FACTORS AND LEVELS ON DESIGN OF EXPERIMENT, EFECTIVE CHOICE UNDER CONSTRAINS

The problem of design of experiment with resource constraints is investigated. For a complex system intended for experimental research, before using the well known advanced methods of factorial design, you must first create a simplified mathematical model that represents an incomplete abbreviated description of the system. At the same time, on this simplification from all objectively existing independent parameters of the system remain only the most important parameters, which is a forced procedure due to the natural limitations of the resources available to perform the experimental study. The same constraints limit the number of values assigned to each of the parameters (factor levels number). The article is devoted to the modification of the existing method of discretization of such a model with a rational choice of discretization parameters in accordance with the existing limitations, but with an extremely unreliable in terms of convergence iterative solution procedure. The main ideas of the modified approach are as follows: 0) The choice of the number of levels of factors is proportional to the importance of the relevant parameters and the reduction to the problem of finding a fixed point (as in the known method). 1) Probability partition (instead of partition into equal length intervals) for discretization and selection of representative values of the parameter, which allows to find an exact simple expression for its Shannon entropy. 2) Transition from multi- to one-parameter (coefficient of proportionality as an indicator of parameterization) representation of nonlinear mapping, its decomposition and simplification of the iterative process. 3) Finding the initial value of the coefficient of proportionality for a factor with average relevance and calculations for other factors, followed by iterative refinement. The iterative process is guaranteed to coincide, because the consideration of small and large values of the scalar parameter allows us to use the theorem on the intermediate value of a continuous function. Then, with the help of the developed procedure, two tasks on the assignment of the number of factor levels for situations with small and large resource constraints are solved, the corresponding complications in the calculations and ways to overcome them are indicated.

Statistical theory of catalytic hydrogen oxidation processes. Basic equations

A statistical description for the processes of catalytic hydrogen oxidation is proposed taking into account the reaction--diffusion processes for magnetoactive ions and atoms adsorbed on the metal surface. The basic non-Markov transfer equations are obtained for the abbreviated description parameters of reaction-diffusion processes for magnetoactive ions and atoms adsorbed on the metal surface in the method of nonequilibrium statistical Zubarev operator. Weakly nonequilibrium reaction-diffusion processes are also considered.

The renin–angiotensin system: An integrated view of lung disease and coagulopathy in COVID-19 and therapeutic implications

The renin–angiotensin system (RAS) has long been appreciated as a major regulator of blood pressure, but has more recently been recognized as a mechanism for modulating inflammation as well. While there has been concern in COVID-19 patients over the use of drugs that target this system, the RAS has not been explored fully as a druggable target. The abbreviated description of the RAS suggests that its dysregulation may be at the center of COVID-19.

The Valuation Of Losses: Contrasting Views

Forensic economists often present to the courts an estimate of the value of amounts required to compensate for particular losses. Such estimates, dependent upon particular sets of unique circumstances, the timing of benefits and losses, and the replacement cost of the value of the specific losses sustained, vary over a wide range.Wide variations in these estimates, no matter the validity of the amounts projected, may prevent acceptance of any specific estimate by the judicial system. That is, the constraints imposed by the institutional structure of the judicial system may act to restrict the acceptability of properly estimated, economically justifiable estimates.Thus, if victims are "to be made whole" (a non-conflicting goal of both the courts and forensic economists) means to rectify institutional alienation must be developed and maintained. The Primary goal of this paper is to, at least in part, provide some insight into accomplishing this goal. In doing this, the following procedure is being followed: first, following an introduction an abbreviated description of the methods used by economists when making their estimates is provided; second, the legal-institutional criteria imposed by the legal system and used to determine the acceptability of any given estimate is outlined; and, third a means of forecasting the legal acceptability of any specific economic estimate is presented. The economist can then use that knowledge when preparing testimony, thus increasing the probability that the resulting decision will better meet the standards imposed by the judicial system, without violating economic norms.

Succeeding in School: A Qualitative Study of Primarily American Indian Students’ Use of an Online Intervention

This article provides an abbreviated description of a qualitative study of the Succeeding in School (SIS) program, an Internet-based intervention designed to help students reflect on key elements of academic and career success. The American School Counselor Association's National Standards call for school counselors to focus on the academic, career, and personal/social development of students. Strengths-Based School Counseling (Galassi & Akos, 2007) suggests that school counselors should implement that call through promoting context-based development for all students, promoting individual student strengths, and promoting strengths-enhancing environments. Students used the SIS program to identify personal strengths and characteristics, as well as strengths-enhancing aspects of their environment useful for achieving academic and career success.

A Brief History of the Yield Stress

This short article is a summary of a recently published, lengthy review [1] in which the author challenges the often-accepted view that materials have yield stresses, below which no flow takes place. However, following the introduction of the new generation of controlled-stress rheometers it is shown that when careful measurements are made below the supposed ’yield stress‘, flow does actually take place. The argument for the nonexistence of the yield stress as a physical entity now seems insuperable. However, in spite of this, it is nevertheless accepted that an apparent yield stress is a useful mathematical abbreviated description of limited data over a given range of flow conditions. This yield stress parameter can be used effectively for predicting flow, but only within the region of the original measurement that furnished the yield stress.