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This paper presents a substructural logic of sequents with very restricted exchange and weakening rules. It is sound with respect to sequences of measurements of a quantic system. A sound and complete semantics is provided. The semantic…

In this review, We discussed the theoretical foundation and experimental discovery of different topological electronic states of material in condensed matter. At first, we briefly reviewed the conventional electronic states, which have been…

Beyond Standard Model theories describing the electro-weak sector must exhibit a large separation of scales (or "walking") to account for a light, 125 GeV Higgs boson and the fact that so far no other resonances have been observed. Large…

Double semigroups have two associative operations $\circ, \bullet$ related by the interchange relation: $( a \bullet b ) \circ ( c \bullet d ) \equiv ( a \circ c ) \bullet ( b \circ d )$. Kock \cite{Kock2007} (2007) discovered a…

This thesis contains an introductory chapter on orbifolds. The following chapter explains the foundations of orientifolds. Chapters 4-7 present own research. In chapter 4 we quantize open strings with linear boundary conditions, as they…

This article surveys the physics of systems proximate to Mott insulators, and presents a classification using conventional and topological order parameters. This classification offers a valuable perspective on a variety of conducting…

Correspondences between the Thomson Problem and atomic electron shell-filling patterns are observed as systematic non-uniformities in the distribution of potential energy necessary to change configurations of $N\le 100$ electrons into…

We construct a metric space whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both omega+1, where omega is the smallest infinite ordinal number. Therefore, we prove that the omega conjecture is not…

Crack-templated networks, metallic frameworks fabricated from crack patterns in sacrificial thin films, can exhibit high optical transmittance, high electric conductivity, and a host of other properties attractive for applications. Despite…

It has been suggested that cold dark matter (CDM) has difficulties in explaining tentative evidence for noncuspy halo profiles in small galaxies, and the low velocity dispersions observed in the largest Milky Way satellites ("too big to…

The moduli space of rank-n commutative algebras equipped with an ordered basis is an affine scheme B_n of finite type over Z, with geometrically connected fibers. It is smooth if and only if n <= 3. It is reducible if n >= 8 (and the…

It is known that strict omega-categories are equivalent through the nerve functor to complicial sets and to sets with complicial identities. It follows that complicial sets are equivalent to sets with complicial identities. We discuss these…

By combining the generalized exterior algebra of forms over a noncommutative algebra with the gauging of discrete directions and the associated Higgs fields, we consider the construction of the bosonic sector of left-right symmetric models…

Designing molecular organic semiconductors with distinct frontier orbitals is key for the development of devices with desirable properties. Generating defined organic nanostructures with atomic precision can be accomplished by on-surface…

A new approach to composite superconformal strings is considered . This composite string model has two scales: first one (~1 Gev) is for edging surfaces and second one (Planck scale) is for ridge surfaces . Nonlinear realization of…

We discuss the role of the broken symmetries in the connection of the shell, collective and cluster models. The cluster-shell competition is described in terms of cold quantum phases. Stable quasi-dynamical U(3) symmetry is found for…

The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the…

We investigate symmetric grain boundaries in a lamellar diblock copolymer system. The form of the interface between two grains strongly depends on the angle $\theta$, between the normals of the grains. When this angle is small, the lamellae…

Commensurate scale relations are perturbative QCD predictions which relate observable to observable at fixed relative scale, such as the "generalized Crewther relation", which connects the Bjorken and Gross-Llewellyn Smith deep inelastic…

A new model for calculating the structure of bound states of interacting particles is considered. The model takes into account the noncommutativity of the space and impulse operators plus the correlation equations for the indeterminacy of…