Related papers: An Ultimate Hyperfinite Ultralogic Unification for…
Given a group satisfying sufficient finiteness properties, we discuss a group algebra criterion for vanishing of all its cohomology groups with unitary coefficients in a certain degree.
New sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper.
The standard model of particle physics is marvelously successful. However, it is obviously not a complete or final theory. I shall argue here that the structure of the standard model gives some quite concrete, compelling hints regarding…
The topological classification of all known non-magnetic crystalline compounds is now complete, revealing thousands of new candidate topological materials waiting to be explored in the lab.
The paper gives the main lines of a general theory for physical measurements.
We construct super Yang-Mills theories with extended supersymmetry on hypercubic lattices of various dimensions keeping one or two supercharges exactly. Gauge fields are represented by ordinary unitary link variables, and the exact…
We show that every (not necessarily saturated) fusion system can be realized as a full subcategory of the fusion system of a finite group. This result extends our previous work \cite{Park2010} and complements the related result…
We show the rigid singularity theorem, that is, a globally hyperbolic spacetime satisfying the strong energy condition and containing past trapped sets, either is timelike geodesically incomplete or splits isometrically as space $\times$…
The unification of gauge couplings suggests that there is an underlying (supersymmetric) unification of the strong, electromagnetic and weak interactions. The prediction of the unification scale may be the first quantitative indication that…
The derivation of reduced MHD models for fusion plasma is here formulated as a special instance of the general theory of singular limit of hyperbolic system of PDEs with large operator. This formulation allows to use the general results of…
Effective field theories exploit a separation of scales in physical systems in order to perform systematically improvable, model-independent calculations. They are ideally suited to describe universal aspects of a wide range of physical…
Tate cohomology has been generalised by several authors using different constructions that have applications in group theory, ring theory and homotopical algebra. Therefore, there is a need for a uniform account that explains why their…
We study Euclidean lattice formulations of non-gauge supersymmetric models with up to four supercharges in various dimensions. We formulate the conditions under which the interacting lattice theory can exactly preserve one or more nilpotent…
We present new algorithm for computing the union and intersection of all justifications for a given ontological consequence without first computing the set of all justifications. Through an empirical evaluation, we show that our approach…
The cosmological consequences of particle physics grand unified theories (GUTs) are studied. Cosmological models are implemented in realistic particle physics models. Models consistent from both particle physics and cosmological…
Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a…
We define a certain finite set in set theory $\{x\mid\varphi(x)\}$ and prove that it exhibits a universal extension property: it can be any desired particular finite set in the right set-theoretic universe and it can become successively any…
We obtain universal bounds on the energy of codes and for designs in Hamming spaces. Our bounds hold for a large class of potential functions, allow unified treatment, and can be viewed as a generalization of the Levenshtein bounds for…
We solve the problem of achieving the optimal physical approximation of the transposition for pure states of arbitrary quantum systems for finite and infinite dimensions. A unitary realization is also given for any finite dimension, which…
We show that many important natural science models in their mathematical formulation can be reduced to non-strictly hyperbolic systems of the same kind. This allows the same methods to be applied to them so that some essential results…