Inaccuracy in arc power calculation through a product of voltage and current averages

Power is an indirect measurand, determined by processing voltage and current analogue signals through calculations. Using arc welding as a case study, the objective of this work was to bring up subsidies for power calculation. Based on the definitions of correlation and covariance in statistics, a mathematical demonstration was developed to point out the difference between the product of two averages (e.g. P = $$\overline{U} x \overline{I}$$ U ¯ x I ¯ ) and the average of the products (e.g. P = ($$\overline{UxI}$$ UxI ¯ ). Complementarily, a brief on U and I waveform distortion sources were discussed, emphasising the difference between signal standard deviations and measurement errors. It was demonstrated that the product of two averages is not the same as the average of the products, unless in specific conditions (when the variables are fully correlated). It was concluded that the statistical correlation can easily flag the interrelation, but if assisted by covariance, these statistics quantify the inaccuracy between approaches. Finally, although the statistics' determination is easy to implement, it is proposed that power should always be calculated as the average of the instantaneous U and I products. It is also proposed that measurement error sources should be observed and mitigated, since they predictably interfere in power calculation accuracy.

Non velut Reges, sed ministros et praecones veritatis: Pastor in the Early Modern Philosophical Discourse

Early Modern philosophy pays some attention to the image of minister of reli­gion. While its anticlericalism is well known, the positive program of pastor seems to be neglected. This article considers the structure and grounds of this positive image, concentrating on the texts of Hobbes, Spinoza and Pufendorf. It argues that the universal and yet subjective natural light turns out to be the key element for the image of pastor. The method of mathematical demonstration al­lows early Modern philosophers to establish the clear and distinct grounds of morality. They demand the same basis for the pastoral care that should consist of teaching and preaching. The same universal and subjective grounds underlie the division of power and authority between sovereign and individual. Conse­quently, pastor is deprived of any form of power except for the power of demon­stration. The doctrine preached by the pastor should be coherent to the natural light. The use of eloquence or any (other) form of coercion is not allowed for him. Otherwise this doctrine is designated as superstition, i.e. political, moral and epistemic evil. This kind of reasoning brings the pastor under control of in­stances of the reason (represented e.g. by the philosophers) and the sovereign. Finally, the assumption is made that the structure of this ideal Early Modern pas­tor sets the limits of rational-legal order of authority of the religious leader.

Demonstration in geometry: historical and philosophical perspectives

In this article, we weave historical-philosophical reflections about demonstration in mathematics, based on works of researchers that discuss the different philosophical perspectives on the topic, more specifically on geometry. We focus first on demonstration and its relationship with intuition and figural representations. Second, we criticize Poincaré’s conception of mathematical demonstration. Third, we reflect, in a non-exhaustive way, on the philosophy of demonstration in geometry, confronting Kant’s conceptions with the axiomatizations of the non-Euclidean geometries. In this text, we do not adopt a single definition that would cover all modes of scientific validation, since we admit the possibility of an evolution of ideas about the validity of a proposition. Not to fall into the symmetrical flaws of the glorification of the Ancients or even being ungrateful to them, we must start from the naive idea that the demonstration has a historical origin and, therefore, maintains a historical character, but we should be more attentive to what characterizes, in its particularity or even its uniqueness, the productions of past and present centuries. Keywords: Philosophy of demonstration; Axiomatization; Induction; Intuition; Representation.

Demonstration of time dilation using the centripetal acceleration of a clock

A mathematical demonstration is made to derive the inverse form of the Lorentz factor using as a tool the centripetal acceleration of a clock hand. When a resistance is applied against the motion of a clock hand, the centripetal acceleration decreases. The ratio between the final centripetal acceleration of the clock hand and its initial centripetal acceleration gives a ratio between two squared velocities. By squaring root this ratio, we obtain the equivalent form of the inverted Lorentz factor.

Discounted Cash Flow Methods in Lease versus Purchase Analysis—A Technical Note

The earlier framework uses the before-tax cost of debt as the discount rate in valuation of lease contracts for the reason that such framework explicitly includes the interest tax credits as a component of each period’s cash flows. The short-cut or modern standard textbook approaches use after-tax cost of debt as the discount rate for the reason that it ignores the interest tax credits. Some existing literatures state the two approaches are equivalent without exploring the reasons analytically. This note provides a mathematical demonstration showing, the two approaches are not equivalent accompanied by numerical examples.

The constitution of physics and the certainty of mathematics in the 16th century scholastic philosophy

Traditionally, it is believed that one of the most important phenomena in the history of "new" science, i.e. the science of Early Modern times, is the emergence of mathematical natural science. However, in the 16th century the status of physics and mathematics within the framework of scientific knowledge was far from being so unambiguous. In this article, we consider and analyze the arguments of the late Peripatetic author of the late 16th century – the learned Jesuit Benedict Pereira – in favor of his thesis about "non-scientific character" of mathematical disciplines. These arguments focus not on the weaker (less perfect) status of the reality of the mathematical object, but on the nature of mathematical demonstration and mathematical knowledge as such. Pereira shows in detail that mathematics does not meet the criteria of scientific knowledge (in the sense of "Second Analytics"), because the middle terms in its demonstrations are non-proper, general and accidental, and mathematics itself is not a knowledge of the real causes. In sum, in Pereira's consideration mathematics turns out to be some sort of “operational art” rather than a necessary knowledge of the truth from real causes. A comparison of the scientific status of physical and mathematical knowledge in Pereira makes it possible to clarify the conditions for the emergence of modern mathematical physics.

A Mathematical Demonstration of the Viability of Profit/Loss Sharing as a Debt Alternative in Presence of Market Frictions

We posit a simple mathematical model to show that a profit-and-loss sharing contract can be formed between a capital seeker and capital provider as a potential alternative to institutional debt financing. The major methodological tool used is that of Nash bargaining; utilising the matching theory proposition of Pissarides (2000). Our posited model demonstrates that a ‘match’ between a capital seeker and a capital provider can occur even in the presence of embedded market frictions arising out of information asymmetries as are especially rife in the emerging markets. This is an important result especially for marginal borrowers in emerging economies and we present supporting empirical evidence that indicates profit-and-loss sharing being increasingly seen as an effective alternative financing to long-term borrowing. JEL Classification: C78, D53, G23

Alternative demonstration of the entropy evolution in least time

Open systems evolve towards states of greater entropy, so they come into balance with their surroundings. Also, this evolution occurs in least time. This work presents a mathematical demonstration of this principle.

On the improvement of computational accuracy during the construction of transportation lines

Objective: To obtain analytic dependences for profile cubage volume calculation of subgrades (side hill fills), ditch cuts (side hill cuts), as well as borrow pits, soil banks, drainage ditches and other structures. Methods: Integral calculus and stereometry was applied. Results: New analytic dependencies for profile cubage volume calculation of subgrades (side hill fills), ditch cuts (side hill cuts), borrow pits, soil banks and drainage ditches were deducted. Relative errors of calculating the given profile cubage volume were determined in comparison with conventional methods for calculating the values in question. Mathematical demonstration of the given analytic dependencies, as well as the analysis of the latter was carried out. Practical importance: Computational accuracy of profile cubage volume of subgrades (side hill fills), ditch cuts (side hill cuts), borrow pits, soil banks and drainage ditches may be improved based on the examined dependencies. Research results may be applied in the design of information systems. The latter promptly implement the introduced analytic dependencies of more effective calculation indices and test planning of large earthwork volumes.