Inverses and n-uncial property of Jacobian elliptic functions

The inverses of Jacobi elliptic functions possess an apparently-non-crucial property: they provide almost-everywhere-conformal maps on a hemisphere onto a torus and so, onto a parallelogram. Thus, they produce map projections on the sphere generalizing the famous quincuncial projection of Charles S. Peirce. Besides providing a general practical definition of n-uncial map and proving that all the considered inverse elliptic functions are n-uncial, we give operative handy formulas to calculate these maps. To the best of our knowledge, these useful formulas have not been all together published before, except for Pierce projection. We look forward to their numerical implementation. By the way, we also classify the resulting map projections according the number of singularities.

PROOFS OF URYSOHN’S LEMMA AND THE TIETZE EXTENSION THEOREM VIA THE CANTOR FUNCTION

Urysohn’s lemma is a crucial property of normal spaces that deals with separation of closed sets by continuous functions. It is also a fundamental ingredient in proving the Tietze extension theorem, another property of normal spaces that deals with the existence of extensions of continuous functions. Using the Cantor function, we give alternative proofs for Urysohn’s lemma and the Tietze extension theorem.

A Computational Study on Fairness of the Tendermint Blockchain Protocol

Fairness is a crucial property for blockchain systems since it affects the participation: the ones that find the system fair tend to stay or enter, the ones that find the system unfair tend to leave. While current literature mainly focuses on fairness for Bitcoin-like blockchains, little has been done to analyze Tendermint. Tendermint is a blockchain technology that uses a committee-based consensus algorithm, which finds an agreement among a set of block creators (called validators), even if some are malicious. Validators are regularly selected to the committee based on their investments. When a validator does not have enough asset to invest, it can increase it with the help of participants that delegate their assets to the validators (called delegators). In this paper, we implement the default Tendermint model and a Tendermint model for fairness in a multi-agent blockchain simulator where participants are modeled as rational agents who enter or leave the system based on their utility values. We conducted experiments for both models where agents have different investment strategies and with various numbers of delegators. In the light of our experimental evaluation, we observed that while, for both models, the fairness decreases and the system shrinks in the absence of delegators, the fairness increases, and the system expands for the second model in the presence of delegators.

Efficiency of Novel Photocatalytic Coating and Consolidants for Protection of Valuable Mineral Substrates

In the process of protection and consolidation of valuable materials, the efficiency is the crucial property that needs to be considered. TiO2/ZnAl layered double hydroxide (LDH) coating and silicate- and carbonate-based consolidants were synthesized and proposed to be used for protection and consolidation of four porous mineral substrates: brick, stone, render and mortar. The photocatalytic efficiency of TiO2/ZnAl LDH coating, as well as consolidation efficiency of two consolidants, both applied on model substrates, were studied. The photocatalytic coating showed significant activity and performed well after the durability tests involving rinsing and freezing/thawing procedures. After treatment with both consolidants, a serious enhancement of consolidation of the used substrates was found. On the other hand, the application of TiO2/ZnAl LDH, as well as consolidants, caused negligible changes in the water vapour permeability values and in appearance of the porous mineral substrates, indicating a high level of compatibility.

Evolution of the reactive surface area of ferrihydrite: time, pH, and temperature dependency of growth by Ostwald ripening

Surface area is a crucial property of ferrihydrite that has been assessed by probing it with PO4.

Sign-reference equivalence research methods in humans and animals

Human language based on symbolization or sign-referent equivalence relations. The paper focuses on methods of studying the process of developing of sign-referent equivalence. Subject is trained in Matching-To-Sample task: for example, reinforcing of stimulus B if the sample was A, and stimulus D if the sample was C. Following test allows to reveal if new relations (for example, symmetry, if subject chooses stimulus A if the sample was B) appeared spontaneously. Human subjects usually pass this test successfully. This result may be explained by repeated demonstration of sign-referent symmetry during language learning and using. Our paper is dedicated to methods features which can be used to study sign-reference developing in human and animals. We discuss factors that leads to appearance of this crucial property of stimulus equivalence.

Combinatory logic

Combinatory logic comprises a battery of formalisms for expressing and studying properties of operations constitutive to contemporary logic and its applications. The sole syntactic category in combinatory logic is that of the applicative term. Closed terms are called ‘combinators’; there is no binding of variables. Systems containing the basic combinators S and K exhibit the crucial property of combinatorial completeness: every routine expressible in the system can be captured by a term composed of these two combinators alone. Combinatory logic is a close relative of Church’s lambda calculus. M. Schönfinkel first introduced and defined basic combinators in 1920 in assaying foundations for mathematics that avoid bound variables and take operations, rather than sets, as fundamental. H. Curry later rediscovered the combinators (and coined the term ‘combinatory logic’) independently of Schönfinkel. Curry constructed various formal systems for combinatory logic and, throughout most of the subject’s history, was the central figure in the research. In 1969, D. Scott succeeded in constructing set-theoretic, functional models for the lambda calculus and combinatory logic. Since then semantic studies of combinatory systems, together with research on their applications to computer science and further development as foundational systems, have dominated the field.

Deception

Recent events that revolve around fake news indicate that humans are more susceptible than ever to mental manipulation by powerful technological tools. In the future these tools may become autonomous. One crucial property of autonomous agents is their potential ability to deceive. From this research we hope to understand the potential risks and benefits of deceptive artificial agents. The method we propose to study deceptive agents is by making them interact with agents that detect deception and analyse what emerges from these interactions given multiple setups such as formalisations of scenarios inspired from historical cases of deception.

Electrochemical oxidation stability of anions for modern battery electrolytes: a CBS and DFT study

The electrochemical stability vs. oxidation is a crucial property of anions in order to be suitable as components in lithium-ion batteries.