Can Producers’ Price War End Up in an Optimal Allocation?

The paper presents a theoretical framework for the phenomenon of the price war in the context of general equilibrium, with special attention to the production system. The natural question that arises is whether Nash-optimal production plans being the reactions to the changing prices can finally approximate a Nash-optimal production plan at the end of this war. To provide an answer, the production system is described as a parametric-multicriteria game. Referring to some results on the lower semicontinuty of the parametric weak-multicriteria Nash equilibria, we provide a positive answer for the stated problem.

Constructing the three-qudit unextendible product bases with strong nonlocality

The unextendible product bases (UPB) are interesting members of the family of orthogonal product bases. In this paper, we investigate the construction of 3-qudit UPB with strong nonlocality. First, a UPB set in ${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{3}}$ of size 19 is presented based on the Shifts UPB. By mapping the system to a Rubik's Cube, we provide a general method of constructing UPB in ${{C}^{d}}\otimes {{C}^{d}}\otimes {{C}^{d}}$ of size ${{\left(d-1 \right)}^{3}}+2d+5$, whose corresponding Rubik's Cube is composed of four parts. Second, for the more general case where the dimensions of parties are different, we extend the classical tile structure to the 3-qudit system and propose the Tri-tile structure. By means of this structure, a ${{C}^{4}}\otimes {{C}^{4}}\otimes {{C}^{5}}$ system of size 38 is obtained based on a ${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{4}}$ system of size 19. Then, we generalize this approach to ${{C}^{{{d}_{1}}}}\otimes {{C}^{{{d}_{2}}}}\otimes {{C}^{{{d}_{3}}}}$ system which also consists of four parts. Our research provides a positive answer to the open question raised in [Halder, et al., PRL, 122, 040403 (2019)], indicating that there do exist UPB that can exhibit strong quantum nonlocality without entanglement.

Should Violence Against Robots be Banned?

This paper addresses the following question: “Should violence against robots be banned?” Such a question is usually associated with a query concerning the moral status of robots. If an entity has moral status, then concomitant responsibilities toward it arise. Despite the possibility of a positive answer to the title question on the grounds of the moral status of robots, legal changes are unlikely to occur in the short term. However, if the matter regards public violence rather than mere violence, the issue of the moral status of robots may be avoided, and legal changes could be made in the short term. Prohibition of public violence against robots focuses on public morality rather than on the moral status of robots. The wrongness of such acts is not connected with the intrinsic characteristics of robots but with their performance in public. This form of prohibition would be coherent with the existing legal system, which eliminates certain behaviors in public places through prohibitions against acts such as swearing, going naked, and drinking alcohol.

On Jonsson varieties and quasivarieties

In this paper, new objects of research are identified, both from the standpoint of model theory and from the standpoint of universal algebra. Particularly, the Jonsson spectra of the Jonsson varieties and the Jonsson quasivarieties are considered. Basic concepts of 3 types of convexity are given: locally convex theory, ϕ(x)-convex theory, J-ϕ(x)-convex theory. Also, the inner and outer worlds of the model of the class of theories are considered. The main result is connected with the question of W. Forrest, which is related to the existential closed ness of an algebraically closed variety. This article gives a sufficient condition for a positive answer to this question.

Плюригармонические определимые функции в некоторых $o$-минимальных расширениях вещественного поля

In this paper, we first try to solve the following problem: If a pluriharmonic function $f$ is definable in an arbitrary o-minimal expansion of the structure of the real field $\overline{\mathbb{R}}:=(\mathbb{R},+,-,.,0,1,<)$, does this function be locally the real part of a holomorphic function which is definable in the same expansion? In Proposition 2.1 below, we prove that this problem has a positive answer if the Weierstrass division theorem holds true for the system of the rings of real analytic definable germs at the origin of $\mathbb{R}^n$. We obtain the same answer for an o-minimal expansion of the real field which is pfaffian closed (Proposition 2.6) for the harmonic functions. In the last section, we are going to show that the Weierstrass division theorem does not hold true for the rings of germs of real analytic functions at $0\in\mathbb{R}^n$ which are definable in the o-minimal structure $(\overline{\mathbb{R}}, x^{\alpha_1},\ldots,x^{\alpha_p})$, here $\alpha_1,\ldots,\alpha_p$ are irrational real numbers.

THE USE OF VOKOSCREEN AS A LEARNING VIDEO WITH ENGLISH SPEAKING SKILL IN E-LEARNING

The goal of this study is to find out to what extent the Use of Vokoscreen as a Learning Video on students’ speaking skill in E-Learning at SMP Yapidh district Jati Asih. This research used descriptive qualitative method. The participants are 35 students on grade IX at SMP Yapidh. These students are chosen because they would have practical examination. The instruments are observation and interview. The result showed that the most students answered paid attention to the researchers’ explanation, they used vokoscreen application well, they joined actively in learning activity, they made an interesting presentation based on a topic, felt happy using vokoscreen as a learning video, and more confident in speaking English activity. Only a few students could not maximal in this learning because their internet connection and some private problems. The interview result showed that all students said positive answer about their opinion used vokoscreen application on speaking activity. There are 35 participants answered “like” and 2 participants answered dislike. Based on the results of this investigate could conclude that the foremost students on grade nineth at SMPIT Yapidh are propelled and appreciated on speaking activity in e-learning using vokoscreen as learning video, in reality the result of this inquire about demonstrated that the students more certainty and incremen their briefly speaking English.

A Positive Answer for 3IM+1CM Problem with a General Difference Polynomial

In this paper, the 3IM+1CM theorem with a general difference polynomial L z , f will be established by using new methods and technologies. Note that the obtained result is valid when the sum of the coefficient of L z , f is equal to zero or not. Thus, the theorem with the condition that the sum of the coefficient of L z , f is equal to zero is also a good extension for recent results. However, it is new for the case that the sum of the coefficient of L z , f is not equal to zero. In fact, the main difficulty of proof is also from this case, which causes the traditional theorem invalid. On the other hand, it is more interesting that the nonconstant finite-order meromorphic function f can be exactly expressed for the case f ≡ − L z , f . Furthermore, the sharpness of our conditions and the existence of the main result are illustrated by examples. In particular, the main result is also valid for the discrete analytic functions.

Existence of Walrasian equilibria with discontinuous, non-ordered, interdependent and price-dependent preferences, without free disposal, and without compact consumption sets

We extend a result on existence of Walrasian equilibria in He and Yannelis (Econ Theory 61:497–513, 2016) by replacing the compactness assumption on consumption sets made there by the standard assumption that these sets are closed and bounded from below. This provides a positive answer to a question explicitly raised in He and Yannelis (Econ Theory 61:497–513, 2016). Our new equilibrium existence theorem generalizes many results in the literature as we do not require any transitivity or completeness or continuity assumption on preferences, initial endowments need not be in the interior of the consumption sets, preferences may be interdependent and price-dependent, and no monotonicity or local non satiation is needed for any of the agents.

From absolute nonsense to the world’s operating system

Informatics, its artefacts and methods, have fundamentally changed our society and world, from the individual personal level up to the current geo-political powerplay between the US, China and Europe. Information Technology serves as the operating system of our society. This change has happened over the last 30 – 40 years, and the result should be compared with our historic views and expectations. At the same time, despite the enormous success of our discipline, it has serious shortcomings. I discuss some of them, especially the issue of online platforms, and describe a positive “answer”: Digital Humanism. This approach does not only describe and analyze the man – machine relationship, but also underlines the importance of humans in this development: we have to interfere – technology is not god given. This fundamental idea is already supported by a growing number of academics and practitioners from different disciplines and fields.