Using Physical Quantities in Applied Mathematical Problems with Maple

The present article discusses units of measure and their base units, work environments built in the Units package of the computer algebra system Maple. An analysis is drawn of the tools of the application in connection with the use of physical quantities and their features. Maple’s main commands are arranged in groups depending on the function. Some applied mathematical problems are given as examples making use of derivative, integral and differential equations.

Applied Aspects of Mathematical Modeling and Optimization of Dynamics of Charged Beams

The complex of questions connected with the analysis, estimation and structural-parametrical optimization of dynamic system is considered in this article. Connection of such problems with tasks of control by beams of trajectories is emphasized. The special attention is concentrated on the review and analysis of spent scientific researches, the attention is stressed to their constructability and applied directedness. Efficiency of the developed algorithmic and software is demonstrated on the tasks of modeling and optimization of output beam characteristics in linear resonance accelerators.

Numerical Solution of Fractional Diffusion-Wave Equation with two Space Variables by Matrix Method

Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.

Principles of Extremum and Application to some Problems of Analysis

AMS subject classification: 41A17, 41A50, 49Kxx, 90C25.

Well-Posedness and Conditioning of Optimization Problems

AMS subject classification: 49K40, 90C31.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

A domain decomposition based algorithm for non-linear 2D inverse heat conduction problems

Inverse heat conduction problems (IHCPs) appear in many important scientific and technological fields. Hence analysis, design, implementation and testing of inverse algorithms are also of great scientific and technological interest. The numerical simulation of 2-D and –D inverse (or even direct) problems involves a considerable amount of computation. Therefore, the investigation and exploitation of parallel properties of such algorithms are equally becoming very important. Domain decomposition (DD) methods are widely used to solve large scale engineering problems and to exploit their inherent ability for the solution of such problems.

The parallel solution of early-exercise Asian options with stochastic volatility

This paper describes an parallel semi-Lagrangian finite difference approach to the pricing of early exercise Asian Options on assets with a stochastic volatility. A multigrid procedure is described for the fast iterative solution of the discrete linear complementarity problems that result. The accuracy and performance of this approach is improved considerably by a strike-price related analytic transformation of asset prices. Asian options are contingent claims with payoffs that depend on the average price of an asset over some time interval. The payoff may depend on this average and a fixed strike price (Fixed Strike Asians) or it may depend on the average and the asset price (Floating Strike Asians). The option may also permit early exercise (American contract) or confine the holder to a fixed exercise date (European contract). The Fixed Strike Asian with early exercise is considered here where continuous arithmetic averaging has been used. Pricing such an option where the asset price has a stochastic volatility leads to the requirement to solve a tri-variate partial differential inequation in the three state variables of asset price, average price and volatility (or equivalently, variance). The similarity transformations [6] used with Floating Strike Asian options to reduce the dimensionality of the problem are not applicable to Fixed Strikes and so the numerical solution of a tri-variate problem is necessary. The computational challenge is to provide accurate solutions sufficiently quickly to support realtime trading activities at a reasonable cost in terms of hardware requirements.

Efficient Solution of Rational Conics

We present efficient algorithms for solving Legendre equations over Q (equivalently, for finding rational points on rational conics) and parametrizing all solutions. Unlike existing algorithms, no integer factorization is required, provided that the prime factors of the discriminant are known.

Application of mathematical models to mycotoxins children risk assessment: a case study of Portuguese children exposure to co-occurring mycotoxins in processed cereal-based foods

People, animals and the environment can be exposed to multiple chemicals at once from a variety of sources, but current risk assessment is usually carried out based on one chemical substance at a time. In human health risk assessment, ingestion of food is considered a major route of exposure to many contaminants, namely mycotoxins, a wide group of fungal secondary metabolites that are known to potentially cause toxicity and carcinogenic outcomes. Mycotoxins are commonly found in a variety of foods including those intended for consumption by infants and young children and have been found in processed cereal-based foods available in the Portuguese market. The use of mathematical models, including probabilistic approaches using Monte Carlo simulations, constitutes a prominent issue in human health risk assessment in general and in mycotoxins exposure assessment in particular. The present study aims to characterize, for the first time, the risk associated with the exposure of Portuguese children to single and multiple mycotoxins present in processed cereal-based foods (CBF). Portuguese children (0-3 years old) food consumption data (n=103) were collected using a 3 days food diary. Contamination data concerned the quantification of 12 mycotoxins (aflatoxins, ochratoxin A, fumonisins and trichothecenes) were evaluated in 20 CBF samples marketed in 2014 and 2015 in Lisbon; samples were analyzed by HPLC-FLD, LC-MS/MS and GC-MS. Daily exposure of children to mycotoxins was performed using deterministic and probabilistic approaches. Different strategies were used to treat the left censored data. For aflatoxins, as carcinogenic compounds, the margin of exposure (MoE) was calculated as a ratio of BMDL (benchmark dose lower confidence limit) to the aflatoxin exposure. The magnitude of the MoE gives an indication of the risk level. For the remaining mycotoxins, the output of exposure was compared to the dose reference values (TDI) in order to calculate the hazard quotients (ratio between exposure and a reference dose, HQ). For the cumulative risk assessment of multiple mycotoxins, the concentration addition (CA) concept was used. The combined margin of exposure (MoET) and the hazard index (HI) were calculated for aflatoxins and the remaining mycotoxins, respectively. 71% of CBF analyzed samples were contaminated with mycotoxins (with values below the legal limits) and approximately 56% of the studied children consumed CBF at least once in these 3 days. Preliminary results showed that children exposure to single mycotoxins present in CBF were below the TDI. Aflatoxins MoE and MoET revealed a reduced potential risk by exposure through consumption of CBF (with values around 10000 or more). HQ and HI values for the remaining mycotoxins were below 1. Children are a particularly vulnerable population group to food contaminants and the present results point out an urgent need to establish legal limits and control strategies regarding the presence of multiple mycotoxins in children foods in order to protect their health. The development of packaging materials with antifungal properties is a possible solution to control the growth of moulds and consequently to reduce mycotoxin production, contributing to guarantee the quality and safety of foods intended for children consumption.

Paths in remnant movement: A single solution to three problems in the Polish OVS syntax

On the one hand it has been advanced that remnant movement (RM) serves as a replacement for head movement and leads to certain permutations in word order while it disallows some others (e.g. Cinque (2005)), on the other hand, little attention has been devoted to the consequences RM has for clausal syntax. In this work, I illustrate one such consequence, namely the rise of crossing and nesting movement dependencies and their reflexes. In particular, I make a case for the existence of massive RM that involves entire clausal subtrees in Polish. The analysis provides a uniform solution to three robust puzzles in the Polish OVS construction in a straightforward way.

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.

Comparison Of The Solution Of Histidine-tryptophan-alfacetoglutarate With Histidine-tryptophan-glutamate As Cardioplegic Agents In Isolated Rat Hearts: An Immunohistochemical Study.

Cardiac arrest during heart surgery is a common procedure and allows the surgeon to perform surgical procedures in an environment free of blood and movement. Using a model of isolated rat heart, the authors compare a new cardioplegic solution containing histidine-tryptophan-glutamate (group 2) with the histidine-tryptophan-alphacetoglutarate (group 1) routinely used by some cardiac surgeons. To assess caspase, IL-8 and KI-67 in isolated rat hearts using immunohistochemistry. 20 Wistar male rats were anesthetized and heparinized. The chest was opened, cardioctomy was performed and 40 ml/kg of the appropriate cardioplegic solution was infused. The hearts were kept for 2 hours at 4ºC in the same solution, and thereafter, placed in the Langendorff apparatus for 30 minutes with Ringer-Locke solution. Immunohistochemistry analysis of caspase, IL-8, and KI-67 were performed. The concentration of caspase was lower in group 2 and Ki-67 was higher in group 2, both P<0.05. There was no statistical difference between the values of IL-8 between the groups. Histidine-tryptophan-glutamate solution was better than histidine-tryptophan-alphacetoglutarate solution because it reduced caspase (apoptosis), increased KI-67 (cell proliferation), and showed no difference in IL-8 levels compared to group 1. This suggests that the histidine-tryptophan-glutamate solution was more efficient than the histidine-tryptophan-alphacetoglutarate for the preservation of hearts of rat cardiomyocytes.

Changes in parents' and self-reports of behavioral problems in Brazilian adolescents after behavioral treatment with urine alarm for nocturnal enuresis

PURPOSE: Compare parents' reports of youth problems (PRYP) with adolescent problems self-reports (APSR) pre/post behavioral treatment of nocturnal enuresis (NE) based on the use of a urine alarm. MATERIALS AND METHODS: Adolescents (N = 19) with mono-symptomatic (primary or secondary) nocturnal enuresis group treatment for 40 weeks. Discharge criterion was established as 8 weeks with consecutive dry nights. PRYP and APSR were scored by the Child Behavior Checklist (CBCL) and Youth Self-Report (YSR). RESULTS: Pre-treatment data: 1) Higher number of clinical cases based on parent report than on self-report for Internalizing Problems (IP) (13/19 vs. 4/19), Externalizing Problems (EP) (7/19 vs. 5/19) and Total Problem (TP) (11/19 vs. 5/19); 2) Mean PRYP scores for IP (60.8) and TP (61) were within the deviant range (T score ≥ 60); while mean PRYP scores for EP (57.4) and mean APSR scores (IP = 52.4, EP = 49.5, TP = 52.4) were within the normal range. Difference between PRYP' and APSR' scores was significant. Post treatment data: 1) Discharge for majority of the participants (16/19); 2) Reduction in the number of clinical cases on parental evaluation: 9/19 adolescents remained within clinical range for IP, 2/19 for EP, and 7/19 for TP. 3) All post-treatment mean scores were within the normal range; the difference between pre and post evaluation scores was significant for PRYP. CONCLUSIONS: The behavioral treatment based on the use of urine alarm is effective for adolescents with mono-symptomatic (primary and secondary) nocturnal enuresis. The study favors the hypothesis that enuresis is a cause, not a consequence, of other behavioral problems.