The Ring Learning-With-Errors (LWE) problem, whose security is based on hard ideal lattice problems, has proven to be a promising primitive with diverse applications in cryptography. There are however recent discoveries of faster algorithms for the principal ideal SVP problem, and attempts to generalize the attack to non-principal ideals. In this work, we study the LWE problem on group rings, a...

The concept of a Hopf algebra originated in topology. Classically, Hopf algebras are defined on the basis of unital modules over commutative, unital rings. The intention of the present work is to study Hopf algebra formalism (§1.2) from a universal-algebraic point of view, within the context of entropic varieties. In an entropic variety, the operations of each algebra are homomorphisms, and ten...

Peripheral primitive neuroectodermal tumor (pPNET) is a highly aggressive small round cell tumor belonging to PNET/Ewing sarcoma family. Ovarian tumors composed of primitive neuroectodermal elements are extremely rare. Herein we reported two cases of peripheral primitive neuroectodermal tumors of ovary in two patients with different clinical presentations. Definite diagnoses were made bas...

Fully homomorphic encryption (FHE) allows anyone to perform computations on encrypted data, despite not having the secret decryption key. Since the Gentry’s work in 2009, the primitive has interested many researchers. In this paper, we stress that any computations performed on encrypted data are constrained to the encrypted domain (finite fields or rings). This restriction makes the primitive u...

The paper presents a study on the morphology of inflatable membranes and their application in space habitat design. The study is focused on the role of physical constraints on pneumatic membranes as a form generating factor in two aspects (1) the definition of elements (primitive shapes) and (2) the definition of a set of rules. The primitive (generic) shapes for pneumatics must be in an initia...

primitive neuroectodermal tumors of the kidney are rare tumors representing about 1% of all sarcomas. extraskeletal primitive neuroectodermal tumors may be found in the genitourinary tract, the testes, ovaries, uterus, or pancreas. renal primitive neuroec- todermal tumors are frequently aggressive and almost 30% of all newly diagnosed cases present with distant metastases. surgical intervention...

Introduction. A celebrated theorem of N. Jacobson [7] asserts that if (1) x*(x) =x for every x in a ring R, where n(x) is an integer greater than one, then R is commutative. In a recent paper [2], I. N. Herstein has shown that it is enough to require that (1) holds for those x in R which are commutators: x= [y, z]=yz — zy of two elements of R. The purpose of this note is to show that if R has n...

Abstract Here, we report on the Quaternary Volsci Volcanic Field (VVF, central Italy). In light of new 40 Ar/ 39 Ar geochronological data and compositional characterization juvenile eruptive products, refine history VVF activity, outline implications pre-eruptive magma system continental subduction processes involved. Different from nearby volcanic districts Roman Campanian Provinces, was chara...

primitive  neuroectodermal  tumor  (pnet)  of  kidney  is  an  extremely  rare  renal  neoplasm  with only about fifty reported cases in literature.  presumably,of neural crest origin, these tumors behave  aggressively  and  carry  a  poor prognosis.  we  report  a  case  of  22-year  old  female  patient complaining of left loin pain with recurrent hematuria for last 3 months. on clinical exam...