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be a hypersurface with an isolated singularity at the origin defined by the holomorphic function
. The Yau algebra
is defined to be the Lie algebra of derivations of the moduli algebra
, that is,
. It is known that
is finite dimensional and its dimension
is called the Yau number. We introduce a new series of Lie algebras, that is,
th Yau algebras
, which are a generalization of the Yau algebra. The algebra
is defined to be the Lie algebra of derivations of the
th moduli algebra
, that is,
is the maximal ideal of
th Yau number is the dimension of
, which we denote by
. In particular,
is exactly the Yau algebra, that is,
. These numbers
are new numerical analytic invariants of singularities. In this paper we formulate a conjecture that
We prove this conjecture for a large class of singularities.
be a hypersurface with an isolated singularity at the origin defined by the holomorphic function
. The Yau algebra,
, is the Lie algebra of derivations of the moduli algebra of
. It is a finite-dimensional solvable algebra and its dimension
is the Yau number. Fewnomial singularities are those which can be defined by an
indeterminates. Yau and Zuo [‘A sharp upper estimate conjecture for the Yau number of weighted homogeneous isolated hypersurface singularity’, Pure Appl. Math. Q.12(1) (2016), 165–181] conjectured a bound for the Yau number and proved that this conjecture holds for binomial isolated hypersurface singularities. In this paper, we verify this conjecture for weighted homogeneous fewnomial surface singularities.
In the last three decades the life insurance industry was rocked by a series of mis-selling scandals such as endowment mortgage, personal pension and payment protection insurance mis-selling. Regulators have stepped in to try to address the underlying causes and improve customer protection by introducing more stringent regulation targeted at sales practices and remuneration, product design, disclosure and ongoing monitoring together with significantly larger financial penalties for non-compliance. Against this background, the paper considers whether customers understanding of risks and outcomes associated with life insurance products can be further improved and how poor customer outcomes can be avoided in the future. We acknowledge the complexity of these issues, which involve many stakeholders, covering all stages of the product lifecycle and customer journey and being impacted by a constantly changing regulatory landscape. We first review the current regulatory landscape across both the United Kingdom and other jurisdictions, concluding that whilst regulators have acted to improve customer protection, gaps still remain, particularly around the areas of disclosure and consideration of changing customers’ needs throughout product lifetimes. The paper then considers how the current situation could be improved for customers in a cost effective manner. We focus on improvements in disclosure, needs-based selling, ongoing assessment and communication as a means of ensuring that products continue to meet the customers’ needs and risk profile, and on introducing a duty of care which would force financial services firms to act in the best interests of their customers. In this paper we present our preliminary thoughts and recommendations. Some of the recommendations will cost something to implement, and should therefore be supported by cost-benefit analyses that would weigh these costs against the potentially larger benefits to both customers and the insurance industry.
Unavailability of irrigation water for early sowing has remained a constant problem in cold arid deserts of Ladakh. In order to get a solution to this problem, a 2-yr farmers’ participatory research trial with best bet agronomic management on artificial glacier water harvesting technology was conducted. The technology involves collecting water from natural glaciers that melt during late December. The water is diverted toward a shed constructed with stone embankments set up at regular intervals. The area is chosen where there is minimum interference of solar radiation, generally between two mountain slopes or ridge that is on the leeward side. The melted water is that melts from the natural glacier impeded by the embankments and get frozen here. This frozen water starts melting in late March and is used for both pre sowing and initial crop water requirement. It also ensures early sowing of wheat by creating additional 45-day window which leads to introduction of long- and medium-duration wheat varieties to replace decades old locally grown short-duration varieties. The work was initiated with a benchmark survey of 100 farmers to get an understanding of present irrigation scenario, crop management practices and date of sowing. Data from 99 farmer participating trial of wheat conducted after or from bench mark survey clearly indicated that the effect of water shortage can be seen on yield and yield attributing characters due to unavailability of pre sowing irrigation and water requirement at imperative growth stages and may also lead to terminal heat stress in wheat crop. Out of total number of irrigations applied, initial two irrigations can be compensated by artificial glacier water harvesting technique, leading to a revolution in the agriculture scenario of the tribal population by introduction of long- and medium-duration wheat varieties in cold arid desert of Ladakh for the very first time. It was observed that wheat seeding done in first fortnight of April gave better yields in comparison to late seeded wheat. Moreover, the long-duration varieties (LDVs) or medium-duration varieties (MDVs) sown under late condition gave better yield in comparison to locally grown short-duration varieties sown at same time. Yield potential of LDVs and MDVs of wheat under late sowing was found quite low in comparison to early-sown wheat, still when compared with the performance of locally grown wheat the yields were more even if the local varieties were sown early. The outcome of this study will help the farmers of tribal, cold arid community in harvesting better wheat yields by timely sowing of the wheat crop accompanied with better bet agronomic management practices. Government initiative is further required to ensure better outreach of complete crop management strategies to the tribal farming community of the region in order to ensure food security and improve their socioeconomic status.
Spatial confinement effects on plasma parameters and surface morphology of laser-ablated Mg are studied by introducing a metallic blocker as well as argon (Ar) gas at different pressures. Nd: YAG laser at various fluences ranging from 7 to 28 J/cm2 was employed to generate Mg plasma. Confinement effects offered by metallic blocker are investigated by placing the blocker at different distances of 6, 8, and 10 mm from the target surface; whereas spatial confinement offered by environmental gas is explored under four different pressures of 5, 10, 20, and 50 Torr. Laser-induced breakdown spectroscopy analysis revealed that both plasma parameters, that is, excitation temperature and electron number density initially are strongly dependent upon both pressures of environmental gases and distances of blockers. The maximum electron temperature of Mg plasma is achieved at Ar gas pressure of 20 Torr, whereas maximum electron number density is achieved at 50 Torr. It is also observed that spatial confinement offered by metallic blocker is responsible for the significant enhancement of both electron temperature and electron number density of Mg plasma. Maximum values of electron temperature and electron number density without blocker are 8335 K and 2.4 × 1016 cm−3, respectively, whereas these values are enhanced to 12,200 K and 4 × 1016 cm−3 in the presence of blocker. Physical mechanisms responsible for the enhancement of Mg plasma parameters are plasma compression, confinement and pronounced collisional excitations due to reflection of shock waves. Scanning electron microscope analysis was performed to explore the surface morphology of laser-ablated Mg. It reveals the formation of ripples and channels that become more distinct in the presence of blocker due to plasma confinement. The optimum combination of blocker distance, fluence and Ar pressure can identify the suitable conditions for defining the role of plasma parameters for surface structuring.
The poultry industry is currently facing a serious problem of controlling coccidiosis, owing to the development of drug resistance against commonly available anticoccidials. Furthermore, an increasing demand in the consumers for drug residue free poultry and poultry products has led to the development of alternative strategies for the treatment and control of avian coccidiosis. In response to the invasion of Eimeria species in coccidiosis, oxidative stress is created by host cellular response which imparts pathology to the host tissue besides damaging the parasite. Hence, in order to alleviate the damage caused by oxidative stress during coccidiosis, the use of essential oils (EOs) rich in antioxidant compounds is being considered as an appealing approach. However, results are very divergent and often not as satisfactory as expected. Essential oils, as natural products, obtained from aromatic plants have the potential to serve as an alternate to anticoccidials. The present work aims to review the current state of knowledge, informative collection of results obtained over the years and to attain a critical decision in aspects of the use of EOs as anticoccidials.
This work examines the magnetohydrodynamic (MHD) flow of second grade fluid due to a stretching cylinder with viscous dissipation. Advance heat transfer technique namely the Newtonian heating is employed to explore the characteristics of heat transfer phenomenon in the presence of Joule heating. Mass transfer is discussed with the combination of both homogeneous and heterogeneous reactions. Diffusion coefficients of species A and B are considered of the same size. Heat production due to chemical reaction is assumed negligible. Appropriate transformations are employed to convert the nonlinear partial differential equations to the nonlinear ordinary differential equations. Convergent solutions of momentum, energy and concentration equations are developed. Characteristics of different involved parameters on the velocity and temperature fields are shown graphically. Numerical values of skin friction coefficient and Nusselt number are computed and analyzed. Higher values of homogeneous reaction parameter results in the reduction of concentration profile while opposite behavior is observed for heterogeneous reaction parameter.
Present paper addresses the numerical study of Sisko fluid model over stretching cylinder with variable thermal conductivity. The governing equations are simplified by incorporating the boundary layer approximations. After employing suitable similarity transformations partial differential equations are reduced to ordinary differential equations. To obtain numerical solution shooting method in conjunction with Runge-Kutta-Fehlberg method is used. For the analysis of model, variations due to different physical parameters involved in momentum and heat equations are reflected through graphs. Also, the effects of physical parameters on skin-friction coefficient and Nusselt number are represented through graphs as well as tables.
The linear operator plays an important role in the computational process of Homotopy Analysis Method (HAM). In HAM frame any kind of linear operator can be chosen to develop a solution. Hence, it is easy to introduce the modified/physical parameter dependent linear operators. The effective use of these operators has been judged through solving fluid flow problems. Modification in linear operators affects the solution and improves the computational efficiency of HAM for larger values of parameters. The convergence rate of the solution is rapid and several times higher resulting in lesser computational time.
In this study, a new centrifugal instability mode, which dominates within the boundary-layer flow over a slender rotating cone in still fluid, is used for the first time to model the problem within an enforced oncoming axial flow. The resulting problem necessitates an updated similarity solution to represent the basic flow more accurately than previous studies in the literature. The new mean flow field is subsequently perturbed, leading to disturbance equations that are solved via numerical and short-wavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundary-layer flow undergoes competition between the streamwise flow component, due to the oncoming flow, and the rotational flow component, due to effect of the spinning cone surface, which can be described mathematically in terms of a control parameter, namely the ratio of streamwise to axial flow. For a slender cone rotating in a sufficiently strong axial flow, the instability mode breaks down into Görtler-type counter-rotating spiral vortices, governed by an underlying centrifugal mechanism, which is consistent with experimental and theoretical studies for a slender rotating cone in otherwise still fluid.
GaN and its alloys are promising candidates for high temperature thermoelectric (TE) materials due to their high Seebeck coefficient and high thermal and mechanical stability. Moreover, these materials can overcome the toxicity concern of current Te-based TE materials, such as Bi2Te3 and PbTe. These materials have recently shown a higher Seebeck coefficient than that of SiGe in high temperature region because their large bandgap characteristic eliminates the bipolar conduction. In this study, we report the room temperature thermoelectric properties of p-type Mg doped GaN, grown by metalorganic chemical vapor deposition (MOCVD) on sapphire substrate with various carrier concentrations. Undoped and n-type GaN are also incorporated with p-type GaN films to make comparison. The structural, optical, electrical, and thermal properties of the samples were examined by X-ray diffraction, photoluminescence, van der Pauw hall-effect, and thermal gradient methods, respectively. The Seebeck coefficient ranging from 710-900µV/K at room temperature of Mg: GaN were observed, which further indicated their potential TE applications.
Thermoelectric (TE) materials have gained renewed interests in last decades for both power generation and energy conservation from waste-heat harvesting. Research in the discovery of best TE materials such as, bulk materials, complex structures, and low dimensional play crucial role to achieve high efficiency TE materials. Wide bandgap materials like ZnO can be promising candidate for high efficiency TE power generation owing to its low-cost, nontoxicity, and stability at high temperatures. In this paper, room temperature TE properties of thin film ZnO grown by metal organic vapor deposition (MOCVD) are reported. TE properties of thin film GaN are also studied as reference to that of thin film ZnO. Moreover, high resolution x-ray diffraction (HRXRD), room temperature photoluminescence (PL) with deep ultraviolet (DUV) spectroscopy (excitation at 248nm), hall effect, and thermal gradient methods have been employed to investigate the effect of structural, optical, electrical, and thermal properties of the samples, respectively. The effect of doping concentrations and structural defects on Seebeck coefficients of thin film ZnO are systematically studied and discussed in this work.
Necrotic enteritis (NE) caused by Clostridium spp. is an economically significant bacterial disease of poultry worldwide. Traditionally the disease has been prevented through feed supplementation with antibiotics sub-therapeutically as antimicrobial growth promoters (AGPs). However this practice has led to the emergence of resistant pathogenic microbes and drug residues, potentially threatening animal and public health. Therefore the marketing and incorporation of AGPs into poultry feed has been banned in Europe which has exacerbated the incidence of NE, bringing about huge economic losses to poultry farmers. Poultry researchers, exporters and consumers have emphasised AGP-free poultry rearing and have been searching for non-antibiotic and cost effective alternatives to control NE. Strategies suggested include vaccination, coccidiosis control, probiotics, competitive exclusion products, prebiotics, egg yolk immunoglobulins, bacteriophages (or phage gene products), organic acids, feed enzymes, plants and plants extracts/essential oils and nutritional changes.
There are many predisposing as well as virulence factors for NE induction and pathogenesis and more are expected to be discovered in the future. The ambiguous pathogenesis trend of the disease is still hindering the development of a potent active vaccine against NE. The choice of a single and fully effective approach is difficult. However, probiotics and specific egg yolk immunoglobulins (IgYs) alone or in combination could serve as promising strategies for controlling NE in broilers in the absence of AGPs.
Internal gravity wavetrains in continuously stratified fluids are generally unstable as a result of resonant triad interactions which, in the inviscid limit, amplify short-scale perturbations with frequency equal to one half of that of the underlying wave. This so-called parametric subharmonic instability (PSI) has been studied extensively for spatially and temporally monochromatic waves. Here, an asymptotic analysis of PSI for time-harmonic plane waves with locally confined spatial profile is made, in an effort to understand how such wave beams differ, in regard to PSI, from monochromatic plane waves. The discussion centres upon a system of coupled evolution equations that govern the interaction of a small-amplitude wave beam with short-scale subharmonic wavepackets in a nearly inviscid uniformly stratified Boussinesq fluid. For beams with general localized profile, it is found that triad interactions are not strong enough to bring about instability in the limited time that subharmonic perturbations overlap with the beam. On the other hand, for quasi-monochromatic wave beams whose profile comprises a sinusoidal carrier modulated by a locally confined envelope, PSI is possible if the beam is wide enough. In this instance, a stability criterion is proposed which, under given flow conditions, provides the minimum number of carrier wavelengths a beam of small amplitude must comprise for instability to arise.
In this paper, a new method is presented that allows an intelligent manipulator robotic system to track a human hand from far distance in 3D space and estimate its orientation and position in real time with the goal of ultimately using the algorithm with a robotic spherical wrist system. In this proposed algorithm, several image processing and morphology techniques are used in conjunction with various mathematical formulas to calculate the hand position and orientation. The proposed technique was tested on Remote teleguided virtual Robotic system. Experimental results show that proposed method is a robust technique in terms of the required processing time of estimation of orientation and position of hand.
We present a preliminary 3D potential field extrapolation model of the joint magnetosphere of the close accreting PMS binary V4046 Sgr. The model is derived from magnetic maps obtained as part of a coordinated optical and X-ray observing program.
We present results of the X-ray monitoring of V4046 Sgr, a close classical T Tauri star binary, with both components accreting material. The 360 ks long XMM observation allowed us to measure the plasma densities at different temperatures, and to check whether and how the density varies with time. We find that plasma at temperatures of 1–4 MK has high densities, and we observe correlated and simultaneous density variations of plasma, probed by O VII and Ne IX triplets. These results strongly indicate that all the inspected He-like triplets are produced by high-density plasma heated in accretion shocks, and located at the base of accretion flows.
To report a case of first branchial arch abnormality and the problems associated with misdiagnosis. A succinct literature review is included.
Teaching hospital in Scotland.
A 10-year-old girl presented with localised erythema and swelling in the left parotid region. This was treated with antibiotics and incision and drainage. She re-presented four years later with a history of recurrent discharge. A first branchial arch abnormality was suspected and a magnetic resonance imaging scan arranged.
Imaging showed a fluid-filled sinus tract originating adjacent to the anterior wall of the cartilaginous left external auditory canal. The sinus tract was seen to extend anteriorly and inferiorly through the superficial lobe of the left parotid, and to open onto the left cheek lateral to the left masseter. The tract was explored and excised under general anaesthesia, via two separate incisions, with preservation of the facial nerve.
The diagnosis of a first branchial arch abnormality is generally based on a high index of clinical suspicion, when a neck swelling is noted in a child. Magnetic resonance imaging is a useful modality for investigation, and helps to delineate the position of the tract and its relationship to the facial nerve.