Concave compositions are compositions (i.e. ordered partitions) of a number in which the parts decrease up to the middle summand(s) and increase thereafter. Perhaps the most surprising result is for even length, concave compositions where the generating function turns out to be the quotient of two instances of the pentagonal number theorem with variations of sign. The false theta function disco...

We study a class of left-invertible operators which we call weakly concave operators. It includes the and some subclasses expansive strict $m$ -isometries with $m > 2$ . prove Wold-type decomposition for also obtain Berger–Shaw-type theorem analytic finitely cyclic The proofs these results rely heavily on spectral dichotomy provides fairly close relationship, written in terms reciprocal auto...

Freeze-fracture electron microscopy was used to investigate the membrane architectures of high-passage Borrelia burgdorferi B31 and low- and high-passage isolates of B. burgdorferi N40. In all three organisms, fractures occurred almost exclusively through the outer membrane (OM), and the large majority of intramembranous particles were distributed randomly throughout the concave OM leaflet. The...

The silver proteinate reaction was used to stain carbohydrate-rich substances in normal Amoeba proteus and in the developing Golgi apparatus of renucleated amoebae. Normal cells contained stained material, which probably is glycoprotein, in the cell surface, cisternae at the concave pole of the Golgi apparatus, and cytoplasmic vesicles and vacuoles. Previous radioautographic studies had shown t...

Long-term culture and monitoring of individual multicellular spheroids and embryoid bodies (EBs) remains a challenge for in vitro cell propagation. Here, we used a continuous 3D projection printing approach - with an important modification of nonlinear exposure - to generate concave hydrogel microstructures that permit spheroid growth and long-term maintenance, without the need for spheroid tra...

In this paper, the concepts of L-concave structures, concave Linterior operators and concave L-neighborhood systems are introduced. It is shown that the category of L-concave spaces and the category of concave Linterior spaces are isomorphic, and they are both isomorphic to the category of concave L-neighborhood systems whenever L is a completely distributive lattice. Also, it is proved that th...

Cloaking refers to hiding a body from detection by surrounding it with a coating consisting of an unusual anisotropic nonhomogeneous material. The permittivity and permeability of such a cloak are determined by the coordinate transformation of compressing a hidden body into a point or a line. In this work, the scattering properties of cloaked spherical bodies (conducting and dielectric) are inv...