With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral surfaces with non-positive curvature. We show that in the case of such surfaces discrete uniformization via hyper-ideal circle patterns always exists and is uniqu...

In [19], Migliore–Miró-Roig–Nagel show that the Weak Lefschetz property can fail for an ideal I ⊆ K[x 1 ,. .. , x 4 ] generated by powers of linear forms. This is in contrast to the analogous situation in K[x 1 , x 2 , x 3 ], where WLP always holds [24]. We use the inverse system dictionary to connect I to an ideal of fat points, and show that failure of WLP for powers of linear forms is connec...

We consider the notion of an isomorphism between two hyper BCI-algebras and obtain all of the hyper BCI-algebras of order 3. It is shown that there exist 14 proper hyper BCI-algebras and 5 proper weak hyper BCI-algebras of order 3 up to isomorphism. Finally, further study on the theory of hyper BCI-algebra and its related hyper structure and applications of our results in information sciences a...

We discuss the relationship between various weak distributive laws and games in Boolean algebras. In the first part we give some game characterizations for certain forms of Prikry’s “hyper-weak distributive laws”, and in the second part we construct Suslin algebras in which neither player wins a certain hyper-weak distributivity game. We conclude that in the constructible universe L , all the d...

The k-Young lattice Y k is a weak subposet of the Young lattice containing partitions whose first part is bounded by an integer k > 0. The Y k poset was introduced in connection with generalized Schur functions and later shown to be isomorphic to the weak order on the quotient of the affine symmetric group S̃k+1 by a maximal parabolic subgroup. We prove a number of properties for Y k including t...

For investigation of the properties of smooth muscle contraction hypertonically added 40 mm K medium has been used as a routine in this laboratory. Others have used isotonic high K/Na deficient medium for the same purpose. The distinct difference xisting between the mechanical response of guinea pig taenia coli in hyper-40 K medium and that in iso 152 K medium has been reported earlier. The res...