Reflection Positive Doubles

Here we introduce reflection positive doubles, a general framework for reflection positivity, covering a wide variety of systems in statistical physics and quantum field theory. These systems may be bosonic, fermionic, or parafermionic in nature. Within the framework of reflection positive doubles, we give necessary and sufficient conditions for reflection positivity. We use a reflection-invariant cone to implement our construction. Our characterization allows for a direct interpretation in terms of coupling constants, making it easy to check in concrete situations. We illustrate our methods with numerous examples.Comment: 53 pages, 3 figure

Reflection positive doubles

Here we introduce reflection positive doubles, a general framework for reflection positivity, covering a wide variety of systems in statistical physics and quantum field theory. These systems may be bosonic, fermionic, or parafermionic in nature. Within the framework of reflection positive doubles, we give necessary and sufficient conditions for reflection positivity. We use a reflection-invariant cone to implement our construction. Our characterization allows for a direct interpretation in terms of coupling constants, making it easy to check in concrete situations. We illustrate our methods with numerous examples

Tropicalization of classical moduli spaces

The image of the complement of a hyperplane arrangement under a monomial map can be tropicalized combinatorially using matroid theory. We apply this to classical moduli spaces that are associated with complex reflection arrangements. Starting from modular curves, we visit the Segre cubic, the Igusa quartic, and moduli of marked del Pezzo surfaces of degrees 2 and 3. Our primary example is the Burkhardt quartic, whose tropicalization is a 3-dimensional fan in 39-dimensional space. This effectuates a synthesis of concrete and abstract approaches to tropical moduli of genus 2 curves.Comment: 33 page

After All, Africa is Largely a Nonliterate Continent : The Reception of Vatican II in Africa

The article examines critical factors that determined the impact, reception, and implementation of Vatican II in Africa. Drawing on historical accounts, the author identifies and analyzes personalities, contexts, and issues that conditioned and shaped Africa\u27s participation in the council. Looking back 50 years, he argues that while the continent\u27s participation was negligible, shaped by a combination of events and attitudes that either facilitated or hampered reception, concrete examples abound of how the council generated impetus for growth, renewal, and reform in inculturation, interreligious dialogue, theological reflection, and ecclesial collaboration in Africa

Development of Microstrip Antenna Sensor for Concrete

The microwave reflection type sensor using microstrip disk antenna is developed. The purpose of developing the sensor is to monitor the fresh concrete hardening and to determine concrete curing point. The structure of microstrip disk antenna is divided into three parts i.e. radiation surface, substrate and ground plane. This antenna is developed from polytetra fluoroethlene (PTFE) or random micro fibre glass substrate (RTD 5880) with dielectric constant &r = 2.2. The RTD 5880 substrate is selected based on its suitability to operate at the resonant frequency of 10.7 GHz. In developing the microstrip antenna, parameters such as radius of disk, resonant frequency, resistance at resonance, total quality factor, efficiency and bandwidth has to be taken into consideration. The difference between calculation and experimental results of the resonant frequency and resistance at resonance is about 5%. The measurements on fresh concrete and concrete curmg are done in via two techniques namely contact and non-contact. The samples were prepared based on water to cement ratio 0.5, 0.55 and 0.6. These samples are left to dry in natural condition and at room temperature for 1, 3, 7, 14 and 28 days. The results of both techniques showed that reflection from non-contact technique have readings higher than 100 mW and was more stable compared to contact technique. The non-touching technique was also easy to manage when applied to fresh concrete compared to the touching technique. Studies had shown that the power reflection is inversely proportional with concrete curing time. Significant power reflection reduction had occurred during the first three days of curing process. This phenomena was due to accelerated hydration process that happening inside the concrete during that period. As the curing process resumed, hydration process slowed down then reaching approximately a constant rate. It is during this period that the concrete had hardened and gained its strength. Realising the relationship between microwave, moisture content inside the concrete and concrete strength, the microwave moisture sensor is developed to measure the water or moisture content. This approach can be utilized as a technique in non-destructive testing for concrete to monitor concrete hardening process and predict the anticipated concrete strength in order to fulfill design requirement

Integrable Matrix Product States from boundary integrability

We consider integrable Matrix Product States (MPS) in integrable spin chains and show that they correspond to "operator valued" solutions of the so-called twisted Boundary Yang-Baxter (or reflection) equation. We argue that the integrability condition is equivalent to a new linear intertwiner relation, which we call the "square root relation", because it involves half of the steps of the reflection equation. It is then shown that the square root relation leads to the full Boundary Yang-Baxter equations. We provide explicit solutions in a number of cases characterized by special symmetries. These correspond to the "symmetric pairs" $(SU(N),SO(N))$ and $(SO(N),SO(D)\otimes SO(N-D))$, where in each pair the first and second elements are the symmetry groups of the spin chain and the integrable state, respectively. These solutions can be considered as explicit representations of the corresponding twisted Yangians, that are new in a number of cases. Examples include certain concrete MPS relevant for the computation of one-point functions in defect AdS/CFT.Comment: 33 pages, v2: minor corrections, references added, v3: minor modifications, v4: minor modification

Fixed Point Algebras for Easy Quantum Groups

Compact matrix quantum groups act naturally on Cuntz algebras. The first author isolated certain conditions under which the fixed point algebras under this action are Kirchberg algebras. Hence they are completely determined by their $K$-groups. Building on prior work by the second author, we prove that free easy quantum groups satisfy these conditions and we compute the $K$-groups of their fixed point algebras in a general form. We then turn to examples such as the quantum permutation group $S_n^+$, the free orthogonal quantum group $O_n^+$ and the quantum reflection groups $H_n^{s+}$. Our fixed point-algebra construction provides concrete examples of free actions of free orthogonal easy quantum groups, which are related to Hopf-Galois extensions