the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

We present a unified formulation for describing the dynamics of a new class of aquatic multi-body soft robots. This formulation accounts for the continuum hyperelastic nature of the vehicles and for the interaction with the dense fluid across which they dwell. We start by introducing the highly unconventional design concept of a soft underwater vehicle inspired by the octopus capable of swimmin...

OBJECTIVE To determine the effect of soft tissue gas on the accuracy of foreign body detection by realtime sonography. METHODS This was a prospective randomized study using glass, metal, and bone inserted into turkey breasts to simulate human soft tissue foreign bodies. Air was subsequently injected around a random selection of the foreign bodies to simulate soft tissue gas that can accompany...

Soft materials are not only highly deformable, but they also possess rich and diverse body dynamics. Soft body dynamics exhibit a variety of properties, including nonlinearity, elasticity and potentially infinitely many degrees of freedom. Here, we demonstrate that such soft body dynamics can be employed to conduct certain types of computation. Using body dynamics generated from a soft silicone...

Completely soft and flexible robots offer to revolutionize fields ranging from search and rescue to endoscopic surgery. One of the outstanding challenges in this burgeoning field is the chicken-and-egg problem of body-brain design: Development of locomotion requires the preexistence of a locomotion-capable body, and development of a location-capable body requires the preexistence of a locomotiv...

We derive a universal expression for the gravitational radiation energy spectrum $dE^{GW}/d\omega$ at sub-leading order emitted from generic hard scattering of multi-particles or multi-bodies. Our result includes all $\mathcal{O}(\omega)$ corrections to flux $2\rightarrow N$ collision, in both cases massless and massive particles/bodies. also show dependence fluxby quantum spin case particle co...

Soft-body models are common in games to simulate cloth or elastic objects. To realistically simulate soft-body objects, collision detection and response is required. In addition, soft-body models must re-arrange their internal structure to react to the collision. This paper presents a new collision detection and response algorithm which can simulate a variety of soft-body material behaviors ran...

the concept of soft sets, introduced by molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. in this paper, weapply the notion of the soft sets of molodtsov to the theory of hilbert algebras.the notion of soft hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...