of the channel condition. However, some subcarrier can suffer deep fading with multi-paths and the power allocated to the faded subcarrier is likely to be wasted. In this paper, we compute the FER and BER bounds of a coded OFDM system given as convex functions for a given channel coder, inter-leaver and channel response. The power optimization is shown to be a convex optimization problem that can be solved numerically with great efficiency. With the proposed power optimization scheme, near-optimum power allocation for a given coded OFDM system and channel response to minimize FER or BER under a constant transmission power constraint is obtained
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The median (antimedian) set of a profile π = (u1, . . . , uk) of vertices of a graphG is the set of vertices x that minimize (maximize) the remoteness i d(x,ui ). Two algorithms for median graphs G of complexity O(nidim(G)) are designed, where n is the order and idim(G) the isometric dimension of G. The first algorithm computes median sets of profiles and will be in practice often faster than the other algorithm which in addition computes antimedian sets and remoteness functions and works in all partial cubes
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Nonlinear optics is a broad field of research and technology that encompasses subject matter in the field of Physics, Chemistry, and Engineering. It is the branch of Optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light. This nonlinearity is typically only observed at very high light intensities. This area has applications in all optical and electro optical devices used for communication, optical storage and optical computing. Many nonlinear optical effects have proved to be versatile probes for understanding basic and applied problems. Nonlinear optical devices use nonlinear dependence of refractive index or absorption coefficient on the applied field. These nonlinear optical devices are passive devices and are referred to as intelligent or smart materials owing to the fact that the sensing, processing and activating functions required for optical processes are inherent to them which are otherwise separate in dynamic devices.The large interest in nonlinear optical crystalline materials has been motivated by their potential use in the fabrication of all-optical photonic devices. Transparent crystalline materials can exhibit different kinds of optical nonlinearities which are associated with a nonlinear polarization. The choice of the most suitable crystal material for a given application is often far from trivial; it should involve the consideration of many aspects. A high nonlinearity for frequency conversion of ultra-short pulses does not help if the interaction length is strongly limited by a large group velocity mismatch and the low damage threshold limits the applicable optical intensities. Also, it can be highly desirable to use a crystal material which can be critically phasematched at room temperature. Among the different types of nonlinear crystals, metal halides and tartrates have attracted due to their importance in photonics. Metal halides like lead halides have drawn attention because they exhibit interesting features from the stand point of the electron-lattice interaction .These materials are important for their luminescent properties. Tartrate single crystals show many interesting physical properties such as ferroelectric, piezoelectric, dielectric and optical characteristics. They are used for nonlinear optical devices based on their optical transmission characteristics. Among the several tartrate compounds, Strontium tartrate, Calcium tartrate and Cadmium tartrate have received greater attention on account of their ferroelectric, nonlinear optical and spectral characteristics. The present thesis reports the linear and nonlinear aspects of these crystals and their potential applications in the field of photonics.
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Hypoxia is one of the major causes of damage to the fetal and neonatal brain and cardiac functions. in earlier studies we have reported the brain damage caused by hypoxia and resusciation with oxygen and epinephrine and have found that glucose treatment to hypoxic rats and hypoxic rats treated with oxygen shows a reversal of brain damage. during this study the findings may have clinical significance in the proper management of heart and brain functions.
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An attempt is made by the researcher to establish a theory of discrete functions in the complex plane. Classical analysis q-basic theory, monodiffric theory, preholomorphic theory and q-analytic theory have been utilised to develop concepts like differentiation, integration and special functions.
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Friction welding is a solid state joining process that produces coalescence in materials, using the heat developed between surfaces through a combination of mechanical induced rubbing motion and applied load. In rotary friction welding technique heat is generated by the conversion of mechanical energy into thermal energy at the interface of the work pieces during rotation under pressure. Traditionally friction welding is carried out on a dedicated machine because of its adaptability to mass production. In the present work, steps were made to modify a conventional lathe to rotary friction welding set up to obtain friction welding with different interface surface geometries at two different speeds and to carry out tensile characteristic studies. The surface geometries welded include flat-flat, flat-tapered, tapered-tapered, concave-convex and convex-convex. A comparison of maximum load, breaking load and percentage elongation of different welded geometries has been realized through this project. The maximum load and breaking load were found to be highest for weld formed between rotating flat and stationary tapered at 500RPM and the values were 19.219kN and 14.28 kN respectively. The percentage elongation was found to be highest for weld formed between rotating flat and stationary flat at 500RPM and the value was 21.4%. Hence from the studies it is cleared that process parameter like “interfacing surface geometries” of weld specimens have strong influence on tensile characteristics of friction welded joints