To date, most modular robotic systems lack flexibility when increasing the number of modules due to their hard building blocks and rigid connection mechanisms. In order to improve adaptation to environmental changes, softness at the module level might be beneficial. However, coping with softness requires a fundamental rethinking of the way modules are built. A major challenge is to develop a co...

Let $A$ be a Banach ternary algebra over a scalar field $Bbb R$ or $Bbb C$ and $X$ be a ternary Banach $A$--module. Let $sigma,tau$ and $xi$ be linear mappings on $A$, a linear mapping $D:(A,[~]_A)to (X,[~]_X)$ is called a Lie ternary $(sigma,tau,xi)$--derivation, if $$D([a,b,c])=[[D(a)bc]_X]_{(sigma,tau,xi)}-[[D(c)ba]_X]_{(sigma,tau,xi)}$$ for all $a,b,cin A$, where $[abc]_{(sigma,tau,xi)}=ata...

A module is called absolutely indecomposable if it is directly indecomposable in every generic extension of the universe. We want to show the existence of large abelian groups that are absolutely indecomposable. This will follow from a more general result about R-modules over a large class of commutative rings R with endomorphism ring R which remains the same when passing to a generic extension...

Let H be a Hopf algebra in a rigid braided monoidal category with split idempotents. We prove the existence of integrals on (in) H characterized by the universal property, employing results about Hopf modules, and show that their common target (source) object IntH is invertible. The fully braided version of Radford’s formula for the fourth power of the antipode is obtained. Connections of integ...

In this paper, we present a novel packaging architecture for Optoelectronic Multi-Chip-Modules (OEMCM) based on fiber image guides. Fiber image guides (FIGs) are densely packed lattices of small core fibers that have been traditionally used in medical endoscopes and other remote inspection devices. In our chip packaging architecture, small, rigid segments of FIGs are used to fabricate 3D optica...

In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...

Let $\mathcal{O}_{25}$ be the vertex algebraic braided tensor category of finite-length modules for Virasoro Lie algebra at central charge $25$ whose composition factors are irreducible quotients reducible Verma modules. We show that is rigid and its simple objects generate a semisimple subcategory equivalent to an abelian $3$-cocycle twist finite-dimensional $\mathfrak{sl}_2$-modules. also thi...

BACKGROUND Over the past few years novel folding mechanisms of globular proteins have been proposed using minimal lattice and off-lattice models. The factors determining the cooperativity of folding in these models and especially their explicit relation to experiments have not been fully established, however. RESULTS We consider equilibrium folding transitions in lattice models with and witho...

The connections are used to transfer forces and moments due applied loading. capability of the connection in resisting moment is classify types steelwork particularly for cold-formed steel. Classification schemes based on total moment-rotation behavior have been developed aid design analysis connections. Moment-rotation curve commonly describe that can be obtained from either theoretical or exp...

This paper presents a geometric model of the Auslander–Reiten quiver type A together with stability function for which all indecomposable modules are stable. We also introduce new Catalan object we call maximal almost rigid representation. show that its endomorphism algebra is tilted A. define partial order on set representations and use our to this Cambrian lattice.