Modeling working processes of the marine thruster of the PMM-2M ferry-bridge machine

Objective. The article deals with aspects of modeling the working processes occurring in marine thrusters of amphibious vehicles, taking into account the specifics of their operation. Methods. The methods of 3D modeling of propellers in CAD and CAE packages are applied, which can determine and optimize the parameters of ongoing work processes with reliable accuracy. Results. A mathematical construct is proposed that allows calculating the characteristics of marine thrusters of amphibious vehicles. The propeller is designed to provide more thrust compared to the original design, making it possible to increase the speed of movement on the water and reduce the radius of circulation when moving through the water. The calculated version of the propeller provides an increase in thrust by 36%, allows developing a high speed on the water, and significantly reduces the radius of circulation of the ferry-bridge machine when maneuvering on the water. Conclusion. The proposed option for increasing the speed and maneuverability of ferry vehicles on the water is the most effective and least expensive; a promising direction for further research to achieve maximum efficiency is the creation and verification of software, hardware, and methodological complexes for modeling the joint operation of the "marine thruster - hull - power plant" system.

The Einstein and Landau‐Lifshitz pseudotensors—A mathematical note on existence

For a closed system, the conservation of energy and momentum has been affirmed through a vast array of experiments. In an attempt to reconcile the General Theory of Relativity with these findings, Einstein constructed, ad hoc, his so-called pseudotensor [A. Einstein, Ann. Phys. 49, 769 (1916)]. Yet this solution fell outside the tensorial mathematical structure of his theory. Landau and Lifshitz also constructed, ad hoc, an even more complex pseudotensor, as a proposed improvement upon the work of Einstein [The Classical Theory of Fields (Addison-Wesley Press, Inc., Cambridge, MA, 1951)]. Their pseudotensor is symmetric, unlike that proposed by Einstein. They advance that their pseudotensor yields a conservation law which also included angular momentum. However, once again, this approach leads to a mathematical construct which is not a tensor and thereby falls outside the very mathematical structure of Einstein’s theory. Both pseudotensors, whether that advanced by Einstein or by Landau and Lifshitz, violate the rules of pure mathematics and therefore can hold no place in physics.

Saccade vigor partly reflects the subjective economic value of the visual stimulus

Decisions are made based on the subjective value that the brain assigns to options. However, subjective value is a mathematical construct that cannot be measured directly, but rather inferred from choices. Recent results have demonstrated that reaction time and velocity of movements are modulated by reward, raising the possibility that there is a link between how the brain evaluates an option, and how it controls movements toward that option. Here, we asked people to choose among risky options represented by abstract stimuli, some associated with gain, others with loss. From their choices in decision trials we estimated the subjective value that they assigned to each stimulus. In probe trials, they were presented with a single stimulus at center and made a saccade to a peripheral location. We found that the reaction time and peak velocity of that saccade varied roughly linearly from loss to gain with the subjective value of the stimulus. Naturally, participants differed in how much they valued a given stimulus. Remarkably, those who valued a stimulus more, as evidenced by their choices in decision trials, tended to move with greater vigor in response to that stimulus in probe trials. Thus, saccade vigor partly reflected the subjective value that the brain assigned the stimulus. However, the influence of subjective value on vigor was only a modest predictor of preference: vigor in probe trials allowed us to predict choice in decision trials with roughly 60% accuracy.New and NoteworthyWe found that saccade vigor tends to vary monotonically with subjective value: smallest for stimuli that predict a loss, and highest for stimuli that predict a gain. Notably, between-subject differences in valuation could be gleaned from the between-subject differences in their patterns of vigor. However, the influence of subjective value on vigor was modest, allowing partial ability to infer subjective value for the purpose of predicting choice in decision trials.

Basic Concepts for Game Theory

Game theory has been variously described as the science of strategy or that of conflict resolution. At its core, it has the characteristics of a mathematical construct: a clear set of concepts and assumptions, fundamental theorems, and applications to real world issues. The fact that the issues in question are mostly the domains of the social sciences, however, places game theory in a peculiar position compared to other mathematical and scientific disciplines. Following von Neumann and Morgenstern's book, it is customary to analyze what we call game situations by using parlor games—already existing ones or ones specially constructed for this very purpose—as analytical models. This chapter does this.

On the Need for a Certain Physicality from Quantum Theory

Many attempts have been made at the unification of General Relativity (GR) and Quantum Theory (QT), but there is a fundamental error made with these attempts, as we will discuss. What is the point of such theories? Well, obviously to describe the physical world we live in. QT describes what happens on the tiny scale, and GR describes what happens to bodies on a large scale. The fundamental error in unifying the two subjects is that QT doesn’t provide the physical happenings for GR to work, or in other words, QT describes why the world is the way it is, but not how, and this does not philosophically suffice in GR. Must we simply give up, in that the subjects are two different entities? I think the answer is that we mustn’t. I think that we should put one theory in terms of the basic mechanics of the other, perhaps by simplifying, or perhaps by taking the physical reality to be our guide. Do I believe QT describes the world? Accurately. Do I believe that QT is the physical truth? Of course not… it is simply a mathematical construct to provide a model that allows for us to predict future outcomes. I will begin very simplistic, but the goal for the first part of the paper is to Classically describe the physical mechanics of QT. I will stick with particles in their ground state, and hence no translational motion.

Knowledge Creation

The paradox of knowledge creation is the fact that we don't know yet what knowledge is and how to deal with it from the managerial point of view. The Gordian knot of this reality is represented by the nature and understanding of the dynamics between information and knowledge. In the realm of information science and philosophy the concept of information had been introduced by C. E. Shannon as a mathematical construct in order to solve engineering communication problems. In the realm of epistemology and knowledge management, the central concept of another continuum is knowledge. The continuum is defined as the Data-Information-Knowledge-Wisdom (DIKW) hierarchy. Information in this new continuum is not the same as information from the communication theory, and that generates a lot of confusion among researchers and practitioners. The authors present the main ideas of the DIKW hierarchy and of the centrality of knowledge.

Basic Concepts for Game Theory

Game theory has been variously described as the science of strategy or that of conflict resolution. At its core, it has the characteristics of a mathematical construct: a clear set of concepts and assumptions, fundamental theorems, and applications to real world issues. The fact that the issues in question are mostly the domains of the social sciences, however, places game theory in a peculiar position compared to other mathematical and scientific disciplines. Following von Neumann and Morgenstern's book, it is customary to analyze what we call game situations by using parlor games—already existing ones or ones specially constructed for this very purpose—as analytical models. This chapter does this.

NONCONNECTEDNESS OF THE SET OF BANKRUPTCY-FREE MONEY EQUILIBRIA IN THE STATIC ECONOMY: A CONSTRUCTIVE EXAMPLE

A static economy in which nominal taxes and transfers are balanced, as proposed by Balasko and Shell (1993), typically has a continuum of equilibrium money prices. This paper presents a constructive example in which the set of equilibrium money prices is not connected. By allowing negative consumption as a mathematical construct, closed form solutions for equilibrium tax-adjusted income are derived. The main result of the example implies that bankrupt taxpayers with negative tax-adjusted income can be free from bankruptcy as the price of money increases. This paradoxical outcome is similar to that of the transfer paradox, as suggested by Gale (1974), where tax-transfer plans make taxpayers better off.

Preliminary Imaging of Red Blood Cells in Turbulent Flow

Considerable uncertainty exists about how momentum and energy are transferred to cells in turbulent flow, which has been shown to cause six times more damage to red blood cells (RBC’s) than laminar flow with the same mean wall shear stress [Kameneva, et al. 2004]. Though it is a purely mathematical construct to yield closure of the time-averaged Navier-Stokes equation for a continuum fluid, which is not valid at the scale of the cell, Reynolds stress has been used as an empirical indicator for damage potential [Sallam & Hwang 1984]. Other scales, including local viscous stress [Jones 1995], flow of plasma around inertia cells [Quinlan & Dooley 2007], shear within eddies [Quinlan & Dooley 2007] and shear between rigid cells within an eddy [Antiga & Steinman 2009], have been forwarded. To provide data to validate these models, an imaging system was assembled to directly observe RBC’s in turbulent flow under a microscope.