The main results of the combinatorial theory of maximal biprefix codes of words (Ckari, Perrin, Schtitzenberger) are extended to the codes of paths in a graph in this paper: degree and decoding of double-infinite paths, finiteness of codes of a given degree, the CCsari-Schiitzenberger algorithm, derivation and integration of codes will be discussed.

We show that the BRST Lagrangian double copy construction of $\mathcal{N}=0$ supergravity as `square' Yang-Mills theory finds a natural interpretation in terms homotopy algebras. significantly expand on our previous work arguing validity at loop level, and we give detailed derivation copied operator. Our constructions are very general can be applied to vast set examples.

In this paper, the main transmission mechanism of double servo drive symmetrical toggle press was taken as object study. The theoretical derivation its motion characteristics carried out. A parametric model established to analyze rigid body kinematics. kinematic performance improved by rigid-flexible coupling. research results could provide an important reference for development large-tonnage w...

Recent important topic in nanoscience concerns gold nanocluster assemblies and their interesting optical/chiroptical studies [1]. One way to fabricate such assemblies is to use cross-linkers, and better control of strong binding between the gold nanoclusters should be achieved using α,ω-dithiols. Aggregation of gold nanoclusters via cross-linking with α,ω-dithiols is a well-known phenomenon, bu...

Self-energy corrections involving logarithms of the parameter Zα can often be derived within a simplified approach , avoiding calculational difficulties typical of the problematic non-logarithmic corrections (as customary in bound-state quantum electrodynamics, we denote by Z the nuclear charge number, and by α the fine-structure constant). For some logarithmic corrections, it is sufficient to ...

Self-energy corrections involving logarithms of the parameter Zα can often be derived within a simplified approach , avoiding calculational difficulties typical of the problematic non-logarithmic corrections (as customary in bound-state quantum electrodynamics, we denote by Z the nuclear charge number, and by α the fine-structure constant). For some logarithmic corrections, it is sufficient to ...

We study quadratic Lie algebras over a field K of null characteristic which admit, at the same time, a symplectic structure. We see that if K is algebraically closed every such Lie algebra may be constructed as the T∗-extension of a nilpotent algebra admitting an invertible derivation and also as the double extension of another quadratic symplectic Lie algebra by the one-dimensional Lie algebra...

Previous work (Pradines, 1966, Aof and Brown, 1992) has given a setting for a holon-omy Lie groupoid of a locally Lie groupoid. Here we develop analogous 2-dimensional notions starting from a locally Lie crossed module of groupoids. This involves replacing the Ehresmann notion of a local smooth coadmissible section of a groupoid by a local smooth coadmissible homotopy (or free derivation) for t...