Let X be a non empty complex normed space structure and let s1 be a sequence of X. The functor ( ∑ κ α=0(s1)(α))κ∈N yielding a sequence of X is defined as follows: (Def. 1) ( ∑ κ α=0(s1)(α))κ∈N(0) = s1(0) and for every natural number n holds ( ∑ κ α=0(s1)(α))κ∈N(n + 1) = ( ∑ κ α=0(s1)(α))κ∈N(n) + s1(n + 1). One can prove the following proposition (1) Let X be an add-associative right zeroed rig...

There have been numerous results showing that a measurable cardinal κ can carry exactly α normal measures in a model of GCH, where α is a cardinal at most κ++. Starting with just one measurable cardinal, we have [9] (for α = 1), [10] (for α = κ++, the maximum possible) and [1] (for α = κ+, after collapsing κ++). In addition, under stronger large cardinal hypotheses, one can handle the remaining...

In this work, the improvement of SiC power MOSFET performance achieved using high-κ gate-dielectrics instead standard SiO2 is investigated by means advanced gate-impedance characterization. The benefit with high dielectric constant demonstrated comparing MOSFETs pure high-κ, a stack SiO2/high-κ, as well SiO2. Namely, fabricated show superior to commercial SiO2/SiC interface respect channel resi...

We discuss Shelah, Väänänen and Veli£kovi¢'s recently introduced κ-antichain property for (κ, 1)-simpli ed morasses. We give a streamlined characterization of the property, and show how the property can be destroyed by forcing and hence that it is consistent that no (ω, 1)-simpli ed morasses have the property. We brie y touch on the combination of the antichain property with complete amalgamati...

The paper is concerned with methods for blowing power of singular cardinals using short extenders. Thus, for example, starting with κ of cofinality ω with {α < κ | o(α) ≥ α+n} cofinal in κ for every n < ω we construct a cardinal preserving extension having the same bounded subsets of κ and satisfying 2κ = κ+δ+1 for any δ < א1.

We present a new forcing notion combining diagonal supercompact Prikry focing with interleaved extender based forcing. We start with a supercompact cardinal κ. In the final model the cofinality of κ is ω, the singular cardinal hypothesis fails at κ and GCH holds below κ. Moreover we define a scale at κ, which has a stationary set of bad points in the ground model.

We prove equiconsistency results concerning gaps between a singular strong limit cardinal κ of cofinality א0 and its power under assumptions that 2 κ = κ+δ+1 for a cardinal δ < κ and some weak form of the Singular Cardinal Hypothesis below κ.

Let X be a non empty normed structure and let s1 be a sequence of X. The functor ( ∑ κ α=0(s1)(α))κ∈N yielding a sequence of X is defined as follows: (Def. 1) ( ∑ κ α=0(s1)(α))κ∈N(0) = s1(0) and for every natural number n holds ( ∑ κ α=0(s1)(α))κ∈N(n + 1) = ( ∑ κ α=0(s1)(α))κ∈N(n) + s1(n + 1). One can prove the following proposition (1) Let X be an add-associative right zeroed right complementa...

We study a one-parameter family of discrete dynamical systems called the κ-color firefly cellular automata, proposed by the author in [13] as discrete models for finite-state pulse-coupled inhibitory oscillators. At each discrete time t , each vertex in a graph has a state (color) in {0, · · · ,κ−1}, and a special color b(κ) = bκ−1 2 c is designated as the ‘blinking’ color. During each transiti...

During B cell development, the precursor B cell receptor (pre-BCR) checkpoint is thought to increase immunoglobulin κ light chain (Igκ) locus accessibility to the V(D)J recombinase. Accordingly, pre-B cells lacking the pre-BCR signaling molecules Btk or Slp65 showed reduced germline V(κ) transcription. To investigate whether pre-BCR signaling modulates V(κ) accessibility through enhancer-mediat...