A projective algebraic manifold M is a complex manifold in certain projective space CPm, m ≥ dimC M = n. The hyperplane line bundle of CPm restricts to an ample line bundle L onM . The bundle is a polarization onM . Suppose g is a Kähler metric on M . We say g is a polarized Kähler metric with respect to L, if the corresponding Kähler form represents the first Chern class c1(L) of L in H 2(M,Z)...

This paper deals with several aspects of epimorphisms in the category MFrm of metric frames and contractive homomorphisms. In particular, it is shown that (i) the epicomplete metric frames are uniquely determined by the power-set lattices of sets, (ii) episurjective is the same as Boolean, (iii) a metric frame has an epicompletion iff it is spatial, and (iv) the subcategory of epicomplete L in ...

In this paper, we define the concept of compatible and weakly compatible mappings in b-metric spaces and inspired by the Ciric and et. al method, we produce appropriate conditions for given the unique common fixed point for a family of the even number of self-maps with together another two self-maps in a complete b-metric spaces. Also, we generalize this common fixed point theorem for a seq...

Since it was firstly introduced by Torra and Narukawa (The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 2009, pp. 1378–1382), the hesitant fuzzy set has attracted more and more attention due to its powerfulness and efficiency in representing uncertainty and vagueness. This paper extends the classical VIKOR (vlsekriterijumska optimizacija i kompromisno resenje in serb...

The conjecture that the p-relative distance, %p(α, α̃) = |α − α̃|/ p √|α|p + |α̃|p, is a metric is proved.

MARATHE, JAYDEEP P. METRIC: Tracking Memory Bottlenecks via Binary Rewriting (Under the direction of Assistant Professor Dr. Frank Mueller). Over recent decades, computing speeds have grown much faster than memory access speeds. This differential rate of improvement between processor speeds and memory speeds has led to an ever-increasing processor-memory gap. Overall computing speeds for for mo...

In many practical situations, we are faced with a necessity to combine sophisticated mathematical knowledge about the analyzed systems with informal expert knowledge. To make this combination natural, it is desirable to reformulate the abstract mathematical knowledge in understandable intuitive terms. In this paper, we show how this can be done for an abstract metric. 1 For Data Fusion, It Is D...