v. dannon showed that spherical curves in e4 can be given by frenet-like equations, and he thengave an integral characterization for spherical curves in e4 . in this paper, lorentzian spherical timelike andspacelike curves in the space time 41 r are shown to be given by frenet-like equations of timelike andspacelike curves in the euclidean space e3 and the minkowski 3-space 31 r . thus, finding...

for all x∈H . When A = B the frame is said to be tight and if in addition, A = B = 1 it is termed a Parseval frame. When F = { fi}i=1 is a frame, we shall abuse notations and denote by F again, the n×M matrix whose ith column is fi, and where n is the dimension of H . Using this notation, the frame operator is the n×n matrix S=FF∗ where F∗ is the adjoint of F . It is a folklore to note that F i...

BACKGROUND The diagnosis of myeloma, a plasma dyscrasia, often results from the workup of unexplained renal disease. Persistent renal failure in myeloma is commonly caused by tubular nephropathy due to circulating immunoglobulins and free light chains. Myeloma cast nephropathy is characterized by crystalline precipitates of monoclonal light chains within distal tubules. Immunoglobulin crystalli...

Let κQnt be the category of of κ-quantales, quantales closed under κ-joins in which the monoid identity is the largest element. (κ is an infinite regular cardinal.) Although the lack of lattice completeness in this setting would seem to mitigate against the techniques which lend themselves so readily to the calculation of frame quotients, we show how to easily compute κQnt quotients by applying...

The κ−Poincare group and its algebra in an arbitrary basis are constructed. The κ−deformation of the Weyl group and its algebra in any dimentions and in the reference frame in which g00 = 0 are discussed.

Subtle alternative splicing leads to the formation of RNA variants lacking or including a small number of nucleotides. To date, the impact of subtle alternative splicing phenomena on protein biosynthesis has been studied in frame-preserving incidents. On the contrary, mRNA isoforms derived from frame-shifting events were poorly studied and generally characterized as non-coding. This work provid...

We study general methods to build forking-like notions in the framework of tame abstract elementary classes (AECs) with amalgamation. We show that whenever such classes are categorical in a high-enough cardinal, they admit a good frame: a forking-like notion for types of singleton elements. Theorem 0.1 (Superstability from categoricity). Let K be a (< κ)-tame AEC with amalgamation. If κ = iκ > ...

We describe firstly the basic features of quantum κ-Poincaré symmetries with their Hopf algebra structure. The quantum κ-Poincaré framework in any basis relates rigidly the quantum κ-Poincaré algebra with quantum κ-Poincaré group, noncommutative space-time and κ-deformed phase space. Further we present the approach of Doubly Special Relativity (DSR) theories, which introduce (in the version DSR...