Related papers: One is all you need: Second-order Unification with…
Higher dimensional grand unified theories, with gauge symmetry breaking by orbifold compactification, possess SU(5) breaking at fixed points, and do not automatically lead to tree-level gauge coupling unification. A new framework is…
The t-b-tau unification with positive Higgs mass parameter \mu\ in the minimal supersymmetric standard model prefers "just so" Higgs splitting and a light gluino < 500 GeV which appears to be ruled out by the recent LHC searches. We…
We construct gauge theory of SU(3)xSU(2)xU(1) by spectral cover from F-theory and ask how the Standard Model is extended under minimal assumptions on Higgs sector. For the requirement on different numbers between Higgs pairs and matter…
We construct an $SO(10)$ grand unified theory in the formulation of non-com-\break mutative geometry. The geometry of space-time is that of a product of a continuos four dimensional manifold times a discrete set of points. The properties of…
We consider the low energy implications including particle spectroscopy of SO(10) inspired t-b-tau Yukawa coupling unification with mu < 0, where mu is the coefficient of the bilinear Higgs mixing term of the minimal supersymmetric standard…
We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…
Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in [Phys. Rev. D…
We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.
It is known that for binary codes one can use Gr\"obner bases to obtain a subset of codewords of minimal support that can be used to determine the second generalized Hamming weight of the code. In this paper we establish conditions on a…
Identifying structural parameters in linear simultaneous-equation models is a longstanding challenge. Recent work exploits information in higher-order moments of non-Gaussian data. In this literature, the structural errors are typically…
We investigate supersymmetric SO(10) GUT model with \mu<0. The requirements of top-bottom-tau Yukawa unification, correct radiative electroweak symmetry breaking and agreement with the present experimental data may be met when the soft…
Disjoint union is a partial binary operation returning the union of two sets if they are disjoint and undefined otherwise. A disjoint-union partial algebra of sets is a collection of sets closed under disjoint unions, whenever they are…
We consider Grand Unified Theories based on $SO(10)$ which originate from string/$M$ theory on $G_2$ manifolds or Calabi-Yau spaces with discrete symmetries. In this framework we are naturally led to a novel solution of the doublet-triplet…
We study nominal anti-unification, which is concerned with computing least general generalizations for given terms-in-context. In general, the problem does not have a least general solution, but if the set of atoms permitted in…
This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and…
We consider the quantum mechanics of a particle on the coset superspace $SU(2|1)/[U(1)\times U(1)]$, which is a super-flag manifold with $SU(2)/U(1)\cong S^2$ `body'. By incorporating the Wess-Zumino terms associated with the $U(1)\times…
We develop a method to recognize admissibility of $\Pi_{2}$-rules, relating this problem to a specific instance of the unification problem with linear constants restriction, called here "unification with simple variable restriction". It is…
In this article, we bypass the detailed symmetry breaking pathways established in [1]. Instead, a direct route from the Spin(10) model to the Standard Model is enabled via a single algebraic constraint. This single constraint, however, may…
Let $A$ be a unital operator algebra. Let us assume that every {\it bounded\/} unital homomorphism $u\colon \ A\to B(H)$ is similar to a {\it contractive\/} one. Let $\text{\rm Sim}(u) = \inf\{\|S\|\, \|S^{-1}\|\}$ where the infimum runs…
It is well-known that every first-order property on words is expressible using at most three variables. The subclass of properties expressible with only two variables is also quite interesting and well-studied. We prove precise structure…