In this paper we execute the solution procedure for second order linear fuzzy differenceequation by Lagrange’s multiplier method. In crisp sense the differenceequation are easy to solve, but when we take in fuzzy sense it forms a system ofdifferenceequation which is not so easy to solve. By the help of Lagrange’s multiplier we can solved it easily. The results are illustrated by two different numerical examples and followed by two applications.
Based on the analysis of the solutions of the hybrid new Keynesian IS curve I arrive at the conclusion that this curve is backward looking regardless of the size of the forward coefficient. The backward solutionof the new Keynesian IS curve expectational differenceequation implies that the current interest rate as well as the expected future real interest rates do not matter for the determination of current output gap. In the canonical new Keynesian Taylor- rule model, the central bank promises to make nominal interest higher when inflation is above its target. When the elasticity of substitution is less than or equal to one (σ ≤ 1) the higher interest rate does not bring about a reduced level of aggregate demand in the current period. Instead, it yields a higher level of aggregate demand in the current period and in the next period. Current inflation would increase due to a positive current output gap and a higher expected inflation, unless inflation jumps to a locally bounded equilibrium. 12
promoting actions is a good tool for product life cycle management for increasing the patent life of existing products. Fast Disintegrating Tablets is the best delivery system when needs a rapid onset of action. Today, for the treatment of allergies, cold, and flu symptoms, ODTs are more widely available as OTC products. The target population has expanded to those who want convenient dosing anywhere, anytime, without water. The potential for such dosage forms is promising because of the availability of new technologies combined with strong market acceptance and patient demand. By paying close attention to advances in technologies, pharmaceutical companies can take advantage of ODTs for product line extensions or for first-to-market products. With continued development of new pharmaceutical excipients, one can expect the emergence of more novel technologies for ODTs in the days to come.
The examined model is a computational solver from the NuscaS system , which is used for simulating thermomechanical phenomena in solidifying castings. It is based upon the heat conduction equation with a source term, solved using enthalpy formulation of solidification . The finite element method is applied for spatial discretization, which allows to obtain a system of matrix equations with the derivative with respect to time. Integration is performed using the two-step Dupont II scheme .
The Schrödinger equation being a partial differential equation describes the quantum state of a physical system and the changes in that system with respect to time. It was first time formulated by Schrödinger in 1925(Schrödinger, 1926) . In the sense of classical mechanics, the governing equation predicts the behavior of a system mathematically at any time after the initial state of the system is set and this corresponds to the Newton’s law F ma . In the language of quantum mechanics, the Schrödinger equation is analogous to Newton’s law for quantum mechanical system (which usually involves molecules, atoms, sub-atomic particles, whether moving freely, bounded or localized). It is not as simple algebraic operation but in general form it is a linear partial differential equation that describes the evaluation of time of the wave function system (Griffiths, 2004).
In this section, we test the Belov-Chaltikian lattice equation to verify the efficiency of the GDTM-Padé technique. We compare the performance of the GDTM-Padé technique with the original GDTM algorithm. All the numerical computations are performed by Ma- thematica 7.0.
In this paper, a new method is introduced to solve a two-dimensional Fredholm integral equation. The method is based on the approximation by Gaussian radial basis functions and triangular nodes and weights. Also, a new quadrature is introduced to approximate the two dimensional integrals which is called the triangular method. The results of the example illustrate the accuracy of the proposed method increases.
Consumers are willing to pay a premium for products made in socially and environmentally responsible ways. Consumers claim that they are willing to pay a higher price for products of socially responsible firms, but are not willing to spend time on figuring out which firm is socially responsible. At the same time, a segment of consumers continue to buy products from firms with well acknowledged bad ethical conducts. Consumers do not act as what they claim. A small number of highly ethical consumers do exist. They care much about producers‘ CSR in their buying and consumption choices (Carrigan & Attalla, 2001). Carrigan and Attalla (2001) categorized consumers into four types based on their ethical awareness and ethical purchase intention. Consumers with low ethical awareness and low ethical purchase intention are called oblivious consumers. Confused and uncertain consumers are those with low ethical awareness but show high ethical purchase intention. Consumers with high ethical awareness who do not make purchase intention accordingly are cynical and disinterested consumers. The last type is caring and ethical consumers who obtain sufficient CSR information and are highly ethical in their purchase activities. Carrigan and Attalla (2001) also pointed out that consumers are not the only stakeholders of a business. Other stakeholders such as employees, environmental organizations may care much about a firm‘s CSR. Each stakeholder group has a focus on firms‘ CSR. The focus is usually what influences their interest most. When addressing CSR, firms need always engage the target stakeholders and their focus of concerns. Philanthropy seen everywhere without any consumer engagement has little contribution to consumer choice. Consumers‘ awareness of firms‘ CSR is limited in general, so opportunities exist in the communication of corporate social performance and social responsibility initiatives with consumers. Even though consumers‘ choices are not significantly influenced by a firm‘s CSR, it is still important to be socially responsible in business operations. Consumers may have more CSR information and become more ethical in their purchasing behavior in the future. In addition, the new generation may behave differently to socially responsible companies‘ products.
QAP is a NP-hard problem that has been studied by a number of researchers in combinatorial optimization through the second half of the 20 th century and which continues to excite the curiosity of many others, both in the study of exact algorithms and through the formulation of information mechanisms for heuristics. The exact approach is severely limited by the high complexity of the problem, a difficult 30-order instance (Nug30) having been solved exactly only through a huge work of metacomputing. More recent years have seen an increased interest in the use of metaheuristic schemes: some examples are [AQB99], [BT94], [AOT00], [CMMT97], [Ma00], [TRFR01] and [TS95].
tive α, β, as |ω| → ∞), real parts of both functions are bounded by positive value, and their the Fourier trans- forms satisfy the H¨older condition on R. The Wiener- Hopf integral equation is an integral equation, which in 75 years of its history has been impressed all who use it to almost all branches of engineering, mathemat- ical physics, and applied mathematics. The technique to solve a Wiener-Hopf integral equation, named the Riemann-Hilbert technique, still, remains an extremely important tool for modern scientists, and the areas of application continue to broaden, a good review may be found in , among others. The Riemann-Hilbert tech- nique is theoretically well developed. However, to over- come problem caused by slow evaluation and existence singularises near the integral contour some approximate methods have to be considered, which do not receive enough attention from authors. Until 2000, there does
A nonlinear wave phenomenon is the important area of scientific research, which many scientists in the past have studied about mathematical models explaining the wave behavior. There are mathematical models which describe the dynamic of wave behaviors–for example, the KdV equation, the RLW equation, the Rosenau equation, and many others –. The KdV equation has been used in very wide applications, such as magnetic fluid waves, ion sound waves, and longitudinal astigmatic waves –. The RLW equation, which was first proposed by Peregrine ,  provides an explanation on a different situation of a nonlinear dispersive wave from the more classical KdV equation. The RLW equation is one of models which are encountered in many areas, e.g. ion–acoustic plasma waves, magnetohydro- dynamic plasma waves, and shallow water waves. Since the case of wave–wave and wave–wall interactions cannot be described by the KdV equation, Rosenau ,  proposed an equation for describing the dynamic of dense discrete systems; it is known as the Rosenue equation. The existence and uniqueness of the solution for the Rosenau equation were proved by Park , . For the further consideration of the nonlinear wave, a viscous term u xxt needs to be included:
, , , where : and : are continuously differentiable functions and , are some intervals of real numbers. Furthermore, a solution , ∞ of system (2) is uniquely determined by initial conditions , for , , . Along with the system (2), we consider the corresponding vector map , , , , , , , . An equilibrium point of system (2) is a point , that satisfies
Abstract: The life of bucket teeth in shovel and dragline deployed in handling of overburden rock is an important contributor to the stores cost and is also responsible for the loss of valuable availability and utilisation time of these critical equipment. To ascertain the effect of rock type on longevity of bucket teeth, a study has been conducted in two large opencast mines of Singrauli Coalfields. The results of this study is presented in this paper. There was a significant variation as compared to the actual figures of the mine, it establish useful relationship between the type of mineral present in the overburden and the life of bucket teeth of shovel and dragline.
Stratonovich sense) arises as a prototype model in understanding a wide variety of phenomena. It appears in modeling transport in porous media, suspended sediment transport in open-channel flows, advective transport of substances, waves motions in random media and from turbulent transport theory, u(x, t) be the concentration of a passive substance convected by a turbulent fluid, such as smoke in turbulent air.
Moreover, the logistic equation was published in 1838 by Pierre Franc¸ois Verhulst to model the growth of world population and was based on the assessment of population statistics available, complementing the theory of exponential growth of Thomas Robert Malthus. It can be applied to models with time dependence and has a wide application area since the inhibiting factors are taken into consideration. Furthermore, the logistic equation proved applicable in a series of probabilistic events and related to chaos theory and industrial and business dynamics [7, 25]. Recently, the logistic equation has been applied to describe the growth of populations both in the laboratory natural habitat, limiting the growth by influence of competition, mortality and fertility factors. However, the logistic model does not fit very well in cases where there are more complex relationships acting as interactions within food webs or several features that occur in most cases in nature dependencies[5, 6, 7, 8, 9, 22]. Aiming to generalize the logistic equation and give a better description for some of those events, El-Sayed, at all , studied the corresponding fractional-order logistic by a numerical analyze.
We have approached a theoretical description of the tem- poral evolution of the modified van der Pol oscillator with an additive Gaussian white noise in the region where birhythmic- ity (in the absence of noise) occurs. To get an analytical insight on this system we have used an explicit solution based on the phase-amplitude approximation of the Fokker-Planck equation to analytically derive the probability distributions. The activation energies associated to the switches between different attractors have been derived analytically and numeri- cally. We have found that the agreement is fairly good. The characteristics of the birhythmic properties in a modified van der Pol oscillator are strongly influenced by both the nonlin- ear coefficients a, b and the noise intensity D. The boundary of the existence of multi-limit-cycle solutions, in the paramet- ric (a,b)-plane, decreases with the increase of the noise inten- sity D. Finally, the analytic estimate of the stability of the two attractors varies with the control parameters (the dissipation a and b) in a way that resembles phase transitions: for most pa- rameters value the system is located around only one attractor, the other being visited with a vanishingly small probability. Only at special values of the control parameters the residence times are comparable, in agreement with experimental obser- vations of birhythmicity in Biological systems: the passage from an attractor to another only occurs by varying the exter- nal parameters and not under the influence of noise. 43,44
4. Musaev V.K. Vozdeystvie prodol’noy stupenchatoy volny na podkreplennoe krugloe otverstie v uprugoy srede [Impact of the Longitudinal Steo-shaped Wave on a Supported Circular Hole in an Elastic Medium]. All-Union Conference “Modern Problems of Structural Mechanics and Strength of Aircrafts.” Collected abstracts. Moscow Institute of Aviation, 1983, p. 51.
subsequent decreases over-time lagged inflation on the right-hand side, are significant. Columns (3) to (8) of Table 2 present panel estimates with time and fixed-effects for the various samples and two calendars of IT adoption described in Table 1. From column (3) to (4), I change from MSH’s to BS’s IT calendar – the one used by LY – to check how important it is to vary the dates of IT adoption. The different calendars of IT adoption make a quantitative difference, but not important enough to change the qualitative result that IT mattered . BS’s IT adoption dates reduce the IT direct impact on the average inflation level from -1.37 to -1.01 percentage points, or its implied cumulative effect from -2.28 to -1.68 percentage points. Anyway, the IT effect is still significantly important, different from LY’s irrelevance conclusion (in their Table 3, Panel A), and differences between columns (3) and (4) mainly reflect that my identification strategy of a one- year lag in policy effects matches better with MSH’s calendar.