The Weirdness Theorem and the Origin of Quantum Paradoxes

We argue that there is a simple, unique, reason for all quantum paradoxes, and that such a reason is not uniquely related to quantum theory. It is rather a mathematical question that arises at the intersection of logic, probability, and computation. We give our ‘weirdness theorem’ that characterises the conditions under which the weirdness will show up. It shows that whenever logic has bounds due to the algorithmic nature of its tasks, then weirdness arises in the special form of negative probabilities or non-classical evaluation functionals. Weirdness is not logical inconsistency, however. It is only the expression of the clash between an unbounded and a bounded view of computation in logic. We discuss the implication of these results for quantum mechanics, arguing in particular that its interpretation should ultimately be computational rather than exclusively physical. We develop in addition a probabilistic theory in the real numbers that exhibits the phenomenon of entanglement, thus concretely showing that the latter is not specific to quantum mechanics.

[[EQUATION]]-optimal Designs for Hierarchical Linear Models: an Equivalence Theorem and a Nature-inspired Meta-heuristic Algorithm

Hierarchical linear models are widely used in many research disciplines and estimation issues for such models are generally well addressed. Design issues are relatively much less discussed for hierarchical linear models but there is an increasing interest as these models grow in popularity. This paper discusses [[EQUATION]] -optimality for predicting individual parameters in such models and establishes an equivalence theorem for confirming the [[EQUATION]] -optimality of an approximate design. Because the criterion is non-differentiable and requires solving multiple nested optimization problems, it is much harder to find and study [[EQUATION]] -optimal designs analytically. We propose a nature-inspired meta-heuristic algorithm called competitive swarm optimizer (CSO) to generate [[EQUATION]] -optimal designs for linear mixed models with different means and covariance structures. We further demonstrate that CSO is flexible and generally effective for finding the widely used locally [[EQUATION]] -optimal designs for nonlinear models with multiple interacting factors and some of the random effects are correlated. Our numerical results for a few examples suggest that [[EQUATION]] and [[EQUATION]] -optimal designs may be equivalent and we establish that [[EQUATION]] and [[EQUATION]] -optimal designs for hierarchical linear models are equivalent when the models have only a random intercept only. The challenging mathematical question whether their equivalence applies more generally to other hierarchical models remains elusive.

Introduction

This introductory chapter provides a quick review of the basic concepts of general relativity relevant to this work. The main object of Albert Einstein's general relativity is the spacetime. The nonlinear stability of the Kerr family is one of the most pressing issues in mathematical general relativity today. Roughly, the problem is to show that all spacetime developments of initial data sets, sufficiently close to the initial data set of a Kerr spacetime, behave in the large like a (typically another) Kerr solution. This is not only a deep mathematical question but one with serious astrophysical implications. Indeed, if the Kerr family would be unstable under perturbations, black holes would be nothing more than mathematical artifacts. The goal of this book is to prove the nonlinear stability of the Schwarzschild spacetime under axially symmetric polarized perturbations, namely, solutions of the Einstein vacuum equations for asymptotically flat 1 + 3 dimensional Lorentzian metrics which admit a hypersurface orthogonal spacelike Killing vectorfield Z with closed orbits.

Learning Mathematics: One Minute

This game is made with purpose to educate student in terms of mathematical skill combined with fun adventure game. The target audience is the students should be primary-school (10-13 years old). This is an educational game and made on purpose to create a difference method to present solving a mathematical problem to the audience. The user will play a game where the character is chased by a dog and must avoid obstacles such as river. In each level of the game, the user must find a door in which they must solve the mathematical question as pass code. Successful in solving the mathematical question will bring user to another level. This game is made with 3 level and must be completed within 1 minute. This game can be used as a tool for learning. The level of mathematical questions is simple mathematical quiz, designed with objective to teach early age students.

Application-oriented mathematical algorithms for group testing

Group testing is a widely used protocol which aims to test a small group of people to identify whether at least one of them is infected. It is particularly efficient if the infection rate is low, because it only requires a single test if everybody in the group is negative. The most efficient use of group testing is a complex mathematical question. However, the answer highly depends on practical parameters and restrictions, which are partially ignored by the mathematical literature. This paper aims to offer practically efficient group testing algorithms, focusing on the current COVID-19 epidemic.

The Effect of Using The Strategy of Solving The Mathematical Question of Achievement and Motivation Towards Mathematics in The Tenth Grade Students in Jordan: أثر استخدام استراتيجية حل المسألة الرياضية في التحصيل والدافعية نحو مبحث الرياضيات لدى طالبات الصف العاشر الأساسي في الأُردن

The present study aimed to identify the effect of using the strategy of solving the mathematical problem in achievement and motivation to wards mathematics among the tenth grade students in Jordan. The study population consists of (60) students from the tenth grade. The researcher used the semi-experimental method. To achieve the objectives of the study, the test and motivation questionnaire was designed to solve the mathematical problem. The study found that the rewire statistically significant differences in the level of importance (α = 0.05) between the mean of the experimental group and the average of the control group in achievement and motivation due to the use of a strategy to solve a mathematical problem in teaching mathematics for the experimental group. Which encourage students to learn, increasing their motivation to learn, the need for teachers to use strategies to solve the problem, thereby increasing their achievement.

A ousadia do π ser racional

Pi (π) is used to represent the most known mathematical constant. By definition, π is the ratio of the circumference of a circle to its diameter. In other words, π is equal to the circumference divided by the diameter (π = c / d). Conversely, the circumference is equal to π times the diameter (c = π . d). No matter how big or small a circle is, pi will always be the same number. The first calculation of π was made by Archimedes of Syracuse (287-212 BC) who approached the area of a circle using the Pythagorean Theorem to find the areas of two regular polygons: the polygon inscribed within the circle and the polygon within which circle was circumscribed. Since the real area of the circle is between the areas of the inscribed and circumscribed polygons, the polygon areas gave the upper and lower limits to the area of the circle. Archimedes knew he had not found the exact value of π, but only an approximation within these limits. In this way, Archimedes showed that π is between 3 1/7 (223/71) and 3 10/71 (22/7). This research demonstrates that the value of π is 3.15 and can be represented by a fraction of integers, a/b, being therefore a Rational Number. It also demonstrates by means of an exercise that π = 3.15 is exact in 100% in the mathematical question.

Meningkatkan Kemampuan Berpikir Kritis Melalui Problem Posing

<p><em>This study aims to explain how the problem posing approach adopted in the study of mathematics can develop students' critical thinking skills. The method used in this research is literature study (library research). The data in this study is a secondary data such as the results of the research as scientific books, scientific journals, research reports, and other relevant sources. Data analysis techniques in the study include three stages, namely organize, synthesize, and identify.</em></p><p><em>These results showed that the problem posing approach to the stages of learning, among others (1) create a situation of mathematics; (2) create a mathematical question; (3) solve math problem; (4) to apply mathematics, has relevance to the indicators on critical thinking skills, which include interpretation, analysis, evaluation, and decision. Overall, it was concluded that the students' critical thinking skills can be improved by the application of problem posing approach in the learning process.</em></p>