Search

Abstract Murthy [1] introduced the concept of the Smarandache Cyclic Determinant Natural Sequence, the Smarandache Cyclic Arithmetic Determinant Sequence, the Smarandache Bisymmetric Determinant Natural Sequence, and the Smarandache Bisymmetric Arithmetic [...]

The epistemological foundation of unity of knowledge is used to formulate a system-model of participatory socioeconomic development. The micro-properties of such a participatory development approach are deeply ethical in nature. In order to bring out the endogenous role of ethics derived from the moral law in reference to the epistemic foundation, and thereby explain their impact on the socioeconomic development experience, the methods of topological space and topological mappings are found to be appropriate for formalizing the complex nature of participatory dynamics. They emerge in the midst of institutional and organic interaction, integration, and evolution. The application of topological methods to participatory socioeconomic development thus opens up a field that is rarely used by mathematical economists. In this sense this article is an original contribution to the area of ethical development theory and its topological explanation and application. KEYWORDS: Evolutionary epistemology, mathematical model, participatory development.

Capacity expansion problems (CEPs) and weight reduction problems (WRPs) are considered in connection with bottleneck optimization problems. It is shown that WRP can be reformulated as a parametric combinatorial optimization problem.

Autorotation is an abnormal mode of operation for a helicopter because no powerplant torque is applied to the main rotor. Thus, descending flight requires an upward flow of air through the rotor to sustain rotation and, therefore, lift. There is a negligible literature on the flight mechanics of helicopter autorotation, although the aerodynamic phenomenon is well understood. The objective of this paper is, therefore, to examine helicopter flight mechanics across the autorotation flight envelope, while addressing the modeling requirements for simulation in autorotation. A nonlinear individual blade/blade element model of a conventional single main and tail rotor helicopter is used to generate a variety of data, including trim states, time, and frequency responses. It is concluded that contemporary mathematical modeling can mimic the general performance characteristics of helicopters in autorotation with no special development. Although rotorspeed can vary significantly, even during maneuvers that embody only small perturbations in the body states, linearized models can remain an appropriate basis for analysis. Finally, distinctive aspects of helicopter flight mechanics in autorotation, dissimilar to level flight, are readily explained, and it is suggested that they are benign in nature.

A basic challenge in systems biology is to understand the dynamical behavior of gene regulation networks. Current approaches aim at determining the network structure based on genomic-scale data. However, the network connectivity alone is not sufficient to define its dynamics; one needs to also specify the kinetic parameters for the regulation reactions. Here, we ask whether effective kinetic parameters can be assigned to a transcriptional network based on expression data. We present a combined experimental and theoretical approach based on accurate high temporal-resolution measurement of promoter activities from living cells by using green fluorescent protein (GFP) reporter plasmids. We present algorithms that use these data to assign effective kinetic parameters within a mathematical model of the network. To demonstrate this, we employ a well defined network, the SOS DNA repair system of Escherichia coll. We find a strikingly detailed temporal program of expression that correlates with the functional role of the SOS genes and is driven by a hierarchy of effective kinetic parameter strengths for the various promoters. The calculated parameters can be used to determine the kinetics of all SOS genes given the expression profile of just one representative, allowing a significant reduction in complexity. The concentration profile of the master SOS transcriptional repressor can be calculated, demonstrating that relative protein levels may be determined from purely transcriptional data. This finding opens the possibility of assigning kinetic parameters to transcriptional networks on a genomic scale.

Usage of assurance regions of weights to model relative importance of differnt criteria, for ranking finite set of alternatives through linear utilities subject to random distribution of coefficients, is discussed.

Comparison of stochastic dynamic model with fixed mix portfolio model of mathematical analysis is presented.

Usage of multi-criteria analysis for development of mathematical model, for planning helicopter missions as part of disaster relief operations, is discussed.

Underestimation of gluconeogenesis by the [[U-.sup.13][C.sub.6]]glucose method: effect of lack of isotope equilibrium. Am J Physiol Endocrinol Metab 282: E376-E385, 2002. First published October 16, 2001; 10.1152/ajpendo.00210.2001.--Among the many tracer methods to indirectly estimate gluconeogenesis in humans, the [[U-.sup.13][C.sub.6]]glucose method as proposed by Tayek and Katz (Am J Physiol Endocrinol Metab 270: E709-E717, 1996; Am J Physiol Endocrinol Metab 272: E476-E484, 1997) has the advantage of being able to simultaneously estimate hepatic glucose output and fractional gluconeogenesis. However, Landau et al. (Landau BR, J Wahren, K Ekberg, SF Previs, D Yang, and H Brunengraber. Am J Physiol Endocrinol Metab 274: E954-E961, 1998) have shown that this method underestimates the rate of gluconeogenesis. The underestimation has been attributed to tracer dilution by other three-carbon substrates and the lack of isotopic steady state. Using a computer simulation of [[U-.sup.13][C.sub.6]]glucose infusion, we demonstrate that the lack of isotope equilibrium in both the lactate and glucose compartments contributes substantially to the underestimation of gluconeogenesis. [[U-sup.13][C.sub.6]]glucose experiments were performed with the addition of a primed constant infusion of [[U-.sup.13][C.sub.3]]lactate and the delay in M3 glucose equilibrium estimated from the isotopic steady-state value determined by modeling M3 glucose to a single-exponential fit. We found that, even with the addition of [[U-.sup.13][C.sub.3]]lactate infusion, the M3 glucose enrichment of the last timed sample was ~20% less than the isotopic steady-state value. Thus the lack of isotopic equilibrium of the glucose compartment potentially accounts for 20% of the underestimation of gluconeogenesis. The underestimation of gluconeogenesis using [[U-.sup.13][C.sub.6]] glucose without the additional infusion of [[U-.sup.13][C.sub.3]] lactate in previous publications is expected to be even greater because of the lack of isotope equilibrium in both the lactate and glucose compartments. These findings are consistent with the results from our computer simulation. mathematical modeling; mass isotopomer distribution analysis, stable isotopes

Research shows that concentric optimum annular fin with a step change in thicknesses transfer more heat than optimum annular disc fins per unit of fin volume and fin volume and length.

This paper presents the basic equations for a mathematical model of sediment-laden flow in a nonorthogonal curvilinear coordinate system. The equations were derived using a tensor analysis of two-phase flow and incorporate a natural variable-density turbulence model with nonequilibrium sediment transport. Correspondingly, a free-surface and the bottom sediment concentration are employed to provide the boundary conditions at the river surface and the riverbed. The finite analytic method is used to solve the equations of mass and momentum conservation and also the transport equation for suspended sediment. To demonstrate the method, the sediment deposition for the Three Gorges Project is considered. The mathematical model specifies the boundary conditions for the inlet and outlet using data from physical model experiments. The results for the mathematical model were tested against laboratory measurements from the physical model experiment. Good agreement and accuracy were obtained.

Results describe Navier-Stokes equations in a two-dimensional compressible form using staggered grid central finite volume method. Data indicate that the procedure is capable of resolving shocks and boundary-layer and simulation of boundary-layer detachment.

Data envelopment analysis (DEA) involves a set of mathematical programming-based techniques and models which are used to evaluate relative efficiency of observed decision making units (DMUs). One of the topics of interest in DEA is sensitivity analysis of a specific DMU unit under evaluation. An expert has proposed a new approach to sensitivity analysis resulting in regions of stability of DMU units. Some examples are presented to illustrate that, in certain cases, the results of the new approach do not hold.

The Time Warp optimistic technique is one method of ensuring correct results in parallel and distributed simulations but its efficiency depends on the efficacy of the technique used for state saving and operation. A hybrid method for checkpointing using both periodical and incremental state saving techniques for large Time Warp distributed simulations is presented. It is also analytically compared with the periodical state saving and incremental state saving methods.

The use of a chemical model based on the master equation (ME) approach to describe the dynamics including local fluctuations of an excitable, spatially extended chemical system is discussed. Results of the ME simulations using this simple, realistic chemical model indicate that internal fluctuations can induce local excitations which strongly disturb the behavior predicted by phenomenological dynamics for spatially extended excitable systems.

What exactly is science? This question has received considerable attention from contemporary philosophers of science, notably Popper (1968) on the central role of falsifiability in scientific theory, Kuhn (1962) on [...]

The interplay of internal and external entities is still beneficial in several situations for the discovery of completely standard outcomes, despite the fact that transfer of a standard result to a non-standard model cannot be taken as a new result. The power of non-standard analysis results from the saturation principle and the use of external sets. Non-standard constructions provide a more convenient and efficient use of higher order sets, eventually rendering one to really discover new results when interpreting non-standard outcome in the standard models.

A general existence result for a specific Stackelberg revelation game is established to arrive at a standard approach to the problem of existence of optimal auctions for a a wide array of auction environments. When systematically specializing the revelation game to include different types of auctions, the presence of optimal Bayesian auction mechanisms for single and multiple unit auctions and for contract auctions with moral hazard and adverse selection are deduced.

The Bk-monotonicity is a stricter condition than Maskin monotonicity, however, it is significant for Nash implementation. The Bk-monotonicity can be utilized to demonstrate that several social choice correspondences that satisfy Maskin monotonicity cannot be Nash implemented. The method employs k as a natural number that indexes a specific condition and where the condition only becomes more restrictive as k increases.

Lagrange multipliers can be employed in an incentive-constrained problem, which is a maximization problem in an infinite horizon set-up, with constraints that the continuation value from any period has to be bigger than an outside alternative value. The technique is best exemplified in a problem of optimal taxation, in which the sequence is not time-consistent.

The Schubert calculus for G/B can be completely determined by a certain matrix related to the Kostant polynomials introduced in section 5 of Bernstein, Gelfand, and Gelfand [Bernstein, I., Gelfand, I. & Gelfand, S. (1973) Russ. Math. Surv. 28, 1-26]. The polynomials are defined by vanishing properties on the orbit of a regular point under the action of the Weyl group. For each element w in the Weyl group the polynomials also have nonzero values on the orbit points corresponding to elements which are larger in the Bruhat order than w. The main theorem given here is an explicit formula for these values. The matrix of orbit values can be used to determine the cup product for the cohomology ring for G/B, using only linear algebra or as described by Lascoux and Schutzenberger [Lascoux, A. & Schutzenberger, M.-P. (1982) C. R. Seances Acad. Sci. Ser. A 294, 447-450]. Complete proofs of all the theorems will appear in a forthcoming paper.

Six thousand years of sediment accumulation and autocompaction in a transgressive valley-fill deposit are simulated numerically. Rates of accumulation of freshwater organic-rich mud, subtidal mud, and organic-rich mud of the modern salt marsh are specified by using existing sedimentologic, paleontologic, and geochronologic data. Processes of pore-water expulsion and autocompaction are determined from finite-strain consolidation theory. Model parameters for subtidal mud facies are determined from laboratory consolidation tests. Model parameters for organic-rich deposits are determined by sampling equivalent modern sedimentary environments and by model calibration. Model calibration involves (1) reproducing the present distribution of void ratios measured in a 7.6 m Vibracore, (2) correctly calculating the preserved thickness of lithologic units, and (3) determining a history of elevation changes of the sediment surface that is consistent with the Delaware sea-level curve and the known sequence of paleoenvironments of Wolfe Glade, Delaware. The results indicate that preserved horizons in the 10 m Holocene section of Wolfe Glade have been lowered a maximum of 2.3 m. The rate of lowering due to autocompaction alone has been one-half to one-third of the rate of sea-level rise during most of the past 6000 yr. Numerical experiments suggest that organic-rich freshwater wetland deposits are primarily responsible for the extensive autocompaction at Wolfe Glade. Our approach may be used to correct Holocene coastal stratigraphic data for autocompaction, but careful model calibration (based in part on the stratigraphy) will usually be required.

This article discusses how the principle of countability is established and proven. Topics include mathematical analysis and axiomatic sets.

For the bilinear Hilbert transform given by: H fg(x) = p.v. [integral of] f(x - y)g(x + y)dy/y, we announce the inequality [Mathematical Expression Omitted], provided 2 < [p.sub.1], [p.sub.2] < [infinity], 1/[p.sub.3] = 1/[p.sub.1] + 1/[p.sub.2] and 1 < [p.sub.3] < 2.

Electrical signal transmission lines give rise to a resonant structure formed of rational right triangles. When there is a time delay in a signal travelling along a line, then resonance occurs. These observations can be used for the effective teaching of rational right triangles. A description of the resonant structure made from electrical signal transmission lines, and how it forms right triangles with rational side lengths, is given.

Byline: J. Razmi, M.S. Amalnik, B. Ostadi Scheduling of railways is one of the NP-Hard problems which have been introduced more than two decades ago. Many mathematical models have been published for optimisation of the railways. However, none of those models can be applied to the Iranian Railway because of its specific situation regarding monorail routes, station capacity, etc. In this paper, a dynamic programming model has been introduced to schedule cargo trains based on the timetable of passenger trains that have priority in relation to cargo transportation. The objectives of this model are maximising the capacity of cargo train movement and minimising the stoppage time. It also considers several constraints including passenger train timetables, and the movement of only one train through a block at a time, etc. This model has been run in the Islamic Republic of Iran Railway Corporation and the results are presented in this paper.

The generalization of the mathematical principles of reinforcement (MPR) was tested on humans with the help of experiments. These experiments certified support for extending MPR to the behavior of human participants.

This paper presents closed-form mathematical models for an acoustic duct with general boundary conditions. These infinite-dimensional models are derived using symbolic computations. A new method to obtain finite dimensional approximations of infinite-dimensional models using quartic functions is presented. The theoretical models are compared with the experimental data obtained for the KSU duct. The experimental results of a new robust broadband feedback controller, designed using passivity-based techniques, are presented. The controller design is shown to be robust to the unmodeled dynamics and parametric uncertainty. [DOI: 10.1115/1.1311793]

The functional form W = ([W.sub.0][K.sup.c] + [W.sub.f] [t.sup.c])/([K.sup.c] + [t.sup.c]), where W is body size at age t, [W.sub.0] and [W.sub.f] are the zero- and infinite-time values of W, respectively, and K and c are constants, is derived. This new generalized Michaelis-Menten-type equation provides a flexible model for animal growth capable of describing sigmoidal and diminishing returns behavior. The parameters of the nonlinear model are open to biological interpretation and can be used to calculate reliable estimates of growth traits, such as maximum or average postnatal growth rates. To evaluate the new model, the derived equation and standard growth functions such as the Gompertz and Richards were used to fit 83 growth data sets of different animal species (fish, mice, hamsters, rats, guinea pigs, rabbits, cats, dogs, broilers, turkeys, sheep, goats, pigs, horses, and cattle) with a large range in body size. A comparative study was carried out based on mathematical, statistical, and biological characteristics of the models. The statistical goodness-of-fit achieved with the new model was similar to that of Richards, and both were slightly superior to the Gompertz. The new model differed from the others with respect to some of the estimated growth traits, but there were highly significant correlation coefficients between estimates obtained with the different models, and the ranking of animals based on growth parameters computed with the new function agreed with the rankings computed by the other models. Therefore, the new model, with its variable inflection point, was able to adequately describe growth in a wide variety of animals, to fit a range of data showing sigmoidal growth patterns, and to provide satisfactory estimates of traits for quantifying the growth characteristics of each type of animal. Key Words: Animal Species, Growth, Growth Curves, Mathematical Models, Nonlinear Equations, Sigmoidal Functions

The purpose of this paper is to analyse the interdependence of merger decisions over time. Using the Fudenberg-Tirole (American Economic Review 74 (1984), 361-368) taxonomy of business strategies, we provide a general discussion of merger decisions made in sequence by disjoint groups of firms. In a linear Cournot model, we retrieve all four business strategies of the general taxonomy by allowing for cost savings due to merger. We find that the prospects of a subsequent merger decision have an ambiguous effect on the profitability of the first merger. We also show, in our general framework, that, when merger decisions are interdependent over time, the condition of Farrell and Shapiro (American Economic Review 80 (1990), 107-126) overestimates a merger's actual external effect. Keywords: Mergers; Sequential moves; Competition policy

This paper presents a method for computing the response of a 1D elastic continuum induced by a multi-degree-of-freedom (MDOF) oscillator traveling over it. The continuum and the oscillator are nonconservative systems with proportional damping. Unlike most studies in the field, the solution method does not address a particular type of continuous structure and oscillator. Instead, a rigorous mathematical formulation is presented that can be applied to a broad class of proportionally damped 1D continua and MDOF oscillators, regardless of boundary conditions. The problem is reduced to the integration of a system of linear differential equations with time-dependent coefficients. These coefficients are found to depend on natural frequencies, damping ratios, and eigenfunctions and eigenvectors of the continuum and the oscillator. The method is tested on numerical examples and results are compared to those available in the literature. As a practical application, the method can be used to analyze vehicle-bridge interaction problems.

This article discusses the problem with probability in random walk mathematics. Topics include proof theorems and the theory of probability.

The stability of the Walrasian tatonnement model in discrete time is investigated. Discrete time impacts on expectations, disequilibrium trading and temporary equilibrium. Many conditions sufficient for continuous time are sufficient for stability in discrete time.

An investment planning model is developed to consider the effect of product and factor price changes on investment decisions. Impact is stronger on the macrolevel and then filters through to all sectors. Maximization of the objective function even if misspecified is optimal.

Formulation is provided to test the Barro type model of output and unanticipated money growth even when the model is mispecified. A set of assumations are found necessary and uncontroversial. Lagged monetary shocks are included.