Galois Theory and Solvable Equations of Prime Degree

In this article we review classical and modern Galois theory with historical evolution and prove a criterion of Galois for solvability of an irreducible separable polynomial of prime degree over an arbitrary field k and give many illustrative examples.

Numerical analysis on thermoacoustic prime movers for development of pulse tube cryocoolers

Thermo Acoustic Prime Movers (TAPMs) are being considered as the ideal choice for driving the Pulse Tube Cryocoolers replacing the conventional compressors. The advantages are the absence of moving components and they can be driven by low grade energy as such as fuel, gas, solar energy, waste heat etc. While the development of such TAPMs is in progress in our laboratory, their design and fabrication should be guided by numerical modeling and this may be done by several methods such as solving the energy equation 1], enthalpy flow model 2], CFD 3], etc. We have used CFD technique, since it provides a better insight into the velocity and temperature profiles. The analysis is carried out by varying parameters such as (a) temperature difference across the stack, (b) stack and resonator lengths and (c) different working fluids such as air, nitrogen, argon etc. The theoretical results are compared with the experimental data wherever possible and they are in reasonably good agreement with each other. The analysis indicate that (i) larger temperature difference across the stack leads to increased acoustic amplitude, (ii) longer resonator leads to decrease in frequency with lesser amplitude and (iii) there exists an optimal stack length for the best performance of TAPM. These results are presented here.

Experimental and theoretical investigation of thermoacoustic prime mover

The thermoacoustic prime mover is part of an interesting class of prime movers that can be used to generate clean energy and to drive cryogenic refrigeration systems. A thermoacoustic prime mover has been built based on the linear thermoacoustic model, which consumes thermal energy and produces acoustic energy. The objective of this article is to design a thermoacoustic prime mover that can be used as a drive for a thermoacoustic refrigerator. It is found that stack plate length and its distance from the closed end have a significant effect on the thermal efficiency of the prime mover. For different stack center positions, there is an optimum length of stack plate that has a significant effect on the performance of the thermoacoustic prime mover in terms of temperature gradient, frequency, and pressure amplitude. In this study, the experiments have been done on the thermoacoustic prime mover by varying stack position and its length with constant blockage ratio and resonator length. The results obtained from the experiments have been compared to the theoretical results acquired from DeltaEc Software.

Computational fluid dynamics simulation of open ended thermoacoustic prime mover with straight and tapered resonator

A thermoacoustic refrigerator driven by a thermoacoustic primemover is an effective way to produce durable and long lasting refrigeration due to high reliability, no exotic materials, and no moving parts. Resonator geometry is also one of the important factors that influence the performance of a thermoacoustic prime mover, namely, frequency. Computational fluid dynamics simulation of performance comparison of thermoacoustic prime mover with a straight and tapered resonator is chosen for the present study under an identical stack condition with the air as a working fluid. The frequency and pressure amplitude of oscillations obtained from simulation results were found to be more in the tapered resonator than the straight resonator. Apart from computational fluid dynamics simulation, the simulation studies have also been conducted using design environment for low-amplitude thermoacoustic energy conversion, which predicts the performance of thermoacoustic primemover comparatively well. Simulation results from computational fluid dynamics and design environment for low-amplitude thermoacoustic energy conversion were compared and found to be matching well, representing the good validity of computational fluid dynamics modeling.

Influence of operational and geometrical parameters on the performance of twin thermoacoustic prime mover

Thermoacoustics is the interaction between heat and sound, which are useful in designing heat engines and heat pumps. Research in the field of thermoacoustics focuses on the demand to improve the performance which is achieved by altering operational, geometrical and fluid parameters. The present study deals with improving the performance of twin thermoacoustic prime mover, which has gained the significant importance in the recent years for the production of high amplitude sound waves. The performance of twin thermoacoustic prime mover is evaluated in terms of onset temperature difference, resonance frequency and pressure amplitude of the acoustic waves by varying the resonator length and charge pressures of fluid medium nitrogen. DeltaEC, the free simulation software developed by LANL, USA is employed in the present study to simulate the performance of twin thermoacoustic prime mover. Experimental and simulated results are compared and the deviation is found to be within 10%.

Experimental and simulation studies on the performance of standing wave thermoacoustic prime mover for pulse tube refrigerator

The thermoacoustic prime mover (TAPM) has gained considerable attention as a pressure wave generator to drive pulse tube refrigerator (PTR) due to no moving parts, reasonable efficiency, use of environmental friendly working fluids etc. To drive PTCs, lower frequencies (f) with larger pressure amplitudes (Delta P) are essential, which are affected by geometric and operating parameters of TAPM as well as working fluids. For driving PTRs, a twin standing wave TAPM is built and studied by using different working fluids such as helium, argon, nitrogen and their binary mixtures. Simulation results of DeltaEc are compared with experimental data wherever possible. DeltaEc predicts slightly increased resonance frequencies, but gives larger Delta P and lower temperature difference Delta T across stack. High mass number working fluid leads to lower frequency with larger Delta P, but higher Delta T. Studies indicate that the binary gas mixture of right composition with lower Delta T can be arrived at to drive TAPM of given geometry. (C) 2013 Elsevier Ltd and IIR. All rights reserved.

Experimental investigation of a thermoacoustic refrigerator driven by a standing wave twin thermoacoustic prime mover

The objective of this study is to analyse the performance of thermoacoustic refrigerator (TAR) measured in terms of hot end temperature and temperature difference across refrigerator stack with two different spacing namely 0.4 mm and 0.8 mm and stack used in refrigerating section was made of low thermal conductivity materials namely Mylar sheet and photographic film & the experiments were carried out at 1 MPa pressure using helium as working fluid. High powered acoustic wave with frequency of 460 Hz and pressure amplitude of congruent to 0.07 MPa was obtained from twin thermoacoustic prime mover (TAPM) and this acoustic wave produced temperature difference of 16 degrees C across the Mylar sheet stack made of 0.4 mm spacing in refrigerator section. From this study, it has been inferred that twin TAPM can act as efficient drive for TAR. (C) 2013 Elsevier Ltd and IIR. All rights reserved.

Simulation studies on the performance of thermoacoustic prime movers and refrigerator

The prime movers and refrigerators based on thermoacoustics have gained considerable importance toward practical applications in view of the absence of moving components, reasonable efficiency, use of environmental friendly working fluids, etc. Devices such as twin Standing Wave ThermoAcoustic Prime Mover (SWTAPM), Traveling Wave ThermoAcoustic Prime Mover (TWTAPM) and thermoacoustically driven Standing Wave ThermoAcoustic Refrigerator (SWTAR) have been studied by researchers. The numerical modeling and simulation play a vital role in their development. In our efforts to build the above thermoacoustic systems, we have carried out numerical analysis using the procedures of CFD on the above systems. The results of the analysis are compared with those of DeltaEC (freeware from LANL, USA) simulations and the experimental results wherever possible. For the CFD analysis commercial code Fluent 6.3.26 has been used along with the necessary boundary conditions for different working fluids at various average pressures. The results of simulation indicate that choice of the working fluid and the average pressure are critical to the performance of the above thermoacoustic devices. Also it is observed that the predictions through the CFD analysis are closer to the experimental results in most cases, compared to those of DeltaEC simulations. (C) 2015 Elsevier Ltd. All rights reserved.

Immune responses against hepatitis C virus genotype 3a virus-like particles in mice: A novel VLP prime-adenovirus boost strategy

Chronic hepatitis C virus (HCV) infection represents a major health threat to global population. In India, approximately 15-20% of cases of chronic liver diseases are caused by HCV infection. Although, new drug treatments hold great promise for HCV eradication in infected individuals, the treatments are highly expensive. A vaccine for preventing or treating HCV infection would be of great value, particularly in developing countries. Several preclinical trials of virus-like particle (VLP) based vaccine strategies are in progress throughout the world. Previously, using baculovirus based system, we have reported the production of hepatitis C virus-like particles (HCV-LPs) encoding structural proteins for genotype 3a, which is prevalent in India. In the present study, we have generated HCV-LPs using adenovirus based system and tried different immunization strategies by using combinations of both kinds of HCV-LPs with other genotype 3a-based immunogens. HCV-LPs and peptides based ELISAs were used to evaluate antibody responses generated by these combinations. Cell-mediated immune responses were measured by using T-cell proliferation assay and intracellular cytokine staining. We observed that administration of recombinant adenoviruses expressing HCV structural proteins as final booster enhances both antibody as well as T-cell responses. Additionally, reduction of binding of VLP and JFH1 virus to human hepatocellular carcinoma cells demonstrated the presence of neutralizing antibodies in immunized sera. Taken together, our results suggest that the combined regimen of VLP followed by recombinant adenovirus could more effectively inhibit HCV infection, endorsing the novel vaccine strategy. (C) 2015 Elsevier Ltd. All rights reserved.

Part I. Kinetics of coarsening of the gamma-prime precipitate in nickel-silicon alloys. Part II. Rate of crystallization of an amorphous Fe-P-C alloy

The coarsening kinetics of Ni₃ Si(γ') precipitate in a binary Ni-Si alloy containing 6.5 wt. % silicon was studied by magnetic techniques and transmission electronmicroscopy. A calibration curve was established to determine the concentration of silicon in the matrix. The variation of the Si content of the Ni-rich matrix as a function of time follows Lifshitz and Wagner theory for diffusion controlled coarsening phenomena. The estimated values of equilibrium solubility of silicon in the matrix represent the true coherent equilibrium solubilities.

The experimental particle-size distributions and average particle size were determined from dark field electron micrographs. The average particle size varies linearly with t^-1/3 as suggested by Lifshitz and Wagner. The experimental distributions of particle sizes differ slightly from the theoretical curve at the early stages of aging, but the agreement is satisfactory at the later stages. The values of diffusion coefficient of silicon, interfacial free energy and activation energy were calculated from the results of coarsening kinetics. The experimental value of effective diffusion coefficient is in satisfactory agreement with the value predicted by the application of irreversible the rmodynamics to the process of volume constrained growth of coherent precipitate during coarsening. The coherent γ' particles in Ni-Sialloy unlike those in Ni-Al and Ni-Ti seem to lose coherency at high temperature. A mechanism for the formation of semi-coherent precipitate is suggested.

On the distribution of the signs of the conjugates of the cyclotomic units in the maximal real subfield of the qth cyclotomic field, q A prime

Let F = Ǫ(ζ + ζ ^–1) be the maximal real subfield of the cyclotomic field Ǫ(ζ) where ζ is a primitive qth root of unity and q is an odd rational prime. The numbers u₁=-1, u_k=(ζ^k-ζ^-k)/(ζ-ζ^-1), k=2,…,p, p=(q-1)/2, are units in F and are called the cyclotomic units. In this thesis the sign distribution of the conjugates in F of the cyclotomic units is studied.

Let G(F/Ǫ) denote the Galoi's group of F over Ǫ, and let V denote the units in F. For each σϵ G(F/Ǫ) and μϵV define a mapping sgn_σ: V→GF(2) by sgn_σ(μ) = 1 iff σ(μ) ˂ 0 and sgn_σ(μ) = 0 iff σ(μ) ˃ 0. Let {σ₁, ... , σ_p} be a fixed ordering of G(F/Ǫ). The matrix M_q=(sgn_σj(v_i) ) , i, j = 1, ... , p is called the matrix of cyclotomic signatures. The rank of this matrix determines the sign distribution of the conjugates of the cyclotomic units. The matrix of cyclotomic signatures is associated with an ideal in the ring GF(2) [x] / (x^p+ 1) in such a way that the rank of the matrix equals the GF(2)-dimension of the ideal. It is shown that if p = (q-1)/ 2 is a prime and if 2 is a primitive root mod p, then M_q is non-singular. Also let p be arbitrary, let ℓ be a primitive root mod q and let L = {i | 0 ≤ i ≤ p-1, the least positive residue of defined by ℓⁱ mod q is greater than p}. Let H_q(x) ϵ GF(2)[x] be defined by H_q(x) = g. c. d. ((Σ xⁱ/I ϵ L) (x+1) + 1, x^p + 1). It is shown that the rank of M_q equals the difference p - degree H_q(x).

Further results are obtained by using the reciprocity theorem of class field theory. The reciprocity maps for a certain abelian extension of F and for the infinite primes in F are associated with the signs of conjugates. The product formula for the reciprocity maps is used to associate the signs of conjugates with the reciprocity maps at the primes which lie above (2). The case when (2) is a prime in F is studied in detail. Let T denote the group of totally positive units in F. Let U be the group generated by the cyclotomic units. Assume that (2) is a prime in F and that p is odd. Let F₍₂₎ denote the completion of F at (2) and let V₍₂₎ denote the units in F₍₂₎. The following statements are shown to be equivalent. 1) The matrix of cyclotomic signatures is non-singular. 2) U∩T = U². 3) U∩F²₍₂₎ = U². 4) V₍₂₎/ V₍₂₎² = ˂v₁ V₍₂₎²˃ ʘ…ʘ˂v_p V₍₂₎²˃ ʘ ˂3V₍₂₎²˃.

The rank of M_q was computed for 5≤q≤929 and the results appear in tables. On the basis of these results and additional calculations the following conjecture is made: If q and p = (q -1)/ 2 are both primes, then M_q is non-singular.

Strengthening effectiveness of policy directives of the LVFO Council of Ministers on Lake Victoria, Uganda

Research was done to assess the dissemination and implementation by the Fisheries Department, Local Govemments and beach management units and the awareness, acceptance and compliance among fishers to the CoM Directives on management of Lake Victoria fisheries. Conducted by the National Fisheries Resources Research Institute (NaFIRRI), the research focused on the implementation and effectiveness of measures following the LYFO Council of Ministers (CoM) Directives for improved management of the fisheries of Lake Victoria, with particular reference to the 2009 CoM Directives as a case study, it was established that many of the Directives have not been implemented. In cases where the directives were implemented, their effectiveness remains questionable. While steps were taken to disseminate and implement the Directives, there were some challenges, including the unclear legal status of the directives, limited dissemination materials and poor methods of dissemination, language barriers and inadequate resources for enforcement.

基于Vega Prime的多水下机器人视景仿真系统的设计与实现

介绍了一套多水下机器人三维视景仿真系统。该系统采用虚拟现实技术，利用虚拟仿真软件VegaPrime 与Visual C++.NET 2003 混合编程实现三维视景仿真。它主要用于海洋环境的模拟和多水下机器人运行时的位姿更新、碰撞检测、环境效果及各种特效的实时显示。此外，它还具有响应各种输入/输出设备的功能和通过人性化图形界面接口与用户进行交互的功能。