Mathematics

A study of operating condition and design methods is presented that enables the amplifiers to achieve the upper limit of their power gain at frequencies close to the device f max .Using the gain-plane approach, the necessary and sufficient conditions to achieve this theoretical upper limit are obtained and the results are analytically verified. As will be demonstrated, the maximum power gain is achieved if and only if the imaginary part of Y 12 /Y 21 becomes zero and the device operates at the edge of the unconditional stability region. In addition, a generic circuit solution comprising both a Y -a n daZ-embedding network is proposed to achieve this upper limit. Simulations of a CMOS amplifier surrounded by an exemplary YZ-embedding network verify this study.

This paper presents the design of a high efficiency, low THD, 5.7GHz fully differential power amplifier for wireless communications in a standard 0.18µm CMOS technology. The power amplifier employs a fully differential class-E topology to achieve high power efficiency by exploiting its soft-switching property. In order to achieve high operating frequency, an injection-locked oscillator is utilized, which makes the output voltage of the power amplifier tuned at the input signal frequency. A complementary CMOS cross-coupled pair topology is employed to realize the LC-tank oscillator because it has lower phasenoise, thereby giving lower THD than the single NMOS cross-coupled pair topology. The proposed power amplifier can deliver 25dBm output power to a 50 load at 5.7GHz with 42.6% power-added efficiency (PAE) from 1.8V supply voltage.

This paper presents a spectrally-weighted balanced truncation technique for RLC interconnects, when the interconnect circuit parameters change as a result of variations in the manufacturing process. The salient features of this algorithm are the inclusion of the parameter variation in the RLC interconnect, the guaranteed stability of the reduced transfer function, and the availability of provable frequency-weighted error bounds for the reduced-order system. This paper shows that the balanced truncation technique is an effective model-order reduction technique when variations in the circuit parameters are taken into consideration. Experimental results show that the new variational spectrally-weighted balanced truncation attains, on average, 20% more accuracy than the variational Krylovsubspace-based model-order reduction techniques while the run-time is also, on average, 5% faster.

This paper presents a spectrally-weighted balanced truncation technique for tightly coupled integated circuit interconnects, when the interconnect circuit parameters change as a result of statistical variations in the manufacturing process. The salient features of this algorithm are the inclusion of the parameter variation in the RLC interconnect, the guaranteed passivity of the reduced transfer function, and the availability of provable spectrally-weighted error bounds for the reduced-order system. This paper shows that the variational balanced truncation technique produces reduced systems that accurately follow the time-and frequency-domain responses of the original system when variations in the circuit parameters are taken into consideration. Experimental results show that the new variational spectrally-weighted balanced truncation attains, in average, 30% more accuracy than the variational Krylov-subspacebased model-order reduction techniques.

In this paper, we give a new approach to solving the 2-variable subnormal completion problem (SCP for short). To this aim, we extend the notion of recursively generated weighted shifts, introduced by R. Curto and L. Fialkow, to 2-variable case. We next provide "concrete" necessary and sufficient conditions for the existence of solutions to the 2-variable SCP with minimal Berger measure. Furthermore, a short alternative proof to the propagation phenomena, for the subnormal weighted shifts in 2-variable, is given.

We introduce a new strategy in solving the truncated complex moment problem. To this aim we investigate recursive doubly indexed sequences and their characteristic polynomials. A characterization of recursive doubly indexed moment sequences is provided. As a simple application, we obtain a computable solution to the complex moment problem for cubic harmonic characteristic polynomials of the form z 3 + az + bz, where a and b are arbitrary real numbers. We also recapture a recent result due to Curto-Yoo given for cubic column relations in M (3) of the form Z 3 = itZ + uZ with t, u real numbers satisfying some suitable inequalities. Furthermore, we solve the truncated complex moment problem with column dependence relations of the form Z k+1 = 0≤n+m≤k anmZ n Z m (anm ∈ C).

High frequencies at which ultrasonic waves travel give rise to nonlinear phenomena. In thermoviscous fluids, these are captured by Blackstock's acoustic wave equation with strong damping. We revisit in this work its well-posedness analysis. By exploiting the parabolic-like character of this equation due to strong dissipation, we construct a time-weighted energy framework for investigating its local solvability. In this manner, we obtain the small-data well-posedness on bounded domains under less restrictive regularity assumptions on the initial conditions compared to the known results. Furthermore, we prove that such initial boundary-value problems for the Blackstock equation are globally solvable and that their solution decays exponentially fast to the steady state.

This study aims to build a superior strategy in the company precast concrete with a Resource Based View approach at PT. ABX, as well as generate strategies in exploiting resources, capabilities, competitive advantages to create sustainable strategies for the company. The research method used is qualitative based on phenomenology. The research results show that to improve employee performance, it is necessary to carry out work evaluations and targets. Combine the company's human resources and physical resources by placing employees who are competent and experienced in their fields. To increase the knowledge, skills and abilities of employees, companies need to conduct training. To expedite the precast concrete production process, companies need to have a batching plant. Evaluate the production process and routinely carry out material tests and concrete tests to maintain quality and quality. Promotion through digital media, such as Google, websites and other social media. Maintain...

In random experiments, most analyses are based on interpretation of the difference between the means of experiment and control groups. Therefore, studying the difference between the variances of the experiment and control groups may also be useful in interpreting the analysis results. This study focuses on interval estimation with sample variance estimators based on Winsorized Mean and Trimmed Mean for the difference of the variances of two nonnormal populations. In the simulation study, confidence intervals based on robust estimators for the difference of the variances of two non-normally distributed populations were compared in terms of coverage probabilities and average length widths. According to simulation study, it was determined that the coverage probabilities of confidence intervals based on robust estimators were very close to the nominal confidence level in any case. However, it was seen that the average length widths of confidence intervals obtained with sample variance estimator based on Trimmed Mean were narrower compared to the average length widths of confidence intervals obtained with sample variance estimator based on Winsorized Mean. In addition, it was determined that these results were the same when the Type I error is different. According to these results, it will be appropriate to prefer interval estimations obtained with sample variance estimator based on Trimmed Mean since it provides narrower confidence interval for the difference of the variances of two nonnormal populations.

Many of the test statistics which used to test $H:\theta=\theta_0$ are constructed under a postulated model. However, when the postulated model is not correct, the true significance level $\alpha^{'}$ will be different than the significance level of the postulated model $\alpha$. The significance level $\alpha$ is used in the test statistic whether or not the hypothesis is rejected or not rejected, so determining the true significance level is important in the hypothesis tests. In this paper, when the normality assumption in hypothesis tests is violated, the true significance level for testing hypothesis about the location $\mu$ and scale $\sigma$ parameters under different contaminated distributions is obtained. As a result, the robustness of significance levels  is investigated.

The Burr III distribution is used in a wide variety of fields of lifetime data analysis, reliability theory, and financial literature, etc. It is defined on the positive axis and has two shape parameters, say c and k. These shape parameters make the distribution quite flexible. They also control the tail behavior of the distribution. In this study, we extent the Burr III distribution to the real axis and also add a skewness parameter, say ε, with epsilon-skew extension approach. When the parameters c and k have a relation such that ck ≈ 1 or ck < 1, it is skewed unimodal. Otherwise, it is skewed bimodal with the same level of peaks on the negative and positive sides of real line. Thus, ESBIII distribution can capture fitting the various data sets even when the number of parameters are three. Location and scale form of this distribution are also given. Some distributional properties of the new distribution are investigated. The maximum likelihood (ML) estimation method for the parameters of ESBIII is considered. The robustness properties of ML estimators are studied and also tail behaviour of ESBIII distribution is examined. The applications on real data are considered to illustrate the modeling capacity of this distribution in the class of bimodal distributions.

Objective:-To evaluate anthropometric measurements and its relation with gonadotropin secretion in patients with polycystic ovary syndrome (PCOS). Study Design:-Cross-sectional study. Methodology:-Hundred oligomenorrhic PCOS women of reproductive age (18 -40 years) were studied. The data recorded on a prescribed proforma included current age, age at menarche, menstrual irregularities, presence of hirsutism, acne, infertility, familial nature, blood pressure, BMI and waisthip ratio. Blood samples for gonadotropin assay were taken randomly on day 6th to 30th of menstrual cycle. Kruskul Wallis test was used to assess the influence of BMI levels on LH:FSH values. Spearman rank correlation was used for correlation assessment. Results:-The mean weight was 67.34 ±11.02 kg and mean BMI was 28.21 ±4.42 kg/m2. There was no significant difference in mean LH/FSH ratio (p=.575) among BMI groups. However, there was a positive correlation between BMI and LH:FSH ratio (p=0.048, r=0.161). Conclusion:-There was high frequency of obesity (70%) in women with PCOS. Although no significant difference was found between mean LH:FSH ratio among different BMI groups levels but significant correlation between BMI levels and LH: FSH suggested that there was positive relation between BMI and LH: FSH.

Inflammation and renal tubular injury are major features of acute kidney injury (AKI). Many cytokines and chemokines are released from injured tubular cells and acts as proinflammatory mediators. However, the role of IL-19 in the pathogenesis of AKI is not defined yet. In bilateral renal ischemia/reperfusion injury (IRI)-induced and HgCl 2 -induced AKI animal models, realtime quantitative (RTQ)-PCR showed that the kidneys, livers, and lungs of AKI mice expressed significantly higher IL-19 and its receptors than did sham control mice. Immunohistochemical staining showed that IL-19 and its receptors were strongly stained in the kidney, liver, and lung tissue of AKI mice. In vitro, IL-19 upregulated MCP-1, TGF-b1, and IL-19, and induced mitochondria-dependent apoptosis in murine renal tubular epithelial M-1 cells. IL-19 upregulated TNF-a and IL-10 in cultured HepG2 cells, and it increased IL-1b and TNF-a expression in cultured A549 cells. In vivo, after renal IRI or a nephrotoxic dose of HgCl 2 treatment, IL-20R1-deficient mice (the deficiency blocks IL-19 signaling) showed lower levels of blood urea nitrogen (BUN) in serum and less tubular damage than did wild-type mice. Therefore, we conclude that IL-19 mediates kidney, liver, and lung tissue damage in murine AKI and that blocking IL-19 signaling may provide a potent therapeutic strategy for treating AKI.

We propose a non-deterministic CNOT gate based on a quantum cloner, a quantum switch based on all optical routing of single photon by single photon, a quantum-dot spin in a double-sided optical microcavity with two photonic qubits, delay lines and other linear optical photonic devices. Our CNOT provides a fidelity of 78% with directly useful outputs for a quantum computing circuit and requires no ancillary qubits or electron spin measurements.

Penelitian ini bertujuan untuk mengetahui pengaruh penerapan prinsip good corporate governance terhadap kualitas laporan keuangan di PT Pelabuhan Indonesia IV. Desain penelitian ini menggunakan metode deskriptif analitis dengan pendekatan studi kasus. Teknik pengambilan sampel menggunakan total sampling dengan jumlah sampel 20 karyawan PT Pelabuhan Indonesia IV. Pengumpulan data menggunakan kuisioner yang diberikan kepada responden. Analisis statistik yang digunakan dalam penelitian ini adalah menggunakan analisis statistik regresi linier. Hasil penelitian menerangkan bahwa mayoritas karyawan setuju dengan penerapan prinsip GCG yaitu masing-masing 50% untuk variabel transparansi, 50% untuk variabel akuntabilitas, dan 65% untuk variabel responsibility serta 50% untuk kualitas laporan keuangan dan untuk semua variabel tidak ada (0%) yang mengatakan tidak setuju maupun sangat tidak setuju. Selain itu, prinsip good corporate governance berpengaruh terhadap kualitas laporan keuangan.

Ranking of intuitionsitic fuzzy number plays a vital role in decision making and other intuitionistic fuzzy applications. In this paper, we propose a new ranking method of intuitionistic fuzzy number based on distance measure. We first define a distance measure for interval numbers based on L p metric and further generalize the idea for intuitionistic fuzzy number by forming interval with their respective value and ambiguity indices. Finally, some comparative results are given in tabular form.

This paper focuses on the study of two characteristics of trapezoidal intuitionistic fuzzy number (TRIFN), viz., Value index and Ambiguity index. Based on these two indexes, we develop an algorithm for ranking of trapezoidal intuitionistic fuzzy number (TRIFN). Furthermore, we present an application of this ranking method in multi attribute group decision making problem. An illustrative numerical example demonstrate our approach to multi attribute group decision making problem.

In this paper, we study the linear fractional programming (LFP) problems under intuitionistic fuzzy setting. The problem is considered as a fully fuzzy linear fractional programming problem where the variables and parameters both are characterized by trapezoidal intuitionistic fuzzy number. Ranking of intuitionistic fuzzy numbers has been used to solve the problem by simplex method. An algorithm has been developed to present our approach. One numerical example has been solved to demonstrate our methodology.

Ranking of intuitionsitic fuzzy number plays a vital role in decision making and other intuitionistic fuzzy applications. In this paper, we propose a new ranking method of intuitionistic fuzzy number based on distance measure. We first define a distance measure for interval numbers based on L p metric and further generalize the idea for intuitionistic fuzzy number by forming interval with their respective value and ambiguity indices. Finally, some comparative results are given in tabular form.

This paper describes two different methods to deal with the fuzzy shortest path problems. The first one is to study fuzzy shortest path in a network by Bellman dynamic programming approach and the second one is to study same problems by multi objective linear programming (MOLP) technique. It is considered that the edge weights of the network as uncertain. To analyze this idea of uncertainty four examples have been taken with two different network where edge weights have been presented by triangular fuzzy numbers and trapezoidal fuzzy numbers respectively. Both the problems have been solved by the above two methods. In the first method sign distance ranking procedure has been applied to get real value of the fuzzy edge weights where as in the second method MOLP, only 0-1 variables have been considered to get integer solution without using the Branch and Bound technique. It is observed that the length of the shortest paths in fuzzy sense as obtained by both the methods are same/almost same and the shortest path corresponds to the actual path in the network. It is obvious that fuzzy shortest path is an extension of the crisp problem.

The publications of the Studies series are dedicated to key subjects in the history and development of know ledge, bringing together perspectives from different fields and combining sourcebased empirical research with theoretically guided approaches. The Proceedings series presents the results of scientific meetings on current issues and supports, at the same time, further cooperation on these issues by offering an electronic platform with further resources and the possibility for comments and interactions. The Textbooks volumes are prepared by leading experts in the relevant fields.

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As stated in the title, the book tells the mathematical history of division in extreme and mean ratio (DEMR) from the beginnings through the 18th century. The nonmathematical history of the same famous ratio, under which aspect it is most often called by its alias "the Golden Number," is in reserve for another book. The mathematical history, on the other hand, includes both the theory and the construction of the ratio itself and constructions which make use (or might make use) of the division. The book is thus also a history of constructions and discussions of the pentagon, the decagon, the icosahedron, and the dodecahedron. The earliest extant source mentioning DEMR is Euclid's Elements. It is therefore fully appropriate that the book starts with a detailed exposition of all propositions and definitions from the Elements somehow related to the DEMR or its applications. After a chapter on mathematical topics essential to the discussion (concepts relating to the question of "geometrical algebra," "side and diagonal numbers," incommensurability, and the "Euclidean algorithm"), the author goes back in time to see how much can be inferred about the pre-Euclidean history of the concept. Next comes an (apparently exhaustive) presentation of constructions, discussions, and calculations related to DEMR from Archimedes to Mascheroni. Finally, a first appendix arrays the variety of names given to DEMR, while a second appendix quotes the opinions of Campanus, Pacioli, Ramus, Kepler, and others concerning its marvellous power. Up to the time of the Elements (ca. 300 B.C.), the history of DEMR has to be based on indirect evidence. Since the mid-19th century, a wealth of theories, hypotheses, and speculations has grown from this absence of constraints on scholarly imagination. Herz-Fischler offers a broad and liberal survey that includes all serious attempts to deal with the subject (and a few less serious), and then discusses these various interpretations in the light of available evidence. Many properties of DEMR are easily demonstrated by means of the pentagram, which sources from later Antiquity connect with the Pythagorean order. Therefore, Herz-Fischler goes through the early occurrences of the pentagram, in ostraca, graffiti, and coins. He argues convincingly that prehistoric and Bronze Age pentagrams and an Old Babylonian calculation of the area of a pentagon have nothing to do with the matter, and, what is more important, that a figure in such widespread use (be it for decoration or with some hypothetical symbolic meaning) could hardly have been utilized as a specific symbol of recognition by the early Pythagoreans. He demonstrates, moreover, that there is no particular reason to believe brought to you by CORE View metadata, citation and similar papers at core.ac.uk

In this paper, a new partial-normalized least mean square (partial-NLMS) algorithm for updating the coefficients of an adaptive FIR digital filter (ADF) is proposed. The new adaptive algorithm is modified to overcome the NLMS method's problem , about unstability when very small input enters into the filter, and the LMS method's gradient

A novel class of bit-flipping (BF) algorithms for decoding low-density parity-check (LDPC) codes is presented. The proposed algorithms, which are called gradient descent bit flipping (GDBF) algorithms, can be regarded as simplified gradient descent algorithms. Based on gradient descent formulation, the proposed algorithms are naturally derived from a simple non-linear objective function.

We previously developed two NMF algorithms (QL1-NMF1 and QL1-NMF2) using the quasi-L1 norm for analyzing environmental ELF magnetic field measurements. When the data included many outliers, the QL1-NMF algorithms returned better results than other BSS algorithms using the L1 norm. However, the derivative of the cost function in QL1-NMF1 was not based on a monotonically increasing function. This problem decreased the validity of the algorithm. QL1-NMF2 had serious problems with stability though it was based on a monotonically increasing derivative. The method therefore required an improvement of validity and stability. In the work described in this paper, we introduced new update functions that were based on a monotonically increasing derivative. Computer simulation results and real data results confirmed the new algorithm worked more stability than the previous one. Moreover, we showed the new algorithm was fast and accurate.

Imprecise information on any system is addressed by possibility theory wherein the system is modeled as a fuzzy set. Alpha level representation of a fuzzy set in the form of an interval defines the possibility theory. Uncertainty of any model in this context is quantified as mean value ± standard deviation of a possibilistic (imprecise) parameter. This paper presents the possibilistic statistical techniques to estimate the mean and standard deviation of a possibilistic parameter of subsurface solute transport model. The solute transport model parameters, such as groundwater velocity, solute dispersion coefficient, etc., are sparse and imprecise in nature. Such parameters are characterized by the possibility distribution. In this paper, analytical expression of solute transport model is used to estimate the mean value and standard deviation of possibilistic spatial and temporal concentration of solute.

A hortelã-pimenta é uma planta cultivada principalmente para a produção de óleo essencial e biomassa, que pode ser influenciada pelas condições ambientais. Este estudo teve como objetivo avaliar a produção de biomassa e o teor de óleo essencial de hortelã (Mentha arvensis L.) Sob o efeito de diferentes espaçamentos entre linhas nos horários de plantio e colheita. O experimento foi conduzido em delineamento de blocos ao acaso, com três repetições e seis tratamentos em fatorial 2x3, dois espaçamentos (0,40 x 0,30 me 0,60 x 0,30 m) e três épocas de colheita (6:00 às 7:00, 10:00 às 11:00 e 16:00 às 17:00). As características avaliadas foram: clorofila total, temperatura das folhas no período da colheita (° C), biomassa fresca total das folhas (t ha-1), biomassa seca total das folhas (t ha-1), biomassa fresca total da parte aérea (t ha-1), biomassa seca total da parte aérea (t ha-1) e teor de óleo essencial com base na biomassa seca das folhas (% óleo). O espaçamento de 0,40 x 0,30 m foi...

Background In a study performed on multiplex Multiple Sclerosis (MS) Sardinian families to identify disease causing plasma proteins, application of Mendelian Randomization (MR) methods encounters difficulties due to relatedness of individuals, correlation between finely mapped genotype instrumental variables (IVs) and presence of missing exposures. Method We specialize the method of Berzuini et al (2018) to deal with these difficulties. The proposed method allows pedigree structure to enter the specification of the outcome distribution via kinship matrix, and treating missing exposures as additional parameters to be estimated from the data. It also acknowledges possible correlation between instruments by replacing the originally proposed independence prior for IV-specific pleiotropic effect with a g-prior. Based on correlated (r2&lt; 0.2) IVs, we analysed the data of four candidate MS-causing proteins by using both the independence and the g-prior. Results 95% credible intervals for...

Designing efficient and stable algorithm for finding the eigenvalues and eigenvectors is very important from the static as well as the dynamic aspect in coupled problems. Modal analysis requires first few significant eigenvectors and eigenvalues while direct integration requires the highest value to ascertain the length of the time step that satisfies the stability condition. The paper first presents the modification of the well known WYD method for a solution of single field problems: an efficient and numerically stable algorithm for computing eigenvalues and the corresponding eigenvectors. The modification is based on the special choice of the starting vector. The starting vector is the static solution of displacements for the applied load, defined as the product of the mass matrix and the unit displacement vector. The starting vector is very close to the theoretical solution, which is important in cases of small subspaces. Additionally, the paper briefly presents the adopted formulation for solving the fluid-structure coupled systems problems which is based on a separate solution for each field. Individual fields (fluid and structure) are solved independently, taking in consideration the interaction information transfer between them at every stage of the iterative solution process. The assessment of eigenvalues and eigenvectors for multiple fields is also presented. This eigen problem is more complicated than the one for the ordinary structural analysis, as the formulation produces non-symmetrical matrices. Finally, a numerical example for the eigen solution coupled fluidstructure problem is presented to show the efficiency and the accuracy of the developed algorithm.

The adjustment of grid steps which guarantees that particles methods yield no numerical diffusion inevitably induces overshooting errors in the solution of the parabolic partial differential equations with space variable coefficients. In this paper we give an evaluation of the overshooting errors of the &quot;global random walk&quot; algorithm (GRW), a computational efficient method used in simulations for transport in environmental problems. The evaluation is performed by comparisons between the GRW solutions and those of the &quot;biased global random walk&quot; algorithm (BGRW), a cellular automaton, which is computationally more expensive but is also free of overshooting errors. The reference problem was the diffusive transport in a random velocity field, a model for the transport of the contaminant solutes in groundwater. The evaluation reveals that, for an optimum choice of the parameters, GRW results for time intervals of practical interest lie in ranges of acceptable precisi...

Concentrations of chemical species transported in random environments need to be statistically characterized by probability density functions (PDF). Solutions to evolution equations for the one-point one-time PDF are usually based on systems of computational particles described by Itô equations. We establish consistency conditions relating the concentration statistics to that of the Itô process and the solution of its associated Fokker-Planck equation to that of the PDF equation. In this frame, we use a recently proposed numerical method which approximates PDFs by particle densities obtained with a global random walk (GRW) algorithm. The GRW-PDF approach is illustrated for a problem of contaminant transport in groundwater.

Evolution equations for probability density functions (PDFs) and filtered density functions (FDFs) of random species concentrations weighted by conserved scalars are formulated as Fokker-Planck equations describing stochastically equivalent processes in concentration-position spaces. This approach provides consistent numerical PDF/FDF solutions, given by the density in the concentration-position space of an ensemble of computational particles governed by the associated Itô equations. The solutions are obtained by a global random walk (GRW) algorithm, which is stable, free of numerical diffusion, and practically insensitive to the increase of the number of particles. The general FDF approach and the GRW numerical solution are illustrated for a reduced complexity problem consisting of the transport of a single scalar in groundwater. Randomness is induced by the stochastic parameterization of the hydraulic conductivity, characterized by short range correlations and small variance. The objective is to infer the statistics of the random concentration sampled at the plume center of mass, integrated over the transverse dimension of a two-dimensional spatial domain. The PDF/FDF problem can therefore be formulated in a two-dimensional domain as well, a spatial dimension and one in the concentration space. The upscaled drift and diffusion coefficients describing the PDF transport in the physical space are estimated on singletrajectories of diffusion in velocity fields with short-range correlations, owing to their self-averaging property. The mixing coefficients describing the PDF transport in concentration spaces are parameterized by the trend and the noise inferred from the statistical analysis of an ensemble of simulated concentration time series, as well as by classical mixing models. A Gaussian spatial filter applied to a Kraichnan velocity field generator is used to construct coarse-grained simulations (CGS) for FDF problems. The purposes of the CGS simulations are two-fold: first to understand the significance of the FDF approach from a practical point of view and its relation to the PDF approach; second to investigate the limits of the mixing models considered here and the desirable features of the mixing models for groundwater systems.

The Global Random Walk algorithm performs simultaneously the tracking of large collections of particles and permits massive simulations at reasonable costs. Applications were developed for transport in systems with anisotropic, non-homogeneous, and randomly distributed parameters. As a first illustration we present simulations for diffusion in human skin. Further, a case study for contaminant transport in groundwater shows that the realizations of the transport process converge in mean square limit to a Gaussian diffusion. This investigation also indicates that the use of the Kraichnan routine, based on periodic random fields, yields reliable simulations of transport in Gaussian velocity fields.

Longitudinal dispersion coefficients in given realizations of the transport computed by two currently used approximations of the first-order in velocity variance are compared with accurate global random walk simulations. The comparisons are performed for the same ensemble of realizations of the Darcy velocity field, approximated by a quasi-periodic random field, for log-normal hydraulic conductivity with small variance and finite correlation lengths. The results show that, at finite times of about one dispersion time scale, the mean coefficient is underestimated by ≈ 20% and the fluctuations are overestimated by ≈ 80%. At larger times the errors decrease monotonously and the first-order approximations yield fairly good predictions for the mean and the fluctuations of the dispersion coefficient.

Whenever one uses translation invariant mean Green's functions to describe the behavior in the mean and to estimate dispersion coefficients for diffusion in random velocity fields, the spatial homogeneity of the transition probability of the transport process is implicitly assumed. This property can be proved for deterministic initial conditions if, in addition to the statistical homogeneity of the space-random velocity field, the existence of unique classical solutions of the transport equations is ensured. When uniqueness condition fails and translation invariance of the mean Green's function cannot be assumed, as in the case of nonsmooth samples of random velocity fields with exponential correlations, asymptotic dispersion coefficients can still be estimated within an alternative approach using the Itô equation. Numerical simulations confirm the predicted asymptotic behavior of the coefficients, but they also show their dependence on initial conditions at early times, a signature of inhomogeneous transition probabilities. Such memory effects are even more relevant for random initial conditions, which are a result of the past evolution of the process of diffusion in correlated velocity fields, and they persist indefinitely in case of power law correlations. It was found that the transition probabilities for successive times can be spatially homogeneous only if a long-time normal diffusion limit exits. Moreover, when transition probabilities, for either deterministic or random initial states, are spatially homogeneous, they can be explicitly written as Gaussian distributions.

It was proved that balance equations for systems with corpuscular structure can be derived if a kinematic description by piece-wise analytic functions is available . This article presents a rigorous derivation of an one-dimensional hydrodynamic model for the stock price evolution. The kinematic description is given by a set of time functions describing the evolution of the stock price.

A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested.

We discuss a prototypical reaction-diffusion-flow problem in saturated/unsaturated porous media. The special features of our problem are: the reaction produces water and therefore the flow and transport are coupled in both directions and moreover, the reaction may alter the microstructure. This means we have a variable porosity in our model. For the spatial discretization we propose a mass conservative scheme based on the mixed finite element method (MFEM). The scheme is semiimplicit in time. Error estimates are obtained for some particular cases. We apply our finite element methodology for the case of concrete carbonation -one of the most important physico-chemical processes affecting the durability of concrete.

Smooth concentration fields and balance equations for systems of random walkers are obtained by using the coarsegrained space‐time averaging method from ]5[ and averages over the statistical ensemble. This yields a new cellular automaton numerical model for diffusion processes. The number of particles and the averaging space‐time scale needed to approximate the concentration, with a given precision, are obtained. Applications were made for systems with small concentrations and diffusion in random fields.

The Global Random Walk algorithm (GRW) performs a simultaneous tracking on a fixed grid of huge numbers of particles at costs comparable to those of a single-trajectory simulation by the traditional Particle Tracking (PT) approach. Statistical ensembles of GRW simulations of a typical advection-dispersion process in groundwater systems with randomly distributed spatial parameters are used to obtain reliable estimations of the input parameters for the upscaled transport model and of their correlations, input-output correlations, as well as full probability distributions of the input and output parameters.

Relationships between statistical properties of Eulerian velocity (in a fixed reference frame) and Lagrangian velocity (i.e. the velocity of marked molecules) are examined for the case of diffusion in velocity fields described by random space functions. Assuming a constant diffusion coefficient and a divergence-free homogeneous Eulerian random field, we give simple proofs of the statistical homogeneity of the Lagrangian velocity field and of the equality between the Lagrangian and Eulerian one-point marginal probability densities. Further, we analyze numerical simulations using velocity fields generated with a classical randomization method. The numerical Eulerian velocity is homogeneous within a reasonably small confidence interval. Surprisingly, at early times the Lagrangian mean velocity still depends on the starting point of the trajectory and shows small oscillations which, however, are well beyond the confidence interval for the Eulerian mean velocity. We demonstrate that the lack of strict statistical homogeneity of the Lagrangian velocity induces a dependence of the second moment of the ensemble averaged concentration on the initial concentration distribution. At large times, the simulated Lagrangian mean velocity tends to the Eulerian mean velocity and the second moment of the mean concentration loses the memory of the initial conditions.