In this paper we are concerned with cuts in models of Samuel Buss' theories of bounded arithmetic, i.e. theories like $S_{2}^i$ and $T_{2}^i$. In correspondence with polynomial induction, we consider a rather new notion of cut that we call p-cut. We also consider small cuts, i.e. cuts that are bounded above by a small element. We study the basic properties of p-cuts and small cuts. In particula...

We revisit 't Hooft anomalies in (1+1)$d$ non-spin quantum field theory, starting from the consistency and locality conditions, find that consistent U(1) gravitational cannot always be canceled by properly quantized (2+1)$d$ classical Chern-Simons actions. On one hand, we prove certain exotic can only realized non-reflection-positive or non-compact theories; on other without insisting reflectio...

We consider representations of meromorphic bosonic chiral conformal field theories, and demonstrate that such a representation is completely specified by a state within the theory. The necessary and sufficient conditions upon this state are derived, and, because of their form, we show that we may extend the representation to a representation of a suitable larger conformal field theory. In parti...

We compute gravitational and axial anomaly for D-type (2, 0) theories realized on N pairs of coincident M5-branes at R/Z2 orbifold fixed point. We first summarize work by Harvey, Minasian, and Moore on A-type (2, 0) theories, and then extend it to include the effect of orbifold fixed point. The net anomaly inflow follows when we further take into account the consistency of T /Z2 M-theory orbifo...

introduction: reflection is considered as a critical characteristic in professional competitions. despite propagation of reflection as an important educational issue and existence of several helpful patterns, instructions conducted by teachers to explaining and expanding of it, are very little. studies related to this topic were mainly performed in the field of nursing. therefore, we decided to...

Abstract The current paper studies the formal properties of Global Reflection Principle, to wit assertion “All theorems $\mathrm {Th}$ are true,” where is a theory in language arithmetic and truth predicate satisfies usual Tarskian inductive conditions for formulae arithmetic. We fix gap Kotlarski’s proof from [15], showing that Principle Peano Arithmetic provable compositional with bounded ind...

In the present paper, the problem of light reflection from a birefringent medium and thin film is considered. First, the analytical equations governing the propagation of a plane and harmonic electromagnetic wave in an infinite, birefringent, linear, non-dispersive, non-absorbing, and non-magnetic medium is derived from Maxwell equations. Then, using phase matching condition and boundary condit...