Non-standard Formulation Research Articles

A Nonstandard Formulation of Bohmian Mechanics

A Nonstandard Formulation of Bohmian Mechanics

Synthesis of Parameters of Proportionally-Integral and Proportionally-Integral-Differential Controllers for Stationary Linear Objects with Nonzero Initial Conditions

The problem of the synthesis of proportional-integrating (PI) and proportional-integral-differentiating (PID) controllers in a nonstandard formulation is considered. For a linear one-dimensional control object with nonzero initial conditions, it is required to find a controller that is optimal in the sense of a quadratic functional of the state of the object with a regularization additive in control. The synthesis procedure is a solution of the corresponding quadratic optimization problem using a method similar to the conjugate gradient method (the direction at each step is calculated by the conjugate gradient method, and the step length is calculated by the Armijo rule). Numerical examples illustrate the effectiveness of the proposed algorithm in the synthesis of controllers for models of control objects that are common in practice.

A viscoelastic Mooney–Rivlin model for adhesive curing and first steps toward its calibration based on photoelasticity measurements

The transition of polymer adhesives from an initially liquid to a fully cured viscoelastic state is accompanied by three phenomenological effects, namely an increase in stiffness and viscosity in conjunction with a decrease in volume (curing shrinkage). Under consideration of these phenomena, some of us (Hossain et al. in Computational Mechanics 46:363-375, 2010) have devised a generic, viscoelastic finite strain framework for the simulation of the curing process of adhesives, which renders a thermodynamically consistent model regardless of the selected free energy density. In the present work, this generic curing framework is modified by means of more precise integration schemes and is applied to a hyperelastic Mooney–Rivlin material based on an additive volumetric-isochoric split of the strain energy density. The benefit of this decomposition is directly related to the distinct material responses of various polymers to volumetric and isochoric deformations [4]. The resulting Mooney–Rivlin curing model provides the foundation for implementing a user-defined material subroutine (UMAT) in Abaqus requiring the Cauchy stress and a non-standard formulation of the tangent operator. To this end, the corresponding transformations are presented. Additionally, a first attempt to determine the evolution of the curing-dependent material parameters through optimization with respect to a photoelasticity measurement is presented. A subset of the material properties, which reflect the emergence of shrinkage stresses inside a ceramic-epoxy composite after its fabrication, is determined via inverse parameter identification. However, due to a lack of experimental data and some rather strong assumptions made on the physics involved, this demonstration can currently be considered only as a proof-of-concept.

Combination With Long-Acting Injectable Antipsychotics and Utilization of Nonstandard Formulations as Compliance Enhancing Methods for Clozapine Users: A Systematic Review and A Case Series.

Combining clozapine with a long-acting injectable antipsychotic (LAI) or using different, nonstandard formulations of the compound may improve treatment outcomes. We aimed to investigate the utility of the clozapine-LAI combination and different formulations of clozapine for compliance problems of clozapine treatment, and to describe a case series on the combined treatment. We conducted a PubMed search with no date restriction. The number and length of hospitalizations, the results of clinical scales, and adverse events were recorded. We also present a case series of 18 patients using the clozapine-LAI combination. Data were collected from the medical charts and electronic records. We extracted 9 records describing the use of the clozapine-LAI combination. The case reports and mirror-image studies showed a significant reduction in the number of hospitalizations, length of hospital stays, and number of visits to the emergency department on the combined treatment with no serious adverse events. We included 11 articles for clozapine formulations. The case reports and retrospective data suggested that short-acting intramuscular clozapine was often well tolerated and resulted in an increased acceptance of oral clozapine in the acute phase of illness. In our case series, illness severity and the number of hospitalization per year significantly decreased after the combined treatment, besides a significant improvement in the functioning scores. Hyperprolactinemia and extrapyramidal side effects were reported due to concomitant LAIs. Despite the encouraging evidence, the present data are preliminary and mostly based on retrospective studies, and oral-dissolving tablets or oral liquid formulations of clozapine have insufficient evidence for clinical practice. Well-designed, controlled, follow-up studies are needed for both clozapine-LAI combination and different formulations of clozapine.

A Statistical Basis for Reporting Strength of Evidence as Pool Reduction

This article establishes a statistical basis for an evidence-reporting strategy that interprets strength of evidence in terms of a reduction in the size of a pool of relevant conceptual objects. The strategy is motivated by debates in forensic science, wherein the pool would consist of sources of forensic material. An advantage of using the pool-reduction strategy is that it highlights uncertainty that cannot be resolved by empirical considerations. It is shown mathematically to reflect a nonstandard formulation of a Bayes factor, and to extend for use in problems of general quantitative inference. A number of conventions are proposed for full effectiveness of the strategy’s implementation in practice.

Stability of smooth periodic travelling waves in the Camassa–Holm equation

AbstractWe solve the open problem of spectral stability of smooth periodic waves in the Camassa–Holm equation. The key to obtaining this result is that the periodic waves of the Camassa–Holm equation can be characterized by an alternative Hamiltonian structure, different from the standard formulation common to the Korteweg‐de Vries equation. The standard formulation has the disadvantage that the period function is not monotone and the quadratic energy form may have two rather than one negative eigenvalues. We prove that the nonstandard formulation has the advantage that the period function is monotone and the quadratic energy form has only one simple negative eigenvalue. We deduce a precise condition for the spectral and orbital stability of the smooth periodic travelling waves and show numerically that this condition is satisfied in the open region where the smooth periodic waves exist.

A grid function formulation of a class of ill-posed parabolic equations

We study an ill-posed forward-backward parabolic equation with techniques of nonstandard analysis. Equations of this form arise in many applications, ranging from the description of phase transitions, to the dynamics of aggregating populations, and to image enhancing. The equation is ill-posed in the sense that it only has measure-valued solutions that in general are not unique. By using grid functions of nonstandard analysis, we derive a continuous-in-time and discrete-in-space formulation for the ill-posed problem. This nonstandard formulation is well-posed and formally equivalent to the classical PDE, and has a unique grid solution that satisfies the properties of an entropy measure-valued solution for the original problem. By exploiting the strength of the nonstandard formulation, we are able to characterize the asymptotic behaviour of the grid solutions and to prove that they satisfy a conjecture formulated by Smarrazzo for the measure-valued solutions to the ill-posed problem.

(Four) Dual Plaquette 3D Ising Models.

A characteristic feature of the plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the plaquette Ising and the X-Cube model is similar to that between the quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin–Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.

The Study of Automatic Examination in the Teaching of Official Document Writing

Official Document writing teaching is an important way for the government and its administrative departments for pre-job training to ensure that recruits can be competent at their administrative functions and service responsibilities, and plays an important role in the process of administrative management. As the most frequently used and the largest number of important tools in the daily management process of administrative organs, official documents are the most formal and scientific way in many methods of administrative management. However, there are still a great deal of teasers, such as the non-standard formulation of official documents, inappropriate content and expression, which occur from time to time in practice. If these teasers could be dealt with in the process of examination in the teaching of official document writing in time, these teasers will be solved in advance. Therefore, it is necessary to study the norms of official document examination in common use.

Pediatric dosage forms—challenges and recent developments: A critical review

Pediatric population is a diverse group comprising of different subgroups. The use of unlicensed and off-label medicines for treating children is widespread due to the non-availability of suitable dosage forms for this age group. Although the physiological differences related to the diverse age group remain an important consideration, various other challenges such as insufficient background information on drug molecule, excipient safety, taste-masking issues, technology requirements, low profitability, limitations in conduct of clinical trials, and lack of regulatory clarity are also important factors adversely affecting pediatric dosage form development. These factors are discussed in this review. Liquids are the most preferred dosage form for children, especially of lower age. However, in the absence of suitable or labeled dosage forms, physicians and caretakers are left with no choice but to use off-label, “specials,” or extemporaneously prepared formulations. All such nonstandard formulations are devoid of relevant scientific data and hence pose a high risk to pediatric patients. The situation is even more serious with developing countries, where health care guidelines and controls for pediatric patients scarcely exist. Although, in the recent years, the safe, effective, and labeled dosage forms are increasingly becoming available, pediatric development still struggles to find a place in the mainstream pharmaceutical development programs.

ТВОРЧИЙ ПОТЕНЦІАЛ ЯК ЕЛЕМЕНТ КОНКУРЕНТОСПРОМОЖНОСТІ МАЙБУТНЬОГО ФАХІВЦЯ

The training of specialists for the service sector is aimed exclusively at the training of qualified professionals, competent, flexible and mobile, with the creative approach to solving the problem prevailing over other means. The current state of affairs in the sphere of hotel and restaurant business and tourism demands from the society as a whole and educational establishments, in particular the formation of a person who has creativity, craving for the search for extraordinary variants of the way out of the situation with the smallest losses, sufficient level of intellectual development, behavioral flexibility, rationalism and autonomy, which is extremely necessary in the actual harsh conditions of doing business in principle. The terms of work in the sphere of hotel and restaurant business and tourism are filled with a huge number of crisis, stressful situations, which require from the employees of lightning-fast acceptance of flexible decisions with non-standard formulation. Today it is impossible to surprise an employer and get an ordinary job with the ability to solve trivial, standard tasks. On this basis, the issue of training staff in educational institutions that would have sufficient creative potential, able to intensify creative thinking and quickly find opportunities to solve problems is very acute. The author of the article notes that in the education system more attention should be paid to the development of creative thinking and creative approach of students especially those who will work in the service sector. The author stresses that the development of creativity in students is very important and must be engaged into the modern world, he believes that active creative thinking is inherent in each. But socium, the influence of the environment where people study or work, as well as the system of prohibitions from the younger years block the growth and development of this parameter.

Influenza vaccine strategies for solid organ transplant recipients.

The aim of this study was to highlight recent evidence on important aspects of influenza vaccination in solid organ transplant recipients. Influenza vaccine is the most evaluated vaccine in transplant recipients. The immunogenicity of the vaccine is suboptimal after transplantation. Newer formulations such as inactivated unadjuvanted high-dose influenza vaccine and the administration of a booster dose within the same season have shown to increase response rates. Intradermal vaccination and adjuvanted vaccines did not show clear benefit over standard influenza vaccines. Recent studies in transplant recipients do not suggest a higher risk for allograft rejection, neither after vaccination with a standard influenza vaccine nor after the administration of nonstandard formulation (high-dose, adjuvanted vaccines), routes (intradermally) or a booster dose. Nevertheless, influenza vaccine coverage in transplant recipients is still unsatisfactory low, potentially due to misinterpretation of risks and benefits. Annual influenza vaccination is well tolerated and is an important part of long-term care of solid organ transplant recipients.

Optimal control of low-frequency electromagnetic fields in multiply connected conductors

A class of optimal control problems for electromagnetic fields is considered. Special emphasis is laid on a non-standard H-based formulation of the equations of low-frequency electromagnetism in multiply connected conductors. By this technique, the low-frequency Maxwell equations can be solved with reduced computational complexity. While the magnetic field H in the conductor is obtained from an elliptic equation with the operator, an elliptic equation with the operator is set up for a potential in the isolator. Both equations are coupled by appropriate interface conditions. In all problems, the electrical current is controlled in the conducting domain. We discuss two optimal control problems with distributed control. A standard quadratic tracking type objective functional is minimized in the first problem, while a convex non-differentiable functional with -sparsity term is considered in the second. For all problems, the associated sensitivity analysis is performed.

Validation of robust SPH schemes for fully compressible multiphase flows

The present study examines the ability of the SPH number-density scheme to treat multiphase problems of the fully compressible regime. The number-density scheme is extended to the fully compressible regime, using the standard variational SPH framework and incorporate artificial diffusion coming from a generic formula. Aiming at robust schemes, we adopt the differential form of mass conservation. The performance of this scheme is studied with the help of two benchmark tests. It is shown that the standard variational framework of SPH may treat multiphase processes in the fully compressible regime, without reverting to non-standard formulations. The SPH solutions are compared to solutions coming from the Arbitrary Lagrangian Eulerian method and are validated against exact solutions.

Increasing the operating area of shunt active filters by advanced nonlinear control

This work is aimed to rigorously manage voltage saturation and maximum current constraints in Shunt Active Filters. In thisrespect, assuming “unconstrained” control algorithms have already been defined to achieve standard objectives for such devices(i.e. current tracking for harmonic compensation and DC-bus voltage boundness), a plug-in unit, oriented to extend the systemoperating region and at the same time preserving good performance under large transients and overload conditions, is presented.This solution allows to improve availability, robustness and composability of Shunt Active Filters, which are expected to be keyfeatures in present and next generation complex and possibly “smart” power grids. The proposed unit is composed by two parts.First, a suitable anti-windup strategy is defined in order to deal with control input saturation. Its main purpose is to preserve theoriginal “unconstrained error dynamics”, in face of input saturation, while guaranteeing low computational burden and reducedperformance impairment (the latter goal, in harmonic compensation context, leads to rather non-standard problem formulation).To this aim, the anti-windup acts on the current references through a suitably-designed additional dynamics. Then, in order to copewith current limitations, an additional strategy has been designed; again the current references is suitably shaped to comply withthe features and bounds of the system, augmented with the above-mentioned anti-windup solution. The proposed scheme can besimply joined to any kind of unconstrained controller adopted to steer Shunt Active Filters. In this work, an Internal-Model-basedcurrent controller is adopted as a benchmark case. The proposed approach is validate through extensive simulation tests.

Extraction of VLSI Multiconductor Transmission Line Parameters by Complementarity

Solving lossy multiconductor transmission line (MTL) equations is of fundamental importance for the design and signal integrity verification of interconnections in VLSI systems. It is well established that the critical issue is the efficient and accurate electrical characterization of the MTLs through the determination of their per-unit-length parameters. In this respect, the so-called complementarity has the potential to become a fast and accurate method for the extraction of these parameters. Besides the value of the parameters, in fact, complementarity provides rigorous error bounds for them. Despite this important feature, commercial software do not use complementarity yet, due to the fact that there are unsolved theoretical issues related to the nonstandard formulation based on the electric vector potential. Some attempts to fill this gap have been already reported. The aim of this paper is to fill this gap by introducing a general formulation based on the electric vector potential highlighting the advantages of complementarity with respect to the standard first- and second-order finite element formulations.

Industry Update: the Latest Developments in Therapeutic Delivery

This month’s snapshot of events in the therapeutic delivery arena covers the period 21 June–21 July 2010 inclusive. Overall it was a highly successful month for companies working in the field, with five products based on nonstandard formulation technologies achieving regulatory approval either in the USA or in the EU. It also saw a number of business negotiations come to fruition, including the announced merger between Biovail and Valeant and the takeover of Abraxis by Celgene. However, the period also witnessed some disappointments, one of the most notable of which is Pfizer’s planned withdrawal of Mylotarg® from the market. The information is sourced from company websites and press releases.

A tabu search with an oscillation strategy for the discriminant analysis problem

This article proposes a tabu search approach to solve a mathematical programming formulation of the linear classification problem, which consists of determining an hyperplane that separates two groups of points as well as possible in ℜ m . The tabu search approach proposed is based on a non-standard formulation using linear system infeasibility. The search space is the set of bases defined on the matrix that describes the linear system. The moves are performed by pivoting on a specified row and column. On real machine learning databases, our approach compares favorably with implementations based on parametric programming and irreducible infeasible constraint sets. Additional computational results for randomly generated instances confirm that our method provides a suitable alternative to the mixed integer programming formulation that is solved by a commercial code when the number of attributes m increases.

NONSTANDARD ANALYSIS, FRACTAL PROPERTIES AND BROWNIAN MOTION

In this paper I explore a nonstandard formulation of Hausdorff dimension. By considering an adapted form of the counting measure formulation of Lebesgue measure, I prove a nonstandard version of Frostman's lemma and find that Hausdorff dimension can be computed through a counting argument rather than by taking the infimum of a sum of certain covers. This formulation is then applied to obtain a simple proof of the doubling of the dimension of certain sets under a Brownian motion.

A comparison of non-standard solvers for ODEs describing cellular reactions in the heart

Mathematical models for the electrical activity in cardiac cells are normally formulated as systems of ordinary differential equations (ODEs). The equations are nonlinear and describe processes occurring on a wide range of time scales. Under normal accuracy requirements, this makes the systems stiff and therefore challenging to solve numerically. As standard implicit solvers are difficult to implement, explicit solvers such as the forward Euler method are commonly used, despite their poor efficiency. Non-standard formulations of the forward Euler method, derived from the analytical solution of linear ODEs, can give significantly improved performance while maintaining simplicity of implementation. In this paper we study the performance of three non-standard methods on two different cell models with comparable complexity but very different stiffness characteristics.